exp.c

vxworks libc库源代码

/* exp.c - math routines */

/* Copyright 1992-1993 Wind River Systems, Inc. */

/*
modification history
--------------------
01e,05feb93,jdi  doc changes based on kdl review.
01d,02dec92,jdi  doc tweaks.
01c,28oct92,jdi  documentation cleanup.
01b,20sep92,smb  documentation additions
01a,08jul92,smb  documentation.
*/

/*
DESCRIPTION
* Copyright (c) 1985 Regents of the University of California.
* All rights reserved.
*
* Redistribution and use in source and binary forms are permitted
* provided that the above copyright notice and this paragraph are
* duplicated in all such forms and that any documentation,
* advertising materials, and other materials related to such
* distribution and use acknowledge that the software was developed
* by the University of California, Berkeley.  The name of the
* University may not be used to endorse or promote products derived
* from this software without specific prior written permission.
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*
* All recipients should regard themselves as participants in an ongoing
* research project and hence should feel obligated to report their
* experiences (good or bad) with these elementary function codes, using
* the sendbug(8) program, to the authors.
*
SEE ALSO: American National Standard X3.159-1989
NOMANUAL
*/

#include "vxWorks.h"
#include "math.h"

#if defined(vax)||defined(tahoe)	/* VAX D format */
#ifdef vax
#define _0x(A,B)	0x/**/A/**/B
#else	/* vax */
#define _0x(A,B)	0x/**/B/**/A
#endif	/* vax */
/* static double */
/* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
/* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC */
/* lnhuge =  9.4961163736712506989E1     , Hex  2^  7   *  .BDEC1DA73E9010 */
/* lntiny = -9.5654310917272452386E1     , Hex  2^  7   * -.BF4F01D72E33AF */
/* invln2 =  1.4426950408889634148E0     ; Hex  2^  1   *  .B8AA3B295C17F1 */
/* p1     =  1.6666666666666602251E-1    , Hex  2^-2    *  .AAAAAAAAAAA9F1 */
/* p2     = -2.7777777777015591216E-3    , Hex  2^-8    * -.B60B60B5F5EC94 */
/* p3     =  6.6137563214379341918E-5    , Hex  2^-13   *  .8AB355792EF15F */
/* p4     = -1.6533902205465250480E-6    , Hex  2^-19   * -.DDEA0E2E935F84 */
/* p5     =  4.1381367970572387085E-8    , Hex  2^-24   *  .B1BB4B95F52683 */
static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
static long    lnhugex[] = { _0x(ec1d,43bd), _0x(9010,a73e)};
static long    lntinyx[] = { _0x(4f01,c3bf), _0x(33af,d72e)};
static long    invln2x[] = { _0x(aa3b,40b8), _0x(17f1,295c)};
static long        p1x[] = { _0x(aaaa,3f2a), _0x(a9f1,aaaa)};
static long        p2x[] = { _0x(0b60,bc36), _0x(ec94,b5f5)};
static long        p3x[] = { _0x(b355,398a), _0x(f15f,792e)};
static long        p4x[] = { _0x(ea0e,b6dd), _0x(5f84,2e93)};
static long        p5x[] = { _0x(bb4b,3431), _0x(2683,95f5)};
#define    ln2hi    (*(double*)ln2hix)
#define    ln2lo    (*(double*)ln2lox)
#define   lnhuge    (*(double*)lnhugex)
#define   lntiny    (*(double*)lntinyx)
#define   invln2    (*(double*)invln2x)
#define       p1    (*(double*)p1x)
#define       p2    (*(double*)p2x)
#define       p3    (*(double*)p3x)
#define       p4    (*(double*)p4x)
#define       p5    (*(double*)p5x)

#else	/* defined(vax)||defined(tahoe) */
static double
p1     =  1.6666666666666601904E-1    , /*Hex  2^-3    *  1.555555555553E */
p2     = -2.7777777777015593384E-3    , /*Hex  2^-9    * -1.6C16C16BEBD93 */
p3     =  6.6137563214379343612E-5    , /*Hex  2^-14   *  1.1566AAF25DE2C */
p4     = -1.6533902205465251539E-6    , /*Hex  2^-20   * -1.BBD41C5D26BF1 */
p5     =  4.1381367970572384604E-8    , /*Hex  2^-25   *  1.6376972BEA4D0 */
ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */
lnhuge =  7.1602103751842355450E2     , /*Hex  2^  9   *  1.6602B15B7ECF2 */
lntiny = -7.5137154372698068983E2     , /*Hex  2^  9   * -1.77AF8EBEAE354 */
invln2 =  1.4426950408889633870E0     ; /*Hex  2^  0   *  1.71547652B82FE */
#endif	/* defined(vax)||defined(tahoe) */

/*****************************************************************************
*
* exp - compute an exponential value (ANSI)
*
* This routine returns the exponential value of <x> in
* double precision (IEEE double, 53 bits).
*
* A range error occurs if <x> is too large.
*
* INTERNAL:
* 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 exp(r) by
*
*         exp(r) = 1 + r + r*R1/(2-R1)
*
*     where:
*
*         R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2))))
*
* (3)     exp(x) = 2^k * exp(r)
*
* INCLUDE FILES: math.h
*
* RETURNS: The double-precision exponential value of <x>.
*
* Special cases:
*     If <x> is +INF or NaN, exp() returns <x>.
*     If <x> is -INF, it returns 0.
*
* SEE ALSO: mathALib
*
* INTERNAL:
* Coded in C by K.C. Ng, 1/19/85;
* Revised by K.C. Ng on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
*/

double exp
    (
    double x	/* exponent */
    )

    {
	double scalb(), copysign(), z,hi,lo,c;
	int k,finite();

#if !defined(vax)&&!defined(tahoe)
	if(x!=x) return(x);	/* x is NaN */
#endif	/* !defined(vax)&&!defined(tahoe) */
	if( x <= lnhuge ) {
		if( x >= lntiny ) {

		    /* argument reduction : x --> x - k*ln2 */

			k=invln2*x+copysign(0.5,x);	/* k=NINT(x/ln2) */

		    /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */

			hi=x-k*ln2hi;
			x=hi-(lo=k*ln2lo);

		    /* return 2^k*[1+x+x*c/(2+c)]  */
			z=x*x;
			c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
			return  scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);

		}
		/* end of x > lntiny */

		else
		     /* exp(-big#) underflows to zero */
		     if(finite(x))  return(scalb(1.0,-5000));

		     /* exp(-INF) is zero */
		     else return(0.0);
	}
	/* end of x < lnhuge */

	else
	/* exp(INF) is INF, exp(+big#) overflows to INF */
	    return( finite(x) ?  scalb(1.0,5000)  : x);
    }