newlib/libm/mathfp/s_tanh.c

   1
   2 /* @(#)z_tanh.c 1.0 98/08/13 */
   3 /*****************************************************************
   4  * The following routines are coded directly from the algorithms
   5  * and coefficients given in "Software Manual for the Elementary
   6  * Functions" by William J. Cody, Jr. and William Waite, Prentice
   7  * Hall, 1980.
   8  *****************************************************************/
   9
  10 /*
  11
  12 FUNCTION
  13         <<tanh>>, <<tanhf>>---hyperbolic tangent
  14
  15 INDEX
  16 tanh
  17 INDEX
  18 tanhf
  19
  20 SYNOPSIS
  21         #include <math.h>
  22         double tanh(double <[x]>);
  23         float tanhf(float <[x]>);
  24
  25 DESCRIPTION
  26
  27 <<tanh>> computes the hyperbolic tangent of
  28 the argument <[x]>.  Angles are specified in radians.
  29
  30 <<tanh(<[x]>)>> is defined as
  31 . sinh(<[x]>)/cosh(<[x]>)
  32
  33 <<tanhf>> is identical, save that it takes and returns <<float>> values.
  34
  35 RETURNS
  36 The hyperbolic tangent of <[x]> is returned.
  37
  38 PORTABILITY
  39 <<tanh>> is ANSI C.  <<tanhf>> is an extension.
  40
  41 */
  42
  43 /******************************************************************
  44  * Hyperbolic Tangent
  45  *
  46  * Input:
  47  *   x - floating point value
  48  *
  49  * Output:
  50  *   hyperbolic tangent of x
  51  *
  52  * Description:
  53  *   This routine calculates hyperbolic tangent.
  54  *
  55  *****************************************************************/
  56
  57 #include <float.h>
  58 #include "fdlibm.h"
  59 #include "zmath.h"
  60
  61 #ifndef _DOUBLE_IS_32BITS
  62
  63 static const double LN3_OVER2 = 0.54930614433405484570;
  64 static const double p[] = { -0.16134119023996228053e+4,
  65                             -0.99225929672236083313e+2,
  66                             -0.96437492777225469787 };
  67 static const double q[] = { 0.48402357071988688686e+4,
  68                             0.22337720718962312926e+4,
  69                             0.11274474380534949335e+3 };
  70
  71 double
  72 tanh (double x)
  73 {
  74   double f, res, g, P, Q, R;
  75
  76   f = fabs (x);
  77
  78   /* Check if the input is too big. */
  79   if (f > BIGX)
  80     res = 1.0;
  81
  82   else if (f > LN3_OVER2)
  83     res = 1.0 - 2.0 / (exp (2 * f) + 1.0);
  84
  85   /* Check if the input is too small. */
  86   else if (f < z_rooteps)
  87     res = f;
  88
  89   /* Calculate the Taylor series. */
  90   else
  91     {
  92       g = f * f;
  93
  94       P = (p[2] * g + p[1]) * g + p[0];
  95       Q = ((g + q[2]) * g + q[1]) * g + q[0];
  96       R = g * (P / Q);
  97
  98       res = f + f * R;
  99     }
 100
 101   if (x < 0.0)
 102     res = -res;
 103
 104   return (res);
 105 }
 106
 107 #endif /* _DOUBLE_IS_32BITS */