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Fix some exceptional cases where the sign of the result is unspecified

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but must still satisfy csinh(conj(z)) == conj(csinh(z)) and csinh(-z) ==
-csinh(z).  This allows eliminating two negations from csin(z).

In collaboration with:	bde
This commit is contained in:
Tijl Coosemans 2015-06-15 20:16:53 +00:00
parent 5a74378c7b
commit f0f050e0f9
2 changed files with 43 additions and 47 deletions
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59
lib/msun/src/s_csinh.c
View File

@ -32,6 +32,8 @@
*
* Exceptional values are noted in the comments within the source code.
* These values and the return value were taken from n1124.pdf.
* The sign of the result for some exceptional values is unspecified but
* must satisfy both sinh(conj(z)) == conj(sinh(z)) and sinh(-z) == -sinh(z).
*/
#include <sys/cdefs.h>
@ -63,7 +65,7 @@ csinh(double complex z)
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
return (CMPLX(sinh(x), y));
if (ix < 0x40360000) /* small x: normal case */
if (ix < 0x40360000) /* |x| < 22: normal case */
return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y)));
/* |x| >= 22, so cosh(x) ~= exp(|x|) */
@ -83,27 +85,24 @@ csinh(double complex z)
}
/*
* sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN.
* The sign of 0 in the result is unspecified. Choice = normally
* the same as dNaN. Raise the invalid floating-point exception.
* sinh(+-0 +- I Inf) = +-0 + I dNaN.
* The sign of 0 in the result is unspecified. Choice = same sign
* as the argument. Raise the invalid floating-point exception.
*
* sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN).
* The sign of 0 in the result is unspecified. Choice = normally
* the same as d(NaN).
* sinh(+-0 +- I NaN) = +-0 + I d(NaN).
* The sign of 0 in the result is unspecified. Choice = same sign
* as the argument.
*/
if ((ix | lx) == 0 && iy >= 0x7ff00000)
return (CMPLX(copysign(0, x * (y - y)), y - y));
if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */
return (CMPLX(x, y - y));
/*
* sinh(+-Inf +- I 0) = +-Inf + I +-0.
*
* sinh(NaN +- I 0) = d(NaN) + I +-0.
*/
if ((iy | ly) == 0 && ix >= 0x7ff00000) {
if (((hx & 0xfffff) | lx) == 0)
return (CMPLX(x, y));
return (CMPLX(x, copysign(0, y)));
}
if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */
return (CMPLX(x + x, y));
/*
* sinh(x +- I Inf) = dNaN + I dNaN.
@ -113,45 +112,45 @@ csinh(double complex z)
* Optionally raises the invalid floating-point exception for finite
* nonzero x. Choice = don't raise (except for signaling NaNs).
*/
if (ix < 0x7ff00000 && iy >= 0x7ff00000)
return (CMPLX(y - y, x * (y - y)));
if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */
return (CMPLX(y - y, y - y));
/*
* sinh(+-Inf + I NaN) = +-Inf + I d(NaN).
* The sign of Inf in the result is unspecified. Choice = normally
* the same as d(NaN).
* The sign of Inf in the result is unspecified. Choice = same sign
* as the argument.
*
* sinh(+-Inf +- I Inf) = +Inf + I dNaN.
* The sign of Inf in the result is unspecified. Choice = always +.
* Raise the invalid floating-point exception.
* sinh(+-Inf +- I Inf) = +-Inf + I dNaN.
* The sign of Inf in the result is unspecified. Choice = same sign
* as the argument. Raise the invalid floating-point exception.
*
* sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y)
*/
if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
if (ix == 0x7ff00000 && lx == 0) {
if (iy >= 0x7ff00000)
return (CMPLX(x * x, x * (y - y)));
return (CMPLX(x, y - y));
return (CMPLX(x * cos(y), INFINITY * sin(y)));
}
/*
* sinh(NaN + I NaN) = d(NaN) + I d(NaN).
* sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2).
*
* sinh(NaN +- I Inf) = d(NaN) + I d(NaN).
* sinh(NaN +- I Inf) = d(NaN, dNaN) + I d(NaN, dNaN).
* Optionally raises the invalid floating-point exception.
* Choice = raise.
*
* sinh(NaN + I y) = d(NaN) + I d(NaN).
* sinh(NaN + I y) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception for finite
* nonzero y. Choice = don't raise (except for signaling NaNs).
*/
return (CMPLX((x * x) * (y - y), (x + x) * (y - y)));
return (CMPLX((x + x) * (y - y), (x * x) * (y - y)));
}
double complex
csin(double complex z)
{
/* csin(z) = -I * csinh(I * z) */
z = csinh(CMPLX(-cimag(z), creal(z)));
return (CMPLX(cimag(z), -creal(z)));
/* csin(z) = -I * csinh(I * z) = I * conj(csinh(I * conj(z))). */
z = csinh(CMPLX(cimag(z), creal(z)));
return (CMPLX(cimag(z), creal(z)));
}

31
lib/msun/src/s_csinhf.c
View File

@ -25,7 +25,7 @@
*/
/*
* Hyperbolic sine of a complex argument z. See s_csinh.c for details.
* Float version of csinh(). See s_csinh.c for details.
*/
#include <sys/cdefs.h>
@ -56,13 +56,13 @@ csinhf(float complex z)
if (ix < 0x7f800000 && iy < 0x7f800000) {
if (iy == 0)
return (CMPLXF(sinhf(x), y));
if (ix < 0x41100000) /* small x: normal case */
if (ix < 0x41100000) /* |x| < 9: normal case */
return (CMPLXF(sinhf(x) * cosf(y), coshf(x) * sinf(y)));
/* |x| >= 9, so cosh(x) ~= exp(|x|) */
if (ix < 0x42b17218) {
/* x < 88.7: expf(|x|) won't overflow */
h = expf(fabsf(x)) * 0.5f;
h = expf(fabsf(x)) * 0.5F;
return (CMPLXF(copysignf(h, x) * cosf(y), h * sinf(y)));
} else if (ix < 0x4340b1e7) {
/* x < 192.7: scale to avoid overflow */
@ -75,31 +75,28 @@ csinhf(float complex z)
}
}
if (ix == 0 && iy >= 0x7f800000)
return (CMPLXF(copysignf(0, x * (y - y)), y - y));
if (ix == 0) /* && iy >= 0x7f800000 */
return (CMPLXF(x, y - y));
if (iy == 0 && ix >= 0x7f800000) {
if ((hx & 0x7fffff) == 0)
return (CMPLXF(x, y));
return (CMPLXF(x, copysignf(0, y)));
}
if (iy == 0) /* && ix >= 0x7f800000 */
return (CMPLXF(x + x, y));
if (ix < 0x7f800000 && iy >= 0x7f800000)
return (CMPLXF(y - y, x * (y - y)));
if (ix < 0x7f800000) /* && iy >= 0x7f800000 */
return (CMPLXF(y - y, y - y));
if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
if (ix == 0x7f800000) {
if (iy >= 0x7f800000)
return (CMPLXF(x * x, x * (y - y)));
return (CMPLXF(x, y - y));
return (CMPLXF(x * cosf(y), INFINITY * sinf(y)));
}
return (CMPLXF((x * x) * (y - y), (x + x) * (y - y)));
return (CMPLXF((x + x) * (y - y), (x * x) * (y - y)));
}
float complex
csinf(float complex z)
{
z = csinhf(CMPLXF(-cimagf(z), crealf(z)));
return (CMPLXF(cimagf(z), -crealf(z)));
z = csinhf(CMPLXF(cimagf(z), crealf(z)));
return (CMPLXF(cimagf(z), crealf(z)));
}