/* Compute x^2 + y^2 - 1, without large cancellation error. | |

Copyright (C) 2012 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" | |

#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 (__float128 *hi, __float128 *lo, __float128 x, __float128 y) | |

{ | |

/* Apply Dekker's algorithm. */ | |

*hi = x + y; | |

*lo = (x - *hi) + y; | |

} | |

/* Calculate X * Y exactly and store the result in *HI + *LO. It is | |

given that the values are small enough that no overflow occurs and | |

large enough (or zero) that no underflow occurs. */ | |

static inline void | |

mul_split (__float128 *hi, __float128 *lo, __float128 x, __float128 y) | |

{ | |

/* Fast built-in fused multiply-add. */ | |

*hi = x * y; | |

*lo = fmaq (x, y, -*hi); | |

} | |

/* 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 either X >= | |

0.75 or Y >= 0.5. */ | |

__float128 | |

__quadmath_x2y2m1q (__float128 x, __float128 y) | |

{ | |

__float128 vals[4]; | |

size_t i; | |

/* FIXME: SET_RESTORE_ROUNDL (FE_TONEAREST); */ | |

mul_split (&vals[1], &vals[0], x, x); | |

mul_split (&vals[3], &vals[2], y, y); | |

if (x >= 0.75Q) | |

vals[1] -= 1.0Q; | |

else | |

{ | |

vals[1] -= 0.5Q; | |

vals[3] -= 0.5Q; | |

} | |

qsort (vals, 4, 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 (i = 0; i <= 2; i++) | |

{ | |

add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); | |

qsort (vals + i + 1, 3 - i, sizeof (__float128), compare); | |

} | |

/* Now any error from this addition will be small. */ | |

return vals[3] + vals[2] + vals[1] + vals[0]; | |

} |