154 lines
5.3 KiB
C
154 lines
5.3 KiB
C
/* exp__E.c - math routines */
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/* Copyright 1992 Wind River Systems, Inc. */
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/*
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modification history
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--------------------
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01b,20sep92,smb documentation additions.
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01a,08jul92,smb documentation.
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*/
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/*
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DESCRIPTION
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted
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* provided that the above copyright notice and this paragraph are
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* duplicated in all such forms and that any documentation,
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* advertising materials, and other materials related to such
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* distribution and use acknowledge that the software was developed
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* by the University of California, Berkeley. The name of the
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* University may not be used to endorse or promote products derived
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* from this software without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
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* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*
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* All recipients should regard themselves as participants in an ongoing
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* research project and hence should feel obligated to report their
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* experiences (good or bad) with these elementary function codes, using
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* the sendbug(8) program, to the authors.
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*
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SEE ALSO: American National Standard X3.159-1989
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NOMANUAL
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*/
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#include "vxWorks.h"
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#include "math.h"
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#if defined(vax)||defined(tahoe) /* VAX D format */
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#ifdef vax
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#define _0x(A,B) 0x/**/A/**/B
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#else /* vax */
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#define _0x(A,B) 0x/**/B/**/A
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#endif /* vax */
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/* static double */
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/* p1 = 1.5150724356786683059E-2 , Hex 2^ -6 * .F83ABE67E1066A */
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/* p2 = 6.3112487873718332688E-5 , Hex 2^-13 * .845B4248CD0173 */
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/* q1 = 1.1363478204690669916E-1 , Hex 2^ -3 * .E8B95A44A2EC45 */
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/* q2 = 1.2624568129896839182E-3 , Hex 2^ -9 * .A5790572E4F5E7 */
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/* q3 = 1.5021856115869022674E-6 ; Hex 2^-19 * .C99EB4604AC395 */
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static long p1x[] = { _0x(3abe,3d78), _0x(066a,67e1)};
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static long p2x[] = { _0x(5b42,3984), _0x(0173,48cd)};
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static long q1x[] = { _0x(b95a,3ee8), _0x(ec45,44a2)};
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static long q2x[] = { _0x(7905,3ba5), _0x(f5e7,72e4)};
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static long q3x[] = { _0x(9eb4,36c9), _0x(c395,604a)};
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#define p1 (*(double*)p1x)
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#define p2 (*(double*)p2x)
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#define q1 (*(double*)q1x)
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#define q2 (*(double*)q2x)
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#define q3 (*(double*)q3x)
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#else /* defined(vax)||defined(tahoe) */
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static double
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p1 = 1.3887401997267371720E-2 , /*Hex 2^ -7 * 1.C70FF8B3CC2CF */
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p2 = 3.3044019718331897649E-5 , /*Hex 2^-15 * 1.15317DF4526C4 */
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q1 = 1.1110813732786649355E-1 , /*Hex 2^ -4 * 1.C719538248597 */
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q2 = 9.9176615021572857300E-4 ; /*Hex 2^-10 * 1.03FC4CB8C98E8 */
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#endif /* defined(vax)||defined(tahoe) */
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/*******************************************************************************
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*
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* exp_E -
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*
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* exp__E(x,c)
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* ASSUMPTION: c << x SO THAT fl(x+c)=x.
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* (c is the correction term for x)
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* exp__E RETURNS
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*
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* / exp(x+c) - 1 - x , 1E-19 < |x| < .3465736
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* exp__E(x,c) = |
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* \ 0 , |x| < 1E-19.
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*
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* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
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* KERNEL FUNCTION OF EXP, EXPM1, POW FUNCTIONS
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* CODED IN C BY K.C. NG, 1/31/85;
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* REVISED BY K.C. NG on 3/16/85, 4/16/85.
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*
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* Required system supported function:
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* copysign(x,y)
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*
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* Method:
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* 1. Rational approximation. Let r=x+c.
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* Based on
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* 2 * sinh(r/2)
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* exp(r) - 1 = ---------------------- ,
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* cosh(r/2) - sinh(r/2)
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* exp__E(r) is computed using
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* x*x (x/2)*W - ( Q - ( 2*P + x*P ) )
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* --- + (c + x*[---------------------------------- + c ])
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* 2 1 - W
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* where P := p1*x^2 + p2*x^4,
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* Q := q1*x^2 + q2*x^4 (for 56 bits precision, add q3*x^6)
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* W := x/2-(Q-x*P),
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*
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* (See the listing below for the values of p1,p2,q1,q2,q3. The poly-
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* nomials P and Q may be regarded as the approximations to sinh
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* and cosh :
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* sinh(r/2) = r/2 + r * P , cosh(r/2) = 1 + Q . )
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*
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* The coefficients were obtained by a special Remez algorithm.
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*
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* Approximation error:
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*
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* | exp(x) - 1 | 2**(-57), (IEEE double)
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* | ------------ - (exp__E(x,0)+x)/x | <=
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* | x | 2**(-69). (VAX D)
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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NOMANUAL
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*/
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double exp__E(x,c)
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double x,c;
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{
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static double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19;
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double copysign(),z,p,q,xp,xh,w;
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if(copysign(x,one)>small) {
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z = x*x ;
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p = z*( p1 +z* p2 );
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#if defined(vax)||defined(tahoe)
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q = z*( q1 +z*( q2 +z* q3 ));
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#else /* defined(vax)||defined(tahoe) */
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q = z*( q1 +z* q2 );
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#endif /* defined(vax)||defined(tahoe) */
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xp= x*p ;
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xh= x*half ;
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w = xh-(q-xp) ;
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p = p+p;
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c += x*((xh*w-(q-(p+xp)))/(one-w)+c);
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return(z*half+c);
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}
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/* end of |x| > small */
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else {
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if(x!=zero) one+small; /* raise the inexact flag */
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return(copysign(zero,x));
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}
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}
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