gonzui: t2ex/bsd_source/lib/libc/src_bsd/math/b_exp_

    1: /*      $OpenBSD: b_exp__D.c,v 1.5 2009/10/27 23:59:29 deraadt Exp $ */
    2: /*
    3:  * Copyright (c) 1985, 1993
    4:  *      The Regents of the University of California.  All rights reserved.
    5:  *
    6:  * Redistribution and use in source and binary forms, with or without
    7:  * modification, are permitted provided that the following conditions
    8:  * are met:
    9:  * 1. Redistributions of source code must retain the above copyright
   10:  *    notice, this list of conditions and the following disclaimer.
   11:  * 2. Redistributions in binary form must reproduce the above copyright
   12:  *    notice, this list of conditions and the following disclaimer in the
   13:  *    documentation and/or other materials provided with the distribution.
   14:  * 3. Neither the name of the University nor the names of its contributors
   15:  *    may be used to endorse or promote products derived from this software
   16:  *    without specific prior written permission.
   17:  *
   18:  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
   19:  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   20:  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
   21:  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
   22:  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
   23:  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
   24:  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
   25:  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
   26:  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
   27:  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   28:  * SUCH DAMAGE.
   29:  */
   30: 
   31: /* EXP(X)
   32:  * RETURN THE EXPONENTIAL OF X
   33:  * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
   34:  * CODED IN C BY K.C. NG, 1/19/85;
   35:  * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
   36:  *
   37:  * Required system supported functions:
   38:  *      scalb(x,n)
   39:  *      copysign(x,y)
   40:  *      finite(x)
   41:  *
   42:  * Method:
   43:  *      1. Argument Reduction: given the input x, find r and integer k such
   44:  *         that
   45:  *                         x = k*ln2 + r,  |r| <= 0.5*ln2 .
   46:  *         r will be represented as r := z+c for better accuracy.
   47:  *
   48:  *      2. Compute exp(r) by
   49:  *
   50:  *              exp(r) = 1 + r + r*R1/(2-R1),
   51:  *         where
   52:  *              R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
   53:  *
   54:  *      3. exp(x) = 2^k * exp(r) .
   55:  *
   56:  * Special cases:
   57:  *      exp(INF) is INF, exp(NaN) is NaN;
   58:  *      exp(-INF)=  0;
   59:  *      for finite argument, only exp(0)=1 is exact.
   60:  *
   61:  * Accuracy:
   62:  *      exp(x) returns the exponential of x nearly rounded. In a test run
   63:  *      with 1,156,000 random arguments on a VAX, the maximum observed
   64:  *      error was 0.869 ulps (units in the last place).
   65:  */
   66: 
   67: #include "math.h"
   68: #include "math_private.h"
   69: 
   70: static const double p1 = 0x1.555555555553ep-3;
   71: static const double p2 = -0x1.6c16c16bebd93p-9;
   72: static const double p3 = 0x1.1566aaf25de2cp-14;
   73: static const double p4 = -0x1.bbd41c5d26bf1p-20;
   74: static const double p5 = 0x1.6376972bea4d0p-25;
   75: static const double ln2hi = 0x1.62e42fee00000p-1;
   76: static const double ln2lo = 0x1.a39ef35793c76p-33;
   77: static const double lnhuge = 0x1.6602b15b7ecf2p9;
   78: static const double lntiny = -0x1.77af8ebeae354p9;
   79: static const double invln2 = 0x1.71547652b82fep0;
   80: 
   81: /* returns exp(r = x + c) for |c| < |x| with no overlap.  */
   82: 
   83: double
   84: __exp__D(double x, double c)
   85: {
   86:         double z, hi, lo;
   87:         int k;
   88: 
   89:         if (isnan(x))  /* x is NaN */
   90:                 return(x);
   91:         if ( x <= lnhuge ) {
   92:                 if ( x >= lntiny ) {
   93: 
   94:                     /* argument reduction : x --> x - k*ln2 */
   95:                         z = invln2*x;
   96:                         k = z + copysign(.5, x);
   97: 
   98:                     /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
   99: 
  100:                         hi=(x-k*ln2hi);                      /* Exact. */
  101:                         x= hi - (lo = k*ln2lo-c);
  102:                     /* return 2^k*[1+x+x*c/(2+c)]  */
  103:                         z=x*x;
  104:                         c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
  105:                         c = (x*c)/(2.0-c);
  106: 
  107:                         return  scalb(1.+(hi-(lo - c)), k);
  108:                 }
  109:                 /* end of x > lntiny */
  110: 
  111:                 else
  112:                      /* exp(-big#) underflows to zero */
  113:                      if(finite(x))  return(scalb(1.0,-5000));
  114: 
  115:                      /* exp(-INF) is zero */
  116:                      else return(0.0);
  117:         }
  118:         /* end of x < lnhuge */
  119: 
  120:         else
  121:         /* exp(INF) is INF, exp(+big#) overflows to INF */
  122:             return( finite(x) ?  scalb(1.0,5000)  : x);
  123: }