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.
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.
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.
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/>. */
20 #include <math_private.h>
21 #include <mul_splitl.h>
24 /* Calculate X + Y exactly and store the result in *HI + *LO. It is
25 given that |X| >= |Y| and the values are small enough that no
29 add_split (long double *hi
, long double *lo
, long double x
, long double y
)
31 /* Apply Dekker's algorithm. */
36 /* Compare absolute values of floating-point values pointed to by P
40 compare (const void *p
, const void *q
)
42 long double pld
= fabsl (*(const long double *) p
);
43 long double qld
= fabsl (*(const long double *) q
);
52 /* Return X^2 + Y^2 - 1, computed without large cancellation error.
53 It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >=
57 __x2y2m1l (long double x
, long double y
)
60 SET_RESTORE_ROUNDL (FE_TONEAREST
);
61 mul_splitl (&vals
[1], &vals
[0], x
, x
);
62 mul_splitl (&vals
[3], &vals
[2], y
, y
);
64 qsort (vals
, 5, sizeof (long double), compare
);
65 /* Add up the values so that each element of VALS has absolute value
66 at most equal to the last set bit of the next nonzero
68 for (size_t i
= 0; i
<= 3; i
++)
70 add_split (&vals
[i
+ 1], &vals
[i
], vals
[i
+ 1], vals
[i
]);
71 qsort (vals
+ i
+ 1, 4 - i
, sizeof (long double), compare
);
73 /* Now any error from this addition will be small. */
74 return vals
[4] + vals
[3] + vals
[2] + vals
[1] + vals
[0];