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| author | Joseph Myers <joseph@codesourcery.com> | 2015-06-23 14:35:18 +0000 |
|---|---|---|
| committer | Joseph Myers <joseph@codesourcery.com> | 2015-06-23 14:35:18 +0000 |
| commit | b59549574efeeecf124de05c9183c120eaaa56f0 (patch) | |
| tree | ae18151390fc556d7ad3fa74246b032ce9dd6db8 /sysdeps/ieee754 | |
| parent | b57525f1a376149840f740a31535681c07152ba4 (diff) | |
| download | glibc-b59549574efeeecf124de05c9183c120eaaa56f0.zip glibc-b59549574efeeecf124de05c9183c120eaaa56f0.tar.gz glibc-b59549574efeeecf124de05c9183c120eaaa56f0.tar.bz2 | |
Fix exp2, exp2f spurious underflows (bug 18219).
The dbl-64 and flt-32 implementations of exp2 functions produce
spurious underflow exceptions. The underlying reason is the same in
both cases: the computation works as (2^a - 1)*2^b + 2^b for suitably
chosen a and b, where a has small magnitude so 2^a - 1 can be computed
with a low-degree polynomial approximation, and (2^a - 1)*2^b can
underflow even when the final result does not. This patch fixes this
by adjusting the threshold for when scaling is used to avoid
intermediate underflow so it works for any possible value of a where
the final result would not underflow.
Tested for x86_64 and x86.
[BZ #18219]
* sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Reduce
threshold on absolute value of exponent for which scaling is used.
* sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Likewise.
* math/auto-libm-test-in: Add more tests of exp2.
* math/auto-libm-test-out: Regenerated.
Diffstat (limited to 'sysdeps/ieee754')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_exp2.c | 4 | ||||
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_exp2f.c | 4 |
2 files changed, 6 insertions, 2 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_exp2.c b/sysdeps/ieee754/dbl-64/e_exp2.c index 948a756..30f0a8f 100644 --- a/sysdeps/ieee754/dbl-64/e_exp2.c +++ b/sysdeps/ieee754/dbl-64/e_exp2.c @@ -96,7 +96,9 @@ __ieee754_exp2 (double x) /* 3. Compute ex2 = 2^(t/512+e+ex). */ ex2_u.d = exp2_accuratetable[tval & 511]; tval >>= 9; - unsafe = abs (tval) >= -DBL_MIN_EXP - 1; + /* x2 is an integer multiple of 2^-54; avoid intermediate + underflow from the calculation of x22 * x. */ + unsafe = abs (tval) >= -DBL_MIN_EXP - 56; ex2_u.ieee.exponent += tval >> unsafe; scale_u.d = 1.0; scale_u.ieee.exponent += tval - (tval >> unsafe); diff --git a/sysdeps/ieee754/flt-32/e_exp2f.c b/sysdeps/ieee754/flt-32/e_exp2f.c index f3e3a8e..0b75a7e 100644 --- a/sysdeps/ieee754/flt-32/e_exp2f.c +++ b/sysdeps/ieee754/flt-32/e_exp2f.c @@ -89,7 +89,9 @@ __ieee754_exp2f (float x) /* 3. Compute ex2 = 2^(t/255+e+ex). */ ex2_u.f = __exp2f_atable[tval & 255]; tval >>= 8; - unsafe = abs(tval) >= -FLT_MIN_EXP - 1; + /* x2 is an integer multiple of 2^-30; avoid intermediate + underflow from the calculation of x22 * x. */ + unsafe = abs(tval) >= -FLT_MIN_EXP - 32; ex2_u.ieee.exponent += tval >> unsafe; scale_u.f = 1.0; scale_u.ieee.exponent += tval - (tval >> unsafe); |