libquadmath: Fix up THREEp96 constant in expq

Here is a cherry-pick from glibc [BZ #32411] fix.

As mentioned by the reporter in a pull request against gcc-mirror,
the THREEp96 constant in e_expl.c is incorrect, it is actually 0x3.p+94f128
rather than 0x3.p+96f128.

The algorithm uses that to compute the t2 integer (tval2), by whose
delta it adjusts the x+xl pair and then in the result uses the precomputed
exp value for that entry.
Using 0x3.p+94f128 rather than 0x3.p+96f128 results in tval2 sometimes
being one smaller, sometimes one larger than the desired value, thus can mean
the x+xl pair after adjustment will be larger in absolute value than it
should be.

DesWursters created a test program for this
https://github.com/DesWurstes/comparefloats
and his results were
total: 1135000000 not_equal: 4322 earlier_score: 674 later_score: 3648
I've modified this so with
https://sourceware.org/bugzilla/show_bug.cgi?id=32411#c3
so that it actually tests pseudo-random _Float128 values with range
(-16384.,16384) with strong bias on values larger than 0.0002 in absolute
value (so that tval1/tval2 aren't zero most of the time) and that gave
total: 10000000000 not_equal: 29861 earlier_score: 4606 later_score: 25255
So, in both cases, in most cases the change doesn't result in any differences,
and in those rare cases where does, about 85% have smaller ulp than without
the patch.
Additionally I've tried
https://sourceware.org/bugzilla/show_bug.cgi?id=32411#c4
and in 2 billion iterations it didn't find any case where x+xl after the
adjustments without this change would be smaller in absolute value compared
to x+xl after the adjustments with this change.

2025-04-09  Jakub Jelinek  <jakub@redhat.com>

	* math/expq.c (C): Fix up THREEp96 constant.

diff --git a/libquadmath/math/expq.c b/libquadmath/math/expq.c
index 1aaad91c244622c93a54722c71d3623b8087ece3..171598824f124f45def25ddf119723ada6960467 100644 (file)
--- a/libquadmath/math/expq.c
+++ b/libquadmath/math/expq.c
@@ -74,7 +74,7 @@ static const __float128 C[] = {
 
 /* 3x2^96 */
 #define THREEp96 C[2]
- 59421121885698253195157962752.0Q,
+ 237684487542793012780631851008.0Q,
 
 /* 3x2^103 */
 #define THREEp103 C[3]