sysdeps/ieee754/ldbl-128ibm/e_sinhl.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12
  13 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $";
  15 #endif
  16
  17 /* __ieee754_sinh(x)
  18  * Method :
  19  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
  20  *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
  21  *      2.
  22  *                                                  E + E/(E+1)
  23  *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
  24  *                                                      2
  25  *
  26  *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
  27  *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
  28  *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
  29  *
  30  * Special cases:
  31  *      sinh(x) is |x| if x is +INF, -INF, or NaN.
  32  *      only sinh(0)=0 is exact for finite x.
  33  */
  34
  35 #include "math.h"
  36 #include "math_private.h"
  37
  38 #ifdef __STDC__
  39 static const long double one = 1.0, shuge = 1.0e307;
  40 #else
  41 static long double one = 1.0, shuge = 1.0e307;
  42 #endif
  43
  44 #ifdef __STDC__
  45         long double __ieee754_sinhl(long double x)
  46 #else
  47         long double __ieee754_sinhl(x)
  48         long double x;
  49 #endif
  50 {
  51         long double t,w,h;
  52         int64_t ix,jx;
  53
  54     /* High word of |x|. */
  55         GET_LDOUBLE_MSW64(jx,x);
  56         ix = jx&0x7fffffffffffffffLL;
  57
  58     /* x is INF or NaN */
  59         if(ix>=0x7ff0000000000000LL) return x+x;
  60
  61         h = 0.5;
  62         if (jx<0) h = -h;
  63     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
  64         if (ix < 0x4036000000000000LL) {        /* |x|<22 */
  65             if (ix<0x3e20000000000000LL)        /* |x|<2**-29 */
  66                 if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */
  67             t = __expm1l(fabsl(x));
  68             if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one));
  69             return h*(t+t/(t+one));
  70         }
  71
  72     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
  73         if (ix < 0x40862e42fefa39efLL)  return h*__ieee754_expl(fabsl(x));
  74
  75     /* |x| in [log(maxdouble), overflowthresold] */
  76         if (ix <= 0x408633ce8fb9f87dLL) {
  77             w = __ieee754_expl(0.5*fabsl(x));
  78             t = h*w;
  79             return t*w;
  80         }
  81
  82     /* |x| > overflowthresold, sinh(x) overflow */
  83         return x*shuge;
  84 }