111
|
1 /* Compute x^2 + y^2 - 1, without large cancellation error.
|
145
|
2 Copyright (C) 2012-2018 Free Software Foundation, Inc.
|
111
|
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
|
|
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
|
|
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.
|
145
|
50 It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >=
|
|
51 0.5. */
|
111
|
52
|
|
53 __float128
|
|
54 __quadmath_x2y2m1q (__float128 x, __float128 y)
|
|
55 {
|
145
|
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);
|
111
|
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. */
|
145
|
65 for (size_t i = 0; i <= 3; i++)
|
111
|
66 {
|
|
67 add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]);
|
145
|
68 qsort (vals + i + 1, 4 - i, sizeof (__float128), compare);
|
111
|
69 }
|
|
70 /* Now any error from this addition will be small. */
|
145
|
71 return vals[4] + vals[3] + vals[2] + vals[1] + vals[0];
|
111
|
72 }
|