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. 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 "quadmath-imp.h" 20 21/* Calculate X + Y exactly and store the result in *HI + *LO. It is 22 given that |X| >= |Y| and the values are small enough that no 23 overflow occurs. */ 24 25static inline void 26add_split (__float128 *hi, __float128 *lo, __float128 x, __float128 y) 27{ 28 /* Apply Dekker's algorithm. */ 29 *hi = x + y; 30 *lo = (x - *hi) + y; 31} 32 33/* Compare absolute values of floating-point values pointed to by P 34 and Q for qsort. */ 35 36static int 37compare (const void *p, const void *q) 38{ 39 __float128 pld = fabsq (*(const __float128 *) p); 40 __float128 qld = fabsq (*(const __float128 *) q); 41 if (pld < qld) 42 return -1; 43 else if (pld == qld) 44 return 0; 45 else 46 return 1; 47} 48 49/* Return X^2 + Y^2 - 1, computed without large cancellation error. 50 It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= 51 0.5. */ 52 53__float128 54__quadmath_x2y2m1q (__float128 x, __float128 y) 55{ 56 __float128 vals[5]; 57 SET_RESTORE_ROUNDF128 (FE_TONEAREST); 58 mul_splitq (&vals[1], &vals[0], x, x); 59 mul_splitq (&vals[3], &vals[2], y, y); 60 vals[4] = -1; 61 qsort (vals, 5, sizeof (__float128), compare); 62 /* Add up the values so that each element of VALS has absolute value 63 at most equal to the last set bit of the next nonzero 64 element. */ 65 for (size_t i = 0; i <= 3; i++) 66 { 67 add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); 68 qsort (vals + i + 1, 4 - i, sizeof (__float128), compare); 69 } 70 /* Now any error from this addition will be small. */ 71 return vals[4] + vals[3] + vals[2] + vals[1] + vals[0]; 72} 73