1 2 /* @(#)e_hypot.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 #ifndef lint 15 static char rcsid[] = "$FreeBSD$"; 16 #endif 17 18 /* __ieee754_hypot(x,y) 19 * 20 * Method : 21 * If (assume round-to-nearest) z=x*x+y*y 22 * has error less than sqrt(2)/2 ulp, than 23 * sqrt(z) has error less than 1 ulp (exercise). 24 * 25 * So, compute sqrt(x*x+y*y) with some care as 26 * follows to get the error below 1 ulp: 27 * 28 * Assume x>y>0; 29 * (if possible, set rounding to round-to-nearest) 30 * 1. if x > 2y use 31 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y 32 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else 33 * 2. if x <= 2y use 34 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) 35 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 36 * y1= y with lower 32 bits chopped, y2 = y-y1. 37 * 38 * NOTE: scaling may be necessary if some argument is too 39 * large or too tiny 40 * 41 * Special cases: 42 * hypot(x,y) is INF if x or y is +INF or -INF; else 43 * hypot(x,y) is NAN if x or y is NAN. 44 * 45 * Accuracy: 46 * hypot(x,y) returns sqrt(x^2+y^2) with error less 47 * than 1 ulps (units in the last place) 48 */ 49 50 #include "math.h" 51 #include "math_private.h" 52 53 double 54 __ieee754_hypot(double x, double y) 55 { 56 double a=x,b=y,t1,t2,y1,y2,w; 57 int32_t j,k,ha,hb; 58 59 GET_HIGH_WORD(ha,x); 60 ha &= 0x7fffffff; 61 GET_HIGH_WORD(hb,y); 62 hb &= 0x7fffffff; 63 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 64 SET_HIGH_WORD(a,ha); /* a <- |a| */ 65 SET_HIGH_WORD(b,hb); /* b <- |b| */ 66 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ 67 k=0; 68 if(ha > 0x5f300000) { /* a>2**500 */ 69 if(ha >= 0x7ff00000) { /* Inf or NaN */ 70 u_int32_t low; 71 w = a+b; /* for sNaN */ 72 GET_LOW_WORD(low,a); 73 if(((ha&0xfffff)|low)==0) w = a; 74 GET_LOW_WORD(low,b); 75 if(((hb^0x7ff00000)|low)==0) w = b; 76 return w; 77 } 78 /* scale a and b by 2**-600 */ 79 ha -= 0x25800000; hb -= 0x25800000; k += 600; 80 SET_HIGH_WORD(a,ha); 81 SET_HIGH_WORD(b,hb); 82 } 83 if(hb < 0x20b00000) { /* b < 2**-500 */ 84 if(hb <= 0x000fffff) { /* subnormal b or 0 */ 85 u_int32_t low; 86 GET_LOW_WORD(low,b); 87 if((hb|low)==0) return a; 88 t1=0; 89 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ 90 b *= t1; 91 a *= t1; 92 k -= 1022; 93 } else { /* scale a and b by 2^600 */ 94 ha += 0x25800000; /* a *= 2^600 */ 95 hb += 0x25800000; /* b *= 2^600 */ 96 k -= 600; 97 SET_HIGH_WORD(a,ha); 98 SET_HIGH_WORD(b,hb); 99 } 100 } 101 /* medium size a and b */ 102 w = a-b; 103 if (w>b) { 104 t1 = 0; 105 SET_HIGH_WORD(t1,ha); 106 t2 = a-t1; 107 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); 108 } else { 109 a = a+a; 110 y1 = 0; 111 SET_HIGH_WORD(y1,hb); 112 y2 = b - y1; 113 t1 = 0; 114 SET_HIGH_WORD(t1,ha+0x00100000); 115 t2 = a - t1; 116 w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); 117 } 118 if(k!=0) { 119 u_int32_t high; 120 t1 = 1.0; 121 GET_HIGH_WORD(high,t1); 122 SET_HIGH_WORD(t1,high+(k<<20)); 123 return t1*w; 124 } else return w; 125 } 126