184 lines
6.1 KiB
C
184 lines
6.1 KiB
C
/* exp.c - math routines */
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/* Copyright 1992-1993 Wind River Systems, Inc. */
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/*
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modification history
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--------------------
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01e,05feb93,jdi doc changes based on kdl review.
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01d,02dec92,jdi doc tweaks.
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01c,28oct92,jdi documentation cleanup.
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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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/* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */
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/* ln2lo = 1.6465949582897081279E-12 , Hex 2^-39 * .E7BCD5E4F1D9CC */
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/* lnhuge = 9.4961163736712506989E1 , Hex 2^ 7 * .BDEC1DA73E9010 */
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/* lntiny = -9.5654310917272452386E1 , Hex 2^ 7 * -.BF4F01D72E33AF */
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/* invln2 = 1.4426950408889634148E0 ; Hex 2^ 1 * .B8AA3B295C17F1 */
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/* p1 = 1.6666666666666602251E-1 , Hex 2^-2 * .AAAAAAAAAAA9F1 */
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/* p2 = -2.7777777777015591216E-3 , Hex 2^-8 * -.B60B60B5F5EC94 */
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/* p3 = 6.6137563214379341918E-5 , Hex 2^-13 * .8AB355792EF15F */
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/* p4 = -1.6533902205465250480E-6 , Hex 2^-19 * -.DDEA0E2E935F84 */
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/* p5 = 4.1381367970572387085E-8 , Hex 2^-24 * .B1BB4B95F52683 */
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static long ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
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static long ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
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static long lnhugex[] = { _0x(ec1d,43bd), _0x(9010,a73e)};
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static long lntinyx[] = { _0x(4f01,c3bf), _0x(33af,d72e)};
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static long invln2x[] = { _0x(aa3b,40b8), _0x(17f1,295c)};
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static long p1x[] = { _0x(aaaa,3f2a), _0x(a9f1,aaaa)};
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static long p2x[] = { _0x(0b60,bc36), _0x(ec94,b5f5)};
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static long p3x[] = { _0x(b355,398a), _0x(f15f,792e)};
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static long p4x[] = { _0x(ea0e,b6dd), _0x(5f84,2e93)};
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static long p5x[] = { _0x(bb4b,3431), _0x(2683,95f5)};
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#define ln2hi (*(double*)ln2hix)
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#define ln2lo (*(double*)ln2lox)
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#define lnhuge (*(double*)lnhugex)
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#define lntiny (*(double*)lntinyx)
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#define invln2 (*(double*)invln2x)
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#define p1 (*(double*)p1x)
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#define p2 (*(double*)p2x)
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#define p3 (*(double*)p3x)
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#define p4 (*(double*)p4x)
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#define p5 (*(double*)p5x)
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#else /* defined(vax)||defined(tahoe) */
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static double
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p1 = 1.6666666666666601904E-1 , /*Hex 2^-3 * 1.555555555553E */
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p2 = -2.7777777777015593384E-3 , /*Hex 2^-9 * -1.6C16C16BEBD93 */
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p3 = 6.6137563214379343612E-5 , /*Hex 2^-14 * 1.1566AAF25DE2C */
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p4 = -1.6533902205465251539E-6 , /*Hex 2^-20 * -1.BBD41C5D26BF1 */
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p5 = 4.1381367970572384604E-8 , /*Hex 2^-25 * 1.6376972BEA4D0 */
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ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */
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ln2lo = 1.9082149292705877000E-10 , /*Hex 2^-33 * 1.A39EF35793C76 */
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lnhuge = 7.1602103751842355450E2 , /*Hex 2^ 9 * 1.6602B15B7ECF2 */
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lntiny = -7.5137154372698068983E2 , /*Hex 2^ 9 * -1.77AF8EBEAE354 */
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invln2 = 1.4426950408889633870E0 ; /*Hex 2^ 0 * 1.71547652B82FE */
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#endif /* defined(vax)||defined(tahoe) */
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/*****************************************************************************
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*
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* exp - compute an exponential value (ANSI)
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*
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* This routine returns the exponential value of <x> in
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* double precision (IEEE double, 53 bits).
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*
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* A range error occurs if <x> is too large.
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*
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* INTERNAL:
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* Method:
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* (1) Argument Reduction: given the input <x>, find <r> and integer <k>
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* such that:
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*
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* x = k*ln2 + r, |r| <= 0.5*ln2
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*
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* <r> will be represented as r := z+c for better accuracy.
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*
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* (2) Compute exp(r) by
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*
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* exp(r) = 1 + r + r*R1/(2-R1)
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*
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* where:
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*
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* R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2))))
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*
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* (3) exp(x) = 2^k * exp(r)
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*
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* INCLUDE FILES: math.h
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*
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* RETURNS: The double-precision exponential value of <x>.
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*
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* Special cases:
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* If <x> is +INF or NaN, exp() returns <x>.
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* If <x> is -INF, it returns 0.
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*
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* SEE ALSO: mathALib
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*
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* INTERNAL:
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* Coded in C by K.C. Ng, 1/19/85;
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* Revised by K.C. Ng on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
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*/
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double exp
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(
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double x /* exponent */
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)
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{
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double scalb(), copysign(), z,hi,lo,c;
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int k,finite();
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#if !defined(vax)&&!defined(tahoe)
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if(x!=x) return(x); /* x is NaN */
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#endif /* !defined(vax)&&!defined(tahoe) */
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if( x <= lnhuge ) {
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if( x >= lntiny ) {
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/* argument reduction : x --> x - k*ln2 */
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k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
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/* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
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hi=x-k*ln2hi;
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x=hi-(lo=k*ln2lo);
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/* return 2^k*[1+x+x*c/(2+c)] */
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z=x*x;
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c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
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return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
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}
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/* end of x > lntiny */
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else
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/* exp(-big#) underflows to zero */
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if(finite(x)) return(scalb(1.0,-5000));
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/* exp(-INF) is zero */
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else return(0.0);
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}
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/* end of x < lnhuge */
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else
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/* exp(INF) is INF, exp(+big#) overflows to INF */
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return( finite(x) ? scalb(1.0,5000) : x);
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}
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