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Diffstat (limited to 'sysdeps/ieee754/cabs.c')
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diff --git a/sysdeps/ieee754/cabs.c b/sysdeps/ieee754/cabs.c new file mode 100644 index 0000000..6b0d4c4 --- /dev/null +++ b/sysdeps/ieee754/cabs.c @@ -0,0 +1,228 @@ +/* + * 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[] = "@(#)cabs.c 5.6 (Berkeley) 10/9/90"; +#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. + */ +#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(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 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) . + */ + +double +cabs(z) +struct __cabs_complex z; +{ + return hypot(z.__x,z.__y); +} + +double +z_abs(z) +struct __cabs_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 |