| /* 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]; |

| } |