From 21797a27c6e914bf6ce788c90ce313bf2a87d9bd Mon Sep 17 00:00:00 2001 From: Xiaodi Wu Date: Sat, 12 Aug 2017 14:57:28 -0500 Subject: [PATCH] Update documentation --- css/jazzy.css | 348 ++++ css/jazzy.css.scss | 589 ------ .../NumericAnnex.docset/Contents/Info.plist | 20 + .../Contents/Resources/Documents/Classes.html | 213 ++ .../Resources/Documents/Classes/Random.html | 356 ++++ .../Documents/Classes/Random/Xoroshiro.html | 297 +++ .../Resources/Documents/Extensions.html | 282 +++ .../Documents/Extensions/BinaryInteger.html | 485 +++++ .../Documents/Extensions/Double.html | 837 ++++++++ .../Resources/Documents/Extensions/Float.html | 837 ++++++++ .../Documents/Extensions/FloatingPoint.html | 357 ++++ .../Documents/Extensions/UnsignedInteger.html | 310 +++ .../Resources/Documents/Functions.html | 322 +++ .../Resources/Documents/Protocols.html | 286 +++ .../Resources/Documents/Protocols/Math.html | 1636 +++++++++++++++ .../Resources/Documents/Protocols/PRNG.html | 824 ++++++++ .../Resources/Documents/Protocols/Real.html | 561 +++++ .../Contents/Resources/Documents/Structs.html | 304 +++ .../Resources/Documents/Structs/Complex.html | 1822 +++++++++++++++++ .../Resources/Documents/Structs/Rational.html | 1634 +++++++++++++++ .../Resources/Documents/Typealiases.html | 210 ++ .../Resources/Documents/css/highlight.css | 186 ++ .../Resources/Documents/css/jazzy.css | 348 ++++ .../Contents/Resources/Documents/index.html | 247 +++ .../Contents/Resources/Documents/js/jazzy.js | 15 + .../Resources/Documents/js/jquery.min.js | 4 + .../Contents/Resources/docSet.dsidx | Bin 0 -> 81920 bytes docsets/NumericAnnex.tgz | Bin 0 -> 92846 bytes docsets/NumericAnnex.xml | 1 + 29 files changed, 12742 insertions(+), 589 deletions(-) create mode 100644 css/jazzy.css delete mode 100644 css/jazzy.css.scss create mode 100644 docsets/NumericAnnex.docset/Contents/Info.plist create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes/Random.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes/Random/Xoroshiro.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/BinaryInteger.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/Double.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/Float.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/FloatingPoint.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/UnsignedInteger.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Functions.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/Math.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/PRNG.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/Real.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs/Complex.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs/Rational.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/Typealiases.html create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/css/highlight.css create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/css/jazzy.css create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/Documents/index.html create mode 100755 docsets/NumericAnnex.docset/Contents/Resources/Documents/js/jazzy.js create mode 100755 docsets/NumericAnnex.docset/Contents/Resources/Documents/js/jquery.min.js create mode 100644 docsets/NumericAnnex.docset/Contents/Resources/docSet.dsidx create mode 100644 docsets/NumericAnnex.tgz create mode 100644 docsets/NumericAnnex.xml diff --git a/css/jazzy.css b/css/jazzy.css new file mode 100644 index 0000000..58293e3 --- /dev/null +++ b/css/jazzy.css @@ -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; } } + .toc details > .wrapper p { + margin: 0; + color: #333; + font-weight: 500; + break-after: avoid-column; + -webkit-column-break-after: avoid; } + .toc details > .wrapper p a[href] { + color: inherit; } + .toc details > .wrapper ul { + margin: 0; + padding-left: 0; + color: #b3b3b3; + list-style: square inside; } + .toc details > .wrapper ul a[href] { + color: #808080; } + +.group { + border-bottom: 1px solid #ddd; + padding-top: 0; } + .group:last-child { + border-bottom: none; } + .group:last-child > ul > li:last-child { + padding-bottom: 16px; } + .group a[name]::before { + content: ""; + display: block; } + .group > ul { + margin: 0; + padding: 0; } + .group > ul > li { + width: 100%; + border-bottom: 1px solid #ddd; + padding: 0 0 15px; + list-style: none; } + .group > ul > li:last-child { + border-bottom: none; } + .group > ul > li .declaration-note { + color: #808080; + font-weight: normal; + font-size: 16px; } + +.aside, .language { + overflow-y: hidden; + margin: 16px 0; + border-left: 6px solid #d0d0d0; + border-radius: 4px; + padding: 8px 12px; + background-color: #f7f7f7; } + .aside .aside-title, .language .aside-title { + margin: 0; + padding-bottom: 0; + color: #aaa; + 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; } + .aside p:last-child, .language p:last-child { + margin-bottom: 0; } + +.language { + border-left: 6px solid #99bcdf; + background-color: #f0f5fa; } + .language .aside-title { + color: #4183c4; } + +.aside-warning { + border-left: 6px solid #ffda73; + background-color: #fff8e6; } + .aside-warning .aside-title { + color: #fb0; } + +footer { + padding: 16px; + background: #444; + color: #ddd; + font-size: 14px; + line-height: inherit; } + footer p { + margin: 0; } + footer a[href] { + color: #fff; } + +html.dash header, html.dash nav { + display: none; } diff --git a/css/jazzy.css.scss b/css/jazzy.css.scss deleted file mode 100644 index 57bde10..0000000 --- a/css/jazzy.css.scss +++ /dev/null @@ -1,589 +0,0 @@ -@import url("https://fonts.googleapis.com/css?family=Source+Code+Pro:400,500,600,700"); - -// =========================================================================== -// Variables -// =========================================================================== - -$unit: 4px; - -$body_background: #fff; -$body_text_color: #333; -$body_font_family: -apple-system, BlinkMacSystemFont, "Segoe UI", Arial, sans-serif; - -$light_heading_color: #777; -$heading_font_weight: 500; - -$link_color: #4183c4; - -$border_radius: $unit; - -$quote_border: (1.5 * $unit) solid #e6e6e6; -$quote_background_color: #fafafa; -$quote_color: #858585; - -$table_border_color: #ddd; -$table_border: 1px solid $table_border_color; -$table_alternate_row_color: #fbfbfb; - -$pre_border_width: 1px; -$pre_border_color: #e6e6e6; -$pre_border: $pre_border_width solid $pre_border_color; -$pre_background_color: #f9f9f9; - -$code_font_family: "Source Code Pro", Menlo, Consolas, "Liberation Mono", Courier, monospace; - -// ----- Header - -$header_background_color: #333; -$header_link_color: #fff; -$doc_coverage_color: #999; - -// ----- Navigation - -$nav_max_width: 60 * $unit - 1px; - -$nav_border_width: 1px; -$nav_border: $nav_border_width solid #ddd; -$nav_background_color: #fbfbfb; -$nav_title_color: #333; -$nav_task_color: #808080; - -// ----- Content - -$content_padding: 8 * $unit; -$content_max_width: 180 * $unit; - -$toc_border_width: $nav_border_width; -$toc_border: $nav_border; -$toc_background_color: $nav_background_color; -$toc_title_color: $nav_title_color; -$toc_task_color: $nav_task_color; - -$declaration_language_title_color: #4183c4; -$declaration_language_background_color: lighten($declaration_language_title_color, 45%); -$declaration_language_border: (1.5 * $unit) solid lighten($declaration_language_title_color, 22.5%); - -$aside_color: #aaa; -$aside_background_color: lighten($aside_color, 30%); -$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; - } -} - -.language { - border-left: $declaration_language_border; - background-color: $declaration_language_background_color; - - .aside-title { - color: $declaration_language_title_color; - } -} - -.aside-warning { - border-left: $aside_warning_border; - background-color: $aside_warning_background_color; - - .aside-title { - color: $aside_warning_color; - } -} - -// =========================================================================== -// Footer -// =========================================================================== - -footer { - padding: 4 * $unit; - background: $footer_background_color; - color: $footer_text_color; - font-size: 3.5 * $unit; - line-height: inherit; - - p { - margin: 0; - } - - a[href] { - color: $footer_link_color; - } -} - -// =========================================================================== -// Dash -// =========================================================================== - -html.dash { - header, nav { - display: none; - } -} diff --git a/docsets/NumericAnnex.docset/Contents/Info.plist b/docsets/NumericAnnex.docset/Contents/Info.plist new file mode 100644 index 0000000..c1a327a --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Info.plist @@ -0,0 +1,20 @@ + + + + + CFBundleIdentifier + com.jazzy.numericannex + CFBundleName + NumericAnnex + DocSetPlatformFamily + numericannex + isDashDocset + + dashIndexFilePath + index.html + isJavaScriptEnabled + + DashDocSetFamily + dashtoc + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes.html new file mode 100644 index 0000000..55f8c81 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes.html @@ -0,0 +1,213 @@ + + + + + + Classes Reference + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Classes

+

The following classes are available globally.

+ +
+
+
+
+
+ Topics +
+ +
+
+
+
+
+
+
    +
  • +
    + + +

    + Random +

    +
    +
    +

    A pseudo-random number generator (PRNG) that implements +xorshift128+, an efficient linear-feedback shift register.

    +
    +

    Warning

    + Once seeded from cryptographically secure random bytes, an +instance of Random generates high-quality random numbers but is not a +cryptographically secure PRNG. + +
    + +

    To generate random numbers, create your own instance of Random with an +internal state seeded from cryptographically secure random bytes:

    +
    let random = Random()!
+let x = random.uniform() as Int
+
+// You can also pass the desired result type as an argument.
+let y = random.uniform(Int.self)
+
+if x > y {
+  print("Here's a random value between 0 and 42 (inclusive):")
+  print(random.uniform(a: 0, b: 42))
+} else {
+  print("Here's a random value between -42 and 0 (inclusive):")
+  print(random.uniform(a: -42, b: 0))
+}
+
    +
    +

    See also

    + Random.Xoroshiro, PRNG + +
    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public final class Random : PRNG
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes/Random.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes/Random.html new file mode 100644 index 0000000..6a0a082 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes/Random.html @@ -0,0 +1,356 @@ + + + + + + Random Class Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Random

+
+
+ 
public final class Random : PRNG
+ +
+
+

A pseudo-random number generator (PRNG) that implements +xorshift128+, an efficient linear-feedback shift register.

+
+

Warning

+ Once seeded from cryptographically secure random bytes, an +instance of Random generates high-quality random numbers but is not a +cryptographically secure PRNG. + +
+ +

To generate random numbers, create your own instance of Random with an +internal state seeded from cryptographically secure random bytes:

+
let random = Random()!
+let x = random.uniform() as Int
+
+// You can also pass the desired result type as an argument.
+let y = random.uniform(Int.self)
+
+if x > y {
+  print("Here's a random value between 0 and 42 (inclusive):")
+  print(random.uniform(a: 0, b: 42))
+} else {
+  print("Here's a random value between -42 and 0 (inclusive):")
+  print(random.uniform(a: -42, b: 0))
+}
+
+
+

See also

+ Random.Xoroshiro, PRNG + +
+ +
+
+
+
+
+ Topics +
+ + +
+
+
+
+
+
+
    +
  • +
    + + +

    + state +

    +
    +
    +

    The internal state of the pseudo-random number generator.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var state: (UInt64, UInt64)
    + +
    +
    +
    • +
  • +
    + + +

    + init(state:) +

    +
    +
    +

    Creates a pseudo-random number generator with the given internal state.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(state: (UInt64, UInt64))
    + +
    +
    +
    +
    Parameters
    +
    +
    state
    +
    +

    The value to be used as the generator’s internal state.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init() +

    +
    +
    +

    Creates a pseudo-random number generator with an internal state seeded +using cryptographically secure random bytes.

    + +

    If cryptographically secure random bytes are unavailable, the result is +nil.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public convenience init?()
    + +
    +
    +
    • +
  • +
    + + +

    + next() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func next() -> UInt64?
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + Xoroshiro +

    +
    +
    +

    A pseudo-random number generator (PRNG) that implements xoroshiro128+, a +successor to xorshift128+ devised by S. Vigna and D. Blackman.

    +
    +

    Warning

    + Once seeded from cryptographically secure random bytes, an +instance of Random.Xoroshiro generates high-quality random numbers but +is not a cryptographically secure PRNG. + +
    + +

    To generate random numbers, create your own instance of Random.Xoroshiro +with an internal state seeded from cryptographically secure random bytes:

    +
    let random = Random.Xoroshiro()!
+let x = random.uniform() as Int
+
+// You can also pass the desired result type as an argument.
+let y = random.uniform(Int.self)
+
+if x > y {
+  print("Here's a random value between 0 and 42 (inclusive):")
+  print(random.uniform(a: 0, b: 42))
+} else {
+  print("Here's a random value between -42 and 0 (inclusive):")
+  print(random.uniform(a: -42, b: 0))
+}
+
    +
    +

    See also

    + Random, PRNG + +
    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public final class Xoroshiro : PRNG
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes/Random/Xoroshiro.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes/Random/Xoroshiro.html new file mode 100644 index 0000000..6719ea4 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Classes/Random/Xoroshiro.html @@ -0,0 +1,297 @@ + + + + + + Xoroshiro Class Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Xoroshiro

+
+
+ 
public final class Xoroshiro : PRNG
+ +
+
+

A pseudo-random number generator (PRNG) that implements xoroshiro128+, a +successor to xorshift128+ devised by S. Vigna and D. Blackman.

+
+

Warning

+ Once seeded from cryptographically secure random bytes, an +instance of Random.Xoroshiro generates high-quality random numbers but +is not a cryptographically secure PRNG. + +
+ +

To generate random numbers, create your own instance of Random.Xoroshiro +with an internal state seeded from cryptographically secure random bytes:

+
let random = Random.Xoroshiro()!
+let x = random.uniform() as Int
+
+// You can also pass the desired result type as an argument.
+let y = random.uniform(Int.self)
+
+if x > y {
+  print("Here's a random value between 0 and 42 (inclusive):")
+  print(random.uniform(a: 0, b: 42))
+} else {
+  print("Here's a random value between -42 and 0 (inclusive):")
+  print(random.uniform(a: -42, b: 0))
+}
+
+
+

See also

+ Random, PRNG + +
+ +
+
+
+
+
+ Topics +
+ +
+
+
+
+
+
+
    +
  • +
    + + +

    + state +

    +
    +
    +

    The internal state of the pseudo-random number generator.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var state: (UInt64, UInt64)
    + +
    +
    +
    • +
  • +
    + + +

    + init(state:) +

    +
    +
    +

    Creates a pseudo-random number generator with the given internal state.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(state: (UInt64, UInt64))
    + +
    +
    +
    +
    Parameters
    +
    +
    state
    +
    +

    The value to be used as the generator’s internal state.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init() +

    +
    +
    +

    Creates a pseudo-random number generator with an internal state seeded +using cryptographically secure random bytes.

    + +

    If cryptographically secure random bytes are unavailable, the result is +nil.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public convenience init?()
    + +
    +
    +
    • +
  • +
    + + +

    + next() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func next() -> UInt64?
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions.html new file mode 100644 index 0000000..edf63ee --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions.html @@ -0,0 +1,282 @@ + + + + + + Extensions Reference + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Extensions

+

The following extensions are available globally.

+ +
+
+
+
+
+ Topics +
+ + + +
+
+
+
+
+
+
    +
  • +
    + + +

    + BinaryInteger +

    +
    +
    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    protocol BinaryInteger : Hashable, Numeric, CustomStringConvertible, Strideable
    + +
    +
    +
    • +
  • +
    + + +

    + UnsignedInteger +

    +
    +
    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    protocol UnsignedInteger : BinaryInteger where Self.Magnitude : BinaryInteger
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + Float +

    +
    +
    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    struct Float
    + +
    +
    +
    • +
  • +
    + + +

    + Double +

    +
    +
    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    struct Double
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + FloatingPoint +

    +
    +
    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    protocol FloatingPoint : SignedNumeric, Strideable, Hashable
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/BinaryInteger.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/BinaryInteger.html new file mode 100644 index 0000000..312d57b --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/BinaryInteger.html @@ -0,0 +1,485 @@ + + + + + + BinaryInteger Extension Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

BinaryInteger

+
+
+ 
protocol BinaryInteger : Hashable, Numeric, CustomStringConvertible, Strideable
+ +
+
+ +
+
+
+
+
+ Topics +
+

Exponentiation

+ +

Square Root

+ +

Cube Root

+ +

Factoring

+ +

Factoring (Fixed-Width)

+ +

Initializers

+ +
+
+
+
+
+
+
+ + +

Exponentiation

+
+
    +
  • +
    + + +

    + pow(_:_:) +

    +
    +
    +

    Returns the result of raising base to the power of exponent, rounded +to a representable value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func pow(_ base: Self, _ exponent: Self) -> Self
    + +
    +
    +
    • +
+
+
+
+ + +

Square Root

+
+
    +
  • +
    + + +

    + sqrt(_:) +

    +
    +
    +

    Returns the square root of x, rounding toward zero. If x is negative, +a runtime error may occur.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func sqrt(_ x: Self) -> Self
    + +
    +
    +
    • +
+
+
+
+ + +

Cube Root

+
+
    +
  • +
    + + +

    + cbrt(_:) +

    +
    +
    +

    Returns the cube root of x, rounding toward zero.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func cbrt(_ x: Self) -> Self
    + +
    +
    +
    • +
+
+
+
+ + +

Factoring

+
+
    +
  • +
    + + +

    + gcd(_:_:) +

    +
    +
    +

    Returns the greatest common divisor of a and b.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func gcd(_ a: Self, _ b: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + lcm(_:_:) +

    +
    +
    +

    Returns the least common multiple of a and b.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func lcm(_ a: Self, _ b: Self) -> Self
    + +
    +
    +
    • +
+
+
+
+ + +

Factoring (Fixed-Width)

+
+
    +
  • +
    + + +

    + gcdReportingOverflow(_:_:) +

    +
    +
    +

    Returns the greatest common divisor of a and b and a flag to indicate +whether overflow occurred during the operation.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func gcdReportingOverflow(_ a: Self, _ b: Self)
+    -> (partialValue: Self, overflow: Bool)
    + +
    +
    +
    • +
  • +
    + + +

    + lcmReportingOverflow(_:_:) +

    +
    +
    +

    Returns the least common multiple of a and b and a flag to indicate +whether overflow occurred during the operation.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func lcmReportingOverflow(_ a: Self, _ b: Self)
+    -> (partialValue: Self, overflow: Bool)
    + +
    +
    +
    • +
  • +
    + + +

    + lcmFullWidth(_:_:) +

    +
    +
    +

    Returns the high and low parts of the least common multiple of a and b +computed using full-width arithmetic.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func lcmFullWidth(_ a: Self, _ b: Self)
+    -> (high: Self, low: Self.Magnitude)
    + +
    +
    +
    • +
+
+
+
+ + +

Initializers

+
+
    +
  • +
    + + +

    + init(exactly:) +

    +
    +
    +

    Creates a new binary integer from the given rational value, if it can be +represented exactly.

    + +

    If source is not representable exactly, the result is nil.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init?<U>(exactly source: Rational<U>)
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    +

    A rational value to convert to a binary integer.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init(_:) +

    +
    +
    +

    Creates a new binary integer from the given rational value, rounding +toward zero.

    + +

    If source is outside the bounds of this type after rounding toward zero, +a runtime error may occur.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init<U>(_ source: Rational<U>)
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    +

    A rational value to convert to a binary integer.

    +
    +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/Double.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/Double.html new file mode 100644 index 0000000..f52be4e --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/Double.html @@ -0,0 +1,837 @@ + + + + + + Double Extension Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Double

+
+
+ 
struct Double
+ +
+
+ +
+
+
+
+
+ Topics +
+

Real

+ +
+
+
+
+
+
+
+ + +

Real

+
+
    +
  • +
    + + +

    + e +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var e: Double
    + +
    +
    +
    • +
  • +
    + + +

    + phi +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var phi: Double
    + +
    +
    +
    • +
  • +
    + + +

    + pow(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func pow(_ base: Double, _ exponent: Double) -> Double
    + +
    +
    +
    +
    Parameters
    +
    +
    base
    +
    + +
    +
    exponent
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + naturalExponential() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func naturalExponential() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + binaryExponential() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func binaryExponential() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + commonExponential() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func commonExponential() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + naturalExponentialMinusOne() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func naturalExponentialMinusOne() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + naturalLogarithm() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func naturalLogarithm() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + binaryLogarithm() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func binaryLogarithm() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + commonLogarithm() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func commonLogarithm() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + naturalLogarithmOnePlus() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func naturalLogarithmOnePlus() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + cubeRoot() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func cubeRoot() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + sine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func sine() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + cosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func cosine() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + tangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func tangent() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + inverseSine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseSine() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + inverseCosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseCosine() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + inverseTangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseTangent() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicSine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func hyperbolicSine() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicCosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func hyperbolicCosine() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicTangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func hyperbolicTangent() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicSine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseHyperbolicSine() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicCosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseHyperbolicCosine() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicTangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseHyperbolicTangent() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + hypot(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func hypot(_ x: Double, _ y: Double) -> Double
    + +
    +
    +
    +
    Parameters
    +
    +
    x
    +
    + +
    +
    y
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + inverseTangent(dividingBy:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseTangent(dividingBy other: Double) -> Double
    + +
    +
    +
    +
    Parameters
    +
    +
    other
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + error() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func error() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + complementaryError() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func complementaryError() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + gamma() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func gamma() -> Double
    + +
    +
    +
    • +
  • +
    + + +

    + logarithmicGamma() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func logarithmicGamma() -> Double
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/Float.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/Float.html new file mode 100644 index 0000000..f17227c --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/Float.html @@ -0,0 +1,837 @@ + + + + + + Float Extension Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Float

+
+
+ 
struct Float
+ +
+
+ +
+
+
+
+
+ Topics +
+

Real

+ +
+
+
+
+
+
+
+ + +

Real

+
+
    +
  • +
    + + +

    + e +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var e: Float
    + +
    +
    +
    • +
  • +
    + + +

    + phi +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var phi: Float
    + +
    +
    +
    • +
  • +
    + + +

    + pow(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func pow(_ base: Float, _ exponent: Float) -> Float
    + +
    +
    +
    +
    Parameters
    +
    +
    base
    +
    + +
    +
    exponent
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + naturalExponential() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func naturalExponential() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + binaryExponential() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func binaryExponential() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + commonExponential() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func commonExponential() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + naturalExponentialMinusOne() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func naturalExponentialMinusOne() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + naturalLogarithm() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func naturalLogarithm() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + binaryLogarithm() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func binaryLogarithm() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + commonLogarithm() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func commonLogarithm() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + naturalLogarithmOnePlus() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func naturalLogarithmOnePlus() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + cubeRoot() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func cubeRoot() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + sine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func sine() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + cosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func cosine() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + tangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func tangent() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + inverseSine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseSine() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + inverseCosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseCosine() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + inverseTangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseTangent() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicSine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func hyperbolicSine() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicCosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func hyperbolicCosine() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicTangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func hyperbolicTangent() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicSine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseHyperbolicSine() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicCosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseHyperbolicCosine() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicTangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseHyperbolicTangent() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + hypot(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func hypot(_ x: Float, _ y: Float) -> Float
    + +
    +
    +
    +
    Parameters
    +
    +
    x
    +
    + +
    +
    y
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + inverseTangent(dividingBy:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseTangent(dividingBy other: Float) -> Float
    + +
    +
    +
    +
    Parameters
    +
    +
    other
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + error() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func error() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + complementaryError() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func complementaryError() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + gamma() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func gamma() -> Float
    + +
    +
    +
    • +
  • +
    + + +

    + logarithmicGamma() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func logarithmicGamma() -> Float
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/FloatingPoint.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/FloatingPoint.html new file mode 100644 index 0000000..7321668 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/FloatingPoint.html @@ -0,0 +1,357 @@ + + + + + + FloatingPoint Extension Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

FloatingPoint

+
+
+ 
protocol FloatingPoint : SignedNumeric, Strideable, Hashable
+ +
+
+ +
+
+
+
+
+ Topics +
+

Initializers

+ +
+
+
+
+
+
+
+ + +

Initializers

+
+
    +
  • +
    + + +

    + init(_:) +

    +
    +
    +

    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.

    + +

    If two representable values are equally close, the result of rounding is +the value with more trailing zeros in its significand bit pattern.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(_ source: Rational<Int>)
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    +

    The rational value to convert to a floating-point value.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init(_:) +

    +
    +
    +

    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.

    + +

    If two representable values are equally close, the result of rounding is +the value with more trailing zeros in its significand bit pattern.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(_ source: Rational<Int8>)
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    +

    The rational value to convert to a floating-point value.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init(_:) +

    +
    +
    +

    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.

    + +

    If two representable values are equally close, the result of rounding is +the value with more trailing zeros in its significand bit pattern.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(_ source: Rational<Int16>)
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    +

    The rational value to convert to a floating-point value.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init(_:) +

    +
    +
    +

    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.

    + +

    If two representable values are equally close, the result of rounding is +the value with more trailing zeros in its significand bit pattern.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(_ source: Rational<Int32>)
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    +

    The rational value to convert to a floating-point value.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init(_:) +

    +
    +
    +

    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.

    + +

    If two representable values are equally close, the result of rounding is +the value with more trailing zeros in its significand bit pattern.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(_ source: Rational<Int64>)
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    +

    The rational value to convert to a floating-point value.

    +
    +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/UnsignedInteger.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/UnsignedInteger.html new file mode 100644 index 0000000..232b0be --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Extensions/UnsignedInteger.html @@ -0,0 +1,310 @@ + + + + + + UnsignedInteger Extension Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

UnsignedInteger

+
+
+ 
protocol UnsignedInteger : BinaryInteger where Self.Magnitude : BinaryInteger
+ +
+
+ +
+
+
+
+
+ Topics +
+

Cube Root

+ +

Factoring

+ +

Factoring (Fixed-Width)

+ +
+
+
+
+
+
+
+ + +

Cube Root

+
+
    +
  • +
    + + +

    + cbrt(_:) +

    +
    +
    +

    Returns the cube root of x, rounding toward zero.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func cbrt(_ x: Self) -> Self
    + +
    +
    +
    • +
+
+
+
+ + +

Factoring

+
+
    +
  • +
    + + +

    + gcd(_:_:) +

    +
    +
    +

    Returns the greatest common divisor of a and b.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func gcd(_ a: Self, _ b: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + lcm(_:_:) +

    +
    +
    +

    Returns the least common multiple of a and b.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func lcm(_ a: Self, _ b: Self) -> Self
    + +
    +
    +
    • +
+
+
+
+ + +

Factoring (Fixed-Width)

+
+
    +
  • +
    + + +

    + lcmReportingOverflow(_:_:) +

    +
    +
    +

    Returns the least common multiple of a and b and a flag to indicate +whether overflow occurred during the operation.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func lcmReportingOverflow(_ a: Self, _ b: Self)
+    -> (partialValue: Self, overflow: Bool)
    + +
    +
    +
    • +
  • +
    + + +

    + lcmFullWidth(_:_:) +

    +
    +
    +

    Returns the high and low parts of the least common multiple of a and b +computed using full-width arithmetic.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func lcmFullWidth(_ a: Self, _ b: Self)
+    -> (high: Self, low: Self.Magnitude)
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Functions.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Functions.html new file mode 100644 index 0000000..25eb6a4 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Functions.html @@ -0,0 +1,322 @@ + + + + + + Functions Reference + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Functions

+

The following functions are available globally.

+ +
+
+
+
+
+ Topics +
+ + +
+
+
+
+
+
+
    +
  • +
    + + +

    + abs(_:) +

    +
    +
    +

    Returns the absolute value (magnitude, modulus) of z.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func abs<T>(_ z: Complex<T>) -> Complex<T>
    + +
    +
    +
    • +
  • +
    + + +

    + sqrt(_:) +

    +
    +
    +

    Returns the square root of z.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func sqrt<T>(_ z: Complex<T>) -> Complex<T>
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + abs(_:) +

    +
    +
    +

    Returns the absolute value (magnitude) of x.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func abs<T>(_ x: Rational<T>) -> Rational<T>
    + +
    +
    +
    • +
  • +
    + + +

    + ceil(_:) +

    +
    +
    +

    Returns the closest integral value greater than or equal to x.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func ceil<T>(_ x: Rational<T>) -> Rational<T>
    + +
    +
    +
    • +
  • +
    + + +

    + floor(_:) +

    +
    +
    +

    Returns the closest integral value less than or equal to x.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func floor<T>(_ x: Rational<T>) -> Rational<T>
    + +
    +
    +
    • +
  • +
    + + +

    + round(_:) +

    +
    +
    +

    Returns the closest integral value; if two values are equally close, returns +the one with greater magnitude.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func round<T>(_ x: Rational<T>) -> Rational<T>
    + +
    +
    +
    • +
  • +
    + + +

    + trunc(_:) +

    +
    +
    +

    Returns the closest integral value with magnitude less than or equal to that +of x.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func trunc<T>(_ x: Rational<T>) -> Rational<T>
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols.html new file mode 100644 index 0000000..09f19c7 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols.html @@ -0,0 +1,286 @@ + + + + + + Protocols Reference + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Protocols

+

The following protocols are available globally.

+ +
+
+
+
+
+ Topics +
+ + + +
+
+
+
+
+
+
    +
  • +
    + + +

    + PRNG +

    +
    +
    +

    A pseudo-random number generator (PRNG).

    + +

    Reference types that conform to PRNG 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.

    +

    Considerations for Conforming Types

    + +

    For clarity to end users, custom PRNGs may be implemented in an extension to +Random. For instance, the xoroshiro128+ algorithm is implemented in a +final class named Random.Xoroshiro.

    + +

    The static methods _entropy(_:) and _entropy(_:count:) return +cryptographically secure random bytes that may be useful for seeding your +custom PRNG. However, these methods may return nil if the requested number +of random bytes is not available, and they are not recommended as a routine +source of random data.

    +

    Adding Other Probability Distributions

    + +

    Many built-in protocol extension methods make use of the primitive, +overloaded method _random(_:bitCount:). You may wish to use the same +method in new protocol extension methods that return pseudo-random +values from other probability distributions.

    + +

    The method _random(_:bitCount:) generates uniformly distributed binary +floating-point values in the half-open range [0, 1) with a precision of +either bitCount 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 ** x), where ** is the +exponentiation operator and x is the lesser of bitCount and the bit +width of the integer type.

    + +

    For end users, however, the recommended spelling for a uniformly distributed +numeric value is uniform(); that method is overloaded to permit custom +minimum and maximum values for the uniform distribution.

    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public protocol PRNG : class, IteratorProtocol, Sequence
+where Element : FixedWidthInteger & UnsignedInteger,
+  SubSequence : Sequence,
+  Element == SubSequence.Element
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + Real +

    +
    +
    +

    A floating-point type that supports elementary functions and a selection of +special functions.

    + +

    The Real protocol provides a suitable basis for writing functions that +work on any floating-point type that supports the required functions.

    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public protocol Real : Math, FloatingPoint
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + Math +

    +
    +
    +

    A signed numeric type that supports elementary functions.

    + +

    The Math protocol provides a suitable basis for writing functions that +work on any real or complex floating-point type that supports the required +functions.

    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public protocol Math : SignedNumeric
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/Math.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/Math.html new file mode 100644 index 0000000..72b560e --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/Math.html @@ -0,0 +1,1636 @@ + + + + + + Math Protocol Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Math

+
+
+ 
public protocol Math : SignedNumeric
+ +
+
+

A signed numeric type that supports elementary functions.

+ +

The Math protocol provides a suitable basis for writing functions that +work on any real or complex floating-point type that supports the required +functions.

+ +
+
+
+
+
+ Topics +
+ + +
+
+
+
+
+
+
    +
  • +
    + + +

    + pi +

    +
    +
    +

    The mathematical constant pi (π).

    + +

    This value should be rounded toward zero to keep user computations with +angles from inadvertently ending up in the wrong quadrant. A type that +conforms to the Math protocol provides the value for pi at its best +possible precision.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    static var pi: Self
    + +
    +
    +
    • +
  • +
    + + +

    + e + Default implementation +

    +
    +
    +

    The mathematical constant e, or Euler’s number.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    static var e: Self
    + +
    +
    +
    • +
  • +
    + + +

    + phi + Default implementation +

    +
    +
    +

    The mathematical constant phi (φ), or golden ratio.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    static var phi: Self
    + +
    +
    +
    • +
  • +
    + + +

    + /(_:_:) +

    +
    +
    +

    Returns the quotient obtained by dividing the first value by the second, +rounded to a representable value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    static func / (lhs: Self, rhs: Self) -> Self
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    +

    The value to divide.

    +
    +
    rhs
    +
    +

    The value by which to divide lhs.

    +
    +
    +
    +
    • +
  • +
    + + +

    + /=(_:_:) +

    +
    +
    +

    Divides the left-hand side by the right-hand side and stores the quotient +in the left-hand side, rounded to a representable value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    static func /= (lhs: inout Self, rhs: Self)
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    +

    The value to divide.

    +
    +
    rhs
    +
    +

    The value by which to divide lhs.

    +
    +
    +
    +
    • +
  • +
    + + +

    + pow(_:_:) +

    +
    +
    +

    Returns the result of raising base to the power of exponent, rounded +to a representable value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    static func pow(_ base: Self, _ exponent: Self) -> Self
    + +
    +
    +
    +
    Parameters
    +
    +
    base
    +
    +

    The base to be raised to the power of exponent.

    +
    +
    exponent
    +
    +

    The exponent by which to raise base.

    +
    +
    +
    +
    • +
  • +
    + + +

    + naturalExponential() +

    +
    +
    +

    Returns the natural exponential of the value, rounded to a representable +value.

    + +

    The natural exponential of a value x is e (2.7182818…) raised to the +power of x.

    +
    +

    See also

    + exp(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func naturalExponential() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + binaryExponential() + Default implementation +

    +
    +
    +

    Returns the binary exponential of the value, rounded to a representable +value.

    + +

    The binary exponential of a value x is 2 raised to the power of x.

    +
    +

    See also

    + exp2(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func binaryExponential() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + commonExponential() + Default implementation +

    +
    +
    +

    Returns the common exponential of the value, rounded to a representable +value.

    + +

    The common exponential of a value x is 10 raised to the power of x.

    +
    +

    See also

    + exp10(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func commonExponential() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + naturalExponentialMinusOne() + Default implementation +

    +
    +
    +

    Returns the result of subtracting one from the natural exponential of the +value, rounded to a representable value.

    + +

    The natural exponential of a value x is e (2.7182818…) raised to the +power of x.

    + +

    This function is more accurate than x.naturalExponential() - 1 for +values of x close to zero.

    +
    +

    See also

    + expm1(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func naturalExponentialMinusOne() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + naturalLogarithm() +

    +
    +
    +

    Returns the natural (base e) logarithm of the value, rounded to a +representable value.

    +
    +

    See also

    + log(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func naturalLogarithm() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + binaryLogarithm() + Default implementation +

    +
    +
    +

    Returns the binary (base 2) logarithm of the value, rounded to a +representable value.

    +
    +

    See also

    + log2(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func binaryLogarithm() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + commonLogarithm() + Default implementation +

    +
    +
    +

    Returns the common (base 10) logarithm of the value, rounded to a +representable value.

    +
    +

    See also

    + log10(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func commonLogarithm() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + naturalLogarithmOnePlus() + Default implementation +

    +
    +
    +

    Returns the natural (base e) logarithm of the result of adding one to +the value, rounded to a representable value.

    +
    +

    See also

    + log1p(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func naturalLogarithmOnePlus() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + squareRoot() +

    +
    +
    +

    Returns the square root of the value, rounded to a representable value.

    +
    +

    See also

    + sqrt(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func squareRoot() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + cubeRoot() +

    +
    +
    +

    Returns the cube root of the value, rounded to a representable value.

    +
    +

    See also

    + cbrt(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func cubeRoot() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + sine() +

    +
    +
    +

    Returns the sine of the value (given in radians), rounded to a +representable value.

    +
    +

    See also

    + sin(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func sine() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + cosine() +

    +
    +
    +

    Returns the cosine of the value (given in radians), rounded to a +representable value.

    +
    +

    See also

    + cos(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func cosine() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + tangent() + Default implementation +

    +
    +
    +

    Returns the tangent of the value (given in radians), rounded to a +representable value.

    +
    +

    See also

    + tan(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func tangent() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + inverseSine() +

    +
    +
    +

    Returns the principal value of the inverse sine of the value, rounded to a +representable value.

    +
    +

    See also

    + asin(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func inverseSine() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + inverseCosine() +

    +
    +
    +

    Returns the principal value of the inverse cosine of the value, rounded to +a representable value.

    +
    +

    See also

    + acos(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func inverseCosine() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + inverseTangent() +

    +
    +
    +

    Returns the principal value of the inverse tangent of the value, rounded +to a representable value.

    +
    +

    See also

    + atan(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func inverseTangent() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicSine() +

    +
    +
    +

    Returns the hyperbolic sine of the value, rounded to a representable +value.

    +
    +

    See also

    + sinh(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func hyperbolicSine() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicCosine() +

    +
    +
    +

    Returns the hyperbolic cosine of the value, rounded to a representable +value.

    +
    +

    See also

    + cosh(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func hyperbolicCosine() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicTangent() + Default implementation +

    +
    +
    +

    Returns the hyperbolic tangent of the value, rounded to a representable +value.

    +
    +

    See also

    + tanh(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func hyperbolicTangent() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicSine() +

    +
    +
    +

    Returns the principal value of the inverse hyperbolic sine of the value, +rounded to a representable value.

    +
    +

    See also

    + asinh(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func inverseHyperbolicSine() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicCosine() +

    +
    +
    +

    Returns the principal value of the inverse hyperbolic cosine of the value, +rounded to a representable value.

    +
    +

    See also

    + acosh(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func inverseHyperbolicCosine() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicTangent() +

    +
    +
    +

    Returns the principal value of the inverse hyperbolic tangent of the +value, rounded to a representable value.

    +
    +

    See also

    + atanh(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func inverseHyperbolicTangent() -> Self
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + exp(_:) + Extension method +

    +
    +
    +

    Returns the natural exponential of x, rounded to a representable value.

    + +

    The natural exponential of a value x is e (2.7182818…) raised to the +power of x.

    +
    +

    See also

    + naturalExponential() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func exp(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + exp2(_:) + Extension method +

    +
    +
    +

    Returns the binary exponential of x, rounded to a representable value.

    + +

    The binary exponential of a value x is 2 raised to the power of x.

    +
    +

    See also

    + binaryExponential() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func exp2(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + exp10(_:) + Extension method +

    +
    +
    +

    Returns the common exponential of x, rounded to a representable value.

    + +

    The common exponential of a value x is 10 raised to the power of x.

    +
    +

    See also

    + commonExponential() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func exp10(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + expm1(_:) + Extension method +

    +
    +
    +

    Returns the result of subtracting one from the natural exponential of x, +rounded to a representable value.

    + +

    The natural exponential of a value x is e (2.7182818…) raised to the +power of x.

    + +

    This function is more accurate than .exp(x) - 1 for values of x close +to zero.

    +
    +

    See also

    + naturalExponentialMinusOne() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func expm1(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + log(_:) + Extension method +

    +
    +
    +

    Returns the natural (base e) logarithm of x, rounded to a +representable value.

    +
    +

    See also

    + naturalLogarithm() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func log(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + log2(_:) + Extension method +

    +
    +
    +

    Returns the binary (base 2) logarithm of x, rounded to a representable +value.

    +
    +

    See also

    + binaryLogarithm() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func log2(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + log10(_:) + Extension method +

    +
    +
    +

    Returns the common (base 10) logarithm of x, rounded to a representable +value.

    +
    +

    See also

    + commonLogarithm() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func log10(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + log1p(_:) + Extension method +

    +
    +
    +

    Returns the natural (base e) logarithm of the result of adding one to +x, rounded to a representable value.

    +
    +

    See also

    + naturalLogarithmOnePlus() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func log1p(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + sqrt(_:) + Extension method +

    +
    +
    +

    Returns the square root of x, rounded to a representable value.

    +
    +

    See also

    + squareRoot() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func sqrt(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + cbrt(_:) + Extension method +

    +
    +
    +

    Returns the cube root of x, rounded to a representable value.

    +
    +

    See also

    + cubeRoot() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func cbrt(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + sin(_:) + Extension method +

    +
    +
    +

    Returns the sine of x (given in radians), rounded to a representable +value.

    +
    +

    See also

    + sine() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func sin(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + cos(_:) + Extension method +

    +
    +
    +

    Returns the cosine of x (given in radians), rounded to a representable +value.

    +
    +

    See also

    + cosine() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func cos(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + tan(_:) + Extension method +

    +
    +
    +

    Returns the tangent of x (given in radians), rounded to a representable +value.

    +
    +

    See also

    + tangent() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func tan(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + asin(_:) + Extension method +

    +
    +
    +

    Returns the principal value of the inverse sine of x, rounded to a +representable value.

    +
    +

    See also

    + inverseSine() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func asin(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + acos(_:) + Extension method +

    +
    +
    +

    Returns the principal value of the inverse cosine of x, rounded to a +representable value.

    +
    +

    See also

    + inverseCosine() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func acos(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + atan(_:) + Extension method +

    +
    +
    +

    Returns the principal value of the inverse tangent of x, rounded to a +representable value.

    +
    +

    See also

    + inverseTangent() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func atan(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + sinh(_:) + Extension method +

    +
    +
    +

    Returns the hyperbolic sine of x, rounded to a representable value.

    +
    +

    See also

    + hyperbolicSine() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func sinh(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + cosh(_:) + Extension method +

    +
    +
    +

    Returns the hyperbolic cosine of x, rounded to a representable value.

    +
    +

    See also

    + hyperbolicCosine() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func cosh(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + tanh(_:) + Extension method +

    +
    +
    +

    Returns the hyperbolic tangent of x, rounded to a representable value.

    +
    +

    See also

    + hyperbolicTangent() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func tanh(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + asinh(_:) + Extension method +

    +
    +
    +

    Returns the principal value of the inverse hyperbolic sine of x, rounded +to a representable value.

    +
    +

    See also

    + inverseHyperbolicSine() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func asinh(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + acosh(_:) + Extension method +

    +
    +
    +

    Returns the principal value of the inverse hyperbolic cosine of x, +rounded to a representable value.

    +
    +

    See also

    + inverseHyperbolicCosine() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func acosh(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + atanh(_:) + Extension method +

    +
    +
    +

    Returns the principal value of the inverse hyperbolic tangent of x, +rounded to a representable value.

    +
    +

    See also

    + inverseHyperbolicTangent() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func atanh(_ x: Self) -> Self
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/PRNG.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/PRNG.html new file mode 100644 index 0000000..f796693 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/PRNG.html @@ -0,0 +1,824 @@ + + + + + + PRNG Protocol Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

PRNG

+
+
+ 
public protocol PRNG : class, IteratorProtocol, Sequence
+where Element : FixedWidthInteger & UnsignedInteger,
+  SubSequence : Sequence,
+  Element == SubSequence.Element
+ +
+
+

A pseudo-random number generator (PRNG).

+ +

Reference types that conform to PRNG 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.

+

Considerations for Conforming Types

+ +

For clarity to end users, custom PRNGs may be implemented in an extension to +Random. For instance, the xoroshiro128+ algorithm is implemented in a +final class named Random.Xoroshiro.

+ +

The static methods _entropy(_:) and _entropy(_:count:) return +cryptographically secure random bytes that may be useful for seeding your +custom PRNG. However, these methods may return nil if the requested number +of random bytes is not available, and they are not recommended as a routine +source of random data.

+

Adding Other Probability Distributions

+ +

Many built-in protocol extension methods make use of the primitive, +overloaded method _random(_:bitCount:). You may wish to use the same +method in new protocol extension methods that return pseudo-random +values from other probability distributions.

+ +

The method _random(_:bitCount:) generates uniformly distributed binary +floating-point values in the half-open range [0, 1) with a precision of +either bitCount 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 ** x), where ** is the +exponentiation operator and x is the lesser of bitCount and the bit +width of the integer type.

+ +

For end users, however, the recommended spelling for a uniformly distributed +numeric value is uniform(); that method is overloaded to permit custom +minimum and maximum values for the uniform distribution.

+ +
+
+
+
+
+ Topics +
+ + + + +
+
+
+
+
+
+
    +
  • +
    + + +

    + State +

    +
    +
    +

    A type that can represent the internal state of the pseudo-random number +generator.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    associatedtype State
    + +
    +
    +
    • +
  • +
    + + +

    + state +

    +
    +
    +

    The internal state of the pseudo-random number generator.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    var state: State
    + +
    +
    +
    • +
  • +
    + + +

    + init(state:) +

    +
    +
    +

    Creates a pseudo-random number generator with the given internal state.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    init(state: State)
    + +
    +
    +
    +
    Parameters
    +
    +
    state
    +
    +

    The value to be used as the generator’s internal state.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init() +

    +
    +
    +

    Creates a pseudo-random number generator with an internal state seeded +using cryptographically secure random bytes.

    + +

    If cryptographically secure random bytes are unavailable, the result is +nil.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    init?()
    + +
    +
    +
    • +
  • +
    + + +

    + max + Default implementation +

    +
    +
    +

    The maximum value that may be generated by the pseudo-random number +generator.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    static var max: Element
    + +
    +
    +
    • +
  • +
    + + +

    + min + Default implementation +

    +
    +
    +

    The minimum value that may be generated by the pseudo-random number +generator.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    static var min: Element
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + _randomBitWidth + Extension method +

    +
    +
    +

    The number of pseudo-random bits available from a value generated by the +pseudo-random number generator.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var _randomBitWidth: Int
    + +
    +
    +
    • +
  • +
    + + +

    + _entropy(_:) + Extension method +

    +
    +
    +

    Returns a value filled with data from a source of cryptographically secure +random bytes, or nil if a sufficient number of cryptographically secure +random bytes is unavailable.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func _entropy<
+    T : FixedWidthInteger & UnsignedInteger
+  >(_: T.Type = T.self) -> T?
    + +
    +
    +
    • +
  • +
    + + +

    + _entropy(_:count:) + Extension method +

    +
    +
    +

    Returns an array of count values filled with data from a source of +cryptographically secure random bytes, or nil if a sufficient number of +cryptographically secure random bytes is unavailable.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func _entropy<
+    T : FixedWidthInteger & UnsignedInteger
+  >(_: T.Type = T.self, count: Int) -> [T]?
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + _random(_:bitCount:) + Extension method +

    +
    +
    +

    Generates a pseudo-random unsigned integer of type T in the range from 0 +to 2 ** min(bitCount, T.bitWidth) (exclusive), where ** is the +exponentiation operator.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func _random<T : FixedWidthInteger & UnsignedInteger>(
+    _: T.Type = T.self, bitCount: Int = T.bitWidth
+  ) -> T
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:a:b:) + Extension method +

    +
    +
    +

    Generates a pseudo-random unsigned integer of type T in the range from +a through b (inclusive) from the discrete uniform distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : FixedWidthInteger & UnsignedInteger>(
+    _: T.Type = T.self, a: T, b: T
+  ) -> T
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:) + Extension method +

    +
    +
    +

    Generates a pseudo-random unsigned integer of type T in the range from +T.min through T.max (inclusive) from the discrete uniform +distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : FixedWidthInteger & UnsignedInteger>(
+    _: T.Type = T.self
+  ) -> T
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:a:b:count:) + Extension method +

    +
    +
    +

    Generates a sequence of count pseudo-random unsigned integers of type +T in the range from a through b (inclusive) from the discrete +uniform distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : FixedWidthInteger & UnsignedInteger>(
+    _: T.Type = T.self, a: T, b: T, count: Int
+  ) -> UnfoldSequence<T, Int>
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:count:) + Extension method +

    +
    +
    +

    Generates a sequence of count pseudo-random unsigned integers of type +T in the range from T.min through T.max (inclusive) from the +discrete uniform distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : FixedWidthInteger & UnsignedInteger>(
+    _: T.Type = T.self, count: Int
+  ) -> UnfoldSequence<T, Int>
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:a:b:) + Extension method +

    +
    +
    +

    Generates a pseudo-random signed integer of type T in the range from a +through b (inclusive) from the discrete uniform distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : FixedWidthInteger & SignedInteger>(
+    _: T.Type = T.self, a: T, b: T
+  ) -> T where T.Magnitude : FixedWidthInteger & UnsignedInteger
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:) + Extension method +

    +
    +
    +

    Generates a pseudo-random signed integer of type T in the range from +T.min through T.max (inclusive) from the discrete uniform +distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : FixedWidthInteger & SignedInteger>(
+    _: T.Type = T.self
+  ) -> T where T.Magnitude : FixedWidthInteger & UnsignedInteger
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:a:b:count:) + Extension method +

    +
    +
    +

    Generates a sequence of count pseudo-random signed integers of type T +in the range from a through b (inclusive) from the discrete uniform +distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : FixedWidthInteger & SignedInteger>(
+    _: T.Type = T.self, a: T, b: T, count: Int
+  ) -> UnfoldSequence<T, Int>
+  where T.Magnitude : FixedWidthInteger & UnsignedInteger
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:count:) + Extension method +

    +
    +
    +

    Generates a sequence of count pseudo-random signed integers of type T +in the range from T.min through T.max (inclusive) from the discrete +uniform distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : FixedWidthInteger & SignedInteger>(
+    _: T.Type = T.self, count: Int
+  ) -> UnfoldSequence<T, Int>
+  where T.Magnitude : FixedWidthInteger & UnsignedInteger
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + _random(_:bitCount:) + Extension method +

    +
    +
    +

    Generates a pseudo-random binary floating-point value of type T in the +range from 0 to 1 (exclusive) with min(bitCount, T.significandBitCount) +bits of precision.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func _random<T : BinaryFloatingPoint>(
+    _: T.Type = T.self, bitCount: Int = T.significandBitCount
+  ) -> T
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:a:b:) + Extension method +

    +
    +
    +

    Generates a pseudo-random binary floating-point value of type T in the +range from a to b (exclusive) from the uniform distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : BinaryFloatingPoint>(
+    _: T.Type = T.self, a: T, b: T
+  ) -> T
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:) + Extension method +

    +
    +
    +

    Generates a pseudo-random binary floating-point value of type T in the +range from 0 to 1 (exclusive) from the uniform distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : BinaryFloatingPoint>(_: T.Type = T.self) -> T
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:a:b:count:) + Extension method +

    +
    +
    +

    Generates a sequence of count pseudo-random binary floating-point values +of type T in the range from a to b (exclusive) from the uniform +distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : BinaryFloatingPoint>(
+    _: T.Type = T.self, a: T, b: T, count: Int
+  ) -> UnfoldSequence<T, Int>
    + +
    +
    +
    • +
  • +
    + + +

    + uniform(_:count:) + Extension method +

    +
    +
    +

    Generates a sequence of count pseudo-random binary floating-point values +of type T in the range from 0 to 1 (exclusive) from the uniform +distribution.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func uniform<T : BinaryFloatingPoint>(
+    _: T.Type = T.self, count: Int
+  ) -> UnfoldSequence<T, Int>
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/Real.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/Real.html new file mode 100644 index 0000000..16db41f --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Protocols/Real.html @@ -0,0 +1,561 @@ + + + + + + Real Protocol Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Real

+
+
+ 
public protocol Real : Math, FloatingPoint
+ +
+
+

A floating-point type that supports elementary functions and a selection of +special functions.

+ +

The Real protocol provides a suitable basis for writing functions that +work on any floating-point type that supports the required functions.

+ +
+
+
+
+
+ Topics +
+ + + +
+
+
+
+
+
+
    +
  • +
    + + +

    + hypot(_:_:) + Default implementation +

    +
    +
    +

    Returns the hypotenuse of a right-angle triangle with legs (catheti) of +length x and y, preventing avoidable arithmetic overflow and +underflow. The return value is the square root of the sum of squares of +the arguments.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    static func hypot(_ x: Self, _ y: Self) -> Self
    + +
    +
    +
    +
    Parameters
    +
    +
    x
    +
    +

    The length of one leg (cathetus) of a right-angle triangle.

    +
    +
    y
    +
    +

    The length of the other leg (cathetus) of a right-angle triangle.

    +
    +
    +
    +
    • +
  • +
    + + +

    + inverseTangent(dividingBy:) + Default implementation +

    +
    +
    +

    Returns the inverse tangent of self / other, using the signs of self +and other to determine the quadrant of the computed angle.

    + +

    If self == 0 && other == 0, the return value is still finite.

    +
    +

    See also

    +

    atan2(_:_:)

    + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func inverseTangent(dividingBy other: Self) -> Self
    + +
    +
    +
    +
    Parameters
    +
    +
    other
    +
    +

    The divisor by which to divide self.

    +
    +
    +
    +
    • +
  • +
    + + +

    + error() +

    +
    +
    +

    Returns the value of the error function of self.

    +
    +

    See also

    + erf(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func error() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + complementaryError() +

    +
    +
    +

    Returns the value of the complementary error function of self.

    +
    +

    See also

    + erfc(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func complementaryError() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + gamma() +

    +
    +
    +

    Returns the value of the gamma function of self.

    +
    +

    See also

    + tgamma(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func gamma() -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + logarithmicGamma() +

    +
    +
    +

    Returns the value of the logarithmic gamma function of self.

    +
    +

    See also

    + lgamma(_:) + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    func logarithmicGamma() -> Self
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + cubeRoot() + Extension method +

    +
    +
    +

    Returns the cube root of the value, rounded to a representable value +(default implementation).

    +
    +

    Note

    +

    This method is required by the protocol Math; it is not an +extension method.

    + +
    +
    +

    See also

    +

    cbrt(_:)

    + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func cubeRoot() -> Self
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + atan2(_:_:) + Extension method +

    +
    +
    +

    Returns the inverse tangent of y / x, using the signs of y and x to +determine the quadrant of the computed angle.

    + +

    If x == 0 && y == 0, the return value is still finite.

    +
    +

    See also

    +

    inverseTangent(dividingBy:)

    + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func atan2(_ y: Self, _ x: Self) -> Self
    + +
    +
    +
    +
    Parameters
    +
    +
    y
    +
    +

    The value to divide.

    +
    +
    x
    +
    +

    The divisor by which to divide y.

    +
    +
    +
    +
    • +
  • +
    + + +

    + erf(_:) + Extension method +

    +
    +
    +

    Returns the value of the error function of x.

    +
    +

    See also

    + error() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func erf(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + erfc(_:) + Extension method +

    +
    +
    +

    Returns the value of the complementary error function of x.

    +
    +

    See also

    + complementaryError() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func erfc(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + tgamma(_:) + Extension method +

    +
    +
    +

    Returns the value of the gamma function of x.

    +
    +

    See also

    + gamma() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func tgamma(_ x: Self) -> Self
    + +
    +
    +
    • +
  • +
    + + +

    + lgamma(_:) + Extension method +

    +
    +
    +

    Returns the value of the logarithmic gamma function of x.

    +
    +

    See also

    + logarithmicGamma() + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func lgamma(_ x: Self) -> Self
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs.html new file mode 100644 index 0000000..1bcfbdf --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs.html @@ -0,0 +1,304 @@ + + + + + + Structs Reference + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Structs

+

The following structs are available globally.

+ +
+
+
+
+
+ Topics +
+ + +
+
+
+
+
+
+
    +
  • +
    + + +

    + Complex +

    +
    +
    +

    A type to represent a complex value in Cartesian form.

    +
    +

    Note

    + Complex64 is a type alias for Complex<Float> and Complex128 is +a type alias for Complex<Double>. + +
    + +

    Create new instances of Complex<T> using integer or floating-point +literals and the imaginary unit Complex<T>.i. For example:

    +
    let x = 2 + 4 * .i // `x` is of type `Complex<Double>`
+let y = 3.5 + 7 * .i // `y` is of type `Complex<Double>`
+
+let z: Complex64 = .e + .pi * .i // `z` is of type `Complex<Float>`
+
    +

    Additional Considerations

    + +

    Floating-point types have special values that represent infinity or NaN +(not a number). Complex functions in different languages may return +different results when working with special values.

    + +

    Many complex functions have branch cuts, 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.

    + +

    Implementations in Complex<T> adhere to the C standard (Annex G) as +closely as possible with respect to special values and branch cuts.

    + +

    To users unfamiliar with complex functions, the principal value returned by +some complex functions may be unexpected. For example, +Double.cbrt(-8) == -2, which is the real root, while +Complex.cbrt(-8) == 2 * Complex.exp(.i * .pi / 3), which is the +principal root.

    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public struct Complex<T : Real> : Codable
+where T : Codable & _ExpressibleByBuiltinFloatLiteral
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + Rational +

    +
    +
    +

    A type to represent a rational value.

    +
    +

    Note

    + Ratio is a type alias for Rational<Int>. + +
    + +

    Create new instances of Rational<T> by using integer literals and the +division (/) operator. For example:

    +
    let x = 1 / 3 as Ratio // `x` is of type `Rational<Int>`
+let y = 2 as Ratio // `y` is of type `Rational<Int>`
+let z: Ratio = 2 / 3 // `z` is also of type `Rational<Int>`
+
+print(x + y + z) // Prints "3"
+
    + +

    You can create an unreduced fraction by using the initializer +Rational<T>.init(numerator:denominator:). For example:

    +
    let a = Ratio(numerator: 3, denominator: 3)
+print(a) // Prints "3/3"
+
    + +

    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 canonicalized is the canonical +form of any value.

    +

    Additional Considerations

    +

    Special Values

    + +

    Rational<T> 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 (not a number).

    + +

    As with floating-point types, Rational<T>.infinity compares greater than +every finite value and negative infinity, and -Rational<T>.infinity +compares less than every finite value and positive infinity. Infinite values +of the same sign compare equal to each other.

    + +

    As with floating-point types, Rational<T>.nan does not compare equal to +any other value, including another NaN. Use the property isNaN to test if +a value is NaN. Rational<T> arithmetic operations are intended to +propagate NaN in the same manner as analogous floating-point operations.

    +

    Numerical Limits

    + +

    When a value of type Rational<T> 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, -1 / T.min cannot be +represented as a value of type Rational<T> because abs(T.min) cannot be +represented as a value of type T.

    + +

    To ensure that every representable value of type Rational<T> has a +representable magnitude and reciprocal of the same type, an overflow trap +occurs when the division (/) operator is used to create a value of type +Rational<T> with numerator T.min.

    + + See more… +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public struct Rational<T : SignedInteger> : Codable
+where T : Codable & _ExpressibleByBuiltinIntegerLiteral,
+  T.Magnitude : UnsignedInteger,
+  T.Magnitude.Magnitude == T.Magnitude
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs/Complex.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs/Complex.html new file mode 100644 index 0000000..f949e59 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs/Complex.html @@ -0,0 +1,1822 @@ + + + + + + Complex Struct Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Complex

+
+
+ 
public struct Complex<T : Real> : Codable
+where T : Codable & _ExpressibleByBuiltinFloatLiteral
+ +
+
+

A type to represent a complex value in Cartesian form.

+
+

Note

+ Complex64 is a type alias for Complex<Float> and Complex128 is +a type alias for Complex<Double>. + +
+ +

Create new instances of Complex<T> using integer or floating-point +literals and the imaginary unit Complex<T>.i. For example:

+
let x = 2 + 4 * .i // `x` is of type `Complex<Double>`
+let y = 3.5 + 7 * .i // `y` is of type `Complex<Double>`
+
+let z: Complex64 = .e + .pi * .i // `z` is of type `Complex<Float>`
+
+

Additional Considerations

+ +

Floating-point types have special values that represent infinity or NaN +(not a number). Complex functions in different languages may return +different results when working with special values.

+ +

Many complex functions have branch cuts, 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.

+ +

Implementations in Complex<T> adhere to the C standard (Annex G) as +closely as possible with respect to special values and branch cuts.

+ +

To users unfamiliar with complex functions, the principal value returned by +some complex functions may be unexpected. For example, +Double.cbrt(-8) == -2, which is the real root, while +Complex.cbrt(-8) == 2 * Complex.exp(.i * .pi / 3), which is the +principal root.

+ +
+
+
+
+
+ Topics +
+

Stored Properties

+ +

Initializers

+ +

Initializers (Constrained)

+ +

Static Properties

+
    +
  • i
    • +
+

Computed Properties

+ +

Methods

+ +

ExpressibleByFloatLiteral

+ +

ExpressibleByIntegerLiteral

+ +

CustomStringConvertible

+ +

Equatable

+ +

Hashable

+ +

Numeric

+ +

SignedNumeric

+ +

Math

+ +
+
+
+
+
+
+
+ + +

Stored Properties

+
+
    +
  • +
    + + +

    + real +

    +
    +
    +

    The real component of the complex value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var real: T
    + +
    +
    +
    • +
  • +
    + + +

    + imaginary +

    +
    +
    +

    The imaginary component of the complex value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var imaginary: T
    + +
    +
    +
    • +
+
+
+
+ + +

Initializers

+
+
    +
  • +
    + + +

    + init(real:imaginary:) +

    +
    +
    +

    Creates a new value from the given real and imaginary components.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(real: T = 0, imaginary: T = 0)
    + +
    +
    +
    +
    Parameters
    +
    +
    real
    +
    +

    The new value’s real component.

    +
    +
    imaginary
    +
    +

    The new value’s imaginary component.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init(r:theta:) +

    +
    +
    +

    Creates a new value from the given polar coordinates (r, theta).

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(r: T, theta: T)
    + +
    +
    +
    +
    Parameters
    +
    +
    r
    +
    +

    The new value’s radial coordinate.

    +
    +
    theta
    +
    +

    The new value’s angular coordinate.

    +
    +
    +
    +
    • +
+
+
+
+ + +

Initializers (Constrained)

+
+
    +
  • +
    + + +

    + init(_:) +

    +
    +
    +

    Creates a new value from the given real component, rounded to the closest +possible representation.

    +
    +

    Note

    +

    This initializer creates only instances of +Complex<T> where T : BinaryFloatingPoint.

    + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(_ real: Float)
    + +
    +
    +
    +
    Parameters
    +
    +
    real
    +
    +

    The value to convert to a real component of type T.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init(_:) +

    +
    +
    +

    Creates a new value from the given real component, rounded to the closest +possible representation.

    +
    +

    Note

    +

    This initializer creates only instances of +Complex<T> where T : BinaryFloatingPoint.

    + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(_ real: Double)
    + +
    +
    +
    +
    Parameters
    +
    +
    real
    +
    +

    The value to convert to a real component of type T.

    +
    +
    +
    +
    • +
+
+
+
+ + +

Static Properties

+
+
    +
  • +
    + + +

    + i +

    +
    +
    +

    The imaginary unit i.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var i: Complex
    + +
    +
    +
    • +
+
+
+
+ + +

Computed Properties

+
+
    +
  • +
    + + +

    + argument +

    +
    +
    +

    The principal argument (phase angle) of this value.

    + +

    Special cases are handled as if calling T.atan2(imaginary, real). The +result lies in the range [-π, π].

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var argument: T
    + +
    +
    +
    • +
  • +
    + + +

    + isCanonical +

    +
    +
    +

    A Boolean value indicating whether the instance’s representation is in +canonical form.

    + +

    A complex value is represented in canonical form if the its real and +imaginary components are both represented in canonical form, as defined in +the IEEE 754 specification. Every Float or Double value is +canonical.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public struct Complex<T : Real> : Codable
+where T : Codable & _ExpressibleByBuiltinFloatLiteral
    + +
    +
    +
    • +
  • +
    + + +

    + isFinite +

    +
    +
    +

    A Boolean value indicating whether the instance is finite.

    + +

    A complex value is finite if its real and imaginary components are both +finite. A component is finite if it is not infinity or NaN.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isFinite: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + isInfinite +

    +
    +
    +

    A Boolean value indicating whether the instance is infinite.

    + +

    A complex value is infinite if at least one of its components (real or +imaginary) is infinite, even if the other component is NaN.

    + +

    Note that isFinite and isInfinite do not form a dichotomy because NaN +is neither finite nor infinite.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isInfinite: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + isNaN +

    +
    +
    +

    A Boolean value indicating whether the instance is NaN (not a number).

    + +

    A complex value is NaN if at least one of its components (real or +imaginary) is NaN and the other component is not infinite.

    + +

    Because NaN is not equal to any value, including NaN, use this property +instead of the equal-to operator (==) or not-equal-to operator (!=) to +test whether a value is or is not NaN.

    + +

    This property is true for both quiet and signaling NaNs.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isNaN: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + isSignalingNaN +

    +
    +
    +

    A Boolean value indicating whether the instance is a signaling NaN.

    + +

    A complex value is a signaling NaN if at least one of its components (real +or imaginary) is a signaling NaN and the other component is not infinite.

    + +

    Signaling NaNs typically raise the Invalid flag when used in general +computing operations.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isSignalingNaN: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + isZero +

    +
    +
    +

    A Boolean value indicating whether the instance is equal to zero.

    + +

    A complex value is equal to zero if its real and imaginary components both +represent either -0.0 or +0.0.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isZero: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + magnitude +

    +
    +
    +

    The magnitude (modulus, absolute value) of this value.

    + +

    Special cases are handled as if calling T.hypot(real, imaginary).

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var magnitude: T
    + +
    +
    +
    • +
  • +
    + + +

    + squaredMagnitude +

    +
    +
    +

    The squared magnitude (field norm, absolute square) of this value.

    + +

    This is less costly to compute than magnitude and, in some cases, can be +used in its place. For example, if a.magnitude > b.magnitude, then +a.squaredMagnitude > b.squaredMagnitude.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var squaredMagnitude: T
    + +
    +
    +
    • +
+
+
+
+ + +

Methods

+
+
    +
  • +
    + + +

    + conjugate() +

    +
    +
    +

    Returns the complex conjugate of this value, obtained by reversing the +sign of the imaginary component.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func conjugate() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + projection() +

    +
    +
    +

    Returns the projection of this value onto the Riemann sphere.

    + +

    For most values z, z.projection() == z. The projection of any complex +infinity is positive real infinity. The sign of the imaginary component is +preserved in the sign of zero; that is, +z.projection().imaginary.sign == z.imaginary.sign.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func projection() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + reciprocal() +

    +
    +
    +

    Returns the reciprocal (multiplicative inverse) of this value, or NaN +(not a number) if this value is infinite, NaN, or zero.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func reciprocal() -> Complex
    + +
    +
    +
    • +
+
+
+
+ + +

ExpressibleByFloatLiteral

+
+
    +
  • +
    + + +

    + init(floatLiteral:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(floatLiteral value: T)
    + +
    +
    +
    +
    Parameters
    +
    +
    value
    +
    + +
    +
    +
    +
    • +
+
+
+
+ + +

ExpressibleByIntegerLiteral

+
+
    +
  • +
    + + +

    + init(integerLiteral:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(integerLiteral value: Int)
    + +
    +
    +
    +
    Parameters
    +
    +
    value
    +
    + +
    +
    +
    +
    • +
+
+
+
+ + +

CustomStringConvertible

+
+
    +
  • +
    + + +

    + description +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var description: String
    + +
    +
    +
    • +
+
+
+
+ + +

Equatable

+
+
    +
  • +
    + + +

    + ==(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func == (lhs: Complex, rhs: Complex) -> Bool
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
+
+
+
+ + +

Hashable

+
+
    +
  • +
    + + +

    + hashValue +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var hashValue: Int
    + +
    +
    +
    • +
+
+
+
+ + +

Numeric

+
+
    +
  • +
    + + +

    + init(exactly:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init?<U>(exactly source: U) where U : BinaryInteger
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + +(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func + (lhs: Complex, rhs: Complex) -> Complex
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + +=(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func += (lhs: inout Complex, rhs: Complex)
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + -(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func - (lhs: Complex, rhs: Complex) -> Complex
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + -=(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func -= (lhs: inout Complex, rhs: Complex)
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + *(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func * (lhs: Complex, rhs: Complex) -> Complex
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + *=(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func *= (lhs: inout Complex, rhs: Complex)
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
+
+
+
+ + +

SignedNumeric

+
+
    +
  • +
    + + +

    + -(_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static prefix func - (operand: Complex) -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + negate() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public mutating func negate()
    + +
    +
    +
    • +
+
+
+
+ + +

Math

+
+
    +
  • +
    + + +

    + pi +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var pi: Complex
    + +
    +
    +
    • +
  • +
    + + +

    + e +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var e: Complex
    + +
    +
    +
    • +
  • +
    + + +

    + phi +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var phi: Complex
    + +
    +
    +
    • +
  • +
    + + +

    + /(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func / (lhs: Complex, rhs: Complex) -> Complex
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + /=(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func /= (lhs: inout Complex, rhs: Complex)
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + pow(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func pow(_ base: Complex, _ exponent: Complex) -> Complex
    + +
    +
    +
    +
    Parameters
    +
    +
    base
    +
    + +
    +
    exponent
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + naturalExponential() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func naturalExponential() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + naturalLogarithm() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func naturalLogarithm() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + commonLogarithm() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func commonLogarithm() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + squareRoot() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func squareRoot() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + cubeRoot() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func cubeRoot() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + sine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func sine() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + cosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func cosine() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + tangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func tangent() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + inverseSine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseSine() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + inverseCosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseCosine() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + inverseTangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseTangent() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicSine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func hyperbolicSine() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicCosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func hyperbolicCosine() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + hyperbolicTangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func hyperbolicTangent() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicSine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseHyperbolicSine() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicCosine() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseHyperbolicCosine() -> Complex
    + +
    +
    +
    • +
  • +
    + + +

    + inverseHyperbolicTangent() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func inverseHyperbolicTangent() -> Complex
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs/Rational.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs/Rational.html new file mode 100644 index 0000000..286b557 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Structs/Rational.html @@ -0,0 +1,1634 @@ + + + + + + Rational Struct Reference + + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Rational

+
+
+ 
public struct Rational<T : SignedInteger> : Codable
+where T : Codable & _ExpressibleByBuiltinIntegerLiteral,
+  T.Magnitude : UnsignedInteger,
+  T.Magnitude.Magnitude == T.Magnitude
+ +
+
+

A type to represent a rational value.

+
+

Note

+ Ratio is a type alias for Rational<Int>. + +
+ +

Create new instances of Rational<T> by using integer literals and the +division (/) operator. For example:

+
let x = 1 / 3 as Ratio // `x` is of type `Rational<Int>`
+let y = 2 as Ratio // `y` is of type `Rational<Int>`
+let z: Ratio = 2 / 3 // `z` is also of type `Rational<Int>`
+
+print(x + y + z) // Prints "3"
+
+ +

You can create an unreduced fraction by using the initializer +Rational<T>.init(numerator:denominator:). For example:

+
let a = Ratio(numerator: 3, denominator: 3)
+print(a) // Prints "3/3"
+
+ +

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 canonicalized is the canonical +form of any value.

+

Additional Considerations

+

Special Values

+ +

Rational<T> 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 (not a number).

+ +

As with floating-point types, Rational<T>.infinity compares greater than +every finite value and negative infinity, and -Rational<T>.infinity +compares less than every finite value and positive infinity. Infinite values +of the same sign compare equal to each other.

+ +

As with floating-point types, Rational<T>.nan does not compare equal to +any other value, including another NaN. Use the property isNaN to test if +a value is NaN. Rational<T> arithmetic operations are intended to +propagate NaN in the same manner as analogous floating-point operations.

+

Numerical Limits

+ +

When a value of type Rational<T> 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, -1 / T.min cannot be +represented as a value of type Rational<T> because abs(T.min) cannot be +represented as a value of type T.

+ +

To ensure that every representable value of type Rational<T> has a +representable magnitude and reciprocal of the same type, an overflow trap +occurs when the division (/) operator is used to create a value of type +Rational<T> with numerator T.min.

+ +
+
+
+
+
+ Topics +
+

Stored Properties

+ +

Initializers

+ +

Initializers (Constrained)

+ +

Static Properties

+ +

Static Methods

+ +

Computed Properties

+ +

Methods

+ +

ExpressibleByIntegerLiteral

+ +

CustomStringConvertible

+ +

Equatable

+ +

Hashable

+ +

Comparable

+ +

Strideable

+ +

Numeric

+ +

SignedNumeric

+ +
+
+
+
+
+
+
+ + +

Stored Properties

+
+
    +
  • +
    + + +

    + numerator +

    +
    +
    +

    The numerator of the rational value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var numerator: T
    + +
    +
    +
    • +
  • +
    + + +

    + denominator +

    +
    +
    +

    The denominator of the rational value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var denominator: T
    + +
    +
    +
    • +
+
+
+
+ + +

Initializers

+
+
    +
  • +
    + + +

    + init(numerator:denominator:) +

    +
    +
    +

    Creates a new value from the given numerator and denominator without +computing its canonical form (i.e., without reducing to lowest terms).

    + +

    To create a value reduced to lowest terms, use the division (/) +operator. For example:

    +
    let x = 3 / 3 as Rational<Int>
+print(x) // Prints "1"
+
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(numerator: T, denominator: T)
    + +
    +
    +
    +
    Parameters
    +
    +
    numerator
    +
    +

    The new value’s numerator.

    +
    +
    denominator
    +
    +

    The new value’s denominator.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init(_:) +

    +
    +
    +

    Creates a new rational value from the given binary integer.

    + +

    If source or its magnitude is not representable as a numerator of type +T, a runtime error may occur.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init<Source : BinaryInteger>(_ source: Source)
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    +

    A binary integer to convert to a rational value.

    +
    +
    +
    +
    • +
  • +
    + + +

    + init(_:) +

    +
    +
    +

    Creates a new rational value from the given binary floating-point value.

    + +

    If source or its magnitude is not representable exactly as a ratio of +two signed integers of type T, a runtime error may occur.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init<Source : BinaryFloatingPoint>(_ source: Source)
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    +

    A binary floating-point value to convert to a rational value.

    +
    +
    +
    +
    • +
+
+
+
+ + +

Initializers (Constrained)

+
+
    +
  • +
    + + +

    + init(exactly:) +

    +
    +
    +

    Creates a new rational value from the given binary floating-point value, +if it can be represented exactly.

    + +

    If source or its magnitude is not representable exactly as a ratio of +two signed integers of type T, the result is nil.

    +
    +

    Note

    +

    This initializer creates only instances of +Rational<T> where T : FixedWidthInteger.

    + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init?<Source : BinaryFloatingPoint>(exactly source: Source)
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    +

    A floating-point value to convert to a rational value.

    +
    +
    +
    +
    • +
+
+
+
+ + +

Static Properties

+
+
    +
  • +
    + + +

    + infinity +

    +
    +
    +

    Positive infinity.

    + +

    Infinity compares greater than all finite numbers and equal to other +(positive) infinite values.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var infinity: Rational
    + +
    +
    +
    • +
  • +
    + + +

    + nan +

    +
    +
    +

    A quiet NaN (not a number).

    + +

    A NaN compares not equal, not greater than, and not less than every value, +including itself. Passing a NaN to an operation generally results in NaN.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static var nan: Rational
    + +
    +
    +
    • +
+
+
+
+ + +

Static Methods

+
+
    +
  • +
    + + +

    + /(_:_:) +

    +
    +
    +

    Returns the quotient obtained by dividing the first value by the second, +trapping in case of arithmetic overflow.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func / (lhs: Rational, rhs: Rational) -> Rational
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    +

    The value to divide.

    +
    +
    rhs
    +
    +

    The value by which to divide lhs.

    +
    +
    +
    +
    • +
  • +
    + + +

    + /=(_:_:) +

    +
    +
    +

    Divides the left-hand side by the right-hand side and stores the quotient +in the left-hand side, trapping in case of arithmetic overflow.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func /= (lhs: inout Rational, rhs: Rational)
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    +

    The value to divide.

    +
    +
    rhs
    +
    +

    The value by which to divide lhs.

    +
    +
    +
    +
    • +
+
+
+
+ + +

Computed Properties

+
+
    +
  • +
    + + +

    + canonical +

    +
    +
    +

    The canonical representation of this value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var canonical: Rational
    + +
    +
    +
    • +
  • +
    + + +

    + isCanonical +

    +
    +
    +

    A Boolean value indicating whether the instance’s representation is in +canonical form.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isCanonical: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + isFinite +

    +
    +
    +

    A Boolean value indicating whether the instance is finite.

    + +

    All values other than NaN and infinity are considered finite.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isFinite: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + isInfinite +

    +
    +
    +

    A Boolean value indicating whether the instance is infinite.

    + +

    Note that isFinite and isInfinite do not form a dichotomy because NaN +is neither finite nor infinite.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isInfinite: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + isNaN +

    +
    +
    +

    A Boolean value indicating whether the instance is NaN (not a number).

    + +

    Because NaN is not equal to any value, including NaN, use this property +instead of the equal-to operator (==) or not-equal-to operator (!=) to +test whether a value is or is not NaN.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isNaN: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + isProper +

    +
    +
    +

    A Boolean value indicating whether the instance is a proper fraction.

    + +

    A fraction is proper if and only if the absolute value of the fraction is +less than 1.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isProper: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + isZero +

    +
    +
    +

    A Boolean value indicating whether the instance is equal to zero.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var isZero: Bool
    + +
    +
    +
    • +
  • +
    + + +

    + magnitude +

    +
    +
    +

    The magnitude (absolute value) of this value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var magnitude: Rational
    + +
    +
    +
    • +
  • +
    + + +

    + mixed +

    +
    +
    +

    The mixed form representing this value.

    + +

    If the value is not finite, the mixed form has zero as its whole part and +the value as its fractional part.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var mixed: (whole: T, fractional: Rational)
    + +
    +
    +
    • +
  • +
    + + +

    + sign +

    +
    +
    +

    The sign of this value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var sign: Sign
    + +
    +
    +
    • +
+
+
+
+ + +

Methods

+
+
    +
  • +
    + + +

    + reciprocal() +

    +
    +
    +

    Returns the reciprocal (multiplicative inverse) of this value.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func reciprocal() -> Rational
    + +
    +
    +
    • +
  • +
    + + +

    + rounded(_:) +

    +
    +
    +

    Returns this value rounded to an integral value using the specified +rounding rule.

    +
    let x = 7 / 2 as Rational<Int>
+print(x.rounded()) // Prints "4"
+print(x.rounded(.towardZero)) // Prints "3"
+print(x.rounded(.up)) // Prints "4"
+print(x.rounded(.down)) // Prints "3"
+
    + +

    See the FloatingPointRoundingRule enumeration for more information about +the available rounding rules.

    +
    +

    See also

    +

    round(_:), RoundingRule

    + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func rounded(
+    _ rule: RoundingRule = .toNearestOrAwayFromZero
+  ) -> Rational
    + +
    +
    +
    +
    Parameters
    +
    +
    rule
    +
    +

    The rounding rule to use.

    +
    +
    +
    +
    • +
  • +
    + + +

    + round(_:) +

    +
    +
    +

    Rounds the value to an integral value using the specified rounding rule.

    +
    var x = 7 / 2 as Rational<Int>
+x.round() // x == 4
+
+var x = 7 / 2 as Rational<Int>
+x.round(.towardZero) // x == 3
+
+var x = 7 / 2 as Rational<Int>
+x.round(.up) // x == 4
+
+var x = 7 / 2 as Rational<Int>
+x.round(.down) // x == 3
+
    + +

    See the FloatingPointRoundingRule enumeration for more information about +the available rounding rules.

    +
    +

    See also

    +

    round(_:), RoundingRule

    + +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public mutating func round(_ rule: RoundingRule = .toNearestOrAwayFromZero)
    + +
    +
    +
    +
    Parameters
    +
    +
    rule
    +
    +

    The rounding rule to use.

    +
    +
    +
    +
    • +
+
+
+
+ + +

ExpressibleByIntegerLiteral

+
+
    +
  • +
    + + +

    + init(integerLiteral:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init(integerLiteral value: T)
    + +
    +
    +
    +
    Parameters
    +
    +
    value
    +
    + +
    +
    +
    +
    • +
+
+
+
+ + +

CustomStringConvertible

+
+
    +
  • +
    + + +

    + description +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var description: String
    + +
    +
    +
    • +
+
+
+
+ + +

Equatable

+
+
    +
  • +
    + + +

    + ==(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func == (lhs: Rational, rhs: Rational) -> Bool
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
+
+
+
+ + +

Hashable

+
+
    +
  • +
    + + +

    + hashValue +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public var hashValue: Int
    + +
    +
    +
    • +
+
+
+
+ + +

Comparable

+
+
    +
  • +
    + + +

    + <(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func < (lhs: Rational, rhs: Rational) -> Bool
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + >(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func > (lhs: Rational, rhs: Rational) -> Bool
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + <=(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func <= (lhs: Rational, rhs: Rational) -> Bool
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + >=(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func >= (lhs: Rational, rhs: Rational) -> Bool
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
+
+
+
+ + +

Strideable

+
+
    +
  • +
    + + +

    + distance(to:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func distance(to other: Rational) -> Rational
    + +
    +
    +
    • +
  • +
    + + +

    + advanced(by:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public func advanced(by amount: Rational) -> Rational
    + +
    +
    +
    • +
+
+
+
+ + +

Numeric

+
+
    +
  • +
    + + +

    + init(exactly:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public init?<U>(exactly source: U) where U : BinaryInteger
    + +
    +
    +
    +
    Parameters
    +
    +
    source
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + +(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func + (lhs: Rational, rhs: Rational) -> Rational
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + +=(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func += (lhs: inout Rational, rhs: Rational)
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + -(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func - (lhs: Rational, rhs: Rational) -> Rational
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + -=(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func -= (lhs: inout Rational, rhs: Rational)
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + *(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func * (lhs: Rational, rhs: Rational) -> Rational
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
  • +
    + + +

    + *=(_:_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static func *= (lhs: inout Rational, rhs: Rational)
    + +
    +
    +
    +
    Parameters
    +
    +
    lhs
    +
    + +
    +
    rhs
    +
    + +
    +
    +
    +
    • +
+
+
+
+ + +

SignedNumeric

+
+
    +
  • +
    + + +

    + -(_:) +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public static prefix func - (operand: Rational) -> Rational
    + +
    +
    +
    • +
  • +
    + + +

    + negate() +

    +
    +
    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public mutating func negate()
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/Typealiases.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Typealiases.html new file mode 100644 index 0000000..18ded97 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/Typealiases.html @@ -0,0 +1,210 @@ + + + + + + Typealiases Reference + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+

Typealiases

+

The following typealiases are available globally.

+ +
+
+
+
+
+ Topics +
+ + +
+
+
+
+
+
+
    +
  • +
    + + +

    + Sign +

    +
    +
    +

    The mathematical sign of a number.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public typealias Sign = FloatingPointSign
    + +
    +
    +
    • +
+
+
+
    +
  • +
    + + +

    + RoundingRule +

    +
    +
    +

    A rule for rounding a number.

    + +
    +
    +
    Declaration
    +
    +

    Swift

    + 
    public typealias RoundingRule = FloatingPointRoundingRule
    + +
    +
    +
    • +
+
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/css/highlight.css b/docsets/NumericAnnex.docset/Contents/Resources/Documents/css/highlight.css new file mode 100644 index 0000000..6dac1a3 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/css/highlight.css @@ -0,0 +1,186 @@ +/* Credit to https://gist.github.com/wataru420/2048287 */ +.highlight { + /* Comment */ + /* Error */ + /* Keyword */ + /* Operator */ + /* Comment.Multiline */ + /* Comment.Preproc */ + /* Comment.Single */ + /* Comment.Special */ + /* Generic.Deleted */ + /* Generic.Deleted.Specific */ + /* Generic.Emph */ + /* Generic.Error */ + /* Generic.Heading */ + /* Generic.Inserted */ + /* Generic.Inserted.Specific */ + /* Generic.Output */ + /* Generic.Prompt */ + /* Generic.Strong */ + /* Generic.Subheading */ + /* 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; 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} + +/* +@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; 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+ padding-top: 0; } + .group:last-child { + border-bottom: none; } + .group:last-child > ul > li:last-child { + padding-bottom: 16px; } + .group a[name]::before { + content: ""; + display: block; } + .group > ul { + margin: 0; + padding: 0; } + .group > ul > li { + width: 100%; + border-bottom: 1px solid #ddd; + padding: 0 0 15px; + list-style: none; } + .group > ul > li:last-child { + border-bottom: none; } + .group > ul > li .declaration-note { + color: #808080; + font-weight: normal; + font-size: 16px; } + +.aside, .language { + overflow-y: hidden; + margin: 16px 0; + border-left: 6px solid #d0d0d0; + border-radius: 4px; + padding: 8px 12px; + background-color: #f7f7f7; } + .aside .aside-title, .language .aside-title { + margin: 0; + padding-bottom: 0; + color: #aaa; + 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; } + .aside p:last-child, .language p:last-child { + margin-bottom: 0; } + +.language { + border-left: 6px solid #99bcdf; + background-color: #f0f5fa; } + .language .aside-title { + color: #4183c4; } + +.aside-warning { + border-left: 6px solid #ffda73; + background-color: #fff8e6; } + .aside-warning .aside-title { + color: #fb0; } + +footer { + padding: 16px; + background: #444; + color: #ddd; + font-size: 14px; + line-height: inherit; } + footer p { + margin: 0; } + footer a[href] { + color: #fff; } + +html.dash header, html.dash nav { + display: none; } diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/index.html b/docsets/NumericAnnex.docset/Contents/Resources/Documents/index.html new file mode 100644 index 0000000..8a9c069 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/index.html @@ -0,0 +1,247 @@ + + + + + + NumericAnnex Reference + + + + + + + + +
+

+ NumericAnnex Reference + (100% documented) +

+

+ View on GitHub +

+

+ Install in Dash +

+
+
+ +
+
+
+
+ +

NumericAnnex

+ +

Build Status +codecov

+ +

NumericAnnex supplements the numeric facilities provided in the Swift standard +library.

+

Features

+ +
    +
  • BinaryInteger exponentiation, square root, cube root, greatest common +divisor, and least common multiple functions.
    • +
  • Complex, a value type to represent complex values in Cartesian form.
    • +
  • Rational, a value type to represent rational values, which supports division +by zero.
    • +
  • Random and Random.Xoroshiro, two reference types implementing efficient +pseudo-random number generators.
    • +
  • Math, a protocol for types providing square root, cube root, and elementary +transcendental functions.
    • +
  • Real, a protocol for floating-point types providing a selection of special +functions.
    • +
  • PRNG, a protocol for pseudo-random number generators.
    • +
+ +
+

Note: This project is in the early stages of development and is not +production-ready at this time.

+
+

Requirements

+ +

NumericAnnex now requires Xcode 9 beta 5 or a recent development snapshot of +Swift 4.0 that includes the revised numeric protocols.

+ +

It requires either Darwin.C (macOS) or Glibc (Linux) for transcendental +functions provided by the C standard library and either Security (macOS) or +Glibc (Linux) for cryptographically secure random bytes.

+

Installation

+ +

After NumericAnnex has been cloned or downloaded locally, build the library with +the command swift build (macOS) or swift build -Xcc -D_GNU_SOURCE (Linux). +Tests can be run with the command swift test (macOS) or +swift test -Xcc -D_GNU_SOURCE (Linux). An Xcode project can be generated with +the command swift package generate-xcodeproj.

+ +

Swift Package Manager can also be used to +add the package as a dependency for your own project. See Swift documentation +for details.

+

Basic Usage

+
import NumericAnnex
+
+var x: Ratio = 1 / 4
+// Ratio is a type alias for Rational<Int>.
+
+print(x.reciprocal())
+// Prints "4".
+
+x *= 8
+print(x + x)
+// Prints "4".
+
+x = Ratio(Float.phi) // Golden ratio.
+print(x)
+// Prints "13573053/8388608".
+
+var z: Complex64 = 42 * .i
+// Complex64 is a type alias for Complex<Float>.
+
+print(Complex.sqrt(z))
+// Prints "4.58258 + 4.58258i".
+
+z = .pi + .i * .log(2 - .sqrt(3))
+print(Complex.cos(z).real)
+// Prints "-2.0".
+
+

Documentation

+ +

All public protocols, types, and functions have been carefully documented in the +code. See the formatted reference for +details.

+ +

The project adheres to many design patterns found in the Swift standard library. +For example, Math types provide methods such as cubeRoot() and tangent() +just as FloatingPoint types provide methods such as squareRoot().

+ +

No free functions are declared in this library unless they overload existing +ones in the Swift standard library. Instead, functions such as cbrt(_:) and +tan(_:) 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., Complex128.cbrt(-8) != -2).

+

Future Directions

+ +
    +
  • [ ] Add more tests, including performance tests
    • +
  • [ ] Design and implement additional methods on PRNG
    • +
  • [ ] Design and implement BigInt
    • +
+

License

+ +

All original work is released under the MIT license. See +LICENSE for details.

+ +

Portions of the complex square root and elementary transcendental functions use +checks for special values adapted from libc++. Code in libc++ is dual-licensed +under the MIT and UIUC/NCSA licenses.

+ +
+
+
+
+
+ + + + diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/js/jazzy.js b/docsets/NumericAnnex.docset/Contents/Resources/Documents/js/jazzy.js new file mode 100755 index 0000000..5156f86 --- /dev/null +++ b/docsets/NumericAnnex.docset/Contents/Resources/Documents/js/jazzy.js @@ -0,0 +1,15 @@ +window.jazzy = { 'docset': false }; +if (typeof window.dash != 'undefined') { + document.documentElement.className += ' dash'; + window.jazzy.docset = true; +} +if (navigator.userAgent.match(/xcode/i)) { + document.documentElement.className += ' xcode'; + window.jazzy.docset = true; +} + +// Dumb down quotes within code blocks that delimit strings instead of quotations +// https://github.com/realm/jazzy/issues/714 +$("code q").replaceWith(function () { + return ["\"", $(this).contents(), "\""]; +}); diff --git a/docsets/NumericAnnex.docset/Contents/Resources/Documents/js/jquery.min.js b/docsets/NumericAnnex.docset/Contents/Resources/Documents/js/jquery.min.js new file mode 100755 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