sysdeps/ieee754/dbl-64/s_tanh.c

   1 /* @(#)s_tanh.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 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
  15 #endif
  16
  17 /* Tanh(x)
  18  * Return the Hyperbolic Tangent of x
  19  *
  20  * Method :
  21  *                                     x    -x
  22  *                                    e  - e
  23  *      0. tanh(x) is defined to be -----------
  24  *                                     x    -x
  25  *                                    e  + e
  26  *      1. reduce x to non-negative by tanh(-x) = -tanh(x).
  27  *      2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
  28  *                                              -t
  29  *          2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
  30  *                                             t + 2
  31  *                                                   2
  32  *          1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
  33  *                                                 t + 2
  34  *          22.0   <  x <= INF    : tanh(x) := 1.
  35  *
  36  * Special cases:
  37  *      tanh(NaN) is NaN;
  38  *      only tanh(0)=0 is exact for finite argument.
  39  */
  40
  41 #include <math.h>
  42 #include <math_private.h>
  43
  44 static const double one=1.0, two=2.0, tiny = 1.0e-300;
  45
  46 double __tanh(double x)
  47 {
  48         double t,z;
  49         int32_t jx,ix,lx;
  50
  51     /* High word of |x|. */
  52         EXTRACT_WORDS(jx,lx,x);
  53         ix = jx&0x7fffffff;
  54
  55     /* x is INF or NaN */
  56         if(ix>=0x7ff00000) {
  57             if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
  58             else       return one/x-one;    /* tanh(NaN) = NaN */
  59         }
  60
  61     /* |x| < 22 */
  62         if (ix < 0x40360000) {          /* |x|<22 */
  63             if ((ix | lx) == 0)
  64                 return x;               /* x == +-0 */
  65             if (ix<0x3c800000)          /* |x|<2**-55 */
  66                 return x*(one+x);       /* tanh(small) = small */
  67             if (ix>=0x3ff00000) {       /* |x|>=1  */
  68                 t = __expm1(two*fabs(x));
  69                 z = one - two/(t+two);
  70             } else {
  71                 t = __expm1(-two*fabs(x));
  72                 z= -t/(t+two);
  73             }
  74     /* |x| > 22, return +-1 */
  75         } else {
  76             z = one - tiny;             /* raised inexact flag */
  77         }
  78         return (jx>=0)? z: -z;
  79 }
  80 weak_alias (__tanh, tanh)
  81 #ifdef NO_LONG_DOUBLE
  82 strong_alias (__tanh, __tanhl)
  83 weak_alias (__tanh, tanhl)
  84 #endif