mirror of https://git.musl-libc.org/git/musl
Szabolcs Nagy
14 years ago
3 changed files with 72 additions and 171 deletions
@ -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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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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{ |
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double t, h; |
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int32_t ix, jx; |
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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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union {double f; uint64_t i;} u = {.f = x}; |
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uint32_t w; |
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double t, h, absx; |
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h = 0.5; |
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if (jx < 0) h = -h; |
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/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ |
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if (ix < 0x40360000) { /* |x|<22 */ |
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if (ix < 0x3e300000) /* |x|<2**-28 */ |
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/* raise inexact, return x */ |
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if (huge+x > 1.0) |
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if (u.i >> 63) |
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h = -h; |
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/* |x| */ |
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u.i &= (uint64_t)-1/2; |
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absx = u.f; |
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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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t = expm1(fabs(x)); |
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if (ix < 0x3ff00000) |
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return h*(2.0*t - t*t/(t+1.0)); |
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return h*(t + t/(t+1.0)); |
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return h*(2*t - t*t/(t+1)); |
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} |
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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)); |
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} |
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/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ |
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if (ix < 0x40862E42) |
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return h*exp(fabs(x)); |
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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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/* |x| > log(DBL_MAX) or nan */ |
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/* note: the result is stored to handle overflow */ |
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t = 2*h*__expo2(absx); |
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return t; |
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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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static const float huge = 1.0e37; |
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float sinhf(float x) |
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{ |
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float t, h; |
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int32_t ix, jx; |
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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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union {float f; uint32_t i;} u = {.f = x}; |
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uint32_t w; |
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float t, h, absx; |
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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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/* |x| in [0,9], return sign(x)*0.5*(E+E/(E+1))) */ |
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if (ix < 0x41100000) { /* |x|<9 */ |
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if (ix < 0x39800000) /* |x|<2**-12 */ |
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/* raise inexact, return x */ |
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if (huge+x > 1.0f) |
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/* |x| */ |
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u.i &= 0x7fffffff; |
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absx = u.f; |
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w = u.i; |
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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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t = expm1f(fabsf(x)); |
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if (ix < 0x3f800000) |
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return h*(2.0f*t - t*t/(t+1.0f)); |
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return h*(t + t/(t+1.0f)); |
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return h*(2*t - t*t/(t+1)); |
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} |
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return h*(t + t/(t+1)); |
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} |
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/* |x| in [9, logf(maxfloat)] return 0.5*exp(|x|) */ |
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if (ix < 0x42b17217) |
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return h*expf(fabsf(x)); |
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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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/* |x| > logf(FLT_MAX) or nan */ |
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t = 2*h*__expo2f(absx); |
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return t; |
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} |
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