math

README

soft-math

Software algorithms for 32bit math functions.

Work in progress. Some functions may not be implemented fully.

Documentation

Overview

Package math provides basic constants and mathematical functions.

This package does not guarantee bit-identical results across architectures.

Index

• Constants
• func Abs(x float64) float64
• func AbsS(x float32) float32
• func AcosS(x float32) float32
• func AsinS(x float32) float32
• func Atan2S(y, x float32) float32
• func AtanS(x float32) float32
• func CopysignS(x, y float32) float32
• func CosS(y float32) float32
• func ExpS(x float32) float32
• func Float32bits(f float32) uint32
• func Float32frombits(b uint32) float32
• func Float64bits(f float64) uint64
• func Float64frombits(b uint64) float64
• func FrexpS(f float32) (frac float32, exp int)
• func Inf(sign int) float64
• func InfS(sign int) float32
• func IsInf(f float64, sign int) bool
• func IsInfS(f float32, sign int) bool
• func IsNaN(f float64) (is bool)
• func IsNaNS(f float32) (is bool)
• func LdexpS(frac float32, exp int) float32
• func LogS(x float32) float32
• func ModfS(f float32) (inte float32, frac float32)
• func NaN() float64
• func NaNS() float32
• func PowS(x, y float32) float32
• func SinS(x float32) float32
• func SqrtS(x float32) float32

Constants

const (
	E   = 2.71828182845904523536028747135266249775724709369995957496696763 // https://oeis.org/A001113
	Pi  = 3.14159265358979323846264338327950288419716939937510582097494459 // https://oeis.org/A000796
	Phi = 1.61803398874989484820458683436563811772030917980576286213544862 // https://oeis.org/A001622

	Sqrt2   = 1.41421356237309504880168872420969807856967187537694807317667974 // https://oeis.org/A002193
	SqrtE   = 1.64872127070012814684865078781416357165377610071014801157507931 // https://oeis.org/A019774
	SqrtPi  = 1.77245385090551602729816748334114518279754945612238712821380779 // https://oeis.org/A002161
	SqrtPhi = 1.27201964951406896425242246173749149171560804184009624861664038 // https://oeis.org/A139339

	Ln2    = 0.693147180559945309417232121458176568075500134360255254120680009 // https://oeis.org/A002162
	Log2E  = 1 / Ln2
	Ln10   = 2.30258509299404568401799145468436420760110148862877297603332790 // https://oeis.org/A002392
	Log10E = 1 / Ln10
)

Mathematical constants.

const (
	MaxFloat32             = 0x1p127 * (1 + (1 - 0x1p-23)) // 3.40282346638528859811704183484516925440e+38
	SmallestNonzeroFloat32 = 0x1p-126 * 0x1p-23            // 1.401298464324817070923729583289916131280e-45

	MaxFloat64             = 0x1p1023 * (1 + (1 - 0x1p-52)) // 1.79769313486231570814527423731704356798070e+308
	SmallestNonzeroFloat64 = 0x1p-1022 * 0x1p-52            // 4.9406564584124654417656879286822137236505980e-324
)

Floating-point limit values. Max is the largest finite value representable by the type. SmallestNonzero is the smallest positive, non-zero value representable by the type.

const (
	MaxInt    = 1<<(intSize-1) - 1
	MinInt    = -1 << (intSize - 1)
	MaxInt8   = 1<<7 - 1
	MinInt8   = -1 << 7
	MaxInt16  = 1<<15 - 1
	MinInt16  = -1 << 15
	MaxInt32  = 1<<31 - 1
	MinInt32  = -1 << 31
	MaxInt64  = 1<<63 - 1
	MinInt64  = -1 << 63
	MaxUint   = 1<<intSize - 1
	MaxUint8  = 1<<8 - 1
	MaxUint16 = 1<<16 - 1
	MaxUint32 = 1<<32 - 1
	MaxUint64 = 1<<64 - 1
)

Integer limit values.

Functions

func Abs

func Abs(x float64) float64

Abs returns the absolute value of x.

Special cases are:

Abs(±Inf) = +Inf
Abs(NaN) = NaN

func AbsS

func AbsS(x float32) float32

func AcosS

func AcosS(x float32) float32

func AsinS

func AsinS(x float32) float32

func Atan2S

func Atan2S(y, x float32) float32

func AtanS

func AtanS(x float32) float32

func CopysignS

func CopysignS(x, y float32) float32

Copysign returns a value with the magnitude of x and the sign of y.

func CosS

func CosS(y float32) float32

func ExpS

func ExpS(x float32) float32

Exp returns e**x, the base-e exponential of x.

Special cases are:

Exp(+Inf) = +Inf
Exp(NaN) = NaN

Very large values overflow to 0 or +Inf. Very small values underflow to 1.

func Float32bits

func Float32bits(f float32) uint32

Float32bits returns the IEEE 754 binary representation of f, with the sign bit of f and the result in the same bit position. Float32bits(Float32frombits(x)) == x.

func Float32frombits

func Float32frombits(b uint32) float32

Float32frombits returns the floating-point number corresponding to the IEEE 754 binary representation b, with the sign bit of b and the result in the same bit position. Float32frombits(Float32bits(x)) == x.

func Float64bits

func Float64bits(f float64) uint64

Float64bits returns the IEEE 754 binary representation of f, with the sign bit of f and the result in the same bit position, and Float64bits(Float64frombits(x)) == x.

func Float64frombits

func Float64frombits(b uint64) float64

Float64frombits returns the floating-point number corresponding to the IEEE 754 binary representation b, with the sign bit of b and the result in the same bit position. Float64frombits(Float64bits(x)) == x.

func FrexpS

func FrexpS(f float32) (frac float32, exp int)

Frexp breaks f into a normalized fraction and an integral power of two. It returns frac and exp satisfying f == frac × 2**exp, with the absolute value of frac in the interval [½, 1).

Special cases are:

Frexp(±0) = ±0, 0
Frexp(±Inf) = ±Inf, 0
Frexp(NaN) = NaN, 0

func Inf

func Inf(sign int) float64

Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.

func InfS

func InfS(sign int) float32

Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.

func IsInf

func IsInf(f float64, sign int) bool

IsInf reports whether f is an infinity, according to sign. If sign > 0, IsInf reports whether f is positive infinity. If sign < 0, IsInf reports whether f is negative infinity. If sign == 0, IsInf reports whether f is either infinity.

func IsInfS

func IsInfS(f float32, sign int) bool

func IsNaN

func IsNaN(f float64) (is bool)

IsNaN reports whether f is an IEEE 754 “not-a-number” value.

func IsNaNS

func IsNaNS(f float32) (is bool)

IsNaNS reports whether f is an IEEE 754 “not-a-number” value.

func LdexpS

func LdexpS(frac float32, exp int) float32

func LogS

func LogS(x float32) float32

func ModfS

func ModfS(f float32) (inte float32, frac float32)

Modf returns integer and fractional floating-point numbers that sum to f. Both values have the same sign as f.

Special cases are:

Modf(±Inf) = ±Inf, NaN
Modf(NaN) = NaN, NaN

func NaN

func NaN() float64

NaN returns an IEEE 754 “not-a-number” value.

func NaNS

func NaNS() float32

NaN returns an IEEE 754 “not-a-number” value.

func PowS

func PowS(x, y float32) float32

func SinS

func SinS(x float32) float32

func SqrtS

func SqrtS(x float32) float32