math - The Go Programming Language

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
)

Mathematical constants. Reference: http://oeis.org/Axxxxxx

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.

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.

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 of x.

Special case is:

Acos(x) = NaN if x < -1 or x > 1

func Acosh

func Acosh(x float64) float64

Acosh(x) calculates the inverse hyperbolic cosine of x.

Special cases are:

Acosh(+Inf) = +Inf
Acosh(x) = NaN if x < 1
Acosh(NaN) = NaN

func Asin

func Asin(x float64) float64

Asin returns the arcsine of x.

Special cases are:

Asin(0) = 0
Asin(x) = NaN if x < -1 or x > 1

func Asinh

func Asinh(x float64) float64

Asinh(x) calculates the inverse hyperbolic sine of x.

Special cases are:

Asinh(0) = 0
Asinh(Inf) = Inf
Asinh(NaN) = NaN

func Atan

func Atan(x float64) float64

Atan returns the arctangent of x.

Special cases are:

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

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

func Atanh

func Atanh(x float64) float64

Atanh(x) calculates 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 Cbrt

func Cbrt(x float64) float64

Cbrt returns the cube root of its argument.

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

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.

Special cases are:

Cos(Inf) = NaN
Cos(NaN) = NaN

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

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(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:

Erfc(+Inf) = 0
Erfc(-Inf) = 2
Erfc(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.

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(0) = 0
Floor(Inf) = Inf
Floor(NaN) = 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**exp, with the absolute value of frac in the interval [?, 1).

Special cases are:

Frexp(0) = 0, 0
Frexp(Inf) = Inf, 0
Frexp(NaN) = NaN, 0

func Gamma

func Gamma(x float64) float64

Gamma(x) returns the Gamma function of x.

Special cases are:

Gamma(Inf) = Inf
Gamma(NaN) = NaN

Large values overflow to +Inf. Zero and negative integer arguments return Inf.

func Hypot

func Hypot(p, q float64) float64

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

Special cases are:

Hypot(p, q) = +Inf if p or q is infinite
Hypot(p, q) = NaN if p or q is NaN

func Ilogb

func Ilogb(x float64) int

Ilogb(x) 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 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 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(x) 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 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.

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 Pow10

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 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 Signbit

func Signbit(x float64) bool

Signbit returns true if x is negative or negative zero.

func Sin

func Sin(x float64) float64

Sin returns the sine of x.

Special cases are:

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

func Sincos

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

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

Special cases are:

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

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

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

func Tan

func Tan(x float64) float64

Tan returns the tangent of x.

Special cases are:

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

func Tanh

func Tanh(x float64) float64

Tanh computes the hyperbolic tangent of x.

Special cases are:

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

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

Subdirectories

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

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