94 lines
2.5 KiB
C
94 lines
2.5 KiB
C
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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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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $";
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#endif
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/* __ieee754_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-narrow-eval.h>
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#include <math_private.h>
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#include <math-underflow.h>
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#include <libm-alias-finite.h>
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static const double one = 1.0, shuge = 1.0e307;
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double
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__ieee754_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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uint32_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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if (__glibc_unlikely (ix >= 0x7ff00000))
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return x + x;
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h = 0.5;
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if (jx < 0)
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h = -h;
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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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{
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if (__glibc_unlikely (ix < 0x3e300000)) { /* |x|<2**-28 */
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math_check_force_underflow (x);
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if (shuge + x > one)
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return x;
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/* sinh(tiny) = tiny with inexact */
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}
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t = __expm1 (fabs (x));
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if (ix < 0x3ff00000)
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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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if (ix < 0x40862e42)
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return h * __ieee754_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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if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (uint32_t) 0x8fb9f87d)))
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{
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w = __ieee754_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 math_narrow_eval (x * shuge);
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}
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libm_alias_finite (__ieee754_sinh, __sinh)
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