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math: cosh cleanup

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do fabs by hand, don't check for nan and inf separately
This commit is contained in:
Szabolcs Nagy 2012-12-12 01:39:23 +01:00
parent 9c6b1de0fb
commit 14cc9c7f38
3 changed files with 63 additions and 70 deletions
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41
src/math/cosh.c
View File

@ -23,7 +23,7 @@
* 2
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : cosh(x) := huge*huge (overflow)
* ln2ovft < x : cosh(x) := inf (overflow)
*
* Special cases:
* cosh(x) is |x| if x is +INF, -INF, or NaN.
@ -32,43 +32,40 @@
#include "libm.h"
static const double huge = 1.0e300;
double cosh(double x)
{
double t, w;
int32_t ix;
union {double f; uint64_t i;} u = {.f = x};
uint32_t ix;
double t;
GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
/* x is INF or NaN */
if (ix >= 0x7ff00000)
return x*x;
/* |x| */
u.i &= (uint64_t)-1/2;
x = u.f;
ix = u.i >> 32;
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if (ix < 0x3fd62e43) {
t = expm1(fabs(x));
w = 1.0+t;
t = expm1(x);
if (ix < 0x3c800000)
return w; /* cosh(tiny) = 1 */
return 1.0 + (t*t)/(w+w);
return 1;
return 1 + t*t/(2*(1+t));
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|))/2; */
if (ix < 0x40360000) {
t = exp(fabs(x));
t = exp(x);
return 0.5*t + 0.5/t;
}
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862E42)
return 0.5*exp(fabs(x));
if (ix < 0x40862e42)
return 0.5*exp(x);
/* |x| in [log(maxdouble), overflowthresold] */
if (ix <= 0x408633CE)
return __expo2(fabs(x));
if (ix <= 0x408633ce)
return __expo2(x);
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
/* overflow (or nan) */
x *= 0x1p1023;
return x;
}

35
src/math/coshf.c
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@ -15,43 +15,40 @@
#include "libm.h"
static const float huge = 1.0e30;
float coshf(float x)
{
float t, w;
int32_t ix;
union {float f; uint32_t i;} u = {.f = x};
uint32_t ix;
float t;
GET_FLOAT_WORD(ix, x);
ix &= 0x7fffffff;
/* x is INF or NaN */
if (ix >= 0x7f800000)
return x*x;
/* |x| */
u.i &= 0x7fffffff;
x = u.f;
ix = u.i;
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if (ix < 0x3eb17218) {
t = expm1f(fabsf(x));
w = 1.0f+t;
t = expm1f(x);
if (ix < 0x39800000)
return 1.0f; /* cosh(tiny) = 1 */
return 1.0f + (t*t)/(w+w);
return 1;
return 1 + t*t/(2*(1+t));
}
/* |x| in [0.5*ln2,9], return (exp(|x|)+1/exp(|x|))/2; */
if (ix < 0x41100000) {
t = expf(fabsf(x));
t = expf(x);
return 0.5f*t + 0.5f/t;
}
/* |x| in [9, log(maxfloat)] return 0.5f*exp(|x|) */
if (ix < 0x42b17217)
return 0.5f*expf(fabsf(x));
return 0.5f*expf(x);
/* |x| in [log(maxfloat), overflowthresold] */
if (ix <= 0x42b2d4fc)
return __expo2f(fabsf(x));
return __expo2f(x);
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
/* |x| > overflowthresold or nan */
x *= 0x1p127f;
return x;
}

55
src/math/coshl.c
View File

@ -23,7 +23,7 @@
* 2
* 22 <= x <= lnovft : coshl(x) := expl(x)/2
* lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2)
* ln2ovft < x : coshl(x) := huge*huge (overflow)
* ln2ovft < x : coshl(x) := inf (overflow)
*
* Special cases:
* coshl(x) is |x| if x is +INF, -INF, or NaN.
@ -38,49 +38,48 @@ long double coshl(long double x)
return cosh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
static const long double huge = 1.0e4900L;
long double coshl(long double x)
{
long double t,w;
int32_t ex;
union {
long double f;
struct{uint64_t m; uint16_t se; uint16_t pad;} i;
} u = {.f = x};
unsigned ex = u.i.se & 0x7fff;
long double t;
uint32_t mx,lx;
/* High word of |x|. */
GET_LDOUBLE_WORDS(ex, mx, lx, x);
ex &= 0x7fff;
/* x is INF or NaN */
if (ex == 0x7fff) return x*x;
/* |x| */
u.i.se = ex;
x = u.f;
mx = u.i.m >> 32;
lx = u.i.m;
/* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
if (ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
t = expm1l(fabsl(x));
w = 1.0 + t;
if (ex < 0x3fbc) return w; /* cosh(tiny) = 1 */
return 1.0+(t*t)/(w+w);
if (ex < 0x3fff-2 || (ex == 0x3fff-2 && mx < 0xb17217f7)) {
t = expm1l(x);
if (ex < 0x3fff-64)
return 1;
return 1 + t*t/(2*(1+t));
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
t = expl(fabsl(x));
if (ex < 0x3fff+4 || (ex == 0x3fff+4 && mx < 0xb0000000)) {
t = expl(x);
return 0.5*t + 0.5/t;
}
/* |x| in [22, ln(maxdouble)] return 0.5*exp(|x|) */
if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
return 0.5*expl(fabsl(x));
if (ex < 0x3fff+13 || (ex == 0x3fff+13 && mx < 0xb1700000))
return 0.5*expl(x);
/* |x| in [log(maxdouble), log(2*maxdouble)) */
if (ex == 0x400c && (mx < 0xb174ddc0u ||
(mx == 0xb174ddc0u && lx < 0x31aec0ebu)))
{
w = expl(0.5*fabsl(x));
t = 0.5*w;
return t*w;
if (ex == 0x3fff+13 && (mx < 0xb174ddc0 ||
(mx == 0xb174ddc0 && lx < 0x31aec0eb))) {
t = expl(0.5*x);
return 0.5*t*t;
}
/* |x| >= log(2*maxdouble), cosh(x) overflow */
return huge*huge;
/* |x| >= log(2*maxdouble) or nan */
return x*0x1p16383L;
}
#endif