0,0 → 1,83 |
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/* @(#)e_sinh.c 5.1 93/09/24 */ |
/* |
* ==================================================== |
* 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. |
* ==================================================== |
*/ |
|
/* __ieee754_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. |
*/ |
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#include "fdlibm.h" |
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#ifdef __STDC__ |
static const double one = 1.0, shuge = 1.0e307; |
#else |
static double one = 1.0, shuge = 1.0e307; |
#endif |
|
#ifdef __STDC__ |
double sinh(double x) |
#else |
double sinh(x) |
double x; |
#endif |
{ |
double t,w,h; |
__int32_t ix,jx; |
__uint32_t lx; |
|
/* High word of |x|. */ |
GET_HIGH_WORD(jx,x); |
ix = jx&0x7fffffff; |
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/* x is INF or NaN */ |
if(ix>=0x7ff00000) return x+x; |
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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 */ |
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ |
t = expm1(fabs(x)); |
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); |
return h*(t+t/(t+one)); |
} |
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/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ |
if (ix < 0x40862E42) return h * exp(fabs(x)); |
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/* |x| in [log(maxdouble), overflowthresold] */ |
GET_LOW_WORD(lx,x); |
if (ix<0x408633CE || (ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) { |
w = exp(0.5*fabs(x)); |
t = h*w; |
return t*w; |
} |
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/* |x| > overflowthresold, sinh(x) overflow */ |
return x*shuge; |
} |
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