compiler/stdc/math/ld128/e_sinhl.c

   1 /* @(#)e_sinh.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 /*
  14  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
  15  *
  16  * Permission to use, copy, modify, and distribute this software for any
  17  * purpose with or without fee is hereby granted, provided that the above
  18  * copyright notice and this permission notice appear in all copies.
  19  *
  20  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  21  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  22  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  23  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  24  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  25  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  26  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  27  */
  28
  29 /* sinhl(x)
  30  * Method :
  31  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
  32  *      1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
  33  *      2.
  34  *                                                   E + E/(E+1)
  35  *          0        <= x <= 25     :  sinhl(x) := --------------, E=expm1l(x)
  36  *                                                       2
  37  *
  38  *          25       <= x <= lnovft :  sinhl(x) := expl(x)/2
  39  *          lnovft   <= x <= ln2ovft:  sinhl(x) := expl(x/2)/2 * expl(x/2)
  40  *          ln2ovft  <  x           :  sinhl(x) := x*shuge (overflow)
  41  *
  42  * Special cases:
  43  *      sinhl(x) is |x| if x is +INF, -INF, or NaN.
  44  *      only sinhl(0)=0 is exact for finite x.
  45  */
  46
  47 #include <openlibm_math.h>
  48
  49 #include "math_private.h"
  50
  51 static const long double one = 1.0, shuge = 1.0e4931L,
  52 ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
  53
  54 long double
  55 sinhl(long double x)
  56 {
  57   long double t, w, h;
  58   uint32_t jx, ix;
  59   ieee_quad_shape_type u;
  60
  61   /* Words of |x|. */
  62   u.value = x;
  63   jx = u.parts32.mswhi;
  64   ix = jx & 0x7fffffff;
  65
  66   /* x is INF or NaN */
  67   if (ix >= 0x7fff0000)
  68     return x + x;
  69
  70   h = 0.5;
  71   if (jx & 0x80000000)
  72     h = -h;
  73
  74   /* Absolute value of x.  */
  75   u.parts32.mswhi = ix;
  76
  77   /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
  78   if (ix <= 0x40044000)
  79     {
  80       if (ix < 0x3fc60000) /* |x| < 2^-57 */
  81         if (shuge + x > one)
  82           return x;             /* sinh(tiny) = tiny with inexact */
  83       t = expm1l (u.value);
  84       if (ix < 0x3fff0000)
  85         return h * (2.0 * t - t * t / (t + one));
  86       return h * (t + t / (t + one));
  87     }
  88
  89   /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
  90   if (ix <= 0x400c62e3) /* 11356.375 */
  91     return h * expl (u.value);
  92
  93   /* |x| in [log(maxdouble), overflowthreshold]
  94      Overflow threshold is log(2 * maxdouble).  */
  95   if (u.value <= ovf_thresh)
  96     {
  97       w = expl (0.5 * u.value);
  98       t = h * w;
  99       return t * w;
 100     }
 101
 102   /* |x| > overflowthreshold, sinhl(x) overflow */
 103   return x * shuge;
 104 }