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 #ifndef lint 14 static char rcsid[] = "$FreeBSD$"; 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 "math_private.h" 51 52 double 53 __ieee754_hypot(double x, double y) 54 { 55 double a=x,b=y,t1,t2,y1,y2,w; 56 int32_t j,k,ha,hb; 57 58 GET_HIGH_WORD(ha,x); 59 ha &= 0x7fffffff; 60 GET_HIGH_WORD(hb,y); 61 hb &= 0x7fffffff; 62 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 63 SET_HIGH_WORD(a,ha); /* a <- |a| */ 64 SET_HIGH_WORD(b,hb); /* b <- |b| */ 65 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ 66 k=0; 67 if(ha > 0x5f300000) { /* a>2**500 */ 68 if(ha >= 0x7ff00000) { /* Inf or NaN */ 69 u_int32_t low; 70 w = a+b; /* for sNaN */ 71 GET_LOW_WORD(low,a); 72 if(((ha&0xfffff)|low)==0) w = a; 73 GET_LOW_WORD(low,b); 74 if(((hb^0x7ff00000)|low)==0) w = b; 75 return w; 76 } 77 /* scale a and b by 2**-600 */ 78 ha -= 0x25800000; hb -= 0x25800000; k += 600; 79 SET_HIGH_WORD(a,ha); 80 SET_HIGH_WORD(b,hb); 81 } 82 if(hb < 0x20b00000) { /* b < 2**-500 */ 83 if(hb <= 0x000fffff) { /* subnormal b or 0 */ 84 u_int32_t low; 85 GET_LOW_WORD(low,b); 86 if((hb|low)==0) return a; 87 t1=0; 88 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ 89 b *= t1; 90 a *= t1; 91 k -= 1022; 92 } else { /* scale a and b by 2^600 */ 93 ha += 0x25800000; /* a *= 2^600 */ 94 hb += 0x25800000; /* b *= 2^600 */ 95 k -= 600; 96 SET_HIGH_WORD(a,ha); 97 SET_HIGH_WORD(b,hb); 98 } 99 } 100 /* medium size a and b */ 101 w = a-b; 102 if (w>b) { 103 t1 = 0; 104 SET_HIGH_WORD(t1,ha); 105 t2 = a-t1; 106 w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); 107 } else { 108 a = a+a; 109 y1 = 0; 110 SET_HIGH_WORD(y1,hb); 111 y2 = b - y1; 112 t1 = 0; 113 SET_HIGH_WORD(t1,ha+0x00100000); 114 t2 = a - t1; 115 w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); 116 } 117 if(k!=0) { 118 u_int32_t high; 119 t1 = 1.0; 120 GET_HIGH_WORD(high,t1); 121 SET_HIGH_WORD(t1,high+(k<<20)); 122 return t1*w; 123 } else return w; 124 } 125