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author | Szabolcs Nagy <szabolcs.nagy@arm.com> | 2018-07-03 13:05:31 +0100 |
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committer | Corinna Vinschen <corinna@vinschen.de> | 2018-07-06 10:29:01 +0200 |
commit | 2805b07fa1f54ef001c2ce78618e8efc87155232 (patch) | |
tree | 1d54b22c61463070bd3ee28fa9014c19962685e4 /newlib/libm | |
parent | 6a85e1a4e5a01dec3b423eb172b3ad9155487e75 (diff) | |
download | newlib-2805b07fa1f54ef001c2ce78618e8efc87155232.zip newlib-2805b07fa1f54ef001c2ce78618e8efc87155232.tar.gz newlib-2805b07fa1f54ef001c2ce78618e8efc87155232.tar.bz2 |
Fix large ulp error in pow without fma very near 1.0
The !HAVE_FAST_FMA code path split r = z/c - 1 into r = rhi + rlo such
that when z = 1-tiny and c = 1 then rlo and rhi could have much larger
magnitude than r which later caused large rounding errors.
So do a nearest rounding instead of truncation at the split.
In newlib with default settings this was observable on some arm targets
that enable the new math code but has no fma.
Diffstat (limited to 'newlib/libm')
-rw-r--r-- | newlib/libm/common/pow.c | 6 |
1 files changed, 4 insertions, 2 deletions
diff --git a/newlib/libm/common/pow.c b/newlib/libm/common/pow.c index 11964e3..a5504e5 100644 --- a/newlib/libm/common/pow.c +++ b/newlib/libm/common/pow.c @@ -79,11 +79,13 @@ log_inline (uint64_t ix, double_t *tail) logc = T[i].logc; logctail = T[i].logctail; - /* r = z/c - 1, arranged to be exact. */ + /* Note: 1/c is j/N or j/N/2 where j is an integer in [N,2N) and + |z/c - 1| < 1/N, so r = z/c - 1 is exactly representible. */ #if HAVE_FAST_FMA r = fma (z, invc, -1.0); #else - double_t zhi = asdouble (iz & (-1ULL << 32)); + /* Split z such that rhi, rlo and rhi*rhi are exact and |rlo| <= |r|. */ + double_t zhi = asdouble ((iz + (1ULL << 31)) & (-1ULL << 32)); double_t zlo = z - zhi; double_t rhi = zhi * invc - 1.0; double_t rlo = zlo * invc; |