1  /* Compute x^2 + y^2 - 1, without large cancellation error.
       2     Copyright (C) 2012-2023 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     <https://www.gnu.org/licenses/>.  */
      18  
      19  #include <math.h>
      20  #include <math_private.h>
      21  #include <float.h>
      22  
      23  /* Return X^2 + Y^2 - 1, computed without large cancellation error.
      24     It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >=
      25     0.5.  */
      26  
      27  float
      28  __x2y2m1f (float x, float y)
      29  {
      30    double dx = x, dy = y;
      31    return (float) ((dx - 1) * (dx + 1) + dy * dy);
      32  }