sysdeps/libm-ieee754/e_sinhl.c

   1 /* e_asinhl.c -- long double version of e_asinh.c.
   2  * Conversion to long double by Ulrich Drepper,
   3  * Cygnus Support, drepper@cygnus.com.
   4  */
   5
   6 /*
   7  * ====================================================
   8  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   9  *
  10  * Developed at SunPro, a Sun Microsystems, Inc. business.
  11  * Permission to use, copy, modify, and distribute this
  12  * software is freely granted, provided that this notice
  13  * is preserved.
  14  * ====================================================
  15  */
  16
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 static char rcsid[] = "$NetBSD: $";
  19 #endif
  20
  21 /* __ieee754_sinhl(x)
  22  * Method :
  23  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
  24  *      1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
  25  *      2.
  26  *                                                   E + E/(E+1)
  27  *          0        <= x <= 25     :  sinhl(x) := --------------, E=expm1l(x)
  28  *                                                       2
  29  *
  30  *          25       <= x <= lnovft :  sinhl(x) := expl(x)/2
  31  *          lnovft   <= x <= ln2ovft:  sinhl(x) := expl(x/2)/2 * expl(x/2)
  32  *          ln2ovft  <  x           :  sinhl(x) := x*shuge (overflow)
  33  *
  34  * Special cases:
  35  *      sinhl(x) is |x| if x is +INF, -INF, or NaN.
  36  *      only sinhl(0)=0 is exact for finite x.
  37  */
  38
  39 #include "math.h"
  40 #include "math_private.h"
  41
  42 #ifdef __STDC__
  43 static const long double one = 1.0, shuge = 1.0e4931L;
  44 #else
  45 static long double one = 1.0, shuge = 1.0e4931L;
  46 #endif
  47
  48 #ifdef __STDC__
  49         long double __ieee754_sinhl(long double x)
  50 #else
  51         long double __ieee754_sinhl(x)
  52         long double x;
  53 #endif
  54 {
  55         long double t,w,h;
  56         u_int32_t jx,ix,i0,i1;
  57
  58     /* Words of |x|. */
  59         GET_LDOUBLE_WORDS(jx,i0,i1,x);
  60         ix = jx&0x7fff;
  61
  62     /* x is INF or NaN */
  63         if(ix==0x7fff) return x+x;
  64
  65         h = 0.5;
  66         if (jx<0) h = -h;
  67     /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
  68         if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */
  69             if (ix<0x3fe3)              /* |x|<2**-28 */
  70                 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
  71             t = __expm1l(fabsl(x));
  72             if(ix<0x3fff) return h*(2.0*t-t*t/(t+one));
  73             return h*(t+t/(t+one));
  74         }
  75
  76     /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
  77         if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
  78                 return h*__ieee754_expl(fabsl(x));
  79
  80     /* |x| in [log(maxdouble), overflowthreshold] */
  81         if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0
  82                                            || (i0 == 0xb174ddc0
  83                                                && i1 <= 0x31aec0ea)))) {
  84             w = __ieee754_expl(0.5*fabsl(x));
  85             t = h*w;
  86             return t*w;
  87         }
  88
  89     /* |x| > overflowthreshold, sinhl(x) overflow */
  90         return x*shuge;
  91 }