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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c | 93 |
1 files changed, 93 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c new file mode 100644 index 0000000000..0bdb9a1848 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c @@ -0,0 +1,93 @@ +/* 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. */ + +long double +__x2y2m1l (long double x, long double y) +{ + double vals[13]; + SET_RESTORE_ROUND (FE_TONEAREST); + union ibm_extended_long_double xu, yu; + xu.ld = x; + yu.ld = y; + if (fabs (xu.d[1].d) < 0x1p-500) + xu.d[1].d = 0.0; + if (fabs (yu.d[1].d) < 0x1p-500) + yu.d[1].d = 0.0; + mul_split (&vals[1], &vals[0], xu.d[0].d, xu.d[0].d); + mul_split (&vals[3], &vals[2], xu.d[0].d, xu.d[1].d); + vals[2] *= 2.0; + vals[3] *= 2.0; + mul_split (&vals[5], &vals[4], xu.d[1].d, xu.d[1].d); + mul_split (&vals[7], &vals[6], yu.d[0].d, yu.d[0].d); + mul_split (&vals[9], &vals[8], yu.d[0].d, yu.d[1].d); + vals[8] *= 2.0; + vals[9] *= 2.0; + mul_split (&vals[11], &vals[10], yu.d[1].d, yu.d[1].d); + vals[12] = -1.0; + qsort (vals, 13, 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 <= 11; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 12 - i, sizeof (double), compare); + } + /* Now any error from this addition will be small. */ + long double retval = (long double) vals[12]; + for (size_t i = 11; i != (size_t) -1; i--) + retval += (long double) vals[i]; + return retval; +} |