sysdeps/ieee754/ldbl-96/s_tanhl.c

   1 /* s_tanhl.c -- long double version of s_tanh.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 /* tanhl(x)
  22  * Return the Hyperbolic Tangent of x
  23  *
  24  * Method :
  25  *                                      x    -x
  26  *                                     e  - e
  27  *      0. tanhl(x) is defined to be -----------
  28  *                                      x    -x
  29  *                                     e  + e
  30  *      1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
  31  *      2.  0      <= x <= 2**-55 : tanhl(x) := x*(one+x)
  32  *                                               -t
  33  *          2**-55 <  x <=  1     : tanhl(x) := -----; t = expm1l(-2x)
  34  *                                              t + 2
  35  *                                                    2
  36  *          1      <= x <=  23.0  : tanhl(x) := 1-  ----- ; t=expm1l(2x)
  37  *                                                  t + 2
  38  *          23.0   <  x <= INF    : tanhl(x) := 1.
  39  *
  40  * Special cases:
  41  *      tanhl(NaN) is NaN;
  42  *      only tanhl(0)=0 is exact for finite argument.
  43  */
  44
  45 #include <math.h>
  46 #include <math_private.h>
  47
  48 static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
  49
  50 long double __tanhl(long double x)
  51 {
  52         long double t,z;
  53         int32_t se;
  54         u_int32_t j0,j1,ix;
  55
  56     /* High word of |x|. */
  57         GET_LDOUBLE_WORDS(se,j0,j1,x);
  58         ix = se&0x7fff;
  59
  60     /* x is INF or NaN */
  61         if(ix==0x7fff) {
  62             /* for NaN it's not important which branch: tanhl(NaN) = NaN */
  63             if (se&0x8000) return one/x-one;    /* tanhl(-inf)= -1; */
  64             else           return one/x+one;    /* tanhl(+inf)=+1 */
  65         }
  66
  67     /* |x| < 23 */
  68         if (ix < 0x4003 || (ix == 0x4003 && j0 < 0xb8000000u)) {/* |x|<23 */
  69             if ((ix|j0|j1) == 0)
  70                 return x;               /* x == +- 0 */
  71             if (ix<0x3fc8)              /* |x|<2**-55 */
  72                 return x*(one+tiny);    /* tanh(small) = small */
  73             if (ix>=0x3fff) {   /* |x|>=1  */
  74                 t = __expm1l(two*fabsl(x));
  75                 z = one - two/(t+two);
  76             } else {
  77                 t = __expm1l(-two*fabsl(x));
  78                 z= -t/(t+two);
  79             }
  80     /* |x| > 23, return +-1 */
  81         } else {
  82             z = one - tiny;             /* raised inexact flag */
  83         }
  84         return (se&0x8000)? -z: z;
  85 }
  86 weak_alias (__tanhl, tanhl)