1  /* @(#)e_hypot.c 5.1 93/09/24 */
  2  /*
  3   * ====================================================
  4   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  5   *
  6   * Developed at SunPro, a Sun Microsystems, Inc. business.
  7   * Permission to use, copy, modify, and distribute this
  8   * software is freely granted, provided that this notice 
  9   * is preserved.
 10   * ====================================================
 11   */
 12  
 13  #if defined(LIBM_SCCS) && !defined(lint)
 14  static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $";
 15  #endif
 16  
 17  /* __ieee754_hypot(x,y)
 18   *
 19   * Method :                  
 20   *	If (assume round-to-nearest) z=x*x+y*y 
 21   *	has error less than sqrt(2)/2 ulp, than 
 22   *	sqrt(z) has error less than 1 ulp (exercise).
 23   *
 24   *	So, compute sqrt(x*x+y*y) with some care as 
 25   *	follows to get the error below 1 ulp:
 26   *
 27   *	Assume x>y>0;
 28   *	(if possible, set rounding to round-to-nearest)
 29   *	1. if x > 2y  use
 30   *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
 31   *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
 32   *	2. if x <= 2y use
 33   *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
 34   *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 
 35   *	y1= y with lower 32 bits chopped, y2 = y-y1.
 36   *		
 37   *	NOTE: scaling may be necessary if some argument is too 
 38   *	      large or too tiny
 39   *
 40   * Special cases:
 41   *	hypot(x,y) is INF if x or y is +INF or -INF; else
 42   *	hypot(x,y) is NAN if x or y is NAN.
 43   *
 44   * Accuracy:
 45   * 	hypot(x,y) returns sqrt(x^2+y^2) with error less 
 46   * 	than 1 ulps (units in the last place) 
 47   */
 48  
 49  #include "math.h"
 50  #include "mathP.h"
 51  
 52  #ifdef __STDC__
 53  	double __ieee754_hypot(double x, double y)
 54  #else
 55  	double __ieee754_hypot(x,y)
 56  	double x, y;
 57  #endif
 58  {
 59  	double a=x,b=y,t1,t2,y1,y2,w;
 60  	int32_t j,k,ha,hb;
 61  
 62  	GET_HIGH_WORD(ha,x);
 63  	ha &= 0x7fffffff;
 64  	GET_HIGH_WORD(hb,y);
 65  	hb &= 0x7fffffff;
 66  	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
 67  	SET_HIGH_WORD(a,ha);	/* a <- |a| */
 68  	SET_HIGH_WORD(b,hb);	/* b <- |b| */
 69  	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
 70  	k=0;
 71  	if(ha > 0x5f300000) {	/* a>2**500 */
 72  	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
 73  	       u_int32_t low;
 74  	       w = a+b;			/* for sNaN */
 75  	       GET_LOW_WORD(low,a);
 76  	       if(((ha&0xfffff)|low)==0) w = a;
 77  	       GET_LOW_WORD(low,b);
 78  	       if(((hb^0x7ff00000)|low)==0) w = b;
 79  	       return w;
 80  	   }
 81  	   /* scale a and b by 2**-600 */
 82  	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
 83  	   SET_HIGH_WORD(a,ha);
 84  	   SET_HIGH_WORD(b,hb);
 85  	}
 86  	if(hb < 0x20b00000) {	/* b < 2**-500 */
 87  	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */	
 88  	        u_int32_t low;
 89  		GET_LOW_WORD(low,b);
 90  		if((hb|low)==0) return a;
 91  		t1=0;
 92  		SET_HIGH_WORD(t1,0x7fd00000);	/* t1=2^1022 */
 93  		b *= t1;
 94  		a *= t1;
 95  		k -= 1022;
 96  	    } else {		/* scale a and b by 2^600 */
 97  	        ha += 0x25800000; 	/* a *= 2^600 */
 98  		hb += 0x25800000;	/* b *= 2^600 */
 99  		k -= 600;
100  		SET_HIGH_WORD(a,ha);
101  		SET_HIGH_WORD(b,hb);
102  	    }
103  	}
104      /* medium size a and b */
105  	w = a-b;
106  	if (w>b) {
107  	    t1 = 0;
108  	    SET_HIGH_WORD(t1,ha);
109  	    t2 = a-t1;
110  	    w  = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
111  	} else {
112  	    a  = a+a;
113  	    y1 = 0;
114  	    SET_HIGH_WORD(y1,hb);
115  	    y2 = b - y1;
116  	    t1 = 0;
117  	    SET_HIGH_WORD(t1,ha+0x00100000);
118  	    t2 = a - t1;
119  	    w  = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
120  	}
121  	if(k!=0) {
122  	    u_int32_t high;
123  	    t1 = 1.0;
124  	    GET_HIGH_WORD(high,t1);
125  	    SET_HIGH_WORD(t1,high+(k<<20));
126  	    return t1*w;
127  	} else return w;
128  }