diff options
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c')
-rw-r--r-- | REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c | 75 |
1 files changed, 75 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c b/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c new file mode 100644 index 0000000000..70d33de74c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c @@ -0,0 +1,75 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012-2017 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 <math.h> +#include <math_private.h> +#include <mul_split.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 (double *hi, double *lo, double x, 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) +{ + double pd = fabs (*(const double *) p); + double qd = fabs (*(const double *) q); + if (pd < qd) + return -1; + else if (pd == qd) + 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. */ + +double +__x2y2m1 (double x, double y) +{ + double vals[5]; + SET_RESTORE_ROUND (FE_TONEAREST); + mul_split (&vals[1], &vals[0], x, x); + mul_split (&vals[3], &vals[2], y, y); + vals[4] = -1.0; + qsort (vals, 5, sizeof (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 (double), compare); + } + /* Now any error from this addition will be small. */ + return vals[4] + vals[3] + vals[2] + vals[1] + vals[0]; +} |