modules/fdlibm/src/s_tanh.cpp

   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 //#include <sys/cdefs.h>
  14 //__FBSDID("$FreeBSD$");
  15
  16 /* Tanh(x)
  17  * Return the Hyperbolic Tangent of x
  18  *
  19  * Method :
  20  *                                     x    -x
  21  *                                    e  - e
  22  *      0. tanh(x) is defined to be -----------
  23  *                                     x    -x
  24  *                                    e  + e
  25  *      1. reduce x to non-negative by tanh(-x) = -tanh(x).
  26  *      2.  0      <= x <  2**-28 : tanh(x) := x with inexact if x != 0
  27  *                                              -t
  28  *          2**-28 <= x <  1      : tanh(x) := -----; t = expm1(-2x)
  29  *                                             t + 2
  30  *                                                   2
  31  *          1      <= x <  22     : tanh(x) := 1 - -----; t = expm1(2x)
  32  *                                                 t + 2
  33  *          22     <= x <= INF    : tanh(x) := 1.
  34  *
  35  * Special cases:
  36  *      tanh(NaN) is NaN;
  37  *      only tanh(0)=0 is exact for finite argument.
  38  */
  39
  40 #include <float.h>
  41
  42 #include "math_private.h"
  43
  44 static const volatile double tiny = 1.0e-300;
  45 static const double one = 1.0, two = 2.0, huge = 1.0e300;
  46
  47 double
  48 tanh(double x)
  49 {
  50         double t,z;
  51         int32_t jx,ix;
  52
  53         GET_HIGH_WORD(jx,x);
  54         ix = jx&0x7fffffff;
  55
  56     /* x is INF or NaN */
  57         if(ix>=0x7ff00000) {
  58             if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
  59             else       return one/x-one;    /* tanh(NaN) = NaN */
  60         }
  61
  62     /* |x| < 22 */
  63         if (ix < 0x40360000) {          /* |x|<22 */
  64             if (ix<0x3e300000) {        /* |x|<2**-28 */
  65                 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
  66             }
  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;             /* raise inexact flag */
  77         }
  78         return (jx>=0)? z: -z;
  79 }