1 /* $NetBSD: n_pow.c,v 1.7 2003/08/07 16:44:52 agc 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. Neither the name of the University nor the names of its contributors 15 * may be used to endorse or promote products derived from this software 16 * without specific prior written permission. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 28 * SUCH DAMAGE. 29 */ 30 31 #ifndef lint 32 #if 0 33 static char sccsid[] = "@(#)pow.c 8.1 (Berkeley) 6/4/93"; 34 #endif 35 #endif /* not lint */ 36 37 /* POW(X,Y) 38 * RETURN X**Y 39 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 40 * CODED IN C BY K.C. NG, 1/8/85; 41 * REVISED BY K.C. NG on 7/10/85. 42 * KERNEL pow_P() REPLACED BY P. McILROY 7/22/92. 43 * Required system supported functions: 44 * scalb(x,n) 45 * logb(x) 46 * copysign(x,y) 47 * finite(x) 48 * drem(x,y) 49 * 50 * Required kernel functions: 51 * exp__D(a,c) exp(a + c) for |a| << |c| 52 * struct d_double dlog(x) r.a + r.b, |r.b| < |r.a| 53 * 54 * Method 55 * 1. Compute and return log(x) in three pieces: 56 * log(x) = n*ln2 + hi + lo, 57 * where n is an integer. 58 * 2. Perform y*log(x) by simulating muti-precision arithmetic and 59 * return the answer in three pieces: 60 * y*log(x) = m*ln2 + hi + lo, 61 * where m is an integer. 62 * 3. Return x**y = exp(y*log(x)) 63 * = 2^m * ( exp(hi+lo) ). 64 * 65 * Special cases: 66 * (anything) ** 0 is 1 ; 67 * (anything) ** 1 is itself; 68 * (anything) ** NaN is NaN; 69 * NaN ** (anything except 0) is NaN; 70 * +(anything > 1) ** +INF is +INF; 71 * -(anything > 1) ** +INF is NaN; 72 * +-(anything > 1) ** -INF is +0; 73 * +-(anything < 1) ** +INF is +0; 74 * +(anything < 1) ** -INF is +INF; 75 * -(anything < 1) ** -INF is NaN; 76 * +-1 ** +-INF is NaN and signal INVALID; 77 * +0 ** +(anything except 0, NaN) is +0; 78 * -0 ** +(anything except 0, NaN, odd integer) is +0; 79 * +0 ** -(anything except 0, NaN) is +INF and signal DIV-BY-ZERO; 80 * -0 ** -(anything except 0, NaN, odd integer) is +INF with signal; 81 * -0 ** (odd integer) = -( +0 ** (odd integer) ); 82 * +INF ** +(anything except 0,NaN) is +INF; 83 * +INF ** -(anything except 0,NaN) is +0; 84 * -INF ** (odd integer) = -( +INF ** (odd integer) ); 85 * -INF ** (even integer) = ( +INF ** (even integer) ); 86 * -INF ** -(anything except integer,NaN) is NaN with signal; 87 * -(x=anything) ** (k=integer) is (-1)**k * (x ** k); 88 * -(anything except 0) ** (non-integer) is NaN with signal; 89 * 90 * Accuracy: 91 * pow(x,y) returns x**y nearly rounded. In particular, on a SUN, a VAX, 92 * and a Zilog Z8000, 93 * pow(integer,integer) 94 * always returns the correct integer provided it is representable. 95 * In a test run with 100,000 random arguments with 0 < x, y < 20.0 96 * on a VAX, the maximum observed error was 1.79 ulps (units in the 97 * last place). 98 * 99 * Constants : 100 * The hexadecimal values are the intended ones for the following constants. 101 * The decimal values may be used, provided that the compiler will convert 102 * from decimal to binary accurately enough to produce the hexadecimal values 103 * shown. 104 */ 105 106 #include <errno.h> 107 #include <math.h> 108 109 #include "mathimpl.h" 110 111 #if (defined(__vax__) || defined(tahoe)) 112 #define TRUNC(x) x = (double) (float) x 113 #define _IEEE 0 114 #else 115 #define _IEEE 1 116 #define endian (((*(int *) &one)) ? 1 : 0) 117 #define TRUNC(x) *(((int *) &x)+endian) &= 0xf8000000 118 #define infnan(x) 0.0 119 #endif /* __vax__ or tahoe */ 120 121 static const double zero=0.0, one=1.0, two=2.0, negone= -1.0; 122 123 static double pow_P (double, double); 124 125 float 126 powf(float x, float y) 127 { 128 return pow((double) x, (double) (y)); 129 } 130 131 double 132 pow(double x, double y) 133 { 134 double t; 135 if (y==zero) 136 return (one); 137 else if (y==one || (_IEEE && x != x)) 138 return (x); /* if x is NaN or y=1 */ 139 else if (_IEEE && y!=y) /* if y is NaN */ 140 return (y); 141 else if (!finite(y)) /* if y is INF */ 142 if ((t=fabs(x))==one) /* +-1 ** +-INF is NaN */ 143 return (y - y); 144 else if (t>one) 145 return ((y<0)? zero : ((x<zero)? y-y : y)); 146 else 147 return ((y>0)? zero : ((x<0)? y-y : -y)); 148 else if (y==two) 149 return (x*x); 150 else if (y==negone) 151 return (one/x); 152 /* x > 0, x == +0 */ 153 else if (copysign(one, x) == one) 154 return (pow_P(x, y)); 155 156 /* sign(x)= -1 */ 157 /* if y is an even integer */ 158 else if ( (t=drem(y,two)) == zero) 159 return (pow_P(-x, y)); 160 161 /* if y is an odd integer */ 162 else if (copysign(t,one) == one) 163 return (-pow_P(-x, y)); 164 165 /* Henceforth y is not an integer */ 166 else if (x==zero) /* x is -0 */ 167 return ((y>zero)? -x : one/(-x)); 168 else if (_IEEE) 169 return (zero/zero); 170 else 171 return (infnan(EDOM)); 172 } 173 174 /* kernel function for x >= 0 */ 175 static double 176 pow_P(double x, double y) 177 { 178 struct Double s, t; 179 double huge = 1e300, tiny = 1e-300; 180 181 if (x == zero) { 182 if (y > zero) 183 return (zero); 184 else if (_IEEE) 185 return (huge*huge); 186 else 187 return (infnan(ERANGE)); 188 } 189 if (x == one) 190 return (one); 191 if (!finite(x)) { 192 if (y < zero) 193 return (zero); 194 else if (_IEEE) 195 return (huge*huge); 196 else 197 return (infnan(ERANGE)); 198 } 199 if (y >= 7e18) { /* infinity */ 200 if (x < 1) 201 return(tiny*tiny); 202 else if (_IEEE) 203 return (huge*huge); 204 else 205 return (infnan(ERANGE)); 206 } 207 208 /* Return exp(y*log(x)), using simulated extended */ 209 /* precision for the log and the multiply. */ 210 211 s = __log__D(x); 212 t.a = y; 213 TRUNC(t.a); 214 t.b = y - t.a; 215 t.b = s.b*y + t.b*s.a; 216 t.a *= s.a; 217 s.a = t.a + t.b; 218 s.b = (t.a - s.a) + t.b; 219 return (__exp__D(s.a, s.b)); 220 } 221