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 #include <sys/cdefs.h> 15 __FBSDID("$FreeBSD$"); 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 <float.h> 50 51 #include "math.h" 52 #include "math_private.h" 53 54 double 55 __ieee754_hypot(double x, double y) 56 { 57 double a,b,t1,t2,y1,y2,w; 58 int32_t j,k,ha,hb; 59 60 GET_HIGH_WORD(ha,x); 61 ha &= 0x7fffffff; 62 GET_HIGH_WORD(hb,y); 63 hb &= 0x7fffffff; 64 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 65 a = fabs(a); 66 b = fabs(b); 67 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ 68 k=0; 69 if(ha > 0x5f300000) { /* a>2**500 */ 70 if(ha >= 0x7ff00000) { /* Inf or NaN */ 71 u_int32_t low; 72 /* Use original arg order iff result is NaN; quieten sNaNs. */ 73 w = fabs(x+0.0)-fabs(y+0.0); 74 GET_LOW_WORD(low,a); 75 if(((ha&0xfffff)|low)==0) w = a; 76 GET_LOW_WORD(low,b); 77 if(((hb^0x7ff00000)|low)==0) w = b; 78 return w; 79 } 80 /* scale a and b by 2**-600 */ 81 ha -= 0x25800000; hb -= 0x25800000; k += 600; 82 SET_HIGH_WORD(a,ha); 83 SET_HIGH_WORD(b,hb); 84 } 85 if(hb < 0x20b00000) { /* b < 2**-500 */ 86 if(hb <= 0x000fffff) { /* subnormal b or 0 */ 87 u_int32_t low; 88 GET_LOW_WORD(low,b); 89 if((hb|low)==0) return a; 90 t1=0; 91 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ 92 b *= t1; 93 a *= t1; 94 k -= 1022; 95 } else { /* scale a and b by 2^600 */ 96 ha += 0x25800000; /* a *= 2^600 */ 97 hb += 0x25800000; /* b *= 2^600 */ 98 k -= 600; 99 SET_HIGH_WORD(a,ha); 100 SET_HIGH_WORD(b,hb); 101 } 102 } 103 /* medium size a and b */ 104 w = a-b; 105 if (w>b) { 106 t1 = 0; 107 SET_HIGH_WORD(t1,ha); 108 t2 = a-t1; 109 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); 110 } else { 111 a = a+a; 112 y1 = 0; 113 SET_HIGH_WORD(y1,hb); 114 y2 = b - y1; 115 t1 = 0; 116 SET_HIGH_WORD(t1,ha+0x00100000); 117 t2 = a - t1; 118 w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); 119 } 120 if(k!=0) { 121 u_int32_t high; 122 t1 = 1.0; 123 GET_HIGH_WORD(high,t1); 124 SET_HIGH_WORD(t1,high+(k<<20)); 125 return t1*w; 126 } else return w; 127 } 128 129 #if LDBL_MANT_DIG == 53 130 __weak_reference(hypot, hypotl); 131 #endif 132