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Revert "math/cmplx: handle special cases"

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This reverts CL 169501.

Reason for revert: The new tests fail at least on s390x and MIPS. This is likely a minor bug in the compiler or runtime. But this point in the release cycle is not the time to debug these details, which are unlikely to be new. Let's try again for 1.15.

Updates #29320
Fixes #35443

Change-Id: I2218b2083f8974b57d528e3742524393fc72b355
Reviewed-on: https://go-review.googlesource.com/c/go/+/206037
Run-TryBot: Ian Lance Taylor <iant@golang.org>
Reviewed-by: Bryan C. Mills <bcmills@google.com>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
This commit is contained in:
Ian Lance Taylor 2019-11-08 02:40:10 +00:00 committed by Brad Fitzpatrick
parent e038c7e418
commit f5e89c2214
8 changed files with 142 additions and 830 deletions
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3
src/math/cmplx/abs.go
View File

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

68
src/math/cmplx/asin.go
View File

@ -49,31 +49,8 @@ import "math"
// Asin returns the inverse sine of x.
func Asin(x complex128) complex128 {
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))
if imag(x) == 0 && math.Abs(real(x)) <= 1 {
return complex(math.Asin(real(x)), imag(x))
}
ct := complex(-imag(x), real(x)) // i * x
xx := x * x
@ -85,31 +62,8 @@ func Asin(x complex128) complex128 {
// Asinh returns the inverse hyperbolic sine of x.
func Asinh(x complex128) complex128 {
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))
if imag(x) == 0 && math.Abs(real(x)) <= 1 {
return complex(math.Asinh(real(x)), imag(x))
}
xx := x * x
x1 := complex(1+real(xx), imag(xx)) // 1 + x*x
@ -137,9 +91,6 @@ 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
@ -182,17 +133,6 @@ 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))
}
x2 := real(x) * real(x)
a := 1 - x2 - imag(x)*imag(x)
if a == 0 {

807
src/math/cmplx/cmath_test.go
View File

@ -291,190 +291,48 @@ var tanh = []complex128{
(-1.0000000491604982429364892e+00 - 2.901873195374433112227349e-08i),
}
// special cases conform to C99 standard appendix G.6 Complex arithmetic
var inf, nan = math.Inf(1), math.NaN()
// special cases
var vcAbsSC = []complex128{
NaN(),
}
var absSC = []float64{
math.NaN(),
}
var acosSC = []struct {
in,
want complex128
}{
// G.6.1.1
{complex(zero, zero),
complex(math.Pi/2, -zero)},
{complex(-zero, zero),
complex(math.Pi/2, -zero)},
{complex(zero, nan),
complex(math.Pi/2, nan)},
{complex(-zero, nan),
complex(math.Pi/2, nan)},
{complex(1.0, inf),
complex(math.Pi/2, -inf)},
{complex(1.0, nan),
NaN()},
{complex(-inf, 1.0),
complex(math.Pi, -inf)},
{complex(inf, 1.0),
complex(0.0, -inf)},
{complex(-inf, inf),
complex(3*math.Pi/4, -inf)},
{complex(inf, inf),
complex(math.Pi/4, -inf)},
{complex(inf, nan),
complex(nan, -inf)}, // imaginary sign unspecified
{complex(-inf, nan),
complex(nan, inf)}, // imaginary sign unspecified
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
complex(nan, -inf)},
{NaN(),
NaN()},
var vcAcosSC = []complex128{
NaN(),
}
var acoshSC = []struct {
in,
want complex128
}{
// G.6.2.1
{complex(zero, zero),
complex(zero, math.Pi/2)},
{complex(-zero, zero),
complex(zero, math.Pi/2)},
{complex(1.0, inf),
complex(inf, math.Pi/2)},
{complex(1.0, nan),
NaN()},
{complex(-inf, 1.0),
complex(inf, math.Pi)},
{complex(inf, 1.0),
complex(inf, zero)},
{complex(-inf, inf),
complex(inf, 3*math.Pi/4)},
{complex(inf, inf),
complex(inf, math.Pi/4)},
{complex(inf, nan),
complex(inf, nan)},
{complex(-inf, nan),
complex(inf, nan)},
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
complex(inf, nan)},
{NaN(),
NaN()},
var acosSC = []complex128{
NaN(),
}
var asinSC = []struct {
in,
want complex128
}{
// Derived from Asin(z) = -i * Asinh(i * z), G.6 #7
{complex(zero, zero),
complex(zero, zero)},
{complex(1.0, inf),
complex(0, inf)},
{complex(1.0, nan),
NaN()},
{complex(inf, 1),
complex(math.Pi/2, inf)},
{complex(inf, inf),
complex(math.Pi/4, inf)},
{complex(inf, nan),
complex(nan, inf)}, // imaginary sign unspecified
{complex(nan, zero),
NaN()},
{complex(nan, 1),
NaN()},
{complex(nan, inf),
complex(nan, inf)},
{NaN(),
NaN()},
var vcAcoshSC = []complex128{
NaN(),
}
var asinhSC = []struct {
in,
want complex128
}{
// G.6.2.2
{complex(zero, zero),
complex(zero, zero)},
{complex(1.0, inf),
complex(inf, math.Pi/2)},
{complex(1.0, nan),
NaN()},
{complex(inf, 1.0),
complex(inf, zero)},
{complex(inf, inf),
complex(inf, math.Pi/4)},
{complex(inf, nan),
complex(inf, nan)},
{complex(nan, zero),
complex(nan, zero)},
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
complex(inf, nan)}, // sign of real part unspecified
{NaN(),
NaN()},
var acoshSC = []complex128{
NaN(),
}
var atanSC = []struct {
in,
want complex128
}{
// Derived from Atan(z) = -i * Atanh(i * z), G.6 #7
{complex(0, zero),
complex(0, zero)},
{complex(0, nan),
NaN()},
{complex(1.0, zero),
complex(math.Pi/4, zero)},
{complex(1.0, inf),
complex(math.Pi/2, zero)},
{complex(1.0, nan),
NaN()},
{complex(inf, 1),
complex(math.Pi/2, zero)},
{complex(inf, inf),
complex(math.Pi/2, zero)},
{complex(inf, nan),
complex(math.Pi/2, zero)},
{complex(nan, 1),
NaN()},
{complex(nan, inf),
complex(nan, zero)},
{NaN(),
NaN()},
var vcAsinSC = []complex128{
NaN(),
}
var atanhSC = []struct {
in,
want complex128
}{
// G.6.2.3
{complex(zero, zero),
complex(zero, zero)},
{complex(zero, nan),
complex(zero, nan)},
{complex(1.0, zero),
complex(inf, zero)},
{complex(1.0, inf),
complex(0, math.Pi/2)},
{complex(1.0, nan),
NaN()},
{complex(inf, 1.0),
complex(zero, math.Pi/2)},
{complex(inf, inf),
complex(zero, math.Pi/2)},
{complex(inf, nan),
complex(0, nan)},
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
complex(zero, math.Pi/2)}, // sign of real part not specified.
{NaN(),
NaN()},
var asinSC = []complex128{
NaN(),
}
var vcAsinhSC = []complex128{
NaN(),
}
var asinhSC = []complex128{
NaN(),
}
var vcAtanSC = []complex128{
NaN(),
}
var atanSC = []complex128{
NaN(),
}
var vcAtanhSC = []complex128{
NaN(),
}
var atanhSC = []complex128{
NaN(),
}
var vcConjSC = []complex128{
NaN(),
@ -482,105 +340,23 @@ var vcConjSC = []complex128{
var conjSC = []complex128{
NaN(),
}
var cosSC = []struct {
in,
want complex128
}{
// Derived from Cos(z) = Cosh(i * z), G.6 #7
{complex(zero, zero),
complex(1.0, -zero)},
{complex(zero, inf),
complex(inf, -zero)},
{complex(zero, nan),
complex(nan, zero)}, // imaginary sign unspecified
{complex(1.0, inf),
complex(inf, -inf)},
{complex(1.0, nan),
NaN()},
{complex(inf, zero),
complex(nan, -zero)},
{complex(inf, 1.0),
NaN()},
{complex(inf, inf),
complex(inf, nan)}, // real sign unspecified
{complex(inf, nan),
NaN()},
{complex(nan, zero),
complex(nan, -zero)}, // imaginary sign unspecified
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
complex(inf, nan)},
{NaN(),
NaN()},
var vcCosSC = []complex128{
NaN(),
}
var coshSC = []struct {
in,
want complex128
}{
// G.6.2.4
{complex(zero, zero),
complex(1.0, zero)},
{complex(zero, inf),
complex(nan, zero)}, // imaginary sign unspecified
{complex(zero, nan),
complex(nan, zero)}, // imaginary sign unspecified
{complex(1.0, inf),
NaN()},
{complex(1.0, nan),
NaN()},
{complex(inf, zero),
complex(inf, zero)},
{complex(inf, 1.0),
complex(inf*math.Cos(1.0), inf*math.Sin(1.0))}, // +inf cis(y)
{complex(inf, inf),
complex(inf, nan)}, // real sign unspecified
{complex(inf, nan),
complex(inf, nan)},
{complex(nan, zero),
complex(nan, zero)}, // imaginary sign unspecified
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
NaN()},
{NaN(),
NaN()},
var cosSC = []complex128{
NaN(),
}
var expSC = []struct {
in,
want complex128
}{
// G.6.3.1
{complex(zero, zero),
complex(1.0, zero)},
{complex(-zero, zero),
complex(1.0, zero)},
{complex(1.0, inf),
NaN()},
{complex(1.0, nan),
NaN()},
{complex(inf, zero),
complex(inf, zero)},
{complex(-inf, 1.0),
complex(math.Copysign(0.0, math.Cos(1.0)), math.Copysign(0.0, math.Sin(1.0)))}, // +0 cis(y)
{complex(inf, 1.0),
complex(inf*math.Cos(1.0), inf*math.Sin(1.0))}, // +inf cis(y)
{complex(-inf, inf),
complex(zero, zero)}, // real and imaginary sign unspecified
{complex(inf, inf),
complex(inf, nan)}, // real sign unspecified
{complex(-inf, nan),
complex(zero, zero)}, // real and imaginary sign unspecified
{complex(inf, nan),
complex(inf, nan)}, // real sign unspecified
{complex(nan, zero),
complex(nan, zero)},
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
NaN()},
{NaN(),
NaN()},
var vcCoshSC = []complex128{
NaN(),
}
var coshSC = []complex128{
NaN(),
}
var vcExpSC = []complex128{
NaN(),
}
var expSC = []complex128{
NaN(),
}
var vcIsNaNSC = []complex128{
complex(math.Inf(-1), math.Inf(-1)),
@ -604,70 +380,17 @@ var isNaNSC = []bool{
false,
true,
}
var logSC = []struct {
in,
want complex128
}{
// G.6.3.2
{complex(zero, zero),
complex(-inf, zero)},
{complex(-zero, zero),
complex(-inf, math.Pi)},
{complex(1.0, inf),
complex(inf, math.Pi/2)},
{complex(1.0, nan),
NaN()},
{complex(-inf, 1.0),
complex(inf, math.Pi)},
{complex(inf, 1.0),
complex(inf, 0.0)},
{complex(-inf, inf),
complex(inf, 3*math.Pi/4)},
{complex(inf, inf),
complex(inf, math.Pi/4)},
{complex(-inf, nan),
complex(inf, nan)},
{complex(inf, nan),
complex(inf, nan)},
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
complex(inf, nan)},
{NaN(),
NaN()},
var vcLogSC = []complex128{
NaN(),
}
var log10SC = []struct {
in,
want complex128
}{
// derived from Log special cases via Log10(x) = math.Log10E*Log(x)
{complex(zero, zero),
complex(-inf, zero)},
{complex(-zero, zero),
complex(-inf, float64(math.Log10E)*float64(math.Pi))},
{complex(1.0, inf),
complex(inf, float64(math.Log10E)*float64(math.Pi/2))},
{complex(1.0, nan),
NaN()},
{complex(-inf, 1.0),
complex(inf, float64(math.Log10E)*float64(math.Pi))},
{complex(inf, 1.0),
complex(inf, 0.0)},
{complex(-inf, inf),
complex(inf, float64(math.Log10E)*float64(3*math.Pi/4))},
{complex(inf, inf),
complex(inf, float64(math.Log10E)*float64(math.Pi/4))},
{complex(-inf, nan),
complex(inf, nan)},
{complex(inf, nan),
complex(inf, nan)},
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
complex(inf, nan)},
{NaN(),
NaN()},
var logSC = []complex128{
NaN(),
}
var vcLog10SC = []complex128{
NaN(),
}
var log10SC = []complex128{
NaN(),
}
var vcPolarSC = []complex128{
NaN(),
@ -683,153 +406,35 @@ var powSC = []complex128{
NaN(),
NaN(),
}
var sinSC = []struct {
in,
want complex128
}{
// Derived from Sin(z) = -i * Sinh(i * z), G.6 #7
{complex(zero, zero),
complex(zero, zero)},
{complex(zero, inf),
complex(zero, inf)},
{complex(zero, nan),
complex(zero, nan)},
{complex(1.0, inf),
complex(inf, inf)},
{complex(1.0, nan),
NaN()},
{complex(inf, zero),
complex(nan, zero)},
{complex(inf, 1.0),
NaN()},
{complex(inf, inf),
complex(nan, inf)},
{complex(inf, nan),
NaN()},
{complex(nan, zero),
complex(nan, zero)},
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
complex(nan, inf)},
{NaN(),
NaN()},
var vcSinSC = []complex128{
NaN(),
}
var sinhSC = []struct {
in,
want complex128
}{
// G.6.2.5
{complex(zero, zero),
complex(zero, zero)},
{complex(zero, inf),
complex(zero, nan)}, // real sign unspecified
{complex(zero, nan),
complex(zero, nan)}, // real sign unspecified
{complex(1.0, inf),
NaN()},
{complex(1.0, nan),
NaN()},
{complex(inf, zero),
complex(inf, zero)},
{complex(inf, 1.0),
complex(inf*math.Cos(1.0), inf*math.Sin(1.0))}, // +inf cis(y)
{complex(inf, inf),
complex(inf, nan)}, // real sign unspecified
{complex(inf, nan),
complex(inf, nan)}, // real sign unspecified
{complex(nan, zero),
complex(nan, zero)},
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
NaN()},
{NaN(),
NaN()},
var sinSC = []complex128{
NaN(),
}
var sqrtSC = []struct {
in,
want complex128
}{
// G.6.4.2
{complex(zero, zero),
complex(zero, zero)},
{complex(-zero, zero),
complex(zero, zero)},
{complex(1.0, inf),
complex(inf, inf)},
{complex(nan, inf),
complex(inf, inf)},
{complex(1.0, nan),
NaN()},
{complex(-inf, 1.0),
complex(zero, inf)},
{complex(inf, 1.0),
complex(inf, zero)},
{complex(-inf, nan),
complex(nan, inf)}, // imaginary sign unspecified
{complex(inf, nan),
complex(inf, nan)},
{complex(nan, 1.0),
NaN()},
{NaN(),
NaN()},
var vcSinhSC = []complex128{
NaN(),
}
var tanSC = []struct {
in,
want complex128
}{
// Derived from Tan(z) = -i * Tanh(i * z), G.6 #7
{complex(zero, zero),
complex(zero, zero)},
{complex(zero, nan),
complex(zero, nan)},
{complex(1.0, inf),
complex(zero, 1.0)},
{complex(1.0, nan),
NaN()},
{complex(inf, 1.0),
NaN()},
{complex(inf, inf),
complex(zero, 1.0)},
{complex(inf, nan),
NaN()},
{complex(nan, zero),
NaN()},
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
complex(zero, 1.0)},
{NaN(),
NaN()},
var sinhSC = []complex128{
NaN(),
}
var tanhSC = []struct {
in,
want complex128
}{
// G.6.2.6
{complex(zero, zero),
complex(zero, zero)},
{complex(1.0, inf),
NaN()},
{complex(1.0, nan),
NaN()},
{complex(inf, 1.0),
complex(1.0, math.Copysign(0.0, math.Sin(2*1.0)))}, // 1 + i 0 sin(2y)
{complex(inf, inf),
complex(1.0, zero)}, // imaginary sign unspecified
{complex(inf, nan),
complex(1.0, zero)}, // imaginary sign unspecified
{complex(nan, zero),
complex(nan, zero)},
{complex(nan, 1.0),
NaN()},
{complex(nan, inf),
NaN()},
{NaN(),
NaN()},
var vcSqrtSC = []complex128{
NaN(),
}
var sqrtSC = []complex128{
NaN(),
}
var vcTanSC = []complex128{
NaN(),
}
var tanSC = []complex128{
NaN(),
}
var vcTanhSC = []complex128{
NaN(),
}
var tanhSC = []complex128{
NaN(),
}
// branch cut continuity checks
@ -891,7 +496,13 @@ func cTolerance(a, b complex128, e float64) bool {
func cSoclose(a, b complex128, e float64) bool { return cTolerance(a, b, e) }
func cVeryclose(a, b complex128) bool { return cTolerance(a, b, 4e-16) }
func cAlike(a, b complex128) bool {
return alike(real(a), real(b)) && alike(imag(a), imag(b))
switch {
case IsNaN(a) && IsNaN(b):
return true
case a == b:
return math.Signbit(real(a)) == math.Signbit(real(b)) && math.Signbit(imag(a)) == math.Signbit(imag(b))
}
return false
}
func TestAbs(t *testing.T) {
@ -912,13 +523,9 @@ func TestAcos(t *testing.T) {
t.Errorf("Acos(%g) = %g, want %g", vc[i], f, acos[i])
}
}
for _, v := range acosSC {
if f := Acos(v.in); !cAlike(v.want, f) {
t.Errorf("Acos(%g) = %g, want %g", v.in, f, v.want)
}
// Acos(Conj(z)) == Conj(Acos(z))
if f := Acos(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Acos(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
for i := 0; i < len(vcAcosSC); i++ {
if f := Acos(vcAcosSC[i]); !cAlike(acosSC[i], f) {
t.Errorf("Acos(%g) = %g, want %g", vcAcosSC[i], f, acosSC[i])
}
}
for _, pt := range branchPoints {
@ -933,15 +540,10 @@ func TestAcosh(t *testing.T) {
t.Errorf("Acosh(%g) = %g, want %g", vc[i], f, acosh[i])
}
}
for _, v := range acoshSC {
if f := Acosh(v.in); !cAlike(v.want, f) {
t.Errorf("Acosh(%g) = %g, want %g", v.in, f, v.want)
for i := 0; i < len(vcAcoshSC); i++ {
if f := Acosh(vcAcoshSC[i]); !cAlike(acoshSC[i], f) {
t.Errorf("Acosh(%g) = %g, want %g", vcAcoshSC[i], f, acoshSC[i])
}
// Acosh(Conj(z)) == Conj(Acosh(z))
if f := Acosh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Acosh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
}
for _, pt := range branchPoints {
if f0, f1 := Acosh(pt[0]), Acosh(pt[1]); !cVeryclose(f0, f1) {
@ -955,21 +557,9 @@ func TestAsin(t *testing.T) {
t.Errorf("Asin(%g) = %g, want %g", vc[i], f, asin[i])
}
}
for _, v := range asinSC {
if f := Asin(v.in); !cAlike(v.want, f) {
t.Errorf("Asin(%g) = %g, want %g", v.in, f, v.want)
}
if cAlike(-v.in, Conj(v.in)) && !cAlike(-v.want, Conj(v.want)) {
// The following conditions can't simultaneously be satisfied for this input.
continue
}
// Asin(Conj(z)) == Asin(Sinh(z))
if f := Asin(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Asin(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
// Asin(-z) == -Asin(z)
if f := Asin(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
t.Errorf("Asin(%g) = %g, want %g", -v.in, f, -v.want)
for i := 0; i < len(vcAsinSC); i++ {
if f := Asin(vcAsinSC[i]); !cAlike(asinSC[i], f) {
t.Errorf("Asin(%g) = %g, want %g", vcAsinSC[i], f, asinSC[i])
}
}
for _, pt := range branchPoints {
@ -984,21 +574,9 @@ func TestAsinh(t *testing.T) {
t.Errorf("Asinh(%g) = %g, want %g", vc[i], f, asinh[i])
}
}
for _, v := range asinhSC {
if f := Asinh(v.in); !cAlike(v.want, f) {
t.Errorf("Asinh(%g) = %g, want %g", v.in, f, v.want)
}
if cAlike(-v.in, Conj(v.in)) && !cAlike(-v.want, Conj(v.want)) {
// The following conditions can't simultaneously be satisfied for this input.
continue
}
// Asinh(Conj(z)) == Asinh(Sinh(z))
if f := Asinh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Asinh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
// Asinh(-z) == -Asinh(z)
if f := Asinh(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
t.Errorf("Asinh(%g) = %g, want %g", -v.in, f, -v.want)
for i := 0; i < len(vcAsinhSC); i++ {
if f := Asinh(vcAsinhSC[i]); !cAlike(asinhSC[i], f) {
t.Errorf("Asinh(%g) = %g, want %g", vcAsinhSC[i], f, asinhSC[i])
}
}
for _, pt := range branchPoints {
@ -1013,21 +591,9 @@ func TestAtan(t *testing.T) {
t.Errorf("Atan(%g) = %g, want %g", vc[i], f, atan[i])
}
}
for _, v := range atanSC {
if f := Atan(v.in); !cAlike(v.want, f) {
t.Errorf("Atan(%g) = %g, want %g", v.in, f, v.want)
}
if cAlike(-v.in, Conj(v.in)) && !cAlike(-v.want, Conj(v.want)) {
// The following conditions can't simultaneously be satisfied for this input.
continue
}
// Atan(Conj(z)) == Conj(Atan(z))
if f := Atan(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Atan(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
// Atan(-z) == -Atan(z)
if f := Atan(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
t.Errorf("Atan(%g) = %g, want %g", -v.in, f, -v.want)
for i := 0; i < len(vcAtanSC); i++ {
if f := Atan(vcAtanSC[i]); !cAlike(atanSC[i], f) {
t.Errorf("Atan(%g) = %g, want %g", vcAtanSC[i], f, atanSC[i])
}
}
for _, pt := range branchPoints {
@ -1042,21 +608,9 @@ func TestAtanh(t *testing.T) {
t.Errorf("Atanh(%g) = %g, want %g", vc[i], f, atanh[i])
}
}
for _, v := range atanhSC {
if f := Atanh(v.in); !cAlike(v.want, f) {
t.Errorf("Atanh(%g) = %g, want %g", v.in, f, v.want)
}
if cAlike(-v.in, Conj(v.in)) && !cAlike(-v.want, Conj(v.want)) {
// The following conditions can't simultaneously be satisfied for this input.
continue
}
// Atanh(Conj(z)) == Conj(Atanh(z))
if f := Atanh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Atanh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
// Atanh(-z) == -Atanh(z)
if f := Atanh(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
t.Errorf("Atanh(%g) = %g, want %g", -v.in, f, -v.want)
for i := 0; i < len(vcAtanhSC); i++ {
if f := Atanh(vcAtanhSC[i]); !cAlike(atanhSC[i], f) {
t.Errorf("Atanh(%g) = %g, want %g", vcAtanhSC[i], f, atanhSC[i])
}
}
for _, pt := range branchPoints {
@ -1083,21 +637,9 @@ func TestCos(t *testing.T) {
t.Errorf("Cos(%g) = %g, want %g", vc[i], f, cos[i])
}
}
for _, v := range cosSC {
if f := Cos(v.in); !cAlike(v.want, f) {
t.Errorf("Cos(%g) = %g, want %g", v.in, f, v.want)
}
if cAlike(-v.in, Conj(v.in)) && !cAlike(v.want, Conj(v.want)) {
// The following conditions can't simultaneously be satisfied for this input.
continue
}
// Cos(Conj(z)) == Cos(Cosh(z))
if f := Cos(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Cos(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
// Cos(-z) == Cos(z)
if f := Cos(-v.in); !cAlike(v.want, f) && !cAlike(v.in, -v.in) {
t.Errorf("Cos(%g) = %g, want %g", -v.in, f, v.want)
for i := 0; i < len(vcCosSC); i++ {
if f := Cos(vcCosSC[i]); !cAlike(cosSC[i], f) {
t.Errorf("Cos(%g) = %g, want %g", vcCosSC[i], f, cosSC[i])
}
}
}
@ -1107,21 +649,9 @@ func TestCosh(t *testing.T) {
t.Errorf("Cosh(%g) = %g, want %g", vc[i], f, cosh[i])
}
}
for _, v := range coshSC {
if f := Cosh(v.in); !cAlike(v.want, f) {
t.Errorf("Cosh(%g) = %g, want %g", v.in, f, v.want)
}
if cAlike(-v.in, Conj(v.in)) && !cAlike(v.want, Conj(v.want)) {
// The following conditions can't simultaneously be satisfied for this input.
continue
}
// Cosh(Conj(z)) == Conj(Cosh(z))
if f := Cosh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Cosh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
// Cosh(-z) == Cosh(z)
if f := Cosh(-v.in); !cAlike(v.want, f) && !cAlike(v.in, -v.in) {
t.Errorf("Cosh(%g) = %g, want %g", -v.in, f, v.want)
for i := 0; i < len(vcCoshSC); i++ {
if f := Cosh(vcCoshSC[i]); !cAlike(coshSC[i], f) {
t.Errorf("Cosh(%g) = %g, want %g", vcCoshSC[i], f, coshSC[i])
}
}
}
@ -1131,13 +661,9 @@ func TestExp(t *testing.T) {
t.Errorf("Exp(%g) = %g, want %g", vc[i], f, exp[i])
}
}
for _, v := range expSC {
if f := Exp(v.in); !cAlike(v.want, f) {
t.Errorf("Exp(%g) = %g, want %g", v.in, f, v.want)
}
// Exp(Conj(z)) == Exp(Cosh(z))
if f := Exp(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Exp(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
for i := 0; i < len(vcExpSC); i++ {
if f := Exp(vcExpSC[i]); !cAlike(expSC[i], f) {
t.Errorf("Exp(%g) = %g, want %g", vcExpSC[i], f, expSC[i])
}
}
}
@ -1154,13 +680,9 @@ func TestLog(t *testing.T) {
t.Errorf("Log(%g) = %g, want %g", vc[i], f, log[i])
}
}
for _, v := range logSC {
if f := Log(v.in); !cAlike(v.want, f) {
t.Errorf("Log(%g) = %g, want %g", v.in, f, v.want)
}
// Log(Conj(z)) == Conj(Log(z))
if f := Log(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Log(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
for i := 0; i < len(vcLogSC); i++ {
if f := Log(vcLogSC[i]); !cAlike(logSC[i], f) {
t.Errorf("Log(%g) = %g, want %g", vcLogSC[i], f, logSC[i])
}
}
for _, pt := range branchPoints {
@ -1175,13 +697,9 @@ func TestLog10(t *testing.T) {
t.Errorf("Log10(%g) = %g, want %g", vc[i], f, log10[i])
}
}
for _, v := range log10SC {
if f := Log10(v.in); !cAlike(v.want, f) {
t.Errorf("Log10(%g) = %g, want %g", v.in, f, v.want)
}
// Log10(Conj(z)) == Conj(Log10(z))
if f := Log10(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Log10(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
for i := 0; i < len(vcLog10SC); i++ {
if f := Log10(vcLog10SC[i]); !cAlike(log10SC[i], f) {
t.Errorf("Log10(%g) = %g, want %g", vcLog10SC[i], f, log10SC[i])
}
}
}
@ -1246,22 +764,9 @@ func TestSin(t *testing.T) {
t.Errorf("Sin(%g) = %g, want %g", vc[i], f, sin[i])
}
}
for _, v := range sinSC {
if f := Sin(v.in); !cAlike(v.want, f) {
t.Errorf("Sin(%g) = %g, want %g", v.in, f, v.want)
}
if cAlike(-v.in, Conj(v.in)) && !cAlike(-v.want, Conj(v.want)) {
// The following conditions can't simultaneously be satisfied for this input.
continue
}
// Sin(Conj(z)) == Conj(Sin(z))
if f := Sin(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Sinh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
// Sin(-z) == -Sin(z)
if f := Sin(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
t.Errorf("Sinh(%g) = %g, want %g", -v.in, f, -v.want)
for i := 0; i < len(vcSinSC); i++ {
if f := Sin(vcSinSC[i]); !cAlike(sinSC[i], f) {
t.Errorf("Sin(%g) = %g, want %g", vcSinSC[i], f, sinSC[i])
}
}
}
@ -1271,21 +776,9 @@ func TestSinh(t *testing.T) {
t.Errorf("Sinh(%g) = %g, want %g", vc[i], f, sinh[i])
}
}
for _, v := range sinhSC {
if f := Sinh(v.in); !cAlike(v.want, f) {
t.Errorf("Sinh(%g) = %g, want %g", v.in, f, v.want)
}
if cAlike(-v.in, Conj(v.in)) && !cAlike(-v.want, Conj(v.want)) {
// The following conditions can't simultaneously be satisfied for this input.
continue
}
// Sinh(Conj(z)) == Conj(Sinh(z))
if f := Sinh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Sinh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
// Sinh(-z) == -Sinh(z)
if f := Sinh(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
t.Errorf("Sinh(%g) = %g, want %g", -v.in, f, -v.want)
for i := 0; i < len(vcSinhSC); i++ {
if f := Sinh(vcSinhSC[i]); !cAlike(sinhSC[i], f) {
t.Errorf("Sinh(%g) = %g, want %g", vcSinhSC[i], f, sinhSC[i])
}
}
}
@ -1295,13 +788,9 @@ func TestSqrt(t *testing.T) {
t.Errorf("Sqrt(%g) = %g, want %g", vc[i], f, sqrt[i])
}
}
for _, v := range sqrtSC {
if f := Sqrt(v.in); !cAlike(v.want, f) {
t.Errorf("Sqrt(%g) = %g, want %g", v.in, f, v.want)
}
// Sqrt(Conj(z)) == Conj(Sqrt(z))
if f := Sqrt(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Sqrt(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
for i := 0; i < len(vcSqrtSC); i++ {
if f := Sqrt(vcSqrtSC[i]); !cAlike(sqrtSC[i], f) {
t.Errorf("Sqrt(%g) = %g, want %g", vcSqrtSC[i], f, sqrtSC[i])
}
}
for _, pt := range branchPoints {
@ -1316,21 +805,9 @@ func TestTan(t *testing.T) {
t.Errorf("Tan(%g) = %g, want %g", vc[i], f, tan[i])
}
}
for _, v := range tanSC {
if f := Tan(v.in); !cAlike(v.want, f) {
t.Errorf("Tan(%g) = %g, want %g", v.in, f, v.want)
}
if cAlike(-v.in, Conj(v.in)) && !cAlike(-v.want, Conj(v.want)) {
// The following conditions can't simultaneously be satisfied for this input.
continue
}
// Tan(Conj(z)) == Conj(Tan(z))
if f := Tan(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Tan(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
// Tan(-z) == -Tan(z)
if f := Tan(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
t.Errorf("Tan(%g) = %g, want %g", -v.in, f, -v.want)
for i := 0; i < len(vcTanSC); i++ {
if f := Tan(vcTanSC[i]); !cAlike(tanSC[i], f) {
t.Errorf("Tan(%g) = %g, want %g", vcTanSC[i], f, tanSC[i])
}
}
}
@ -1340,21 +817,9 @@ func TestTanh(t *testing.T) {
t.Errorf("Tanh(%g) = %g, want %g", vc[i], f, tanh[i])
}
}
for _, v := range tanhSC {
if f := Tanh(v.in); !cAlike(v.want, f) {
t.Errorf("Tanh(%g) = %g, want %g", v.in, f, v.want)
}
if cAlike(-v.in, Conj(v.in)) && !cAlike(-v.want, Conj(v.want)) {
// The following conditions can't simultaneously be satisfied for this input.
continue
}
// Tanh(Conj(z)) == Conj(Tanh(z))
if f := Tanh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
t.Errorf("Tanh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
}
// Tanh(-z) == -Tanh(z)
if f := Tanh(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
t.Errorf("Tanh(%g) = %g, want %g", -v.in, f, -v.want)
for i := 0; i < len(vcTanhSC); i++ {
if f := Tanh(vcTanhSC[i]); !cAlike(tanhSC[i], f) {
t.Errorf("Tanh(%g) = %g, want %g", vcTanhSC[i], f, tanhSC[i])
}
}
}

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

@ -49,23 +49,6 @@ 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

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

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

@ -51,19 +51,6 @@ 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)
@ -84,19 +71,6 @@ 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)
@ -122,19 +96,6 @@ 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)
@ -154,19 +115,6 @@ 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

@ -65,8 +65,6 @@ 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

@ -57,16 +57,6 @@ import "math"
// 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)
@ -91,16 +81,6 @@ 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()