216 lines
6.6 KiB
C
216 lines
6.6 KiB
C
/*
|
|
* 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. All advertising materials mentioning features or use of this software
|
|
* must display the following acknowledgement:
|
|
* This product includes software developed by the University of
|
|
* California, Berkeley and its contributors.
|
|
* 4. 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[] = "@(#)pow.c 8.1 (Berkeley) 6/4/93";
|
|
#endif /* not lint */
|
|
|
|
/* POW(X,Y)
|
|
* RETURN X**Y
|
|
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
|
|
* CODED IN C BY K.C. NG, 1/8/85;
|
|
* REVISED BY K.C. NG on 7/10/85.
|
|
* KERNEL pow_P() REPLACED BY P. McILROY 7/22/92.
|
|
* Required system supported functions:
|
|
* scalb(x,n)
|
|
* logb(x)
|
|
* copysign(x,y)
|
|
* finite(x)
|
|
* drem(x,y)
|
|
*
|
|
* Required kernel functions:
|
|
* exp__D(a,c) exp(a + c) for |a| << |c|
|
|
* struct d_double dlog(x) r.a + r.b, |r.b| < |r.a|
|
|
*
|
|
* 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 muti-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) ).
|
|
*
|
|
* Special cases:
|
|
* (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 NaN;
|
|
* +-(anything > 1) ** -INF is +0;
|
|
* +-(anything < 1) ** +INF is +0;
|
|
* +(anything < 1) ** -INF is +INF;
|
|
* -(anything < 1) ** -INF is NaN;
|
|
* +-1 ** +-INF is NaN and signal INVALID;
|
|
* +0 ** +(anything except 0, NaN) is +0;
|
|
* -0 ** +(anything except 0, NaN, odd integer) is +0;
|
|
* +0 ** -(anything except 0, NaN) is +INF and signal DIV-BY-ZERO;
|
|
* -0 ** -(anything except 0, NaN, odd integer) 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 ** -(anything except integer,NaN) is NaN with signal;
|
|
* -(x=anything) ** (k=integer) is (-1)**k * (x ** k);
|
|
* -(anything except 0) ** (non-integer) is NaN with signal;
|
|
*
|
|
* Accuracy:
|
|
* pow(x,y) returns x**y nearly rounded. In particular, on a SUN, a VAX,
|
|
* and a Zilog Z8000,
|
|
* pow(integer,integer)
|
|
* always returns the correct integer provided it is representable.
|
|
* In a test run with 100,000 random arguments with 0 < x, y < 20.0
|
|
* on a VAX, the maximum observed error was 1.79 ulps (units in 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 <errno.h>
|
|
#include <math.h>
|
|
|
|
#include "mathimpl.h"
|
|
|
|
#if (defined(vax) || defined(tahoe))
|
|
#define TRUNC(x) x = (double) (float) x
|
|
#define _IEEE 0
|
|
#else
|
|
#define _IEEE 1
|
|
#define endian (((*(int *) &one)) ? 1 : 0)
|
|
#define TRUNC(x) *(((int *) &x)+endian) &= 0xf8000000
|
|
#define infnan(x) 0.0
|
|
#endif /* vax or tahoe */
|
|
|
|
const static double zero=0.0, one=1.0, two=2.0, negone= -1.0;
|
|
|
|
static double pow_P __P((double, double));
|
|
|
|
double pow(x,y)
|
|
double x,y;
|
|
{
|
|
double t;
|
|
if (y==zero)
|
|
return (one);
|
|
else if (y==one || (_IEEE && x != x))
|
|
return (x); /* if x is NaN or y=1 */
|
|
else if (_IEEE && y!=y) /* if y is NaN */
|
|
return (y);
|
|
else if (!finite(y)) /* if y is INF */
|
|
if ((t=fabs(x))==one) /* +-1 ** +-INF is NaN */
|
|
return (y - y);
|
|
else if (t>one)
|
|
return ((y<0)? zero : ((x<zero)? y-y : y));
|
|
else
|
|
return ((y>0)? zero : ((x<0)? y-y : -y));
|
|
else if (y==two)
|
|
return (x*x);
|
|
else if (y==negone)
|
|
return (one/x);
|
|
/* x > 0, x == +0 */
|
|
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 if (_IEEE)
|
|
return (zero/zero);
|
|
else
|
|
return (infnan(EDOM));
|
|
}
|
|
/* kernel function for x >= 0 */
|
|
static double
|
|
#ifdef _ANSI_SOURCE
|
|
pow_P(double x, double y)
|
|
#else
|
|
pow_P(x, y) double x, y;
|
|
#endif
|
|
{
|
|
struct Double s, t, __log__D();
|
|
double __exp__D(), huge = 1e300, tiny = 1e-300;
|
|
|
|
if (x == zero)
|
|
if (y > zero)
|
|
return (zero);
|
|
else if (_IEEE)
|
|
return (huge*huge);
|
|
else
|
|
return (infnan(ERANGE));
|
|
if (x == one)
|
|
return (one);
|
|
if (!finite(x))
|
|
if (y < zero)
|
|
return (zero);
|
|
else if (_IEEE)
|
|
return (huge*huge);
|
|
else
|
|
return (infnan(ERANGE));
|
|
if (y >= 7e18) /* infinity */
|
|
if (x < 1)
|
|
return(tiny*tiny);
|
|
else if (_IEEE)
|
|
return (huge*huge);
|
|
else
|
|
return (infnan(ERANGE));
|
|
|
|
/* Return exp(y*log(x)), using simulated extended */
|
|
/* precision for the log and the multiply. */
|
|
|
|
s = __log__D(x);
|
|
t.a = y;
|
|
TRUNC(t.a);
|
|
t.b = y - t.a;
|
|
t.b = s.b*y + t.b*s.a;
|
|
t.a *= s.a;
|
|
s.a = t.a + t.b;
|
|
s.b = (t.a - s.a) + t.b;
|
|
return (__exp__D(s.a, s.b));
|
|
}
|