pkg/math/math.go

// Copyright 2018 The CUE Authors
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

// Copyright 2018 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

//go:generate qgo -exclude=32,^Next,^Max,^Smallest,^Min,bits,Inf,NaN,Round,Trunc,Ceil,Floor$ extract math

package math

import "math"

// Abs returns the absolute value of x.
//
// Special cases are:
//	Abs(±Inf) = +Inf
//	Abs(NaN) = NaN
func Abs(x float64) float64 {
	return math.Abs(x)
}

// Acosh returns the inverse hyperbolic cosine of x.
//
// Special cases are:
//	Acosh(+Inf) = +Inf
//	Acosh(x) = NaN if x < 1
//	Acosh(NaN) = NaN
func Acosh(x float64) float64 {
	return math.Acosh(x)
}

// Asin returns the arcsine, in radians, of x.
//
// Special cases are:
//	Asin(±0) = ±0
//	Asin(x) = NaN if x < -1 or x > 1
func Asin(x float64) float64 {
	return math.Asin(x)
}

// Acos returns the arccosine, in radians, of x.
//
// Special case is:
//	Acos(x) = NaN if x < -1 or x > 1
func Acos(x float64) float64 {
	return math.Acos(x)
}

// Asinh returns the inverse hyperbolic sine of x.
//
// Special cases are:
//	Asinh(±0) = ±0
//	Asinh(±Inf) = ±Inf
//	Asinh(NaN) = NaN
func Asinh(x float64) float64 {
	return math.Asinh(x)
}

// Atan returns the arctangent, in radians, of x.
//
// Special cases are:
//      Atan(±0) = ±0
//      Atan(±Inf) = ±Pi/2
func Atan(x float64) float64 {
	return math.Atan(x)
}

// 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 Atan2(y, x float64) float64 {
	return math.Atan2(y, x)
}

// 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 Atanh(x float64) float64 {
	return math.Atanh(x)
}

// Cbrt returns the cube root of x.
//
// Special cases are:
//	Cbrt(±0) = ±0
//	Cbrt(±Inf) = ±Inf
//	Cbrt(NaN) = NaN
func Cbrt(x float64) float64 {
	return math.Cbrt(x)
}

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

// Copysign returns a value with the magnitude
// of x and the sign of y.
func Copysign(x, y float64) float64 {
	return math.Copysign(x, y)
}

// 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 Dim(x, y float64) float64 {
	return math.Dim(x, y)
}

// Erf returns the error function of x.
//
// Special cases are:
//	Erf(+Inf) = 1
//	Erf(-Inf) = -1
//	Erf(NaN) = NaN
func Erf(x float64) float64 {
	return math.Erf(x)
}

// Erfc returns the complementary error function of x.
//
// Special cases are:
//	Erfc(+Inf) = 0
//	Erfc(-Inf) = 2
//	Erfc(NaN) = NaN
func Erfc(x float64) float64 {
	return math.Erfc(x)
}

// 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 Erfinv(x float64) float64 {
	return math.Erfinv(x)
}

// 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 Erfcinv(x float64) float64 {
	return math.Erfcinv(x)
}

// 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 Exp(x float64) float64 {
	return math.Exp(x)
}

// Exp2 returns 2**x, the base-2 exponential of x.
//
// Special cases are the same as Exp.
func Exp2(x float64) float64 {
	return math.Exp2(x)
}

// 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 Expm1(x float64) float64 {
	return math.Expm1(x)
}

// 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 Gamma(x float64) float64 {
	return math.Gamma(x)
}

// 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 Hypot(p, q float64) float64 {
	return math.Hypot(p, q)
}

// J0 returns the order-zero Bessel function of the first kind.
//
// Special cases are:
//	J0(±Inf) = 0
//	J0(0) = 1
//	J0(NaN) = NaN
func J0(x float64) float64 {
	return math.J0(x)
}

// 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 Y0(x float64) float64 {
	return math.Y0(x)
}

// J1 returns the order-one Bessel function of the first kind.
//
// Special cases are:
//	J1(±Inf) = 0
//	J1(NaN) = NaN
func J1(x float64) float64 {
	return math.J1(x)
}

// 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 Y1(x float64) float64 {
	return math.Y1(x)
}

// Jn returns the order-n Bessel function of the first kind.
//
// Special cases are:
//	Jn(n, ±Inf) = 0
//	Jn(n, NaN) = NaN
func Jn(n int, x float64) float64 {
	return math.Jn(n, x)
}

// 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
func Yn(n int, x float64) float64 {
	return math.Yn(n, x)
}

// 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 Ldexp(frac float64, exp int) float64 {
	return math.Ldexp(frac, exp)
}

// Log returns the natural logarithm of x.
//
// Special cases are:
//	Log(+Inf) = +Inf
//	Log(0) = -Inf
//	Log(x < 0) = NaN
//	Log(NaN) = NaN
func Log(x float64) float64 {
	return math.Log(x)
}

// Log10 returns the decimal logarithm of x.
// The special cases are the same as for Log.
func Log10(x float64) float64 {
	return math.Log10(x)
}

// Log2 returns the binary logarithm of x.
// The special cases are the same as for Log.
func Log2(x float64) float64 {
	return math.Log2(x)
}

// 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 Log1p(x float64) float64 {
	return math.Log1p(x)
}

// Logb returns the binary exponent of x.
//
// Special cases are:
//	Logb(±Inf) = +Inf
//	Logb(0) = -Inf
//	Logb(NaN) = NaN
func Logb(x float64) float64 {
	return math.Logb(x)
}

// Ilogb returns the binary exponent of x as an integer.
//
// Special cases are:
//	Ilogb(±Inf) = MaxInt32
//	Ilogb(0) = MinInt32
//	Ilogb(NaN) = MaxInt32
func Ilogb(x float64) int {
	return math.Ilogb(x)
}

// 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 Mod(x, y float64) float64 {
	return math.Mod(x, y)
}

// 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 Pow(x, y float64) float64 {
	return math.Pow(x, y)
}

// 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 Pow10(n int) float64 {
	return math.Pow10(n)
}

// 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 Remainder(x, y float64) float64 {
	return math.Remainder(x, y)
}

// Signbit returns true if x is negative or negative zero.
func Signbit(x float64) bool {
	return math.Signbit(x)
}

// Cos returns the cosine of the radian argument x.
//
// Special cases are:
//	Cos(±Inf) = NaN
//	Cos(NaN) = NaN
func Cos(x float64) float64 {
	return math.Cos(x)
}

// Sin returns the sine of the radian argument x.
//
// Special cases are:
//	Sin(±0) = ±0
//	Sin(±Inf) = NaN
//	Sin(NaN) = NaN
func Sin(x float64) float64 {
	return math.Sin(x)
}

// Sinh returns the hyperbolic sine of x.
//
// Special cases are:
//	Sinh(±0) = ±0
//	Sinh(±Inf) = ±Inf
//	Sinh(NaN) = NaN
func Sinh(x float64) float64 {
	return math.Sinh(x)
}

// Cosh returns the hyperbolic cosine of x.
//
// Special cases are:
//	Cosh(±0) = 1
//	Cosh(±Inf) = +Inf
//	Cosh(NaN) = NaN
func Cosh(x float64) float64 {
	return math.Cosh(x)
}

// Sqrt returns the square root of x.
//
// Special cases are:
//	Sqrt(+Inf) = +Inf
//	Sqrt(±0) = ±0
//	Sqrt(x < 0) = NaN
//	Sqrt(NaN) = NaN
func Sqrt(x float64) float64 {
	return math.Sqrt(x)
}

// Tan returns the tangent of the radian argument x.
//
// Special cases are:
//	Tan(±0) = ±0
//	Tan(±Inf) = NaN
//	Tan(NaN) = NaN
func Tan(x float64) float64 {
	return math.Tan(x)
}

// Tanh returns the hyperbolic tangent of x.
//
// Special cases are:
//	Tanh(±0) = ±0
//	Tanh(±Inf) = ±1
//	Tanh(NaN) = NaN
func Tanh(x float64) float64 {
	return math.Tanh(x)
}