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NumericAnnex
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Merge branch 'master' of https://github.com/xwu/NumericAnnex

This commit is contained in:
Xiaodi Wu 2017-08-11 21:41:29 -05:00
parent cef815d55c 7130751257
commit 4b921315f9
6 changed files with 38 additions and 45 deletions
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6
.travis.yml
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@ -6,9 +6,9 @@ matrix:
dist: trusty
before_install:
- wget -q -O - https://swift.org/keys/all-keys.asc | gpg --import -
- wget https://swift.org/builds/swift-4.0-branch/ubuntu1404/swift-4.0-DEVELOPMENT-SNAPSHOT-2017-07-13-a/swift-4.0-DEVELOPMENT-SNAPSHOT-2017-07-13-a-ubuntu14.04.tar.gz
- tar xzf swift-4.0-DEVELOPMENT-SNAPSHOT-2017-07-13-a-ubuntu14.04.tar.gz
- export PATH=${PWD}/swift-4.0-DEVELOPMENT-SNAPSHOT-2017-07-13-a-ubuntu14.04/usr/bin:"${PATH}"
- wget https://swift.org/builds/swift-4.0-branch/ubuntu1404/swift-4.0-DEVELOPMENT-SNAPSHOT-2017-08-04-a/swift-4.0-DEVELOPMENT-SNAPSHOT-2017-08-04-a-ubuntu14.04.tar.gz
- tar xzf swift-4.0-DEVELOPMENT-SNAPSHOT-2017-08-04-a-ubuntu14.04.tar.gz
- export PATH=${PWD}/swift-4.0-DEVELOPMENT-SNAPSHOT-2017-08-04-a-ubuntu14.04/usr/bin:"${PATH}"
script:
- swift test -Xcc -D_GNU_SOURCE=1
- os: osx

42
Sources/IntegerAlgorithms.swift
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@ -51,8 +51,8 @@ extension BinaryInteger {
while shift >= 0 {
result *= 2
let temporary = 2 * result + 1
if temporary <= x &>> shift {
x -= temporary &<< shift
if temporary <= x >> shift {
x -= temporary << shift
result += 1
}
shift -= 2
@ -77,8 +77,8 @@ extension UnsignedInteger {
while shift >= 0 {
result *= 2
let temporary = 3 * result * (result + 1) + 1
if temporary <= x &>> shift {
x -= temporary &<< shift
if temporary <= x >> shift {
x -= temporary << shift
result += 1
}
shift -= 3
@ -99,20 +99,20 @@ extension UnsignedInteger {
var a = a, b = b, shift = 0 as Self
while ((a | b) & 1) == 0 {
a &>>= 1
b &>>= 1
a >>= 1
b >>= 1
shift += 1
}
// Now, shift is equal to log2(k), where k is the greatest power of 2
// dividing a and b.
while (a & 1) == 0 { a &>>= 1 } // Now, a is odd.
while (a & 1) == 0 { a >>= 1 } // Now, a is odd.
repeat {
while (b & 1) == 0 { b &>>= 1 } // Now, b is odd.
while (b & 1) == 0 { b >>= 1 } // Now, b is odd.
if a > b { swap(&a, &b) } // Now, a < b.
b -= a
} while b != 0
// Restore common factors of 2.
return a &<< shift
return a << shift
}
/// Returns the least common multiple of `a` and `b`.
@ -132,8 +132,8 @@ extension UnsignedInteger where Self : FixedWidthInteger {
/// Returns the least common multiple of `a` and `b` and a flag to indicate
/// whether overflow occurred during the operation.
public static func lcmReportingOverflow(_ a: Self, _ b: Self)
-> (partialValue: Self, overflow: ArithmeticOverflow) {
if a == 0 || b == 0 { return (partialValue: 0, overflow: .none) }
-> (partialValue: Self, overflow: Bool) {
if a == 0 || b == 0 { return (0, false) }
return (a / .gcd(a, b)).multipliedReportingOverflow(by: b)
}
@ -192,25 +192,19 @@ where Self : FixedWidthInteger,
/// Returns the greatest common divisor of `a` and `b` and a flag to indicate
/// whether overflow occurred during the operation.
public static func gcdReportingOverflow(_ a: Self, _ b: Self)
-> (partialValue: Self, overflow: ArithmeticOverflow) {
let t = Self(extendingOrTruncating: Magnitude.gcd(a.magnitude, b.magnitude))
return (
partialValue: t,
overflow: ArithmeticOverflow(t < 0)
)
-> (partialValue: Self, overflow: Bool) {
let t = Self(truncatingIfNeeded: Magnitude.gcd(a.magnitude, b.magnitude))
return (t, t < 0)
}
// @_transparent // @_inlineable
/// Returns the least common multiple of `a` and `b` and a flag to indicate
/// whether overflow occurred during the operation.
public static func lcmReportingOverflow(_ a: Self, _ b: Self)
-> (partialValue: Self, overflow: ArithmeticOverflow) {
-> (partialValue: Self, overflow: Bool) {
let (t, overflow) = Magnitude.lcmReportingOverflow(a.magnitude, b.magnitude)
let u = Self(extendingOrTruncating: t)
return (
partialValue: u,
overflow: ArithmeticOverflow(overflow == .overflow || u < 0)
)
let u = Self(truncatingIfNeeded: t)
return (u, overflow || u < 0)
}
// @_transparent // @_inlineable
@ -219,6 +213,6 @@ where Self : FixedWidthInteger,
public static func lcmFullWidth(_ a: Self, _ b: Self)
-> (high: Self, low: Self.Magnitude) {
let t = Magnitude.lcmFullWidth(a.magnitude, b.magnitude)
return (high: Self(t.high), low: t.low)
return (Self(t.high), t.low)
}
}

5
Sources/Math.swift
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@ -5,11 +5,10 @@
// Created by Xiaodi Wu on 3/31/17.
//
/// A signed numeric type that provides square root, cube root, and elementary
/// transcendental functions.
/// 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 which provides the required
/// work on any real or complex floating-point type that supports the required
/// functions.
public protocol Math : SignedNumeric {
/// The mathematical constant pi (_π_).

7
Sources/PRNG.swift
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@ -169,7 +169,7 @@ extension PRNG {
bitCount == T.bitWidth {
// It is an awkward way of spelling `next()`, but it is necessary.
guard let next = first(where: { _ in true }) else { fatalError() }
return T(extendingOrTruncating: next)
return T(truncatingIfNeeded: next)
}
let (quotient, remainder) =
@ -179,15 +179,14 @@ extension PRNG {
// Call `next()` at least `quotient` times.
for i in 0..<quotient {
guard let next = first(where: { $0 <= max }) else { fatalError() }
temporary +=
T(extendingOrTruncating: next) &<< (randomBitWidth * i)
temporary += T(truncatingIfNeeded: next) &<< (randomBitWidth * i)
}
// If `remainder != 0`, call `next()` at least one more time.
if remainder != 0 {
guard let next = first(where: { $0 <= max }) else { fatalError() }
let mask = Element.max &>> (Element.bitWidth - remainder)
temporary +=
T(extendingOrTruncating: next & mask) &<< (randomBitWidth * quotient)
T(truncatingIfNeeded: next & mask) &<< (randomBitWidth * quotient)
}
return temporary
}

5
Sources/Real.swift
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@ -11,10 +11,11 @@ import Glibc
import Darwin.C
#endif
/// A floating-point type that provides a selection of special functions.
/// 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 provides the required functions.
/// work on any floating-point type that supports the required functions.
public protocol Real : Math, FloatingPoint {
/// Returns the hypotenuse of a right-angle triangle with legs (catheti) of
/// length `x` and `y`, preventing avoidable arithmetic overflow and

18
Tests/NumericAnnexTests/FactoringTests.swift
View File

@ -11,7 +11,7 @@ class FactoringTests : XCTestCase {
XCTAssertEqual(Int.gcd(24, 60), 12)
XCTAssertEqual(Int.gcd(42, 56), 14)
XCTAssertTrue(Int8.gcdReportingOverflow(-128, -128).overflow == .overflow)
XCTAssertTrue(Int8.gcdReportingOverflow(-128, -128).overflow)
// Test special values.
XCTAssertEqual(UInt.gcd(0, 42), 42)
@ -29,12 +29,12 @@ class FactoringTests : XCTestCase {
XCTAssertEqual(Int8.lcmFullWidth(33, 48).high, 2)
XCTAssertEqual(Int8.lcmFullWidth(33, 48).low, 16)
XCTAssertEqual(Int8.lcmReportingOverflow(33, 48).partialValue, 16)
XCTAssertTrue(Int8.lcmReportingOverflow(33, 48).overflow == .overflow)
XCTAssertTrue(Int8.lcmReportingOverflow(33, 48).overflow)
XCTAssertEqual(UInt8.lcmFullWidth(33, 48).high, 2)
XCTAssertEqual(UInt8.lcmFullWidth(33, 48).low, 16)
XCTAssertEqual(UInt8.lcmReportingOverflow(33, 48).partialValue, 16)
XCTAssertTrue(UInt8.lcmReportingOverflow(33, 48).overflow == .overflow)
XCTAssertTrue(UInt8.lcmReportingOverflow(33, 48).overflow)
// Test special values.
XCTAssertEqual(UInt.lcm(0, 42), 0)
@ -44,32 +44,32 @@ class FactoringTests : XCTestCase {
XCTAssertEqual(Int8.lcmFullWidth(0, 42).high, 0)
XCTAssertEqual(Int8.lcmFullWidth(0, 42).low, 0)
XCTAssertEqual(Int8.lcmReportingOverflow(0, 42).partialValue, 0)
XCTAssertTrue(Int8.lcmReportingOverflow(0, 42).overflow == .none)
XCTAssertFalse(Int8.lcmReportingOverflow(0, 42).overflow)
XCTAssertEqual(Int8.lcmFullWidth(42, 0).high, 0)
XCTAssertEqual(Int8.lcmFullWidth(42, 0).low, 0)
XCTAssertEqual(Int8.lcmReportingOverflow(42, 0).partialValue, 0)
XCTAssertTrue(Int8.lcmReportingOverflow(42, 0).overflow == .none)
XCTAssertFalse(Int8.lcmReportingOverflow(42, 0).overflow)
XCTAssertEqual(Int8.lcmFullWidth(0, 0).high, 0)
XCTAssertEqual(Int8.lcmFullWidth(0, 0).low, 0)
XCTAssertEqual(Int8.lcmReportingOverflow(0, 0).partialValue, 0)
XCTAssertTrue(Int8.lcmReportingOverflow(0, 0).overflow == .none)
XCTAssertFalse(Int8.lcmReportingOverflow(0, 0).overflow)
XCTAssertEqual(UInt8.lcmFullWidth(0, 42).high, 0)
XCTAssertEqual(UInt8.lcmFullWidth(0, 42).low, 0)
XCTAssertEqual(UInt8.lcmReportingOverflow(0, 42).partialValue, 0)
XCTAssertTrue(UInt8.lcmReportingOverflow(0, 42).overflow == .none)
XCTAssertFalse(UInt8.lcmReportingOverflow(0, 42).overflow)
XCTAssertEqual(UInt8.lcmFullWidth(42, 0).high, 0)
XCTAssertEqual(UInt8.lcmFullWidth(42, 0).low, 0)
XCTAssertEqual(UInt8.lcmReportingOverflow(42, 0).partialValue, 0)
XCTAssertTrue(UInt8.lcmReportingOverflow(42, 0).overflow == .none)
XCTAssertFalse(UInt8.lcmReportingOverflow(42, 0).overflow)
XCTAssertEqual(UInt8.lcmFullWidth(0, 0).high, 0)
XCTAssertEqual(UInt8.lcmFullWidth(0, 0).low, 0)
XCTAssertEqual(UInt8.lcmReportingOverflow(0, 0).partialValue, 0)
XCTAssertTrue(UInt8.lcmReportingOverflow(0, 0).overflow == .none)
XCTAssertFalse(UInt8.lcmReportingOverflow(0, 0).overflow)
}
static var allTests = [