4.3BSD - /usr/src/usr.lib/libm/tanh.c

   1: /*
   2:  * Copyright (c) 1985 Regents of the University of California.
   3:  *
   4:  * Use and reproduction of this software are granted  in  accordance  with
   5:  * the terms and conditions specified in  the  Berkeley  Software  License
   6:  * Agreement (in particular, this entails acknowledgement of the programs'
   7:  * source, and inclusion of this notice) with the additional understanding
   8:  * that  all  recipients  should regard themselves as participants  in  an
   9:  * ongoing  research  project and hence should  feel  obligated  to report
  10:  * their  experiences (good or bad) with these elementary function  codes,
  11:  * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
  12:  */
  13: 
  14: #ifndef lint
  15: static char sccsid[] = "@(#)tanh.c	4.3 (Berkeley) 8/21/85";
  16: #endif not lint
  17: 
  18: /* TANH(X)
  19:  * RETURN THE HYPERBOLIC TANGENT OF X
  20:  * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
  21:  * CODED IN C BY K.C. NG, 1/8/85;
  22:  * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
  23:  *
  24:  * Required system supported functions :
  25:  *	copysign(x,y)
  26:  *	finite(x)
  27:  *
  28:  * Required kernel function:
  29:  *	expm1(x)	...exp(x)-1
  30:  *
  31:  * Method :
  32:  *	1. reduce x to non-negative by tanh(-x) = - tanh(x).
  33:  *	2.
  34:  *	    0      <  x <=  1.e-10 :  tanh(x) := x
  35:  *					          -expm1(-2x)
  36:  *	    1.e-10 <  x <=  1      :  tanh(x) := --------------
  37:  *					         expm1(-2x) + 2
  38:  *							  2
  39:  *	    1      <= x <=  22.0   :  tanh(x) := 1 -  ---------------
  40:  *						      expm1(2x) + 2
  41:  *	    22.0   <  x <= INF     :  tanh(x) := 1.
  42:  *
  43:  *	Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
  44:  *
  45:  * Special cases:
  46:  *	tanh(NaN) is NaN;
  47:  *	only tanh(0)=0 is exact for finite argument.
  48:  *
  49:  * Accuracy:
  50:  *	tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
  51:  *	In a test run with 1,024,000 random arguments on a VAX, the maximum
  52:  *	observed error was 2.22 ulps (units in the last place).
  53:  */
  54: 
  55: double tanh(x)
  56: double x;
  57: {
  58:     static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
  59:     double expm1(), t, copysign(), sign;
  60:     int finite();
  61: 
  62: #ifndef VAX
  63:     if(x!=x) return(x); /* x is NaN */
  64: #endif
  65: 
  66:     sign=copysign(one,x);
  67:     x=copysign(x,one);
  68:     if(x < 22.0)
  69:         if( x > one )
  70:         return(copysign(one-two/(expm1(x+x)+two),sign));
  71:         else if ( x > small )
  72:         {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
  73:         else        /* raise the INEXACT flag for non-zero x */
  74:         {big+x; return(copysign(x,sign));}
  75:     else if(finite(x))
  76:         return (sign+1.0E-37); /* raise the INEXACT flag */
  77:     else
  78:         return(sign);   /* x is +- INF */
  79: }

Defined functions

Defined variables