lib/libm/src/b_exp.c

   1 /*      $NetBSD: b_exp.c,v 1.1 2012/05/05 17:54:14 christos Exp $       */
   2
   3 /*
   4  * Copyright (c) 1985, 1993
   5  *      The Regents of the University of California.  All rights reserved.
   6  *
   7  * Redistribution and use in source and binary forms, with or without
   8  * modification, are permitted provided that the following conditions
   9  * are met:
  10  * 1. Redistributions of source code must retain the above copyright
  11  *    notice, this list of conditions and the following disclaimer.
  12  * 2. Redistributions in binary form must reproduce the above copyright
  13  *    notice, this list of conditions and the following disclaimer in the
  14  *    documentation and/or other materials provided with the distribution.
  15  * 3. All advertising materials mentioning features or use of this software
  16  *    must display the following acknowledgement:
  17  *      This product includes software developed by the University of
  18  *      California, Berkeley and its contributors.
  19  * 4. Neither the name of the University nor the names of its contributors
  20  *    may be used to endorse or promote products derived from this software
  21  *    without specific prior written permission.
  22  *
  23  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  24  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  25  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  26  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  27  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  28  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  29  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  30  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  31  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  32  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  33  * SUCH DAMAGE.
  34  */
  35
  36 /* @(#)exp.c    8.1 (Berkeley) 6/4/93 */
  37 #include <sys/cdefs.h>
  38 #if 0
  39 __FBSDID("$FreeBSD: release/9.0.0/lib/msun/bsdsrc/b_exp.c 176449 2008-02-22 02:26:51Z das $");
  40 #else
  41 __RCSID("$NetBSD: b_exp.c,v 1.1 2012/05/05 17:54:14 christos Exp $");
  42 #endif
  43
  44
  45 /* EXP(X)
  46  * RETURN THE EXPONENTIAL OF X
  47  * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
  48  * CODED IN C BY K.C. NG, 1/19/85;
  49  * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
  50  *
  51  * Required system supported functions:
  52  *      scalb(x,n)
  53  *      copysign(x,y)
  54  *      finite(x)
  55  *
  56  * Method:
  57  *      1. Argument Reduction: given the input x, find r and integer k such
  58  *         that
  59  *                         x = k*ln2 + r,  |r| <= 0.5*ln2 .
  60  *         r will be represented as r := z+c for better accuracy.
  61  *
  62  *      2. Compute exp(r) by
  63  *
  64  *              exp(r) = 1 + r + r*R1/(2-R1),
  65  *         where
  66  *              R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
  67  *
  68  *      3. exp(x) = 2^k * exp(r) .
  69  *
  70  * Special cases:
  71  *      exp(INF) is INF, exp(NaN) is NaN;
  72  *      exp(-INF)=  0;
  73  *      for finite argument, only exp(0)=1 is exact.
  74  *
  75  * Accuracy:
  76  *      exp(x) returns the exponential of x nearly rounded. In a test run
  77  *      with 1,156,000 random arguments on a VAX, the maximum observed
  78  *      error was 0.869 ulps (units in the last place).
  79  */
  80
  81 #include "math.h"
  82 #include "math_private.h"
  83
  84 static const double p1 = 0x1.555555555553ep-3;
  85 static const double p2 = -0x1.6c16c16bebd93p-9;
  86 static const double p3 = 0x1.1566aaf25de2cp-14;
  87 static const double p4 = -0x1.bbd41c5d26bf1p-20;
  88 static const double p5 = 0x1.6376972bea4d0p-25;
  89 static const double ln2hi = 0x1.62e42fee00000p-1;
  90 static const double ln2lo = 0x1.a39ef35793c76p-33;
  91 static const double lnhuge = 0x1.6602b15b7ecf2p9;
  92 static const double lntiny = -0x1.77af8ebeae354p9;
  93 static const double invln2 = 0x1.71547652b82fep0;
  94
  95 /* returns exp(r = x + c) for |c| < |x| with no overlap.  */
  96
  97 double
  98 __exp__D(double x, double c)
  99 {
 100         double  z,hi,lo;
 101         int k;
 102
 103         if (x != x)     /* x is NaN */
 104                 return(x);
 105         if ( x <= lnhuge ) {
 106                 if ( x >= lntiny ) {
 107
 108                     /* argument reduction : x --> x - k*ln2 */
 109                         z = invln2*x;
 110                         k = z + copysign(.5, x);
 111
 112                     /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
 113
 114                         hi=(x-k*ln2hi);                 /* Exact. */
 115                         x= hi - (lo = k*ln2lo-c);
 116                     /* return 2^k*[1+x+x*c/(2+c)]  */
 117                         z=x*x;
 118                         c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
 119                         c = (x*c)/(2.0-c);
 120
 121                         return  scalb(1.+(hi-(lo - c)), k);
 122                 }
 123                 /* end of x > lntiny */
 124
 125                 else
 126                      /* exp(-big#) underflows to zero */
 127                      if(finite(x))  return(scalb(1.0,-5000));
 128
 129                      /* exp(-INF) is zero */
 130                      else return(0.0);
 131         }
 132         /* end of x < lnhuge */
 133
 134         else
 135         /* exp(INF) is INF, exp(+big#) overflows to INF */
 136             return( finite(x) ?  scalb(1.0,5000)  : x);
 137 }