math

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v0.3.0-beta.5.0...-f1c6bd8 Latest Latest
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 Go to latest Published: Feb 27, 2021 License: Apache-2.0 Imports: 6 Imported by: 0

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Constants

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

Exponent and precision limits.

View Source 
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.

View Source 
const (
	Below = -1
	Exact = 0
	Above = 1
)

Constants describing the Accuracy of a Float.

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

Mathematical constants.

View Source 
const MaxBase = 62

MaxBase is the largest number base accepted for string conversions.

Variables

This section is empty.

Functions

func Abs 

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

Abs returns the absolute value of x.

Special case: Abs(±Inf) = +Inf

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

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

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

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

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

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 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 

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 

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 

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

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

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 *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 

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 *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 

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 

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 

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 

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 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 Jacobi 

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 

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 Log 

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 

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 

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 *internal.Decimal) (*internal.Decimal, error)

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 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 MultipleOf 

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

MultipleOf reports whether x is a multiple of y.

func Pow 

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 

func Pow10(n int32) *internal.Decimal

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

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 *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 

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 

func Signbit(x *internal.Decimal) 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

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 the radian argument x.

Special cases are: 

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

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

func Trunc 

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 

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

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