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 /* hypot(x,y) 14 * 15 * Method : 16 * If (assume round-to-nearest) z=x*x+y*y 17 * has error less than sqrt(2)/2 ulp, than 18 * sqrt(z) has error less than 1 ulp (exercise). 19 * 20 * So, compute sqrt(x*x+y*y) with some care as 21 * follows to get the error below 1 ulp: 22 * 23 * Assume x>y>0; 24 * (if possible, set rounding to round-to-nearest) 25 * 1. if x > 2y use 26 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y 27 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else 28 * 2. if x <= 2y use 29 * t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y)) 30 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 31 * yy1= y with lower 32 bits chopped, y2 = y-yy1. 32 * 33 * NOTE: scaling may be necessary if some argument is too 34 * large or too tiny 35 * 36 * Special cases: 37 * hypot(x,y) is INF if x or y is +INF or -INF; else 38 * hypot(x,y) is NAN if x or y is NAN. 39 * 40 * Accuracy: 41 * hypot(x,y) returns sqrt(x^2+y^2) with error less 42 * than 1 ulps (units in the last place) 43 */ 44 45 #include "math.h" 46 #include "math_private.h" 47 48 double 49 hypot(double x, double y) 50 { 51 double a=x,b=y,t1,t2,yy1,y2,w; 52 int32_t j,k,ha,hb; 53 54 GET_HIGH_WORD(ha,x); 55 ha &= 0x7fffffff; 56 GET_HIGH_WORD(hb,y); 57 hb &= 0x7fffffff; 58 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 59 SET_HIGH_WORD(a,ha); /* a <- |a| */ 60 SET_HIGH_WORD(b,hb); /* b <- |b| */ 61 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ 62 k=0; 63 if(ha > 0x5f300000) { /* a>2**500 */ 64 if(ha >= 0x7ff00000) { /* Inf or NaN */ 65 u_int32_t low; 66 w = a+b; /* for sNaN */ 67 GET_LOW_WORD(low,a); 68 if(((ha&0xfffff)|low)==0) w = a; 69 GET_LOW_WORD(low,b); 70 if(((hb^0x7ff00000)|low)==0) w = b; 71 return w; 72 } 73 /* scale a and b by 2**-600 */ 74 ha -= 0x25800000; hb -= 0x25800000; k += 600; 75 SET_HIGH_WORD(a,ha); 76 SET_HIGH_WORD(b,hb); 77 } 78 if(hb < 0x20b00000) { /* b < 2**-500 */ 79 if(hb <= 0x000fffff) { /* subnormal b or 0 */ 80 u_int32_t low; 81 GET_LOW_WORD(low,b); 82 if((hb|low)==0) return a; 83 t1=0; 84 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ 85 b *= t1; 86 a *= t1; 87 k -= 1022; 88 } else { /* scale a and b by 2^600 */ 89 ha += 0x25800000; /* a *= 2^600 */ 90 hb += 0x25800000; /* b *= 2^600 */ 91 k -= 600; 92 SET_HIGH_WORD(a,ha); 93 SET_HIGH_WORD(b,hb); 94 } 95 } 96 /* medium size a and b */ 97 w = a-b; 98 if (w>b) { 99 t1 = 0; 100 SET_HIGH_WORD(t1,ha); 101 t2 = a-t1; 102 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); 103 } else { 104 a = a+a; 105 yy1 = 0; 106 SET_HIGH_WORD(yy1,hb); 107 y2 = b - yy1; 108 t1 = 0; 109 SET_HIGH_WORD(t1,ha+0x00100000); 110 t2 = a - t1; 111 w = sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b))); 112 } 113 if(k!=0) { 114 u_int32_t high; 115 t1 = 1.0; 116 GET_HIGH_WORD(high,t1); 117 SET_HIGH_WORD(t1,high+(k<<20)); 118 return t1*w; 119 } else return w; 120 } 121