https://gcc.gnu.org/bugzilla/show_bug.cgi?id=83800
Bug ID: 83800
Summary: [libquadmath] M_SQRT2q & sqrtq(2.0Q) off by one ULP ?
Product: gcc
Version: 7.2.0
Status: UNCONFIRMED
Severity: normal
Priority: P3
Component: c
Assignee: unassigned at gcc dot gnu.org
Reporter: sisyphus1 at optusnet dot com.au
Target Milestone: ---
Hi,
Why does quadmath.h define M_SQRT2q to be 1.4142135623730950488016887242096981Q
(0x1.6a09e667f3bcc908b2fb1366ea96p+0) when a closer approximation is
0x1.6a09e667f3bcc908b2fb1366ea95p+0 ?
If I've calculated it correctly:
0x1.6a.....96p+0 exceeds sqrt(2) by approx 9.84e-35.
0x1.6a.....95p+0 falls short of sqrt(2) by approx 9.42e-35, and is therefore
the nearest value.
And 0x1.6a.....95p+0 is the value that the MPFR library returns for sqrt(2) for
113-bit precision, rounded to nearest.
Is this a bug in gcc ? .... or are there mitigating factors to be considered ?
Note also that sqrtq(2.0Q) returns the "wrong" value of 0x1.6a.....96p+0.
In fact, it seems that sqrtq(x) returns a significand of 0x1.6a.....96p
whenever x is a power of 2 that has an irrational square root.
Cheers,
Rob
