[New-bugs-announce] [issue5512] Streamline integer division

[Mark Dickinson]

New submission from Mark Dickinson <dickinsm at gmail.com>:

Here's a patch that streamlines the x_divrem function in 
Objects/longobject.c.  More benchmarks are needed, but the initial 
results are promising:  for py3k, on a 32-bit machine with 15-bit 
digits, Victor's pidigits benchmark runs almost twice as fast with this 
patch (numbers below).

Patch details
=============

- Normalize inputs by shifting instead of multiplying and dividing.
  This halves the number of divisions used in the algorithm.

- Streamline innermost loop.

- Save an iteration of outer loop around half the time.

- Save an object allocation:  only 3 allocations per x_divrem call
  instead of 4.

- Remove special case where initial quotient estimate is >= PyLong_BASE.
  There's no need for this, since the 'digit' type holds values up
  to 2*PyLong_BASE - 1.

- Make q type digit instead of type twodigits:  this halves the size
  of the multiplication in the innermost loop.

Benchmark results
=================

Using the pidigits_bestof.py script that's posted in the issue 4258 
discussion, on a non-debug build of py3k (r70465), on OS X 10.5.6/Core 2 
Duo:

Unpatched
---------
Macintosh-3:py3k dickinsm$ ./python.exe ../pidigits_bestof.py 2000
performing a warm up run...
running
sys.int_info= sys.int_info(bits_per_digit=15, sizeof_digit=2)
Time; 2234.6 ms
Time; 2232.2 ms
Time; 2227.9 ms
Time; 2225.7 ms
Time; 2229.8 ms
Best Time; 2225.7 ms

Patched
-------
dickinsm$ ./python.exe ../pidigits_bestof.py 2000
performing a warm up run...
running
sys.int_info= sys.int_info(bits_per_digit=15, sizeof_digit=2)
Time; 1175.6 ms
Time; 1176.5 ms
Time; 1177.3 ms
Time; 1179.5 ms
Time; 1168.5 ms
Best Time; 1168.5 ms

So the patch gives a speedup of around 90%.  This particular benchmark 
is heavy on the divisions though, so I'd expect lesser speedups for 
other benchmarks.

----------
assignee: marketdickinson
components: Interpreter Core
files: faster_integer_division.patch
keywords: patch
messages: 83781
nosy: marketdickinson
priority: normal
severity: normal
status: open
title: Streamline integer division
type: performance
versions: Python 2.7, Python 3.1
Added file: http://bugs.python.org/file13368/faster_integer_division.patch

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Python tracker <report at bugs.python.org>
<http://bugs.python.org/issue5512>
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