1 /* $NetBSD: n_cabs.c,v 1.5 2003/08/07 16:44:50 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 static char sccsid[] = "@(#)cabs.c 8.1 (Berkeley) 6/4/93"; 33 #endif /* not lint */ 34 35 /* HYPOT(X,Y) 36 * RETURN THE SQUARE ROOT OF X^2 + Y^2 WHERE Z=X+iY 37 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 38 * CODED IN C BY K.C. NG, 11/28/84; 39 * REVISED BY K.C. NG, 7/12/85. 40 * 41 * Required system supported functions : 42 * copysign(x,y) 43 * finite(x) 44 * scalb(x,N) 45 * sqrt(x) 46 * 47 * Method : 48 * 1. replace x by |x| and y by |y|, and swap x and 49 * y if y > x (hence x is never smaller than y). 50 * 2. Hypot(x,y) is computed by: 51 * Case I, x/y > 2 52 * 53 * y 54 * hypot = x + ----------------------------- 55 * 2 56 * sqrt ( 1 + [x/y] ) + x/y 57 * 58 * Case II, x/y <= 2 59 * y 60 * hypot = x + -------------------------------------------------- 61 * 2 62 * [x/y] - 2 63 * (sqrt(2)+1) + (x-y)/y + ----------------------------- 64 * 2 65 * sqrt ( 1 + [x/y] ) + sqrt(2) 66 * 67 * 68 * 69 * Special cases: 70 * hypot(x,y) is INF if x or y is +INF or -INF; else 71 * hypot(x,y) is NAN if x or y is NAN. 72 * 73 * Accuracy: 74 * hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units 75 * in the last place). See Kahan's "Interval Arithmetic Options in the 76 * Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics 77 * 1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate 78 * code follows in comments.) In a test run with 500,000 random arguments 79 * on a VAX, the maximum observed error was .959 ulps. 80 * 81 * Constants: 82 * The hexadecimal values are the intended ones for the following constants. 83 * The decimal values may be used, provided that the compiler will convert 84 * from decimal to binary accurately enough to produce the hexadecimal values 85 * shown. 86 */ 87 #define _LIBM_STATIC 88 #include "mathimpl.h" 89 90 vc(r2p1hi, 2.4142135623730950345E0 ,8279,411a,ef32,99fc, 2, .9A827999FCEF32) 91 vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B) 92 vc(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65) 93 94 ic(r2p1hi, 2.4142135623730949234E0 , 1, 1.3504F333F9DE6) 95 ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5) 96 ic(sqrt2, 1.4142135623730951455E0 , 0, 1.6A09E667F3BCD) 97 98 #ifdef vccast 99 #define r2p1hi vccast(r2p1hi) 100 #define r2p1lo vccast(r2p1lo) 101 #define sqrt2 vccast(sqrt2) 102 #endif 103 104 double 105 hypot(double x, double y) 106 { 107 static const double zero=0, one=1, 108 small=1.0E-18; /* fl(1+small)==1 */ 109 static const ibig=30; /* fl(1+2**(2*ibig))==1 */ 110 double t,r; 111 int exp; 112 113 if(finite(x)) 114 if(finite(y)) 115 { 116 x=copysign(x,one); 117 y=copysign(y,one); 118 if(y > x) 119 { t=x; x=y; y=t; } 120 if(x == zero) return(zero); 121 if(y == zero) return(x); 122 exp= logb(x); 123 if(exp-(int)logb(y) > ibig ) 124 /* raise inexact flag and return |x| */ 125 { one+small; return(x); } 126 127 /* start computing sqrt(x^2 + y^2) */ 128 r=x-y; 129 if(r>y) { /* x/y > 2 */ 130 r=x/y; 131 r=r+sqrt(one+r*r); } 132 else { /* 1 <= x/y <= 2 */ 133 r/=y; t=r*(r+2.0); 134 r+=t/(sqrt2+sqrt(2.0+t)); 135 r+=r2p1lo; r+=r2p1hi; } 136 137 r=y/r; 138 return(x+r); 139 140 } 141 142 else if(y==y) /* y is +-INF */ 143 return(copysign(y,one)); 144 else 145 return(y); /* y is NaN and x is finite */ 146 147 else if(x==x) /* x is +-INF */ 148 return (copysign(x,one)); 149 else if(finite(y)) 150 return(x); /* x is NaN, y is finite */ 151 #if !defined(__vax__)&&!defined(tahoe) 152 else if(y!=y) return(y); /* x and y is NaN */ 153 #endif /* !defined(__vax__)&&!defined(tahoe) */ 154 else return(copysign(y,one)); /* y is INF */ 155 } 156 157 /* CABS(Z) 158 * RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER Z = X + iY 159 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 160 * CODED IN C BY K.C. NG, 11/28/84. 161 * REVISED BY K.C. NG, 7/12/85. 162 * 163 * Required kernel function : 164 * hypot(x,y) 165 * 166 * Method : 167 * cabs(z) = hypot(x,y) . 168 */ 169 170 struct complex { double x, y; }; 171 172 double 173 cabs(z) 174 struct complex z; 175 { 176 return hypot(z.x,z.y); 177 } 178 179 double 180 z_abs(z) 181 struct complex *z; 182 { 183 return hypot(z->x,z->y); 184 } 185 186 /* A faster but less accurate version of cabs(x,y) */ 187 #if 0 188 double hypot(x,y) 189 double x, y; 190 { 191 static const double zero=0, one=1; 192 small=1.0E-18; /* fl(1+small)==1 */ 193 static const ibig=30; /* fl(1+2**(2*ibig))==1 */ 194 double temp; 195 int exp; 196 197 if(finite(x)) 198 if(finite(y)) 199 { 200 x=copysign(x,one); 201 y=copysign(y,one); 202 if(y > x) 203 { temp=x; x=y; y=temp; } 204 if(x == zero) return(zero); 205 if(y == zero) return(x); 206 exp= logb(x); 207 x=scalb(x,-exp); 208 if(exp-(int)logb(y) > ibig ) 209 /* raise inexact flag and return |x| */ 210 { one+small; return(scalb(x,exp)); } 211 else y=scalb(y,-exp); 212 return(scalb(sqrt(x*x+y*y),exp)); 213 } 214 215 else if(y==y) /* y is +-INF */ 216 return(copysign(y,one)); 217 else 218 return(y); /* y is NaN and x is finite */ 219 220 else if(x==x) /* x is +-INF */ 221 return (copysign(x,one)); 222 else if(finite(y)) 223 return(x); /* x is NaN, y is finite */ 224 else if(y!=y) return(y); /* x and y is NaN */ 225 else return(copysign(y,one)); /* y is INF */ 226 } 227 #endif 228