go: cuelang.org/go/pkg/math Index | Files | Directories

package math

import "cuelang.org/go/pkg/math"

Index

Package Files

big.go manual.go math.go pkg.go

Constants

❖
const (
    MaxExp  = 2147483647  // largest supported exponent
    MinExp  = -2147483648 // smallest supported exponent
    MaxPrec = 4294967295  // largest (theoretically) supported precision; likely memory-limited
)

Exponent and precision limits.

❖
const (
    ToNearestEven = 0 // == IEEE 754-2008 roundTiesToEven
    ToNearestAway = 1 // == IEEE 754-2008 roundTiesToAway
    ToZero        = 2 // == IEEE 754-2008 roundTowardZero
    AwayFromZero  = 3 // no IEEE 754-2008 equivalent
    ToNegativeInf = 4 // == IEEE 754-2008 roundTowardNegative
    ToPositiveInf = 5 // == IEEE 754-2008 roundTowardPositive
)

These constants define supported rounding modes.

❖
const (
    Below = -1
    Exact = 0
    Above = 1
)

Constants describing the Accuracy of a Float.

❖
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  = 1000000000000000000000000000000000000000000000000000000000000000 / 693147180559945309417232121458176568075500134360255254120680009
    Ln10   = 2.30258509299404568401799145468436420760110148862877297603332790 // https://oeis.org/A002392
    Log10E = 10000000000000000000000000000000000000000000000000000000000000 / 23025850929940456840179914546843642076011014886287729760333279
)

Mathematical constants.

❖
const MaxBase = 62

MaxBase is the largest number base accepted for string conversions.

func Abs Uses

❖
func Abs(x *internal.Decimal) (*internal.Decimal, error)

Abs returns the absolute value of x.

Special case: Abs(±Inf) = +Inf

func Acos Uses

❖
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 Acosh Uses

❖
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 Asin Uses

❖
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 Asinh Uses

❖
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 Atan Uses

❖
func Atan(x float64) float64

Atan returns the arctangent, in radians, of x.

Special cases are: 

Atan(±0) = ±0
Atan(±Inf) = ±Pi/2

func Atan2 Uses

❖
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 Uses

❖
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 Cbrt Uses

❖
func Cbrt(x *internal.Decimal) (*internal.Decimal, error)

Cbrt returns the cube root of x.

Special cases are: 

Cbrt(±0) = ±0
Cbrt(±Inf) = ±Inf
Cbrt(NaN) = NaN

func Ceil Uses

❖
func Ceil(x *internal.Decimal) (*big.Int, error)

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 Uses

❖
func Copysign(x, y *internal.Decimal) *internal.Decimal

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

func Cos Uses

❖
func Cos(x float64) float64

Cos returns the cosine of the radian argument x.

Special cases are: 

Cos(±Inf) = NaN
Cos(NaN) = NaN

func Cosh Uses

❖
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 Uses

❖
func Dim(x, y *internal.Decimal) (*internal.Decimal, error)

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 Uses

❖
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 Uses

❖
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 Uses

❖
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 Uses

❖
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 Uses

❖
func Exp(x *internal.Decimal) (*internal.Decimal, error)

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 Uses

❖
func Exp2(x *internal.Decimal) (*internal.Decimal, error)

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

Special cases are the same as Exp.

func Expm1 Uses

❖
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 Floor Uses

❖
func Floor(x *internal.Decimal) (*big.Int, error)

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 Gamma Uses

❖
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 Uses

❖
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 Uses

❖
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 J0 Uses

❖
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 Uses

❖
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 Jacobi Uses

❖
func Jacobi(x, y *big.Int) int

Jacobi returns the Jacobi symbol (x/y), either +1, -1, or 0. The y argument must be an odd integer.

func Jn Uses

❖
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 Uses

❖
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 Log Uses

❖
func Log(x *internal.Decimal) (*internal.Decimal, error)

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 Uses

❖
func Log10(x *internal.Decimal) (*internal.Decimal, error)

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

func Log1p Uses

❖
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 Uses

❖
func Log2(x *internal.Decimal) (*internal.Decimal, error)

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

func Logb Uses

❖
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 Mod Uses

❖
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 MultipleOf Uses

❖
func MultipleOf(x, y *internal.Decimal) (bool, error)

MultipleOf reports whether x is a multiple of y.

func Pow Uses

❖
func Pow(x, y *internal.Decimal) (*internal.Decimal, error)

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 Uses

❖
func Pow10(n int32) *internal.Decimal

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

func Remainder Uses

❖
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 Uses

❖
func Round(x *internal.Decimal) (*big.Int, error)

Round returns the nearest integer, rounding half away from zero.

Special cases are: 

Round(±0) = ±0
Round(±Inf) = ±Inf
Round(NaN) = NaN

func RoundToEven Uses

❖
func RoundToEven(x *internal.Decimal) (*big.Int, error)

RoundToEven returns the nearest integer, rounding ties to even.

Special cases are: 

RoundToEven(±0) = ±0
RoundToEven(±Inf) = ±Inf
RoundToEven(NaN) = NaN

func Signbit Uses

❖
func Signbit(x *internal.Decimal) bool

Signbit reports whether x is negative or negative zero.

func Sin Uses

❖
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 Sinh Uses

❖
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 Uses

❖
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 Uses

❖
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 Tanh Uses

❖
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 Trunc Uses

❖
func Trunc(x *internal.Decimal) (*big.Int, error)

Trunc returns the integer value of x.

Special cases are: 

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

func Y0 Uses

❖
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 Uses

❖
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 Uses

❖
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

Directories

PathSynopsis
bits

Package math imports 6 packages (graph) and is imported by 2 packages. Updated 2021-01-25. Refresh now. Tools for package owners.