Line data    Source code

       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           0 : tanh(double x)
      49             : {
      50             :         double t,z;
      51             :         int32_t jx,ix;
      52             : 
      53           0 :         GET_HIGH_WORD(jx,x);
      54           0 :         ix = jx&0x7fffffff;
      55             : 
      56             :     /* x is INF or NaN */
      57           0 :         if(ix>=0x7ff00000) {
      58           0 :             if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
      59           0 :             else       return one/x-one;    /* tanh(NaN) = NaN */
      60             :         }
      61             : 
      62             :     /* |x| < 22 */
      63           0 :         if (ix < 0x40360000) {               /* |x|<22 */
      64           0 :             if (ix<0x3e300000) {     /* |x|<2**-28 */
      65           0 :                 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
      66             :             }
      67           0 :             if (ix>=0x3ff00000) {    /* |x|>=1  */
      68           0 :                 t = expm1(two*fabs(x));
      69           0 :                 z = one - two/(t+two);
      70             :             } else {
      71           0 :                 t = expm1(-two*fabs(x));
      72           0 :                 z= -t/(t+two);
      73             :             }
      74             :     /* |x| >= 22, return +-1 */
      75             :         } else {
      76           0 :             z = one - tiny;             /* raise inexact flag */
      77             :         }
      78           0 :         return (jx>=0)? z: -z;
      79             : }