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
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@ -1,71 +1,39 @@
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/* origin: FreeBSD /usr/src/lib/msun/src/e_sinh.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* sinh(x)
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* Method :
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* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
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* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
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* 2.
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* E + E/(E+1)
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* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
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* 2
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*
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* 22 <= x <= lnovft : sinh(x) := exp(x)/2
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* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
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* ln2ovft < x : sinh(x) := x*shuge (overflow)
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*
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* Special cases:
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* sinh(x) is |x| if x is +INF, -INF, or NaN.
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* only sinh(0)=0 is exact for finite x.
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*/
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#include "libm.h"
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#include "libm.h"
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static const double huge = 1.0e307;
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/* sinh(x) = (exp(x) - 1/exp(x))/2
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* = (exp(x)-1 + (exp(x)-1)/exp(x))/2
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* = x + x^3/6 + o(x^5)
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*/
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double sinh(double x)
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double sinh(double x)
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{
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{
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double t, h;
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union {double f; uint64_t i;} u = {.f = x};
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int32_t ix, jx;
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uint32_t w;
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double t, h, absx;
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/* High word of |x|. */
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GET_HIGH_WORD(jx, x);
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ix = jx & 0x7fffffff;
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/* x is INF or NaN */
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if (ix >= 0x7ff00000)
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return x + x;
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h = 0.5;
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h = 0.5;
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if (jx < 0) h = -h;
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if (u.i >> 63)
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/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
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h = -h;
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if (ix < 0x40360000) { /* |x|<22 */
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/* |x| */
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if (ix < 0x3e300000) /* |x|<2**-28 */
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u.i &= (uint64_t)-1/2;
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/* raise inexact, return x */
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absx = u.f;
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if (huge+x > 1.0)
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w = u.i >> 32;
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/* |x| < log(DBL_MAX) */
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if (w < 0x40862e42) {
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t = expm1(absx);
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if (w < 0x3ff00000) {
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if (w < 0x3ff00000 - (26<<20))
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/* note: inexact is raised by expm1 */
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/* note: this branch avoids underflow */
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return x;
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return x;
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t = expm1(fabs(x));
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return h*(2*t - t*t/(t+1));
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if (ix < 0x3ff00000)
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}
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return h*(2.0*t - t*t/(t+1.0));
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/* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
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return h*(t + t/(t+1.0));
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return h*(t + t/(t+1));
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}
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}
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/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
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/* |x| > log(DBL_MAX) or nan */
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if (ix < 0x40862E42)
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/* note: the result is stored to handle overflow */
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return h*exp(fabs(x));
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t = 2*h*__expo2(absx);
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return t;
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/* |x| in [log(maxdouble), overflowthresold] */
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if (ix <= 0x408633CE)
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return h * 2.0 * __expo2(fabs(x)); /* h is for sign only */
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/* |x| > overflowthresold, sinh(x) overflow */
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return x*huge;
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}
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}
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@ -1,57 +1,31 @@
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/* origin: FreeBSD /usr/src/lib/msun/src/e_sinhf.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include "libm.h"
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#include "libm.h"
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static const float huge = 1.0e37;
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float sinhf(float x)
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float sinhf(float x)
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{
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{
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float t, h;
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union {float f; uint32_t i;} u = {.f = x};
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int32_t ix, jx;
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uint32_t w;
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float t, h, absx;
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GET_FLOAT_WORD(jx, x);
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ix = jx & 0x7fffffff;
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/* x is INF or NaN */
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if (ix >= 0x7f800000)
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return x + x;
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h = 0.5;
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h = 0.5;
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if (jx < 0)
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if (u.i >> 31)
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h = -h;
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h = -h;
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/* |x| in [0,9], return sign(x)*0.5*(E+E/(E+1))) */
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/* |x| */
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if (ix < 0x41100000) { /* |x|<9 */
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u.i &= 0x7fffffff;
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if (ix < 0x39800000) /* |x|<2**-12 */
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absx = u.f;
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/* raise inexact, return x */
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w = u.i;
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if (huge+x > 1.0f)
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/* |x| < log(FLT_MAX) */
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if (w < 0x42b17217) {
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t = expm1f(absx);
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if (w < 0x3f800000) {
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if (w < 0x3f800000 - (12<<23))
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return x;
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return x;
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t = expm1f(fabsf(x));
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return h*(2*t - t*t/(t+1));
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if (ix < 0x3f800000)
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}
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return h*(2.0f*t - t*t/(t+1.0f));
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return h*(t + t/(t+1));
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return h*(t + t/(t+1.0f));
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}
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}
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/* |x| in [9, logf(maxfloat)] return 0.5*exp(|x|) */
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/* |x| > logf(FLT_MAX) or nan */
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if (ix < 0x42b17217)
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t = 2*h*__expo2f(absx);
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return h*expf(fabsf(x));
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return t;
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/* |x| in [logf(maxfloat), overflowthresold] */
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if (ix <= 0x42b2d4fc)
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return h * 2.0f * __expo2f(fabsf(x)); /* h is for sign only */
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/* |x| > overflowthresold, sinh(x) overflow */
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return x*huge;
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}
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}
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@ -1,32 +1,3 @@
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/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_sinhl.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* sinhl(x)
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* Method :
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* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
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* 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
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* 2.
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* E + E/(E+1)
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* 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
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* 2
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*
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* 25 <= x <= lnovft : sinhl(x) := expl(x)/2
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* lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
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* ln2ovft < x : sinhl(x) := x*huge (overflow)
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*
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* Special cases:
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* sinhl(x) is |x| if x is +INF, -INF, or NaN.
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* only sinhl(0)=0 is exact for finite x.
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*/
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#include "libm.h"
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#include "libm.h"
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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@ -35,47 +6,35 @@ long double sinhl(long double x)
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return sinh(x);
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return sinh(x);
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}
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}
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#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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static const long double huge = 1.0e4931L;
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long double sinhl(long double x)
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long double sinhl(long double x)
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{
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{
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long double t,w,h;
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union {
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uint32_t jx,ix,i0,i1;
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long double f;
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struct{uint64_t m; uint16_t se; uint16_t pad;} i;
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/* Words of |x|. */
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} u = {.f = x};
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GET_LDOUBLE_WORDS(jx, i0, i1, x);
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unsigned ex = u.i.se & 0x7fff;
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ix = jx & 0x7fff;
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long double h, t, absx;
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/* x is INF or NaN */
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if (ix == 0x7fff) return x + x;
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h = 0.5;
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h = 0.5;
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if (jx & 0x8000)
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if (u.i.se & 0x8000)
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h = -h;
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h = -h;
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/* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
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/* |x| */
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if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x| < 25 */
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u.i.se = ex;
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if (ix < 0x3fdf) /* |x|<2**-32 */
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absx = u.f;
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if (huge + x > 1.0)
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return x;/* sinh(tiny) = tiny with inexact */
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/* |x| < log(LDBL_MAX) */
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t = expm1l(fabsl(x));
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if (ex < 0x3fff+13 || (ex == 0x3fff+13 && u.i.m>>32 < 0xb17217f7)) {
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if (ix < 0x3fff)
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t = expm1l(absx);
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return h*(2.0*t - t*t/(t + 1.0));
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if (ex < 0x3fff) {
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return h*(t + t/(t + 1.0));
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if (ex < 0x3fff-32)
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return x;
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return h*(2*t - t*t/(1+t));
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}
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return h*(t + t/(t+1));
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}
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}
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/* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
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/* |x| > log(LDBL_MAX) or nan */
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if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
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t = expl(0.5*absx);
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return h*expl(fabsl(x));
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return h*t*t;
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/* |x| in [log(maxdouble), overflowthreshold] */
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if (ix < 0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 ||
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(i0 == 0xb174ddc0 && i1 <= 0x31aec0ea)))) {
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w = expl(0.5*fabsl(x));
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t = h*w;
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return t*w;
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}
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/* |x| > overflowthreshold, sinhl(x) overflow */
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return x*huge;
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}
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}
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#endif
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#endif
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