/* $NetBSD: n_cabs.c,v 1.5 2003/08/07 16:44:50 agc Exp $ */ /* * Copyright (c) 1985, 1993 * The 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. 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[] = "@(#)cabs.c 8.1 (Berkeley) 6/4/93"; #endif /* not lint */ /* HYPOT(X,Y) * RETURN THE SQUARE ROOT OF X^2 + Y^2 WHERE Z=X+iY * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) * CODED IN C BY K.C. NG, 11/28/84; * REVISED BY K.C. NG, 7/12/85. * * Required system supported functions : * copysign(x,y) * finite(x) * scalb(x,N) * sqrt(x) * * Method : * 1. replace x by |x| and y by |y|, and swap x and * y if y > x (hence x is never smaller than y). * 2. Hypot(x,y) is computed by: * Case I, x/y > 2 * * y * hypot = x + ----------------------------- * 2 * sqrt ( 1 + [x/y] ) + x/y * * Case II, x/y <= 2 * y * hypot = x + -------------------------------------------------- * 2 * [x/y] - 2 * (sqrt(2)+1) + (x-y)/y + ----------------------------- * 2 * sqrt ( 1 + [x/y] ) + sqrt(2) * * * * Special cases: * hypot(x,y) is INF if x or y is +INF or -INF; else * hypot(x,y) is NAN if x or y is NAN. * * Accuracy: * hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units * in the last place). See Kahan's "Interval Arithmetic Options in the * Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics * 1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate * code follows in comments.) In a test run with 500,000 random arguments * on a VAX, the maximum observed error was .959 ulps. * * 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. */ #define _LIBM_STATIC #include "mathimpl.h" vc(r2p1hi, 2.4142135623730950345E0 ,8279,411a,ef32,99fc, 2, .9A827999FCEF32) vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B) vc(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65) ic(r2p1hi, 2.4142135623730949234E0 , 1, 1.3504F333F9DE6) ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5) ic(sqrt2, 1.4142135623730951455E0 , 0, 1.6A09E667F3BCD) #ifdef vccast #define r2p1hi vccast(r2p1hi) #define r2p1lo vccast(r2p1lo) #define sqrt2 vccast(sqrt2) #endif double hypot(double x, double y) { static const double zero=0, one=1, small=1.0E-18; /* fl(1+small)==1 */ static const ibig=30; /* fl(1+2**(2*ibig))==1 */ double t,r; int exp; if(finite(x)) if(finite(y)) { x=copysign(x,one); y=copysign(y,one); if(y > x) { t=x; x=y; y=t; } if(x == zero) return(zero); if(y == zero) return(x); exp= logb(x); if(exp-(int)logb(y) > ibig ) /* raise inexact flag and return |x| */ { one+small; return(x); } /* start computing sqrt(x^2 + y^2) */ r=x-y; if(r>y) { /* x/y > 2 */ r=x/y; r=r+sqrt(one+r*r); } else { /* 1 <= x/y <= 2 */ r/=y; t=r*(r+2.0); r+=t/(sqrt2+sqrt(2.0+t)); r+=r2p1lo; r+=r2p1hi; } r=y/r; return(x+r); } else if(y==y) /* y is +-INF */ return(copysign(y,one)); else return(y); /* y is NaN and x is finite */ else if(x==x) /* x is +-INF */ return (copysign(x,one)); else if(finite(y)) return(x); /* x is NaN, y is finite */ #if !defined(__vax__)&&!defined(tahoe) else if(y!=y) return(y); /* x and y is NaN */ #endif /* !defined(__vax__)&&!defined(tahoe) */ else return(copysign(y,one)); /* y is INF */ } /* CABS(Z) * RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER Z = X + iY * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) * CODED IN C BY K.C. NG, 11/28/84. * REVISED BY K.C. NG, 7/12/85. * * Required kernel function : * hypot(x,y) * * Method : * cabs(z) = hypot(x,y) . */ struct complex { double x, y; }; double cabs(z) struct complex z; { return hypot(z.x,z.y); } double z_abs(z) struct complex *z; { return hypot(z->x,z->y); } /* A faster but less accurate version of cabs(x,y) */ #if 0 double hypot(x,y) double x, y; { static const double zero=0, one=1; small=1.0E-18; /* fl(1+small)==1 */ static const ibig=30; /* fl(1+2**(2*ibig))==1 */ double temp; int exp; if(finite(x)) if(finite(y)) { x=copysign(x,one); y=copysign(y,one); if(y > x) { temp=x; x=y; y=temp; } if(x == zero) return(zero); if(y == zero) return(x); exp= logb(x); x=scalb(x,-exp); if(exp-(int)logb(y) > ibig ) /* raise inexact flag and return |x| */ { one+small; return(scalb(x,exp)); } else y=scalb(y,-exp); return(scalb(sqrt(x*x+y*y),exp)); } else if(y==y) /* y is +-INF */ return(copysign(y,one)); else return(y); /* y is NaN and x is finite */ else if(x==x) /* x is +-INF */ return (copysign(x,one)); else if(finite(y)) return(x); /* x is NaN, y is finite */ else if(y!=y) return(y); /* x and y is NaN */ else return(copysign(y,one)); /* y is INF */ } #endif
