1 /* Compute x^2 + y^2 - 1, without large cancellation error.
2 Copyright (C) 2012-2018 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <http://www.gnu.org/licenses/>. */
18
19 #include "quadmath-imp.h"
20
21 /* Calculate X + Y exactly and store the result in *HI + *LO. It is
22 given that |X| >= |Y| and the values are small enough that no
23 overflow occurs. */
24
25 static inline void
add_split(__float128 * hi,__float128 * lo,__float128 x,__float128 y)26 add_split (__float128 *hi, __float128 *lo, __float128 x, __float128 y)
27 {
28 /* Apply Dekker's algorithm. */
29 *hi = x + y;
30 *lo = (x - *hi) + y;
31 }
32
33 /* Compare absolute values of floating-point values pointed to by P
34 and Q for qsort. */
35
36 static int
compare(const void * p,const void * q)37 compare (const void *p, const void *q)
38 {
39 __float128 pld = fabsq (*(const __float128 *) p);
40 __float128 qld = fabsq (*(const __float128 *) q);
41 if (pld < qld)
42 return -1;
43 else if (pld == qld)
44 return 0;
45 else
46 return 1;
47 }
48
49 /* Return X^2 + Y^2 - 1, computed without large cancellation error.
50 It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >=
51 0.5. */
52
53 __float128
__quadmath_x2y2m1q(__float128 x,__float128 y)54 __quadmath_x2y2m1q (__float128 x, __float128 y)
55 {
56 __float128 vals[5];
57 SET_RESTORE_ROUNDF128 (FE_TONEAREST);
58 mul_splitq (&vals[1], &vals[0], x, x);
59 mul_splitq (&vals[3], &vals[2], y, y);
60 vals[4] = -1;
61 qsort (vals, 5, sizeof (__float128), compare);
62 /* Add up the values so that each element of VALS has absolute value
63 at most equal to the last set bit of the next nonzero
64 element. */
65 for (size_t i = 0; i <= 3; i++)
66 {
67 add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]);
68 qsort (vals + i + 1, 4 - i, sizeof (__float128), compare);
69 }
70 /* Now any error from this addition will be small. */
71 return vals[4] + vals[3] + vals[2] + vals[1] + vals[0];
72 }
73