2fe8fb192f
There is important information about booting non-ack images in docs/UPDATING. ack/aout-format images can't be built any more, and booting clang/ELF-format ones is a little different. Updating to the new boot monitor is recommended. Changes in this commit: . drop boot monitor -> allowing dropping ack support . facility to copy ELF boot files to /boot so that old boot monitor can still boot fairly easily, see UPDATING . no more ack-format libraries -> single-case libraries . some cleanup of OBJECT_FMT, COMPILER_TYPE, etc cases . drop several ack toolchain commands, but not all support commands (e.g. aal is gone but acksize is not yet). . a few libc files moved to netbsd libc dir . new /bin/date as minix date used code in libc/ . test compile fix . harmonize includes . /usr/lib is no longer special: without ack, /usr/lib plays no kind of special bootstrapping role any more and bootstrapping is done exclusively through packages, so releases depend even less on the state of the machine making them now. . rename nbsd_lib* to lib* . reduce mtree
125 lines
3.3 KiB
C
125 lines
3.3 KiB
C
/* @(#)e_hypot.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <sys/cdefs.h>
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#if defined(LIBM_SCCS) && !defined(lint)
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__RCSID("$NetBSD: e_hypot.c,v 1.13 2008/04/25 22:21:53 christos Exp $");
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#endif
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/* __ieee754_hypot(x,y)
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*
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* Method :
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* If (assume round-to-nearest) z=x*x+y*y
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* has error less than sqrt(2)/2 ulp, than
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* sqrt(z) has error less than 1 ulp (exercise).
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*
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* So, compute sqrt(x*x+y*y) with some care as
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* follows to get the error below 1 ulp:
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*
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* Assume x>y>0;
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* (if possible, set rounding to round-to-nearest)
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* 1. if x > 2y use
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* x1*x1+(y*y+(x2*(x+x1))) 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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* 2. if x <= 2y use
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* t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
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* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
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* yy1= y with lower 32 bits chopped, y2 = y-yy1.
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*
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* NOTE: scaling may be necessary if some argument is too
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* large or too tiny
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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
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* than 1 ulps (units in the last place)
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*/
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#include "math.h"
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#include "math_private.h"
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double
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__ieee754_hypot(double x, double y)
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{
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double a=x,b=y,t1,t2,yy1,y2,w;
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int32_t j,k,ha,hb;
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GET_HIGH_WORD(ha,x);
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ha &= 0x7fffffff;
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GET_HIGH_WORD(hb,y);
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hb &= 0x7fffffff;
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if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
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SET_HIGH_WORD(a,ha); /* a <- |a| */
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SET_HIGH_WORD(b,hb); /* b <- |b| */
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if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
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k=0;
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if(ha > 0x5f300000) { /* a>2**500 */
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if(ha >= 0x7ff00000) { /* Inf or NaN */
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u_int32_t low;
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w = a+b; /* for sNaN */
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GET_LOW_WORD(low,a);
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if(((ha&0xfffff)|low)==0) w = a;
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GET_LOW_WORD(low,b);
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if(((hb^0x7ff00000)|low)==0) w = b;
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return w;
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}
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/* scale a and b by 2**-600 */
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ha -= 0x25800000; hb -= 0x25800000; k += 600;
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SET_HIGH_WORD(a,ha);
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SET_HIGH_WORD(b,hb);
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}
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if(hb < 0x20b00000) { /* b < 2**-500 */
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if(hb <= 0x000fffff) { /* subnormal b or 0 */
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u_int32_t low;
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GET_LOW_WORD(low,b);
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if((hb|low)==0) return a;
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t1=0;
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SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
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b *= t1;
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a *= t1;
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k -= 1022;
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} else { /* scale a and b by 2^600 */
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ha += 0x25800000; /* a *= 2^600 */
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hb += 0x25800000; /* b *= 2^600 */
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k -= 600;
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SET_HIGH_WORD(a,ha);
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SET_HIGH_WORD(b,hb);
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}
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}
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/* medium size a and b */
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w = a-b;
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if (w>b) {
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t1 = 0;
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SET_HIGH_WORD(t1,ha);
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t2 = a-t1;
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w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
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} else {
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a = a+a;
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yy1 = 0;
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SET_HIGH_WORD(yy1,hb);
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y2 = b - yy1;
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t1 = 0;
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SET_HIGH_WORD(t1,ha+0x00100000);
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t2 = a - t1;
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w = __ieee754_sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
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}
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if(k!=0) {
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u_int32_t high;
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t1 = 1.0;
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GET_HIGH_WORD(high,t1);
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SET_HIGH_WORD(t1,high+(k<<20));
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return t1*w;
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} else return w;
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}
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