diff options
Diffstat (limited to 'gcc-4.9/libquadmath/math/x2y2m1q.c')
-rw-r--r-- | gcc-4.9/libquadmath/math/x2y2m1q.c | 93 |
1 files changed, 93 insertions, 0 deletions
diff --git a/gcc-4.9/libquadmath/math/x2y2m1q.c b/gcc-4.9/libquadmath/math/x2y2m1q.c new file mode 100644 index 000000000..90bbc2f60 --- /dev/null +++ b/gcc-4.9/libquadmath/math/x2y2m1q.c @@ -0,0 +1,93 @@ +/* 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]; +} |