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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 8 (which is sizeof of uint32_t minus
MANTISSA_WIDTH plus the signal bit):
while (ex > ey)
{
mx << 8;
ex -= 8;
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 | 17.2549 | 12.0318
x86_64 (Ryzen 9) | normal | 85.4096 | 49.9641
x86_64 (Ryzen 9) | close-exponents | 19.1072 | 15.8224
aarch64 (N1) | subnormal | 10.2182 | 6.81778
aarch64 (N1) | normal | 60.0616 | 20.3667
aarch64 (N1) | close-exponents | 11.5256 | 8.39685
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, and multiplication):
Architecture | Input | master | patch
-----------------|-----------------|----------|--------
armhf (N1) | subnormal | 11.6662 | 10.8955
armhf (N1) | normal | 69.2759 | 34.1524
armhf (N1) | close-exponents | 13.6472 | 18.2131
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>
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