Package math

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 Acos(x float64) float64
func Acosh(x float64) float64
func Asin(x float64) float64
func Asinh(x float64) float64
func Atan(x float64) float64
func Atan2(y, x float64) float64
func Atanh(x float64) float64
func Cbrt(x float64) float64
func Ceil(x float64) float64
func Copysign(f, sign float64) float64
func Cos(x float64) float64
func Cosh(x float64) float64
func Dim(x, y float64) float64
func Erf(x float64) float64
func Erfc(x float64) float64
func Erfcinv(x float64) float64
func Erfinv(x float64) float64
func Exp(x float64) float64
func Exp2(x float64) float64
func Expm1(x float64) float64
func FMA(x, y, z float64) float64
func Float32bits(f float32) uint32
func Float32frombits(b uint32) float32
func Float64bits(f float64) uint64
func Float64frombits(b uint64) float64
func Floor(x float64) float64
func Frexp(f float64) (frac float64, exp int)
func Gamma(x float64) float64
func Hypot(p, q float64) float64
func Ilogb(x float64) int
func Inf(sign int) float64
func IsInf(f float64, sign int) bool
func IsNaN(f float64) (is bool)
func J0(x float64) float64
func J1(x float64) float64
func Jn(n int, x float64) float64
func Ldexp(frac float64, exp int) float64
func Lgamma(x float64) (lgamma float64, sign int)
func Log(x float64) float64
func Log10(x float64) float64
func Log1p(x float64) float64
func Log2(x float64) float64
func Logb(x float64) float64
func Max(x, y float64) float64
func Min(x, y float64) float64
func Mod(x, y float64) float64
func Modf(f float64) (int float64, frac float64)
func NaN() float64
func Nextafter(x, y float64) (r float64)
func Nextafter32(x, y float32) (r float32)
func Pow(x, y float64) float64
func Pow10(n int) float64
func Remainder(x, y float64) float64
func Round(x float64) float64
func RoundToEven(x float64) float64
func Signbit(x float64) bool
func Sin(x float64) float64
func Sincos(x float64) (sin, cos float64)
func Sinh(x float64) float64
func Sqrt(x float64) float64
func Tan(x float64) float64
func Tanh(x float64) float64
func Trunc(x float64) float64
func Y0(x float64) float64
func Y1(x float64) float64
func Yn(n int, x float64) float64

Package files

abs.go acosh.go asin.go asinh.go atan.go atan2.go atanh.go bits.go cbrt.go const.go copysign.go dim.go dim_asm.go erf.go erfinv.go exp.go exp2_noasm.go exp_amd64.go exp_asm.go expm1.go floor.go floor_asm.go fma.go frexp.go gamma.go hypot.go hypot_asm.go j0.go j1.go jn.go ldexp.go lgamma.go log.go log10.go log1p.go log_asm.go logb.go mod.go modf.go modf_noasm.go nextafter.go pow.go pow10.go remainder.go signbit.go sin.go sincos.go sinh.go sqrt.go stubs.go tan.go tanh.go trig_reduce.go unsafe.go

Constants

Mathematical 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
)

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 (
    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
)

Integer limit values.

const (
    MaxInt    = 1<<(intSize-1) - 1  // MaxInt32 or MaxInt64 depending on intSize.
    MinInt    = -1 << (intSize - 1) // MinInt32 or MinInt64 depending on intSize.
    MaxInt8   = 1<<7 - 1            // 127
    MinInt8   = -1 << 7             // -128
    MaxInt16  = 1<<15 - 1           // 32767
    MinInt16  = -1 << 15            // -32768
    MaxInt32  = 1<<31 - 1           // 2147483647
    MinInt32  = -1 << 31            // -2147483648
    MaxInt64  = 1<<63 - 1           // 9223372036854775807
    MinInt64  = -1 << 63            // -9223372036854775808
    MaxUint   = 1<<intSize - 1      // MaxUint32 or MaxUint64 depending on intSize.
    MaxUint8  = 1<<8 - 1            // 255
    MaxUint16 = 1<<16 - 1           // 65535
    MaxUint32 = 1<<32 - 1           // 4294967295
    MaxUint64 = 1<<64 - 1           // 18446744073709551615
)

func Abs

func Abs(x float64) float64

Abs returns the absolute value of x.

Special cases are:

Abs(±Inf) = +Inf
Abs(NaN) = NaN

Example

2.0
2.0

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

Example

0.00

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

Example

0.00

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

Example

0.00

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

Example

0.00

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

Example

0.00

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

Example

0.00

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

Example

0.00

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

Example

2.00
3.00

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

Example

2.0

func Copysign

func Copysign(f, sign float64) float64

Copysign returns a value with the magnitude of f and the sign of sign.

Example

-3.20

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

Example

0.00

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

Example

1.00

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

Example

6.00
0.00

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 Erfcinv 1.10

func Erfcinv(x float64) float64

Erfcinv returns the inverse of Erfc(x).

Special cases are:

Erfcinv(0) = +Inf
Erfcinv(2) = -Inf
Erfcinv(x) = NaN if x < 0 or x > 2
Erfcinv(NaN) = NaN

func Erfinv 1.10

func Erfinv(x float64) float64

Erfinv returns the inverse error function of x.

Special cases are:

Erfinv(1) = +Inf
Erfinv(-1) = -Inf
Erfinv(x) = NaN if x < -1 or x > 1
Erfinv(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.

Example

2.72
7.39
0.37

func Exp2

func Exp2(x float64) float64

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

Special cases are the same as Exp.

Example

2.00
0.12

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.

Example

0.010050
-0.632121

func FMA 1.14

func FMA(x, y, z float64) float64

FMA returns x * y + z, computed with only one rounding. (That is, FMA returns the fused multiply-add of x, y, and z.)

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 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

Example

1.0

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**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 Gamma

func Gamma(x float64) float64

Gamma returns the Gamma function of x.

Special cases are:

Gamma(+Inf) = +Inf
Gamma(+0) = +Inf
Gamma(-0) = -Inf
Gamma(x) = NaN for integer x < 0
Gamma(-Inf) = NaN
Gamma(NaN) = NaN

func Hypot

func Hypot(p, q float64) float64

Hypot returns Sqrt(p*p + q*q), taking care to avoid unnecessary overflow and underflow.

Special cases are:

Hypot(±Inf, q) = +Inf
Hypot(p, ±Inf) = +Inf
Hypot(NaN, q) = NaN
Hypot(p, NaN) = NaN

func Ilogb

func Ilogb(x float64) int

Ilogb returns the binary exponent of x as an integer.

Special cases are:

Ilogb(±Inf) = MaxInt32
Ilogb(0) = MinInt32
Ilogb(NaN) = MaxInt32

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 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 IsNaN

func IsNaN(f float64) (is bool)

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

func J0

func J0(x float64) float64

J0 returns the order-zero Bessel function of the first kind.

Special cases are:

J0(±Inf) = 0
J0(0) = 1
J0(NaN) = NaN

func J1

func J1(x float64) float64

J1 returns the order-one Bessel function of the first kind.

Special cases are:

J1(±Inf) = 0
J1(NaN) = NaN

func Jn

func Jn(n int, x float64) float64

Jn returns the order-n Bessel function of the first kind.

Special cases are:

Jn(n, ±Inf) = 0
Jn(n, NaN) = NaN

func Ldexp

func Ldexp(frac float64, exp int) float64

Ldexp is the inverse of Frexp. It returns frac × 2**exp.

Special cases are:

Ldexp(±0, exp) = ±0
Ldexp(±Inf, exp) = ±Inf
Ldexp(NaN, exp) = NaN

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

Log returns the natural logarithm of x.

Special cases are:

Log(+Inf) = +Inf
Log(0) = -Inf
Log(x < 0) = NaN
Log(NaN) = NaN

Example

0.0
1.0

func Log10

func Log10(x float64) float64

Log10 returns the decimal logarithm of x. The special cases are the same as for Log.

Example

2.0

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(±0) = ±0
Log1p(-1) = -Inf
Log1p(x < -1) = NaN
Log1p(NaN) = NaN

func Log2

func Log2(x float64) float64

Log2 returns the binary logarithm of x. The special cases are the same as for Log.

Example

8.0

func Logb

func Logb(x float64) float64

Logb returns the binary exponent of x.

Special cases are:

Logb(±Inf) = +Inf
Logb(0) = -Inf
Logb(NaN) = NaN

func Max

func Max(x, y float64) float64

Max returns the larger of x or y.

Special cases are:

Max(x, +Inf) = Max(+Inf, x) = +Inf
Max(x, NaN) = Max(NaN, x) = NaN
Max(+0, ±0) = Max(±0, +0) = +0
Max(-0, -0) = -0

Note that this differs from the built-in function max when called with NaN and +Inf.

func Min

func Min(x, y float64) float64

Min returns the smaller of x or y.

Special cases are:

Min(x, -Inf) = Min(-Inf, x) = -Inf
Min(x, NaN) = Min(NaN, x) = NaN
Min(-0, ±0) = Min(±0, -0) = -0

Note that this differs from the built-in function min when called with NaN and -Inf.

func Mod

func Mod(x, y float64) float64

Mod 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:

Mod(±Inf, y) = NaN
Mod(NaN, y) = NaN
Mod(x, 0) = NaN
Mod(x, ±Inf) = x
Mod(x, NaN) = NaN

Example

3.0

func Modf

func Modf(f float64) (int float64, frac float64)

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

Example

3.00, 0.14
-2.00, -0.71

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 float64 value after x towards y.

Special cases are:

Nextafter(x, x)   = x
Nextafter(NaN, y) = NaN
Nextafter(x, NaN) = NaN

func Nextafter32 1.4

func Nextafter32(x, y float32) (r float32)

Nextafter32 returns the next representable float32 value after x towards y.

Special cases are:

Nextafter32(x, x)   = x
Nextafter32(NaN, y) = NaN
Nextafter32(x, NaN) = NaN

func Pow

func Pow(x, y float64) float64

Pow returns x**y, the base-x exponential of y.

Special cases are (in order):

Pow(x, ±0) = 1 for any x
Pow(1, y) = 1 for any y
Pow(x, 1) = x for any x
Pow(NaN, y) = NaN
Pow(x, NaN) = NaN
Pow(±0, y) = ±Inf for y an odd integer < 0
Pow(±0, -Inf) = +Inf
Pow(±0, +Inf) = +0
Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
Pow(±0, y) = ±0 for y an odd integer > 0
Pow(±0, y) = +0 for finite y > 0 and not an odd integer
Pow(-1, ±Inf) = 1
Pow(x, +Inf) = +Inf for |x| > 1
Pow(x, -Inf) = +0 for |x| > 1
Pow(x, +Inf) = +0 for |x| < 1
Pow(x, -Inf) = +Inf for |x| < 1
Pow(+Inf, y) = +Inf for y > 0
Pow(+Inf, y) = +0 for y < 0
Pow(-Inf, y) = Pow(-0, -y)
Pow(x, y) = NaN for finite x < 0 and finite non-integer y

Example

8.0

func Pow10

func Pow10(n int) float64

Pow10 returns 10**n, the base-10 exponential of n.

Special cases are:

Pow10(n) =    0 for n < -323
Pow10(n) = +Inf for n > 308

Example

100.0

func Remainder

func Remainder(x, y float64) float64

Remainder returns the IEEE 754 floating-point remainder of x/y.

Special cases are:

Remainder(±Inf, y) = NaN
Remainder(NaN, y) = NaN
Remainder(x, 0) = NaN
Remainder(x, ±Inf) = x
Remainder(x, NaN) = NaN

Example

10.0

func Round 1.10

func Round(x float64) float64

Round returns the nearest integer, rounding half away from zero.

Special cases are:

Round(±0) = ±0
Round(±Inf) = ±Inf
Round(NaN) = NaN

Example

11.0
-11.0

func RoundToEven 1.10

func RoundToEven(x float64) float64

RoundToEven returns the nearest integer, rounding ties to even.

Special cases are:

RoundToEven(±0) = ±0
RoundToEven(±Inf) = ±Inf
RoundToEven(NaN) = NaN

Example

12.0
12.0

func Signbit

func Signbit(x float64) bool

Signbit reports whether x is negative or negative zero.

func Sin

func Sin(x float64) float64

Sin returns the sine of the radian argument x.

Special cases are:

Sin(±0) = ±0
Sin(±Inf) = NaN
Sin(NaN) = NaN

Example

0.00

func Sincos

func Sincos(x float64) (sin, cos float64)

Sincos returns Sin(x), Cos(x).

Special cases are:

Sincos(±0) = ±0, 1
Sincos(±Inf) = NaN, NaN
Sincos(NaN) = NaN, NaN

Example

0.00, 1.00

func Sinh

func Sinh(x float64) float64

Sinh returns the hyperbolic sine of x.

Special cases are:

Sinh(±0) = ±0
Sinh(±Inf) = ±Inf
Sinh(NaN) = NaN

Example

0.00

func Sqrt

func Sqrt(x float64) float64

Sqrt returns the square root of x.

Special cases are:

Sqrt(+Inf) = +Inf
Sqrt(±0) = ±0
Sqrt(x < 0) = NaN
Sqrt(NaN) = NaN

Example

5.0

func Tan

func Tan(x float64) float64

Tan returns the tangent of the radian argument x.

Special cases are:

Tan(±0) = ±0
Tan(±Inf) = NaN
Tan(NaN) = NaN

Example

0.00

func Tanh

func Tanh(x float64) float64

Tanh returns the hyperbolic tangent of x.

Special cases are:

Tanh(±0) = ±0
Tanh(±Inf) = ±1
Tanh(NaN) = NaN

Example

0.00

func Trunc

func Trunc(x float64) float64

Trunc returns the integer value of x.

Special cases are:

Trunc(±0) = ±0
Trunc(±Inf) = ±Inf
Trunc(NaN) = NaN

Example

3.00
-1.00

func Y0

func Y0(x float64) float64

Y0 returns the order-zero Bessel function of the second kind.

Special cases are:

Y0(+Inf) = 0
Y0(0) = -Inf
Y0(x < 0) = NaN
Y0(NaN) = NaN

func Y1

func Y1(x float64) float64

Y1 returns the order-one Bessel function of the second kind.

Special cases are:

Y1(+Inf) = 0
Y1(0) = -Inf
Y1(x < 0) = NaN
Y1(NaN) = NaN

func Yn

func Yn(n int, x float64) float64

Yn returns the order-n Bessel function of the second kind.

Special cases are:

Yn(n, +Inf) = 0
Yn(n ≥ 0, 0) = -Inf
Yn(n < 0, 0) = +Inf if n is odd, -Inf if n is even
Yn(n, x < 0) = NaN
Yn(n, NaN) = NaN

Subdirectories

Name Synopsis
..
big Package big implements arbitrary-precision arithmetic (big numbers).
bits Package bits implements bit counting and manipulation functions for the predeclared unsigned integer types.
cmplx Package cmplx provides basic constants and mathematical functions for complex numbers.
rand Package rand implements pseudo-random number generators suitable for tasks such as simulation, but it should not be used for security-sensitive work.
v2 Package rand implements pseudo-random number generators suitable for tasks such as simulation, but it should not be used for security-sensitive work.