[unix-history] / lib / libm / common_source / pow.c

/*
 * Copyright (c) 1985 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	5.9 (Berkeley) 12/16/92";
#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)
		return ((y>zero)? x : one/x);
	if (x == 1)
		return (one);
	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));
}
Commit	Line	Data
15637ed4 RG	1	/*
	2	* Copyright (c) 1985 Regents of the University of California.
	3	* All rights reserved.
	4	*
	5	* Redistribution and use in source and binary forms, with or without
	6	* modification, are permitted provided that the following conditions
	7	* are met:
	8	* 1. Redistributions of source code must retain the above copyright
	9	* notice, this list of conditions and the following disclaimer.
	10	* 2. Redistributions in binary form must reproduce the above copyright
	11	* notice, this list of conditions and the following disclaimer in the
	12	* documentation and/or other materials provided with the distribution.
	13	* 3. All advertising materials mentioning features or use of this software
	14	* must display the following acknowledgement:
	15	* This product includes software developed by the University of
	16	* California, Berkeley and its contributors.
	17	* 4. Neither the name of the University nor the names of its contributors
	18	* may be used to endorse or promote products derived from this software
	19	* without specific prior written permission.
	20	*
	21	* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
	22	* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	23	* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	24	* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
	25	* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
	26	* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
	27	* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	28	* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	29	* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
	30	* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
	31	* SUCH DAMAGE.
	32	*/
	33
	34	#ifndef lint
78ed81a3	35	static char sccsid[] = "@(#)pow.c 5.9 (Berkeley) 12/16/92";
15637ed4 RG	36	#endif /* not lint */
	37
	38	/* POW(X,Y)
	39	* RETURN X**Y
	40	* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
	41	* CODED IN C BY K.C. NG, 1/8/85;
	42	* REVISED BY K.C. NG on 7/10/85.
78ed81a3	43	* KERNEL pow_P() REPLACED BY P. McILROY 7/22/92.
15637ed4 RG	44	* Required system supported functions:
	45	* scalb(x,n)
	46	* logb(x)
	47	* copysign(x,y)
	48	* finite(x)
	49	* drem(x,y)
	50	*
	51	* Required kernel functions:
78ed81a3	52	* exp__D(a,c) exp(a + c) for \|a\| << \|c\|
78ed81a3	53	* struct d_double dlog(x) r.a + r.b, \|r.b\| < \|r.a\|
15637ed4 RG	54	*
	55	* Method
	56	* 1. Compute and return log(x) in three pieces:
	57	* log(x) = n*ln2 + hi + lo,
	58	* where n is an integer.
	59	* 2. Perform y*log(x) by simulating muti-precision arithmetic and
	60	* return the answer in three pieces:
	61	* ylog(x) = mln2 + hi + lo,
	62	* where m is an integer.
	63	* 3. Return x*y = exp(ylog(x))
	64	* = 2^m * ( exp(hi+lo) ).
	65	*
	66	* Special cases:
	67	* (anything) ** 0 is 1 ;
	68	* (anything) ** 1 is itself;
	69	* (anything) ** NaN is NaN;
	70	* NaN ** (anything except 0) is NaN;
78ed81a3	71	* +(anything > 1) ** +INF is +INF;
78ed81a3	72	* -(anything > 1) ** +INF is NaN;
15637ed4 RG	73	* +-(anything > 1) ** -INF is +0;
15637ed4 RG	74	* +-(anything < 1) ** +INF is +0;
78ed81a3	75	* +(anything < 1) ** -INF is +INF;
78ed81a3	76	* -(anything < 1) ** -INF is NaN;
15637ed4 RG	77	* +-1 ** +-INF is NaN and signal INVALID;
	78	* +0 ** +(anything except 0, NaN) is +0;
	79	* -0 ** +(anything except 0, NaN, odd integer) is +0;
	80	* +0 ** -(anything except 0, NaN) is +INF and signal DIV-BY-ZERO;
	81	* -0 ** -(anything except 0, NaN, odd integer) is +INF with signal;
	82	* -0 (odd integer) = -( +0 (odd integer) );
	83	* +INF ** +(anything except 0,NaN) is +INF;
	84	* +INF ** -(anything except 0,NaN) is +0;
	85	* -INF (odd integer) = -( +INF (odd integer) );
	86	* -INF (even integer) = ( +INF (even integer) );
	87	* -INF ** -(anything except integer,NaN) is NaN with signal;
	88	* -(x=anything) (k=integer) is (-1)k * (x ** k);
	89	* -(anything except 0) ** (non-integer) is NaN with signal;
	90	*
	91	* Accuracy:
	92	* pow(x,y) returns x**y nearly rounded. In particular, on a SUN, a VAX,
	93	* and a Zilog Z8000,
	94	* pow(integer,integer)
	95	* always returns the correct integer provided it is representable.
	96	* In a test run with 100,000 random arguments with 0 < x, y < 20.0
	97	* on a VAX, the maximum observed error was 1.79 ulps (units in the
	98	* last place).
	99	*
	100	* Constants :
	101	* The hexadecimal values are the intended ones for the following constants.
	102	* The decimal values may be used, provided that the compiler will convert
	103	* from decimal to binary accurately enough to produce the hexadecimal values
	104	* shown.
	105	*/
	106
	107	#include <errno.h>
78ed81a3	108	#include <math.h>
15637ed4	109
78ed81a3	110	#include "mathimpl.h"
15637ed4	111
78ed81a3	112	#if (defined(vax) \|\| defined(tahoe))
	113	#define TRUNC(x) x = (double) (float) x
	114	#define _IEEE 0
	115	#else
	116	#define _IEEE 1
	117	#define endian ((((int ) &one)) ? 1 : 0)
	118	#define TRUNC(x) (((int ) &x)+endian) &= 0xf8000000
	119	#define infnan(x) 0.0
	120	#endif /* vax or tahoe */
15637ed4	121
78ed81a3	122	const static double zero=0.0, one=1.0, two=2.0, negone= -1.0;
15637ed4	123
78ed81a3	124	static double pow_P __P((double, double));
15637ed4 RG	125
	126	double pow(x,y)
	127	double x,y;
	128	{
	129	double t;
78ed81a3	130	if (y==zero)
	131	return (one);
	132	else if (y==one \|\| (_IEEE && x != x))
	133	return (x); /* if x is NaN or y=1 */
	134	else if (_IEEE && y!=y) /* if y is NaN */
	135	return (y);
	136	else if (!finite(y)) /* if y is INF */
	137	if ((t=fabs(x))==one) /* +-1 ** +-INF is NaN */
	138	return (y - y);
	139	else if (t>one)
	140	return ((y<0)? zero : ((x<zero)? y-y : y));
	141	else
	142	return ((y>0)? zero : ((x<0)? y-y : -y));
	143	else if (y==two)
	144	return (x*x);
	145	else if (y==negone)
	146	return (one/x);
	147	/* x > 0, x == +0 */
	148	else if (copysign(one, x) == one)
	149	return (pow_P(x, y));
15637ed4 RG	150
	151	/* sign(x)= -1 */
	152	/* if y is an even integer */
78ed81a3	153	else if ( (t=drem(y,two)) == zero)
78ed81a3	154	return (pow_P(-x, y));
15637ed4 RG	155
15637ed4 RG	156	/* if y is an odd integer */
78ed81a3	157	else if (copysign(t,one) == one)
78ed81a3	158	return (-pow_P(-x, y));
15637ed4 RG	159
15637ed4 RG	160	/* Henceforth y is not an integer */
78ed81a3	161	else if (x==zero) /* x is -0 */
	162	return ((y>zero)? -x : one/(-x));
	163	else if (_IEEE)
	164	return (zero/zero);
	165	else
	166	return (infnan(EDOM));
15637ed4	167	}
78ed81a3	168	/* kernel function for x >= 0 */
	169	static double
	170	#ifdef _ANSI_SOURCE
	171	pow_P(double x, double y)
	172	#else
	173	pow_P(x, y) double x, y;
	174	#endif
15637ed4	175	{
78ed81a3	176	struct Double s, t, log__D();
	177	double exp__D(), huge = 1e300, tiny = 1e-300;
	178
	179	if (x == zero)
	180	return ((y>zero)? x : one/x);
	181	if (x == 1)
	182	return (one);
	183	if (y >= 7e18) /* infinity */
	184	if (x < 1)
	185	return(tiny*tiny);
	186	else if (_IEEE)
	187	return (huge*huge);
	188	else
	189	return (infnan(ERANGE));
	190
	191	/* Return exp(ylog(x)), using simulated extended /
	192	/* precision for the log and the multiply. */
	193
	194	s = log__D(x);
	195	t.a = y;
	196	TRUNC(t.a);
	197	t.b = y - t.a;
	198	t.b = s.by + t.bs.a;
	199	t.a *= s.a;
	200	s.a = t.a + t.b;
	201	s.b = (t.a - s.a) + t.b;
	202	return (exp__D(s.a, s.b));
15637ed4	203	}