lib/libm/tanh.c

   1 /*                                                      tanh.c
   2  *
   3  *      Hyperbolic tangent
   4  *
   5  *
   6  *
   7  * SYNOPSIS:
   8  *
   9  * double x, y, tanh();
  10  *
  11  * y = tanh( x );
  12  *
  13  *
  14  *
  15  * DESCRIPTION:
  16  *
  17  * Returns hyperbolic tangent of argument in the range MINLOG to
  18  * MAXLOG.
  19  *
  20  * A rational function is used for |x| < 0.625.  The form
  21  * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
  22  * Otherwise,
  23  *    tanh(x) = sinh(x)/cosh(x) = 1  -  2/(exp(2x) + 1).
  24  *
  25  *
  26  *
  27  * ACCURACY:
  28  *
  29  *                      Relative error:
  30  * arithmetic   domain     # trials      peak         rms
  31  *    DEC       -2,2        50000       3.3e-17     6.4e-18
  32  *    IEEE      -2,2        30000       2.5e-16     5.8e-17
  33  *
  34  */
  35 \f
  36 /*
  37 Cephes Math Library Release 2.8:  June, 2000
  38 Copyright 1984, 1995, 2000 by Stephen L. Moshier
  39 */
  40
  41 #include "mconf.h"
  42
  43 #ifdef UNK
  44 static double P[] = {
  45 -9.64399179425052238628E-1,
  46 -9.92877231001918586564E1,
  47 -1.61468768441708447952E3
  48 };
  49 static double Q[] = {
  50 /* 1.00000000000000000000E0,*/
  51  1.12811678491632931402E2,
  52  2.23548839060100448583E3,
  53  4.84406305325125486048E3
  54 };
  55 #endif
  56 #ifdef DEC
  57 static unsigned short P[] = {
  58 0140166,0161335,0053753,0075126,
  59 0141706,0111520,0070463,0040552,
  60 0142711,0153001,0101300,0025430
  61 };
  62 static unsigned short Q[] = {
  63 /*0040200,0000000,0000000,0000000,*/
  64 0041741,0117624,0051300,0156060,
  65 0043013,0133720,0071251,0127717,
  66 0043227,0060201,0021020,0020136
  67 };
  68 #endif
  69
  70 #ifdef IBMPC
  71 static unsigned short P[] = {
  72 0x6f4b,0xaafd,0xdc5b,0xbfee,
  73 0x682d,0x0e26,0xd26a,0xc058,
  74 0x0563,0x3058,0x3ac0,0xc099
  75 };
  76 static unsigned short Q[] = {
  77 /*0x0000,0x0000,0x0000,0x3ff0,*/
  78 0x1b86,0x8a58,0x33f2,0x405c,
  79 0x35fa,0x0e55,0x76fa,0x40a1,
  80 0x040c,0x2442,0xec10,0x40b2
  81 };
  82 #endif
  83
  84 #ifdef MIEEE
  85 static unsigned short P[] = {
  86 0xbfee,0xdc5b,0xaafd,0x6f4b,
  87 0xc058,0xd26a,0x0e26,0x682d,
  88 0xc099,0x3ac0,0x3058,0x0563
  89 };
  90 static unsigned short Q[] = {
  91 0x405c,0x33f2,0x8a58,0x1b86,
  92 0x40a1,0x76fa,0x0e55,0x35fa,
  93 0x40b2,0xec10,0x2442,0x040c
  94 };
  95 #endif
  96
  97 #ifdef ANSIPROT
  98 extern double fabs ( double );
  99 extern double exp ( double );
 100 extern double polevl ( double, void *, int );
 101 extern double p1evl ( double, void *, int );
 102 #else
 103 double fabs(), exp(), polevl(), p1evl();
 104 #endif
 105 extern double MAXLOG;
 106
 107 double tanh(x)
 108 double x;
 109 {
 110 double s, z;
 111
 112 #ifdef MINUSZERO
 113 if( x == 0.0 )
 114         return(x);
 115 #endif
 116 z = fabs(x);
 117 if( z > 0.5 * MAXLOG )
 118         {
 119         if( x > 0 )
 120                 return( 1.0 );
 121         else
 122                 return( -1.0 );
 123         }
 124 if( z >= 0.625 )
 125         {
 126         s = exp(2.0*z);
 127         z =  1.0  - 2.0/(s + 1.0);
 128         if( x < 0 )
 129                 z = -z;
 130         }
 131 else
 132         {
 133         if( x == 0.0 )
 134           return(x);
 135         s = x * x;
 136         z = polevl( s, P, 2 )/p1evl(s, Q, 3);
 137         z = x * s * z;
 138         z = x + z;
 139         }
 140 return( z );
 141 }