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Improved handling of large x in ccosh{,f}():

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- Handle cases where exp(x) would overflow, but ccosh(x) ~= exp(x) / 2
  shouldn't.
- Use the ccosh(x) ~= exp(x) / 2 approximation to simplify the calculation
  when x is large.

Similarly for csinh().  Also fixed the return value of csinh(-Inf +- 0i).
This commit is contained in:
das 2011-10-21 06:29:32 +00:00
parent f66ae96060
commit 3578083bd5
4 changed files with 83 additions and 15 deletions
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23
lib/msun/src/s_ccosh.c
View File

@ -42,10 +42,12 @@ __FBSDID("$FreeBSD$");
#include "math_private.h"
static const double huge = 0x1p1023;
double complex
ccosh(double complex z)
{
double x, y;
double x, y, h;
int32_t hx, hy, ix, iy, lx, ly;
x = creal(z);
@ -61,8 +63,23 @@ ccosh(double complex z)
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
return (cpack(cosh(x), x * y));
/* XXX We don't handle |x| > DBL_MAX ln(2) yet. */
return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
if (ix < 0x40360000) /* small x: normal case */
return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
/* |x| >= 22, so cosh(x) ~= exp(|x|) */
if (ix < 0x40862e42) {
/* x < 710: exp(|x|) won't overflow */
h = exp(fabs(x)) * 0.5;
return (cpack(h * cos(y), copysign(h, x) * sin(y)));
} else if (ix < 0x4096bbaa) {
/* x < 1455: scale to avoid overflow */
z = __ldexp_cexp(cpack(fabs(x), y), -1);
return (cpack(creal(z), cimag(z) * copysign(1, x)));
} else {
/* x >= 1455: the result always overflows */
h = huge * x;
return (cpack(h * h * cos(y), h * sin(y)));
}
}
/*

23
lib/msun/src/s_ccoshf.c
View File

@ -36,10 +36,12 @@ __FBSDID("$FreeBSD$");
#include "math_private.h"
static const float huge = 0x1p127;
float complex
ccoshf(float complex z)
{
float x, y;
float x, y, h;
int32_t hx, hy, ix, iy;
x = crealf(z);
@ -54,8 +56,23 @@ ccoshf(float complex z)
if (ix < 0x7f800000 && iy < 0x7f800000) {
if (iy == 0)
return (cpackf(coshf(x), x * y));
/* XXX We don't handle |x| > FLT_MAX ln(2) yet. */
return (cpackf(coshf(x) * cosf(y), sinhf(x) * sinf(y)));
if (ix < 0x41100000) /* small x: normal case */
return (cpackf(coshf(x) * cosf(y), sinhf(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;
return (cpackf(h * cosf(y), copysignf(h, x) * sinf(y)));
} else if (ix < 0x4340b1e7) {
/* x < 192.7: scale to avoid overflow */
z = __ldexp_cexpf(cpackf(fabsf(x), y), -1);
return (cpackf(crealf(z), cimagf(z) * copysignf(1, x)));
} else {
/* x >= 192.7: the result always overflows */
h = huge * x;
return (cpackf(h * h * cosf(y), h * sinf(y)));
}
}
if (ix == 0 && iy >= 0x7f800000)

27
lib/msun/src/s_csinh.c
View File

@ -42,10 +42,12 @@ __FBSDID("$FreeBSD$");
#include "math_private.h"
static const double huge = 0x1p1023;
double complex
csinh(double complex z)
{
double x, y;
double x, y, h;
int32_t hx, hy, ix, iy, lx, ly;
x = creal(z);
@ -61,8 +63,23 @@ csinh(double complex z)
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
return (cpack(sinh(x), y));
/* XXX We don't handle |x| > DBL_MAX ln(2) yet. */
return (cpack(sinh(x) * cos(y), cosh(x) * sin(y)));
if (ix < 0x40360000) /* small x: normal case */
return (cpack(sinh(x) * cos(y), cosh(x) * sin(y)));
/* |x| >= 22, so cosh(x) ~= exp(|x|) */
if (ix < 0x40862e42) {
/* x < 710: exp(|x|) won't overflow */
h = exp(fabs(x)) * 0.5;
return (cpack(copysign(h, x) * cos(y), h * sin(y)));
} else if (ix < 0x4096bbaa) {
/* x < 1455: scale to avoid overflow */
z = __ldexp_cexp(cpack(fabs(x), y), -1);
return (cpack(creal(z) * copysign(1, x), cimag(z)));
} else {
/* x >= 1455: the result always overflows */
h = huge * x;
return (cpack(h * cos(y), h * h * sin(y)));
}
}
/*
@ -78,13 +95,13 @@ csinh(double complex z)
return (cpack(copysign(0, x * (y - y)), y - y));
/*
* sinh(+-Inf +- I 0) = +-Inf + I (+-)(+-)0.
* 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 (cpack(x, copysign(0, x) * y));
return (cpack(x, y));
return (cpack(x, copysign(0, y)));
}

25
lib/msun/src/s_csinhf.c
View File

@ -36,10 +36,12 @@ __FBSDID("$FreeBSD$");
#include "math_private.h"
static const float huge = 0x1p127;
float complex
csinhf(float complex z)
{
float x, y;
float x, y, h;
int32_t hx, hy, ix, iy;
x = crealf(z);
@ -54,8 +56,23 @@ csinhf(float complex z)
if (ix < 0x7f800000 && iy < 0x7f800000) {
if (iy == 0)
return (cpackf(sinhf(x), y));
/* XXX We don't handle |x| > FLT_MAX ln(2) yet. */
return (cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y)));
if (ix < 0x41100000) /* small x: normal case */
return (cpackf(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;
return (cpackf(copysignf(h, x) * cosf(y), h * sinf(y)));
} else if (ix < 0x4340b1e7) {
/* x < 192.7: scale to avoid overflow */
z = __ldexp_cexpf(cpackf(fabsf(x), y), -1);
return (cpackf(crealf(z) * copysignf(1, x), cimagf(z)));
} else {
/* x >= 192.7: the result always overflows */
h = huge * x;
return (cpackf(h * cosf(y), h * h * sinf(y)));
}
}
if (ix == 0 && iy >= 0x7f800000)
@ -63,7 +80,7 @@ csinhf(float complex z)
if (iy == 0 && ix >= 0x7f800000) {
if ((hx & 0x7fffff) == 0)
return (cpackf(x, copysignf(0, x) * y));
return (cpackf(x, y));
return (cpackf(x, copysignf(0, y)));
}