1 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, 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 #include <sys/cdefs.h> 14 /* hypot(x,y) 15 * 16 * Method : 17 * If (assume round-to-nearest) z=x*x+y*y 18 * has error less than sqrt(2)/2 ulp, than 19 * sqrt(z) has error less than 1 ulp (exercise). 20 * 21 * So, compute sqrt(x*x+y*y) with some care as 22 * follows to get the error below 1 ulp: 23 * 24 * Assume x>y>0; 25 * (if possible, set rounding to round-to-nearest) 26 * 1. if x > 2y use 27 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y 28 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else 29 * 2. if x <= 2y use 30 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) 31 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 32 * y1= y with lower 32 bits chopped, y2 = y-y1. 33 * 34 * NOTE: scaling may be necessary if some argument is too 35 * large or too tiny 36 * 37 * Special cases: 38 * hypot(x,y) is INF if x or y is +INF or -INF; else 39 * hypot(x,y) is NAN if x or y is NAN. 40 * 41 * Accuracy: 42 * hypot(x,y) returns sqrt(x^2+y^2) with error less 43 * than 1 ulps (units in the last place) 44 */ 45 46 #include <float.h> 47 48 #include "math.h" 49 #include "math_private.h" 50 51 double 52 hypot(double x, double y) 53 { 54 double a,b,t1,t2,y1,y2,w; 55 int32_t j,k,ha,hb; 56 57 GET_HIGH_WORD(ha,x); 58 ha &= 0x7fffffff; 59 GET_HIGH_WORD(hb,y); 60 hb &= 0x7fffffff; 61 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 62 a = fabs(a); 63 b = fabs(b); 64 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ 65 k=0; 66 if(ha > 0x5f300000) { /* a>2**500 */ 67 if(ha >= 0x7ff00000) { /* Inf or NaN */ 68 u_int32_t low; 69 /* Use original arg order iff result is NaN; quieten sNaNs. */ 70 w = fabsl(x+0.0L)-fabs(y+0); 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 = 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 = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); 116 } 117 if(k!=0) { 118 t1 = 0.0; 119 SET_HIGH_WORD(t1,(1023+k)<<20); 120 return t1*w; 121 } else return w; 122 } 123 124 #if LDBL_MANT_DIG == 53 125 __weak_reference(hypot, hypotl); 126 #endif 127