111 lines
2.8 KiB
C
111 lines
2.8 KiB
C
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#ifndef lint
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static char sccsid[] = "@(#)hypot.c 1.1 92/07/30 SMI";
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#endif
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/*
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* Copyright (c) 1987 by Sun Microsystems, Inc.
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*/
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/* hypot(x,y)
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* by K.C. Ng for SUN 4.0 libm.
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* Method :
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* If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has
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* error less than 1 ulp.
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* So, compute sqrt(x*x+y*y) with some care as follows:
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* Assume x>y>0;
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* 1. save and set rounding to round-to-nearest
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* 2. if x > 2y use
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* x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y
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* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
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* 3. if x <= 2y use
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* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
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* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, y1= y with
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* lower 32 bits chopped, y2 = y-y1.
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*
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* NOTE: DO NOT remove parenthsis!
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*
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* Special cases:
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* hypot(x,y) is INF if x or y is +INF or -INF; else
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* hypot(x,y) is NAN if x or y is NAN.
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*
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* Accuracy:
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* hypot(x,y) returns sqrt(x^2+y^2) with error less than 1 ulps (units
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* in the last place)
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*/
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#include <math.h>
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#include "libm.h"
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extern enum fp_direction_type _swapRD();
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static double
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two54 = 134217728.0 * 134217728.0,
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twon54 = 1.0/(134217728.0 * 134217728.0),
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two1022 = 4.49423283715578976932e+307,
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twon1022= 2.22507385850720138309e-308;
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double hypot(x,y)
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double x, y;
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{
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double one = 1.0;
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register n0;
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double ox=x, oy=y; /* keep copy of x and y for SVID */
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double t1,t2,y1,y2,w;
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long *px = (long*)&x,*py=(long*)&y;
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long *pt1 = (long*)&t1,*py1=(long*)&y1;
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enum fp_direction_type rd;
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long i,j,k,nx,ny,nz;
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if ((* (int *) &one) != 0) n0=0; /* not a i386 */
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else n0=1; /* is a i386 */
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px[n0] &= 0x7fffffff; /* clear sign bit of x and y */
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py[n0] &= 0x7fffffff;
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k = 0x7ff00000;
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nx = px[n0]&k; /* exponent of x and y */
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ny = py[n0]&k;
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if(ny > nx) {w=x;x=y;y=w;nz=ny;ny=nx;nx=nz;}
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if((nx-ny)>0x3c00000) {x += y; goto exit;} /* x/y > 2**60 */
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if(nx < 0x5f300000 && ny > 0x23d00000) { /* medium x,y */
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/* save and set RD to Rounding to nearest */
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rd = _swapRD(fp_nearest);
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w = x-y;
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if (w>y) {
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pt1[n0]=px[n0]; pt1[1-n0]=0;
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t2 = x-t1;
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x = sqrt(t1*t1-(y*(-y)-t2*(x+t1)));
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} else {
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x = x+x;
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py1[n0] = py[n0]; py1[1-n0]=0;
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y2 = y - y1;
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pt1[n0] = px[n0]; pt1[1-n0]=0;
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t2 = x - t1;
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x = sqrt(t1*y1-(w*(-w)-(t2*y1+y2*x)));
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}
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if(rd!=fp_nearest) _swapRD(rd); /* restore rounding mode */
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goto exit;
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} else {
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if(nx==k||ny==k) { /* x or y is INF or NaN */
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if(isinf(x)) return x; else
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if(isinf(y)) return y; else return x+y;
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}
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if (ny==0) {
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if (y==0.0||x==0.0) return x+y;
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x *= two1022;
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y *= two1022;
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x = twon1022*hypot(x,y);
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goto exit;
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}
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j = nx-0x3ff00000;
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px[n0] -= j;
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py[n0] -= j;
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pt1[n0] = nx; pt1[1-n0]=0;
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x = t1*hypot(x,y);
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}
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exit:
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if (px[n0]==k) x = SVID_libm_err(ox,oy,4);
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return x;
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}
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