1 /* e_hypotl.c -- long double version of e_hypot.c. 2 * Conversion to long double by Jakub Jelinek, jakub@redhat.com. 3 */ 4 5 /* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16 /* hypotq(x,y) 17 * 18 * Method : 19 * If (assume round-to-nearest) z=x*x+y*y 20 * has error less than sqrtq(2)/2 ulp, than 21 * sqrtq(z) has error less than 1 ulp (exercise). 22 * 23 * So, compute sqrtq(x*x+y*y) with some care as 24 * follows to get the error below 1 ulp: 25 * 26 * Assume x>y>0; 27 * (if possible, set rounding to round-to-nearest) 28 * 1. if x > 2y use 29 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y 30 * where x1 = x with lower 64 bits cleared, x2 = x-x1; else 31 * 2. if x <= 2y use 32 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) 33 * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, 34 * y1= y with lower 64 bits chopped, y2 = y-y1. 35 * 36 * NOTE: scaling may be necessary if some argument is too 37 * large or too tiny 38 * 39 * Special cases: 40 * hypotl(x,y) is INF if x or y is +INF or -INF; else 41 * hypotl(x,y) is NAN if x or y is NAN. 42 * 43 * Accuracy: 44 * hypotl(x,y) returns sqrtq(x^2+y^2) with error less 45 * than 1 ulps (units in the last place) 46 */ 47 48 #include "quadmath-imp.h" 49 50 __float128 51 hypotq(__float128 x, __float128 y) 52 { 53 __float128 a,b,t1,t2,y1,y2,w; 54 int64_t j,k,ha,hb; 55 56 GET_FLT128_MSW64(ha,x); 57 ha &= 0x7fffffffffffffffLL; 58 GET_FLT128_MSW64(hb,y); 59 hb &= 0x7fffffffffffffffLL; 60 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 61 SET_FLT128_MSW64(a,ha); /* a <- |a| */ 62 SET_FLT128_MSW64(b,hb); /* b <- |b| */ 63 if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */ 64 k=0; 65 if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */ 66 if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */ 67 uint64_t low; 68 w = a+b; /* for sNaN */ 69 if (issignalingq (a) || issignalingq (b)) 70 return w; 71 GET_FLT128_LSW64(low,a); 72 if(((ha&0xffffffffffffLL)|low)==0) w = a; 73 GET_FLT128_LSW64(low,b); 74 if(((hb^0x7fff000000000000LL)|low)==0) w = b; 75 return w; 76 } 77 /* scale a and b by 2**-9600 */ 78 ha -= 0x2580000000000000LL; 79 hb -= 0x2580000000000000LL; k += 9600; 80 SET_FLT128_MSW64(a,ha); 81 SET_FLT128_MSW64(b,hb); 82 } 83 if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */ 84 if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */ 85 uint64_t low; 86 GET_FLT128_LSW64(low,b); 87 if((hb|low)==0) return a; 88 t1=0; 89 SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */ 90 b *= t1; 91 a *= t1; 92 k -= 16382; 93 GET_FLT128_MSW64 (ha, a); 94 GET_FLT128_MSW64 (hb, b); 95 if (hb > ha) 96 { 97 t1 = a; 98 a = b; 99 b = t1; 100 j = ha; 101 ha = hb; 102 hb = j; 103 } 104 } else { /* scale a and b by 2^9600 */ 105 ha += 0x2580000000000000LL; /* a *= 2^9600 */ 106 hb += 0x2580000000000000LL; /* b *= 2^9600 */ 107 k -= 9600; 108 SET_FLT128_MSW64(a,ha); 109 SET_FLT128_MSW64(b,hb); 110 } 111 } 112 /* medium size a and b */ 113 w = a-b; 114 if (w>b) { 115 t1 = 0; 116 SET_FLT128_MSW64(t1,ha); 117 t2 = a-t1; 118 w = sqrtq(t1*t1-(b*(-b)-t2*(a+t1))); 119 } else { 120 a = a+a; 121 y1 = 0; 122 SET_FLT128_MSW64(y1,hb); 123 y2 = b - y1; 124 t1 = 0; 125 SET_FLT128_MSW64(t1,ha+0x0001000000000000LL); 126 t2 = a - t1; 127 w = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b))); 128 } 129 if(k!=0) { 130 uint64_t high; 131 t1 = 1; 132 GET_FLT128_MSW64(high,t1); 133 SET_FLT128_MSW64(t1,high+(k<<48)); 134 w *= t1; 135 math_check_force_underflow_nonneg (w); 136 return w; 137 } else return w; 138 } 139