From b59549574efeeecf124de05c9183c120eaaa56f0 Mon Sep 17 00:00:00 2001 From: Joseph Myers Date: Tue, 23 Jun 2015 14:35:18 +0000 Subject: 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. --- sysdeps/ieee754/dbl-64/e_exp2.c | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) (limited to 'sysdeps/ieee754/dbl-64') diff --git a/sysdeps/ieee754/dbl-64/e_exp2.c b/sysdeps/ieee754/dbl-64/e_exp2.c index 948a756df7..30f0a8f529 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); -- cgit 1.4.1