/Go

# Package math

## Overview

Package math provides basic constants and mathematical functions.

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

Sqrt

## 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(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
```

## 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
```

#### Example

```package main

import (
"fmt"
"math"
)

func main() {
const (
a = 3
b = 4
)
c := math.Sqrt(a*a + b*b)
fmt.Printf("%.1f", c)
}
```

## 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
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.