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expm1.c

#include "FEATURE/uwin"

#if !_UWIN || _lib_expm1

void _STUB_expm1(){}

#else

/*
 * Copyright (c) 1985, 1993
 *    The Regents of the University of California.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

#ifndef lint
static char sccsid[] = "@(#)expm1.c 8.1 (Berkeley) 6/4/93";
#endif /* not lint */

/* EXPM1(X)
 * RETURN THE EXPONENTIAL OF X MINUS ONE
 * DOUBLE PRECISION (IEEE 53 BITS, VAX D FORMAT 56 BITS)
 * CODED IN C BY K.C. NG, 1/19/85; 
 * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/21/85, 4/16/85.
 *
 * Required system supported functions:
 *    scalb(x,n)  
 *    copysign(x,y)     
 *    finite(x)
 *
 * Kernel function:
 *    exp__E(x,c)
 *
 * Method:
 *    1. Argument Reduction: given the input x, find r and integer k such 
 *       that
 *                       x = k*ln2 + r,  |r| <= 0.5*ln2 .  
 *       r will be represented as r := z+c for better accuracy.
 *
 *    2. Compute EXPM1(r)=exp(r)-1 by 
 *
 *                EXPM1(r=z+c) := z + exp__E(z,c)
 *
 *    3. EXPM1(x) =  2^k * ( EXPM1(r) + 1-2^-k ).
 *
 *    Remarks: 
 *       1. When k=1 and z < -0.25, we use the following formula for
 *          better accuracy:
 *                EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) )
 *       2. To avoid rounding error in 1-2^-k where k is large, we use
 *                EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 }
 *          when k>56. 
 *
 * Special cases:
 *    EXPM1(INF) is INF, EXPM1(NaN) is NaN;
 *    EXPM1(-INF)= -1;
 *    for finite argument, only EXPM1(0)=0 is exact.
 *
 * Accuracy:
 *    EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with
 *    1,166,000 random arguments on a VAX, the maximum observed error was
 *    .872 ulps (units of the last place).
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following constants.
 * The decimal values may be used, provided that the compiler will convert
 * from decimal to binary accurately enough to produce the hexadecimal values
 * shown.
 */

#include "mathimpl.h"

vc(ln2hi,  6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
vc(ln2lo,  1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
vc(lnhuge, 9.4961163736712506989E1   ,ec1d,43bd,9010,a73e,   7, .BDEC1DA73E9010)
vc(invln2, 1.4426950408889634148E0   ,aa3b,40b8,17f1,295c,   1, .B8AA3B295C17F1)

ic(ln2hi,  6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
ic(ln2lo,  1.9082149292705877000E-10, -33, 1.A39EF35793C76)
ic(lnhuge, 7.1602103751842355450E2,     9, 1.6602B15B7ECF2)
ic(invln2, 1.4426950408889633870E0,     0, 1.71547652B82FE)

#ifdef vccast
#define     ln2hi vccast(ln2hi)
#define     ln2lo vccast(ln2lo)
#define     lnhuge      vccast(lnhuge)
#define     invln2      vccast(invln2)
#endif

extern double expm1(x)
double x;
{
      const static double one=1.0, half=1.0/2.0; 
      double  z,hi,lo,c;
      int k;
#if defined(vax)||defined(tahoe)
      static prec=56;
#else /* defined(vax)||defined(tahoe) */
      static prec=53;
#endif      /* defined(vax)||defined(tahoe) */

#if !defined(vax)&&!defined(tahoe)
      if(x!=x) return(x);     /* x is NaN */
#endif      /* !defined(vax)&&!defined(tahoe) */

      if( x <= lnhuge ) {
            if( x >= -40.0 ) {

                /* argument reduction : x - k*ln2 */
                  k= (int)(invln2*x)+copysign(0.5,x); /* k=NINT(x/ln2) */
                  hi=x-k*ln2hi ; 
                  z=hi-(lo=k*ln2lo);
                  c=(hi-z)-lo;

                  if(k==0) return(z+__exp__E(z,c));
                  if(k==1)
                      if(z< -0.25) 
                        {x=z+half;x +=__exp__E(z,c); return(x+x);}
                      else
                        {z+=__exp__E(z,c); x=half+z; return(x+x);}
                /* end of k=1 */

                  else {
                      if(k<=prec)
                        { x=one-scalb(one,-k); z += __exp__E(z,c);}
                      else if(k<100)
                        { x = __exp__E(z,c)-scalb(one,-k); x+=z; z=one;}
                      else 
                        { x = __exp__E(z,c)+z; z=one;}

                      return (scalb(x+z,k));  
                  }
            }
            /* end of x > lnunfl */

            else 
                 /* expm1(-big#) rounded to -1 (inexact) */
                 if(finite(x))  
                   { ln2hi+ln2lo; return(-one);}

                 /* expm1(-INF) is -1 */
                 else return(-one);
      }
      /* end of x < lnhuge */

      else 
      /*  expm1(INF) is INF, expm1(+big#) overflows to INF */
          return( finite(x) ?  scalb(one,5000) : x);
}

#endif

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