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FloatingPoint.swift.gyb
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// RUN: %empty-directory(%t)
// RUN: %gyb %s -o %t/FloatingPoint.swift
// RUN: %line-directive %t/FloatingPoint.swift -- %target-build-swift -parse-stdlib %t/FloatingPoint.swift -o %t/a.out
// RUN: %target-codesign %t/a.out
// RUN: %line-directive %t/FloatingPoint.swift -- %target-run %t/a.out
// REQUIRES: executable_test
import Swift
import StdlibUnittest
#if !os(Windows) && (arch(i386) || arch(x86_64))
struct Float80Bits : Equatable, CustomStringConvertible {
var signAndExponent: UInt16
var significand: UInt64
init(_ signAndExponent: UInt16, _ significand: UInt64) {
self.signAndExponent = signAndExponent
self.significand = significand
}
var description: String {
return "(\(String(signAndExponent, radix: 16)) \(String(significand, radix: 16)))"
}
}
func == (lhs: Float80Bits, rhs: Float80Bits) -> Bool {
return
lhs.signAndExponent == rhs.signAndExponent &&
lhs.significand == rhs.significand
}
extension Float80 {
var bitPattern: Float80Bits {
let bits = Builtin.bitcast_FPIEEE80_Int80(self._value)
let sixtyFour = Builtin.zextOrBitCast_Int64_Int80((64 as Int64)._value)
return Float80Bits(
UInt16(Builtin.truncOrBitCast_Int80_Int16(
Builtin.lshr_Int80(bits, sixtyFour))),
UInt64(Builtin.truncOrBitCast_Int80_Int64(bits)))
}
init(bitPattern: Float80Bits) {
var result = Builtin.shl_Int80(
Builtin.zextOrBitCast_Int16_Int80(bitPattern.signAndExponent._value),
Builtin.zextOrBitCast_Int64_Int80((64 as Int64)._value))
result = Builtin.or_Int80(
result, Builtin.zextOrBitCast_Int64_Int80(bitPattern.significand._value))
self = Float80(Builtin.bitcast_Int80_FPIEEE80(result))
}
}
#endif
% for (FloatTy, BitPatternTy) in [
% ('Float', 'UInt32'),
% ('Double', 'UInt64'),
% ('Float80', 'Float80Bits')
% ]:
% if FloatTy == 'Float80':
#if !os(Windows) && (arch(i386) || arch(x86_64))
% end
func expectBitwiseEqual(
_ expected: ${FloatTy}, _ actual: ${FloatTy},
_ message: @autoclosure () -> String = "",
stackTrace: SourceLocStack = SourceLocStack(),
showFrame: Bool = true,
file: String = #file, line: UInt = #line
) {
expectEqual(expected.bitPattern, actual.bitPattern, message(),
stackTrace: stackTrace.pushIf(showFrame, file: file, line: line))
}
func expectBitwiseEqual(
bitPattern expected: ${BitPatternTy}, _ actual: ${FloatTy},
_ message: @autoclosure () -> String = "",
stackTrace: SourceLocStack = SourceLocStack(),
showFrame: Bool = true,
file: String = #file, line: UInt = #line
) {
expectBitwiseEqual(${FloatTy}(bitPattern: expected), actual, message(),
stackTrace: stackTrace.pushIf(showFrame, file: file, line: line))
}
% if FloatTy == 'Float80':
#endif
% end
% end
var FloatingPoint = TestSuite("FloatingPoint")
FloatingPoint.test("BinaryFloatingPoint/genericIntegerConversion") {
expectTrue(Double._convert(from: 0) == (value: 0, exact: true))
expectTrue(Double._convert(from: 1) == (value: 1, exact: true))
expectTrue(Double._convert(from: -1) == (value: -1, exact: true))
expectTrue(Double._convert(from: 42) == (value: 42, exact: true))
expectTrue(Double._convert(from: -42) == (value: -42, exact: true))
expectTrue(Double._convert(from: 100) == (value: 100, exact: true))
expectTrue(Double._convert(from: -100) == (value: -100, exact: true))
expectEqual(Double._convert(from: Int64.max).value, Double(Int64.max))
expectEqual(Double._convert(from: Int64.min).value, Double(Int64.min))
var x = ((Int64.max >> 11) + 1) << 11
expectEqual(Double._convert(from: x).value, Double(x))
x = (Int64.max >> 12) << 12 + 1
expectEqual(Double._convert(from: x).value, Double(x))
x = Int64.min + 1
expectEqual(Double._convert(from: x).value, Double(x))
expectEqual(Float._convert(from: Int64.max).value, Float(Int64.max))
expectEqual(Float._convert(from: Int64.min).value, Float(Int64.min))
}
FloatingPoint.test("BinaryFloatingPoint/genericFloatingPointConversion") {
expectTrue(Double._convert(from: 0 as Float) == (value: 0, exact: true))
expectTrue(Double._convert(from: -0.0 as Float) == (value: -0.0, exact: true))
expectTrue(Double._convert(from: 1 as Float) == (value: 1, exact: true))
expectTrue(Double._convert(from: -1 as Float) == (value: -1, exact: true))
expectTrue(
Double._convert(from: Float.infinity) == (value: .infinity, exact: true))
expectTrue(
Double._convert(from: -Float.infinity) == (value: -.infinity, exact: true))
expectTrue(Double._convert(from: Float.nan).value.isNaN)
expectTrue(Float._convert(from: Double.nan).value.isNaN)
expectFalse(Double._convert(from: Float.nan).value.isSignalingNaN)
expectFalse(Float._convert(from: Double.nan).value.isSignalingNaN)
expectTrue(Double._convert(from: Float.signalingNaN).value.isNaN)
expectTrue(Float._convert(from: Double.signalingNaN).value.isNaN)
let x = Float(bitPattern: Float.nan.bitPattern | 0xf)
expectEqual(
Float._convert(from: Double._convert(from: x).value).value.bitPattern,
x.bitPattern)
var y = Double(bitPattern: Double.nan.bitPattern | 0xf)
expectEqual(
Double._convert(from: Float._convert(from: y).value).value.bitPattern,
y.bitPattern)
y = Double(bitPattern: Double.nan.bitPattern | (1 << 32 - 1))
expectNotEqual(
Double._convert(from: Float._convert(from: y).value).value.bitPattern,
y.bitPattern)
expectTrue(Float._convert(from: y).value.isNaN)
expectFalse(Float._convert(from: y).exact)
expectTrue(
Float._convert(from: Double.leastNonzeroMagnitude) ==
(value: 0, exact: false))
expectTrue(
Float._convert(from: -Double.leastNonzeroMagnitude) ==
(value: -0.0, exact: false))
expectTrue(
Double._convert(from: Double.leastNonzeroMagnitude) ==
(value: .leastNonzeroMagnitude, exact: true))
expectTrue(
Double._convert(from: -Double.leastNonzeroMagnitude) ==
(value: -.leastNonzeroMagnitude, exact: true))
y = Double._convert(from: Float.leastNonzeroMagnitude).value / 2
expectTrue(Float._convert(from: y) == (value: 0, exact: false))
y.negate()
expectTrue(Float._convert(from: y) == (value: -0.0, exact: false))
y.negate()
y = y.nextUp
expectTrue(
Float._convert(from: y) == (value: .leastNonzeroMagnitude, exact: false))
y.negate()
expectTrue(
Float._convert(from: y) == (value: -.leastNonzeroMagnitude, exact: false))
expectEqual(
Float._convert(from: Double.leastNormalMagnitude).value,
Float(Double.leastNormalMagnitude))
expectEqual(
Float._convert(from: -Double.leastNormalMagnitude).value,
Float(-Double.leastNormalMagnitude))
expectEqual(Float._convert(from: Double.pi).value, 3.14159265)
y = Double._convert(from: Float._convert(from: Double.pi).value).value.nextUp
expectEqual(Float._convert(from: y).value, 3.14159265)
y.negate()
expectEqual(Float._convert(from: y).value, -3.14159265)
expectTrue(
Float._convert(from: Double.greatestFiniteMagnitude) ==
(value: .infinity, exact: false))
expectTrue(
Float._convert(from: -Double.greatestFiniteMagnitude) ==
(value: -.infinity, exact: false))
expectTrue(
Double._convert(from: Double.greatestFiniteMagnitude) ==
(value: .greatestFiniteMagnitude, exact: true))
expectTrue(
Double._convert(from: -Double.greatestFiniteMagnitude) ==
(value: -.greatestFiniteMagnitude, exact: true))
expectEqual(
Float._convert(
from: Double._convert(from: Float.greatestFiniteMagnitude).value).value,
Float.greatestFiniteMagnitude)
expectEqual(
Float._convert(
from: Double._convert(from: Float.leastNonzeroMagnitude).value).value,
Float.leastNonzeroMagnitude)
}
func positiveOne<T: ExpressibleByIntegerLiteral>() -> T {
return 1
}
func negativeOne<T: ExpressibleByIntegerLiteral>() -> T {
return -1
}
FloatingPoint.test("Float/ExpressibleByIntegerLiteral") {
expectEqual(positiveOne(), 1.0 as Float)
expectEqual(negativeOne(), -1.0 as Float)
}
FloatingPoint.test("Float/ExpressibleByFloatLiteral") {
let x: Float = -0.0
expectBitwiseEqual(bitPattern: 0x8000_0000, x)
}
FloatingPoint.test("Float/staticProperties") {
typealias Ty = Float
// From the FloatingPoint protocol.
expectEqual(2, Ty.radix)
expectBitwiseEqual(bitPattern: 0x7fc0_0000, Ty.nan)
#if !arch(i386) // i386 does not support a signaling nans.
expectBitwiseEqual(bitPattern: 0x7fa0_0000, Ty.signalingNaN)
#endif
expectBitwiseEqual(bitPattern: 0x7f80_0000, Ty.infinity)
expectBitwiseEqual(0x1.ffff_fe__p127, Ty.greatestFiniteMagnitude)
expectBitwiseEqual(0x1.921f_b4__p1, Ty.pi)
expectBitwiseEqual(0x1.0p-23, Ty.ulpOfOne)
expectBitwiseEqual(0x1.0p-126, Ty.leastNormalMagnitude)
#if arch(arm)
expectBitwiseEqual(0x1.0p-126, Ty.leastNonzeroMagnitude)
#else
expectBitwiseEqual(0x1.0p-149, Ty.leastNonzeroMagnitude)
#endif
// From the BinaryFloatingPoint protocol.
expectEqual(8, Ty.exponentBitCount)
expectEqual(23, Ty.significandBitCount)
}
// Tests the float and int conversions work correctly. Each case is special.
FloatingPoint.test("Float/UInt8") {
expectEqual(UInt8.min, UInt8(Float(UInt8.min)))
expectEqual(UInt8.max, UInt8(Float(UInt8.max)))
}
FloatingPoint.test("Float/Int8") {
expectEqual(Int8.min, Int8(Float(Int8.min)))
expectEqual(Int8.max, Int8(Float(Int8.max)))
}
FloatingPoint.test("Float/UInt16") {
expectEqual(UInt16.min, UInt16(Float(UInt16.min)))
expectEqual(UInt16.max, UInt16(Float(UInt16.max)))
}
FloatingPoint.test("Float/Int16") {
expectEqual(Int16.min, Int16(Float(Int16.min)))
expectEqual(Int16.max, Int16(Float(Int16.max)))
}
FloatingPoint.test("Float/UInt32") {
expectEqual(UInt32.min, UInt32(Float(UInt32.min)))
expectCrashLater()
expectEqual(UInt32.max, UInt32(Float(UInt32.max)))
}
FloatingPoint.test("Float/Int32") {
expectEqual(Int32.min, Int32(Float(Int32.min)))
expectCrashLater()
expectEqual(Int32.max, Int32(Float(Int32.max)))
}
FloatingPoint.test("Float/UInt64") {
expectEqual(UInt64.min, UInt64(Float(UInt64.min)))
expectCrashLater()
expectEqual(UInt64.max, UInt64(Float(UInt64.max)))
}
FloatingPoint.test("Float/Int64") {
expectEqual(Int64.min, Int64(Float(Int64.min)))
expectCrashLater()
expectEqual(Int64.max, Int64(Float(Int64.max)))
}
FloatingPoint.test("Double/ExpressibleByIntegerLiteral") {
expectEqual(positiveOne(), 1.0 as Double)
expectEqual(negativeOne(), -1.0 as Double)
}
FloatingPoint.test("Double/ExpressibleByFloatLiteral") {
let x: Double = -0.0
expectBitwiseEqual(bitPattern: 0x8000_0000_0000_0000, x)
}
FloatingPoint.test("Double/staticProperties") {
typealias Ty = Double
// From the FloatingPoint protocol.
expectEqual(2, Ty.radix)
expectBitwiseEqual(bitPattern: 0x7ff8_0000_0000_0000, Ty.nan)
#if !arch(i386) // i386 does not support a signaling nans.
expectBitwiseEqual(bitPattern: 0x7ff4_0000_0000_0000, Ty.signalingNaN)
#endif
expectBitwiseEqual(bitPattern: 0x7ff0_0000_0000_0000, Ty.infinity)
expectBitwiseEqual(0x1.ffff_ffff_ffff_f__p1023, Ty.greatestFiniteMagnitude)
expectBitwiseEqual(0x1.921f_b544_42d1_8__p1, Ty.pi)
expectBitwiseEqual(0x1.0p-52, Ty.ulpOfOne)
expectBitwiseEqual(0x1.0p-1022, Ty.leastNormalMagnitude)
#if arch(arm)
expectBitwiseEqual(0x1.0p-1022, Ty.leastNonzeroMagnitude)
#else
expectBitwiseEqual(0x1.0p-1074, Ty.leastNonzeroMagnitude)
#endif
// From the BinaryFloatingPoint protocol.
expectEqual(11, Ty.exponentBitCount)
expectEqual(52, Ty.significandBitCount)
}
FloatingPoint.test("Double/UInt8") {
expectEqual(UInt8.min, UInt8(Double(UInt8.min)))
expectEqual(UInt8.max, UInt8(Double(UInt8.max)))
}
FloatingPoint.test("Double/Int8") {
expectEqual(Int8.min, Int8(Double(Int8.min)))
expectEqual(Int8.max, Int8(Double(Int8.max)))
}
FloatingPoint.test("Double/UInt16") {
expectEqual(UInt16.min, UInt16(Double(UInt16.min)))
expectEqual(UInt16.max, UInt16(Double(UInt16.max)))
}
FloatingPoint.test("Double/Int16") {
expectEqual(Int16.min, Int16(Double(Int16.min)))
expectEqual(Int16.max, Int16(Double(Int16.max)))
}
FloatingPoint.test("Double/UInt32") {
expectEqual(UInt32.min, UInt32(Double(UInt32.min)))
expectEqual(UInt32.max, UInt32(Double(UInt32.max)))
}
FloatingPoint.test("Double/Int32") {
expectEqual(Int32.min, Int32(Double(Int32.min)))
expectEqual(Int32.max, Int32(Double(Int32.max)))
}
FloatingPoint.test("Double/UInt64") {
expectEqual(UInt64.min, UInt64(Double(UInt64.min)))
expectCrashLater()
expectEqual(UInt64.max, UInt64(Double(UInt64.max)))
}
FloatingPoint.test("Double/Int64") {
expectEqual(Int64.min, Int64(Double(Int64.min)))
expectCrashLater()
expectEqual(Int64.max, Int64(Double(Int64.max)))
}
FloatingPoint.test("Float/HashValueZero") {
let zero: Float = getFloat32(0.0)
let negativeZero: Float = getFloat32(-0.0)
expectNotEqual(zero.bitPattern, negativeZero.bitPattern)
expectEqual(zero.hashValue, negativeZero.hashValue)
}
FloatingPoint.test("Double/HashValueZero") {
let zero: Double = getFloat64(0.0)
let negativeZero: Double = getFloat64(-0.0)
expectNotEqual(zero.bitPattern, negativeZero.bitPattern)
expectEqual(zero.hashValue, negativeZero.hashValue)
}
#if arch(arm)
% for FloatSelf in ['Float32', 'Float64']:
func testSubNormalFlush(_ f: ${FloatSelf}) {
if !f.isSubnormal {
return
}
switch f.sign {
case .plus:
expectBitwiseEqual(.leastNonzeroMagnitude, f.nextUp)
expectBitwiseEqual(0.0, f.nextDown)
case .minus:
expectBitwiseEqual(-0.0, f.nextUp)
expectBitwiseEqual(-.leastNonzeroMagnitude, f.nextDown)
}
}
% end
#endif
extension FloatingPoint {
public var isQuietNaN: Bool { return isNaN && !isSignalingNaN }
}
func genericAbs<T: SignedNumeric & Comparable>(_ x: T) -> T {
return abs(x)
}
%for Self in ['Float', 'Double', 'Float80']:
% if Self == 'Float80':
#if !os(Windows) && (arch(i386) || arch(x86_64))
% end
FloatingPoint.test("${Self}.round") {
for rule in [FloatingPointRoundingRule.toNearestOrAwayFromZero,
FloatingPointRoundingRule.toNearestOrEven,
FloatingPointRoundingRule.towardZero,
FloatingPointRoundingRule.awayFromZero,
FloatingPointRoundingRule.up,
FloatingPointRoundingRule.down] {
// Zeros, integers and infinities round to themselves:
for value in [${Self}(), 1, 1/${Self}.ulpOfOne,
.greatestFiniteMagnitude, .infinity] {
expectBitwiseEqual(value, value.rounded(rule))
expectBitwiseEqual(-value, (-value).rounded(rule))
}
// NaNs "round" to NaNs:
expectTrue(${Self}.nan.rounded(rule).isNaN)
// Now let's try some inexact cases; we're going to stay close to zero,
// and check values close to (half-)integers, because those are the cases
// that people usually get wrong, and they'll reveal simple blunders like
// simply implementing the wrong rounding mode.
for base in stride(from: ${Self}(-3.5), to: 4, by: 0.5) {
for value in [base.nextDown, base, base.nextUp] {
let result = value.rounded(rule)
// Result must be integral. Since we're testing small values, we
// can simply check that Self(Int(result)) == result. For larger
// values this wouldn't be a correct test.'
expectEqual(${Self}(Int(result)), result)
let residual = value - result
// For any rounding rule, abs(residual) must be less than 1, however
// due to rounding the computation can produce 1 exactly.
expectTrue(abs(residual) <= 1)
// Remaining validation checks depend on the rounding rule.
switch rule {
case .toNearestOrAwayFromZero:
expectTrue(abs(residual) < 0.5 ||
abs(residual) == 0.5 && abs(result) > abs(value))
case .toNearestOrEven:
expectTrue(abs(residual) < 0.5 ||
abs(residual) == 0.5 && Int(result) % 2 == 0)
case .towardZero:
expectTrue(abs(result) <= abs(value))
case .awayFromZero:
expectTrue(abs(result) >= abs(value))
case .up:
expectTrue(result >= value)
case .down:
expectTrue(result <= value)
}
}
}
}
}
FloatingPoint.test("${Self}.remainder") {
// Basic sanity tests only; these are only sufficient to provide reassurance
// that a known-good remainder function (e.g. from the C stdlib) has been
// shimmed correctly. They are not sufficient for development of such a
// function, and should not be employed for that purpose.
expectTrue(${Self}(0).remainder(dividingBy: 0).isNaN)
expectTrue(${Self}(1).remainder(dividingBy: 0).isNaN)
expectTrue(${Self}.infinity.remainder(dividingBy: 0).isNaN)
expectTrue(${Self}.infinity.remainder(dividingBy: 1).isNaN)
expectEqual(0, ${Self}(0).remainder(dividingBy: .infinity))
expectEqual(1, ${Self}(1).remainder(dividingBy: .infinity))
expectEqual(-1, ${Self}(2).remainder(dividingBy: 3))
expectEqual(-1, ${Self}(3).remainder(dividingBy: 2))
expectEqual(1, ${Self}(5).remainder(dividingBy: 2))
}
FloatingPoint.test("${Self}.squareRoot") {
// Basic sanity tests only; these are only sufficient to provide reassurance
// that a known-good square root function (e.g. from the C stdlib) has been
// shimmed correctly. They are not sufficient for development of such a
// function, and should not be employed for that purpose.
expectTrue(${Self}(-1).squareRoot().isNaN)
expectTrue(${Self}.nan.squareRoot().isNaN)
expectEqual(-0, ${Self}(-0).squareRoot())
expectEqual(0, ${Self}(0).squareRoot())
expectEqual(1, ${Self}(1).squareRoot())
expectEqual(2, ${Self}(4).squareRoot())
expectEqual(.infinity, ${Self}.infinity.squareRoot())
}
FloatingPoint.test("${Self}.addingProduct") {
// Fails if fma( ) is incorrectly implemented using separate + and *,
// and validates that we have the argument order right for the shimmed
// function.
let one = ${Self}(1)
let ulp = ${Self}.ulpOfOne
expectEqual(ulp*ulp, one.addingProduct(ulp + one, ulp - one))
}
FloatingPoint.test("${Self}/LosslessStringConvertible") {
let instances = [
1.0, -1.0,
0.0, -0.0,
${Self}.infinity, -${Self}.infinity
]
checkLosslessStringConvertible(instances)
expectTrue(Float(String(Float.nan))!.isNaN)
}
FloatingPoint.test("${Self}.significandWidth") {
expectEqual(-1, ${Self}(0).significandWidth)
expectEqual(-1, ${Self}.infinity.significandWidth)
expectEqual(-1, ${Self}.nan.significandWidth)
expectEqual(${Self}.significandBitCount, ${Self}(1).nextUp.significandWidth)
expectEqual(${Self}.significandBitCount, ${Self}(1).nextDown.significandWidth)
expectEqual(0, ${Self}.ulpOfOne.significandWidth)
expectEqual(0, ${Self}(1).significandWidth)
expectEqual(0, ${Self}(2).significandWidth)
expectEqual(1, ${Self}(3).significandWidth)
}
FloatingPoint.test("${Self}.absNegativeZero") {
expectEqual(abs(${Self}(-0.0)), ${Self}(0.0))
expectEqual(genericAbs(${Self}(-0.0)), ${Self}(0.0))
}
% if Self == 'Float80':
#endif
% end
%end
let floatNextUpDownTests: [(Float, Float)] = [
(.greatestFiniteMagnitude, .infinity),
(0x1.ffff_fe__p-1, 1.0), (1.0, 0x1.0000_02__p+0),
(0.0, .leastNonzeroMagnitude),
(0x1.efff_fe__p-1, 0x1.fp-1), (0x1.fp-1, 0x1.f000_02__p-1),
]
FloatingPoint.test("Float.nextUp, .nextDown")
.forEach(in: floatNextUpDownTests) {
(prev, succ) in
#if arch(arm)
if prev.isSubnormal || succ.isSubnormal {
testSubNormalFlush(prev)
testSubNormalFlush(succ)
return
}
#endif
expectBitwiseEqual(succ, prev.nextUp)
expectBitwiseEqual(prev, succ.nextDown)
expectBitwiseEqual(-succ, (-prev).nextDown)
expectBitwiseEqual(-prev, (-succ).nextUp)
}
let doubleNextUpDownTests: [(Double, Double)] = [
(.greatestFiniteMagnitude, .infinity),
(0x1.ffff_ffff_ffff_fp-1, 1.0), (1.0, 0x1.0000_0000_0000_1p+0),
(0.0, .leastNonzeroMagnitude),
(0x1.efff_ffff_ffff_fp-1, 0x1.fp-1), (0x1.fp-1, 0x1.f000_0000_0000_1p-1),
]
FloatingPoint.test("Double.nextUp, .nextDown")
.forEach(in: doubleNextUpDownTests) {
(prev, succ) in
#if arch(arm)
if prev.isSubnormal || succ.isSubnormal {
testSubNormalFlush(prev)
testSubNormalFlush(succ)
return
}
#endif
expectBitwiseEqual(succ, prev.nextUp)
expectBitwiseEqual(prev, succ.nextDown)
expectBitwiseEqual(-succ, (-prev).nextDown)
expectBitwiseEqual(-prev, (-succ).nextUp)
}
%for Self in ['Float', 'Double']:
FloatingPoint.test("${Self}.nextUp, .nextDown/nan") {
let x = ${Self}.nan
expectTrue(x.nextUp.isNaN)
expectTrue(x.nextDown.isNaN)
expectTrue((-x).nextDown.isNaN)
expectTrue((-x).nextUp.isNaN)
}
%end
#if !os(Windows) && (arch(i386) || arch(x86_64))
FloatingPoint.test("Float80/ExpressibleByIntegerLiteral") {
expectEqual(positiveOne(), 1.0 as Float80)
expectEqual(negativeOne(), -1.0 as Float80)
}
FloatingPoint.test("Float80/ExpressibleByFloatLiteral") {
let x: Float80 = -0.0
expectBitwiseEqual(bitPattern: Float80Bits(0x8000, 0), x)
}
FloatingPoint.test("Float80/staticProperties") {
typealias Ty = Double
// From the FloatingPoint protocol.
expectEqual(2, Ty.radix)
expectBitwiseEqual(bitPattern: 0x7ff8_0000_0000_0000, Ty.nan)
#if !arch(i386) // i386 does not support a signaling nans.
expectBitwiseEqual(bitPattern: 0x7ff4_0000_0000_0000, Ty.signalingNaN)
#endif
expectBitwiseEqual(bitPattern: 0x7ff0_0000_0000_0000, Ty.infinity)
expectBitwiseEqual(0x1.ffff_ffff_ffff_f__p1023, Ty.greatestFiniteMagnitude)
expectBitwiseEqual(0x1.921f_b544_42d1_8__p1, Ty.pi)
expectBitwiseEqual(0x1.0p-52, Ty.ulpOfOne)
expectBitwiseEqual(0x1.0p-1022, Ty.leastNormalMagnitude)
expectBitwiseEqual(0x1.0p-1074, Ty.leastNonzeroMagnitude)
// From the BinaryFloatingPoint protocol.
expectEqual(11, Ty.exponentBitCount)
expectEqual(52, Ty.significandBitCount)
}
FloatingPoint.test("Float80/HashValueZero") {
let zero: Float80 = getFloat80(0.0)
let negativeZero: Float80 = getFloat80(-0.0)
expectNotEqual(zero.bitPattern, negativeZero.bitPattern)
expectEqual(zero.hashValue, negativeZero.hashValue)
}
let float80NextUpDownTests: [(Float80, Float80)] = [
(.nan, .nan),
(.greatestFiniteMagnitude, .infinity),
(0x1.ffff_ffff_ffff_fffep-1, 1.0), (1.0, 0x1.0000_0000_0000_0002p+0),
(0.0, .leastNonzeroMagnitude),
(0x1.efff_ffff_ffff_fffep-1, 0x1.fp-1),
(0x1.fp-1, 0x1.f000_0000_0000_0002p-1),
]
FloatingPoint.test("Float80.nextUp, .nextDown")
.forEach(in: float80NextUpDownTests) {
(prev, succ) in
expectBitwiseEqual(succ, prev.nextUp)
expectBitwiseEqual(prev, succ.nextDown)
expectBitwiseEqual(-succ, (-prev).nextDown)
expectBitwiseEqual(-prev, (-succ).nextUp)
}
#endif
% for FloatSelf in ['Float32', 'Float64']:
func checkFloatingPointComparison_${FloatSelf}(
_ expected: ExpectedComparisonResult,
_ lhs: ${FloatSelf}, _ rhs: ${FloatSelf},
//===--- TRACE boilerplate ----------------------------------------------===//
// @autoclosure _ message: () -> String = "",
showFrame: Bool = true,
stackTrace: SourceLocStack = SourceLocStack(),
file: String = #file, line: UInt = #line
) {
let newTrace = stackTrace.pushIf(showFrame, file: file, line: line)
let message = { "expected: lhs=\(lhs) \(expected) rhs=\(rhs)" }
expectEqual(expected.isEQ(), lhs == rhs, message(), stackTrace: newTrace)
expectEqual(expected.isNE(), lhs != rhs, message(), stackTrace: newTrace)
checkHashable(
expectedEqual: expected.isEQ(),
lhs, rhs, message(), stackTrace: newTrace)
expectEqual(expected.isLT(), lhs < rhs, message(), stackTrace: newTrace)
expectEqual(expected.isLE(), lhs <= rhs, message(), stackTrace: newTrace)
expectEqual(expected.isGE(), lhs >= rhs, message(), stackTrace: newTrace)
expectEqual(expected.isGT(), lhs > rhs, message(), stackTrace: newTrace)
checkComparable(expected, lhs, rhs, message(), stackTrace: newTrace)
}
FloatingPoint.test("${FloatSelf}/{Comparable,Hashable,Equatable}") {
// On arm we flush subnormals to zero so testing subnormals won't work.
#if arch(arm)
let interestingValues: [${FloatSelf}] = [
// Interesting floating point values, sorted.
-${FloatSelf}.infinity,
-${FloatSelf}.greatestFiniteMagnitude,
-1.0,
-${FloatSelf}.ulpOfOne,
-${FloatSelf}.leastNormalMagnitude,
-0.0,
0.0,
${FloatSelf}.leastNormalMagnitude,
${FloatSelf}.ulpOfOne,
1.0,
${FloatSelf}.greatestFiniteMagnitude,
${FloatSelf}.infinity,
${FloatSelf}.nan,
${FloatSelf}.signalingNaN,
]
#else
let interestingValues: [${FloatSelf}] = [
// Interesting floating point values, sorted.
-${FloatSelf}.infinity,
-${FloatSelf}.greatestFiniteMagnitude,
-1.0,
-${FloatSelf}.ulpOfOne,
-${FloatSelf}.leastNormalMagnitude,
-${FloatSelf}.leastNormalMagnitude/2,
-${FloatSelf}.leastNonzeroMagnitude,
-0.0,
0.0,
${FloatSelf}.leastNonzeroMagnitude,
${FloatSelf}.leastNormalMagnitude/2,
${FloatSelf}.leastNormalMagnitude,
${FloatSelf}.ulpOfOne,
1.0,
${FloatSelf}.greatestFiniteMagnitude,
${FloatSelf}.infinity,
${FloatSelf}.nan,
${FloatSelf}.signalingNaN,
]
#endif
for lhsIdx in interestingValues.indices {
for rhsIdx in interestingValues.indices {
let lhs = interestingValues[lhsIdx]
let rhs = interestingValues[rhsIdx]
if lhs.isZero && rhs.isZero {
// Special case: 0.0 and -0.0 compare equal.
checkFloatingPointComparison_${FloatSelf}(
ExpectedComparisonResult.eq, lhs, rhs)
} else if lhs.isNaN || rhs.isNaN {
// Special case: NaN is unordered wrt other values.
// - equality comparison with NaN returns false,
// - NaN is not equal to anything, including NaN.
expectFalse(lhs == rhs)
expectTrue(lhs != rhs)
expectFalse(lhs < rhs)
expectFalse(lhs <= rhs)
expectFalse(lhs >= rhs)
expectFalse(lhs > rhs)
} else {
// The sane case.
checkFloatingPointComparison_${FloatSelf}(
lhsIdx < rhsIdx ?
ExpectedComparisonResult.lt :
(lhsIdx == rhsIdx ?
ExpectedComparisonResult.eq :
ExpectedComparisonResult.gt),
lhs, rhs)
}
// Check minimum, maximum, minimumMagnitude and maximumMagnitude.
let min = ${FloatSelf}.minimum(lhs, rhs)
let max = ${FloatSelf}.maximum(lhs, rhs)
let minMag = ${FloatSelf}.minimumMagnitude(lhs, rhs)
let maxMag = ${FloatSelf}.maximumMagnitude(lhs, rhs)
// If either lhs or rhs is signaling, or if both are quiet NaNs, the
// result is a quiet NaN.
if lhs.isSignalingNaN || rhs.isSignalingNaN || (lhs.isNaN && rhs.isNaN) {
expectTrue(min.isQuietNaN)
expectTrue(max.isQuietNaN)
expectTrue(minMag.isQuietNaN)
expectTrue(maxMag.isQuietNaN)
}
// If only one of lhs and rhs is NaN, the result of the min/max
// operations is always the other value. While contrary to all other
// IEEE 754 basic operations, this property is critical to ensure
// that clamping to a valid range behaves as expected.
else if lhs.isNaN && !rhs.isNaN {
expectEqual(min.bitPattern, rhs.bitPattern)
expectEqual(max.bitPattern, rhs.bitPattern)
expectEqual(minMag.bitPattern, rhs.bitPattern)
expectEqual(maxMag.bitPattern, rhs.bitPattern)
}
else if rhs.isNaN && !lhs.isNaN {
expectEqual(min.bitPattern, lhs.bitPattern)
expectEqual(max.bitPattern, lhs.bitPattern)
expectEqual(minMag.bitPattern, lhs.bitPattern)
expectEqual(maxMag.bitPattern, lhs.bitPattern)
}
// If lhs and rhs are equal, min is lhs and max is rhs. This ensures
// that the set {lhs, rhs} is the same as the set {min, max} so long
// as lhs and rhs are non-NaN. This is less important for min/max than
// it is for minMag and maxMag, but it makes sense to define this way.
if lhs <= rhs {
expectEqual(min.bitPattern, lhs.bitPattern)
expectEqual(max.bitPattern, rhs.bitPattern)
} else if lhs > rhs {
expectEqual(max.bitPattern, lhs.bitPattern)
expectEqual(min.bitPattern, rhs.bitPattern)
}
// If lhs and rhs have equal magnitude, minMag is lhs and maxMag is rhs.
// This ensures that the set {lhs, rhs} is the same as the set
// {minMag, maxMag} so long as lhs and rhs are non-NaN; this is a
// restriction of the IEEE 754 rules, but it makes good sense and also
// makes this primitive more useful for building head-tail arithmetic
// operations.
if abs(lhs) <= abs(rhs) {
expectEqual(minMag.bitPattern, lhs.bitPattern)
expectEqual(maxMag.bitPattern, rhs.bitPattern)
} else if abs(lhs) > abs(rhs) {
expectEqual(maxMag.bitPattern, lhs.bitPattern)
expectEqual(minMag.bitPattern, rhs.bitPattern)
}
}
}
}
% end
% for Self in ['Float32', 'Float64', 'Float80']:
#if ${'!os(Windows) && (arch(i386) || arch(x86_64))' if Self == 'Float80' else 'true'}
FloatingPoint.test("${Self}/Strideable") {
// FIXME: the test data could probably be better chosen here, to
// exercise more cases. Note: NaNs (and possibly Infs) are singular
// values with respect to Strideable conformance and aren't expected
// to pass these tests.
let instances: [${Self}] = [-1.0, 0.0, 0.5, 1.0, 1E20]
checkStrideable(
instances, strides: instances,
distanceOracle: { instances[$1] - instances[$0] },
advanceOracle: { instances[$0] + instances[$1] })
}
#endif
% end
FloatingPoint.test("Float32/Literals") {
do {
let f: Float32 = 0.0
expectEqual(0x0000_0000, f.bitPattern)
}
do {
let f: Float32 = -0.0
expectEqual(0x8000_0000, f.bitPattern)
}
do {
let f: Float32 = 1.0
expectEqual(0x3f80_0000, f.bitPattern)
}
do {
let f: Float32 = -1.0
expectEqual(0xbf80_0000, f.bitPattern)
}
do {
let f: Float32 = 0.999999
expectEqual(0x3f7fffef, f.bitPattern)
}
do {
let f: Float32 = 0.9999999
expectEqual(0x3f7ffffe, f.bitPattern)
}
do {
let f: Float32 = 0.99999999
expectEqual(0x3f80_0000, f.bitPattern)
}
// Smallest subnormal.
do {
let f: Float32 = 1.4e-45
expectEqual(0x0000_0001, f.bitPattern)
}
do {
let f: Float32 = -1.4e-45
expectEqual(0x8000_0001, f.bitPattern)
}
// Rounded to zero.
do {
let f: Float32 = 0.7e-45
expectEqual(0x0000_0000, f.bitPattern)
}
do {
let f: Float32 = -0.7e-45
expectEqual(0x8000_0000, f.bitPattern)
}
// Second largest normal.
do {
let f: Float32 = 3.4028232e+38
expectEqual(0x7f7f_fffe, f.bitPattern)
}
do {
let f: Float32 = -3.4028232e+38
expectEqual(0xff7f_fffe, f.bitPattern)
}
// Largest normal.
do {
let f: Float32 = 3.4028234e+38
expectEqual(0x7f7f_ffff, f.bitPattern)
}
do {
let f: Float32 = 340282340000000000000000000000000000000.0
expectEqual(0x7f7f_ffff, f.bitPattern)
}
do {
let f: Float32 = 340282340000000000000000000000000000000
expectEqual(0x7f7f_ffff, f.bitPattern)
}
do {
let f: Float32 = -3.4028234e+38
expectEqual(0xff7f_ffff, f.bitPattern)
}
do {
let f: Float32 = -340282340000000000000000000000000000000.0
expectEqual(0xff7f_ffff, f.bitPattern)
}
do {
let f: Float32 = -340282340000000000000000000000000000000
expectEqual(0xff7f_ffff, f.bitPattern)
}
}
FloatingPoint.test("Float64/Literals") {
do {
let f: Float64 = 0.0
expectEqual(0x0000_0000_0000_0000, f.bitPattern)
}
do {
let f: Float64 = -0.0
expectEqual(0x8000_0000_0000_0000, f.bitPattern)
}
do {
let f: Float64 = 1.0
expectEqual(0x3ff0_0000_0000_0000, f.bitPattern)
}
do {
let f: Float64 = -1.0
expectEqual(0xbff0_0000_0000_0000, f.bitPattern)
}
do {
let f: Float64 = 0.999999999999999
expectEqual(0x3fef_ffff_ffff_fff7, f.bitPattern)
}
do {
let f: Float64 = 0.9999999999999999
expectEqual(0x3fef_ffff_ffff_ffff, f.bitPattern)
}
do {
let f: Float64 = 0.99999999999999999
expectEqual(0x3ff0_0000_0000_0000, f.bitPattern)
}
// Smallest subnormal.
do {
let f: Float64 = 4.0e-324
expectEqual(0x0000_0000_0000_0001, f.bitPattern)
}
do {
let f: Float64 = -4.0e-324
expectEqual(0x8000_0000_0000_0001, f.bitPattern)
}
// Rounded to zero.
do {
let f: Float64 = 2.4e-324
expectEqual(0x0000_0000_0000_0000, f.bitPattern)
}
do {
let f: Float64 = -2.4e-324
expectEqual(0x8000_0000_0000_0000, f.bitPattern)
}
// Second largest normal.
do {
let f: Float64 = 1.79769313486231551e+308
expectEqual(0x7fef_ffff_ffff_fffe, f.bitPattern)
}
do {
let f: Float64 = -1.79769313486231551e+308
expectEqual(0xffef_ffff_ffff_fffe, f.bitPattern)
}
// Largest normal.
do {
let f: Float64 = 1.7976931348623157e+308
expectEqual(0x7fef_ffff_ffff_ffff, f.bitPattern)
}
do {
let f: Float64 = 179769313486231570000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.0
expectEqual(0x7fef_ffff_ffff_ffff, f.bitPattern)
}
do {
let f: Float64 = 179769313486231570000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
expectEqual(0x7fef_ffff_ffff_ffff, f.bitPattern)
}
do {
let f: Float64 = -1.7976931348623157e+308