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/* @(#)e_sinh.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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/* 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 <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, shuge = 1.0e307; |
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double |
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sinh(double x) |
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{ |
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double t,w,h; |
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int32_t ix,jx; |
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u_int32_t lx; |
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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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✗✓ |
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if(ix>=0x7ff00000) return x+x; |
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h = 0.5; |
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✓✓ |
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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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✓✓ |
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if (ix < 0x40360000) { /* |x|<22 */ |
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✓✓ |
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if (ix<0x3e300000) /* |x|<2**-28 */ |
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✓✗ |
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if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ |
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t = expm1(fabs(x)); |
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✓✓ |
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if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); |
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return h*(t+t/(t+one)); |
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} |
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/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ |
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✓✓ |
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if (ix < 0x40862E42) return h*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 || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { |
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w = exp(0.5*fabs(x)); |
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t = h*w; |
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return t*w; |
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} |
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/* |x| > overflowthresold, sinh(x) overflow */ |
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return x*shuge; |
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} |
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DEF_STD(sinh); |
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LDBL_MAYBE_CLONE(sinh); |