Implement C23 pown

C23 adds various <math.h> function families originally defined in TS
18661-4.  Add the pown functions, which are like pow but with an
integer exponent.  That exponent has type long long int in C23; it was
intmax_t in TS 18661-4, and as with other interfaces changed after
their initial appearance in the TS, I don't think we need to support
the original version of the interface.  The test inputs are based on
the subset of test inputs for pow that use integer exponents that fit
in long long.

As the first such template implementation that saves and restores the
rounding mode internally (to avoid possible issues with directed
rounding and intermediate overflows or underflows in the wrong
rounding mode), support also needed to be added for using
SET_RESTORE_ROUND* in such template function implementations.  This
required math-type-macros-float128.h to include <fenv_private.h>, so
it can tell whether SET_RESTORE_ROUNDF128 is defined.  In turn, the
include order with <fenv_private.h> included before <math_private.h>
broke loongarch builds, showing up that
sysdeps/loongarch/math_private.h is really a fenv_private.h file
(maybe implemented internally before the consistent split of those
headers in 2018?) and needed to be renamed to fenv_private.h to avoid
errors with duplicate macro definitions if <math_private.h> is
included after <fenv_private.h>.

The underlying implementation uses __ieee754_pow functions (called
more than once in some cases, where the exponent does not fit in the
floating type).  I expect a custom implementation for a given format,
that only handles integer exponents but handles larger exponents
directly, could be faster and more accurate in some cases.

I encourage searching for worst cases for ulps error for these
implementations (necessarily non-exhaustively, given the size of the
input space).

Tested for x86_64 and x86, and with build-many-glibcs.py.

1 files changed, 377 insertions, 0 deletions

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index cb5d6443b1..7cb8a896ab 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -8151,6 +8151,383 @@ pow 0x1.059c76p+0 0x1.ff80bep+11
 pow 0x1.7ac7cp+5 23
 pow -0x1.7ac7cp+5 23
 
+pown 0 0
+pown 0 -0
+pown -0 0
+pown -0 -0
+
+pown 10 0
+pown 10 -0
+pown -10 0
+pown -10 -0
+
+pown 1 1
+pown 1 -1
+pown 1 0x4fffffffffffffff
+
+# pown (x, +-0) == 1.
+pown 32.75 0
+pown 32.75 -0
+pown -32.75 0
+pown -32.75 -0
+pown 0x1p72 0
+pown 0x1p72 -0
+pown 0x1p-72 0
+pown 0x1p-72 -0
+
+pown 0 1
+pown 0 11
+
+pown -0 1
+pown -0 11
+
+pown 0 2
+
+pown -0 2
+
+# pown (+0, y) == +0 for y an odd integer > 0.
+pown 0.0 27
+pown 0.0 0xffffff
+pown 0.0 0x1fffffffffffff
+
+# pown (-0, y) == -0 for y an odd integer > 0.
+pown -0 27
+pown -0 0xffffff
+pown -0 0x1fffffe
+pown -0 0x1fffffffffffff
+pown -0 0x3ffffffffffffe
+pown -0 0x7fffffffffffffff
+
+# pown (+0, y) == +0 for y > 0 and not an odd integer.
+pown 0.0 4
+pown 0.0 0x1000000
+
+# pown (-0, y) == +0 for y > 0 and not an odd integer.
+pown -0 4
+pown -0 0x1000000
+
+pown 2 4
+pown 256 8
+
+pown -1.0 -0xffffff
+pown -1.0 -0x1fffffe
+pown -1.0 -0x1fffffffffffff
+pown -1.0 -0x3ffffffffffffe
+pown -1.0 -0x7fffffffffffffff
+
+pown -1.0 0xffffff
+pown -1.0 0x1fffffe
+pown -1.0 0x1fffffffffffff
+pown -1.0 0x3ffffffffffffe
+pown -1.0 0x7fffffffffffffff
+
+pown -2.0 126
+pown -2.0 127
+pown -2.0 -126
+pown -2.0 -127
+
+pown -2.0 -0xffffff
+pown -2.0 -0x1fffffe
+pown -2.0 -0x1fffffffffffff
+pown -2.0 -0x3ffffffffffffe
+pown -2.0 -0x7fffffffffffffff
+
+pown -2.0 0xffffff
+pown -2.0 0x1fffffe
+pown -2.0 0x1fffffffffffff
+pown -2.0 0x3ffffffffffffe
+pown -2.0 0x7fffffffffffffff
+
+pown -max -2
+pown -max -3
+pown -max 2
+pown -max 3
+
+pown -max -0xffffff
+pown -max -0x1fffffe
+pown -max -0x1fffffffffffff
+pown -max -0x3ffffffffffffe
+pown -max -0x7fffffffffffffff
+
+pown -max 0xffffff
+pown -max 0x1fffffe
+pown -max 0x1fffffffffffff
+pown -max 0x3ffffffffffffe
+pown -max 0x7fffffffffffffff
+
+pown -0x1p65 2
+pown -0x1p65 3
+pown -0x1p65 4
+pown -0x1p65 5
+pown -0x1p43 3
+pown -0x1p43 4
+pown -0x1p43 5
+pown -0x1p33 4
+pown -0x1p33 5
+pown -0x1p26 5
+pown -0x1p-65 -2
+pown -0x1p-65 -3
+pown -0x1p-65 -4
+pown -0x1p-65 -5
+pown -0x1p-43 -3
+pown -0x1p-43 -4
+pown -0x1p-43 -5
+pown -0x1p-33 -4
+pown -0x1p-33 -5
+pown -0x1p-26 -5
+
+pown -0x1p513 2
+pown -0x1p513 3
+pown -0x1p513 4
+pown -0x1p513 5
+pown -0x1p342 3
+pown -0x1p342 4
+pown -0x1p342 5
+pown -0x1p257 4
+pown -0x1p257 5
+pown -0x1p205 5
+pown -0x1p-513 -2
+pown -0x1p-513 -3
+pown -0x1p-513 -4
+pown -0x1p-513 -5
+pown -0x1p-342 -3
+pown -0x1p-342 -4
+pown -0x1p-342 -5
+pown -0x1p-257 -4
+pown -0x1p-257 -5
+pown -0x1p-205 -5
+
+pown -0x1p8192 2
+pown -0x1p8192 3
+pown -0x1p8192 4
+pown -0x1p8192 5
+pown -0x1p5462 3
+pown -0x1p5462 4
+pown -0x1p5462 5
+pown -0x1p4097 4
+pown -0x1p4097 5
+pown -0x1p3277 5
+pown -0x1p64 257
+pown -0x1p-8192 -2
+pown -0x1p-8192 -3
+pown -0x1p-8192 -4
+pown -0x1p-8192 -5
+pown -0x1p-5462 -3
+pown -0x1p-5462 -4
+pown -0x1p-5462 -5
+pown -0x1p-4097 -4
+pown -0x1p-4097 -5
+pown -0x1p-3277 -5
+pown -0x1p-64 -257
+
+pown -0.5 126
+pown -0.5 127
+pown -0.5 -126
+pown -0.5 -127
+
+pown -0.5 -0xffffff
+pown -0.5 -0x1fffffe
+pown -0.5 -0x1fffffffffffff
+pown -0.5 -0x3ffffffffffffe
+pown -0.5 -0x7fffffffffffffff
+
+pown -0.5 0xffffff
+pown -0.5 0x1fffffe
+pown -0.5 0x1fffffffffffff
+pown -0.5 0x3ffffffffffffe
+pown -0.5 0x7fffffffffffffff
+
+pown -min -2
+pown -min -3
+pown -min 1
+pown -min 2
+pown -min 3
+
+pown -min -0xffffff
+pown -min -0x1fffffe
+pown -min -0x1fffffffffffff
+pown -min -0x3ffffffffffffe
+pown -min -0x7fffffffffffffff
+
+pown -min 0xffffff
+pown -min 0x1fffffe
+pown -min 0x1fffffffffffff
+pown -min 0x3ffffffffffffe
+pown -min 0x7fffffffffffffff
+
+pown 0x0.ffffffp0 10
+pown 0x0.ffffffp0 100
+pown 0x0.ffffffp0 1000
+pown 0x0.ffffffp0 0x1000000
+pown 0x0.ffffffp0 0x40000000
+pown 0x0.ffffffp0 0x48d15980
+pown 0x0.ffffffp0 -10
+pown 0x0.ffffffp0 -100
+pown 0x0.ffffffp0 -1000
+pown 0x0.ffffffp0 -0x1000000
+pown 0x0.ffffffp0 -0x40000000
+pown 0x0.ffffffp0 -0x48d15980
+pown 0x1.000002p0 0x1000000
+pown 0x1.000002p0 0x2468acc0
+pown 0x1.000002p0 -0x2468acc0
+
+pown 0x0.fffffffffffff8p0 0x48d159e26af37c00
+pown 0x0.fffffffffffff8p0 -0x48d159e26af37c00
+pown 0x1.0000000000001p0 0x2468acf13579be00
+pown 0x1.0000000000001p0 -0x2468acf13579be00
+
+pown -0x0.ffffffp0 10
+pown -0x0.ffffffp0 100
+pown -0x0.ffffffp0 1000
+pown -0x0.ffffffp0 0x1000000
+pown -0x0.ffffffp0 0x40000000
+pown -0x0.ffffffp0 0x48d15980
+pown -0x0.ffffffp0 -10
+pown -0x0.ffffffp0 -100
+pown -0x0.ffffffp0 -1000
+pown -0x0.ffffffp0 -0x1000000
+pown -0x0.ffffffp0 -0x40000000
+pown -0x0.ffffffp0 -0x48d15980
+pown -0x1.000002p0 0x1000000
+pown -0x1.000002p0 0x2468acc0
+pown -0x1.000002p0 -0x2468acc0
+
+pown -0x0.fffffffffffff8p0 0x48d159e26af37c00
+pown -0x0.fffffffffffff8p0 -0x48d159e26af37c00
+pown -0x1.0000000000001p0 0x2468acf13579be00
+pown -0x1.0000000000001p0 -0x2468acf13579be00
+
+pown 0x1.000002p0 0x40000000
+pown -0x1.000002p0 0x40000000
+pown 0x1.00000ep0 0x40000000
+pown -0x1.00000ep0 0x40000000
+
+pown 10.0 4932
+pown 10.0 4931
+pown 10.0 4930
+pown 10.0 4929
+pown 10.0 -4931
+pown 10.0 -4930
+pown 10.0 -4929
+pown 1e27 182
+pown 1e27 -182
+
+pown 2.0 -100000
+
+pown 0x1.00001p1 -126
+pown -0x1.00002p1 -126
+pown 0x1.00003p1 -126
+pown -0x1.00004p1 -126
+pown 0x1.00005p1 -126
+pown -0x1.00006p1 -126
+pown 0x1.00007p1 -126
+pown 0x1.00001p1 -969
+pown -0x1.00002p1 -969
+pown 0x1.00003p1 -969
+pown -0x1.00004p1 -969
+pown 0x1.00005p1 -969
+pown -0x1.00006p1 -969
+pown 0x1.00007p1 -969
+pown 0x1.00001p1 -1022
+pown -0x1.00002p1 -1022
+pown 0x1.00003p1 -1022
+pown -0x1.00004p1 -1022
+pown 0x1.00005p1 -1022
+pown -0x1.00006p1 -1022
+pown 0x1.00007p1 -1022
+pown 0x1.00001p1 -16382
+pown -0x1.00002p1 -16382
+pown 0x1.00003p1 -16382
+pown -0x1.00004p1 -16382
+pown 0x1.00005p1 -16382
+pown -0x1.00006p1 -16382
+pown 0x1.00007p1 -16382
+pown 0x1.00001p1 -16383
+pown -0x1.00002p1 -16383
+pown 0x1.00003p1 -16383
+pown -0x1.00004p1 -16383
+pown 0x1.00005p1 -16383
+pown -0x1.00006p1 -16383
+pown 0x1.00007p1 -16383
+pown 0x0.ffff1p-1 126
+pown -0x0.ffff2p-1 126
+pown 0x0.ffff3p-1 126
+pown -0x0.ffff4p-1 126
+pown 0x0.ffff5p-1 126
+pown -0x0.ffff6p-1 126
+pown 0x0.ffff7p-1 126
+pown 0x0.ffff1p-1 969
+pown -0x0.ffff2p-1 969
+pown 0x0.ffff3p-1 969
+pown -0x0.ffff4p-1 969
+pown 0x0.ffff5p-1 969
+pown -0x0.ffff6p-1 969
+pown 0x0.ffff7p-1 969
+pown 0x0.ffff1p-1 1022
+pown -0x0.ffff2p-1 1022
+pown 0x0.ffff3p-1 1022
+pown -0x0.ffff4p-1 1022
+pown 0x0.ffff5p-1 1022
+pown -0x0.ffff6p-1 1022
+pown 0x0.ffff7p-1 1022
+pown 0x0.ffff1p-1 16382
+pown -0x0.ffff2p-1 16382
+pown 0x0.ffff3p-1 16382
+pown -0x0.ffff4p-1 16382
+pown 0x0.ffff5p-1 16382
+pown -0x0.ffff6p-1 16382
+pown 0x0.ffff7p-1 16382
+pown 0x0.ffff1p-1 16383
+pown -0x0.ffff2p-1 16383
+pown 0x0.ffff3p-1 16383
+pown -0x0.ffff4p-1 16383
+pown 0x0.ffff5p-1 16383
+pown -0x0.ffff6p-1 16383
+pown 0x0.ffff7p-1 16383
+pown 0x2.000b3p0 -1022
+pown 0x2.000582p0 -1022
+
+pown 10 -1
+pown 10 -2
+pown 10 -3
+pown 10 -4
+pown 10 -5
+pown 10 -6
+pown 10 -7
+
+pown 0x0.ffffffffffffffffp0 1
+pown 0x0.ffffffffffffffffp0 2
+pown 0x0.ffffffffffffffffp0 3
+pown 0x0.ffffffffffffffffp0 4
+pown 0x0.ffffffffffffffffp0 5
+pown 0x0.ffffffffffffffffp0 6
+pown 0x0.ffffffffffffffffp0 7
+pown 0x0.ffffffffffffffffp0 -1
+pown 0x0.ffffffffffffffffp0 -2
+pown 0x0.ffffffffffffffffp0 -3
+pown 0x0.ffffffffffffffffp0 -4
+pown 0x0.ffffffffffffffffp0 -5
+pown 0x0.ffffffffffffffffp0 -6
+pown 0x0.ffffffffffffffffp0 -7
+
+pown 0x1.0000000000000002p0 1
+pown 0x1.0000000000000002p0 2
+pown 0x1.0000000000000002p0 3
+pown 0x1.0000000000000002p0 4
+pown 0x1.0000000000000002p0 5
+pown 0x1.0000000000000002p0 6
+pown 0x1.0000000000000002p0 7
+pown 0x1.0000000000000002p0 -1
+pown 0x1.0000000000000002p0 -2
+pown 0x1.0000000000000002p0 -3
+pown 0x1.0000000000000002p0 -4
+pown 0x1.0000000000000002p0 -5
+pown 0x1.0000000000000002p0 -6
+pown 0x1.0000000000000002p0 -7
+
+pown 0x1.7ac7cp+5 23
+pown -0x1.7ac7cp+5 23
+
 powr 10 0
 powr 10 -0