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| author | Adhemerval Zanella Netto <adhemerval.zanella@linaro.org> | 2023-03-20 13:01:16 -0300 |
|---|---|---|
| committer | Adhemerval Zanella <adhemerval.zanella@linaro.org> | 2023-04-03 16:36:24 -0300 |
| commit | 34b9f8bc170810c44184ad57ecf1800587e752a6 (patch) | |
| tree | 9be9f9e44652729248cfef192eafa4227d670752 /math | |
| parent | 5c11701c518276fcf12ff7d8f27e3c7102e97542 (diff) | |
| download | glibc-34b9f8bc170810c44184ad57ecf1800587e752a6.tar.gz glibc-34b9f8bc170810c44184ad57ecf1800587e752a6.tar.xz glibc-34b9f8bc170810c44184ad57ecf1800587e752a6.zip | |
math: Improve fmod
This uses a new algorithm similar to already proposed earlier [1].
With x = mx * 2^ex and y = my * 2^ey (mx, my, ex, ey being integers),
the simplest implementation is:
mx * 2^ex == 2 * mx * 2^(ex - 1)
while (ex > ey)
{
mx *= 2;
--ex;
mx %= my;
}
With mx/my being mantissa of double floating pointer, on each step the
argument reduction can be improved 11 (which is sizeo of uint64_t minus
MANTISSA_WIDTH plus the signal bit):
while (ex > ey)
{
mx << 11;
ex -= 11;
mx %= my;
} */
The implementation uses builtin clz and ctz, along with shifts to
convert hx/hy back to doubles. Different than the original patch,
this path assume modulo/divide operation is slow, so use multiplication
with invert values.
I see the following performance improvements using fmod benchtests
(result only show the 'mean' result):
Architecture | Input | master | patch
-----------------|-----------------|----------|--------
x86_64 (Ryzen 9) | subnormals | 19.1584 | 12.5049
x86_64 (Ryzen 9) | normal | 1016.51 | 296.939
x86_64 (Ryzen 9) | close-exponents | 18.4428 | 16.0244
aarch64 (N1) | subnormal | 11.153 | 6.81778
aarch64 (N1) | normal | 528.649 | 155.62
aarch64 (N1) | close-exponents | 11.4517 | 8.21306
I also see similar improvements on arm-linux-gnueabihf when running on
the N1 aarch64 chips, where it a lot of soft-fp implementation (for
modulo, clz, ctz, and multiplication):
Architecture | Input | master | patch
-----------------|-----------------|----------|--------
armhf (N1) | subnormal | 15.908 | 15.1083
armhf (N1) | normal | 837.525 | 244.833
armhf (N1) | close-exponents | 16.2111 | 21.8182
Instead of using the math_private.h definitions, I used the
math_config.h instead which is used on newer math implementations.
Co-authored-by: kirill <kirill.okhotnikov@gmail.com>
[1] https://sourceware.org/pipermail/libc-alpha/2020-November/119794.html
Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
Diffstat (limited to 'math')
| -rw-r--r-- | math/libm-test-fmod.inc | 14 |
1 files changed, 14 insertions, 0 deletions
diff --git a/math/libm-test-fmod.inc b/math/libm-test-fmod.inc index 39fd02f9ef..8841c1332c 100644 --- a/math/libm-test-fmod.inc +++ b/math/libm-test-fmod.inc @@ -152,6 +152,16 @@ static const struct test_ff_f_data fmod_test_data[] = TEST_ff_f (fmod, 6.5, -2.25L, 2.0L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), TEST_ff_f (fmod, -6.5, -2.25L, -2.0L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, 0x1.e848p+18, 0x1.6p+3, 0x1.8p+2, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, 0x1.e848p+18, -0x1.6p+3, 0x1.8p+2, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x1.e848p+18, 0x1.6p+3, -0x1.8p+2, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x1.e848p+18, -0x1.6p+3, -0x1.8p+2, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + + TEST_ff_f (fmod, 0x1.4p+2, 0x1p+0, 0x0p+0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, 0x1.4p+2, -0x1p+0, 0x0p+0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x1.4p+2, 0x1p+0, -0x0p+0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x1.4p+2, -0x1p+0, -0x0p+0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, max_value, max_value, 0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), TEST_ff_f (fmod, max_value, -max_value, 0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), TEST_ff_f (fmod, max_value, min_value, 0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), @@ -216,6 +226,10 @@ static const struct test_ff_f_data fmod_test_data[] = TEST_ff_f (fmod, -0x1p1023L, -0x3p-1073L, -0x1p-1073L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), TEST_ff_f (fmod, -0x1p1023L, 0x3p-1022L, -0x1p-1021L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), TEST_ff_f (fmod, -0x1p1023L, -0x3p-1022L, -0x1p-1021L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, 0x0.cded0a47373e9p-1022, 0x0.3212f5b8c8c16p-1022, 0x0.05a1336414391p-1022, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, 0x0.cded0a47373e9p-1022, -0x0.3212f5b8c8c16p-1022, 0x0.05a1336414391p-1022, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x0.cded0a47373e9p-1022, 0x0.3212f5b8c8c16p-1022, -0x0.05a1336414391p-1022, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x0.cded0a47373e9p-1022, -0x0.3212f5b8c8c16p-1022, -0x0.05a1336414391p-1022, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), #endif #if MIN_EXP <= -16381 TEST_ff_f (fmod, 0x1p16383L, 0x3p-16445L, 0x1p-16445L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), |