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d032e0d2 | 1 | /* Compute x^2 + y^2 - 1, without large cancellation error. |
04277e02 | 2 | Copyright (C) 2012-2019 Free Software Foundation, Inc. |
d032e0d2 JM |
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 <math.h> | |
20 | #include <math_private.h> | |
70e2ba33 | 21 | #include <fenv_private.h> |
4482ff22 | 22 | #include <mul_splitl.h> |
d032e0d2 JM |
23 | #include <stdlib.h> |
24 | ||
4482ff22 | 25 | |
d032e0d2 JM |
26 | /* Calculate X + Y exactly and store the result in *HI + *LO. It is |
27 | given that |X| >= |Y| and the values are small enough that no | |
28 | overflow occurs. */ | |
29 | ||
30 | static inline void | |
15089e04 | 31 | add_split (_Float128 *hi, _Float128 *lo, _Float128 x, _Float128 y) |
d032e0d2 JM |
32 | { |
33 | /* Apply Dekker's algorithm. */ | |
34 | *hi = x + y; | |
35 | *lo = (x - *hi) + y; | |
36 | } | |
37 | ||
d032e0d2 JM |
38 | /* Compare absolute values of floating-point values pointed to by P |
39 | and Q for qsort. */ | |
40 | ||
41 | static int | |
42 | compare (const void *p, const void *q) | |
43 | { | |
15089e04 PM |
44 | _Float128 pld = fabsl (*(const _Float128 *) p); |
45 | _Float128 qld = fabsl (*(const _Float128 *) q); | |
d032e0d2 JM |
46 | if (pld < qld) |
47 | return -1; | |
48 | else if (pld == qld) | |
49 | return 0; | |
50 | else | |
51 | return 1; | |
52 | } | |
53 | ||
54 | /* Return X^2 + Y^2 - 1, computed without large cancellation error. | |
a5721ebc JM |
55 | It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= |
56 | 0.5. */ | |
d032e0d2 | 57 | |
15089e04 PM |
58 | _Float128 |
59 | __x2y2m1l (_Float128 x, _Float128 y) | |
d032e0d2 | 60 | { |
15089e04 | 61 | _Float128 vals[5]; |
d032e0d2 | 62 | SET_RESTORE_ROUNDL (FE_TONEAREST); |
4482ff22 PM |
63 | mul_splitl (&vals[1], &vals[0], x, x); |
64 | mul_splitl (&vals[3], &vals[2], y, y); | |
02bbfb41 | 65 | vals[4] = -1; |
15089e04 | 66 | qsort (vals, 5, sizeof (_Float128), compare); |
d032e0d2 JM |
67 | /* Add up the values so that each element of VALS has absolute value |
68 | at most equal to the last set bit of the next nonzero | |
69 | element. */ | |
a5721ebc | 70 | for (size_t i = 0; i <= 3; i++) |
d032e0d2 JM |
71 | { |
72 | add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); | |
15089e04 | 73 | qsort (vals + i + 1, 4 - i, sizeof (_Float128), compare); |
d032e0d2 JM |
74 | } |
75 | /* Now any error from this addition will be small. */ | |
a5721ebc | 76 | return vals[4] + vals[3] + vals[2] + vals[1] + vals[0]; |
d032e0d2 | 77 | } |