Metadata-Version: 1.1
Name: shift_divmod
Version: 0.4.1
Summary: Implement faster divmod() for moduli with trailing 0 bits
Home-page: https://github.com/shlomif/shift_divmod
Author: Shlomi Fish
Author-email: shlomif@cpan.org
License: 3-clause BSD
Description: ==============================================================================
        ShiftDivMod.  Implement faster divmod() for moduli with trailing 0 bits
        ==============================================================================
        :Info: This is the README file for ShiftDivMod.
        :Author: Shlomi Fish <shlomif@cpan.org>
        :Copyright: © 2020, Shlomi Fish.
        :Date: 2020-09-16
        :Version: 0.4.1
        
        .. index: README
        .. image:: https://travis-ci.org/shlomif/shift_divmod.svg?branch=master
           :target: https://travis-ci.org/shlomif/shift_divmod
        
        PURPOSE
        =======
        
        This distribution implements faster divmod() (and ``.mod()``) operations
        for moduli with a large number of trailing 0 bits (where the div/mod base
        is divisible by ``2 ** n`` for an integer `n`).
        
        It should yield the same result as the built-n divmod() function for
        positive numerators (its behaviour for negative ones is currently
        untested and undefined).
        
        Also provided is a port to C and gmplib (= GNU multiple precision):
        https://github.com/shlomif/shift_divmod/tree/master/gmp-shift_divmod
        
        INSTALLATION
        ============
        
        pip3 install shift_divmod
        
        USAGE
        =====
        
        ::
        
            from shift_divmod import ShiftDivMod
        
            base = 997
            shift = 1200
            modder = ShiftDivMod(base, shift)
            # Alternative constructor which may require more
            # work and eventualy calls the default constructor
            modder = ShiftDivMod.from_int(base << shift)
        
            x = 10 ** 500
            # Same as divmod(x, (base << shift))
            print( modder.divmod(x) )
        
        NOTES
        =====
        
        The code from which this distribution has been derived, was proposed as a
        proof-of-concept for a potential improvement for the built in cpython3
        operations here: https://bugs.python.org/issue41487 . However, changing cpython3
        in this manner was rejected.
        
        libdivide ( https://github.com/ridiculousfish/libdivide ) provides a
        different, but also interesting, approach for optimizing division.
        
        BENCHMARKS:
        ===========
        
        On my system, I got these results after running
        ``python3 code/examples/shift_divmod_example.py bench`` (reformated
        for clarity):
        
        ::
        
            {'val': 5206685, 'time': 38.86349368095398, 'reached': 1000,
             'interrupted': False, 'mode': 'gen_shift_mod'}
            {'val': 5206685, 'time': 39.018390417099, 'reached': 1000,
             'interrupted': False, 'mode': 'shiftmodpre'}
            {'val': mpz(5206685), 'time': 167.4433994293213, 'reached': 1000,
             'interrupted': False, 'mode': 'gmpy'}
            {'val': 3346424, 'time': 229.94409656524658, 'reached': 25,
             'interrupted': True, 'mode': 'builtinops'}
        
            System:    Kernel: 5.8.8-200.fc32.x86_64 x86_64 bits: 64
                Desktop: KDE Plasma 5.18.5
                       Distro: Fedora release 32 (Thirty Two)
            CPU:       Info: Quad Core model: Intel Core i5-8259U
                bits: 64 type: MT MCP L2 cache: 6144 KiB
                       Speed: 1600 MHz min/max: 400/3800 MHz Core speeds (MHz):
                            1: 1600 2: 1600 3: 1601
                       4: 1600 5: 1600 6: 1601 7: 1601 8: 1601
            Graphics:  Device-1: Intel Iris Plus Graphics 655 driver: i915 v: kernel
                       Display: server: Fedora Project
                       X.org 1.20.8 driver: modesetting unloaded: fbdev,vesa
                       resolution: 1920x1080~60Hz
                       OpenGL: renderer: Mesa Intel Iris Plus
                       Graphics 655 (CFL GT3) v: 4.6 Mesa 20.1.7
        
        As can be noticed the shift_divmod based versions are over 4 times faster than
        GMP and much faster than the builtinops which only completed 25 out of 1,000 iterations
        before being interrupted. Note that for that use case, using GMP's modular exponentiation
        seems even faster.
        
        With the C and gmplib version:
        
        - ``mpz_mod`` runs the benchmark in about 160 seconds.
        - ``shift_divmod`` runs the benchmark in about 35 seconds.
        - ``pypy3`` runs the pure-Python code in 25 seconds (!).
        
        The Secret Sauce:
        -----------------
        
        The code utilises the fact that `bitwise operations <https://en.wikipedia.org/wiki/Bitwise_operation>`_
        are fast, and the magic happens in this code:
        
        ::
        
            def divmod(self, inp):
                """calculate divmod(inp, self.n)"""
                if inp < self.n:
                    return 0, inp
                div, mod = divmod((inp >> self.shift), self.base)
                return div, ((mod << self.shift) | (inp & self.mask))
        
        (Or the equivalent but more bureaucratic C and gmplib code.)
        
        Note that ``self.mask`` is precalculated to be
        ``((1 << self.shift) - 1)``.
        
        COPYRIGHT
        ---------
        Copyright © 2020, Shlomi Fish.
        All rights reserved.
        
        Redistribution and use in source and binary forms, with or without
        modification, are permitted provided that the following conditions are
        met:
        
        1. Redistributions of source code must retain the above copyright
           notice, this list of conditions, and the following disclaimer.
        
        2. Redistributions in binary form must reproduce the above copyright
           notice, this list of conditions, and the following disclaimer in the
           documentation and/or other materials provided with the distribution.
        
        3. Neither the name of the author of this software nor the names of
           contributors to this software may be used to endorse or promote
           products derived from this software without specific prior written
           consent.
        
        THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
        "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
        LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
        A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT
        OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
        SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
        LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
        DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
        THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
        (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
        OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
        
Keywords: shift_divmod
Platform: any
Classifier: Development Status :: 1 - Planning
Classifier: Programming Language :: Python
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.5
Classifier: Programming Language :: Python :: 3.6
Classifier: Programming Language :: Python :: 3.7
Classifier: Programming Language :: Python :: 3.8
