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.

My PR114623 change started using soft-fp.h and quad.h for the sqrtq implementation.
Unfortunately, that seems to fail building in some powerpc* configurations, where
TFmode isn't available.
quad.h has:
 #ifndef TFtype
 typedef float TFtype __attribute__ ((mode (TF)));
 #endif
and uses TFtype.  quad.h has:
 /* Define the complex type corresponding to __float128
    ("_Complex __float128" is not allowed) */
 #if (!defined(_ARCH_PPC)) || defined(__LONG_DOUBLE_IEEE128__)
 typedef _Complex float __attribute__((mode(TC))) __complex128;
 #else
 typedef _Complex float __attribute__((mode(KC))) __complex128;
 #endif
with the conditional and KCmode use added during porting of libquadmath
to powerpc*, so I've just defined TFtype for powerpc when __LONG_DOUBLE_IEEE128__
isn't defined; I could define it to float __attribute__ ((mode (KF))) but it
seemed easier to just define it to __float128 which should do the same thing.

2024-08-03  Jakub Jelinek  <jakub@redhat.com>

	PR target/116007
	* math/sqrtq.c (TFtype): For PowerPC without __LONG_DOUBLE_IEEE128__
	define to __float128 before including soft-fp.h and quad.h.

sqrt should be 0.5ulp precise, but the current implementation is less
precise than that.
The following patch uses the soft-fp code (like e.g. glibc for x86) for it
if possible.  I didn't want to replicate the libgcc infrastructure for
choosing the right sfp-machine.h, so the patch just uses a single generic
implementation.  As the code is used solely for the finite positive arguments,
it shouldn't generate NaNs (so the exact form of canonical QNaN/SNaN is
irrelevant), and sqrt for these shouldn't produce underflows/overflows either,
for < 1.0 arguments it always returns larger values than the argument and for
> 1.0 smaller values than the argument.

2024-04-09  Jakub Jelinek  <jakub@redhat.com>

	PR libquadmath/114623
	* sfp-machine.h: New file.
	* math/sqrtq.c: Include from libgcc/soft-fp also soft-fp.h and quad.h
	if possible.
	(USE_SOFT_FP): Define in that case.
	(sqrtq): Use soft-fp based implementation for the finite positive
	arguments if possible.

This patch extends update-quadmath.py to update fmaq from glibc.

The issue in that function was that quadmath-imp.h had a struct in a
union with mant_high and mant_low fields (up to 64-bit) whereas glibc
has mantissa0, mantissa1, mantissa2 and mantissa3 (up to 32-bit).  The
patch changes those fields to be the same as in glibc, moving printf /
strtod code that also uses those fields back to closer to the glibc
form.  This allows fmaq to be updated automatically from glibc (which
brings in at least one bug fix from glibc from 2015).

nanq was also using the mant_high field name, and had other issues: it
only partly initialized the union from which a value was returned, and
setting mant_high to 1 meant a signaling NaN would be returned rather
than a quiet NaN.  This patch fixes those issues as part of updating
it to use the changed interfaces (but does not fix the issue of not
using the argument).

Bootstrapped with no regressions on x86_64-pc-linux-gnu.

	* quadmath-imp.h (ieee854_float128): Use mantissa0, mantissa1,
	mantissa2 and mantissa3 fields instead of mant_high and mant_low.
	Change nan field to ieee_nan.
	* update-quadmath.py (update_sources): Also update fmaq.c.
	* math/nanq.c (nanq): Use ieee_nan field of union.
	Zero-initialize f.  Set quiet_nan field.
	* printf/flt1282mpn.c, printf/printf_fphex.c, strtod/mpn2flt128.c,
	strtod/strtoflt128.c: Use mantissa0, mantissa1, mantissa2 and
	mantissa3 fields.  Use ieee_nan and quiet_nan field.
	* math/fmaq.c: Regenerate from glibc sources with
	update-quadmath.py.

From-SVN: r265874

libquadmath sources are mostly based on glibc sources at present, but
derived from them by a manual editing / substitution process and with
subsequent manual merges.  The manual effort involved in merges means
they are sometimes incomplete and long-delayed.

Since libquadmath was first created, glibc's support for this format
has undergone significant changes so that it can also be used in glibc
to provide *f128 functions for the _Float128 type from TS 18661-3.
This makes it significantly easier to use it for libquadmath in a more
automated fashion, since glibc has a float128_private.h header that
redefines many identifiers as macros as needed for building *f128
functions.

Simply using float128_private.h directly in libquadmath, with
unmodified glibc sources except for changing function names in that
one header to be *q instead of *f128, would be tricky, given its
dependence on lots of other glibc-internal headers (whereas
libquadmath supports non-glibc systems), and also given how some libm
functions in glibc are built from type-generic templates using a
further set of macros rather than from separate function
implementations for each type.

So instead this patch adds a script update-quadmath.py to convert
glibc sources into libquadmath ones, and the script reads
float128_private.h to identify many of the substitutions it should
make.  quadmath-imp.h is updated with various new internal
definitions, taken from glibc as needed; this is the main place
expected to need updating manually when subsequent merges from glibc
are done using the script.  No attempt is made to make the script
output match the details of existing formatting, although the
differences are of a size that makes a rough comparison (ignoring
whitespace) possible.

Two new public interfaces are added to libquadmath, exp2q and
issignalingq, at a new QUADMATH_1.2 symbol version, since those
interfaces are used internally by some of the glibc sources being
merged into libquadmath; although there is a new symbol version, no
change however is made to the libtool version in the libtool-version
file.  Although there are various other interfaces now in glibc libm
but not in libquadmath, this patch does nothing to add such interfaces
(although adding many of them would in fact be easy to do, given the
script).

One internal file (not providing any public interfaces),
math/isinf_nsq.c, is removed, as no longer used by anything in
libquadmath after the merge.

Conditionals in individual source files on <fenv.h> availability or
features are moved into quadmath-imp.h (providing trivial macro
versions of the functions if real implementations aren't available),
to simplify the substitutions in individual source files.  Note
however that I haven't tested for any configurations lacking <fenv.h>,
so further changes could well be needed there.

Two files in libquadmath/math/ are based on glibc sources but not
updated in this patch: fmaq.c and rem_pio2q.c.  Both could be updated
after further changes to the script (and quadmath-imp.h as needed); in
the case of rem_pio2q.c, based on two separate glibc source files,
those separate files would naturally be split out into separate
libquadmath source files in the process (as done in this patch with
expq_table.h and tanq_kernel.c, where previously two glibc source
files had been merged into one libquadmath source file).  complex.c,
nanq.c and sqrtq.c are not based on glibc sources (though four of the
(trivial) functions in complex.c could readily be replaced by instead
using the four corresponding files from glibc, if desired).

libquadmath also has printf/ and strtod/ sources based on glibc, also
mostly not updated for a long time.  Again the script could no doubt
be made to generate those automatically, although that would be a
larger change (effectively some completely separate logic in the
script, not sharing much if anything with the existing code).

Bootstrapped with no regressions on x86_64-pc-linux-gnu.

	PR libquadmath/68686
	* Makefile.am: (libquadmath_la_SOURCES): Remove math/isinf_nsq.c.
	Add math/exp2q.c math/issignalingq.c math/lgammaq_neg.c
	math/lgammaq_product.c math/tanq_kernel.c math/tgammaq_product.c
	math/casinhq_kernel.c.
	* Makefile.in: Regenerate.
	* libquadmath.texi (exp2q, issignalingq): Document.
	* quadmath-imp.h: Include <errno.h>, <limits.h>, <stdbool.h> and
	<fenv.h>.
	(HIGH_ORDER_BIT_IS_SET_FOR_SNAN, FIX_FLT128_LONG_CONVERT_OVERFLOW)
	(FIX_FLT128_LLONG_CONVERT_OVERFLOW, __quadmath_kernel_tanq)
	(__quadmath_gamma_productq, __quadmath_gammaq_r)
	(__quadmath_lgamma_negq, __quadmath_lgamma_productq)
	(__quadmath_lgammaq_r, __quadmath_kernel_casinhq, mul_splitq)
	(math_check_force_underflow_complex, __glibc_likely)
	(__glibc_unlikely, struct rm_ctx, SET_RESTORE_ROUNDF128)
	(libc_feholdsetround_ctx, libc_feresetround_ctx): New.
	(feraiseexcept, fenv_t, feholdexcept, fesetround, feupdateenv)
	(fesetenv, fetestexcept, feclearexcept): Define if not supported
	through <fenv.h>.
	(__quadmath_isinf_nsq): Remove.
	* quadmath.h (exp2q, issignalingq): New.
	* quadmath.map (QUADMATH_1.2): New.
	* quadmath_weak.h (exp2q, issignalingq): New.
	* update-quadmath.py: New file.
	* math/isinf_nsq.c: Remove file.
	* math/casinhq_kernel.c, math/exp2q.c, math/expq_table.h,
	math/issignalingq.c, math/lgammaq_neg.c, math/lgammaq_product.c,
	math/tanq_kernel.c, math/tgammaq_product.c: New files.  Generated
	from glibc sources with update-quadmath.py.
	* math/acoshq.c, math/acosq.c, math/asinhq.c, math/asinq.c,
	math/atan2q.c, math/atanhq.c, math/atanq.c, math/cacoshq.c,
	math/cacosq.c, math/casinhq.c, math/casinq.c, math/catanhq.c,
	math/catanq.c, math/cbrtq.c, math/ccoshq.c, math/ceilq.c,
	math/cexpq.c, math/cimagq.c, math/clog10q.c, math/clogq.c,
	math/conjq.c, math/copysignq.c, math/coshq.c, math/cosq.c,
	math/cosq_kernel.c, math/cprojq.c, math/crealq.c, math/csinhq.c,
	math/csinq.c, math/csqrtq.c, math/ctanhq.c, math/ctanq.c,
	math/erfq.c, math/expm1q.c, math/expq.c, math/fabsq.c,
	math/fdimq.c, math/finiteq.c, math/floorq.c, math/fmaxq.c,
	math/fminq.c, math/fmodq.c, math/frexpq.c, math/hypotq.c,
	math/ilogbq.c, math/isinfq.c, math/isnanq.c, math/j0q.c,
	math/j1q.c, math/jnq.c, math/ldexpq.c, math/lgammaq.c,
	math/llrintq.c, math/llroundq.c, math/log10q.c, math/log1pq.c,
	math/log2q.c, math/logbq.c, math/logq.c, math/lrintq.c,
	math/lroundq.c, math/modfq.c, math/nearbyintq.c,
	math/nextafterq.c, math/powq.c, math/remainderq.c, math/remquoq.c,
	math/rintq.c, math/roundq.c, math/scalblnq.c, math/scalbnq.c,
	math/signbitq.c, math/sincos_table.c, math/sincosq.c,
	math/sincosq_kernel.c, math/sinhq.c, math/sinq.c,
	math/sinq_kernel.c, math/tanhq.c, math/tanq.c, math/tgammaq.c,
	math/truncq.c, math/x2y2m1q.c: Regenerate from glibc sources with
	update-quadmath.py.

From-SVN: r265822

2017-09-01  Michael Meissner  <meissner@linux.vnet.ibm.com>

	PR libquadmath/81848
	* configure.ac (powerpc*-linux*): Use attribute mode KC to create
	complex __float128 on PowerPC instead of attribute mode TC.
	* quadmath.h (__complex128): Likewise.
	* configure: Regenerate.
	* math/cbrtq.c (CBRT2): Use __float128 not long double.
	(CBRT4): Likewise.
	(CBRT2I): Likewise.
	(CBRT4I): Likewise.
	* math/j0q.c (U0): Likewise.
	* math/sqrtq.c (sqrtq): Don't depend on implicit conversion
	between __float128, instead explicitly convert the __float128
	value to long double because the PowerPC does not allow __float128
	and long double in the same expression.

From-SVN: r251613

From-SVN: r250367

	PR libquadmath/65757
	* quadmath-imp.h (math_opt_barrier, math_force_eval,
	math_narrow_eval, math_check_force_underflow,
	math_check_force_underflow_nonneg): Define.
	* math/ceilq.c: Backport changes from upstream glibc
	between 2012-11-01 and 2017-07-13.
	* math/remquoq.c: Likewise.
	* math/expq.c: Likewise.
	* math/llroundq.c: Likewise.
	* math/logq.c: Likewise.
	* math/atanq.c: Likewise.
	* math/nearbyintq.c: Likewise.
	* math/scalblnq.c: Likewise.
	* math/finiteq.c: Likewise.
	* math/atanhq.c: Likewise.
	* math/expm1q.c: Likewise.
	* math/sinhq.c: Likewise.
	* math/log10q.c: Likewise.
	* math/rintq.c: Likewise.
	* math/roundq.c: Likewise.
	* math/fmaq.c: Likewise.
	* math/erfq.c: Likewise.
	* math/log2q.c: Likewise.
	* math/lroundq.c: Likewise.
	* math/j1q.c: Likewise.
	* math/scalbnq.c: Likewise.
	* math/truncq.c: Likewise.
	* math/frexpq.c: Likewise.
	* math/sincosq.c: Likewise.
	* math/tanhq.c: Likewise.
	* math/asinq.c: Likewise.
	* math/coshq.c: Likewise.
	* math/j0q.c: Likewise.
	* math/asinhq.c: Likewise.
	* math/floorq.c: Likewise.
	* math/sinq_kernel.c: Likewise.
	* math/powq.c: Likewise.
	* math/hypotq.c: Likewise.
	* math/sincos_table.c: Likewise.
	* math/rem_pio2q.c: Likewise.
	* math/nextafterq.c: Likewise.
	* math/log1pq.c: Likewise.
	* math/sincosq_kernel.c: Likewise.
	* math/tanq.c: Likewise.
	* math/acosq.c: Likewise.
	* math/lrintq.c: Likewise.
	* math/llrintq.c: Likewise.

From-SVN: r250343

	* Makefile.am (libquadmath_la_SOURCES): Add math/logbq.c.
	* Makefile.in: Regenerate.
	* libquadmath.texi: Document logbq.
	* quadmath.h: Add logbq prototype.
	* quadmath.map: Add logbq.
	* quadmath_weak.h: Add logbq prototype.
	* math/logbq.c: New file

From-SVN: r226748

2013-02-17  Tobias Burnus  <burnus@net-b.de>

        * math/cacoshq.c (cacoshq): Call signbitq instead of signbit.

From-SVN: r196109