/Go

# Package math

## Overview

Package math provides basic constants and mathematical functions.

## Constants

Mathematical constants.

```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
)```

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             = 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)
)```

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 AbsSource

`func Abs(x float64) float64`

Abs returns the absolute value of x.

Special cases are:

```Abs(±Inf) = +Inf
Abs(NaN) = NaN
```

## func AcosSource

`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 AcoshSource

`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 AsinSource

`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 AsinhSource

`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 AtanSource

`func Atan(x float64) float64`

Atan returns the arctangent, in radians, of x.

Special cases are:

```Atan(±0) = ±0
Atan(±Inf) = ±Pi/2
```

## func Atan2Source

`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 AtanhSource

`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 CbrtSource

`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 CeilSource

`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 CopysignSource

`func Copysign(x, y float64) float64`

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

## func CosSource

`func Cos(x float64) float64`

Cos returns the cosine of the radian argument x.

Special cases are:

```Cos(±Inf) = NaN
Cos(NaN) = NaN
```

## func CoshSource

`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 DimSource

`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 ErfSource

`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 ErfcSource

`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 ExpSource

`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 Exp2Source

`func Exp2(x float64) float64`

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

Special cases are the same as Exp.

## func Expm1Source

`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 Float32bitsSource

`func Float32bits(f float32) uint32`

Float32bits returns the IEEE 754 binary representation of f.

## func Float32frombitsSource

`func Float32frombits(b uint32) float32`

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

## func Float64bitsSource

`func Float64bits(f float64) uint64`

Float64bits returns the IEEE 754 binary representation of f.

## func Float64frombitsSource

`func Float64frombits(b uint64) float64`

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

## func FloorSource

`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 FrexpSource

`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 GammaSource

`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 HypotSource

`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 IlogbSource

`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 InfSource

`func Inf(sign int) float64`

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

## func IsInfSource

`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 IsNaNSource

`func IsNaN(f float64) (is bool)`

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

## func J0Source

`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 J1Source

`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 JnSource

`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 LdexpSource

`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 LgammaSource

`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 LogSource

`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
```

## func Log10Source

`func Log10(x float64) float64`

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

## func Log1pSource

`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 Log2Source

`func Log2(x float64) float64`

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

## func LogbSource

`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 MaxSource

`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
```

## func MinSource

`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
```

## func ModSource

`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
```

## func ModfSource

`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
```

## func NaNSource

`func NaN() float64`

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

## func NextafterSource

`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 Nextafter32Source

`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 PowSource

`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
```

## func Pow10Source

`func Pow10(e int) float64`

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

Special cases are:

```Pow10(e) = +Inf for e > 309
Pow10(e) = 0 for e < -324
```

## func RemainderSource

`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
```

## func SignbitSource

`func Signbit(x float64) bool`

Signbit returns true if x is negative or negative zero.

## func SinSource

`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
```

## func SincosSource

`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
```

## func SinhSource

`func Sinh(x float64) float64`

Sinh returns the hyperbolic sine of x.

Special cases are:

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

## func SqrtSource

`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
```

## func TanSource

`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
```

## func TanhSource

`func Tanh(x float64) float64`

Tanh returns the hyperbolic tangent of x.

Special cases are:

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

## func TruncSource

`func Trunc(x float64) float64`

Trunc returns the integer value of x.

Special cases are:

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

## func Y0Source

`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 Y1Source

`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 YnSource

`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
Y1(n, x < 0) = NaN
Y1(n, NaN) = NaN
```

## Subdirectories

Name Synopsis
..
big Package big implements arbitrary-precision arithmetic (big numbers).
cmplx Package cmplx provides basic constants and mathematical functions for complex numbers.
rand Package rand implements pseudo-random number generators.