xmath

package
v1.113.0 Latest Latest
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 Go to latest Published: Apr 26, 2024 License: MPL-2.0 Imports: 5 Imported by: 18

Documentation

Overview

Package xmath provides math-related utilities.

Index

Constants

View Source 
const (
	E   = math.E
	Pi  = math.Pi
	Phi = math.Phi

	Sqrt2   = math.Sqrt2
	SqrtE   = math.SqrtE
	SqrtPi  = math.SqrtPi
	SqrtPhi = math.SqrtPhi

	Ln2    = math.Ln2
	Log2E  = 1 / Ln2
	Ln10   = math.Ln10
	Log10E = 1 / Ln10
)

Mathematical constants. Mostly just re-exported from the math package for convenience.

View Source 
const (
	MaxFloat32             = math.MaxFloat32
	SmallestNonzeroFloat32 = math.SmallestNonzeroFloat32
	MaxFloat64             = math.MaxFloat64
	SmallestNonzeroFloat64 = math.SmallestNonzeroFloat64
)

Floating-point limit values. Mostly just re-exported from the math package for convenience. 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 (
	MaxInt    = math.MaxInt
	MinInt    = math.MinInt
	MaxInt8   = math.MaxInt8
	MinInt8   = math.MinInt8
	MaxInt16  = math.MaxInt16
	MinInt16  = math.MinInt16
	MaxInt32  = math.MaxInt32
	MinInt32  = math.MinInt32
	MaxInt64  = math.MaxInt64
	MinInt64  = math.MinInt64
	MaxUint   = math.MaxUint
	MaxUint8  = math.MaxUint8
	MaxUint16 = math.MaxUint16
	MaxUint32 = math.MaxUint32
	MaxUint64 = math.MaxUint64
)

Integer limit values. Mostly just re-exported from the math package for convenience.

View Source 
const (
	// DegreesToRadians converts a value in degrees to radians when multiplied with the value.
	DegreesToRadians = math.Pi / 180
	// RadiansToDegrees converts a value in radians to degrees when multiplied with the value.
	RadiansToDegrees = 180 / math.Pi
)

Variables

This section is empty.

Functions

func Abs added in v1.66.0 

func Abs[T Numeric](x T) T

Abs returns the absolute value of x.

Special cases are: 

Abs(±Inf) = +Inf
Abs(NaN) = NaN

func Acos added in v1.66.0 

func Acos[T constraints.Float](x T) T

Acos returns the arccosine of x.

func Acosh added in v1.66.0 

func Acosh[T constraints.Float](x T) T

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 added in v1.66.0 

func Asin[T constraints.Float](x T) T

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 added in v1.66.0 

func Asinh[T constraints.Float](x T) T

Asinh returns the inverse hyperbolic sine of x.

Special cases are: 

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

func Atan added in v1.66.0 

func Atan[T constraints.Float](x T) T

Atan returns the arctangent, in radians, of x.

Special cases are: 

Atan(±0) = ±0
Atan(±Inf) = ±Pi/2

func Atan2 added in v1.66.0 

func Atan2[T constraints.Float](y, x T) T

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 added in v1.66.0 

func Atanh[T constraints.Float](x T) T

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 added in v1.66.0 

func Cbrt[T constraints.Float](x T) T

Cbrt returns the cube root of x.

func Ceil added in v1.66.0 

func Ceil[T Numeric](x T) T

Ceil returns the smallest integer value greater than or equal to x.

func Copysign added in v1.66.0 

func Copysign[T constraints.Float](x, y T) T

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

func Cos added in v1.66.0 

func Cos[T constraints.Float](x T) T

Cos returns the cosine of the radian argument x.

Special cases are: 

Cos(±Inf) = NaN
Cos(NaN) = NaN

func Cosh added in v1.66.0 

func Cosh[T constraints.Float](x T) T

Cosh returns the hyperbolic cosine of x.

Special cases are: 

Cosh(±0) = 1
Cosh(±Inf) = +Inf
Cosh(NaN) = NaN

func Dim added in v1.66.0 

func Dim[T constraints.Float](x, y T) T

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 EqualWithin added in v1.89.0 

func EqualWithin[T Numeric](a, b, tolerance T) bool

EqualWithin returns true if a and b are within the given tolerance of each other.

func Erf added in v1.66.0 

func Erf[T constraints.Float](x T) T

Erf returns the error function of x.

Special cases are: 

Erf(+Inf) = 1
Erf(-Inf) = -1
Erf(NaN) = NaN

func Erfc added in v1.66.0 

func Erfc[T constraints.Float](x T) T

Erfc returns the complementary error function of x.

Special cases are: 

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

func Erfcinv added in v1.66.0 

func Erfcinv[T constraints.Float](x T) T

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 added in v1.66.0 

func Erfinv[T constraints.Float](x T) T

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 added in v1.66.0 

func Exp[T constraints.Float](x T) T

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 added in v1.66.0 

func Exp2[T constraints.Float](x T) T

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

Special cases are the same as Exp.

func Expm1 added in v1.66.0 

func Expm1[T constraints.Float](x T) T

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 FMA added in v1.66.0 

func FMA[T constraints.Float](x, y, z T) T

FMA returns x * y + z, computed with only one rounding. (That is, FMA returns the fused multiply-add of x, y, and z.)

func Floor added in v1.66.0 

func Floor[T Numeric](x T) T

Floor returns the greatest integer value less than or equal to x.

func Frexp added in v1.66.0 

func Frexp[T constraints.Float](f T) (frac T, 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 added in v1.66.0 

func Gamma[T constraints.Float](x T) T

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 added in v1.66.0 

func Hypot[T constraints.Float](p, q T) T

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 added in v1.66.0 

func Ilogb[T constraints.Float](x T) 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 added in v1.66.0 

func Inf[T constraints.Float](sign int) T

Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.

func IsInf added in v1.66.0 

func IsInf[T constraints.Float](f T, 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 added in v1.66.0 

func IsNaN[T constraints.Float](f T) bool

IsNaN reports whether f is a "not-a-number" value.

func J0 added in v1.66.0 

func J0[T constraints.Float](x T) T

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 added in v1.66.0 

func J1[T constraints.Float](x T) T

J1 returns the order-one Bessel function of the first kind.

Special cases are: 

J1(±Inf) = 0
J1(NaN) = NaN

func Jn added in v1.66.0 

func Jn[T constraints.Float](n int, x T) T

Jn returns the order-n Bessel function of the first kind.

Special cases are: 

Jn(n, ±Inf) = 0
Jn(n, NaN) = NaN

func Ldexp added in v1.66.0 

func Ldexp[T constraints.Float](frac T, exp int) T

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 added in v1.66.0 

func Lgamma[T constraints.Float](x T) (lgamma T, 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 added in v1.66.0 

func Log[T constraints.Float](x T) T

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 added in v1.66.0 

func Log10[T constraints.Float](x T) T

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

func Log1p added in v1.66.0 

func Log1p[T constraints.Float](x T) T

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 added in v1.66.0 

func Log2[T constraints.Float](x T) T

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

func Logb added in v1.66.0 

func Logb[T constraints.Float](x T) T

Logb returns the binary exponent of x.

Special cases are: 

Logb(±Inf) = +Inf
Logb(0) = -Inf
Logb(NaN) = NaN

func MaxValue added in v1.66.0 

func MaxValue[T Numeric]() T

MaxValue returns the maximum value for the type.

func MinValue added in v1.66.0 

func MinValue[T Numeric]() T

MinValue returns the minimum value for the type.

func Mod added in v1.66.0 

func Mod[T constraints.Float](x, y T) T

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 added in v1.66.0 

func Modf[T constraints.Float](f T) (i, frac T)

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 added in v1.66.0 

func NaN[T constraints.Float]() T

NaN returns the "not-a-number" value.

func Nextafter added in v1.66.0 

func Nextafter[T constraints.Float](x, y T) (r T)

Nextafter returns the next representable float32 value after x towards y.

Special cases are: 

Nextafter(x, x)   = x
Nextafter(NaN, y) = NaN
Nextafter(x, NaN) = NaN

func Pow added in v1.66.0 

func Pow[T constraints.Float](x, y T) T

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 added in v1.66.0 

func Pow10[T constraints.Float](n int) T

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

func Remainder added in v1.66.0 

func Remainder[T constraints.Float](x, y T) T

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[T constraints.Float](x T) T

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

Special cases are: 

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

func RoundToEven added in v1.66.0 

func RoundToEven[T constraints.Float](x T) T

RoundToEven returns the nearest integer, rounding ties to even.

Special cases are: 

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

func Signbit added in v1.66.0 

func Signbit[T constraints.Float](x T) bool

Signbit reports whether x is negative or negative zero.

func Sin added in v1.66.0 

func Sin[T constraints.Float](x T) T

Sin returns the sine of the radian argument x.

Special cases are: 

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

func Sincos added in v1.66.0 

func Sincos[T constraints.Float](x T) (sin, cos T)

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

Special cases are: 

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

func Sinh added in v1.66.0 

func Sinh[T constraints.Float](x T) T

Sinh returns the hyperbolic sine of x.

Special cases are: 

Sinh(±0) = ±0
Sinh(±Inf) = ±Inf
Sinh(NaN) = NaN

func SmallestPositiveNonZeroValue added in v1.89.0 

func SmallestPositiveNonZeroValue[T Numeric]() T

SmallestPositiveNonZeroValue returns the smallest, positive, non-zero value for the type.

func Sqrt added in v1.66.0 

func Sqrt[T constraints.Float](x T) T

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 added in v1.66.0 

func Tan[T constraints.Float](x T) T

Tan returns the tangent of the radian argument x.

Special cases are: 

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

func Tanh added in v1.66.0 

func Tanh[T constraints.Float](x T) T

Tanh returns the hyperbolic tangent of x.

Special cases are: 

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

func Trunc added in v1.66.0 

func Trunc[T constraints.Float](x T) T

Trunc returns the integer value of x.

Special cases are: 

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

func Y0 added in v1.66.0 

func Y0[T constraints.Float](x T) T

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 added in v1.66.0 

func Y1[T constraints.Float](x T) T

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 added in v1.66.0 

func Yn[T constraints.Float](n int, x T) T

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

type BitSet 

type BitSet struct {
	// contains filtered or unexported fields
}

BitSet contains a set of bits.

func (*BitSet) Clear 

func (b *BitSet) Clear(index int)

Clear the bit at 'index'.

func (*BitSet) ClearRange 

func (b *BitSet) ClearRange(start, end int)

ClearRange clears the bits from 'start' to 'end', inclusive.

func (*BitSet) Clone 

func (b *BitSet) Clone() *BitSet

Clone this BitSet.

func (*BitSet) Copy 

func (b *BitSet) Copy(other *BitSet)

Copy the content of 'other' into this BitSet, making them equal.

func (*BitSet) Count 

func (b *BitSet) Count() int

Count returns the number of set bits.

func (*BitSet) Data 

func (b *BitSet) Data() []uint64

Data returns a copy of the underlying storage.

func (*BitSet) EnsureCapacity 

func (b *BitSet) EnsureCapacity(words int)

EnsureCapacity ensures that the BitSet has enough underlying storage to accommodate setting a bit as high as index position 'words' x 64 - 1 without needing to allocate more storage.

func (*BitSet) Equal 

func (b *BitSet) Equal(other *BitSet) bool

Equal returns true if this BitSet is equal to 'other'.

func (*BitSet) FirstSet 

func (b *BitSet) FirstSet() int

FirstSet returns the first set bit. If no bits are set, then -1 is returned.

func (*BitSet) Flip 

func (b *BitSet) Flip(index int)

Flip the bit at 'index'.

func (*BitSet) FlipRange 

func (b *BitSet) FlipRange(start, end int)

FlipRange flips the bits from 'start' to 'end', inclusive.

func (*BitSet) LastSet 

func (b *BitSet) LastSet() int

LastSet returns the last set bit. If no bits are set, then -1 is returned.

func (*BitSet) Load 

func (b *BitSet) Load(data []uint64)

Load replaces the current data with the bits set in 'data'.

func (*BitSet) NextClear 

func (b *BitSet) NextClear(start int) int

NextClear returns the next clear bit starting from 'start'.

func (*BitSet) NextSet 

func (b *BitSet) NextSet(start int) int

NextSet returns the next set bit starting from 'start'. If no bits are set at or beyond 'start', then -1 is returned.

func (*BitSet) PreviousClear 

func (b *BitSet) PreviousClear(start int) int

PreviousClear returns the previous clear bit starting from 'start'. If no bits are clear at or before 'start', then -1 is returned.

func (*BitSet) PreviousSet 

func (b *BitSet) PreviousSet(start int) int

PreviousSet returns the previous set bit starting from 'start'. If no bits are set at or before 'start', then -1 is returned.

func (*BitSet) Reset 

func (b *BitSet) Reset()

Reset the BitSet back to an empty state.

func (*BitSet) Set 

func (b *BitSet) Set(index int)

Set the bit at 'index'.

func (*BitSet) SetRange 

func (b *BitSet) SetRange(start, end int)

SetRange sets the bits from 'start' to 'end', inclusive.

func (*BitSet) State 

func (b *BitSet) State(index int) bool

State returns the state of the bit at 'index'.

func (*BitSet) Trim 

func (b *BitSet) Trim()

Trim the BitSet down to the minimum required to store the set bits.

type Numeric added in v1.66.0 

type Numeric interface {
	constraints.Float | constraints.Integer
}

Numeric is a constraint that permits any integer or float type.

Source Files

View all Source files

Directories

Path Synopsis
f128
f64
Package geom provides geometry primitives.
 Package geom provides geometry primitives.
poly
visibility
Package rand provides a Randomizer based upon the crypto/rand package.
 Package rand provides a Randomizer based upon the crypto/rand package.

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