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Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c | 128 |
1 files changed, 128 insertions, 0 deletions
diff --git a/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c b/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c new file mode 100644 index 0000000000..4379b68c3c --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c @@ -0,0 +1,128 @@ +/* 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 <math.h> +#include <math_private.h> +#include <float.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; +} + +/* 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 (double *hi, double *lo, double x, double y) +{ +#ifdef __FP_FAST_FMA + /* Fast built-in fused multiply-add. */ + *hi = x * y; + *lo = __builtin_fma (x, y, -*hi); +#elif defined FP_FAST_FMA + /* Fast library fused multiply-add, compiler before GCC 4.6. */ + *hi = x * y; + *lo = __fma (x, y, -*hi); +#else + /* Apply Dekker's algorithm. */ + *hi = x * y; +# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1) + double x1 = x * C; + double y1 = y * C; +# undef C + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + double x2 = x - x1; + double y2 = y - y1; + *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; +#endif +} + +/* 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 either X >= + 0.75 or Y >= 0.5. */ + +long double +__x2y2m1l (long double x, long double y) +{ + double vals[12]; + SET_RESTORE_ROUND (FE_TONEAREST); + union ibm_extended_long_double xu, yu; + xu.d = x; + yu.d = y; + if (fabs (xu.dd[1]) < 0x1p-500) + xu.dd[1] = 0.0; + if (fabs (yu.dd[1]) < 0x1p-500) + yu.dd[1] = 0.0; + mul_split (&vals[1], &vals[0], xu.dd[0], xu.dd[0]); + mul_split (&vals[3], &vals[2], xu.dd[0], xu.dd[1]); + vals[2] *= 2.0; + vals[3] *= 2.0; + mul_split (&vals[5], &vals[4], xu.dd[1], xu.dd[1]); + mul_split (&vals[7], &vals[6], yu.dd[0], yu.dd[0]); + mul_split (&vals[9], &vals[8], yu.dd[0], yu.dd[1]); + vals[8] *= 2.0; + vals[9] *= 2.0; + mul_split (&vals[11], &vals[10], yu.dd[1], yu.dd[1]); + if (xu.dd[0] >= 0.75) + vals[1] -= 1.0; + else + { + vals[1] -= 0.5; + vals[7] -= 0.5; + } + qsort (vals, 12, 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 <= 10; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 11 - i, sizeof (double), compare); + } + /* Now any error from this addition will be small. */ + long double retval = (long double) vals[11]; + for (size_t i = 10; i != (size_t) -1; i--) + retval += (long double) vals[i]; + return retval; +} |