1 /* $NetBSD: n_pow.c,v 1.1 1995/10/10 23:37:02 ragge Exp $ */ 2 /* 3 * Copyright (c) 1985, 1993 4 * The Regents of the University of California. All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 3. All advertising materials mentioning features or use of this software 15 * must display the following acknowledgement: 16 * This product includes software developed by the University of 17 * California, Berkeley and its contributors. 18 * 4. Neither the name of the University nor the names of its contributors 19 * may be used to endorse or promote products derived from this software 20 * without specific prior written permission. 21 * 22 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 24 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 25 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 26 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 27 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 28 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 30 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 31 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 32 * SUCH DAMAGE. 33 */ 34 35 #ifndef lint 36 static char sccsid[] = "@(#)pow.c 8.1 (Berkeley) 6/4/93"; 37 #endif /* not lint */ 38 39 /* POW(X,Y) 40 * RETURN X**Y 41 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 42 * CODED IN C BY K.C. NG, 1/8/85; 43 * REVISED BY K.C. NG on 7/10/85. 44 * KERNEL pow_P() REPLACED BY P. McILROY 7/22/92. 45 * Required system supported functions: 46 * scalb(x,n) 47 * logb(x) 48 * copysign(x,y) 49 * finite(x) 50 * drem(x,y) 51 * 52 * Required kernel functions: 53 * exp__D(a,c) exp(a + c) for |a| << |c| 54 * struct d_double dlog(x) r.a + r.b, |r.b| < |r.a| 55 * 56 * Method 57 * 1. Compute and return log(x) in three pieces: 58 * log(x) = n*ln2 + hi + lo, 59 * where n is an integer. 60 * 2. Perform y*log(x) by simulating muti-precision arithmetic and 61 * return the answer in three pieces: 62 * y*log(x) = m*ln2 + hi + lo, 63 * where m is an integer. 64 * 3. Return x**y = exp(y*log(x)) 65 * = 2^m * ( exp(hi+lo) ). 66 * 67 * Special cases: 68 * (anything) ** 0 is 1 ; 69 * (anything) ** 1 is itself; 70 * (anything) ** NaN is NaN; 71 * NaN ** (anything except 0) is NaN; 72 * +(anything > 1) ** +INF is +INF; 73 * -(anything > 1) ** +INF is NaN; 74 * +-(anything > 1) ** -INF is +0; 75 * +-(anything < 1) ** +INF is +0; 76 * +(anything < 1) ** -INF is +INF; 77 * -(anything < 1) ** -INF is NaN; 78 * +-1 ** +-INF is NaN and signal INVALID; 79 * +0 ** +(anything except 0, NaN) is +0; 80 * -0 ** +(anything except 0, NaN, odd integer) is +0; 81 * +0 ** -(anything except 0, NaN) is +INF and signal DIV-BY-ZERO; 82 * -0 ** -(anything except 0, NaN, odd integer) is +INF with signal; 83 * -0 ** (odd integer) = -( +0 ** (odd integer) ); 84 * +INF ** +(anything except 0,NaN) is +INF; 85 * +INF ** -(anything except 0,NaN) is +0; 86 * -INF ** (odd integer) = -( +INF ** (odd integer) ); 87 * -INF ** (even integer) = ( +INF ** (even integer) ); 88 * -INF ** -(anything except integer,NaN) is NaN with signal; 89 * -(x=anything) ** (k=integer) is (-1)**k * (x ** k); 90 * -(anything except 0) ** (non-integer) is NaN with signal; 91 * 92 * Accuracy: 93 * pow(x,y) returns x**y nearly rounded. In particular, on a SUN, a VAX, 94 * and a Zilog Z8000, 95 * pow(integer,integer) 96 * always returns the correct integer provided it is representable. 97 * In a test run with 100,000 random arguments with 0 < x, y < 20.0 98 * on a VAX, the maximum observed error was 1.79 ulps (units in the 99 * last place). 100 * 101 * Constants : 102 * The hexadecimal values are the intended ones for the following constants. 103 * The decimal values may be used, provided that the compiler will convert 104 * from decimal to binary accurately enough to produce the hexadecimal values 105 * shown. 106 */ 107 108 #include <errno.h> 109 #include <math.h> 110 111 #include "mathimpl.h" 112 113 #if (defined(vax) || defined(tahoe)) 114 #define TRUNC(x) x = (double) (float) x 115 #define _IEEE 0 116 #else 117 #define _IEEE 1 118 #define endian (((*(int *) &one)) ? 1 : 0) 119 #define TRUNC(x) *(((int *) &x)+endian) &= 0xf8000000 120 #define infnan(x) 0.0 121 #endif /* vax or tahoe */ 122 123 const static double zero=0.0, one=1.0, two=2.0, negone= -1.0; 124 125 static double pow_P __P((double, double)); 126 127 double pow(x,y) 128 double x,y; 129 { 130 double t; 131 if (y==zero) 132 return (one); 133 else if (y==one || (_IEEE && x != x)) 134 return (x); /* if x is NaN or y=1 */ 135 else if (_IEEE && y!=y) /* if y is NaN */ 136 return (y); 137 else if (!finite(y)) /* if y is INF */ 138 if ((t=fabs(x))==one) /* +-1 ** +-INF is NaN */ 139 return (y - y); 140 else if (t>one) 141 return ((y<0)? zero : ((x<zero)? y-y : y)); 142 else 143 return ((y>0)? zero : ((x<0)? y-y : -y)); 144 else if (y==two) 145 return (x*x); 146 else if (y==negone) 147 return (one/x); 148 /* x > 0, x == +0 */ 149 else if (copysign(one, x) == one) 150 return (pow_P(x, y)); 151 152 /* sign(x)= -1 */ 153 /* if y is an even integer */ 154 else if ( (t=drem(y,two)) == zero) 155 return (pow_P(-x, y)); 156 157 /* if y is an odd integer */ 158 else if (copysign(t,one) == one) 159 return (-pow_P(-x, y)); 160 161 /* Henceforth y is not an integer */ 162 else if (x==zero) /* x is -0 */ 163 return ((y>zero)? -x : one/(-x)); 164 else if (_IEEE) 165 return (zero/zero); 166 else 167 return (infnan(EDOM)); 168 } 169 /* kernel function for x >= 0 */ 170 static double 171 #ifdef _ANSI_SOURCE 172 pow_P(double x, double y) 173 #else 174 pow_P(x, y) double x, y; 175 #endif 176 { 177 struct Double s, t, __log__D(); 178 double __exp__D(), huge = 1e300, tiny = 1e-300; 179 180 if (x == zero) 181 if (y > zero) 182 return (zero); 183 else if (_IEEE) 184 return (huge*huge); 185 else 186 return (infnan(ERANGE)); 187 if (x == one) 188 return (one); 189 if (!finite(x)) 190 if (y < zero) 191 return (zero); 192 else if (_IEEE) 193 return (huge*huge); 194 else 195 return (infnan(ERANGE)); 196 if (y >= 7e18) /* infinity */ 197 if (x < 1) 198 return(tiny*tiny); 199 else if (_IEEE) 200 return (huge*huge); 201 else 202 return (infnan(ERANGE)); 203 204 /* Return exp(y*log(x)), using simulated extended */ 205 /* precision for the log and the multiply. */ 206 207 s = __log__D(x); 208 t.a = y; 209 TRUNC(t.a); 210 t.b = y - t.a; 211 t.b = s.b*y + t.b*s.a; 212 t.a *= s.a; 213 s.a = t.a + t.b; 214 s.b = (t.a - s.a) + t.b; 215 return (__exp__D(s.a, s.b)); 216 } 217