]>
Commit | Line | Data |
---|---|---|
e409716d | 1 | /* e_hypotl.c -- long double version of e_hypot.c. |
2 | * Conversion to long double by Jakub Jelinek, jakub@redhat.com. | |
3 | */ | |
4 | ||
87969c8c | 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 | ||
87969c8c | 16 | /* hypotq(x,y) |
17 | * | |
18 | * Method : | |
19 | * If (assume round-to-nearest) z=x*x+y*y | |
e409716d | 20 | * has error less than sqrtq(2)/2 ulp, than |
21 | * sqrtq(z) has error less than 1 ulp (exercise). | |
87969c8c | 22 | * |
e409716d | 23 | * So, compute sqrtq(x*x+y*y) with some care as |
87969c8c | 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: | |
e409716d | 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. | |
87969c8c | 42 | * |
43 | * Accuracy: | |
e409716d | 44 | * hypotl(x,y) returns sqrtq(x^2+y^2) with error less |
45 | * than 1 ulps (units in the last place) | |
87969c8c | 46 | */ |
47 | ||
48 | #include "quadmath-imp.h" | |
49 | ||
50 | __float128 | |
e409716d | 51 | hypotq(__float128 x, __float128 y) |
87969c8c | 52 | { |
e409716d | 53 | __float128 a,b,t1,t2,y1,y2,w; |
54 | int64_t j,k,ha,hb; | |
87969c8c | 55 | |
e409716d | 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 | } | |
87969c8c | 112 | /* medium size a and b */ |
e409716d | 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; | |
87969c8c | 138 | } |