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/* @(#)e_cosh.c 5.1 93/09/24 */ |
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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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/* cosh(x) |
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* Method : |
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* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 |
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* 1. Replace x by |x| (cosh(x) = cosh(-x)). |
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* 2. |
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* [ exp(x) - 1 ]^2 |
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* 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- |
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* 2*exp(x) |
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* |
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* exp(x) + 1/exp(x) |
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* ln2/2 <= x <= 22 : cosh(x) := ------------------- |
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* 2 |
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* 22 <= x <= lnovft : cosh(x) := exp(x)/2 |
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* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) |
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* ln2ovft < x : cosh(x) := huge*huge (overflow) |
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* |
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* Special cases: |
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* cosh(x) is |x| if x is +INF, -INF, or NaN. |
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* only cosh(0)=1 is exact for finite x. |
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*/ |
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#include <float.h> |
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#include <math.h> |
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#include "math_private.h" |
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static const double one = 1.0, half=0.5, huge = 1.0e300; |
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double |
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cosh(double x) |
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{ |
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double t,w; |
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int32_t ix; |
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u_int32_t lx; |
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/* High word of |x|. */ |
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GET_HIGH_WORD(ix,x); |
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ix &= 0x7fffffff; |
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/* x is INF or NaN */ |
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✗✓ |
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if(ix>=0x7ff00000) return x*x; |
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/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ |
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✓✓ |
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if(ix<0x3fd62e43) { |
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t = expm1(fabs(x)); |
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w = one+t; |
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✓✓ |
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if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ |
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return one+(t*t)/(w+w); |
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} |
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/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ |
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✓✓ |
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if (ix < 0x40360000) { |
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t = exp(fabs(x)); |
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return half*t+half/t; |
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} |
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/* |x| in [22, log(maxdouble)] return half*exp(|x|) */ |
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✓✓ |
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if (ix < 0x40862E42) return half*exp(fabs(x)); |
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/* |x| in [log(maxdouble), overflowthresold] */ |
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GET_LOW_WORD(lx,x); |
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✗✓ |
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if (ix<0x408633CE || |
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((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { |
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w = exp(half*fabs(x)); |
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t = half*w; |
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return t*w; |
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} |
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/* |x| > overflowthresold, cosh(x) overflow */ |
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return huge*huge; |
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} |
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DEF_STD(cosh); |
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LDBL_MAYBE_CLONE(cosh); |