Package math
Overview ▹
Overview ▾
Package math provides basic constants and mathematical functions.
This package does not guarantee bit-identical results across architectures.
Index ▹
Index ▾
Examples
(Expand All)
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 erf.go erfinv.go exp.go exp_asm.go expm1.go floor.go fma.go frexp.go gamma.go hypot.go j0.go j1.go jn.go ldexp.go lgamma.go log.go log10.go log1p.go logb.go mod.go modf.go nextafter.go pow.go pow10.go remainder.go signbit.go sin.go sincos.go sinh.go sqrt.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 = 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 Abs
func Abs(x float64) float64Abs returns the absolute value of x.
Special cases are:
Abs(±Inf) = +Inf
Abs(NaN) = NaN
▹ Example
▾ Example
2.0
2.0
func Acos
func Acos(x float64) float64Acos returns the arccosine, in radians, of x.
Special case is:
Acos(x) = NaN if x < -1 or x > 1
▹ Example
▾ Example
0.00
func Acosh
func Acosh(x float64) float64Acosh returns the inverse hyperbolic cosine of x.
Special cases are:
Acosh(+Inf) = +Inf
Acosh(x) = NaN if x < 1
Acosh(NaN) = NaN
▹ Example
▾ Example
0.00
func Asin
func Asin(x float64) float64Asin returns the arcsine, in radians, of x.
Special cases are:
Asin(±0) = ±0
Asin(x) = NaN if x < -1 or x > 1
▹ Example
▾ Example
0.00
func Asinh
func Asinh(x float64) float64Asinh returns the inverse hyperbolic sine of x.
Special cases are:
Asinh(±0) = ±0
Asinh(±Inf) = ±Inf
Asinh(NaN) = NaN
▹ Example
▾ Example
0.00
func Atan
func Atan(x float64) float64Atan returns the arctangent, in radians, of x.
Special cases are:
Atan(±0) = ±0
Atan(±Inf) = ±Pi/2
▹ Example
▾ Example
0.00
func Atan2
func Atan2(y, x float64) float64Atan2 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
▾ Example
0.00
func Atanh
func Atanh(x float64) float64Atanh 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
▾ Example
0.00
func Cbrt
func Cbrt(x float64) float64Cbrt returns the cube root of x.
Special cases are:
Cbrt(±0) = ±0
Cbrt(±Inf) = ±Inf
Cbrt(NaN) = NaN
▹ Example
▾ Example
2.00
3.00
func Ceil
func Ceil(x float64) float64Ceil returns the least integer value greater than or equal to x.
Special cases are:
Ceil(±0) = ±0
Ceil(±Inf) = ±Inf
Ceil(NaN) = NaN
▹ Example
▾ Example
2.0
func Copysign
func Copysign(x, y float64) float64Copysign returns a value with the magnitude of x and the sign of y.
▹ Example
▾ Example
-3.20
func Cos
func Cos(x float64) float64Cos returns the cosine of the radian argument x.
Special cases are:
Cos(±Inf) = NaN
Cos(NaN) = NaN
▹ Example
▾ Example
0.00
func Cosh
func Cosh(x float64) float64Cosh returns the hyperbolic cosine of x.
Special cases are:
Cosh(±0) = 1
Cosh(±Inf) = +Inf
Cosh(NaN) = NaN
▹ Example
▾ Example
1.00
func Dim
func Dim(x, y float64) float64Dim 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
▾ Example
6.00
0.00
func Erf
func Erf(x float64) float64Erf returns the error function of x.
Special cases are:
Erf(+Inf) = 1
Erf(-Inf) = -1
Erf(NaN) = NaN
func Erfc
func Erfc(x float64) float64Erfc 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) float64Erfcinv 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) float64Erfinv 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) float64Exp 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
▾ Example
2.72
7.39
0.37
func Exp2
func Exp2(x float64) float64Exp2 returns 2**x, the base-2 exponential of x.
Special cases are the same as Exp.
▹ Example
▾ Example
2.00
0.12
func Expm1
func Expm1(x float64) float64Expm1 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
▾ Example
0.010050
-0.632121
func FMA 1.14
func FMA(x, y, z float64) float64FMA 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) uint32Float32bits 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) float32Float32frombits 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) uint64Float64bits 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) float64Float64frombits 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) float64Floor returns the greatest integer value less than or equal to x.
Special cases are:
Floor(±0) = ±0
Floor(±Inf) = ±Inf
Floor(NaN) = NaN
▹ Example
▾ 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) float64Gamma 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) float64Hypot 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) intIlogb 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) float64Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.
func IsInf
func IsInf(f float64, sign int) boolIsInf 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) float64J0 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) float64J1 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) float64Jn 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) float64Ldexp 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) float64Log returns the natural logarithm of x.
Special cases are:
Log(+Inf) = +Inf
Log(0) = -Inf
Log(x < 0) = NaN
Log(NaN) = NaN
▹ Example
▾ Example
0.0
1.0
func Log10
func Log10(x float64) float64Log10 returns the decimal logarithm of x. The special cases are the same as for Log.
▹ Example
▾ Example
2.0
func Log1p
func Log1p(x float64) float64Log1p 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) float64Log2 returns the binary logarithm of x. The special cases are the same as for Log.
▹ Example
▾ Example
8.0
func Logb
func Logb(x float64) float64Logb 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) float64Max 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) float64Min 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) float64Mod 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
▾ 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
▾ Example
3.00, 0.14
-2.00, -0.71
func NaN
func NaN() float64NaN 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) float64Pow 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
▾ Example
8.0
func Pow10
func Pow10(n int) float64Pow10 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
▾ Example
100.0
func Remainder
func Remainder(x, y float64) float64Remainder 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 1.10
func Round(x float64) float64Round returns the nearest integer, rounding half away from zero.
Special cases are:
Round(±0) = ±0
Round(±Inf) = ±Inf
Round(NaN) = NaN
▹ Example
▾ Example
11.0
-11.0
func RoundToEven 1.10
func RoundToEven(x float64) float64RoundToEven returns the nearest integer, rounding ties to even.
Special cases are:
RoundToEven(±0) = ±0
RoundToEven(±Inf) = ±Inf
RoundToEven(NaN) = NaN
▹ Example
▾ Example
12.0
12.0
func Signbit
func Signbit(x float64) boolSignbit reports whether x is negative or negative zero.
func Sin
func Sin(x float64) float64Sin returns the sine of the radian argument x.
Special cases are:
Sin(±0) = ±0
Sin(±Inf) = NaN
Sin(NaN) = NaN
▹ Example
▾ 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
▾ Example
0.00, 1.00
func Sinh
func Sinh(x float64) float64Sinh returns the hyperbolic sine of x.
Special cases are:
Sinh(±0) = ±0
Sinh(±Inf) = ±Inf
Sinh(NaN) = NaN
▹ Example
▾ Example
0.00
func Sqrt
func Sqrt(x float64) float64Sqrt returns the square root of x.
Special cases are:
Sqrt(+Inf) = +Inf
Sqrt(±0) = ±0
Sqrt(x < 0) = NaN
Sqrt(NaN) = NaN
▹ Example
▾ Example
5.0
func Tan
func Tan(x float64) float64Tan returns the tangent of the radian argument x.
Special cases are:
Tan(±0) = ±0
Tan(±Inf) = NaN
Tan(NaN) = NaN
▹ Example
▾ Example
0.00
func Tanh
func Tanh(x float64) float64Tanh returns the hyperbolic tangent of x.
Special cases are:
Tanh(±0) = ±0
Tanh(±Inf) = ±1
Tanh(NaN) = NaN
▹ Example
▾ Example
0.00
func Trunc
func Trunc(x float64) float64Trunc returns the integer value of x.
Special cases are:
Trunc(±0) = ±0
Trunc(±Inf) = ±Inf
Trunc(NaN) = NaN
▹ Example
▾ Example
3.00
-1.00
func Y0
func Y0(x float64) float64Y0 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) float64Y1 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) float64Yn 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. |