pow.c

VXWORKS源代码

/* pow.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"
#include "private/mathP.h"

#if defined(vax)||defined(tahoe)	/* VAX D format */
#include <errno.h>
extern double infnan();
#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 */
/* invln2 =  1.4426950408889634148E0     , Hex  2^  1   *  .B8AA3B295C17F1 */
/* sqrt2  =  1.4142135623730950622E0     ; Hex  2^  1   *  .B504F333F9DE65 */
static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
static long    invln2x[] = { _0x(aa3b,40b8), _0x(17f1,295c)};
static long     sqrt2x[] = { _0x(04f3,40b5), _0x(de65,33f9)};
#define    ln2hi    (*(double*)ln2hix)
#define    ln2lo    (*(double*)ln2lox)
#define   invln2    (*(double*)invln2x)
#define    sqrt2    (*(double*)sqrt2x)
#else	/* defined(vax)||defined(tahoe) */
static double
ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */
invln2 =  1.4426950408889633870E0     , /*Hex  2^  0   *  1.71547652B82FE */
sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */
#endif	/* defined(vax)||defined(tahoe) */

static double zero=0.0, half=1.0/2.0, one=1.0, two=2.0, negone= -1.0;

/*******************************************************************************
*
* pow - compute the value of a number raised to a specified power (ANSI)
*
* This routine returns <x> to the power of <y> in
* double precision (IEEE double, 53 bits).
*
* A domain error occurs if <x> is negative and <y> is not an integral value.
* A domain error occurs if the result cannot be represented when <x> is zero
* and <y> is less than or equal to zero.  A range error may occur.
*
* INTERNAL:
* Method:
* (1) Compute and return log(x) in three pieces:
*
*         log(x) = n*ln2 + hi + lo
*
*     where <n> is an integer.
*
* (2) Perform y*log(x) by simulating multi-precision arithmetic and
*     return the answer in three pieces:
*
*         y*log(x) = m*ln2 + hi + lo
*
*     where <m> is an integer.
*
* (3) Return:
*
*         x**y = exp(y*log(x)) = 2^m * ( exp(hi+lo) )
*
* INCLUDE FILES: math.h
*
* RETURNS: The double-precision value of <x> to the power of <y>.
*
* Special cases:
* .TS
* tab(|);
* l0 c0 l.
*     (anything) ** 0                       | is | 1
*     (anything) ** 1                       | is | itself
*     (anything) ** NaN                     | is | NaN
*     NaN ** (anything except 0)            | is | NaN
*     +-(anything > 1) ** +INF              | is | +INF
*     +-(anything > 1) ** -INF              | is | +0
*     +-(anything < 1) ** +INF              | is | +0
*     +-(anything < 1) ** -INF              | is | +INF
*     +-1 ** +-INF                          | is | NaN, signal INVALID
*     +0 ** +(anything non-0, NaN)          | is | +0
*     -0 ** +(anything non-0, NaN, odd int) | is | +0
*     +0 ** -(anything non-0, NaN)          | is | +INF, signal DIV-BY-ZERO
*     -0 ** -(anything non-0, NaN, odd int) | is | +INF with signal
*     -0 ** (odd integer)                   | =  | -(+0 ** (odd integer))
*     +INF ** +(anything except 0, NaN)     | is | +INF
*     +INF ** -(anything except 0, NaN)     | is | +0
*     -INF ** (odd integer)                 | =  | -(+INF ** (odd integer))
*     -INF ** (even integer)                | =  | (+INF ** (even integer))
*     -INF ** -(any non-integer, NaN)       | is | NaN with signal
*     -(x=anything) ** (k=integer)          | is | (-1)**k * (x ** k)
*     -(anything except 0) ** (non-integer) | is | NaN with signal
* .TE
*
* SEE ALSO: mathALib
*
* INTERNAL:
* Coded in C by K.C. Ng, 1/8/85;
* Revised by K.C. Ng on 7/10/85.
*/

double pow
    (
    double x,	/* operand  */
    double y	/* exponent */
    )

    {
	double drem(),pow_p(),copysign(),t;
	int finite();

	if     (y==zero)      return(one);
	else if(y==one
#if !defined(vax)&&!defined(tahoe)
		||x!=x
#endif	/* !defined(vax)&&!defined(tahoe) */
		) return( x );      /* if x is NaN or y=1 */
#if !defined(vax)&&!defined(tahoe)
	else if(y!=y)         return( y );      /* if y is NaN */
#endif	/* !defined(vax)&&!defined(tahoe) */
	else if(!finite(y))                     /* if y is INF */
	     if((t=copysign(x,one))==one) return(zero/zero);
	     else if(t>one) return((y>zero)?y:zero);
	     else return((y<zero)?-y:zero);
	else if(y==two)       return(x*x);
	else if(y==negone)    return(one/x);

    /* sign(x) = 1 */
	else if(copysign(one,x)==one) return(pow_p(x,y));

    /* sign(x)= -1 */
	/* if y is an even integer */
	else if ( (t=drem(y,two)) == zero)	return( pow_p(-x,y) );

	/* if y is an odd integer */
	else if (copysign(t,one) == one) return( -pow_p(-x,y) );

	/* Henceforth y is not an integer */
	else if(x==zero)	/* x is -0 */
	    return((y>zero)?-x:one/(-x));
	else {			/* return NaN */
#if defined(vax)||defined(tahoe)
	    return (infnan(EDOM));	/* NaN */
#else	/* defined(vax)||defined(tahoe) */
	    return(zero/zero);
#endif	/* defined(vax)||defined(tahoe) */
	}
    }

/****************************************************************************
*
* pow_p -
*
* pow_p(x,y) return x**y for x with sign=1 and finite y *
*
* RETURN:
* NOMANUAL
*/

double pow_p(x,y)
double x,y;
{
        double logb(),scalb(),copysign(),log__L(),exp__E();
        double c,s,t,z,tx,ty;
#ifdef tahoe
	double tahoe_tmp;
#endif	/* tahoe */
        float sx,sy;
	long k=0;
        int n,m;

	if(x==zero||!finite(x)) {           /* if x is +INF or +0 */
#if defined(vax)||defined(tahoe)
	     return((y>zero)?x:infnan(ERANGE));	/* if y<zero, return +INF */
#else	/* defined(vax)||defined(tahoe) */
	     return((y>zero)?x:one/x);
#endif	/* defined(vax)||defined(tahoe) */
	}
	if(x==1.0) return(x);	/* if x=1.0, return 1 since y is finite */

    /* reduce x to z in [sqrt(1/2)-1, sqrt(2)-1] */
        z=scalb(x,-(n=logb(x)));
#if !defined(vax)&&!defined(tahoe)	/* IEEE double; subnormal number */
        if(n <= -1022) {n += (m=logb(z)); z=scalb(z,-m);}
#endif	/* !defined(vax)&&!defined(tahoe) */
        if(z >= sqrt2 ) {n += 1; z *= half;}  z -= one ;

    /* log(x) = nlog2+log(1+z) ~ nlog2 + t + tx */
	s=z/(two+z); c=z*z*half; tx=s*(c+log__L(s*s));
	t= z-(c-tx); tx += (z-t)-c;

   /* if y*log(x) is neither too big nor too small */
	if((s=logb(y)+logb(n+t)) < 12.0)
	    if(s>-60.0) {

	/* compute y*log(x) ~ mlog2 + t + c */
        	s=y*(n+invln2*t);
                m=s+copysign(half,s);   /* m := nint(y*log(x)) */
		k=y;
		if((double)k==y) {	/* if y is an integer */
		    k = m-k*n;
		    sx=t; tx+=(t-sx); }
		else	{		/* if y is not an integer */
		    k =m;
	 	    tx+=n*ln2lo;
		    sx=(c=n*ln2hi)+t; tx+=(c-sx)+t; }
	   /* end of checking whether k==y */

                sy=y; ty=y-sy;          /* y ~ sy + ty */
#ifdef tahoe
		s = (tahoe_tmp = sx)*sy-k*ln2hi;
#else	/* tahoe */
		s=(double)sx*sy-k*ln2hi;        /* (sy+ty)*(sx+tx)-kln2 */
#endif	/* tahoe */
		z=(tx*ty-k*ln2lo);
		tx=tx*sy; ty=sx*ty;
		t=ty+z; t+=tx; t+=s;
		c= -((((t-s)-tx)-ty)-z);

	    /* return exp(y*log(x)) */
		t += exp__E(t,c); return(scalb(one+t,m));
	     }
	/* end of if log(y*log(x)) > -60.0 */

	    else
		/* exp(+- tiny) = 1 with inexact flag */
			{ln2hi+ln2lo; return(one);}
	    else if(copysign(one,y)*(n+invln2*t) <zero)
		/* exp(-(big#)) underflows to zero */
	        	return(scalb(one,-5000));
	    else
	        /* exp(+(big#)) overflows to INF */
	    		return(scalb(one, 5000));

}