Update documentation
This commit is contained in:
Xiaodi Wu
parent
ed1f699270
commit
21797a27c6
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@ -0,0 +1,348 @@
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@import url("https://fonts.googleapis.com/css?family=Source+Code+Pro:400,500,600,700");
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*, *::before, *::after {
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box-sizing: inherit; }
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body {
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box-sizing: border-box;
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margin: 0;
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background: #fff;
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color: #333;
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font: 16px/24px -apple-system, BlinkMacSystemFont, "Segoe UI", Arial, sans-serif; }
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h1 {
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margin: 32px 0 16px;
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font-weight: 500;
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font-size: 28px;
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line-height: 32px; }
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h2 {
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margin: 32px 0 16px;
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font-weight: 500;
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font-size: 24px;
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line-height: 32px; }
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h3 {
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margin: 24px 0 16px;
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font-weight: 500;
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font-size: 20px;
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line-height: 24px; }
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h4 {
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margin: 24px 0 16px;
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font-weight: 500;
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font-size: 16px;
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line-height: 24px; }
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h5 {
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margin: 24px 0 16px;
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font-weight: 500;
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font-size: 16px;
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line-height: 24px;
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color: #777; }
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h6 {
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margin: 24px 0 16px;
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font-weight: 500;
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font-size: 16px;
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line-height: 24px;
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color: #aaaaaa; }
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p {
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margin: 0 0 16px; }
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ul, ol {
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margin: 0 0 16px;
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padding: 0 0 0 32px; }
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blockquote {
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margin: 0 0 16px;
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border-left: 6px solid #e6e6e6;
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border-radius: 4px;
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padding: 16px;
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background-color: #fafafa;
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color: #858585; }
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blockquote > p:last-child {
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margin-bottom: 0; }
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dl {
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margin: 0;
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padding: 0; }
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dt {
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margin: 0 0 16px;
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padding: 0;
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font-weight: 500; }
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dd {
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margin: 0 0 16px;
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padding: 0 0 0 8px; }
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img {
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max-width: 100%; }
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a {
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color: #4183c4;
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text-decoration: none; }
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a:hover, a:focus {
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outline: 0;
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text-decoration: underline; }
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table {
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width: 100%;
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overflow: auto;
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margin: 0 0 12px;
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border-collapse: collapse;
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border-spacing: 0;
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background: #fff; }
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tr:nth-child(2n) {
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background-color: #fbfbfb; }
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th, td {
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border: 1px solid #ddd;
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padding: 7px 11px; }
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pre {
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overflow: auto;
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margin: 0 0 16px;
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border: 1px solid #e6e6e6;
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border-radius: 4px;
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padding: calc(12px - 1px) calc(16px - 1px);
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background: #f9f9f9;
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font-size: inherit;
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line-height: inherit;
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font-family: "Source Code Pro", Menlo, Consolas, "Liberation Mono", Courier, monospace; }
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code {
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font-size: 16px;
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line-height: 16px;
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font-family: "Source Code Pro", Menlo, Consolas, "Liberation Mono", Courier, monospace; }
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pre code {
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padding: 0;
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white-space: pre; }
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body > .wrapper {
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display: flex;
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flex-direction: column; }
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@media only screen and (min-width: 1024px) {
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body > .wrapper {
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flex-direction: row; } }
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header {
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display: flex;
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padding: 8px;
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background: #333;
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color: #999;
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font-size: 14px;
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line-height: inherit; }
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header p {
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margin: 0;
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padding: 0 8px; }
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header p.primary {
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flex: 1; }
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header a[href] {
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color: #fff; }
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nav {
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order: 2; }
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@media only screen and (min-width: 1024px) {
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nav {
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order: 1;
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flex: 0 0 25%;
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max-width: 239px;
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overflow: hidden;
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border-right: 1px solid #ddd;
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padding-bottom: 32px;
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background: #fbfbfb;
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word-wrap: normal; } }
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nav > ul {
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margin: 0;
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padding: 0;
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font-size: 14px;
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line-height: inherit;
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list-style: none; }
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nav > ul > li {
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margin: 8px 0;
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border-bottom: 1px solid #ddd;
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padding: 8px 0 7px 16px; }
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nav > ul > li:last-child {
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margin-bottom: 0; }
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nav > ul > li > p {
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margin: 0; }
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nav > ul > li > p > a[href] {
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color: #333; }
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nav > ul > li > ul {
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margin: 8px 0;
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padding-left: 16px;
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list-style: inherit; }
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nav > ul > li > ul > li {
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white-space: nowrap; }
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nav > ul > li > ul > li > a[href] {
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color: #808080; }
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/*
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@keyframes appear {
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0% { opacity: 0 }
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100% { opacity: 1 }
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}
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*/
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article {
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order: 1;
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border-bottom: 1px solid #ddd;
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padding-bottom: 31px; }
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@media only screen and (min-width: 1024px) {
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article {
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order: 2;
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flex: 1 1 auto;
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border-bottom: none;
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padding-bottom: 32px; } }
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article > section {
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padding: 0 32px; }
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article > section:last-child {
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border-bottom: none; }
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article > section > .wrapper {
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max-width: 720px;
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margin: 0 auto; }
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.declaration .highlight {
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overflow-x: initial;
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margin: 0;
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border: none;
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border-radius: 0;
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padding: 0;
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background-color: transparent; }
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.toc {
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border-top: 1px solid #ddd;
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border-bottom: 1px solid #ddd;
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background-color: #fbfbfb; }
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.toc details {
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max-width: 720px;
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margin: 0 auto;
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padding: 15px 0; }
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.toc details[open] > summary {
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margin-bottom: 8px;
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/*
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& ~ * {
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animation: appear .2s ease-in-out;
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}
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*/ }
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.toc details[open] > summary::after {
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content: ' \2212'; }
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.toc details > summary {
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display: block;
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margin: 0;
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padding-bottom: 0;
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color: #666666;
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font-weight: 500;
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font-size: 12px;
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letter-spacing: 0.2em;
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text-transform: uppercase;
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user-select: none;
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-moz-user-select: none;
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-ms-user-select: none;
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-webkit-user-select: none;
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-webkit-tap-highlight-color: transparent;
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outline: none; }
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.toc details > summary::-webkit-details-marker {
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display: none; }
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.toc details > summary::after {
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content: ' +'; }
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.toc details > .wrapper {
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columns: 1; }
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@media only screen and (min-width: 1024px) {
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.toc details > .wrapper {
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columns: 2;
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column-gap: 16px; } }
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.toc details > .wrapper p {
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margin: 0;
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color: #333;
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font-weight: 500;
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break-after: avoid-column;
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-webkit-column-break-after: avoid; }
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.toc details > .wrapper p a[href] {
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color: inherit; }
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.toc details > .wrapper ul {
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margin: 0;
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padding-left: 0;
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color: #b3b3b3;
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list-style: square inside; }
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.toc details > .wrapper ul a[href] {
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color: #808080; }
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.group {
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border-bottom: 1px solid #ddd;
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padding-top: 0; }
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.group:last-child {
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border-bottom: none; }
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.group:last-child > ul > li:last-child {
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padding-bottom: 16px; }
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.group a[name]::before {
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content: "";
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display: block; }
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.group > ul {
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margin: 0;
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padding: 0; }
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.group > ul > li {
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width: 100%;
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border-bottom: 1px solid #ddd;
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padding: 0 0 15px;
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list-style: none; }
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.group > ul > li:last-child {
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border-bottom: none; }
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.group > ul > li .declaration-note {
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color: #808080;
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font-weight: normal;
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font-size: 16px; }
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.aside, .language {
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overflow-y: hidden;
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margin: 16px 0;
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border-left: 6px solid #d0d0d0;
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border-radius: 4px;
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padding: 8px 12px;
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background-color: #f7f7f7; }
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.aside .aside-title, .language .aside-title {
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margin: 0;
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padding-bottom: 0;
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color: #aaa;
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font-weight: 500;
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font-size: 12px;
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letter-spacing: 0.2em;
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text-transform: uppercase;
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user-select: none;
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-moz-user-select: none;
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-ms-user-select: none;
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-webkit-user-select: none; }
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.aside p:last-child, .language p:last-child {
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margin-bottom: 0; }
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.language {
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border-left: 6px solid #99bcdf;
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background-color: #f0f5fa; }
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.language .aside-title {
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color: #4183c4; }
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.aside-warning {
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border-left: 6px solid #ffda73;
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background-color: #fff8e6; }
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.aside-warning .aside-title {
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color: #fb0; }
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footer {
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padding: 16px;
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background: #444;
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color: #ddd;
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font-size: 14px;
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line-height: inherit; }
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footer p {
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margin: 0; }
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footer a[href] {
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color: #fff; }
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html.dash header, html.dash nav {
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display: none; }
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@ -1,589 +0,0 @@
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@import url("https://fonts.googleapis.com/css?family=Source+Code+Pro:400,500,600,700");
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// ===========================================================================
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// Variables
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// ===========================================================================
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$unit: 4px;
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$body_background: #fff;
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$body_text_color: #333;
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$body_font_family: -apple-system, BlinkMacSystemFont, "Segoe UI", Arial, sans-serif;
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$light_heading_color: #777;
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$heading_font_weight: 500;
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||||||
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|
||||||
$link_color: #4183c4;
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||||||
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$border_radius: $unit;
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|
||||||
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|
||||||
$quote_border: (1.5 * $unit) solid #e6e6e6;
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|
||||||
$quote_background_color: #fafafa;
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|
||||||
$quote_color: #858585;
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|
||||||
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|
||||||
$table_border_color: #ddd;
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|
||||||
$table_border: 1px solid $table_border_color;
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|
||||||
$table_alternate_row_color: #fbfbfb;
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|
||||||
|
|
||||||
$pre_border_width: 1px;
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|
||||||
$pre_border_color: #e6e6e6;
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|
||||||
$pre_border: $pre_border_width solid $pre_border_color;
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|
||||||
$pre_background_color: #f9f9f9;
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|
||||||
|
|
||||||
$code_font_family: "Source Code Pro", Menlo, Consolas, "Liberation Mono", Courier, monospace;
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|
||||||
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|
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// ----- Header
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|
||||||
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|
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$header_background_color: #333;
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|
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$header_link_color: #fff;
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|
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$doc_coverage_color: #999;
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|
||||||
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|
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// ----- Navigation
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|
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|
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$nav_max_width: 60 * $unit - 1px;
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|
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|
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$nav_border_width: 1px;
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|
||||||
$nav_border: $nav_border_width solid #ddd;
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|
||||||
$nav_background_color: #fbfbfb;
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|
||||||
$nav_title_color: #333;
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|
||||||
$nav_task_color: #808080;
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|
||||||
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|
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// ----- Content
|
|
||||||
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|
||||||
$content_padding: 8 * $unit;
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|
||||||
$content_max_width: 180 * $unit;
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|
||||||
|
|
||||||
$toc_border_width: $nav_border_width;
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|
||||||
$toc_border: $nav_border;
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|
||||||
$toc_background_color: $nav_background_color;
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|
||||||
$toc_title_color: $nav_title_color;
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|
||||||
$toc_task_color: $nav_task_color;
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|
||||||
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|
||||||
$declaration_language_title_color: #4183c4;
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|
||||||
$declaration_language_background_color: lighten($declaration_language_title_color, 45%);
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|
||||||
$declaration_language_border: (1.5 * $unit) solid lighten($declaration_language_title_color, 22.5%);
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|
||||||
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|
||||||
$aside_color: #aaa;
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|
||||||
$aside_background_color: lighten($aside_color, 30%);
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|
||||||
$aside_border: (1.5 * $unit) solid lighten($aside_color, 15%);
|
|
||||||
|
|
||||||
$aside_warning_color: #fb0;
|
|
||||||
$aside_warning_background_color: lighten($aside_warning_color, 45%);
|
|
||||||
$aside_warning_border: (1.5 * $unit) solid lighten($aside_warning_color, 22.5%);
|
|
||||||
|
|
||||||
// ----- Footer
|
|
||||||
|
|
||||||
$footer_background_color: #444;
|
|
||||||
$footer_text_color: #ddd;
|
|
||||||
$footer_link_color: #fff;
|
|
||||||
|
|
||||||
|
|
||||||
// ===========================================================================
|
|
||||||
// Mixins
|
|
||||||
// ===========================================================================
|
|
||||||
|
|
||||||
@mixin heading($font-size: 4 * $unit, $line-height: 6 * $unit, $margin: (6 * $unit) 0 (4 * $unit)) {
|
|
||||||
margin: $margin;
|
|
||||||
font-weight: $heading_font_weight;
|
|
||||||
font-size: $font-size;
|
|
||||||
line-height: $line-height;
|
|
||||||
}
|
|
||||||
|
|
||||||
@mixin media {
|
|
||||||
@media only screen and (min-width: $nav_max_width + $nav_border_width + $content_max_width + $content_padding * 2) {
|
|
||||||
@content;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
// ===========================================================================
|
|
||||||
// Base
|
|
||||||
// ===========================================================================
|
|
||||||
|
|
||||||
*, *::before, *::after {
|
|
||||||
box-sizing: inherit;
|
|
||||||
}
|
|
||||||
|
|
||||||
body {
|
|
||||||
box-sizing: border-box;
|
|
||||||
margin: 0;
|
|
||||||
background: $body_background;
|
|
||||||
color: $body_text_color;
|
|
||||||
font: #{4 * $unit}/#{6 * $unit} $body_font_family;
|
|
||||||
}
|
|
||||||
|
|
||||||
// ----- Block elements
|
|
||||||
|
|
||||||
h1 {
|
|
||||||
@include heading(7 * $unit, 8 * $unit, (8 * $unit) 0 (4 * $unit));
|
|
||||||
}
|
|
||||||
|
|
||||||
h2 {
|
|
||||||
@include heading(6 * $unit, 8 * $unit, (8 * $unit) 0 (4 * $unit));
|
|
||||||
}
|
|
||||||
|
|
||||||
h3 {
|
|
||||||
@include heading(5 * $unit);
|
|
||||||
}
|
|
||||||
|
|
||||||
h4 {
|
|
||||||
@include heading;
|
|
||||||
}
|
|
||||||
|
|
||||||
h5 {
|
|
||||||
@include heading;
|
|
||||||
color: $light_heading_color;
|
|
||||||
}
|
|
||||||
|
|
||||||
h6 {
|
|
||||||
@include heading;
|
|
||||||
color: lighten($light_heading_color, 20%);
|
|
||||||
}
|
|
||||||
|
|
||||||
p {
|
|
||||||
margin: 0 0 4 * $unit;
|
|
||||||
}
|
|
||||||
|
|
||||||
ul, ol {
|
|
||||||
margin: 0 0 4 * $unit;
|
|
||||||
padding: 0 0 0 8 * $unit;
|
|
||||||
}
|
|
||||||
|
|
||||||
blockquote {
|
|
||||||
margin: 0 0 4 * $unit;
|
|
||||||
border-left: $quote_border;
|
|
||||||
border-radius: $border_radius;
|
|
||||||
padding: 4 * $unit;
|
|
||||||
background-color: $quote_background_color;
|
|
||||||
color: $quote_color;
|
|
||||||
|
|
||||||
> p:last-child {
|
|
||||||
margin-bottom: 0;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
dl {
|
|
||||||
margin: 0;
|
|
||||||
padding: 0;
|
|
||||||
}
|
|
||||||
|
|
||||||
dt {
|
|
||||||
margin: 0 0 4 * $unit;
|
|
||||||
padding: 0;
|
|
||||||
font-weight: $heading_font_weight;
|
|
||||||
}
|
|
||||||
|
|
||||||
dd {
|
|
||||||
margin: 0 0 4 * unit;
|
|
||||||
padding: 0 0 0 2 * unit;
|
|
||||||
}
|
|
||||||
|
|
||||||
// ----- Inline elements
|
|
||||||
|
|
||||||
img {
|
|
||||||
max-width: 100%;
|
|
||||||
}
|
|
||||||
|
|
||||||
a {
|
|
||||||
color: $link_color;
|
|
||||||
text-decoration: none;
|
|
||||||
|
|
||||||
&:hover, &:focus {
|
|
||||||
outline: 0;
|
|
||||||
text-decoration: underline;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
// ----- Tables
|
|
||||||
|
|
||||||
table {
|
|
||||||
width: 100%;
|
|
||||||
overflow: auto;
|
|
||||||
margin: 0 0 3 * $unit;
|
|
||||||
border-collapse: collapse;
|
|
||||||
border-spacing: 0;
|
|
||||||
background: $body_background;
|
|
||||||
}
|
|
||||||
|
|
||||||
tr:nth-child(2n) {
|
|
||||||
background-color: $table_alternate_row_color;
|
|
||||||
}
|
|
||||||
|
|
||||||
th, td {
|
|
||||||
border: 1px solid $table_border_color;
|
|
||||||
padding: (2 * $unit - 1px) (3 * $unit - 1px);
|
|
||||||
}
|
|
||||||
|
|
||||||
// ----- Code
|
|
||||||
|
|
||||||
pre {
|
|
||||||
overflow: auto;
|
|
||||||
margin: 0 0 4 * $unit;
|
|
||||||
border: $pre_border;
|
|
||||||
border-radius: $border_radius;
|
|
||||||
padding: calc(#{3 * $unit} - #{$pre_border_width}) calc(#{4 * $unit} - #{$pre_border_width});
|
|
||||||
background: $pre_background_color;
|
|
||||||
font-size: inherit;
|
|
||||||
line-height: inherit;
|
|
||||||
font-family: $code_font_family;
|
|
||||||
}
|
|
||||||
|
|
||||||
code {
|
|
||||||
font-size: 4 * $unit;
|
|
||||||
line-height: 4 * $unit;
|
|
||||||
font-family: $code_font_family;
|
|
||||||
}
|
|
||||||
|
|
||||||
pre code {
|
|
||||||
padding: 0;
|
|
||||||
white-space: pre;
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
// ===========================================================================
|
|
||||||
// Layout
|
|
||||||
// ===========================================================================
|
|
||||||
|
|
||||||
body > .wrapper {
|
|
||||||
display: flex;
|
|
||||||
flex-direction: column;
|
|
||||||
|
|
||||||
@include media {
|
|
||||||
flex-direction: row;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
// ===========================================================================
|
|
||||||
// Header
|
|
||||||
// ===========================================================================
|
|
||||||
|
|
||||||
header {
|
|
||||||
display: flex;
|
|
||||||
padding: 2 * $unit;
|
|
||||||
background: $header_background_color;
|
|
||||||
color: $doc_coverage_color;
|
|
||||||
font-size: 3.5 * $unit;
|
|
||||||
line-height: inherit;
|
|
||||||
}
|
|
||||||
|
|
||||||
header p {
|
|
||||||
margin: 0;
|
|
||||||
padding: 0 2 * $unit;
|
|
||||||
}
|
|
||||||
|
|
||||||
header p.primary {
|
|
||||||
flex: 1;
|
|
||||||
}
|
|
||||||
|
|
||||||
header a[href] {
|
|
||||||
color: $header_link_color;
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
// ===========================================================================
|
|
||||||
// Navigation
|
|
||||||
// ===========================================================================
|
|
||||||
|
|
||||||
nav {
|
|
||||||
order: 2;
|
|
||||||
|
|
||||||
@include media {
|
|
||||||
order: 1;
|
|
||||||
flex: 0 0 25%;
|
|
||||||
max-width: $nav_max_width;
|
|
||||||
overflow: hidden;
|
|
||||||
border-right: $nav_border;
|
|
||||||
padding-bottom: $content_padding;
|
|
||||||
background: $nav_background_color;
|
|
||||||
word-wrap: normal;
|
|
||||||
}
|
|
||||||
|
|
||||||
> ul {
|
|
||||||
margin: 0;
|
|
||||||
padding: 0;
|
|
||||||
font-size: 3.5 * $unit;
|
|
||||||
line-height: inherit;
|
|
||||||
list-style: none;
|
|
||||||
|
|
||||||
> li {
|
|
||||||
margin: 2 * $unit 0;
|
|
||||||
border-bottom: $nav_border;
|
|
||||||
padding: (2 * $unit) 0 (2 * $unit - $nav_border_width) (4 * $unit);
|
|
||||||
|
|
||||||
&:last-child {
|
|
||||||
margin-bottom: 0;
|
|
||||||
}
|
|
||||||
|
|
||||||
> p {
|
|
||||||
margin: 0;
|
|
||||||
|
|
||||||
> a[href] {
|
|
||||||
color: $nav_title_color;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
> ul {
|
|
||||||
margin: (2 * $unit) 0;
|
|
||||||
padding-left: (4 * $unit);
|
|
||||||
list-style: inherit;
|
|
||||||
|
|
||||||
> li {
|
|
||||||
white-space: nowrap;
|
|
||||||
|
|
||||||
> a[href] {
|
|
||||||
color: $nav_task_color;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
// ===========================================================================
|
|
||||||
// Content
|
|
||||||
// ===========================================================================
|
|
||||||
|
|
||||||
/*
|
|
||||||
@keyframes appear {
|
|
||||||
0% { opacity: 0 }
|
|
||||||
100% { opacity: 1 }
|
|
||||||
}
|
|
||||||
*/
|
|
||||||
|
|
||||||
article {
|
|
||||||
order: 1;
|
|
||||||
border-bottom: $nav_border;
|
|
||||||
padding-bottom: $content_padding - $nav_border_width;
|
|
||||||
|
|
||||||
@include media {
|
|
||||||
order: 2;
|
|
||||||
flex: 1 1 auto;
|
|
||||||
border-bottom: none;
|
|
||||||
padding-bottom: $content_padding;
|
|
||||||
}
|
|
||||||
|
|
||||||
> section {
|
|
||||||
padding: 0 $content_padding;
|
|
||||||
|
|
||||||
&:last-child {
|
|
||||||
border-bottom: none;
|
|
||||||
}
|
|
||||||
|
|
||||||
> .wrapper {
|
|
||||||
max-width: $content_max_width;
|
|
||||||
margin: 0 auto;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
.declaration .highlight {
|
|
||||||
overflow-x: initial; // This allows the scrollbar to be displayed
|
|
||||||
margin: 0;
|
|
||||||
border: none;
|
|
||||||
border-radius: 0;
|
|
||||||
padding: 0;
|
|
||||||
background-color: transparent;
|
|
||||||
}
|
|
||||||
|
|
||||||
.toc {
|
|
||||||
border-top: $toc_border;
|
|
||||||
border-bottom: $toc_border;
|
|
||||||
background-color: $toc_background_color;
|
|
||||||
|
|
||||||
details {
|
|
||||||
max-width: $content_max_width;
|
|
||||||
margin: 0 auto;
|
|
||||||
padding: 4 * $unit - $toc_border_width 0;
|
|
||||||
|
|
||||||
&[open] {
|
|
||||||
> summary {
|
|
||||||
margin-bottom: 2 * $unit;
|
|
||||||
|
|
||||||
&::after {
|
|
||||||
content: ' \2212';
|
|
||||||
}
|
|
||||||
|
|
||||||
/*
|
|
||||||
& ~ * {
|
|
||||||
animation: appear .2s ease-in-out;
|
|
||||||
}
|
|
||||||
*/
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
> summary {
|
|
||||||
display: block;
|
|
||||||
margin: 0;
|
|
||||||
padding-bottom: 0;
|
|
||||||
color: lighten($toc_title_color, 20%);
|
|
||||||
font-weight: $heading_font_weight;
|
|
||||||
font-size: 3 * $unit;
|
|
||||||
letter-spacing: 0.2em;
|
|
||||||
text-transform: uppercase;
|
|
||||||
user-select: none;
|
|
||||||
-moz-user-select: none;
|
|
||||||
-ms-user-select: none;
|
|
||||||
-webkit-user-select: none;
|
|
||||||
-webkit-tap-highlight-color: transparent;
|
|
||||||
outline: none;
|
|
||||||
|
|
||||||
&::-webkit-details-marker {
|
|
||||||
display: none;
|
|
||||||
}
|
|
||||||
|
|
||||||
&::after {
|
|
||||||
content: ' +';
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
> .wrapper {
|
|
||||||
columns: 1;
|
|
||||||
|
|
||||||
@include media {
|
|
||||||
columns: 2;
|
|
||||||
column-gap: 4 * $unit;
|
|
||||||
}
|
|
||||||
|
|
||||||
p {
|
|
||||||
margin: 0;
|
|
||||||
color: $toc_title_color;
|
|
||||||
font-weight: $heading_font_weight;
|
|
||||||
break-after: avoid-column;
|
|
||||||
-webkit-column-break-after: avoid;
|
|
||||||
|
|
||||||
a[href] {
|
|
||||||
color: inherit;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
ul {
|
|
||||||
margin: 0;
|
|
||||||
padding-left: 0;
|
|
||||||
color: lighten($toc_task_color, 20%);
|
|
||||||
list-style: square inside;
|
|
||||||
|
|
||||||
a[href] {
|
|
||||||
color: $toc_task_color;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
.group {
|
|
||||||
border-bottom: $nav_border;
|
|
||||||
padding-top: 0;
|
|
||||||
|
|
||||||
&:last-child {
|
|
||||||
border-bottom: none;
|
|
||||||
|
|
||||||
> ul > li:last-child {
|
|
||||||
padding-bottom: 4 * $unit;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
a[name] {
|
|
||||||
&::before {
|
|
||||||
content: "";
|
|
||||||
display: block;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
> ul {
|
|
||||||
margin: 0;
|
|
||||||
padding: 0;
|
|
||||||
|
|
||||||
> li {
|
|
||||||
width: 100%;
|
|
||||||
border-bottom: $nav_border;
|
|
||||||
padding: 0 0 (4 * $unit - $nav_border_width);
|
|
||||||
list-style: none;
|
|
||||||
|
|
||||||
&:last-child {
|
|
||||||
border-bottom: none;
|
|
||||||
}
|
|
||||||
|
|
||||||
.declaration-note {
|
|
||||||
color: #808080;
|
|
||||||
font-weight: normal;
|
|
||||||
font-size: 4 * $unit;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
.aside, .language {
|
|
||||||
overflow-y: hidden;
|
|
||||||
margin: 4 * $unit 0;
|
|
||||||
border-left: $aside_border;
|
|
||||||
border-radius: $border_radius;
|
|
||||||
padding: (2 * $unit) (3 * $unit);
|
|
||||||
background-color: $aside_background_color;
|
|
||||||
|
|
||||||
.aside-title {
|
|
||||||
margin: 0;
|
|
||||||
padding-bottom: 0;
|
|
||||||
color: $aside_color;
|
|
||||||
font-weight: $heading_font_weight;
|
|
||||||
font-size: 3 * $unit;
|
|
||||||
letter-spacing: 0.2em;
|
|
||||||
text-transform: uppercase;
|
|
||||||
user-select: none;
|
|
||||||
-moz-user-select: none;
|
|
||||||
-ms-user-select: none;
|
|
||||||
-webkit-user-select: none;
|
|
||||||
}
|
|
||||||
|
|
||||||
p:last-child {
|
|
||||||
margin-bottom: 0;
|
|
||||||
}
|
|
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(100% documented)
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<a href="https://github.com/xwu/NumericAnnex">View on GitHub</a>
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<a href="dash-feed://https%3A%2F%2Fxwu%2Egithub%2Eio%2FNumericAnnex%2Fdocsets%2FNumericAnnex%2Exml">Install in Dash</a>
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<a href="Classes/Random/Xoroshiro.html">– Xoroshiro</a>
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<a href="Extensions/FloatingPoint.html">FloatingPoint</a>
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<a href="Extensions/UnsignedInteger.html">UnsignedInteger</a>
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|
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|
||||||
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<a href="Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
|
||||||
|
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|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
|
||||||
|
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|
||||||
|
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|
||||||
|
<a href="Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
|
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|
||||||
|
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|
||||||
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<a href="Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
||||||
|
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|
||||||
|
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|
||||||
|
<a href="Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
||||||
|
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|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
|
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|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
||||||
|
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|
||||||
|
</ul>
|
||||||
|
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|
||||||
|
<li>
|
||||||
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<p><a href="Protocols.html">Protocols</a></p>
|
||||||
|
<ul>
|
||||||
|
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|
||||||
|
<a href="Protocols/Math.html">Math</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Protocols/PRNG.html">PRNG</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Protocols/Real.html">Real</a>
|
||||||
|
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|
||||||
|
</ul>
|
||||||
|
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|
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||||||
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<p><a href="Structs.html">Structs</a></p>
|
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<ul>
|
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|
||||||
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<a href="Structs/Complex.html">Complex</a>
|
||||||
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|
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|
||||||
|
<a href="Structs/Rational.html">Rational</a>
|
||||||
|
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|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="Typealiases.html">Typealiases</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
||||||
|
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|
||||||
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<li>
|
||||||
|
<a href="Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
|
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<article>
|
||||||
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<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>Classes</h1>
|
||||||
|
<p>The following classes are available globally.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex6RandomC">Random</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
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<section>
|
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|
||||||
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|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex6RandomC"></a>
|
||||||
|
<a name="//apple_ref/swift/Class/Random" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>Random</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>A pseudo-random number generator (PRNG) that implements
|
||||||
|
<a href="http://vigna.di.unimi.it/ftp/papers/xorshiftplus.pdf"><code>xorshift128+</code></a>, an efficient linear-feedback shift register.</p>
|
||||||
|
<div class="aside aside-warning">
|
||||||
|
<p class="aside-title">Warning</p>
|
||||||
|
Once seeded from cryptographically secure random bytes, an
|
||||||
|
instance of <code>Random</code> generates high-quality random numbers but is <em>not</em> a
|
||||||
|
cryptographically secure PRNG.
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>To generate random numbers, create your own instance of <code>Random</code> with an
|
||||||
|
internal state seeded from cryptographically secure random bytes:</p>
|
||||||
|
<pre class="highlight swift"><code><span class="k">let</span> <span class="nv">random</span> <span class="o">=</span> <span class="kt">Random</span><span class="p">()</span><span class="o">!</span>
|
||||||
|
<span class="k">let</span> <span class="nv">x</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">()</span> <span class="k">as</span> <span class="kt">Int</span>
|
||||||
|
|
||||||
|
<span class="c1">// You can also pass the desired result type as an argument.</span>
|
||||||
|
<span class="k">let</span> <span class="nv">y</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="kt">Int</span><span class="o">.</span><span class="k">self</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="k">if</span> <span class="n">x</span> <span class="o">></span> <span class="n">y</span> <span class="p">{</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="s">"Here's a random value between 0 and 42 (inclusive):"</span><span class="p">)</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="mi">42</span><span class="p">))</span>
|
||||||
|
<span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="s">"Here's a random value between -42 and 0 (inclusive):"</span><span class="p">)</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="o">-</span><span class="mi">42</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="mi">0</span><span class="p">))</span>
|
||||||
|
<span class="p">}</span>
|
||||||
|
</code></pre>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="Classes/Random/Xoroshiro.html">Random.Xoroshiro</a></code>, <code><a href="Protocols/PRNG.html">PRNG</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<a href="Classes/Random.html">See more…</a>
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">final</span> <span class="kd">class</span> <span class="kt">Random</span> <span class="p">:</span> <span class="kt"><a href="Protocols/PRNG.html">PRNG</a></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
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|
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|
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|
||||||
|
</article>
|
||||||
|
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|
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|
<footer>
|
||||||
|
<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
|
||||||
|
<p>Generated by <a href="https://github.com/realm/jazzy" target="_blank" rel="external">Jazzy</a> v0.8.3, a <a href="http://realm.io" target="_blank" rel="external">Realm</a> project.</p>
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@ -0,0 +1,356 @@
|
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|
<!DOCTYPE html>
|
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|
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<a href="https://github.com/xwu/NumericAnnex">View on GitHub</a>
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<p>
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|
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<a href="../Classes/Random/Xoroshiro.html">– Xoroshiro</a>
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|
<a href="../Extensions/FloatingPoint.html">FloatingPoint</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/UnsignedInteger.html">UnsignedInteger</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Functions.html">Functions</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Protocols.html">Protocols</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Math.html">Math</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/PRNG.html">PRNG</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Real.html">Real</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Structs.html">Structs</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Structs/Complex.html">Complex</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Structs/Rational.html">Rational</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Typealiases.html">Typealiases</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</nav>
|
||||||
|
<article>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>Random</h1>
|
||||||
|
<div class="declaration">
|
||||||
|
<div class="language">
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">final</span> <span class="kd">class</span> <span class="kt">Random</span> <span class="p">:</span> <span class="kt"><a href="../Protocols/PRNG.html">PRNG</a></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<p>A pseudo-random number generator (PRNG) that implements
|
||||||
|
<a href="http://vigna.di.unimi.it/ftp/papers/xorshiftplus.pdf"><code>xorshift128+</code></a>, an efficient linear-feedback shift register.</p>
|
||||||
|
<div class="aside aside-warning">
|
||||||
|
<p class="aside-title">Warning</p>
|
||||||
|
Once seeded from cryptographically secure random bytes, an
|
||||||
|
instance of <code>Random</code> generates high-quality random numbers but is <em>not</em> a
|
||||||
|
cryptographically secure PRNG.
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>To generate random numbers, create your own instance of <code>Random</code> with an
|
||||||
|
internal state seeded from cryptographically secure random bytes:</p>
|
||||||
|
<pre class="highlight swift"><code><span class="k">let</span> <span class="nv">random</span> <span class="o">=</span> <span class="kt">Random</span><span class="p">()</span><span class="o">!</span>
|
||||||
|
<span class="k">let</span> <span class="nv">x</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">()</span> <span class="k">as</span> <span class="kt">Int</span>
|
||||||
|
|
||||||
|
<span class="c1">// You can also pass the desired result type as an argument.</span>
|
||||||
|
<span class="k">let</span> <span class="nv">y</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="kt">Int</span><span class="o">.</span><span class="k">self</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="k">if</span> <span class="n">x</span> <span class="o">></span> <span class="n">y</span> <span class="p">{</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="s">"Here's a random value between 0 and 42 (inclusive):"</span><span class="p">)</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="mi">42</span><span class="p">))</span>
|
||||||
|
<span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="s">"Here's a random value between -42 and 0 (inclusive):"</span><span class="p">)</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="o">-</span><span class="mi">42</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="mi">0</span><span class="p">))</span>
|
||||||
|
<span class="p">}</span>
|
||||||
|
</code></pre>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../Classes/Random/Xoroshiro.html">Random.Xoroshiro</a></code>, <code><a href="../Protocols/PRNG.html">PRNG</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex6RandomC5states6UInt64V_AFtv">state</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex6RandomCACs6UInt64V_AEt5state_tcfc">init(state:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex6RandomCACSgycfc">init()</a></li>
|
||||||
|
<li><a href="#/s:s16IteratorProtocolP4next7ElementQzSgyF">next()</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex6RandomC9XoroshiroC">Xoroshiro</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex6RandomC5states6UInt64V_AFtv"></a>
|
||||||
|
<a name="//apple_ref/swift/Property/state" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>state</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>The internal state of the pseudo-random number generator.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">state</span><span class="p">:</span> <span class="p">(</span><span class="kt">UInt64</span><span class="p">,</span> <span class="kt">UInt64</span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex6RandomCACs6UInt64V_AEt5state_tcfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init(state:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init(state:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a pseudo-random number generator with the given internal state.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="nv">state</span><span class="p">:</span> <span class="p">(</span><span class="kt">UInt64</span><span class="p">,</span> <span class="kt">UInt64</span><span class="p">))</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>state</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The value to be used as the generator’s internal state.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex6RandomCACSgycfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a pseudo-random number generator with an internal state seeded
|
||||||
|
using cryptographically secure random bytes.</p>
|
||||||
|
|
||||||
|
<p>If cryptographically secure random bytes are unavailable, the result is
|
||||||
|
<code>nil</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="n">convenience</span> <span class="nf">init</span><span class="p">?()</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s16IteratorProtocolP4next7ElementQzSgyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/next()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>next()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">next</span><span class="p">()</span> <span class="o">-></span> <span class="kt">UInt64</span><span class="p">?</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex6RandomC9XoroshiroC"></a>
|
||||||
|
<a name="//apple_ref/swift/Class/Xoroshiro" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>Xoroshiro</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>A pseudo-random number generator (PRNG) that implements <code>xoroshiro128+</code>, a
|
||||||
|
successor to <code>xorshift128+</code> devised by S. Vigna and D. Blackman.</p>
|
||||||
|
<div class="aside aside-warning">
|
||||||
|
<p class="aside-title">Warning</p>
|
||||||
|
Once seeded from cryptographically secure random bytes, an
|
||||||
|
instance of <code>Random.Xoroshiro</code> generates high-quality random numbers but
|
||||||
|
is <em>not</em> a cryptographically secure PRNG.
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>To generate random numbers, create your own instance of <code>Random.Xoroshiro</code>
|
||||||
|
with an internal state seeded from cryptographically secure random bytes:</p>
|
||||||
|
<pre class="highlight swift"><code><span class="k">let</span> <span class="nv">random</span> <span class="o">=</span> <span class="kt">Random</span><span class="o">.</span><span class="kt">Xoroshiro</span><span class="p">()</span><span class="o">!</span>
|
||||||
|
<span class="k">let</span> <span class="nv">x</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">()</span> <span class="k">as</span> <span class="kt">Int</span>
|
||||||
|
|
||||||
|
<span class="c1">// You can also pass the desired result type as an argument.</span>
|
||||||
|
<span class="k">let</span> <span class="nv">y</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="kt">Int</span><span class="o">.</span><span class="k">self</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="k">if</span> <span class="n">x</span> <span class="o">></span> <span class="n">y</span> <span class="p">{</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="s">"Here's a random value between 0 and 42 (inclusive):"</span><span class="p">)</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="mi">42</span><span class="p">))</span>
|
||||||
|
<span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="s">"Here's a random value between -42 and 0 (inclusive):"</span><span class="p">)</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="o">-</span><span class="mi">42</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="mi">0</span><span class="p">))</span>
|
||||||
|
<span class="p">}</span>
|
||||||
|
</code></pre>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../Classes/Random.html">Random</a></code>, <code><a href="../Protocols/PRNG.html">PRNG</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<a href="../Classes/Random/Xoroshiro.html">See more…</a>
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">final</span> <span class="kd">class</span> <span class="kt">Xoroshiro</span> <span class="p">:</span> <span class="kt"><a href="../Protocols/PRNG.html">PRNG</a></span></code></pre>
|
||||||
|
|
||||||
|
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<a href="../../Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
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<section>
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<div class="wrapper">
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||||||
|
<div class="overview">
|
||||||
|
<h1>Xoroshiro</h1>
|
||||||
|
<div class="declaration">
|
||||||
|
<div class="language">
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">final</span> <span class="kd">class</span> <span class="kt">Xoroshiro</span> <span class="p">:</span> <span class="kt"><a href="../../Protocols/PRNG.html">PRNG</a></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<p>A pseudo-random number generator (PRNG) that implements <code>xoroshiro128+</code>, a
|
||||||
|
successor to <code>xorshift128+</code> devised by S. Vigna and D. Blackman.</p>
|
||||||
|
<div class="aside aside-warning">
|
||||||
|
<p class="aside-title">Warning</p>
|
||||||
|
Once seeded from cryptographically secure random bytes, an
|
||||||
|
instance of <code>Random.Xoroshiro</code> generates high-quality random numbers but
|
||||||
|
is <em>not</em> a cryptographically secure PRNG.
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>To generate random numbers, create your own instance of <code>Random.Xoroshiro</code>
|
||||||
|
with an internal state seeded from cryptographically secure random bytes:</p>
|
||||||
|
<pre class="highlight swift"><code><span class="k">let</span> <span class="nv">random</span> <span class="o">=</span> <span class="kt">Random</span><span class="o">.</span><span class="kt">Xoroshiro</span><span class="p">()</span><span class="o">!</span>
|
||||||
|
<span class="k">let</span> <span class="nv">x</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">()</span> <span class="k">as</span> <span class="kt">Int</span>
|
||||||
|
|
||||||
|
<span class="c1">// You can also pass the desired result type as an argument.</span>
|
||||||
|
<span class="k">let</span> <span class="nv">y</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="kt">Int</span><span class="o">.</span><span class="k">self</span><span class="p">)</span>
|
||||||
|
|
||||||
|
<span class="k">if</span> <span class="n">x</span> <span class="o">></span> <span class="n">y</span> <span class="p">{</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="s">"Here's a random value between 0 and 42 (inclusive):"</span><span class="p">)</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="mi">42</span><span class="p">))</span>
|
||||||
|
<span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="s">"Here's a random value between -42 and 0 (inclusive):"</span><span class="p">)</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="nf">uniform</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="o">-</span><span class="mi">42</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="mi">0</span><span class="p">))</span>
|
||||||
|
<span class="p">}</span>
|
||||||
|
</code></pre>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../../Classes/Random.html">Random</a></code>, <code><a href="../../Protocols/PRNG.html">PRNG</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex6RandomC9XoroshiroC5states6UInt64V_AHtv">state</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex6RandomC9XoroshiroCAEs6UInt64V_AGt5state_tcfc">init(state:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex6RandomC9XoroshiroCAESgycfc">init()</a></li>
|
||||||
|
<li><a href="#/s:s16IteratorProtocolP4next7ElementQzSgyF">next()</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex6RandomC9XoroshiroC5states6UInt64V_AHtv"></a>
|
||||||
|
<a name="//apple_ref/swift/Property/state" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>state</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>The internal state of the pseudo-random number generator.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">state</span><span class="p">:</span> <span class="p">(</span><span class="kt">UInt64</span><span class="p">,</span> <span class="kt">UInt64</span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex6RandomC9XoroshiroCAEs6UInt64V_AGt5state_tcfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init(state:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init(state:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a pseudo-random number generator with the given internal state.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="nv">state</span><span class="p">:</span> <span class="p">(</span><span class="kt">UInt64</span><span class="p">,</span> <span class="kt">UInt64</span><span class="p">))</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>state</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The value to be used as the generator’s internal state.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex6RandomC9XoroshiroCAESgycfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a pseudo-random number generator with an internal state seeded
|
||||||
|
using cryptographically secure random bytes.</p>
|
||||||
|
|
||||||
|
<p>If cryptographically secure random bytes are unavailable, the result is
|
||||||
|
<code>nil</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="n">convenience</span> <span class="nf">init</span><span class="p">?()</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s16IteratorProtocolP4next7ElementQzSgyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/next()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>next()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">next</span><span class="p">()</span> <span class="o">-></span> <span class="kt">UInt64</span><span class="p">?</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
</article>
|
||||||
|
</div>
|
||||||
|
<footer>
|
||||||
|
<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
|
||||||
|
<p>Generated by <a href="https://github.com/realm/jazzy" target="_blank" rel="external">Jazzy</a> v0.8.3, a <a href="http://realm.io" target="_blank" rel="external">Realm</a> project.</p>
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|
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|
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<a href="Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
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|
||||||
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<h1>Extensions</h1>
|
||||||
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<p>The following extensions are available globally.</p>
|
||||||
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|
||||||
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|
||||||
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<details open>
|
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<summary>Topics</summary>
|
||||||
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<div class="wrapper">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP">BinaryInteger</a></li>
|
||||||
|
<li><a href="#/s:s15UnsignedIntegerP">UnsignedInteger</a></li>
|
||||||
|
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|
||||||
|
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|
||||||
|
<li><a href="#/s:Sf">Float</a></li>
|
||||||
|
<li><a href="#/s:Sd">Double</a></li>
|
||||||
|
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|
||||||
|
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|
||||||
|
<li><a href="#/s:s13FloatingPointP">FloatingPoint</a></li>
|
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|
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|
||||||
|
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|
||||||
|
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|
||||||
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|
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|
||||||
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<a name="/s:s13BinaryIntegerP"></a>
|
||||||
|
<a name="//apple_ref/swift/Extension/BinaryInteger" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>BinaryInteger</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
<a href="Extensions/BinaryInteger.html">See more…</a>
|
||||||
|
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|
||||||
|
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|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">protocol</span> <span class="kt">BinaryInteger</span> <span class="p">:</span> <span class="kt">Hashable</span><span class="p">,</span> <span class="kt">Numeric</span><span class="p">,</span> <span class="kt">CustomStringConvertible</span><span class="p">,</span> <span class="kt">Strideable</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
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|
||||||
|
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|
||||||
|
<a name="/s:s15UnsignedIntegerP"></a>
|
||||||
|
<a name="//apple_ref/swift/Extension/UnsignedInteger" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>UnsignedInteger</code>
|
||||||
|
</h4>
|
||||||
|
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|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
<a href="Extensions/UnsignedInteger.html">See more…</a>
|
||||||
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|
||||||
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|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">protocol</span> <span class="kt">UnsignedInteger</span> <span class="p">:</span> <span class="kt">BinaryInteger</span> <span class="k">where</span> <span class="k">Self</span><span class="o">.</span><span class="kt">Magnitude</span> <span class="p">:</span> <span class="kt">BinaryInteger</span></code></pre>
|
||||||
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|
||||||
|
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|
||||||
|
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|
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|
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|
||||||
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|
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|
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|
||||||
|
<a name="//apple_ref/swift/Extension/Float" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>Float</code>
|
||||||
|
</h4>
|
||||||
|
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|
||||||
|
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|
||||||
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|
||||||
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|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">struct</span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">struct</span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
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|
||||||
|
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|
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|
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|
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|
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|
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|
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|
||||||
|
<h4>
|
||||||
|
<code>FloatingPoint</code>
|
||||||
|
</h4>
|
||||||
|
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|
||||||
|
<div class="abstract">
|
||||||
|
|
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|
<a href="Extensions/FloatingPoint.html">See more…</a>
|
||||||
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|
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|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">protocol</span> <span class="kt">FloatingPoint</span> <span class="p">:</span> <span class="kt">SignedNumeric</span><span class="p">,</span> <span class="kt">Strideable</span><span class="p">,</span> <span class="kt">Hashable</span></code></pre>
|
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</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Protocols.html">Protocols</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Math.html">Math</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/PRNG.html">PRNG</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Real.html">Real</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Structs.html">Structs</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Structs/Complex.html">Complex</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Structs/Rational.html">Rational</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Typealiases.html">Typealiases</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</nav>
|
||||||
|
<article>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>BinaryInteger</h1>
|
||||||
|
<div class="declaration">
|
||||||
|
<div class="language">
|
||||||
|
<pre class="highlight"><code><span class="kd">protocol</span> <span class="kt">BinaryInteger</span> <span class="p">:</span> <span class="kt">Hashable</span><span class="p">,</span> <span class="kt">Numeric</span><span class="p">,</span> <span class="kt">CustomStringConvertible</span><span class="p">,</span> <span class="kt">Strideable</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<p><a href="#/Exponentiation">Exponentiation</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexE3powxx_xtFZ">pow(_:_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
<p><a href="#/Square%20Root">Square Root</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexE4sqrtxxFZ">sqrt(_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
<p><a href="#/Cube%20Root">Cube Root</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexsAARzs08UnsignedB09MagnitudeRpzlE4cbrtxxFZ">cbrt(_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
<p><a href="#/Factoring">Factoring</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexsAARzs08UnsignedB09MagnitudeRpzlE3gcdxx_xtFZ">gcd(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexsAARzs08UnsignedB09MagnitudeRpzlE3lcmxx_xtFZ">lcm(_:_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
<p><a href="#/Factoring%20(Fixed-Width)">Factoring (Fixed-Width)</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20gcdReportingOverflowx12partialValue_Sb8overflowtx_xtFZ">gcdReportingOverflow(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ">lcmReportingOverflow(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE07lcmFullF0x4high_AF3lowtx_xtFZ">lcmFullWidth(_:_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
<p><a href="#/Initializers">Initializers</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexExSgAC8RationalVyqd__G7exactly_tcs9DecodableRd__s9EncodableRd__s06SignedB0Rd__s021_ExpressibleByBuiltinB7LiteralRd__s08UnsignedB09Magnitudes0C0PRpd__AnP_ANQYd__AQRSlufc">init(exactly:)</a></li>
|
||||||
|
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexExAC8RationalVyqd__Gcs9DecodableRd__s9EncodableRd__s06SignedB0Rd__s021_ExpressibleByBuiltinB7LiteralRd__s08UnsignedB09Magnitudes0C0PRpd__AlN_ALQYd__AORSlufc">init(_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Exponentiation"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Exponentiation" class="dashAnchor"></a>
|
||||||
|
<h3>Exponentiation</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13BinaryIntegerP12NumericAnnexE3powxx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/pow(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>pow(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the result of raising <code>base</code> to the power of <code>exponent</code>, rounded
|
||||||
|
to a representable value.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">pow</span><span class="p">(</span><span class="n">_</span> <span class="nv">base</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">exponent</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Square%20Root"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Square Root" class="dashAnchor"></a>
|
||||||
|
<h3>Square Root</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13BinaryIntegerP12NumericAnnexE4sqrtxxFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/sqrt(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>sqrt(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the square root of <code>x</code>, rounding toward zero. If <code>x</code> is negative,
|
||||||
|
a runtime error may occur.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">sqrt</span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Cube%20Root"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Cube Root" class="dashAnchor"></a>
|
||||||
|
<h3>Cube Root</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13BinaryIntegerP12NumericAnnexsAARzs08UnsignedB09MagnitudeRpzlE4cbrtxxFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/cbrt(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>cbrt(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the cube root of <code>x</code>, rounding toward zero.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">cbrt</span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Factoring"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Factoring" class="dashAnchor"></a>
|
||||||
|
<h3>Factoring</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13BinaryIntegerP12NumericAnnexsAARzs08UnsignedB09MagnitudeRpzlE3gcdxx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/gcd(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>gcd(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the greatest common divisor of <code>a</code> and <code>b</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">gcd</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13BinaryIntegerP12NumericAnnexsAARzs08UnsignedB09MagnitudeRpzlE3lcmxx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/lcm(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>lcm(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the least common multiple of <code>a</code> and <code>b</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lcm</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Factoring%20(Fixed-Width)"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Factoring (Fixed-Width)" class="dashAnchor"></a>
|
||||||
|
<h3>Factoring (Fixed-Width)</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20gcdReportingOverflowx12partialValue_Sb8overflowtx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/gcdReportingOverflow(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>gcdReportingOverflow(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the greatest common divisor of <code>a</code> and <code>b</code> and a flag to indicate
|
||||||
|
whether overflow occurred during the operation.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">gcdReportingOverflow</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
|
||||||
|
<span class="o">-></span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">Bool</span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/lcmReportingOverflow(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>lcmReportingOverflow(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the least common multiple of <code>a</code> and <code>b</code> and a flag to indicate
|
||||||
|
whether overflow occurred during the operation.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lcmReportingOverflow</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
|
||||||
|
<span class="o">-></span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">Bool</span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE07lcmFullF0x4high_AF3lowtx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/lcmFullWidth(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>lcmFullWidth(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the high and low parts of the least common multiple of <code>a</code> and <code>b</code>
|
||||||
|
computed using full-width arithmetic.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lcmFullWidth</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
|
||||||
|
<span class="o">-></span> <span class="p">(</span><span class="nv">high</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">low</span><span class="p">:</span> <span class="k">Self</span><span class="o">.</span><span class="kt">Magnitude</span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Initializers"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Initializers" class="dashAnchor"></a>
|
||||||
|
<h3>Initializers</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13BinaryIntegerP12NumericAnnexExSgAC8RationalVyqd__G7exactly_tcs9DecodableRd__s9EncodableRd__s06SignedB0Rd__s021_ExpressibleByBuiltinB7LiteralRd__s08UnsignedB09Magnitudes0C0PRpd__AnP_ANQYd__AQRSlufc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init(exactly:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init(exactly:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a new binary integer from the given rational value, if it can be
|
||||||
|
represented exactly.</p>
|
||||||
|
|
||||||
|
<p>If <code>source</code> is not representable exactly, the result is <code>nil</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">init</span><span class="p">?</span><span class="o"><</span><span class="kt">U</span><span class="o">></span><span class="p">(</span><span class="n">exactly</span> <span class="nv">source</span><span class="p">:</span> <span class="kt"><a href="../Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">U</span><span class="o">></span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>source</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>A rational value to convert to a binary integer.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13BinaryIntegerP12NumericAnnexExAC8RationalVyqd__Gcs9DecodableRd__s9EncodableRd__s06SignedB0Rd__s021_ExpressibleByBuiltinB7LiteralRd__s08UnsignedB09Magnitudes0C0PRpd__AlN_ALQYd__AORSlufc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a new binary integer from the given rational value, rounding
|
||||||
|
toward zero.</p>
|
||||||
|
|
||||||
|
<p>If <code>source</code> is outside the bounds of this type after rounding toward zero,
|
||||||
|
a runtime error may occur.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">init</span><span class="o"><</span><span class="kt">U</span><span class="o">></span><span class="p">(</span><span class="n">_</span> <span class="nv">source</span><span class="p">:</span> <span class="kt"><a href="../Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">U</span><span class="o">></span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>source</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>A rational value to convert to a binary integer.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
</article>
|
||||||
|
</div>
|
||||||
|
<footer>
|
||||||
|
<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
|
||||||
|
<p>Generated by <a href="https://github.com/realm/jazzy" target="_blank" rel="external">Jazzy</a> v0.8.3, a <a href="http://realm.io" target="_blank" rel="external">Realm</a> project.</p>
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|
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|
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|
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|
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@ -0,0 +1,837 @@
|
||||||
|
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|
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|
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<p class="primary">
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<a href="../index.html">NumericAnnex Reference</a>
|
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(100% documented)
|
||||||
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</p>
|
||||||
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<p>
|
||||||
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<a href="https://github.com/xwu/NumericAnnex">View on GitHub</a>
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||||||
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<p>
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<a href="dash-feed://https%3A%2F%2Fxwu%2Egithub%2Eio%2FNumericAnnex%2Fdocsets%2FNumericAnnex%2Exml">Install in Dash</a>
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<a href="../Classes/Random/Xoroshiro.html">– Xoroshiro</a>
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|
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|
||||||
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|
||||||
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<a href="../Extensions/BinaryInteger.html">BinaryInteger</a>
|
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|
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<a href="../Extensions/Double.html">Double</a>
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|
||||||
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<a href="../Extensions/Float.html">Float</a>
|
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|
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<li>
|
||||||
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<a href="../Extensions/FloatingPoint.html">FloatingPoint</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/UnsignedInteger.html">UnsignedInteger</a>
|
||||||
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</li>
|
||||||
|
</ul>
|
||||||
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|
||||||
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<li>
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||||||
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<p><a href="../Functions.html">Functions</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
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<p><a href="../Protocols.html">Protocols</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Math.html">Math</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/PRNG.html">PRNG</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Real.html">Real</a>
|
||||||
|
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|
||||||
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|
||||||
|
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|
||||||
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||||||
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<p><a href="../Structs.html">Structs</a></p>
|
||||||
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|
||||||
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|
||||||
|
<a href="../Structs/Complex.html">Complex</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Structs/Rational.html">Rational</a>
|
||||||
|
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|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
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<p><a href="../Typealiases.html">Typealiases</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
|
||||||
|
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|
||||||
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|
||||||
|
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|
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<article>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>Double</h1>
|
||||||
|
<div class="declaration">
|
||||||
|
<div class="language">
|
||||||
|
<pre class="highlight"><code><span class="kd">struct</span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<p><a href="#/Real">Real</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP1exvZ">e</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP3phixvZ">phi</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP3powxx_xtFZ">pow(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP18naturalExponentialxyF">naturalExponential()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP17binaryExponentialxyF">binaryExponential()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP17commonExponentialxyF">commonExponential()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP26naturalExponentialMinusOnexyF">naturalExponentialMinusOne()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP16naturalLogarithmxyF">naturalLogarithm()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP15binaryLogarithmxyF">binaryLogarithm()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP15commonLogarithmxyF">commonLogarithm()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP23naturalLogarithmOnePlusxyF">naturalLogarithmOnePlus()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP8cubeRootxyF">cubeRoot()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP4sinexyF">sine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP6cosinexyF">cosine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP7tangentxyF">tangent()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP11inverseSinexyF">inverseSine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP13inverseCosinexyF">inverseCosine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP14inverseTangentxyF">inverseTangent()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP14hyperbolicSinexyF">hyperbolicSine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP16hyperbolicCosinexyF">hyperbolicCosine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP17hyperbolicTangentxyF">hyperbolicTangent()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP21inverseHyperbolicSinexyF">inverseHyperbolicSine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP23inverseHyperbolicCosinexyF">inverseHyperbolicCosine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP24inverseHyperbolicTangentxyF">inverseHyperbolicTangent()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP5hypotxx_xtFZ">hypot(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP14inverseTangentxx10dividingBy_tF">inverseTangent(dividingBy:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP5errorxyF">error()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP18complementaryErrorxyF">complementaryError()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP5gammaxyF">gamma()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP16logarithmicGammaxyF">logarithmicGamma()</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Real"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Real" class="dashAnchor"></a>
|
||||||
|
<h3>Real</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP1exvZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Variable/e" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>e</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="k">var</span> <span class="nv">e</span><span class="p">:</span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP3phixvZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Variable/phi" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>phi</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="k">var</span> <span class="nv">phi</span><span class="p">:</span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP3powxx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/pow(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>pow(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">pow</span><span class="p">(</span><span class="n">_</span> <span class="nv">base</span><span class="p">:</span> <span class="kt">Double</span><span class="p">,</span> <span class="n">_</span> <span class="nv">exponent</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>base</code></dt>
|
||||||
|
<dd>
|
||||||
|
|
||||||
|
</dd>
|
||||||
|
<dt><code>exponent</code></dt>
|
||||||
|
<dd>
|
||||||
|
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP18naturalExponentialxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/naturalExponential()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>naturalExponential()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">naturalExponential</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP17binaryExponentialxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/binaryExponential()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>binaryExponential()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">binaryExponential</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP17commonExponentialxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/commonExponential()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>commonExponential()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">commonExponential</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP26naturalExponentialMinusOnexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/naturalExponentialMinusOne()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>naturalExponentialMinusOne()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">naturalExponentialMinusOne</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP16naturalLogarithmxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/naturalLogarithm()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>naturalLogarithm()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">naturalLogarithm</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP15binaryLogarithmxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/binaryLogarithm()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>binaryLogarithm()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">binaryLogarithm</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP15commonLogarithmxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/commonLogarithm()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>commonLogarithm()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">commonLogarithm</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP23naturalLogarithmOnePlusxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/naturalLogarithmOnePlus()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>naturalLogarithmOnePlus()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">naturalLogarithmOnePlus</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP8cubeRootxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/cubeRoot()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>cubeRoot()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">cubeRoot</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP4sinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/sine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>sine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">sine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP6cosinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/cosine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>cosine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">cosine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP7tangentxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/tangent()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>tangent()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">tangent</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP11inverseSinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseSine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseSine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseSine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
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|
||||||
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|
||||||
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|
||||||
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|
||||||
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||||||
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||||||
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||||||
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|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseCosine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
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||||||
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||||||
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|
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||||||
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||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseTangent</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
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||||||
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||||||
|
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|
||||||
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<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">hyperbolicSine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
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||||||
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|
||||||
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|
||||||
|
<code>hyperbolicCosine()</code>
|
||||||
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|
||||||
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||||||
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|
||||||
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||||||
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||||||
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|
||||||
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|
||||||
|
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|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">hyperbolicCosine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
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||||||
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||||||
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<a name="/s:12NumericAnnex4MathP17hyperbolicTangentxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/hyperbolicTangent()" class="dashAnchor"></a>
|
||||||
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<h4>
|
||||||
|
<code>hyperbolicTangent()</code>
|
||||||
|
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|
||||||
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|
||||||
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|
||||||
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|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">hyperbolicTangent</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
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||||||
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||||||
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|
||||||
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<a name="/s:12NumericAnnex4MathP21inverseHyperbolicSinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseHyperbolicSine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseHyperbolicSine()</code>
|
||||||
|
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|
||||||
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|
||||||
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|
||||||
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||||||
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|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseHyperbolicSine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
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||||||
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||||||
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||||||
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|
||||||
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|
||||||
|
<a name="/s:12NumericAnnex4MathP23inverseHyperbolicCosinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseHyperbolicCosine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseHyperbolicCosine()</code>
|
||||||
|
</h4>
|
||||||
|
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|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
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|
||||||
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|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseHyperbolicCosine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
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|
||||||
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|
||||||
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|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP24inverseHyperbolicTangentxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseHyperbolicTangent()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseHyperbolicTangent()</code>
|
||||||
|
</h4>
|
||||||
|
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|
||||||
|
<div class="abstract">
|
||||||
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|
||||||
|
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|
||||||
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|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseHyperbolicTangent</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
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|
||||||
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||||||
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|
||||||
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|
||||||
|
<a name="/s:12NumericAnnex4RealP5hypotxx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/hypot(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>hypot(_:_:)</code>
|
||||||
|
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|
||||||
|
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|
||||||
|
<div class="abstract">
|
||||||
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|
||||||
|
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|
||||||
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|
||||||
|
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|
||||||
|
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|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">hypot</span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="kt">Double</span><span class="p">,</span> <span class="n">_</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
<h5>Parameters</h5>
|
||||||
|
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|
||||||
|
<dt><code>x</code></dt>
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
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|
||||||
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|
||||||
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|
||||||
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|
||||||
|
<a name="/s:12NumericAnnex4RealP14inverseTangentxx10dividingBy_tF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseTangent(dividingBy:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseTangent(dividingBy:)</code>
|
||||||
|
</h4>
|
||||||
|
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|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
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|
||||||
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|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseTangent</span><span class="p">(</span><span class="n">dividingBy</span> <span class="nv">other</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>other</code></dt>
|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
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||||||
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|
||||||
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|
||||||
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
<code>error()</code>
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">error</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
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|
||||||
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||||||
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||||||
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||||||
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|
||||||
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|
||||||
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|
||||||
|
<a name="//apple_ref/swift/Method/complementaryError()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>complementaryError()</code>
|
||||||
|
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|
||||||
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|
||||||
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|
||||||
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||||||
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||||||
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|
||||||
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|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">complementaryError</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
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||||||
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||||||
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||||||
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||||||
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|
||||||
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|
||||||
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|
||||||
|
<a name="//apple_ref/swift/Method/gamma()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>gamma()</code>
|
||||||
|
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|
||||||
|
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|
||||||
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|
||||||
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|
||||||
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||||||
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|
||||||
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|
||||||
|
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|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">gamma</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
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||||||
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|
||||||
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|
||||||
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|
||||||
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|
||||||
|
<a name="//apple_ref/swift/Method/logarithmicGamma()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>logarithmicGamma()</code>
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
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|
||||||
|
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|
||||||
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|
||||||
|
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|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">logarithmicGamma</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Double</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
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||||||
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||||||
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|
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<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
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||||||
|
<a href="../Classes/Random/Xoroshiro.html">– Xoroshiro</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Extensions.html">Extensions</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/BinaryInteger.html">BinaryInteger</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/Double.html">Double</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/Float.html">Float</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/FloatingPoint.html">FloatingPoint</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/UnsignedInteger.html">UnsignedInteger</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Functions.html">Functions</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Protocols.html">Protocols</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Math.html">Math</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/PRNG.html">PRNG</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Real.html">Real</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Structs.html">Structs</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Structs/Complex.html">Complex</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Structs/Rational.html">Rational</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Typealiases.html">Typealiases</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</nav>
|
||||||
|
<article>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>Float</h1>
|
||||||
|
<div class="declaration">
|
||||||
|
<div class="language">
|
||||||
|
<pre class="highlight"><code><span class="kd">struct</span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<p><a href="#/Real">Real</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP1exvZ">e</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP3phixvZ">phi</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP3powxx_xtFZ">pow(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP18naturalExponentialxyF">naturalExponential()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP17binaryExponentialxyF">binaryExponential()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP17commonExponentialxyF">commonExponential()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP26naturalExponentialMinusOnexyF">naturalExponentialMinusOne()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP16naturalLogarithmxyF">naturalLogarithm()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP15binaryLogarithmxyF">binaryLogarithm()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP15commonLogarithmxyF">commonLogarithm()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP23naturalLogarithmOnePlusxyF">naturalLogarithmOnePlus()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP8cubeRootxyF">cubeRoot()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP4sinexyF">sine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP6cosinexyF">cosine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP7tangentxyF">tangent()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP11inverseSinexyF">inverseSine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP13inverseCosinexyF">inverseCosine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP14inverseTangentxyF">inverseTangent()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP14hyperbolicSinexyF">hyperbolicSine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP16hyperbolicCosinexyF">hyperbolicCosine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP17hyperbolicTangentxyF">hyperbolicTangent()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP21inverseHyperbolicSinexyF">inverseHyperbolicSine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP23inverseHyperbolicCosinexyF">inverseHyperbolicCosine()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP24inverseHyperbolicTangentxyF">inverseHyperbolicTangent()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP5hypotxx_xtFZ">hypot(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP14inverseTangentxx10dividingBy_tF">inverseTangent(dividingBy:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP5errorxyF">error()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP18complementaryErrorxyF">complementaryError()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP5gammaxyF">gamma()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP16logarithmicGammaxyF">logarithmicGamma()</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Real"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Real" class="dashAnchor"></a>
|
||||||
|
<h3>Real</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP1exvZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Variable/e" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>e</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="k">var</span> <span class="nv">e</span><span class="p">:</span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP3phixvZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Variable/phi" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>phi</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="k">var</span> <span class="nv">phi</span><span class="p">:</span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP3powxx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/pow(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>pow(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">pow</span><span class="p">(</span><span class="n">_</span> <span class="nv">base</span><span class="p">:</span> <span class="kt">Float</span><span class="p">,</span> <span class="n">_</span> <span class="nv">exponent</span><span class="p">:</span> <span class="kt">Float</span><span class="p">)</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>base</code></dt>
|
||||||
|
<dd>
|
||||||
|
|
||||||
|
</dd>
|
||||||
|
<dt><code>exponent</code></dt>
|
||||||
|
<dd>
|
||||||
|
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP18naturalExponentialxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/naturalExponential()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>naturalExponential()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">naturalExponential</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP17binaryExponentialxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/binaryExponential()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>binaryExponential()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">binaryExponential</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP17commonExponentialxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/commonExponential()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>commonExponential()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">commonExponential</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP26naturalExponentialMinusOnexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/naturalExponentialMinusOne()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>naturalExponentialMinusOne()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">naturalExponentialMinusOne</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP16naturalLogarithmxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/naturalLogarithm()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>naturalLogarithm()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">naturalLogarithm</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP15binaryLogarithmxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/binaryLogarithm()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>binaryLogarithm()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">binaryLogarithm</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP15commonLogarithmxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/commonLogarithm()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>commonLogarithm()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">commonLogarithm</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP23naturalLogarithmOnePlusxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/naturalLogarithmOnePlus()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>naturalLogarithmOnePlus()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">naturalLogarithmOnePlus</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP8cubeRootxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/cubeRoot()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>cubeRoot()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">cubeRoot</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP4sinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/sine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>sine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">sine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP6cosinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/cosine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>cosine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">cosine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP7tangentxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/tangent()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>tangent()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">tangent</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP11inverseSinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseSine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseSine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseSine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP13inverseCosinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseCosine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseCosine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseCosine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP14inverseTangentxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseTangent()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseTangent()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseTangent</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP14hyperbolicSinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/hyperbolicSine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>hyperbolicSine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">hyperbolicSine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP16hyperbolicCosinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/hyperbolicCosine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>hyperbolicCosine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">hyperbolicCosine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP17hyperbolicTangentxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/hyperbolicTangent()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>hyperbolicTangent()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">hyperbolicTangent</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP21inverseHyperbolicSinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseHyperbolicSine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseHyperbolicSine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseHyperbolicSine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP23inverseHyperbolicCosinexyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseHyperbolicCosine()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseHyperbolicCosine()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseHyperbolicCosine</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP24inverseHyperbolicTangentxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseHyperbolicTangent()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseHyperbolicTangent()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseHyperbolicTangent</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealP5hypotxx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/hypot(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>hypot(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">hypot</span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="kt">Float</span><span class="p">,</span> <span class="n">_</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">Float</span><span class="p">)</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>x</code></dt>
|
||||||
|
<dd>
|
||||||
|
|
||||||
|
</dd>
|
||||||
|
<dt><code>y</code></dt>
|
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||||||
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||||||
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||||||
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||||||
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<a name="//apple_ref/swift/Method/inverseTangent(dividingBy:)" class="dashAnchor"></a>
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||||||
|
<h4>
|
||||||
|
<code>inverseTangent(dividingBy:)</code>
|
||||||
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|
||||||
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|
||||||
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||||||
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<h5>Declaration</h5>
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||||||
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<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverseTangent</span><span class="p">(</span><span class="n">dividingBy</span> <span class="nv">other</span><span class="p">:</span> <span class="kt">Float</span><span class="p">)</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
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||||||
|
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|
||||||
|
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|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
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|
||||||
|
<dt><code>other</code></dt>
|
||||||
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|
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||||||
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|
||||||
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||||||
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<h4>
|
||||||
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|
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||||||
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||||||
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|
||||||
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||||||
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||||||
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|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">error</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
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||||||
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|
||||||
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|
||||||
|
<code>complementaryError()</code>
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||||||
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|
||||||
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||||||
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||||||
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||||||
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<h5>Declaration</h5>
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||||||
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<div class="language">
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||||||
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|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">complementaryError</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
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||||||
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||||||
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||||||
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||||||
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|
||||||
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||||||
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|
||||||
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<h4>
|
||||||
|
<code>gamma()</code>
|
||||||
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||||||
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||||||
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<div class="abstract">
|
||||||
|
|
||||||
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||||||
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|
||||||
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<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">gamma</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
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||||||
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||||||
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|
||||||
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|
||||||
|
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|
||||||
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<a name="/s:12NumericAnnex4RealP16logarithmicGammaxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/logarithmicGamma()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>logarithmicGamma()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">logarithmicGamma</span><span class="p">()</span> <span class="o">-></span> <span class="kt">Float</span></code></pre>
|
||||||
|
|
||||||
|
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|
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|
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||||||
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||||||
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<a href="../Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
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||||||
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<a href="../Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
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|
||||||
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<a href="../Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
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||||||
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||||||
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||||||
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<a href="../Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
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<section>
|
||||||
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<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>FloatingPoint</h1>
|
||||||
|
<div class="declaration">
|
||||||
|
<div class="language">
|
||||||
|
<pre class="highlight"><code><span class="kd">protocol</span> <span class="kt">FloatingPoint</span> <span class="p">:</span> <span class="kt">SignedNumeric</span><span class="p">,</span> <span class="kt">Strideable</span><span class="p">,</span> <span class="kt">Hashable</span></code></pre>
|
||||||
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||||||
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||||||
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<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<p><a href="#/Initializers">Initializers</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s13FloatingPointP12NumericAnnexExAC8RationalVySiGcfc">init(_:)</a></li>
|
||||||
|
<li><a href="#/s:s13FloatingPointP12NumericAnnexExAC8RationalVys4Int8VGcfc">init(_:)</a></li>
|
||||||
|
<li><a href="#/s:s13FloatingPointP12NumericAnnexExAC8RationalVys5Int16VGcfc">init(_:)</a></li>
|
||||||
|
<li><a href="#/s:s13FloatingPointP12NumericAnnexExAC8RationalVys5Int32VGcfc">init(_:)</a></li>
|
||||||
|
<li><a href="#/s:s13FloatingPointP12NumericAnnexExAC8RationalVys5Int64VGcfc">init(_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
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|
||||||
|
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|
||||||
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<section>
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||||||
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||||||
|
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||||||
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|
||||||
|
<a name="/Initializers"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Initializers" class="dashAnchor"></a>
|
||||||
|
<h3>Initializers</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13FloatingPointP12NumericAnnexExAC8RationalVySiGcfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a new floating-point value from the given rational value, after
|
||||||
|
rounding the whole part, the numerator of the fractional part, and the
|
||||||
|
denominator of the fractional part each to the closest possible
|
||||||
|
representation.</p>
|
||||||
|
|
||||||
|
<p>If two representable values are equally close, the result of rounding is
|
||||||
|
the value with more trailing zeros in its significand bit pattern.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">source</span><span class="p">:</span> <span class="kt"><a href="../Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">Int</span><span class="o">></span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>source</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The rational value to convert to a floating-point value.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
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</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13FloatingPointP12NumericAnnexExAC8RationalVys4Int8VGcfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a new floating-point value from the given rational value, after
|
||||||
|
rounding the whole part, the numerator of the fractional part, and the
|
||||||
|
denominator of the fractional part each to the closest possible
|
||||||
|
representation.</p>
|
||||||
|
|
||||||
|
<p>If two representable values are equally close, the result of rounding is
|
||||||
|
the value with more trailing zeros in its significand bit pattern.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">source</span><span class="p">:</span> <span class="kt"><a href="../Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">Int8</span><span class="o">></span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>source</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The rational value to convert to a floating-point value.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13FloatingPointP12NumericAnnexExAC8RationalVys5Int16VGcfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a new floating-point value from the given rational value, after
|
||||||
|
rounding the whole part, the numerator of the fractional part, and the
|
||||||
|
denominator of the fractional part each to the closest possible
|
||||||
|
representation.</p>
|
||||||
|
|
||||||
|
<p>If two representable values are equally close, the result of rounding is
|
||||||
|
the value with more trailing zeros in its significand bit pattern.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">source</span><span class="p">:</span> <span class="kt"><a href="../Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">Int16</span><span class="o">></span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>source</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The rational value to convert to a floating-point value.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13FloatingPointP12NumericAnnexExAC8RationalVys5Int32VGcfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a new floating-point value from the given rational value, after
|
||||||
|
rounding the whole part, the numerator of the fractional part, and the
|
||||||
|
denominator of the fractional part each to the closest possible
|
||||||
|
representation.</p>
|
||||||
|
|
||||||
|
<p>If two representable values are equally close, the result of rounding is
|
||||||
|
the value with more trailing zeros in its significand bit pattern.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">source</span><span class="p">:</span> <span class="kt"><a href="../Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">Int32</span><span class="o">></span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>source</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The rational value to convert to a floating-point value.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s13FloatingPointP12NumericAnnexExAC8RationalVys5Int64VGcfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a new floating-point value from the given rational value, after
|
||||||
|
rounding the whole part, the numerator of the fractional part, and the
|
||||||
|
denominator of the fractional part each to the closest possible
|
||||||
|
representation.</p>
|
||||||
|
|
||||||
|
<p>If two representable values are equally close, the result of rounding is
|
||||||
|
the value with more trailing zeros in its significand bit pattern.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">source</span><span class="p">:</span> <span class="kt"><a href="../Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">Int64</span><span class="o">></span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>source</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The rational value to convert to a floating-point value.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
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|
||||||
|
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|
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|
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<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
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<p>Generated by <a href="https://github.com/realm/jazzy" target="_blank" rel="external">Jazzy</a> v0.8.3, a <a href="http://realm.io" target="_blank" rel="external">Realm</a> project.</p>
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@ -0,0 +1,310 @@
|
||||||
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(100% documented)
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|
||||||
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<a href="https://github.com/xwu/NumericAnnex">View on GitHub</a>
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|
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|
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|
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<a href="../Extensions/Float.html">Float</a>
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<a href="../Extensions/FloatingPoint.html">FloatingPoint</a>
|
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|
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|
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|
<a href="../Extensions/UnsignedInteger.html">UnsignedInteger</a>
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|
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|
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<p><a href="../Functions.html">Functions</a></p>
|
||||||
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<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
||||||
|
</li>
|
||||||
|
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|
||||||
|
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|
||||||
|
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||||||
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<p><a href="../Protocols.html">Protocols</a></p>
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|
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|
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|
<a href="../Protocols/Math.html">Math</a>
|
||||||
|
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|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/PRNG.html">PRNG</a>
|
||||||
|
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|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Real.html">Real</a>
|
||||||
|
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|
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|
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|
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|
||||||
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<a href="../Structs/Rational.html">Rational</a>
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|
||||||
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|
||||||
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<p><a href="../Typealiases.html">Typealiases</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
||||||
|
</li>
|
||||||
|
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|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
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||||||
|
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<article>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>UnsignedInteger</h1>
|
||||||
|
<div class="declaration">
|
||||||
|
<div class="language">
|
||||||
|
<pre class="highlight"><code><span class="kd">protocol</span> <span class="kt">UnsignedInteger</span> <span class="p">:</span> <span class="kt">BinaryInteger</span> <span class="k">where</span> <span class="k">Self</span><span class="o">.</span><span class="kt">Magnitude</span> <span class="p">:</span> <span class="kt">BinaryInteger</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
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</div>
|
||||||
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|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<p><a href="#/Cube%20Root">Cube Root</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexE4cbrtxxFZ">cbrt(_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
<p><a href="#/Factoring">Factoring</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexE3gcdxx_xtFZ">gcd(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexE3lcmxx_xtFZ">lcm(_:_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
<p><a href="#/Factoring%20(Fixed-Width)">Factoring (Fixed-Width)</a></p>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ">lcmReportingOverflow(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE07lcmFullF0x4high_9Magnitudes0C0PQz3lowtx_xtFZ">lcmFullWidth(_:_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Cube%20Root"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Cube Root" class="dashAnchor"></a>
|
||||||
|
<h3>Cube Root</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s15UnsignedIntegerP12NumericAnnexE4cbrtxxFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/cbrt(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>cbrt(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the cube root of <code>x</code>, rounding toward zero.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">cbrt</span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Factoring"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Factoring" class="dashAnchor"></a>
|
||||||
|
<h3>Factoring</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s15UnsignedIntegerP12NumericAnnexE3gcdxx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/gcd(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>gcd(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the greatest common divisor of <code>a</code> and <code>b</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">gcd</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s15UnsignedIntegerP12NumericAnnexE3lcmxx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/lcm(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>lcm(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the least common multiple of <code>a</code> and <code>b</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lcm</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<div>
|
||||||
|
<a name="/Factoring%20(Fixed-Width)"></a>
|
||||||
|
<a name="//apple_ref/swift/Section/Factoring (Fixed-Width)" class="dashAnchor"></a>
|
||||||
|
<h3>Factoring (Fixed-Width)</h3>
|
||||||
|
</div>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/lcmReportingOverflow(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>lcmReportingOverflow(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the least common multiple of <code>a</code> and <code>b</code> and a flag to indicate
|
||||||
|
whether overflow occurred during the operation.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lcmReportingOverflow</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
|
||||||
|
<span class="o">-></span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">Bool</span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE07lcmFullF0x4high_9Magnitudes0C0PQz3lowtx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/lcmFullWidth(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>lcmFullWidth(_:_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the high and low parts of the least common multiple of <code>a</code> and <code>b</code>
|
||||||
|
computed using full-width arithmetic.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lcmFullWidth</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
|
||||||
|
<span class="o">-></span> <span class="p">(</span><span class="nv">high</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">low</span><span class="p">:</span> <span class="k">Self</span><span class="o">.</span><span class="kt">Magnitude</span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
</article>
|
||||||
|
</div>
|
||||||
|
<footer>
|
||||||
|
<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
|
||||||
|
<p>Generated by <a href="https://github.com/realm/jazzy" target="_blank" rel="external">Jazzy</a> v0.8.3, a <a href="http://realm.io" target="_blank" rel="external">Realm</a> project.</p>
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|
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|
||||||
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|
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|
||||||
|
|
@ -0,0 +1,322 @@
|
||||||
|
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|
||||||
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|
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|
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||||||
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|
||||||
|
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|
||||||
|
<p class="primary">
|
||||||
|
<a href="index.html">NumericAnnex Reference</a>
|
||||||
|
(100% documented)
|
||||||
|
</p>
|
||||||
|
<p>
|
||||||
|
<a href="https://github.com/xwu/NumericAnnex">View on GitHub</a>
|
||||||
|
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|
||||||
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<p>
|
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<a href="dash-feed://https%3A%2F%2Fxwu%2Egithub%2Eio%2FNumericAnnex%2Fdocsets%2FNumericAnnex%2Exml">Install in Dash</a>
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<a href="Classes/Random/Xoroshiro.html">– Xoroshiro</a>
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<a href="Extensions/Float.html">Float</a>
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<a href="Extensions/FloatingPoint.html">FloatingPoint</a>
|
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|
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|
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<a href="Extensions/UnsignedInteger.html">UnsignedInteger</a>
|
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|
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|
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|
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<p><a href="Functions.html">Functions</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
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|
||||||
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<p><a href="Protocols.html">Protocols</a></p>
|
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|
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|
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|
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|
||||||
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<a href="Protocols/PRNG.html">PRNG</a>
|
||||||
|
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|
||||||
|
<li>
|
||||||
|
<a href="Protocols/Real.html">Real</a>
|
||||||
|
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|
||||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||||
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<a href="Structs/Rational.html">Rational</a>
|
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|
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|
||||||
|
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|
||||||
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|
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<p><a href="Typealiases.html">Typealiases</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
|
||||||
|
</li>
|
||||||
|
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|
||||||
|
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|
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|
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<article>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>Functions</h1>
|
||||||
|
<p>The following functions are available globally.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
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|
<div class="group">
|
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<ul>
|
||||||
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<li>
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<div>
|
||||||
|
<a name="/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Function/abs(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>abs(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the absolute value (magnitude, modulus) of <code>z</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">abs</span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">(</span><span class="n">_</span> <span class="nv">z</span><span class="p">:</span> <span class="kt"><a href="Structs/Complex.html">Complex</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">)</span> <span class="o">-></span> <span class="kt"><a href="Structs/Complex.html">Complex</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Function/sqrt(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>sqrt(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the square root of <code>z</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">sqrt</span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">(</span><span class="n">_</span> <span class="nv">z</span><span class="p">:</span> <span class="kt"><a href="Structs/Complex.html">Complex</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">)</span> <span class="o">-></span> <span class="kt"><a href="Structs/Complex.html">Complex</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
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|
||||||
|
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|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Function/abs(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>abs(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the absolute value (magnitude) of <code>x</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">abs</span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">)</span> <span class="o">-></span> <span class="kt"><a href="Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Function/ceil(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>ceil(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the closest integral value greater than or equal to <code>x</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">ceil</span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">)</span> <span class="o">-></span> <span class="kt"><a href="Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
</li>
|
||||||
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<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Function/floor(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>floor(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the closest integral value less than or equal to <code>x</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">floor</span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">)</span> <span class="o">-></span> <span class="kt"><a href="Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Function/round(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>round(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the closest integral value; if two values are equally close, returns
|
||||||
|
the one with greater magnitude.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">round</span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">)</span> <span class="o">-></span> <span class="kt"><a href="Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Function/trunc(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>trunc(_:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the closest integral value with magnitude less than or equal to that
|
||||||
|
of <code>x</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">trunc</span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="kt"><a href="Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span><span class="p">)</span> <span class="o">-></span> <span class="kt"><a href="Structs/Rational.html">Rational</a></span><span class="o"><</span><span class="kt">T</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
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|
||||||
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|
||||||
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<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
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<p>Generated by <a href="https://github.com/realm/jazzy" target="_blank" rel="external">Jazzy</a> v0.8.3, a <a href="http://realm.io" target="_blank" rel="external">Realm</a> project.</p>
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<a href="Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
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|
||||||
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<li>
|
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<a href="Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
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<a href="Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
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|
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<a href="Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
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<a href="Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
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<a href="Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
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<a href="Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
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<a href="Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
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|
||||||
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<h1>Protocols</h1>
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||||||
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<p>The following protocols are available globally.</p>
|
||||||
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||||||
|
<li><a href="#/s:12NumericAnnex4PRNGP">PRNG</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP">Real</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4MathP">Math</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGP"></a>
|
||||||
|
<a name="//apple_ref/swift/Protocol/PRNG" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>PRNG</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>A pseudo-random number generator (PRNG).</p>
|
||||||
|
|
||||||
|
<p>Reference types that conform to <code>PRNG</code> are infinite sequences of
|
||||||
|
pseudo-random elements. Protocol extension methods iterate over such a
|
||||||
|
sequence as necessary to generate pseudo-random values from the desired
|
||||||
|
distribution.</p>
|
||||||
|
<h2 id='considerations-for-conforming-types' class='heading'>Considerations for Conforming Types</h2>
|
||||||
|
|
||||||
|
<p>For clarity to end users, custom PRNGs may be implemented in an extension to
|
||||||
|
<code><a href="Classes/Random.html">Random</a></code>. For instance, the <code>xoroshiro128+</code> algorithm is implemented in a
|
||||||
|
final class named <code><a href="Classes/Random/Xoroshiro.html">Random.Xoroshiro</a></code>.</p>
|
||||||
|
|
||||||
|
<p>The static methods <code>_entropy(_:)</code> and <code>_entropy(_:count:)</code> return
|
||||||
|
cryptographically secure random bytes that may be useful for seeding your
|
||||||
|
custom PRNG. However, these methods may return <code>nil</code> if the requested number
|
||||||
|
of random bytes is not available, and they are not recommended as a routine
|
||||||
|
source of random data.</p>
|
||||||
|
<h2 id='adding-other-probability-distributions' class='heading'>Adding Other Probability Distributions</h2>
|
||||||
|
|
||||||
|
<p>Many built-in protocol extension methods make use of the primitive,
|
||||||
|
overloaded method <code>_random(_:bitCount:)</code>. You may wish to use the same
|
||||||
|
method in new protocol extension methods that return pseudo-random
|
||||||
|
values from other probability distributions.</p>
|
||||||
|
|
||||||
|
<p>The method <code>_random(_:bitCount:)</code> generates uniformly distributed binary
|
||||||
|
floating-point values in the half-open range [0, 1) with a precision of
|
||||||
|
either <code>bitCount</code> or the significand bit count of the floating-point type,
|
||||||
|
whichever is less. Additionally, this method generates uniformly distributed
|
||||||
|
unsigned integers in the half-open range [0, 2 ** <em>x</em>), where ** is the
|
||||||
|
exponentiation operator and <em>x</em> is the lesser of <code>bitCount</code> and the bit
|
||||||
|
width of the integer type.</p>
|
||||||
|
|
||||||
|
<p>For end users, however, the recommended spelling for a uniformly distributed
|
||||||
|
numeric value is <code>uniform()</code>; that method is overloaded to permit custom
|
||||||
|
minimum and maximum values for the uniform distribution.</p>
|
||||||
|
|
||||||
|
<a href="Protocols/PRNG.html">See more…</a>
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">protocol</span> <span class="kt">PRNG</span> <span class="p">:</span> <span class="kd">class</span><span class="p">,</span> <span class="kt">IteratorProtocol</span><span class="p">,</span> <span class="kt">Sequence</span>
|
||||||
|
<span class="k">where</span> <span class="kt">Element</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span><span class="p">,</span>
|
||||||
|
<span class="kt">SubSequence</span> <span class="p">:</span> <span class="kt">Sequence</span><span class="p">,</span>
|
||||||
|
<span class="kt">Element</span> <span class="o">==</span> <span class="kt">SubSequence</span><span class="o">.</span><span class="kt">Element</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealP"></a>
|
||||||
|
<a name="//apple_ref/swift/Protocol/Real" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>Real</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>A floating-point type that supports elementary functions and a selection of
|
||||||
|
special functions.</p>
|
||||||
|
|
||||||
|
<p>The <code>Real</code> protocol provides a suitable basis for writing functions that
|
||||||
|
work on any floating-point type that supports the required functions.</p>
|
||||||
|
|
||||||
|
<a href="Protocols/Real.html">See more…</a>
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">protocol</span> <span class="kt">Real</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Math.html">Math</a></span><span class="p">,</span> <span class="kt">FloatingPoint</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4MathP"></a>
|
||||||
|
<a name="//apple_ref/swift/Protocol/Math" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>Math</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>A signed numeric type that supports elementary functions.</p>
|
||||||
|
|
||||||
|
<p>The <code>Math</code> protocol provides a suitable basis for writing functions that
|
||||||
|
work on any real or complex floating-point type that supports the required
|
||||||
|
functions.</p>
|
||||||
|
|
||||||
|
<a href="Protocols/Math.html">See more…</a>
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">protocol</span> <span class="kt">Math</span> <span class="p">:</span> <span class="kt">SignedNumeric</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
</article>
|
||||||
|
</div>
|
||||||
|
<footer>
|
||||||
|
<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
|
||||||
|
<p>Generated by <a href="https://github.com/realm/jazzy" target="_blank" rel="external">Jazzy</a> v0.8.3, a <a href="http://realm.io" target="_blank" rel="external">Realm</a> project.</p>
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|
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|
||||||
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|
||||||
|
<p class="primary">
|
||||||
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<a href="../index.html">NumericAnnex Reference</a>
|
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(100% documented)
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||||||
|
</p>
|
||||||
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<p>
|
||||||
|
<a href="https://github.com/xwu/NumericAnnex">View on GitHub</a>
|
||||||
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</p>
|
||||||
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<p>
|
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<a href="dash-feed://https%3A%2F%2Fxwu%2Egithub%2Eio%2FNumericAnnex%2Fdocsets%2FNumericAnnex%2Exml">Install in Dash</a>
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|
||||||
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<ul>
|
||||||
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<li>
|
||||||
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<a href="../Classes/Random.html">Random</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Classes/Random/Xoroshiro.html">– Xoroshiro</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
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|
||||||
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<li>
|
||||||
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<p><a href="../Extensions.html">Extensions</a></p>
|
||||||
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|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/BinaryInteger.html">BinaryInteger</a>
|
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|
||||||
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<a href="../Extensions/Double.html">Double</a>
|
||||||
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|
||||||
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|
||||||
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<a href="../Extensions/Float.html">Float</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/FloatingPoint.html">FloatingPoint</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/UnsignedInteger.html">UnsignedInteger</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Functions.html">Functions</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Protocols.html">Protocols</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Math.html">Math</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/PRNG.html">PRNG</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Protocols/Real.html">Real</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Structs.html">Structs</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Structs/Complex.html">Complex</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Structs/Rational.html">Rational</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Typealiases.html">Typealiases</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</nav>
|
||||||
|
<article>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>PRNG</h1>
|
||||||
|
<div class="declaration">
|
||||||
|
<div class="language">
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">protocol</span> <span class="kt">PRNG</span> <span class="p">:</span> <span class="kd">class</span><span class="p">,</span> <span class="kt">IteratorProtocol</span><span class="p">,</span> <span class="kt">Sequence</span>
|
||||||
|
<span class="k">where</span> <span class="kt">Element</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span><span class="p">,</span>
|
||||||
|
<span class="kt">SubSequence</span> <span class="p">:</span> <span class="kt">Sequence</span><span class="p">,</span>
|
||||||
|
<span class="kt">Element</span> <span class="o">==</span> <span class="kt">SubSequence</span><span class="o">.</span><span class="kt">Element</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<p>A pseudo-random number generator (PRNG).</p>
|
||||||
|
|
||||||
|
<p>Reference types that conform to <code>PRNG</code> are infinite sequences of
|
||||||
|
pseudo-random elements. Protocol extension methods iterate over such a
|
||||||
|
sequence as necessary to generate pseudo-random values from the desired
|
||||||
|
distribution.</p>
|
||||||
|
<h2 id='considerations-for-conforming-types' class='heading'>Considerations for Conforming Types</h2>
|
||||||
|
|
||||||
|
<p>For clarity to end users, custom PRNGs may be implemented in an extension to
|
||||||
|
<code><a href="../Classes/Random.html">Random</a></code>. For instance, the <code>xoroshiro128+</code> algorithm is implemented in a
|
||||||
|
final class named <code><a href="../Classes/Random/Xoroshiro.html">Random.Xoroshiro</a></code>.</p>
|
||||||
|
|
||||||
|
<p>The static methods <code>_entropy(_:)</code> and <code>_entropy(_:count:)</code> return
|
||||||
|
cryptographically secure random bytes that may be useful for seeding your
|
||||||
|
custom PRNG. However, these methods may return <code>nil</code> if the requested number
|
||||||
|
of random bytes is not available, and they are not recommended as a routine
|
||||||
|
source of random data.</p>
|
||||||
|
<h2 id='adding-other-probability-distributions' class='heading'>Adding Other Probability Distributions</h2>
|
||||||
|
|
||||||
|
<p>Many built-in protocol extension methods make use of the primitive,
|
||||||
|
overloaded method <code>_random(_:bitCount:)</code>. You may wish to use the same
|
||||||
|
method in new protocol extension methods that return pseudo-random
|
||||||
|
values from other probability distributions.</p>
|
||||||
|
|
||||||
|
<p>The method <code>_random(_:bitCount:)</code> generates uniformly distributed binary
|
||||||
|
floating-point values in the half-open range [0, 1) with a precision of
|
||||||
|
either <code>bitCount</code> or the significand bit count of the floating-point type,
|
||||||
|
whichever is less. Additionally, this method generates uniformly distributed
|
||||||
|
unsigned integers in the half-open range [0, 2 ** <em>x</em>), where ** is the
|
||||||
|
exponentiation operator and <em>x</em> is the lesser of <code>bitCount</code> and the bit
|
||||||
|
width of the integer type.</p>
|
||||||
|
|
||||||
|
<p>For end users, however, the recommended spelling for a uniformly distributed
|
||||||
|
numeric value is <code>uniform()</code>; that method is overloaded to permit custom
|
||||||
|
minimum and maximum values for the uniform distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGP5State">State</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGP5state5StateQzv">state</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPx5StateQz5state_tcfc">init(state:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPxSgycfc">init()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGP3max7ElementQzvZ">max</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGP3min7ElementQzvZ">min</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE15_randomBitWidthSivZ">_randomBitWidth</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE8_entropyqd__Sgqd__ms17FixedWidthIntegerRd__s08UnsignedG0Rd__lFZ">_entropy(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE8_entropySayqd__GSgqd__m_Si5countts17FixedWidthIntegerRd__s08UnsignedH0Rd__lFZ">_entropy(_:count:)</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE7_randomqd__qd__m_Si8bitCountts17FixedWidthIntegerRd__s08UnsignedI0Rd__lF">_random(_:bitCount:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE7uniformqd__qd__m_qd__1aqd__1bts17FixedWidthIntegerRd__s08UnsignedG0Rd__lF">uniform(_:a:b:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE7uniformqd__qd__ms17FixedWidthIntegerRd__s08UnsignedG0Rd__lF">uniform(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE7uniforms14UnfoldSequenceVyqd__SiGqd__m_qd__1aqd__1bSi5countts17FixedWidthIntegerRd__s08UnsignedJ0Rd__lF">uniform(_:a:b:count:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE7uniforms14UnfoldSequenceVyqd__SiGqd__m_Si5countts17FixedWidthIntegerRd__s08UnsignedJ0Rd__lF">uniform(_:count:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE7uniformqd__qd__m_qd__1aqd__1bts17FixedWidthIntegerRd__s06SignedG0Rd__sAG9Magnitudes0A0PRpd__s08UnsignedG0ALRQlF">uniform(_:a:b:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE7uniformqd__qd__ms17FixedWidthIntegerRd__s06SignedG0Rd__sAE9Magnitudes0A0PRpd__s08UnsignedG0AJRQlF">uniform(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE7uniforms14UnfoldSequenceVyqd__SiGqd__m_qd__1aqd__1bSi5countts17FixedWidthIntegerRd__s06SignedJ0Rd__sAK9Magnitudes0A0PRpd__s08UnsignedJ0APRQlF">uniform(_:a:b:count:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPAAE7uniforms14UnfoldSequenceVyqd__SiGqd__m_Si5countts17FixedWidthIntegerRd__s06SignedJ0Rd__sAI9Magnitudes0A0PRpd__s08UnsignedJ0ANRQlF">uniform(_:count:)</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPA2aBRzs6UInt64V7ElementRtzlE7_randomqd__qd__m_Si8bitCountts19BinaryFloatingPointRd__lF">_random(_:bitCount:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPA2aBRzs6UInt64V7ElementRtzlE7uniformqd__qd__m_qd__1aqd__1bts19BinaryFloatingPointRd__lF">uniform(_:a:b:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPA2aBRzs6UInt64V7ElementRtzlE7uniformqd__qd__ms19BinaryFloatingPointRd__lF">uniform(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPA2aBRzs6UInt64V7ElementRtzlE7uniforms14UnfoldSequenceVyqd__SiGqd__m_qd__1aqd__1bSi5countts19BinaryFloatingPointRd__lF">uniform(_:a:b:count:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4PRNGPA2aBRzs6UInt64V7ElementRtzlE7uniforms14UnfoldSequenceVyqd__SiGqd__m_Si5countts19BinaryFloatingPointRd__lF">uniform(_:count:)</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGP5State"></a>
|
||||||
|
<a name="//apple_ref/swift/Alias/State" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>State</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>A type that can represent the internal state of the pseudo-random number
|
||||||
|
generator.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="k">associatedtype</span> <span class="kt">State</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGP5state5StateQzv"></a>
|
||||||
|
<a name="//apple_ref/swift/Property/state" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>state</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>The internal state of the pseudo-random number generator.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="k">var</span> <span class="nv">state</span><span class="p">:</span> <span class="kt"><a href="../Protocols/PRNG.html#/s:12NumericAnnex4PRNGP5State">State</a></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPx5StateQz5state_tcfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init(state:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init(state:)</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a pseudo-random number generator with the given internal state.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="nf">init</span><span class="p">(</span><span class="nv">state</span><span class="p">:</span> <span class="kt"><a href="../Protocols/PRNG.html#/s:12NumericAnnex4PRNGP5State">State</a></span><span class="p">)</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>state</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The value to be used as the generator’s internal state.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPxSgycfc"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/init()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>init()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Creates a pseudo-random number generator with an internal state seeded
|
||||||
|
using cryptographically secure random bytes.</p>
|
||||||
|
|
||||||
|
<p>If cryptographically secure random bytes are unavailable, the result is
|
||||||
|
<code>nil</code>.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="nf">init</span><span class="p">?()</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGP3max7ElementQzvZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Variable/max" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>max</code>
|
||||||
|
<span class="declaration-note">Default implementation</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>The maximum value that may be generated by the pseudo-random number
|
||||||
|
generator.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">static</span> <span class="k">var</span> <span class="nv">max</span><span class="p">:</span> <span class="kt">Element</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGP3min7ElementQzvZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Variable/min" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>min</code>
|
||||||
|
<span class="declaration-note">Default implementation</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>The minimum value that may be generated by the pseudo-random number
|
||||||
|
generator.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">static</span> <span class="k">var</span> <span class="nv">min</span><span class="p">:</span> <span class="kt">Element</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE15_randomBitWidthSivZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Variable/_randomBitWidth" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>_randomBitWidth</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>The number of pseudo-random bits available from a value generated by the
|
||||||
|
pseudo-random number generator.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="k">var</span> <span class="nv">_randomBitWidth</span><span class="p">:</span> <span class="kt">Int</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE8_entropyqd__Sgqd__ms17FixedWidthIntegerRd__s08UnsignedG0Rd__lFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/_entropy(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>_entropy(_:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns a value filled with data from a source of cryptographically secure
|
||||||
|
random bytes, or <code>nil</code> if a sufficient number of cryptographically secure
|
||||||
|
random bytes is unavailable.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="n">_entropy</span><span class="o"><</span>
|
||||||
|
<span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span>
|
||||||
|
<span class="o">></span><span class="p">(</span><span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">)</span> <span class="o">-></span> <span class="kt">T</span><span class="p">?</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE8_entropySayqd__GSgqd__m_Si5countts17FixedWidthIntegerRd__s08UnsignedH0Rd__lFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/_entropy(_:count:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>_entropy(_:count:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns an array of <code>count</code> values filled with data from a source of
|
||||||
|
cryptographically secure random bytes, or <code>nil</code> if a sufficient number of
|
||||||
|
cryptographically secure random bytes is unavailable.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="n">_entropy</span><span class="o"><</span>
|
||||||
|
<span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span>
|
||||||
|
<span class="o">></span><span class="p">(</span><span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">count</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-></span> <span class="p">[</span><span class="kt">T</span><span class="p">]?</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE7_randomqd__qd__m_Si8bitCountts17FixedWidthIntegerRd__s08UnsignedI0Rd__lF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/_random(_:bitCount:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>_random(_:bitCount:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a pseudo-random unsigned integer of type <code>T</code> in the range from 0
|
||||||
|
to <code>2 ** min(bitCount, T.bitWidth)</code> (exclusive), where <code>**</code> is the
|
||||||
|
exponentiation operator.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">_random</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">bitCount</span><span class="p">:</span> <span class="kt">Int</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="n">bitWidth</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">T</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE7uniformqd__qd__m_qd__1aqd__1bts17FixedWidthIntegerRd__s08UnsignedG0Rd__lF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:a:b:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:a:b:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a pseudo-random unsigned integer of type <code>T</code> in the range from
|
||||||
|
<code>a</code> through <code>b</code> (inclusive) from the discrete uniform distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">a</span><span class="p">:</span> <span class="kt">T</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">T</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">T</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE7uniformqd__qd__ms17FixedWidthIntegerRd__s08UnsignedG0Rd__lF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a pseudo-random unsigned integer of type <code>T</code> in the range from
|
||||||
|
<code>T.min</code> through <code>T.max</code> (inclusive) from the discrete uniform
|
||||||
|
distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">T</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE7uniforms14UnfoldSequenceVyqd__SiGqd__m_qd__1aqd__1bSi5countts17FixedWidthIntegerRd__s08UnsignedJ0Rd__lF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:a:b:count:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:a:b:count:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a sequence of <code>count</code> pseudo-random unsigned integers of type
|
||||||
|
<code>T</code> in the range from <code>a</code> through <code>b</code> (inclusive) from the discrete
|
||||||
|
uniform distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">a</span><span class="p">:</span> <span class="kt">T</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">T</span><span class="p">,</span> <span class="nv">count</span><span class="p">:</span> <span class="kt">Int</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">UnfoldSequence</span><span class="o"><</span><span class="kt">T</span><span class="p">,</span> <span class="kt">Int</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE7uniforms14UnfoldSequenceVyqd__SiGqd__m_Si5countts17FixedWidthIntegerRd__s08UnsignedJ0Rd__lF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:count:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:count:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a sequence of <code>count</code> pseudo-random unsigned integers of type
|
||||||
|
<code>T</code> in the range from <code>T.min</code> through <code>T.max</code> (inclusive) from the
|
||||||
|
discrete uniform distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">count</span><span class="p">:</span> <span class="kt">Int</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">UnfoldSequence</span><span class="o"><</span><span class="kt">T</span><span class="p">,</span> <span class="kt">Int</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE7uniformqd__qd__m_qd__1aqd__1bts17FixedWidthIntegerRd__s06SignedG0Rd__sAG9Magnitudes0A0PRpd__s08UnsignedG0ALRQlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:a:b:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:a:b:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a pseudo-random signed integer of type <code>T</code> in the range from <code>a</code>
|
||||||
|
through <code>b</code> (inclusive) from the discrete uniform distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">SignedInteger</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">a</span><span class="p">:</span> <span class="kt">T</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">T</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">T</span> <span class="k">where</span> <span class="kt">T</span><span class="o">.</span><span class="kt">Magnitude</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE7uniformqd__qd__ms17FixedWidthIntegerRd__s06SignedG0Rd__sAE9Magnitudes0A0PRpd__s08UnsignedG0AJRQlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a pseudo-random signed integer of type <code>T</code> in the range from
|
||||||
|
<code>T.min</code> through <code>T.max</code> (inclusive) from the discrete uniform
|
||||||
|
distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">SignedInteger</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">T</span> <span class="k">where</span> <span class="kt">T</span><span class="o">.</span><span class="kt">Magnitude</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE7uniforms14UnfoldSequenceVyqd__SiGqd__m_qd__1aqd__1bSi5countts17FixedWidthIntegerRd__s06SignedJ0Rd__sAK9Magnitudes0A0PRpd__s08UnsignedJ0APRQlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:a:b:count:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:a:b:count:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a sequence of <code>count</code> pseudo-random signed integers of type <code>T</code>
|
||||||
|
in the range from <code>a</code> through <code>b</code> (inclusive) from the discrete uniform
|
||||||
|
distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">SignedInteger</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">a</span><span class="p">:</span> <span class="kt">T</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">T</span><span class="p">,</span> <span class="nv">count</span><span class="p">:</span> <span class="kt">Int</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">UnfoldSequence</span><span class="o"><</span><span class="kt">T</span><span class="p">,</span> <span class="kt">Int</span><span class="o">></span>
|
||||||
|
<span class="k">where</span> <span class="kt">T</span><span class="o">.</span><span class="kt">Magnitude</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPAAE7uniforms14UnfoldSequenceVyqd__SiGqd__m_Si5countts17FixedWidthIntegerRd__s06SignedJ0Rd__sAI9Magnitudes0A0PRpd__s08UnsignedJ0ANRQlF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:count:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:count:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a sequence of <code>count</code> pseudo-random signed integers of type <code>T</code>
|
||||||
|
in the range from <code>T.min</code> through <code>T.max</code> (inclusive) from the discrete
|
||||||
|
uniform distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">SignedInteger</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">count</span><span class="p">:</span> <span class="kt">Int</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">UnfoldSequence</span><span class="o"><</span><span class="kt">T</span><span class="p">,</span> <span class="kt">Int</span><span class="o">></span>
|
||||||
|
<span class="k">where</span> <span class="kt">T</span><span class="o">.</span><span class="kt">Magnitude</span> <span class="p">:</span> <span class="kt">FixedWidthInteger</span> <span class="o">&</span> <span class="kt">UnsignedInteger</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPA2aBRzs6UInt64V7ElementRtzlE7_randomqd__qd__m_Si8bitCountts19BinaryFloatingPointRd__lF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/_random(_:bitCount:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>_random(_:bitCount:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a pseudo-random binary floating-point value of type <code>T</code> in the
|
||||||
|
range from 0 to 1 (exclusive) with <code>min(bitCount, T.significandBitCount)</code>
|
||||||
|
bits of precision.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">_random</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryFloatingPoint</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">bitCount</span><span class="p">:</span> <span class="kt">Int</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="n">significandBitCount</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">T</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPA2aBRzs6UInt64V7ElementRtzlE7uniformqd__qd__m_qd__1aqd__1bts19BinaryFloatingPointRd__lF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:a:b:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:a:b:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a pseudo-random binary floating-point value of type <code>T</code> in the
|
||||||
|
range from <code>a</code> to <code>b</code> (exclusive) from the uniform distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryFloatingPoint</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">a</span><span class="p">:</span> <span class="kt">T</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">T</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">T</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPA2aBRzs6UInt64V7ElementRtzlE7uniformqd__qd__ms19BinaryFloatingPointRd__lF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a pseudo-random binary floating-point value of type <code>T</code> in the
|
||||||
|
range from 0 to 1 (exclusive) from the uniform distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryFloatingPoint</span><span class="o">></span><span class="p">(</span><span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">)</span> <span class="o">-></span> <span class="kt">T</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPA2aBRzs6UInt64V7ElementRtzlE7uniforms14UnfoldSequenceVyqd__SiGqd__m_qd__1aqd__1bSi5countts19BinaryFloatingPointRd__lF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:a:b:count:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:a:b:count:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a sequence of <code>count</code> pseudo-random binary floating-point values
|
||||||
|
of type <code>T</code> in the range from <code>a</code> to <code>b</code> (exclusive) from the uniform
|
||||||
|
distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryFloatingPoint</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">a</span><span class="p">:</span> <span class="kt">T</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">T</span><span class="p">,</span> <span class="nv">count</span><span class="p">:</span> <span class="kt">Int</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">UnfoldSequence</span><span class="o"><</span><span class="kt">T</span><span class="p">,</span> <span class="kt">Int</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4PRNGPA2aBRzs6UInt64V7ElementRtzlE7uniforms14UnfoldSequenceVyqd__SiGqd__m_Si5countts19BinaryFloatingPointRd__lF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/uniform(_:count:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>uniform(_:count:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Generates a sequence of <code>count</code> pseudo-random binary floating-point values
|
||||||
|
of type <code>T</code> in the range from 0 to 1 (exclusive) from the uniform
|
||||||
|
distribution.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">uniform</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryFloatingPoint</span><span class="o">></span><span class="p">(</span>
|
||||||
|
<span class="nv">_</span><span class="p">:</span> <span class="kt">T</span><span class="o">.</span><span class="k">Type</span> <span class="o">=</span> <span class="kt">T</span><span class="o">.</span><span class="k">self</span><span class="p">,</span> <span class="nv">count</span><span class="p">:</span> <span class="kt">Int</span>
|
||||||
|
<span class="p">)</span> <span class="o">-></span> <span class="kt">UnfoldSequence</span><span class="o"><</span><span class="kt">T</span><span class="p">,</span> <span class="kt">Int</span><span class="o">></span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
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|
||||||
|
</article>
|
||||||
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|
||||||
|
<footer>
|
||||||
|
<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
|
||||||
|
<p>Generated by <a href="https://github.com/realm/jazzy" target="_blank" rel="external">Jazzy</a> v0.8.3, a <a href="http://realm.io" target="_blank" rel="external">Realm</a> project.</p>
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|
||||||
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@ -0,0 +1,561 @@
|
||||||
|
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|
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|
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|
||||||
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|
||||||
|
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|
||||||
|
<a href="../index.html">NumericAnnex Reference</a>
|
||||||
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(100% documented)
|
||||||
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|
||||||
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<p>
|
||||||
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<a href="https://github.com/xwu/NumericAnnex">View on GitHub</a>
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||||||
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|
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|
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|
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<a href="../Extensions/Float.html">Float</a>
|
||||||
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|
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|
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|
||||||
|
<a href="../Extensions/FloatingPoint.html">FloatingPoint</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Extensions/UnsignedInteger.html">UnsignedInteger</a>
|
||||||
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|
||||||
|
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|
||||||
|
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|
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|
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|
||||||
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<p><a href="../Functions.html">Functions</a></p>
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<p><a href="../Protocols.html">Protocols</a></p>
|
||||||
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|
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|
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|
<a href="../Protocols/Math.html">Math</a>
|
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|
||||||
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|
||||||
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<a href="../Protocols/PRNG.html">PRNG</a>
|
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|
||||||
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|
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<a href="../Structs/Rational.html">Rational</a>
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|
||||||
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|
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<p><a href="../Typealiases.html">Typealiases</a></p>
|
||||||
|
<ul>
|
||||||
|
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|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="../Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
|
||||||
|
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|
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|
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|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>Real</h1>
|
||||||
|
<div class="declaration">
|
||||||
|
<div class="language">
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">protocol</span> <span class="kt">Real</span> <span class="p">:</span> <span class="kt"><a href="../Protocols/Math.html">Math</a></span><span class="p">,</span> <span class="kt">FloatingPoint</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<p>A floating-point type that supports elementary functions and a selection of
|
||||||
|
special functions.</p>
|
||||||
|
|
||||||
|
<p>The <code>Real</code> protocol provides a suitable basis for writing functions that
|
||||||
|
work on any floating-point type that supports the required functions.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
||||||
|
<details open>
|
||||||
|
<summary>Topics</summary>
|
||||||
|
<div class="wrapper">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP5hypotxx_xtFZ">hypot(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP14inverseTangentxx10dividingBy_tF">inverseTangent(dividingBy:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP5errorxyF">error()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP18complementaryErrorxyF">complementaryError()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP5gammaxyF">gamma()</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealP16logarithmicGammaxyF">logarithmicGamma()</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealPAAE8cubeRootxyF">cubeRoot()</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealPAAE5atan2xx_xtFZ">atan2(_:_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealPAAE3erfxxFZ">erf(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealPAAE4erfcxxFZ">erfc(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealPAAE6tgammaxxFZ">tgamma(_:)</a></li>
|
||||||
|
<li><a href="#/s:12NumericAnnex4RealPAAE6lgammaxxFZ">lgamma(_:)</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
|
</section>
|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealP5hypotxx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/hypot(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>hypot(_:_:)</code>
|
||||||
|
<span class="declaration-note">Default implementation</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the hypotenuse of a right-angle triangle with legs (catheti) of
|
||||||
|
length <code>x</code> and <code>y</code>, preventing avoidable arithmetic overflow and
|
||||||
|
underflow. The return value is the square root of the sum of squares of
|
||||||
|
the arguments.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">static</span> <span class="kd">func</span> <span class="nf">hypot</span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">y</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>x</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The length of one leg (cathetus) of a right-angle triangle.</p>
|
||||||
|
</dd>
|
||||||
|
<dt><code>y</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The length of the other leg (cathetus) of a right-angle triangle.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealP14inverseTangentxx10dividingBy_tF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/inverseTangent(dividingBy:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>inverseTangent(dividingBy:)</code>
|
||||||
|
<span class="declaration-note">Default implementation</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the inverse tangent of <code>self / other</code>, using the signs of <code>self</code>
|
||||||
|
and <code>other</code> to determine the quadrant of the computed angle.</p>
|
||||||
|
|
||||||
|
<p>If <code>self == 0 && other == 0</code>, the return value is still finite.</p>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<p><code><a href="../Protocols/Real.html#/s:12NumericAnnex4RealPAAE5atan2xx_xtFZ">atan2(_:_:)</a></code></p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">func</span> <span class="nf">inverseTangent</span><span class="p">(</span><span class="n">dividingBy</span> <span class="nv">other</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>other</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The divisor by which to divide <code>self</code>.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealP5errorxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/error()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>error()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the value of the <a href="http://mathworld.wolfram.com/Erf.html">error function</a> of <code>self</code>.</p>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../Protocols/Real.html#/s:12NumericAnnex4RealPAAE3erfxxFZ">erf(_:)</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">func</span> <span class="nf">error</span><span class="p">()</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealP18complementaryErrorxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/complementaryError()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>complementaryError()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the value of the <a href="http://mathworld.wolfram.com/Erfc.html">complementary error function</a> of <code>self</code>.</p>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../Protocols/Real.html#/s:12NumericAnnex4RealPAAE4erfcxxFZ">erfc(_:)</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">func</span> <span class="nf">complementaryError</span><span class="p">()</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealP5gammaxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/gamma()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>gamma()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the value of the <a href="http://mathworld.wolfram.com/GammaFunction.html">gamma function</a> of <code>self</code>.</p>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../Protocols/Real.html#/s:12NumericAnnex4RealPAAE6tgammaxxFZ">tgamma(_:)</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">func</span> <span class="nf">gamma</span><span class="p">()</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealP16logarithmicGammaxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/logarithmicGamma()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>logarithmicGamma()</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the value of the <a href="http://mathworld.wolfram.com/LogGammaFunction.html">logarithmic gamma function</a> of <code>self</code>.</p>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../Protocols/Real.html#/s:12NumericAnnex4RealPAAE6lgammaxxFZ">lgamma(_:)</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">func</span> <span class="nf">logarithmicGamma</span><span class="p">()</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealPAAE8cubeRootxyF"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/cubeRoot()" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>cubeRoot()</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the cube root of the value, rounded to a representable value
|
||||||
|
(default implementation).</p>
|
||||||
|
<div class="aside aside-note">
|
||||||
|
<p class="aside-title">Note</p>
|
||||||
|
<p>This method is required by the protocol <code><a href="../Protocols/Math.html">Math</a></code>; it is not an
|
||||||
|
extension method.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<p><code>cbrt(_:)</code></p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">cubeRoot</span><span class="p">()</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealPAAE5atan2xx_xtFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/atan2(_:_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>atan2(_:_:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the inverse tangent of <code>y / x</code>, using the signs of <code>y</code> and <code>x</code> to
|
||||||
|
determine the quadrant of the computed angle.</p>
|
||||||
|
|
||||||
|
<p>If <code>x == 0 && y == 0</code>, the return value is still finite.</p>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<p><code><a href="../Protocols/Real.html#/s:12NumericAnnex4RealP14inverseTangentxx10dividingBy_tF">inverseTangent(dividingBy:)</a></code></p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">atan2</span><span class="p">(</span><span class="n">_</span> <span class="nv">y</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="parameters">
|
||||||
|
<h5>Parameters</h5>
|
||||||
|
<dl>
|
||||||
|
<dt><code>y</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The value to divide.</p>
|
||||||
|
</dd>
|
||||||
|
<dt><code>x</code></dt>
|
||||||
|
<dd>
|
||||||
|
<p>The divisor by which to divide <code>y</code>.</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealPAAE3erfxxFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/erf(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>erf(_:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the value of the <a href="http://mathworld.wolfram.com/Erf.html">error function</a> of <code>x</code>.</p>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../Protocols/Real.html#/s:12NumericAnnex4RealP5errorxyF">error()</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">erf</span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealPAAE4erfcxxFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/erfc(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>erfc(_:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the value of the <a href="http://mathworld.wolfram.com/Erfc.html">complementary error function</a> of <code>x</code>.</p>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../Protocols/Real.html#/s:12NumericAnnex4RealP18complementaryErrorxyF">complementaryError()</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">erfc</span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealPAAE6tgammaxxFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/tgamma(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>tgamma(_:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the value of the <a href="http://mathworld.wolfram.com/GammaFunction.html">gamma function</a> of <code>x</code>.</p>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../Protocols/Real.html#/s:12NumericAnnex4RealP5gammaxyF">gamma()</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">tgamma</span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex4RealPAAE6lgammaxxFZ"></a>
|
||||||
|
<a name="//apple_ref/swift/Method/lgamma(_:)" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>lgamma(_:)</code>
|
||||||
|
<span class="declaration-note">Extension method</span>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>Returns the value of the <a href="http://mathworld.wolfram.com/LogGammaFunction.html">logarithmic gamma function</a> of <code>x</code>.</p>
|
||||||
|
<div class="aside aside-see-also">
|
||||||
|
<p class="aside-title">See also</p>
|
||||||
|
<code><a href="../Protocols/Real.html#/s:12NumericAnnex4RealP16logarithmicGammaxyF">logarithmicGamma()</a></code>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lgamma</span><span class="p">(</span><span class="n">_</span> <span class="nv">x</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span> <span class="o">-></span> <span class="k">Self</span></code></pre>
|
||||||
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|
||||||
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|
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<a href="Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
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||||||
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||||||
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<a href="Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
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<a href="Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
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||||||
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<a href="Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
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<a href="Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
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||||||
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||||||
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||||||
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<a href="Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
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||||||
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|
||||||
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<h1>Structs</h1>
|
||||||
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<p>The following structs are available globally.</p>
|
||||||
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|
||||||
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||||||
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<section class="toc">
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||||||
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<details open>
|
||||||
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<summary>Topics</summary>
|
||||||
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<div class="wrapper">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex7ComplexV">Complex</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex8RationalV">Rational</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</details>
|
||||||
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|
||||||
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<div>
|
||||||
|
<a name="/s:12NumericAnnex7ComplexV"></a>
|
||||||
|
<a name="//apple_ref/swift/Struct/Complex" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>Complex</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>A type to represent a complex value in Cartesian form.</p>
|
||||||
|
<div class="aside aside-note">
|
||||||
|
<p class="aside-title">Note</p>
|
||||||
|
<code>Complex64</code> is a type alias for <code>Complex<Float></code> and <code>Complex128</code> is
|
||||||
|
a type alias for <code>Complex<Double></code>.
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>Create new instances of <code>Complex<T></code> using integer or floating-point
|
||||||
|
literals and the imaginary unit <code><a href="Structs/Complex.html#/s:12NumericAnnex7ComplexV1iACyxGvZ">Complex<T>.i</a></code>. For example:</p>
|
||||||
|
<pre class="highlight swift"><code><span class="k">let</span> <span class="nv">x</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">.</span><span class="n">i</span> <span class="c1">// `x` is of type `Complex<Double>`</span>
|
||||||
|
<span class="k">let</span> <span class="nv">y</span> <span class="o">=</span> <span class="mf">3.5</span> <span class="o">+</span> <span class="mi">7</span> <span class="o">*</span> <span class="o">.</span><span class="n">i</span> <span class="c1">// `y` is of type `Complex<Double>`</span>
|
||||||
|
|
||||||
|
<span class="k">let</span> <span class="nv">z</span><span class="p">:</span> <span class="kt">Complex64</span> <span class="o">=</span> <span class="o">.</span><span class="n">e</span> <span class="o">+</span> <span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="o">.</span><span class="n">i</span> <span class="c1">// `z` is of type `Complex<Float>`</span>
|
||||||
|
</code></pre>
|
||||||
|
<h2 id='additional-considerations' class='heading'>Additional Considerations</h2>
|
||||||
|
|
||||||
|
<p>Floating-point types have special values that represent infinity or NaN
|
||||||
|
(<q>not a number</q>). Complex functions in different languages may return
|
||||||
|
different results when working with special values.</p>
|
||||||
|
|
||||||
|
<p>Many complex functions have <a href="http://mathworld.wolfram.com/BranchCut.html">branch cuts</a>, which are curves in the
|
||||||
|
complex plane across which a function is discontinuous. Different languages
|
||||||
|
may adopt different branch cut structures for the same complex function.</p>
|
||||||
|
|
||||||
|
<p>Implementations in <code>Complex<T></code> adhere to the <a href="http://www.open-std.org/JTC1/SC22/WG14/www/standards.html#9899">C standard</a> (Annex G) as
|
||||||
|
closely as possible with respect to special values and branch cuts.</p>
|
||||||
|
|
||||||
|
<p>To users unfamiliar with complex functions, the principal value returned by
|
||||||
|
some complex functions may be unexpected. For example,
|
||||||
|
<code>Double.cbrt(-8) == -2</code>, which is the <strong>real root</strong>, while
|
||||||
|
<code>Complex.cbrt(-8) == 2 * Complex.exp(.i * .pi / 3)</code>, which is the
|
||||||
|
<strong>principal root</strong>.</p>
|
||||||
|
|
||||||
|
<a href="Structs/Complex.html">See more…</a>
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">struct</span> <span class="kt">Complex</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Real.html">Real</a></span><span class="o">></span> <span class="p">:</span> <span class="kt">Codable</span>
|
||||||
|
<span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt">Codable</span> <span class="o">&</span> <span class="n">_ExpressibleByBuiltinFloatLiteral</span></code></pre>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
<div class="group">
|
||||||
|
<ul>
|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex8RationalV"></a>
|
||||||
|
<a name="//apple_ref/swift/Struct/Rational" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>Rational</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>A type to represent a rational value.</p>
|
||||||
|
<div class="aside aside-note">
|
||||||
|
<p class="aside-title">Note</p>
|
||||||
|
<code>Ratio</code> is a type alias for <code>Rational<Int></code>.
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>Create new instances of <code>Rational<T></code> by using integer literals and the
|
||||||
|
division (<code>/</code>) operator. For example:</p>
|
||||||
|
<pre class="highlight swift"><code><span class="k">let</span> <span class="nv">x</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span> <span class="k">as</span> <span class="kt">Ratio</span> <span class="c1">// `x` is of type `Rational<Int>`</span>
|
||||||
|
<span class="k">let</span> <span class="nv">y</span> <span class="o">=</span> <span class="mi">2</span> <span class="k">as</span> <span class="kt">Ratio</span> <span class="c1">// `y` is of type `Rational<Int>`</span>
|
||||||
|
<span class="k">let</span> <span class="nv">z</span><span class="p">:</span> <span class="kt">Ratio</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">/</span> <span class="mi">3</span> <span class="c1">// `z` is also of type `Rational<Int>`</span>
|
||||||
|
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">x</span> <span class="o">+</span> <span class="n">y</span> <span class="o">+</span> <span class="n">z</span><span class="p">)</span> <span class="c1">// Prints "3"</span>
|
||||||
|
</code></pre>
|
||||||
|
|
||||||
|
<p>You can create an unreduced fraction by using the initializer
|
||||||
|
<code><a href="Structs/Rational.html#/s:12NumericAnnex8RationalVACyxGx9numerator_x11denominatortcfc">Rational<T>.init(numerator:denominator:)</a></code>. For example:</p>
|
||||||
|
<pre class="highlight swift"><code><span class="k">let</span> <span class="nv">a</span> <span class="o">=</span> <span class="kt">Ratio</span><span class="p">(</span><span class="nv">numerator</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="nv">denominator</span><span class="p">:</span> <span class="mi">3</span><span class="p">)</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="c1">// Prints "3/3"</span>
|
||||||
|
</code></pre>
|
||||||
|
|
||||||
|
<p>All arithmetic operations on values in canonical form (i.e. reduced to
|
||||||
|
lowest terms) return results in canonical form. However, operations on
|
||||||
|
values not in canonical form may or may not return results that are
|
||||||
|
themselves in canonical form. The property <code>canonicalized</code> is the canonical
|
||||||
|
form of any value.</p>
|
||||||
|
<h2 id='additional-considerations' class='heading'>Additional Considerations</h2>
|
||||||
|
<h3 id='special-values' class='heading'>Special Values</h3>
|
||||||
|
|
||||||
|
<p><code>Rational<T></code> does not prohibit zero as a denominator. Any instance with a
|
||||||
|
positive numerator and zero denominator represents (positive) infinity; any
|
||||||
|
instance with a negative numerator and zero denominator represents negative
|
||||||
|
infinity; and any instance with zero numerator and zero denominator
|
||||||
|
represents NaN (<q>not a number</q>).</p>
|
||||||
|
|
||||||
|
<p>As with floating-point types, <code><a href="Structs/Rational.html#/s:12NumericAnnex8RationalV8infinityACyxGvZ">Rational<T>.infinity</a></code> compares greater than
|
||||||
|
every finite value and negative infinity, and <code>-Rational<T>.infinity</code>
|
||||||
|
compares less than every finite value and positive infinity. Infinite values
|
||||||
|
of the same sign compare equal to each other.</p>
|
||||||
|
|
||||||
|
<p>As with floating-point types, <code><a href="Structs/Rational.html#/s:12NumericAnnex8RationalV3nanACyxGvZ">Rational<T>.nan</a></code> does not compare equal to
|
||||||
|
any other value, including another NaN. Use the property <code>isNaN</code> to test if
|
||||||
|
a value is NaN. <code>Rational<T></code> arithmetic operations are intended to
|
||||||
|
propagate NaN in the same manner as analogous floating-point operations.</p>
|
||||||
|
<h3 id='numerical-limits' class='heading'>Numerical Limits</h3>
|
||||||
|
|
||||||
|
<p>When a value of type <code>Rational<T></code> is in canonical form, the sign of the
|
||||||
|
numerator is the sign of the value; that is, in canonical form, the sign of
|
||||||
|
the denominator is always positive. Therefore, <code>-1 / T.min</code> cannot be
|
||||||
|
represented as a value of type <code>Rational<T></code> because <code>abs(T.min)</code> cannot be
|
||||||
|
represented as a value of type <code>T</code>.</p>
|
||||||
|
|
||||||
|
<p>To ensure that every representable value of type <code>Rational<T></code> has a
|
||||||
|
representable magnitude and reciprocal of the same type, an overflow trap
|
||||||
|
occurs when the division (<code>/</code>) operator is used to create a value of type
|
||||||
|
<code>Rational<T></code> with numerator <code>T.min</code>.</p>
|
||||||
|
|
||||||
|
<a href="Structs/Rational.html">See more…</a>
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">struct</span> <span class="kt">Rational</span><span class="o"><</span><span class="kt">T</span> <span class="p">:</span> <span class="kt">SignedInteger</span><span class="o">></span> <span class="p">:</span> <span class="kt">Codable</span>
|
||||||
|
<span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt">Codable</span> <span class="o">&</span> <span class="n">_ExpressibleByBuiltinIntegerLiteral</span><span class="p">,</span>
|
||||||
|
<span class="kt">T</span><span class="o">.</span><span class="kt">Magnitude</span> <span class="p">:</span> <span class="kt">UnsignedInteger</span><span class="p">,</span>
|
||||||
|
<span class="kt">T</span><span class="o">.</span><span class="kt">Magnitude</span><span class="o">.</span><span class="kt">Magnitude</span> <span class="o">==</span> <span class="kt">T</span><span class="o">.</span><span class="kt">Magnitude</span></code></pre>
|
||||||
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||||||
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|
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||||||
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|
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<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
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<p>Generated by <a href="https://github.com/realm/jazzy" target="_blank" rel="external">Jazzy</a> v0.8.3, a <a href="http://realm.io" target="_blank" rel="external">Realm</a> project.</p>
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|
||||||
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|
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|
||||||
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<a href="Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
|
||||||
|
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|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
|
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|
||||||
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|
||||||
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<a href="Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
|
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|
||||||
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|
||||||
|
<a href="Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
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|
||||||
|
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||||||
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<p><a href="Protocols.html">Protocols</a></p>
|
||||||
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|
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||||||
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||||||
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|
||||||
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||||||
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|
||||||
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|
||||||
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<p><a href="Typealiases.html">Typealiases</a></p>
|
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|
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|
||||||
|
<li>
|
||||||
|
<a href="Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
||||||
|
</li>
|
||||||
|
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|
||||||
|
<a href="Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
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||||||
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|
||||||
|
<section>
|
||||||
|
<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
<h1>Typealiases</h1>
|
||||||
|
<p>The following typealiases are available globally.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</section>
|
||||||
|
<section class="toc">
|
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<details open>
|
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<summary>Topics</summary>
|
||||||
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|
||||||
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|
||||||
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<li><a href="#/s:12NumericAnnex4Signa">Sign</a></li>
|
||||||
|
</ul>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#/s:12NumericAnnex12RoundingRulea">RoundingRule</a></li>
|
||||||
|
</ul>
|
||||||
|
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|
||||||
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|
||||||
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|
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||||||
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|
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||||||
|
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|
||||||
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<a name="/s:12NumericAnnex4Signa"></a>
|
||||||
|
<a name="//apple_ref/swift/Alias/Sign" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>Sign</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>The mathematical sign of a number.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">typealias</span> <span class="kt">Sign</span> <span class="o">=</span> <span class="kt">FloatingPointSign</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
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|
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|
||||||
|
<li>
|
||||||
|
<div>
|
||||||
|
<a name="/s:12NumericAnnex12RoundingRulea"></a>
|
||||||
|
<a name="//apple_ref/swift/Alias/RoundingRule" class="dashAnchor"></a>
|
||||||
|
<h4>
|
||||||
|
<code>RoundingRule</code>
|
||||||
|
</h4>
|
||||||
|
</div>
|
||||||
|
<div class="abstract">
|
||||||
|
<p>A rule for rounding a number.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="declaration">
|
||||||
|
<h5>Declaration</h5>
|
||||||
|
<div class="language">
|
||||||
|
<p class="aside-title">Swift</p>
|
||||||
|
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">typealias</span> <span class="kt">RoundingRule</span> <span class="o">=</span> <span class="kt">FloatingPointRoundingRule</span></code></pre>
|
||||||
|
|
||||||
|
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|
||||||
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||||||
|
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<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
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/* Generic.Traceback */
|
||||||
|
/* Keyword.Constant */
|
||||||
|
/* Keyword.Declaration */
|
||||||
|
/* Keyword.Pseudo */
|
||||||
|
/* Keyword.Reserved */
|
||||||
|
/* Keyword.Type */
|
||||||
|
/* Literal.Number */
|
||||||
|
/* Literal.String */
|
||||||
|
/* Name.Attribute */
|
||||||
|
/* Name.Builtin */
|
||||||
|
/* Name.Class */
|
||||||
|
/* Name.Constant */
|
||||||
|
/* Name.Entity */
|
||||||
|
/* Name.Exception */
|
||||||
|
/* Name.Function */
|
||||||
|
/* Name.Namespace */
|
||||||
|
/* Name.Tag */
|
||||||
|
/* Name.Variable */
|
||||||
|
/* Operator.Word */
|
||||||
|
/* Text.Whitespace */
|
||||||
|
/* Literal.Number.Float */
|
||||||
|
/* Literal.Number.Hex */
|
||||||
|
/* Literal.Number.Integer */
|
||||||
|
/* Literal.Number.Oct */
|
||||||
|
/* Literal.String.Backtick */
|
||||||
|
/* Literal.String.Char */
|
||||||
|
/* Literal.String.Doc */
|
||||||
|
/* Literal.String.Double */
|
||||||
|
/* Literal.String.Escape */
|
||||||
|
/* Literal.String.Heredoc */
|
||||||
|
/* Literal.String.Interpol */
|
||||||
|
/* Literal.String.Other */
|
||||||
|
/* Literal.String.Regex */
|
||||||
|
/* Literal.String.Single */
|
||||||
|
/* Literal.String.Symbol */
|
||||||
|
/* Name.Builtin.Pseudo */
|
||||||
|
/* Name.Variable.Class */
|
||||||
|
/* Name.Variable.Global */
|
||||||
|
/* Name.Variable.Instance */
|
||||||
|
/* Literal.Number.Integer.Long */ }
|
||||||
|
.highlight a {
|
||||||
|
color: inherit; }
|
||||||
|
.highlight .c {
|
||||||
|
color: #007400; }
|
||||||
|
.highlight .err {
|
||||||
|
color: #a61717;
|
||||||
|
background-color: #e3d2d2; }
|
||||||
|
.highlight .k {
|
||||||
|
color: #aa0d91; }
|
||||||
|
.highlight .o {
|
||||||
|
color: #000; }
|
||||||
|
.highlight .cm {
|
||||||
|
color: #007400; }
|
||||||
|
.highlight .cp {
|
||||||
|
color: #007400; }
|
||||||
|
.highlight .c1 {
|
||||||
|
color: #007400; }
|
||||||
|
.highlight .cs {
|
||||||
|
color: #007400; }
|
||||||
|
.highlight .gd {
|
||||||
|
color: #000;
|
||||||
|
background-color: #fdd; }
|
||||||
|
.highlight .gd .x {
|
||||||
|
color: #000;
|
||||||
|
background-color: #faa; }
|
||||||
|
.highlight .ge {
|
||||||
|
font-style: italic; }
|
||||||
|
.highlight .gr {
|
||||||
|
color: #a00; }
|
||||||
|
.highlight .gh {
|
||||||
|
color: #999; }
|
||||||
|
.highlight .gi {
|
||||||
|
color: #000;
|
||||||
|
background-color: #dfd; }
|
||||||
|
.highlight .gi .x {
|
||||||
|
color: #000;
|
||||||
|
background-color: #afa; }
|
||||||
|
.highlight .go {
|
||||||
|
color: #888; }
|
||||||
|
.highlight .gp {
|
||||||
|
color: #555; }
|
||||||
|
.highlight .gs {
|
||||||
|
font-weight: bold; }
|
||||||
|
.highlight .gu {
|
||||||
|
color: #aaa; }
|
||||||
|
.highlight .gt {
|
||||||
|
color: #a00; }
|
||||||
|
.highlight .kc {
|
||||||
|
color: #aa0d91; }
|
||||||
|
.highlight .kd {
|
||||||
|
color: #aa0d91; }
|
||||||
|
.highlight .kp {
|
||||||
|
color: #aa0d91; }
|
||||||
|
.highlight .kr {
|
||||||
|
color: #aa0d91; }
|
||||||
|
.highlight .kt {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .m {
|
||||||
|
color: #000; }
|
||||||
|
.highlight .s {
|
||||||
|
color: #a31515; }
|
||||||
|
.highlight .na {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .nb {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .nc {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .no {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .ni {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .ne {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .nf {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .nn {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .nt {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .nv {
|
||||||
|
color: #000; }
|
||||||
|
.highlight .ow {
|
||||||
|
color: #000; }
|
||||||
|
.highlight .w {
|
||||||
|
color: #bbb; }
|
||||||
|
.highlight .mf {
|
||||||
|
color: #1c00cf; }
|
||||||
|
.highlight .mh {
|
||||||
|
color: #1c00cf; }
|
||||||
|
.highlight .mi {
|
||||||
|
color: #1c00cf; }
|
||||||
|
.highlight .mo {
|
||||||
|
color: #1c00cf; }
|
||||||
|
.highlight .sb {
|
||||||
|
color: #c41a16; }
|
||||||
|
.highlight .sc {
|
||||||
|
color: #1c00cf; }
|
||||||
|
.highlight .sd {
|
||||||
|
color: #c41a16; }
|
||||||
|
.highlight .s2 {
|
||||||
|
color: #c41a16; }
|
||||||
|
.highlight .se {
|
||||||
|
color: #c41a16; }
|
||||||
|
.highlight .sh {
|
||||||
|
color: #c41a16; }
|
||||||
|
.highlight .si {
|
||||||
|
color: #c41a16; }
|
||||||
|
.highlight .sx {
|
||||||
|
color: #c41a16; }
|
||||||
|
.highlight .sr {
|
||||||
|
color: #c41a16; }
|
||||||
|
.highlight .s1 {
|
||||||
|
color: #c41a16; }
|
||||||
|
.highlight .ss {
|
||||||
|
color: #c41a16; }
|
||||||
|
.highlight .bp {
|
||||||
|
color: #999; }
|
||||||
|
.highlight .vc {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .vg {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .vi {
|
||||||
|
color: #2b839f; }
|
||||||
|
.highlight .il {
|
||||||
|
color: #1c00cf; }
|
||||||
|
|
@ -0,0 +1,348 @@
|
||||||
|
@import url("https://fonts.googleapis.com/css?family=Source+Code+Pro:400,500,600,700");
|
||||||
|
*, *::before, *::after {
|
||||||
|
box-sizing: inherit; }
|
||||||
|
|
||||||
|
body {
|
||||||
|
box-sizing: border-box;
|
||||||
|
margin: 0;
|
||||||
|
background: #fff;
|
||||||
|
color: #333;
|
||||||
|
font: 16px/24px -apple-system, BlinkMacSystemFont, "Segoe UI", Arial, sans-serif; }
|
||||||
|
|
||||||
|
h1 {
|
||||||
|
margin: 32px 0 16px;
|
||||||
|
font-weight: 500;
|
||||||
|
font-size: 28px;
|
||||||
|
line-height: 32px; }
|
||||||
|
|
||||||
|
h2 {
|
||||||
|
margin: 32px 0 16px;
|
||||||
|
font-weight: 500;
|
||||||
|
font-size: 24px;
|
||||||
|
line-height: 32px; }
|
||||||
|
|
||||||
|
h3 {
|
||||||
|
margin: 24px 0 16px;
|
||||||
|
font-weight: 500;
|
||||||
|
font-size: 20px;
|
||||||
|
line-height: 24px; }
|
||||||
|
|
||||||
|
h4 {
|
||||||
|
margin: 24px 0 16px;
|
||||||
|
font-weight: 500;
|
||||||
|
font-size: 16px;
|
||||||
|
line-height: 24px; }
|
||||||
|
|
||||||
|
h5 {
|
||||||
|
margin: 24px 0 16px;
|
||||||
|
font-weight: 500;
|
||||||
|
font-size: 16px;
|
||||||
|
line-height: 24px;
|
||||||
|
color: #777; }
|
||||||
|
|
||||||
|
h6 {
|
||||||
|
margin: 24px 0 16px;
|
||||||
|
font-weight: 500;
|
||||||
|
font-size: 16px;
|
||||||
|
line-height: 24px;
|
||||||
|
color: #aaaaaa; }
|
||||||
|
|
||||||
|
p {
|
||||||
|
margin: 0 0 16px; }
|
||||||
|
|
||||||
|
ul, ol {
|
||||||
|
margin: 0 0 16px;
|
||||||
|
padding: 0 0 0 32px; }
|
||||||
|
|
||||||
|
blockquote {
|
||||||
|
margin: 0 0 16px;
|
||||||
|
border-left: 6px solid #e6e6e6;
|
||||||
|
border-radius: 4px;
|
||||||
|
padding: 16px;
|
||||||
|
background-color: #fafafa;
|
||||||
|
color: #858585; }
|
||||||
|
blockquote > p:last-child {
|
||||||
|
margin-bottom: 0; }
|
||||||
|
|
||||||
|
dl {
|
||||||
|
margin: 0;
|
||||||
|
padding: 0; }
|
||||||
|
|
||||||
|
dt {
|
||||||
|
margin: 0 0 16px;
|
||||||
|
padding: 0;
|
||||||
|
font-weight: 500; }
|
||||||
|
|
||||||
|
dd {
|
||||||
|
margin: 0 0 16px;
|
||||||
|
padding: 0 0 0 8px; }
|
||||||
|
|
||||||
|
img {
|
||||||
|
max-width: 100%; }
|
||||||
|
|
||||||
|
a {
|
||||||
|
color: #4183c4;
|
||||||
|
text-decoration: none; }
|
||||||
|
a:hover, a:focus {
|
||||||
|
outline: 0;
|
||||||
|
text-decoration: underline; }
|
||||||
|
|
||||||
|
table {
|
||||||
|
width: 100%;
|
||||||
|
overflow: auto;
|
||||||
|
margin: 0 0 12px;
|
||||||
|
border-collapse: collapse;
|
||||||
|
border-spacing: 0;
|
||||||
|
background: #fff; }
|
||||||
|
|
||||||
|
tr:nth-child(2n) {
|
||||||
|
background-color: #fbfbfb; }
|
||||||
|
|
||||||
|
th, td {
|
||||||
|
border: 1px solid #ddd;
|
||||||
|
padding: 7px 11px; }
|
||||||
|
|
||||||
|
pre {
|
||||||
|
overflow: auto;
|
||||||
|
margin: 0 0 16px;
|
||||||
|
border: 1px solid #e6e6e6;
|
||||||
|
border-radius: 4px;
|
||||||
|
padding: calc(12px - 1px) calc(16px - 1px);
|
||||||
|
background: #f9f9f9;
|
||||||
|
font-size: inherit;
|
||||||
|
line-height: inherit;
|
||||||
|
font-family: "Source Code Pro", Menlo, Consolas, "Liberation Mono", Courier, monospace; }
|
||||||
|
|
||||||
|
code {
|
||||||
|
font-size: 16px;
|
||||||
|
line-height: 16px;
|
||||||
|
font-family: "Source Code Pro", Menlo, Consolas, "Liberation Mono", Courier, monospace; }
|
||||||
|
|
||||||
|
pre code {
|
||||||
|
padding: 0;
|
||||||
|
white-space: pre; }
|
||||||
|
|
||||||
|
body > .wrapper {
|
||||||
|
display: flex;
|
||||||
|
flex-direction: column; }
|
||||||
|
@media only screen and (min-width: 1024px) {
|
||||||
|
body > .wrapper {
|
||||||
|
flex-direction: row; } }
|
||||||
|
|
||||||
|
header {
|
||||||
|
display: flex;
|
||||||
|
padding: 8px;
|
||||||
|
background: #333;
|
||||||
|
color: #999;
|
||||||
|
font-size: 14px;
|
||||||
|
line-height: inherit; }
|
||||||
|
|
||||||
|
header p {
|
||||||
|
margin: 0;
|
||||||
|
padding: 0 8px; }
|
||||||
|
|
||||||
|
header p.primary {
|
||||||
|
flex: 1; }
|
||||||
|
|
||||||
|
header a[href] {
|
||||||
|
color: #fff; }
|
||||||
|
|
||||||
|
nav {
|
||||||
|
order: 2; }
|
||||||
|
@media only screen and (min-width: 1024px) {
|
||||||
|
nav {
|
||||||
|
order: 1;
|
||||||
|
flex: 0 0 25%;
|
||||||
|
max-width: 239px;
|
||||||
|
overflow: hidden;
|
||||||
|
border-right: 1px solid #ddd;
|
||||||
|
padding-bottom: 32px;
|
||||||
|
background: #fbfbfb;
|
||||||
|
word-wrap: normal; } }
|
||||||
|
nav > ul {
|
||||||
|
margin: 0;
|
||||||
|
padding: 0;
|
||||||
|
font-size: 14px;
|
||||||
|
line-height: inherit;
|
||||||
|
list-style: none; }
|
||||||
|
nav > ul > li {
|
||||||
|
margin: 8px 0;
|
||||||
|
border-bottom: 1px solid #ddd;
|
||||||
|
padding: 8px 0 7px 16px; }
|
||||||
|
nav > ul > li:last-child {
|
||||||
|
margin-bottom: 0; }
|
||||||
|
nav > ul > li > p {
|
||||||
|
margin: 0; }
|
||||||
|
nav > ul > li > p > a[href] {
|
||||||
|
color: #333; }
|
||||||
|
nav > ul > li > ul {
|
||||||
|
margin: 8px 0;
|
||||||
|
padding-left: 16px;
|
||||||
|
list-style: inherit; }
|
||||||
|
nav > ul > li > ul > li {
|
||||||
|
white-space: nowrap; }
|
||||||
|
nav > ul > li > ul > li > a[href] {
|
||||||
|
color: #808080; }
|
||||||
|
|
||||||
|
/*
|
||||||
|
@keyframes appear {
|
||||||
|
0% { opacity: 0 }
|
||||||
|
100% { opacity: 1 }
|
||||||
|
}
|
||||||
|
*/
|
||||||
|
article {
|
||||||
|
order: 1;
|
||||||
|
border-bottom: 1px solid #ddd;
|
||||||
|
padding-bottom: 31px; }
|
||||||
|
@media only screen and (min-width: 1024px) {
|
||||||
|
article {
|
||||||
|
order: 2;
|
||||||
|
flex: 1 1 auto;
|
||||||
|
border-bottom: none;
|
||||||
|
padding-bottom: 32px; } }
|
||||||
|
article > section {
|
||||||
|
padding: 0 32px; }
|
||||||
|
article > section:last-child {
|
||||||
|
border-bottom: none; }
|
||||||
|
article > section > .wrapper {
|
||||||
|
max-width: 720px;
|
||||||
|
margin: 0 auto; }
|
||||||
|
|
||||||
|
.declaration .highlight {
|
||||||
|
overflow-x: initial;
|
||||||
|
margin: 0;
|
||||||
|
border: none;
|
||||||
|
border-radius: 0;
|
||||||
|
padding: 0;
|
||||||
|
background-color: transparent; }
|
||||||
|
|
||||||
|
.toc {
|
||||||
|
border-top: 1px solid #ddd;
|
||||||
|
border-bottom: 1px solid #ddd;
|
||||||
|
background-color: #fbfbfb; }
|
||||||
|
.toc details {
|
||||||
|
max-width: 720px;
|
||||||
|
margin: 0 auto;
|
||||||
|
padding: 15px 0; }
|
||||||
|
.toc details[open] > summary {
|
||||||
|
margin-bottom: 8px;
|
||||||
|
/*
|
||||||
|
& ~ * {
|
||||||
|
animation: appear .2s ease-in-out;
|
||||||
|
}
|
||||||
|
*/ }
|
||||||
|
.toc details[open] > summary::after {
|
||||||
|
content: ' \2212'; }
|
||||||
|
.toc details > summary {
|
||||||
|
display: block;
|
||||||
|
margin: 0;
|
||||||
|
padding-bottom: 0;
|
||||||
|
color: #666666;
|
||||||
|
font-weight: 500;
|
||||||
|
font-size: 12px;
|
||||||
|
letter-spacing: 0.2em;
|
||||||
|
text-transform: uppercase;
|
||||||
|
user-select: none;
|
||||||
|
-moz-user-select: none;
|
||||||
|
-ms-user-select: none;
|
||||||
|
-webkit-user-select: none;
|
||||||
|
-webkit-tap-highlight-color: transparent;
|
||||||
|
outline: none; }
|
||||||
|
.toc details > summary::-webkit-details-marker {
|
||||||
|
display: none; }
|
||||||
|
.toc details > summary::after {
|
||||||
|
content: ' +'; }
|
||||||
|
.toc details > .wrapper {
|
||||||
|
columns: 1; }
|
||||||
|
@media only screen and (min-width: 1024px) {
|
||||||
|
.toc details > .wrapper {
|
||||||
|
columns: 2;
|
||||||
|
column-gap: 16px; } }
|
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@ -0,0 +1,247 @@
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<a href="index.html">NumericAnnex Reference</a>
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(100% documented)
|
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</p>
|
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<p>
|
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<a href="https://github.com/xwu/NumericAnnex">View on GitHub</a>
|
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|
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<p>
|
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<a href="dash-feed://https%3A%2F%2Fxwu%2Egithub%2Eio%2FNumericAnnex%2Fdocsets%2FNumericAnnex%2Exml">Install in Dash</a>
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<a href="Classes/Random/Xoroshiro.html">– Xoroshiro</a>
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|
||||||
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<a href="Functions.html#/s:12NumericAnnex3absAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">abs(_:)</a>
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
|
<a href="Functions.html#/s:12NumericAnnex3absAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">abs(_:)</a>
|
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|
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||||||
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<a href="Functions.html#/s:12NumericAnnex4ceilAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">ceil(_:)</a>
|
||||||
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|
||||||
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|
||||||
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<a href="Functions.html#/s:12NumericAnnex5floorAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">floor(_:)</a>
|
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|
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||||||
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<a href="Functions.html#/s:12NumericAnnex5roundAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">round(_:)</a>
|
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|
||||||
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||||||
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<a href="Functions.html#/s:12NumericAnnex4sqrtAA7ComplexVyxGAeA4RealRzs9DecodableRzs9EncodableRzs33_ExpressibleByBuiltinFloatLiteralRzlF">sqrt(_:)</a>
|
||||||
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|
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|
||||||
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<a href="Functions.html#/s:12NumericAnnex5truncAA8RationalVyxGAEs9DecodableRzs9EncodableRzs13SignedIntegerRzs021_ExpressibleByBuiltinH7LiteralRzs08UnsignedH09Magnitudes0A0PRpzAkM_AKQZANRSlF">trunc(_:)</a>
|
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|
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|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
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<p><a href="Protocols.html">Protocols</a></p>
|
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|
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|
||||||
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<a href="Protocols/Math.html">Math</a>
|
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|
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||||||
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<a href="Protocols/PRNG.html">PRNG</a>
|
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|
</li>
|
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|
<li>
|
||||||
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<a href="Protocols/Real.html">Real</a>
|
||||||
|
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|
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|
</ul>
|
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|
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|
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|
||||||
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|
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|
||||||
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<a href="Structs/Rational.html">Rational</a>
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||||||
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<p><a href="Typealiases.html">Typealiases</a></p>
|
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|
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|
||||||
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<a href="Typealiases.html#/s:12NumericAnnex12RoundingRulea">RoundingRule</a>
|
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|
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|
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<a href="Typealiases.html#/s:12NumericAnnex4Signa">Sign</a>
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<article>
|
||||||
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<section>
|
||||||
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<div class="wrapper">
|
||||||
|
<div class="overview">
|
||||||
|
|
||||||
|
<h1 id='numericannex' class='heading'>NumericAnnex</h1>
|
||||||
|
|
||||||
|
<p><a href="https://travis-ci.org/xwu/NumericAnnex"><img src="https://travis-ci.org/xwu/NumericAnnex.svg?branch=master" alt="Build Status"></a>
|
||||||
|
<a href="https://codecov.io/gh/xwu/NumericAnnex"><img src="https://codecov.io/gh/xwu/NumericAnnex/branch/master/graph/badge.svg" alt="codecov"></a></p>
|
||||||
|
|
||||||
|
<p>NumericAnnex supplements the numeric facilities provided in the Swift standard
|
||||||
|
library.</p>
|
||||||
|
<h2 id='features' class='heading'>Features</h2>
|
||||||
|
|
||||||
|
<ul>
|
||||||
|
<li><code>BinaryInteger</code> exponentiation, square root, cube root, greatest common
|
||||||
|
divisor, and least common multiple functions.</li>
|
||||||
|
<li><code>Complex</code>, a value type to represent complex values in Cartesian form.</li>
|
||||||
|
<li><code>Rational</code>, a value type to represent rational values, which supports division
|
||||||
|
by zero.</li>
|
||||||
|
<li><code>Random</code> and <code>Random.Xoroshiro</code>, two reference types implementing efficient
|
||||||
|
pseudo-random number generators.</li>
|
||||||
|
<li><code>Math</code>, a protocol for types providing square root, cube root, and elementary
|
||||||
|
transcendental functions.</li>
|
||||||
|
<li><code>Real</code>, a protocol for floating-point types providing a selection of special
|
||||||
|
functions.</li>
|
||||||
|
<li><code>PRNG</code>, a protocol for pseudo-random number generators.</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
<blockquote>
|
||||||
|
<p>Note: This project is in the early stages of development and is not
|
||||||
|
production-ready at this time.</p>
|
||||||
|
</blockquote>
|
||||||
|
<h2 id='requirements' class='heading'>Requirements</h2>
|
||||||
|
|
||||||
|
<p>NumericAnnex now requires Xcode 9 beta 5 or a recent development snapshot of
|
||||||
|
Swift 4.0 that includes the revised numeric protocols.</p>
|
||||||
|
|
||||||
|
<p>It requires either <code>Darwin.C</code> (macOS) or <code>Glibc</code> (Linux) for transcendental
|
||||||
|
functions provided by the C standard library and either <code>Security</code> (macOS) or
|
||||||
|
<code>Glibc</code> (Linux) for cryptographically secure random bytes.</p>
|
||||||
|
<h2 id='installation' class='heading'>Installation</h2>
|
||||||
|
|
||||||
|
<p>After NumericAnnex has been cloned or downloaded locally, build the library with
|
||||||
|
the command <code>swift build</code> (macOS) or <code>swift build -Xcc -D_GNU_SOURCE</code> (Linux).
|
||||||
|
Tests can be run with the command <code>swift test</code> (macOS) or
|
||||||
|
<code>swift test -Xcc -D_GNU_SOURCE</code> (Linux). An Xcode project can be generated with
|
||||||
|
the command <code>swift package generate-xcodeproj</code>.</p>
|
||||||
|
|
||||||
|
<p><a href="https://swift.org/package-manager/">Swift Package Manager</a> can also be used to
|
||||||
|
add the package as a dependency for your own project. See Swift documentation
|
||||||
|
for details.</p>
|
||||||
|
<h2 id='basic-usage' class='heading'>Basic Usage</h2>
|
||||||
|
<pre class="highlight swift"><code><span class="kd">import</span> <span class="kt">NumericAnnex</span>
|
||||||
|
|
||||||
|
<span class="k">var</span> <span class="nv">x</span><span class="p">:</span> <span class="kt">Ratio</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="mi">4</span>
|
||||||
|
<span class="c1">// Ratio is a type alias for Rational<Int>.</span>
|
||||||
|
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="nf">reciprocal</span><span class="p">())</span>
|
||||||
|
<span class="c1">// Prints "4".</span>
|
||||||
|
|
||||||
|
<span class="n">x</span> <span class="o">*=</span> <span class="mi">8</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">x</span> <span class="o">+</span> <span class="n">x</span><span class="p">)</span>
|
||||||
|
<span class="c1">// Prints "4".</span>
|
||||||
|
|
||||||
|
<span class="n">x</span> <span class="o">=</span> <span class="kt">Ratio</span><span class="p">(</span><span class="kt">Float</span><span class="o">.</span><span class="n">phi</span><span class="p">)</span> <span class="c1">// Golden ratio.</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||||||
|
<span class="c1">// Prints "13573053/8388608".</span>
|
||||||
|
|
||||||
|
<span class="k">var</span> <span class="nv">z</span><span class="p">:</span> <span class="kt">Complex64</span> <span class="o">=</span> <span class="mi">42</span> <span class="o">*</span> <span class="o">.</span><span class="n">i</span>
|
||||||
|
<span class="c1">// Complex64 is a type alias for Complex<Float>.</span>
|
||||||
|
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="kt">Complex</span><span class="o">.</span><span class="nf">sqrt</span><span class="p">(</span><span class="n">z</span><span class="p">))</span>
|
||||||
|
<span class="c1">// Prints "4.58258 + 4.58258i".</span>
|
||||||
|
|
||||||
|
<span class="n">z</span> <span class="o">=</span> <span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="o">.</span><span class="n">i</span> <span class="o">*</span> <span class="o">.</span><span class="nf">log</span><span class="p">(</span><span class="mi">2</span> <span class="o">-</span> <span class="o">.</span><span class="nf">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">))</span>
|
||||||
|
<span class="nf">print</span><span class="p">(</span><span class="kt">Complex</span><span class="o">.</span><span class="nf">cos</span><span class="p">(</span><span class="n">z</span><span class="p">)</span><span class="o">.</span><span class="n">real</span><span class="p">)</span>
|
||||||
|
<span class="c1">// Prints "-2.0".</span>
|
||||||
|
</code></pre>
|
||||||
|
<h2 id='documentation' class='heading'>Documentation</h2>
|
||||||
|
|
||||||
|
<p>All public protocols, types, and functions have been carefully documented in the
|
||||||
|
code. See the <a href="https://xwu.github.io/NumericAnnex/">formatted reference</a> for
|
||||||
|
details.</p>
|
||||||
|
|
||||||
|
<p>The project adheres to many design patterns found in the Swift standard library.
|
||||||
|
For example, <code>Math</code> types provide methods such as <code>cubeRoot()</code> and <code>tangent()</code>
|
||||||
|
just as <code>FloatingPoint</code> types provide methods such as <code>squareRoot()</code>.</p>
|
||||||
|
|
||||||
|
<p>No free functions are declared in this library unless they overload existing
|
||||||
|
ones in the Swift standard library. Instead, functions such as <code>cbrt(_:)</code> and
|
||||||
|
<code>tan(_:)</code> are provided as static members. This avoids collisions with C standard
|
||||||
|
library functions that you may wish to use. It also promotes clarity at the call
|
||||||
|
site when the result of a complex operation differs from that of its real
|
||||||
|
counterpart (e.g., <code>Complex128.cbrt(-8) != -2</code>).</p>
|
||||||
|
<h2 id='future-directions' class='heading'>Future Directions</h2>
|
||||||
|
|
||||||
|
<ul>
|
||||||
|
<li>[ ] Add more tests, including performance tests</li>
|
||||||
|
<li>[ ] Design and implement additional methods on <code>PRNG</code></li>
|
||||||
|
<li>[ ] Design and implement <code>BigInt</code></li>
|
||||||
|
</ul>
|
||||||
|
<h2 id='license' class='heading'>License</h2>
|
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<p>All original work is released under the MIT license. See
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<a href="https://github.com/xwu/NumericAnnex/blob/master/LICENSE">LICENSE</a> for details.</p>
|
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<p>Portions of the complex square root and elementary transcendental functions use
|
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|
checks for special values adapted from libc++. Code in libc++ is dual-licensed
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under the MIT and UIUC/NCSA licenses.</p>
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</div>
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</section>
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</article>
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</div>
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<footer>
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<p>© 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-08-12)</p>
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<p>Generated by <a href="https://github.com/realm/jazzy" target="_blank" rel="external">Jazzy</a> v0.8.3, a <a href="http://realm.io" target="_blank" rel="external">Realm</a> project.</p>
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