mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-15 09:30:06 +00:00
77 lines
2.4 KiB
C
77 lines
2.4 KiB
C
/* Compute x^2 + y^2 - 1, without large cancellation error.
|
|
Copyright (C) 2012-2020 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
|
|
<https://www.gnu.org/licenses/>. */
|
|
|
|
#include <math.h>
|
|
#include <math_private.h>
|
|
#include <fenv_private.h>
|
|
#include <mul_splitl.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 (long double *hi, long double *lo, long double x, long double 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)
|
|
{
|
|
long double pld = fabsl (*(const long double *) p);
|
|
long double qld = fabsl (*(const long double *) 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. */
|
|
|
|
long double
|
|
__x2y2m1l (long double x, long double y)
|
|
{
|
|
long double vals[5];
|
|
SET_RESTORE_ROUNDL (FE_TONEAREST);
|
|
mul_splitl (&vals[1], &vals[0], x, x);
|
|
mul_splitl (&vals[3], &vals[2], y, y);
|
|
vals[4] = -1.0L;
|
|
qsort (vals, 5, sizeof (long double), 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 (long double), compare);
|
|
}
|
|
/* Now any error from this addition will be small. */
|
|
return vals[4] + vals[3] + vals[2] + vals[1] + vals[0];
|
|
}
|