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/* @(#)e_sinh.c 5.1 93/09/24 */
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/* @(#)e_sinh.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_sinh(x)
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/* __ieee754_sinh(x)
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* Method :
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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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* 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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* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
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* 2.
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* 2.
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* E + E/(E+1)
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* E + E/(E+1)
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* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
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* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
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* 2
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* 2
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*
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*
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* 22 <= x <= lnovft : sinh(x) := exp(x)/2
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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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* 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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* ln2ovft < x : sinh(x) := x*shuge (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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* sinh(x) is |x| if x is +INF, -INF, or NaN.
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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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* only sinh(0)=0 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, shuge = 1.0e307;
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static const double one = 1.0, shuge = 1.0e307;
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#else
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#else
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static double one = 1.0, shuge = 1.0e307;
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static double one = 1.0, shuge = 1.0e307;
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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_sinh(double x)
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double __ieee754_sinh(double x)
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#else
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#else
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double __ieee754_sinh(x)
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double __ieee754_sinh(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,h;
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double t,w,h;
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__int32_t ix,jx;
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__int32_t ix,jx;
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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(jx,x);
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GET_HIGH_WORD(jx,x);
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ix = jx&0x7fffffff;
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ix = jx&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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h = 0.5;
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h = 0.5;
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if (jx<0) h = -h;
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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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/* |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 < 0x40360000) { /* |x|<22 */
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if (ix<0x3e300000) /* |x|<2**-28 */
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if (ix<0x3e300000) /* |x|<2**-28 */
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if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
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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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t = expm1(fabs(x));
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if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
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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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return h*(t+t/(t+one));
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}
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}
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/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
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/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
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if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
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if (ix < 0x40862E42) return h*__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 || (ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) {
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if (ix<0x408633CE || (ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) {
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w = __ieee754_exp(0.5*fabs(x));
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w = __ieee754_exp(0.5*fabs(x));
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t = h*w;
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t = h*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, sinh(x) overflow */
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/* |x| > overflowthresold, sinh(x) overflow */
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return x*shuge;
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return x*shuge;
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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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