mirror of git://git.musl-libc.org/musl
math: sinh.c cleanup similar to the cosh one
comments are kept in the double version of the function
This commit is contained in:
Szabolcs Nagy
parent
1aec620f93
commit
f143458223
|
|
@ -1,71 +1,39 @@
|
|||
/* origin: FreeBSD /usr/src/lib/msun/src/e_sinh.c */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
/* sinh(x)
|
||||
* Method :
|
||||
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
|
||||
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
|
||||
* 2.
|
||||
* E + E/(E+1)
|
||||
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
|
||||
* 2
|
||||
*
|
||||
* 22 <= x <= lnovft : sinh(x) := exp(x)/2
|
||||
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
|
||||
* ln2ovft < x : sinh(x) := x*shuge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* sinh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only sinh(0)=0 is exact for finite x.
|
||||
*/
|
||||
|
||||
#include "libm.h"
|
||||
|
||||
static const double huge = 1.0e307;
|
||||
|
||||
/* sinh(x) = (exp(x) - 1/exp(x))/2
|
||||
* = (exp(x)-1 + (exp(x)-1)/exp(x))/2
|
||||
* = x + x^3/6 + o(x^5)
|
||||
*/
|
||||
double sinh(double x)
|
||||
{
|
||||
double t, h;
|
||||
int32_t ix, jx;
|
||||
|
||||
/* High word of |x|. */
|
||||
GET_HIGH_WORD(jx, x);
|
||||
ix = jx & 0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if (ix >= 0x7ff00000)
|
||||
return x + x;
|
||||
union {double f; uint64_t i;} u = {.f = x};
|
||||
uint32_t w;
|
||||
double t, h, absx;
|
||||
|
||||
h = 0.5;
|
||||
if (jx < 0) h = -h;
|
||||
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
|
||||
if (ix < 0x40360000) { /* |x|<22 */
|
||||
if (ix < 0x3e300000) /* |x|<2**-28 */
|
||||
/* raise inexact, return x */
|
||||
if (huge+x > 1.0)
|
||||
if (u.i >> 63)
|
||||
h = -h;
|
||||
/* |x| */
|
||||
u.i &= (uint64_t)-1/2;
|
||||
absx = u.f;
|
||||
w = u.i >> 32;
|
||||
|
||||
/* |x| < log(DBL_MAX) */
|
||||
if (w < 0x40862e42) {
|
||||
t = expm1(absx);
|
||||
if (w < 0x3ff00000) {
|
||||
if (w < 0x3ff00000 - (26<<20))
|
||||
/* note: inexact is raised by expm1 */
|
||||
/* note: this branch avoids underflow */
|
||||
return x;
|
||||
t = expm1(fabs(x));
|
||||
if (ix < 0x3ff00000)
|
||||
return h*(2.0*t - t*t/(t+1.0));
|
||||
return h*(t + t/(t+1.0));
|
||||
return h*(2*t - t*t/(t+1));
|
||||
}
|
||||
/* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
|
||||
return h*(t + t/(t+1));
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
|
||||
if (ix < 0x40862E42)
|
||||
return h*exp(fabs(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
if (ix <= 0x408633CE)
|
||||
return h * 2.0 * __expo2(fabs(x)); /* h is for sign only */
|
||||
|
||||
/* |x| > overflowthresold, sinh(x) overflow */
|
||||
return x*huge;
|
||||
/* |x| > log(DBL_MAX) or nan */
|
||||
/* note: the result is stored to handle overflow */
|
||||
t = 2*h*__expo2(absx);
|
||||
return t;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1,57 +1,31 @@
|
|||
/* origin: FreeBSD /usr/src/lib/msun/src/e_sinhf.c */
|
||||
/*
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include "libm.h"
|
||||
|
||||
static const float huge = 1.0e37;
|
||||
|
||||
float sinhf(float x)
|
||||
{
|
||||
float t, h;
|
||||
int32_t ix, jx;
|
||||
|
||||
GET_FLOAT_WORD(jx, x);
|
||||
ix = jx & 0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if (ix >= 0x7f800000)
|
||||
return x + x;
|
||||
union {float f; uint32_t i;} u = {.f = x};
|
||||
uint32_t w;
|
||||
float t, h, absx;
|
||||
|
||||
h = 0.5;
|
||||
if (jx < 0)
|
||||
if (u.i >> 31)
|
||||
h = -h;
|
||||
/* |x| in [0,9], return sign(x)*0.5*(E+E/(E+1))) */
|
||||
if (ix < 0x41100000) { /* |x|<9 */
|
||||
if (ix < 0x39800000) /* |x|<2**-12 */
|
||||
/* raise inexact, return x */
|
||||
if (huge+x > 1.0f)
|
||||
/* |x| */
|
||||
u.i &= 0x7fffffff;
|
||||
absx = u.f;
|
||||
w = u.i;
|
||||
|
||||
/* |x| < log(FLT_MAX) */
|
||||
if (w < 0x42b17217) {
|
||||
t = expm1f(absx);
|
||||
if (w < 0x3f800000) {
|
||||
if (w < 0x3f800000 - (12<<23))
|
||||
return x;
|
||||
t = expm1f(fabsf(x));
|
||||
if (ix < 0x3f800000)
|
||||
return h*(2.0f*t - t*t/(t+1.0f));
|
||||
return h*(t + t/(t+1.0f));
|
||||
return h*(2*t - t*t/(t+1));
|
||||
}
|
||||
return h*(t + t/(t+1));
|
||||
}
|
||||
|
||||
/* |x| in [9, logf(maxfloat)] return 0.5*exp(|x|) */
|
||||
if (ix < 0x42b17217)
|
||||
return h*expf(fabsf(x));
|
||||
|
||||
/* |x| in [logf(maxfloat), overflowthresold] */
|
||||
if (ix <= 0x42b2d4fc)
|
||||
return h * 2.0f * __expo2f(fabsf(x)); /* h is for sign only */
|
||||
|
||||
/* |x| > overflowthresold, sinh(x) overflow */
|
||||
return x*huge;
|
||||
/* |x| > logf(FLT_MAX) or nan */
|
||||
t = 2*h*__expo2f(absx);
|
||||
return t;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1,32 +1,3 @@
|
|||
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_sinhl.c */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
/* sinhl(x)
|
||||
* Method :
|
||||
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
|
||||
* 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
|
||||
* 2.
|
||||
* E + E/(E+1)
|
||||
* 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
|
||||
* 2
|
||||
*
|
||||
* 25 <= x <= lnovft : sinhl(x) := expl(x)/2
|
||||
* lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
|
||||
* ln2ovft < x : sinhl(x) := x*huge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* sinhl(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only sinhl(0)=0 is exact for finite x.
|
||||
*/
|
||||
|
||||
#include "libm.h"
|
||||
|
||||
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
|
||||
|
|
@ -35,47 +6,35 @@ long double sinhl(long double x)
|
|||
return sinh(x);
|
||||
}
|
||||
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
|
||||
static const long double huge = 1.0e4931L;
|
||||
|
||||
long double sinhl(long double x)
|
||||
{
|
||||
long double t,w,h;
|
||||
uint32_t jx,ix,i0,i1;
|
||||
|
||||
/* Words of |x|. */
|
||||
GET_LDOUBLE_WORDS(jx, i0, i1, x);
|
||||
ix = jx & 0x7fff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if (ix == 0x7fff) return x + x;
|
||||
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 h, t, absx;
|
||||
|
||||
h = 0.5;
|
||||
if (jx & 0x8000)
|
||||
if (u.i.se & 0x8000)
|
||||
h = -h;
|
||||
/* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
|
||||
if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x| < 25 */
|
||||
if (ix < 0x3fdf) /* |x|<2**-32 */
|
||||
if (huge + x > 1.0)
|
||||
return x;/* sinh(tiny) = tiny with inexact */
|
||||
t = expm1l(fabsl(x));
|
||||
if (ix < 0x3fff)
|
||||
return h*(2.0*t - t*t/(t + 1.0));
|
||||
return h*(t + t/(t + 1.0));
|
||||
/* |x| */
|
||||
u.i.se = ex;
|
||||
absx = u.f;
|
||||
|
||||
/* |x| < log(LDBL_MAX) */
|
||||
if (ex < 0x3fff+13 || (ex == 0x3fff+13 && u.i.m>>32 < 0xb17217f7)) {
|
||||
t = expm1l(absx);
|
||||
if (ex < 0x3fff) {
|
||||
if (ex < 0x3fff-32)
|
||||
return x;
|
||||
return h*(2*t - t*t/(1+t));
|
||||
}
|
||||
return h*(t + t/(t+1));
|
||||
}
|
||||
|
||||
/* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
|
||||
if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
|
||||
return h*expl(fabsl(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthreshold] */
|
||||
if (ix < 0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 ||
|
||||
(i0 == 0xb174ddc0 && i1 <= 0x31aec0ea)))) {
|
||||
w = expl(0.5*fabsl(x));
|
||||
t = h*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthreshold, sinhl(x) overflow */
|
||||
return x*huge;
|
||||
/* |x| > log(LDBL_MAX) or nan */
|
||||
t = expl(0.5*absx);
|
||||
return h*t*t;
|
||||
}
|
||||
#endif
|
||||
|
|
|
|||
Loading…
Reference in New Issue