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/* @(#)e_cosh.c 5.1 93/09/24 */
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/* @(#)e_cosh.c 5.1 93/09/24 */
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/*
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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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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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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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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* is preserved.
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* ====================================================
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* ====================================================
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*/
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*/
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/* __ieee754_cosh(x)
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/* __ieee754_cosh(x)
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* Method :
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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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* 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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* 1. Replace x by |x| (cosh(x) = cosh(-x)).
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* 2.
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* 2.
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* [ exp(x) - 1 ]^2
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* [ exp(x) - 1 ]^2
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* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
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* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
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* 2*exp(x)
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* 2*exp(x)
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*
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*
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* exp(x) + 1/exp(x)
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* exp(x) + 1/exp(x)
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* ln2/2 <= x <= 22 : cosh(x) := -------------------
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* ln2/2 <= x <= 22 : cosh(x) := -------------------
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* 2
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* 2
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* 22 <= x <= lnovft : cosh(x) := exp(x)/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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* 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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* ln2ovft < x : cosh(x) := huge*huge (overflow)
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*
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*
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* Special cases:
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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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* 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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* only cosh(0)=1 is exact for finite x.
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*/
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*/
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#include "fdlibm.h"
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#include "fdlibm.h"
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#ifndef _DOUBLE_IS_32BITS
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#ifndef _DOUBLE_IS_32BITS
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#ifdef __STDC__
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#ifdef __STDC__
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static const double one = 1.0, half=0.5, huge = 1.0e300;
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static const double one = 1.0, half=0.5, huge = 1.0e300;
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#else
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#else
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static double one = 1.0, half=0.5, huge = 1.0e300;
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static double one = 1.0, half=0.5, huge = 1.0e300;
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#endif
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#endif
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#ifdef __STDC__
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#ifdef __STDC__
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double __ieee754_cosh(double x)
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double __ieee754_cosh(double x)
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#else
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#else
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double __ieee754_cosh(x)
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double __ieee754_cosh(x)
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double x;
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double x;
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#endif
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#endif
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{
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{
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double t,w;
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double t,w;
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__int32_t ix;
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__int32_t ix;
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__uint32_t lx;
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__uint32_t lx;
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/* High word of |x|. */
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/* High word of |x|. */
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GET_HIGH_WORD(ix,x);
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GET_HIGH_WORD(ix,x);
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ix &= 0x7fffffff;
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ix &= 0x7fffffff;
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/* x is INF or NaN */
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/* x is INF or NaN */
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if(ix>=0x7ff00000) return x*x;
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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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/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
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if(ix<0x3fd62e43) {
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if(ix<0x3fd62e43) {
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t = expm1(fabs(x));
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t = expm1(fabs(x));
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w = one+t;
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w = one+t;
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if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
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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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return one+(t*t)/(w+w);
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}
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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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/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
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if (ix < 0x40360000) {
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if (ix < 0x40360000) {
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t = __ieee754_exp(fabs(x));
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t = __ieee754_exp(fabs(x));
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return half*t+half/t;
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return half*t+half/t;
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}
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}
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/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
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/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
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if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
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if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
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/* |x| in [log(maxdouble), overflowthresold] */
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/* |x| in [log(maxdouble), overflowthresold] */
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GET_LOW_WORD(lx,x);
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GET_LOW_WORD(lx,x);
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if (ix<0x408633CE ||
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if (ix<0x408633CE ||
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(ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) {
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(ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) {
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w = __ieee754_exp(half*fabs(x));
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w = __ieee754_exp(half*fabs(x));
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t = half*w;
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t = half*w;
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return t*w;
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return t*w;
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}
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}
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/* |x| > overflowthresold, cosh(x) overflow */
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/* |x| > overflowthresold, cosh(x) overflow */
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return huge*huge;
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return huge*huge;
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}
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}
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#endif /* defined(_DOUBLE_IS_32BITS) */
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#endif /* defined(_DOUBLE_IS_32BITS) */
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