Author: das
Date: Fri Oct 21 06:29:32 2011
New Revision: 226599
URL: http://svn.freebsd.org/changeset/base/226599
Log:
Improved handling of large x in ccosh{,f}():
- 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).
Modified:
head/lib/msun/src/s_ccosh.c
head/lib/msun/src/s_ccoshf.c
head/lib/msun/src/s_csinh.c
head/lib/msun/src/s_csinhf.c
Modified: head/lib/msun/src/s_ccosh.c
==============================================================================
--- head/lib/msun/src/s_ccosh.c Fri Oct 21 06:28:47 2011 (r226598)
+++ head/lib/msun/src/s_ccosh.c Fri Oct 21 06:29:32 2011 (r226599)
@@ -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)));
+ }
}
/*
Modified: head/lib/msun/src/s_ccoshf.c
==============================================================================
--- head/lib/msun/src/s_ccoshf.c Fri Oct 21 06:28:47 2011
(r226598)
+++ head/lib/msun/src/s_ccoshf.c Fri Oct 21 06:29:32 2011
(r226599)
@@ -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)
Modified: head/lib/msun/src/s_csinh.c
==============================================================================
--- head/lib/msun/src/s_csinh.c Fri Oct 21 06:28:47 2011 (r226598)
+++ head/lib/msun/src/s_csinh.c Fri Oct 21 06:29:32 2011 (r226599)
@@ -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)));
}
Modified: head/lib/msun/src/s_csinhf.c
==============================================================================
--- head/lib/msun/src/s_csinhf.c Fri Oct 21 06:28:47 2011
(r226598)
+++ head/lib/msun/src/s_csinhf.c Fri Oct 21 06:29:32 2011
(r226599)
@@ -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)));
}
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