blob: ec2742927ca69c5ac376bd71c44f9f9d7010e4bd [file] [log] [blame]
// 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.
package math
import (
"math"
"github.com/cockroachdb/apd/v2"
"cuelang.org/go/internal"
)
var apdContext = apd.BaseContext.WithPrecision(24)
// Abs returns the absolute value of x.
//
// Special case: Abs(±Inf) = +Inf
func Abs(x *internal.Decimal) (*internal.Decimal, error) {
var d internal.Decimal
_, err := apdContext.Abs(&d, x)
return &d, err
}
// 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 *internal.Decimal) (*internal.Decimal, error) {
var d internal.Decimal
_, err := apdContext.Cbrt(&d, x)
return &d, err
}
// 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 *internal.Decimal) *internal.Decimal {
var d internal.Decimal
d.Set(x)
d.Negative = y.Negative
return &d
}
var zero = apd.New(0, 0)
// 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 *internal.Decimal) (*internal.Decimal, error) {
var d internal.Decimal
_, err := apdContext.Sub(&d, x, y)
if err != nil {
return nil, err
}
if d.Negative {
return zero, nil
}
return &d, nil
}
// 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 *internal.Decimal) (*internal.Decimal, error) {
var d internal.Decimal
_, err := apdContext.Exp(&d, x)
return &d, err
}
var two = apd.New(2, 0)
// Exp2 returns 2**x, the base-2 exponential of x.
//
// Special cases are the same as Exp.
func Exp2(x *internal.Decimal) (*internal.Decimal, error) {
var d internal.Decimal
_, err := apdContext.Pow(&d, two, x)
return &d, err
}
// 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 *internal.Decimal) (*internal.Decimal, error) {
var d internal.Decimal
_, err := apdContext.Ln(&d, x)
return &d, err
}
// Log10 returns the decimal logarithm of x.
// The special cases are the same as for Log.
func Log10(x *internal.Decimal) (*internal.Decimal, error) {
var d internal.Decimal
_, err := apdContext.Log10(&d, x)
return &d, err
}
// Log2 returns the binary logarithm of x.
// The special cases are the same as for Log.
func Log2(x *internal.Decimal) (*internal.Decimal, error) {
var d, ln2 internal.Decimal
_, _ = apdContext.Ln(&ln2, two)
_, err := apdContext.Ln(&d, x)
if err != nil {
return &d, err
}
_, err = apdContext.Quo(&d, &d, &ln2)
return &d, err
}
// 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 *internal.Decimal) (*internal.Decimal, error) {
var d internal.Decimal
_, err := apdContext.Pow(&d, x, y)
return &d, err
}
// Pow10 returns 10**n, the base-10 exponential of n.
//
func Pow10(n int32) *internal.Decimal {
return apd.New(1, 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 reports whether x is negative or negative zero.
func Signbit(x *internal.Decimal) bool {
return x.Negative
}
// 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)
}