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- /* Compute x^2 + y^2 - 1, without large cancellation error.
- Copyright (C) 2012-2018 Free Software Foundation, Inc.
- This file is part of the GNU C Library.
- The GNU C Library is free software; you can redistribute it and/or
- modify it under the terms of the GNU Lesser General Public
- License as published by the Free Software Foundation; either
- version 2.1 of the License, or (at your option) any later version.
- The GNU C Library is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- Lesser General Public License for more details.
- You should have received a copy of the GNU Lesser General Public
- License along with the GNU C Library; if not, see
- <http://www.gnu.org/licenses/>. */
- #include "quadmath-imp.h"
- /* Calculate X + Y exactly and store the result in *HI + *LO. It is
- given that |X| >= |Y| and the values are small enough that no
- overflow occurs. */
- static inline void
- add_split (__float128 *hi, __float128 *lo, __float128 x, __float128 y)
- {
- /* Apply Dekker's algorithm. */
- *hi = x + y;
- *lo = (x - *hi) + y;
- }
- /* Compare absolute values of floating-point values pointed to by P
- and Q for qsort. */
- static int
- compare (const void *p, const void *q)
- {
- __float128 pld = fabsq (*(const __float128 *) p);
- __float128 qld = fabsq (*(const __float128 *) q);
- if (pld < qld)
- return -1;
- else if (pld == qld)
- return 0;
- else
- return 1;
- }
- /* Return X^2 + Y^2 - 1, computed without large cancellation error.
- It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >=
- 0.5. */
- __float128
- __quadmath_x2y2m1q (__float128 x, __float128 y)
- {
- __float128 vals[5];
- SET_RESTORE_ROUNDF128 (FE_TONEAREST);
- mul_splitq (&vals[1], &vals[0], x, x);
- mul_splitq (&vals[3], &vals[2], y, y);
- vals[4] = -1;
- qsort (vals, 5, sizeof (__float128), compare);
- /* Add up the values so that each element of VALS has absolute value
- at most equal to the last set bit of the next nonzero
- element. */
- for (size_t i = 0; i <= 3; i++)
- {
- add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]);
- qsort (vals + i + 1, 4 - i, sizeof (__float128), compare);
- }
- /* Now any error from this addition will be small. */
- return vals[4] + vals[3] + vals[2] + vals[1] + vals[0];
- }
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