compiler/stdc/math/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 #ifndef lint
  14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_tanh.c,v 1.8 2006/07/05 22:59:33 bde 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**-28 : tanh(x) := x with inexact if x != 0
  28  *                                              -t
  29  *          2**-28 <= x <  1      : tanh(x) := -----; t = expm1(-2x)
  30  *                                             t + 2
  31  *                                                   2
  32  *          1      <= x <  22     : tanh(x) := 1 - -----; t = expm1(2x)
  33  *                                                 t + 2
  34  *          22     <= 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, huge = 1.0e300;
  45
  46 double
  47 tanh(double x)
  48 {
  49         double t,z;
  50         int32_t jx,ix;
  51
  52         GET_HIGH_WORD(jx,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<0x3e300000) {        /* |x|<2**-28 */
  64                 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
  65             }
  66             if (ix>=0x3ff00000) {       /* |x|>=1  */
  67                 t = expm1(two*fabs(x));
  68                 z = one - two/(t+two);
  69             } else {
  70                 t = expm1(-two*fabs(x));
  71                 z= -t/(t+two);
  72             }
  73     /* |x| >= 22, return +-1 */
  74         } else {
  75             z = one - tiny;             /* raise inexact flag */
  76         }
  77         return (jx>=0)? z: -z;
  78 }