math

package
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Published: Jun 14, 2017 License: BSD-3-Clause Imports: 2 Imported by: 0

Documentation

Overview

Package math provides basic constants and mathematical functions.

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

Index

Constants

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

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

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

Mathematical constants.

View Source
const (
	MaxFloat32             = 3.40282346638528859811704183484516925440e+38  // 2**127 * (2**24 - 1) / 2**23
	SmallestNonzeroFloat32 = 1.401298464324817070923729583289916131280e-45 // 1 / 2**(127 - 1 + 23)

	MaxFloat64             = 1.797693134862315708145274237317043567981e+308 // 2**1023 * (2**53 - 1) / 2**52
	SmallestNonzeroFloat64 = 4.940656458412465441765687928682213723651e-324 // 1 / 2**(1023 - 1 + 52)
)

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.

View Source
const (
	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
	MaxUint8  = 1<<8 - 1
	MaxUint16 = 1<<16 - 1
	MaxUint32 = 1<<32 - 1
	MaxUint64 = 1<<64 - 1
)

Integer limit values.

Variables

This section is empty.

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 Acos

func Acos(x float64) float64

Acos returns the arccosine, in radians, of x.

Special case is:

Acos(x) = NaN if x < -1 or x > 1

func Acosh

func Acosh(x float64) float64

Acosh returns the inverse hyperbolic cosine of x.

Special cases are:

Acosh(+Inf) = +Inf
Acosh(x) = NaN if x < 1
Acosh(NaN) = NaN

func Asin

func Asin(x float64) float64

Asin returns the arcsine, in radians, of x.

Special cases are:

Asin(±0) = ±0
Asin(x) = NaN if x < -1 or x > 1

func Asinh

func Asinh(x float64) float64

Asinh returns the inverse hyperbolic sine of x.

Special cases are:

Asinh(±0) = ±0
Asinh(±Inf) = ±Inf
Asinh(NaN) = NaN

func Atan

func Atan(x float64) float64

Atan returns the arctangent, in radians, of x.

Special cases are:

Atan(±0) = ±0
Atan(±Inf) = ±Pi/2

func Atan2

func Atan2(y, x float64) float64

Atan2 returns the arc tangent of y/x, using the signs of the two to determine the quadrant of the return value.

Special cases are (in order):

Atan2(y, NaN) = NaN
Atan2(NaN, x) = NaN
Atan2(+0, x>=0) = +0
Atan2(-0, x>=0) = -0
Atan2(+0, x<=-0) = +Pi
Atan2(-0, x<=-0) = -Pi
Atan2(y>0, 0) = +Pi/2
Atan2(y<0, 0) = -Pi/2
Atan2(+Inf, +Inf) = +Pi/4
Atan2(-Inf, +Inf) = -Pi/4
Atan2(+Inf, -Inf) = 3Pi/4
Atan2(-Inf, -Inf) = -3Pi/4
Atan2(y, +Inf) = 0
Atan2(y>0, -Inf) = +Pi
Atan2(y<0, -Inf) = -Pi
Atan2(+Inf, x) = +Pi/2
Atan2(-Inf, x) = -Pi/2

func Atanh

func Atanh(x float64) float64

Atanh returns the inverse hyperbolic tangent of x.

Special cases are:

Atanh(1) = +Inf
Atanh(±0) = ±0
Atanh(-1) = -Inf
Atanh(x) = NaN if x < -1 or x > 1
Atanh(NaN) = NaN

func Cbrt

func Cbrt(x float64) float64

Cbrt returns the cube root of x.

Special cases are:

Cbrt(±0) = ±0
Cbrt(±Inf) = ±Inf
Cbrt(NaN) = NaN

func Ceil

func Ceil(x float64) float64

Ceil returns the least integer value greater than or equal to x.

Special cases are:

Ceil(±0) = ±0
Ceil(±Inf) = ±Inf
Ceil(NaN) = NaN

func Copysign

func Copysign(x, y float64) float64

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

func Cos

func Cos(x float64) float64

Cos returns the cosine of the radian argument x.

Special cases are:

Cos(±Inf) = NaN
Cos(NaN) = NaN

func Cosh

func Cosh(x float64) float64

Cosh returns the hyperbolic cosine of x.

Special cases are:

Cosh(±0) = 1
Cosh(±Inf) = +Inf
Cosh(NaN) = NaN

func Dim

func Dim(x, y float64) float64

Dim returns the maximum of x-y or 0.

Special cases are:

Dim(+Inf, +Inf) = NaN
Dim(-Inf, -Inf) = NaN
Dim(x, NaN) = Dim(NaN, x) = NaN

func Erf

func Erf(x float64) float64

Erf returns the error function of x.

Special cases are:

Erf(+Inf) = 1
Erf(-Inf) = -1
Erf(NaN) = NaN

func Erfc

func Erfc(x float64) float64

Erfc returns the complementary error function of x.

Special cases are:

Erfc(+Inf) = 0
Erfc(-Inf) = 2
Erfc(NaN) = NaN

func Exp

func Exp(x float64) float64

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 Exp2

func Exp2(x float64) float64

Exp2 returns 2**x, the base-2 exponential of x.

Special cases are the same as Exp.

func Expm1

func Expm1(x float64) float64

Expm1 returns e**x - 1, the base-e exponential of x minus 1. It is more accurate than Exp(x) - 1 when x is near zero.

Special cases are:

Expm1(+Inf) = +Inf
Expm1(-Inf) = -1
Expm1(NaN) = NaN

Very large values overflow to -1 or +Inf.

func Float32bits

func Float32bits(f float32) uint32

Float32bits returns the IEEE 754 binary representation of f.

func Float32frombits

func Float32frombits(b uint32) float32

Float32frombits returns the floating point number corresponding to the IEEE 754 binary representation b.

func Float64bits

func Float64bits(f float64) uint64

Float64bits returns the IEEE 754 binary representation of f.

func Float64frombits

func Float64frombits(b uint64) float64

Float64frombits returns the floating point number corresponding the IEEE 754 binary representation b.

func Floor

func Floor(x float64) float64

Floor returns the greatest integer value less than or equal to x.

Special cases are:

Floor(±0) = ±0
Floor(±Inf) = ±Inf
Floor(NaN) = NaN

func Frexp