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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 . */ #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]; }