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math/cmplx: handle special cases

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Implement special case handling and testing to ensure
conformance with the C99 standard annex G.6 Complex arithmetic.

Fixes #29320

Change-Id: Id72eb4c5a35d5a54b4b8690d2f7176ab11028f1b
Reviewed-on: https://go-review.googlesource.com/c/go/+/220689
Reviewed-by: Robert Griesemer <gri@golang.org>
This commit is contained in:
Brian Kessler 2019-02-01 23:08:45 -07:00 committed by Robert Griesemer
parent da382a3978
commit 4209a9f65a
8 changed files with 912 additions and 141 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

3
src/math/cmplx/abs.go
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@ -3,7 +3,8 @@
// license that can be found in the LICENSE file.
// Package cmplx provides basic constants and mathematical functions for
// complex numbers.
// complex numbers. Special case handling conforms to the C99 standard
// Annex G IEC 60559-compatible complex arithmetic.
package cmplx
import "math"

70
src/math/cmplx/asin.go
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@ -49,8 +49,31 @@ import "math"
// Asin returns the inverse sine of x.
func Asin(x complex128) complex128 {
if imag(x) == 0 && math.Abs(real(x)) <= 1 {
return complex(math.Asin(real(x)), imag(x))
switch re, im := real(x), imag(x); {
case im == 0 && math.Abs(re) <= 1:
return complex(math.Asin(re), im)
case re == 0 && math.Abs(im) <= 1:
return complex(re, math.Asinh(im))
case math.IsNaN(im):
switch {
case re == 0:
return complex(re, math.NaN())
case math.IsInf(re, 0):
return complex(math.NaN(), re)
default:
return NaN()
}
case math.IsInf(im, 0):
switch {
case math.IsNaN(re):
return x
case math.IsInf(re, 0):
return complex(math.Copysign(math.Pi/4, re), im)
default:
return complex(math.Copysign(0, re), im)
}
case math.IsInf(re, 0):
return complex(math.Copysign(math.Pi/2, re), math.Copysign(re, im))
}
ct := complex(-imag(x), real(x)) // i * x
xx := x * x
@ -62,8 +85,31 @@ func Asin(x complex128) complex128 {
// Asinh returns the inverse hyperbolic sine of x.
func Asinh(x complex128) complex128 {
if imag(x) == 0 && math.Abs(real(x)) <= 1 {
return complex(math.Asinh(real(x)), imag(x))
switch re, im := real(x), imag(x); {
case im == 0 && math.Abs(re) <= 1:
return complex(math.Asinh(re), im)
case re == 0 && math.Abs(im) <= 1:
return complex(re, math.Asin(im))
case math.IsInf(re, 0):
switch {
case math.IsInf(im, 0):
return complex(re, math.Copysign(math.Pi/4, im))
case math.IsNaN(im):
return x
default:
return complex(re, math.Copysign(0.0, im))
}
case math.IsNaN(re):
switch {
case im == 0:
return x
case math.IsInf(im, 0):
return complex(im, re)
default:
return NaN()
}
case math.IsInf(im, 0):
return complex(math.Copysign(im, re), math.Copysign(math.Pi/2, im))
}
xx := x * x
x1 := complex(1+real(xx), imag(xx)) // 1 + x*x
@ -91,6 +137,9 @@ func Acos(x complex128) complex128 {
// Acosh returns the inverse hyperbolic cosine of x.
func Acosh(x complex128) complex128 {
if x == 0 {
return complex(0, math.Copysign(math.Pi/2, imag(x)))
}
w := Acos(x)
if imag(w) <= 0 {
return complex(-imag(w), real(w)) // i * w
@ -133,6 +182,19 @@ func Acosh(x complex128) complex128 {
// Atan returns the inverse tangent of x.
func Atan(x complex128) complex128 {
switch re, im := real(x), imag(x); {
case im == 0:
return complex(math.Atan(re), im)
case re == 0 && math.Abs(im) <= 1:
return complex(re, math.Atanh(im))
case math.IsInf(im, 0) || math.IsInf(re, 0):
if math.IsNaN(re) {
return complex(math.NaN(), math.Copysign(0, im))
}
return complex(math.Copysign(math.Pi/2, re), math.Copysign(0, im))
case math.IsNaN(re) || math.IsNaN(im):
return NaN()
}
x2 := real(x) * real(x)
a := 1 - x2 - imag(x)*imag(x)
if a == 0 {

886
src/math/cmplx/cmath_test.go
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File diff suppressed because it is too large Load Diff

17
src/math/cmplx/exp.go
View File

@ -49,6 +49,23 @@ import "math"
// Exp returns e**x, the base-e exponential of x.
func Exp(x complex128) complex128 {
switch re, im := real(x), imag(x); {
case math.IsInf(re, 0):
switch {
case re > 0 && im == 0:
return x
case math.IsInf(im, 0) || math.IsNaN(im):
if re < 0 {
return complex(0, math.Copysign(0, im))
} else {
return complex(math.Inf(1.0), math.NaN())
}
}
case math.IsNaN(re):
if im == 0 {
return complex(math.NaN(), im)
}
}
r := math.Exp(real(x))
s, c := math.Sincos(imag(x))
return complex(r*c, r*s)

3
src/math/cmplx/log.go
View File

@ -60,5 +60,6 @@ func Log(x complex128) complex128 {
// Log10 returns the decimal logarithm of x.
func Log10(x complex128) complex128 {
return math.Log10E * Log(x)
z := Log(x)
return complex(math.Log10E*real(z), math.Log10E*imag(z))
}

52
src/math/cmplx/sin.go
View File

@ -51,6 +51,19 @@ import "math"
// Sin returns the sine of x.
func Sin(x complex128) complex128 {
switch re, im := real(x), imag(x); {
case im == 0 && (math.IsInf(re, 0) || math.IsNaN(re)):
return complex(math.NaN(), im)
case math.IsInf(im, 0):
switch {
case re == 0:
return x
case math.IsInf(re, 0) || math.IsNaN(re):
return complex(math.NaN(), im)
}
case re == 0 && math.IsNaN(im):
return x
}
s, c := math.Sincos(real(x))
sh, ch := sinhcosh(imag(x))
return complex(s*ch, c*sh)
@ -71,6 +84,19 @@ func Sin(x complex128) complex128 {
// Sinh returns the hyperbolic sine of x.
func Sinh(x complex128) complex128 {
switch re, im := real(x), imag(x); {
case re == 0 && (math.IsInf(im, 0) || math.IsNaN(im)):
return complex(re, math.NaN())
case math.IsInf(re, 0):
switch {
case im == 0:
return complex(re, im)
case math.IsInf(im, 0) || math.IsNaN(im):
return complex(re, math.NaN())
}
case im == 0 && math.IsNaN(re):
return complex(math.NaN(), im)
}
s, c := math.Sincos(imag(x))
sh, ch := sinhcosh(real(x))
return complex(c*sh, s*ch)
@ -96,6 +122,19 @@ func Sinh(x complex128) complex128 {
// Cos returns the cosine of x.
func Cos(x complex128) complex128 {
switch re, im := real(x), imag(x); {
case im == 0 && (math.IsInf(re, 0) || math.IsNaN(re)):
return complex(math.NaN(), -im*math.Copysign(0, re))
case math.IsInf(im, 0):
switch {
case re == 0:
return complex(math.Inf(1), -re*math.Copysign(0, im))
case math.IsInf(re, 0) || math.IsNaN(re):
return complex(math.Inf(1), math.NaN())
}
case re == 0 && math.IsNaN(im):
return complex(math.NaN(), 0)
}
s, c := math.Sincos(real(x))
sh, ch := sinhcosh(imag(x))
return complex(c*ch, -s*sh)
@ -115,6 +154,19 @@ func Cos(x complex128) complex128 {
// Cosh returns the hyperbolic cosine of x.
func Cosh(x complex128) complex128 {
switch re, im := real(x), imag(x); {
case re == 0 && (math.IsInf(im, 0) || math.IsNaN(im)):
return complex(math.NaN(), re*math.Copysign(0, im))
case math.IsInf(re, 0):
switch {
case im == 0:
return complex(math.Inf(1), im*math.Copysign(0, re))
case math.IsInf(im, 0) || math.IsNaN(im):
return complex(math.Inf(1), math.NaN())
}
case im == 0 && math.IsNaN(re):
return complex(math.NaN(), im)
}
s, c := math.Sincos(imag(x))
sh, ch := sinhcosh(real(x))
return complex(c*ch, s*sh)

2
src/math/cmplx/sqrt.go
View File

@ -65,6 +65,8 @@ func Sqrt(x complex128) complex128 {
return complex(0, math.Copysign(math.Sqrt(-real(x)), imag(x)))
}
return complex(math.Sqrt(real(x)), imag(x))
} else if math.IsInf(imag(x), 0) {
return complex(math.Inf(1.0), imag(x))
}
if real(x) == 0 {
if imag(x) < 0 {

20
src/math/cmplx/tan.go
View File

@ -60,6 +60,16 @@ import (
// Tan returns the tangent of x.
func Tan(x complex128) complex128 {
switch re, im := real(x), imag(x); {
case math.IsInf(im, 0):
switch {
case math.IsInf(re, 0) || math.IsNaN(re):
return complex(math.Copysign(0, re), math.Copysign(1, im))
}
return complex(math.Copysign(0, math.Sin(2*re)), math.Copysign(1, im))
case re == 0 && math.IsNaN(im):
return x
}
d := math.Cos(2*real(x)) + math.Cosh(2*imag(x))
if math.Abs(d) < 0.25 {
d = tanSeries(x)
@ -84,6 +94,16 @@ func Tan(x complex128) complex128 {
// Tanh returns the hyperbolic tangent of x.
func Tanh(x complex128) complex128 {
switch re, im := real(x), imag(x); {
case math.IsInf(re, 0):
switch {
case math.IsInf(im, 0) || math.IsNaN(im):
return complex(math.Copysign(1, re), math.Copysign(0, im))
}
return complex(math.Copysign(1, re), math.Copysign(0, math.Sin(2*im)))
case im == 0 && math.IsNaN(re):
return x
}
d := math.Cosh(2*real(x)) + math.Cos(2*imag(x))
if d == 0 {
return Inf()