217 lines
6.6 KiB
C
217 lines
6.6 KiB
C
/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)pow.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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/* POW(X,Y)
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* RETURN X**Y
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* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
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* CODED IN C BY K.C. NG, 1/8/85;
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* REVISED BY K.C. NG on 7/10/85.
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* KERNEL pow_P() REPLACED BY P. McILROY 7/22/92.
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* Required system supported functions:
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* scalb(x,n)
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* logb(x)
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* copysign(x,y)
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* finite(x)
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* drem(x,y)
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*
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* Required kernel functions:
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* exp__D(a,c) exp(a + c) for |a| << |c|
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* struct d_double dlog(x) r.a + r.b, |r.b| < |r.a|
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*
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* Method
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* 1. Compute and return log(x) in three pieces:
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* log(x) = n*ln2 + hi + lo,
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* where n is an integer.
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* 2. Perform y*log(x) by simulating muti-precision arithmetic and
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* return the answer in three pieces:
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* y*log(x) = m*ln2 + hi + lo,
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* where m is an integer.
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* 3. Return x**y = exp(y*log(x))
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* = 2^m * ( exp(hi+lo) ).
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*
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* Special cases:
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* (anything) ** 0 is 1 ;
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* (anything) ** 1 is itself;
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* (anything) ** NaN is NaN;
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* NaN ** (anything except 0) is NaN;
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* +(anything > 1) ** +INF is +INF;
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* -(anything > 1) ** +INF is NaN;
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* +-(anything > 1) ** -INF is +0;
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* +-(anything < 1) ** +INF is +0;
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* +(anything < 1) ** -INF is +INF;
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* -(anything < 1) ** -INF is NaN;
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* +-1 ** +-INF is NaN and signal INVALID;
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* +0 ** +(anything except 0, NaN) is +0;
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* -0 ** +(anything except 0, NaN, odd integer) is +0;
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* +0 ** -(anything except 0, NaN) is +INF and signal DIV-BY-ZERO;
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* -0 ** -(anything except 0, NaN, odd integer) is +INF with signal;
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* -0 ** (odd integer) = -( +0 ** (odd integer) );
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* +INF ** +(anything except 0,NaN) is +INF;
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* +INF ** -(anything except 0,NaN) is +0;
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* -INF ** (odd integer) = -( +INF ** (odd integer) );
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* -INF ** (even integer) = ( +INF ** (even integer) );
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* -INF ** -(anything except integer,NaN) is NaN with signal;
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* -(x=anything) ** (k=integer) is (-1)**k * (x ** k);
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* -(anything except 0) ** (non-integer) is NaN with signal;
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*
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* Accuracy:
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* pow(x,y) returns x**y nearly rounded. In particular, on a SUN, a VAX,
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* and a Zilog Z8000,
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* pow(integer,integer)
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* always returns the correct integer provided it is representable.
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* In a test run with 100,000 random arguments with 0 < x, y < 20.0
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* on a VAX, the maximum observed error was 1.79 ulps (units in the
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* last place).
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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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*/
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#include <errno.h>
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#include <math.h>
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#include "mathimpl.h"
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#if (defined(vax) || defined(tahoe))
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#define TRUNC(x) x = (double) (float) x
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#define _IEEE 0
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#else
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#define _IEEE 1
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#define endian (((*(int *) &one)) ? 1 : 0)
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#define TRUNC(x) *(((int *) &x)+endian) &= 0xf8000000
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#define infnan(x) 0.0
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#endif /* vax or tahoe */
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const static double zero=0.0, one=1.0, two=2.0, negone= -1.0;
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static double pow_P __P((double, double));
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double pow(x,y)
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double x,y;
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{
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double t;
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if (y==zero)
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return (one);
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else if (y==one || (_IEEE && x != x))
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return (x); /* if x is NaN or y=1 */
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else if (_IEEE && y!=y) /* if y is NaN */
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return (y);
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else if (!finite(y)) /* if y is INF */
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if ((t=fabs(x))==one) /* +-1 ** +-INF is NaN */
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return (y - y);
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else if (t>one)
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return ((y<0)? zero : ((x<zero)? y-y : y));
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else
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return ((y>0)? zero : ((x<0)? y-y : -y));
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else if (y==two)
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return (x*x);
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else if (y==negone)
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return (one/x);
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/* x > 0, x == +0 */
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else if (copysign(one, x) == one)
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return (pow_P(x, y));
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/* sign(x)= -1 */
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/* if y is an even integer */
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else if ( (t=drem(y,two)) == zero)
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return (pow_P(-x, y));
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/* if y is an odd integer */
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else if (copysign(t,one) == one)
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return (-pow_P(-x, y));
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/* Henceforth y is not an integer */
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else if (x==zero) /* x is -0 */
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return ((y>zero)? -x : one/(-x));
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else if (_IEEE)
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return (zero/zero);
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else
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return (infnan(EDOM));
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}
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/* kernel function for x >= 0 */
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static double
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#ifdef _ANSI_SOURCE
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pow_P(double x, double y)
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#else
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pow_P(x, y) double x, y;
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#endif
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{
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struct Double s, t, __log__D();
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double __exp__D();
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volatile double huge = 1e300, tiny = 1e-300;
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if (x == zero)
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if (y > zero)
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return (zero);
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else if (_IEEE)
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return (huge*huge);
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else
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return (infnan(ERANGE));
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if (x == one)
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return (one);
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if (!finite(x))
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if (y < zero)
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return (zero);
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else if (_IEEE)
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return (huge*huge);
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else
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return (infnan(ERANGE));
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if (y >= 7e18) /* infinity */
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if (x < 1)
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return(tiny*tiny);
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else if (_IEEE)
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return (huge*huge);
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else
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return (infnan(ERANGE));
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/* Return exp(y*log(x)), using simulated extended */
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/* precision for the log and the multiply. */
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s = __log__D(x);
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t.a = y;
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TRUNC(t.a);
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t.b = y - t.a;
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t.b = s.b*y + t.b*s.a;
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t.a *= s.a;
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s.a = t.a + t.b;
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s.b = (t.a - s.a) + t.b;
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return (__exp__D(s.a, s.b));
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}
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