1 2 /* @(#)e_hypot.c 5.1 93/09/24 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunPro, 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 /* __ieee754_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 "fdlibm.h" 47 48 #ifndef _DOUBLE_IS_32BITS 49 50 #ifdef __STDC__ __ieee754_hypot(double x,double y)51 double __ieee754_hypot(double x, double y) 52 #else 53 double __ieee754_hypot(x,y) 54 double x, y; 55 #endif 56 { 57 double a=x,b=y,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 SET_HIGH_WORD(a,ha); /* a <- |a| */ 66 SET_HIGH_WORD(b,hb); /* b <- |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 __uint32_t low; 72 w = a+b; /* for sNaN */ 73 GET_LOW_WORD(low,a); 74 if(((ha&0xfffff)|low)==0) w = a; 75 GET_LOW_WORD(low,b); 76 if(((hb^0x7ff00000)|low)==0) w = b; 77 return w; 78 } 79 /* scale a and b by 2**-600 */ 80 ha -= 0x25800000; hb -= 0x25800000; k += 600; 81 SET_HIGH_WORD(a,ha); 82 SET_HIGH_WORD(b,hb); 83 } 84 if(hb < 0x20b00000) { /* b < 2**-500 */ 85 if(hb <= 0x000fffff) { /* subnormal b or 0 */ 86 __uint32_t low; 87 GET_LOW_WORD(low,b); 88 if((hb|low)==0) return a; 89 t1=0; 90 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ 91 b *= t1; 92 a *= t1; 93 k -= 1022; 94 } else { /* scale a and b by 2^600 */ 95 ha += 0x25800000; /* a *= 2^600 */ 96 hb += 0x25800000; /* b *= 2^600 */ 97 k -= 600; 98 SET_HIGH_WORD(a,ha); 99 SET_HIGH_WORD(b,hb); 100 } 101 } 102 /* medium size a and b */ 103 w = a-b; 104 if (w>b) { 105 t1 = 0; 106 SET_HIGH_WORD(t1,ha); 107 t2 = a-t1; 108 w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); 109 } else { 110 a = a+a; 111 y1 = 0; 112 SET_HIGH_WORD(y1,hb); 113 y2 = b - y1; 114 t1 = 0; 115 SET_HIGH_WORD(t1,ha+0x00100000); 116 t2 = a - t1; 117 w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); 118 } 119 if(k!=0) { 120 __uint32_t high; 121 t1 = 1.0; 122 GET_HIGH_WORD(high,t1); 123 SET_HIGH_WORD(t1,high+(k<<20)); 124 return t1*w; 125 } else return w; 126 } 127 128 #endif /* defined(_DOUBLE_IS_32BITS) */ 129