lib/libm/src/ld80/s_tanhl.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 /* tanhl(x)
  14  * Return the Hyperbolic Tangent of x
  15  *
  16  * Method :
  17  *                                      x    -x
  18  *                                     e  - e
  19  *      0. tanhl(x) is defined to be -----------
  20  *                                      x    -x
  21  *                                     e  + e
  22  *      1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
  23  *      2.  0      <= x <= 2**-55 : tanhl(x) := x*(one+x)
  24  *                                               -t
  25  *          2**-55 <  x <=  1     : tanhl(x) := -----; t = expm1l(-2x)
  26  *                                              t + 2
  27  *                                                    2
  28  *          1      <= x <=  23.0  : tanhl(x) := 1-  ----- ; t=expm1l(2x)
  29  *                                                  t + 2
  30  *          23.0   <  x <= INF    : tanhl(x) := 1.
  31  *
  32  * Special cases:
  33  *      tanhl(NaN) is NaN;
  34  *      only tanhl(0)=0 is exact for finite argument.
  35  */
  36
  37 #include <math.h>
  38
  39 #include "math_private.h"
  40
  41 static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
  42
  43 long double
  44 tanhl(long double x)
  45 {
  46         long double t,z;
  47         int32_t se;
  48         u_int32_t jj0,jj1,ix;
  49
  50     /* High word of |x|. */
  51         GET_LDOUBLE_WORDS(se,jj0,jj1,x);
  52         ix = se&0x7fff;
  53
  54     /* x is INF or NaN */
  55         if(ix==0x7fff) {
  56             /* for NaN it's not important which branch: tanhl(NaN) = NaN */
  57             if (se&0x8000) return one/x-one;    /* tanhl(-inf)= -1; */
  58             else           return one/x+one;    /* tanhl(+inf)=+1 */
  59         }
  60
  61     /* |x| < 23 */
  62         if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {/* |x|<23 */
  63             if ((ix|jj0|jj1) == 0)
  64                 return x;               /* x == +- 0 */
  65             if (ix<0x3fc8)              /* |x|<2**-55 */
  66                 return x*(one+tiny);    /* tanh(small) = small */
  67             if (ix>=0x3fff) {   /* |x|>=1  */
  68                 t = expm1l(two*fabsl(x));
  69                 z = one - two/(t+two);
  70             } else {
  71                 t = expm1l(-two*fabsl(x));
  72                 z= -t/(t+two);
  73             }
  74     /* |x| > 23, return +-1 */
  75         } else {
  76             z = one - tiny;             /* raised inexact flag */
  77         }
  78         return (se&0x8000)? -z: z;
  79 }