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34b9f8bc17
glibc/sysdeps/ieee754/dbl-64
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Adhemerval Zanella Netto 34b9f8bc17 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>
2023-04-03 16:36:24 -03:00
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e_fmod.c math: Improve fmod 2023-04-03 16:36:24 -03:00
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math_config.h math: Improve fmod 2023-04-03 16:36:24 -03:00
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