| /* 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 <math.h> |
| #include <math_private.h> |
| #include <mul_splitl.h> |
| #include <stdlib.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 (long double *hi, long double *lo, long double x, long double 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) |
| { |
| long double pld = fabsl (*(const long double *) p); |
| long double qld = fabsl (*(const long double *) 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. */ |
| |
| long double |
| __x2y2m1l (long double x, long double y) |
| { |
| long double vals[5]; |
| SET_RESTORE_ROUNDL (FE_TONEAREST); |
| mul_splitl (&vals[1], &vals[0], x, x); |
| mul_splitl (&vals[3], &vals[2], y, y); |
| vals[4] = -1.0L; |
| qsort (vals, 5, sizeof (long double), 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 (long double), compare); |
| } |
| /* Now any error from this addition will be small. */ |
| return vals[4] + vals[3] + vals[2] + vals[1] + vals[0]; |
| } |