math

package
v0.0.0-...-8394288 Latest Latest
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 Go to latest Published: May 7, 2022 License: BSD-3-Clause Imports: 3 Imported by: 0

Documentation

Overview

Package math provides basic constants and mathematical functions.

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

Index

Examples

Constants

View Source 
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
)

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
Example 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Acos(1))
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Acosh(1))
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Asin(0))
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Asinh(0))
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Atan(0))
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Atan2(0, 0))
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Atanh(0))
}

Output:

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

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	c := math.Ceil(1.49)
	fmt.Printf("%.1f", c)
}

Output:

2.0

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
Example 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Cos(math.Pi/2))
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Cosh(0))
}

Output:

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

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 

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 

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.

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, 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 
package main

import (
	"fmt"
	"math"
)

func main() {
	c := math.Floor(1.51)
	fmt.Printf("%.1f", c)
}

Output:

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

func Log10 

func Log10(x float64) float64

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

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.

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

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

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

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

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 

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	c := math.Pow(2, 3)
	fmt.Printf("%.1f", c)
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	c := math.Pow10(2)
	fmt.Printf("%.1f", c)
}

Output:

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

func Round 

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	p := math.Round(10.5)
	fmt.Printf("%.1f\n", p)

	n := math.Round(-10.5)
	fmt.Printf("%.1f\n", n)
}

Output:

11.0
-11.0

func RoundToEven 

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	u := math.RoundToEven(11.5)
	fmt.Printf("%.1f\n", u)

	d := math.RoundToEven(12.5)
	fmt.Printf("%.1f\n", d)
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Sin(math.Pi))
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	sin, cos := math.Sincos(0)
	fmt.Printf("%.2f, %.2f", sin, cos)
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Sinh(0))
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

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

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Tan(0))
}

Output:

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 
package main

import (
	"fmt"
	"math"
)

func main() {
	fmt.Printf("%.2f", math.Tanh(0))
}

Output:

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

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

Types

This section is empty.

Source Files

View all Source files

Directories

Path Synopsis
Package big implements arbitrary-precision arithmetic (big numbers).
 Package big implements arbitrary-precision arithmetic (big numbers).
Package bits implements bit counting and manipulation functions for the predeclared unsigned integer types.
 Package bits implements bit counting and manipulation functions for the predeclared unsigned integer types.
Package cmplx provides basic constants and mathematical functions for complex numbers.
 Package cmplx provides basic constants and mathematical functions for complex numbers.
Package rand implements pseudo-random number generators.
 Package rand implements pseudo-random number generators.

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