StdLib/LibC/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 #include  <LibConfig.h>
  13 #include  <sys/EfiCdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz Exp $");
  16 #endif
  17
  18 /* Tanh(x)
  19  * Return the Hyperbolic Tangent of x
  20  *
  21  * Method :
  22  *               x    -x
  23  *              e  - e
  24  *  0. tanh(x) is defined to be -----------
  25  *               x    -x
  26  *              e  + e
  27  *  1. reduce x to non-negative by tanh(-x) = -tanh(x).
  28  *  2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
  29  *                  -t
  30  *      2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
  31  *                 t + 2
  32  *                 2
  33  *      1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
  34  *               t + 2
  35  *      22.0   <  x <= INF    : tanh(x) := 1.
  36  *
  37  * Special cases:
  38  *  tanh(NaN) is NaN;
  39  *  only tanh(0)=0 is exact for finite argument.
  40  */
  41
  42 #include "math.h"
  43 #include "math_private.h"
  44
  45 static const double one=1.0, two=2.0, tiny = 1.0e-300;
  46
  47 double
  48 tanh(double x)
  49 {
  50   double t,z;
  51   int32_t jx,ix;
  52
  53     /* High word of |x|. */
  54   GET_HIGH_WORD(jx,x);
  55   ix = jx&0x7fffffff;
  56
  57     /* x is INF or NaN */
  58   if(ix>=0x7ff00000) {
  59       if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
  60       else       return one/x-one;    /* tanh(NaN) = NaN */
  61   }
  62
  63     /* |x| < 22 */
  64   if (ix < 0x40360000) {    /* |x|<22 */
  65       if (ix<0x3c800000)    /* |x|<2**-55 */
  66     return x*(one+x);     /* tanh(small) = small */
  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;   /* raised inexact flag */
  77   }
  78   return (jx>=0)? z: -z;
  79 }