Package math
import "math"
The math package provides basic constants and mathematical functions.
Package files
acosh.go asin.go asin_decl.go asinh.go atan.go atan2.go atan2_decl.go atan_decl.go atanh.go bits.go cbrt.go const.go copysign.go erf.go exp.go exp2_decl.go exp_decl.go expm1.go fabs.go fabs_decl.go fdim.go floor.go floor_decl.go fmod.go fmod_decl.go frexp.go frexp_decl.go hypot.go hypot_decl.go ldexp.go ldexp_decl.go lgamma.go log.go log1p.go log1p_decl.go log_decl.go modf.go modf_decl.go nextafter.go pow.go pow10.go sin.go sin_decl.go sincos.go sincos_decl.go sinh.go sqrt.go sqrt_decl.go sqrt_port.go tan.go tan_decl.go tanh.go unsafe.goConstants
Mathematical constants. Reference: http://www.research.att.com/~njas/sequences/Axxxxxx
const (
E = 2.71828182845904523536028747135266249775724709369995957496696763 // A001113
Pi = 3.14159265358979323846264338327950288419716939937510582097494459 // A000796
Phi = 1.61803398874989484820458683436563811772030917980576286213544862 // A001622
Sqrt2 = 1.41421356237309504880168872420969807856967187537694807317667974 // A002193
SqrtE = 1.64872127070012814684865078781416357165377610071014801157507931 // A019774
SqrtPi = 1.77245385090551602729816748334114518279754945612238712821380779 // A002161
SqrtPhi = 1.27201964951406896425242246173749149171560804184009624861664038 // A139339
Ln2 = 0.693147180559945309417232121458176568075500134360255254120680009 // A002162
Log2E = 1 / Ln2
Ln10 = 2.30258509299404568401799145468436420760110148862877297603332790 // A002392
Log10E = 1 / Ln10
)
Floating-point limit values. Max is the largest finite value representable by the type. Min is the smallest nonzero value representable by the type.
const (
MaxFloat32 = 3.40282346638528859811704183484516925440e+38 /* 2^127 * (2^24 - 1) / 2^23 */
MinFloat32 = 1.401298464324817070923729583289916131280e-45 /* 1 / 2^(127 - 1 + 23) */
MaxFloat64 = 1.797693134862315708145274237317043567981e+308 /* 2^1023 * (2^53 - 1) / 2^52 */
MinFloat64 = 4.940656458412465441765687928682213723651e-324 /* 1 / 2^(1023 - 1 + 52) */
)
Integer limit values.
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
)
func Acos
func Acos(x float64) float64
func Acosh
func Acosh(x float64) float64
Acosh(x) calculates the inverse hyperbolic cosine of x.
Special cases are:
Acosh(x) = NaN if x < 1 Acosh(NaN) = NaN
func Asin
func Asin(x float64) float64
func Asinh
func Asinh(x float64) float64
Asinh(x) calculates the inverse hyperbolic sine of x.
Special cases are:
Asinh(+Inf) = +Inf Asinh(-Inf) = -Inf Asinh(NaN) = NaN
func Atan
func Atan(x float64) float64
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) = 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(x) calculates the inverse hyperbolic tangent of x.
Special cases are:
Atanh(x) = NaN if x < -1 or x > 1 Atanh(1) = +Inf Atanh(-1) = -Inf Atanh(NaN) = NaN
func Cbrt
func Cbrt(x float64) float64
Cbrt returns the cube root of its argument.
Special cases are:
Exp(+Inf) = +Inf Exp(-Inf) = -Inf Exp(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(+Inf) = +Inf Ceil(-Inf) = -Inf Ceil(NaN) = NaN
func Copysign
func Copysign(x, y float64) float64
Copysign(x, y) 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 x.
func Cosh
func Cosh(x float64) float64
Cosh returns the hyperbolic cosine of x.
func Erf
func Erf(x float64) float64
Erf(x) 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(x) returns the complementary error function of x.
Special cases are:
Erf(+Inf) = 0 Erf(-Inf) = 2 Erf(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 Fabs
func Fabs(x float64) float64
func Fdim
func Fdim(x, y float64) float64
Fdim returns the maximum of x-y or 0.
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(+Inf) = +Inf Floor(-Inf) = -Inf Floor(NaN) = NaN
func Fmax
func Fmax(x, y float64) float64
Fmax returns the larger of x or y.
func Fmin
func Fmin(x, y float64) float64
Fmin returns the smaller of x or y.
func Fmod
func Fmod(x, y float64) float64
Fmod returns the floating-point remainder of x/y. The magnitude of the result is less than y and its sign agrees with that of x.
Special cases are:
if x is not finite, Fmod returns NaN if y is 0 or NaN, Fmod returns NaN
func Frexp
func Frexp(f float64) (frac float64, exp int)
Frexp breaks f into a normalized fraction and an integral power of two. It returns frac and exp satisfying f == frac × 2<sup>exp</sup>, with the absolute value of frac in the interval [½, 1).
func Hypot
func Hypot(x, y float64) float64
func Inf
func Inf(sign int) float64
Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.
func IsInf
func IsInf(f float64, sign int) bool
IsInf returns whether f is an infinity, according to sign. If sign > 0, IsInf returns whether f is positive infinity. If sign < 0, IsInf returns whether f is negative infinity. If sign == 0, IsInf returns whether f is either infinity.
func IsNaN
func IsNaN(f float64) (is bool)
IsNaN returns whether f is an IEEE 754 “not-a-number” value.
func Ldexp
func Ldexp(frac float64, exp int) float64
Ldexp is the inverse of Frexp. It returns frac × 2<sup>exp</sup>.
func Lgamma
func Lgamma(x float64) (lgamma float64, sign int)
Lgamma returns the natural logarithm and sign (-1 or +1) of Gamma(x).
Special cases are:
Lgamma(+Inf) = +Inf Lgamma(0) = +Inf Lgamma(-integer) = +Inf Lgamma(-Inf) = -Inf Lgamma(NaN) = NaN
func Log
func Log(x float64) float64
func Log10
func Log10(x float64) float64
func Log1p
func Log1p(x float64) float64
Log1p returns the natural logarithm of 1 plus its argument x. It is more accurate than Log(1 + x) when x is near zero.
Special cases are:
Log1p(+Inf) = +Inf Log1p(-1) = -Inf Log1p(x < -1) = NaN Log1p(NaN) = NaN
func Log2
func Log2(x float64) float64
func Modf
func Modf(f float64) (int float64, frac float64)
func NaN
func NaN() float64
NaN returns an IEEE 754 “not-a-number” value.
func Nextafter
func Nextafter(x, y float64) (r float64)
Nextafter returns the next representable value after x towards y. If x == y, then x is returned.
Special cases are:
Nextafter(NaN, y) = NaN Nextafter(x, NaN) = NaN
func Pow
func Pow(x, y float64) float64
Pow returns x**y, the base-x exponential of y.
func Pow10
func Pow10(e int) float64
Pow10 returns 10**e, the base-10 exponential of e.
func Sin
func Sin(x float64) float64
Sin returns the sine of x.
func Sincos
func Sincos(x float64) (sin, cos float64)
Sincos(x) returns Sin(x), Cos(x).
Special conditions are:
Sincos(+Inf) = NaN, NaN Sincos(-Inf) = NaN, NaN Sincos(NaN) = NaN, NaN
func Sinh
func Sinh(x float64) float64
Sinh returns the hyperbolic sine of x.
func Sqrt
func Sqrt(x float64) float64
func Tan
func Tan(x float64) float64
func Tanh
func Tanh(x float64) float64
Tanh computes the hyperbolic tangent of x.
func Trunc
func Trunc(x float64) float64
Trunc returns the integer value of x.
Special cases are:
Trunc(+Inf) = +Inf Trunc(-Inf) = -Inf Trunc(NaN) = NaN
Bugs
The manual should define the special cases for all of these functions.