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Fast array processing functions

Project description

Authors: Michael Griffin
Version: 6.0.0 for 2020-03-27
Copyright: 2014 - 2020
License:This document may be distributed under the Apache 2.0 License.
Language:Python 3.5 or later

Introduction

The arrayfunc module provides high speed array processing functions for use with the standard Python array module. These functions are patterned after the functions in the standard Python Itertools and math module together with some additional ones from other sources.

The purpose of these functions is to perform mathematical calculations on arrays faster than using native Python.

See full documentation at: http://arrayfunc.readthedocs.io/en/latest/


Function Summary

The functions fall into several categories.

Filling Arrays

Function Description
count Fill an array with evenly spaced values using a start and step values.
cycle Fill an array with evenly spaced values using a start, stop, and step values, and repeat until the array is filled.
repeat Fill an array with a specified value.

Filtering Arrays

Function Description
afilter Select values from an array based on a boolean criteria.
compress Select values from an array based on another array of boolean values.
dropwhile Select values from an array starting from where a selected criteria fails and proceding to the end.
takewhile Like dropwhile, but starts from the beginning and stops when the criteria fails.

Examining and Searching Arrays

Function Description
findindex Returns the index of the first value in an array to meet the specified criteria.
findindices Searches an array for the array indices which meet the specified criteria and writes the results to a second array. Also returns the number of matches found.

Summarising Arrays

Function Description
aany Returns True if any element in an array meets the selected criteria.
aall Returns True if all element in an array meet the selected criteria.
amax Returns the maximum value in the array.
amin Returns the minimum value in the array.
asum Calculate the arithmetic sum of an array.

Data Conversion

Function Description
convert Convert arrays between data types. The data will be converted into the form required by the output array.

Mathematical operator functions

Function Equivalent to
add x + y
truediv x / y
floordiv x // y
mod x % y
mul x * y
neg -x
pow x**y or math.pow(x, y)
sub x - y
abs_ abs(x)

Comparison operator functions

Function Equivalent to
eq x == y
gt x > y
ge x >= y
lt x < y
le x <= y
ne x != y

Bitwise operator functions

Function Equivalent to
and_ x & y
or_ x | y
xor x ^ y
invert ~x
lshift x << y
rshift x >> y

Power and logarithmic functions

Function Equivalent to
exp math.exp(x)
expm1 math.expm1(x)
log math.log(x)
log10 math.log10(x)
log1p math.log1p(x)
log2 math.log2(x)
sqrt math.sqrt(x)

Hyperbolic functions

Function Equivalent to
acosh math.acosh(x)
asinh math.asinh(x)
atanh math.atanh(x)
cosh math.cosh(x)
sinh math.sinh(x)
tanh math.tanh(x)

Trigonometric functions

Function Equivalent to
acos math.acos(x)
asin math.asin(x)
atan math.atan(x)
atan2 math.atan2(x, y)
cos math.cos(x)
hypot math.hypot(x, y)
sin math.sin(x)
tan math.tan(x)

Angular conversion

Function Equivalent to
degrees math.degrees(x)
radians math.radians(x)

Number-theoretic and representation functions

Function Equivalent to
ceil math.ceil(x)
copysign math.copysign(x, y)
fabs math.fabs(x)
factorial math.factorial(x)
floor math.floor(x)
fmod math.fmod(x, y)
isfinite math.isfinite(x)
isinf math.isinf(x)
isnan math.isnan(x)
ldexp math.ldexp(x, y)
trunc math.trunc(x)

Special functions

Function Equivalent to
erf math.erf(x)
erfc math.erfc(x)
gamma math.gamma(x)
lgamma math.lgamma(x)

Additional functions

Function Equivalent to
fma fma(x, y, z) or x * y + z

Attributes

In addition to functions, a set of attributes are provided representing the platform specific maximum and minimum numerical values for each array type. These attributes are part of the “arraylimits” module.


Supported Array Types

Arrayfunc supports all standard Python 3.x array types.


Performance

Average performance increase on x86_64 Ubuntu with GCC is 100 times faster than native Python. Performance will vary depending on the function, operation, array data type used, and whether overflow checking is enabled, with the performance increase ranging from 50% to 3000 times.

Other platforms show similar improvements.

Detailed performance figures are listed in the full documentation.


Platform support

Arrayfunc is written in ‘C’ and uses the standard C libraries to implement the underlying math functions. Arrayfunc has been tested on the following platforms.

OS Bits Compiler Python Version Tested
Ubuntu 18.04 LTS 64 bit GCC 3.6
Ubuntu 19.10 64 bit GCC 3.7
Ubuntu 20.04 beta 64 bit GCC 3.8
Debian 10 32 bit GCC 3.7
Debian 10 64 bit GCC 3.7
OpenSuse 15 64 bit GCC 3.6
Centos 8 64 bit GCC 3.6
FreeBSD 12 64 bit LLVM 3.7
OpenBSD 6.5 64 bit LLVM 3.6
MS Windows 10 64 bit MS Visual Studio C 2015 3.8
Raspbian (RPi 3) 32 bit GCC 3.7
Ubuntu 19.10 ARM 64 bit GCC 3.7
  • The Raspbian (RPi 3) tests were conducted on a Raspberry Pi 3 ARM CPU running in 32 bit mode.
  • The Ubuntu ARM tests were conducted on a Raspberry Pi 3 ARM CPU running in 64 bit mode.
  • All others were conducted using VMs running on x86 hardware.

Installation

Please note that this is a Python 3 package. To install using Pip, you will need (with Debian package in brackets):

  • The appropriate C compiler and header files (gcc and build-essential).
  • The Python3 development headers (python3-dev).
  • Pip3 together with the corresponding Setuptools (python3-pip).

example:

# Install from PyPI.
pip3 install arrayfunc
# Install from a local copy of the source package (Linux).
pip3 install --no-index --find-links=. arrayfunc
# Windows seems to use "pip" instead of "pip3" for some reason.
pip install arrayfunc

Release History

  • 6.0.0 - Added SIMD support for ARMv8 AARCH64. This is 64 bit ARM on a
    Raspberry Pi3 when running 64 bit Ubuntu. Raspbian is 32 bit only and has 64 bit SIMD vectors. 64 bit ARM has 128 bit SIMD vectors and so offers improved performance.
  • 5.1.1 - Updated and improved help documentation. Also updated test
    platforms and retested.
  • 5.1.0 - This is a bug fix release only, centred around SIMD issues on
    x86-64 with GCC. In a previous release some of the x86-64 SIMD code had been changed to take advantage of a sort of assisted auto-vectorisation present in GCC. However, certain operations on certain integer sizes with certain array types will cause GCC to generate incorrect x86 SIMD operations, producting integer overflow. The functions known to be affected are aall, aany, findindex (B, H, I arrays), eq, ge, gt, le, lt, ne (B, H, I arrays), and rshift (h, i arrays). ARM was not affected. All auto-vectorisation, where used, has been changed back to manually generated SIMD operations for both x86 and ARM. Rshift no longer uses SIMD operations for b, B, h, or i arrays on x86. Lshift no longer supports SIMD operations on b or B arrays on x86. Add and sub no longer use SIMD for B, H, and I arrays on x86. Mul no longer uses SIMD on x86 for any array types. Where SIMD functionality has been removed on x86, it of course is still supported through normal portable CPU instructions. ARM SIMD support was not affected by these changes. Lost SIMD acceleration will be returned to x86 in a later release where possible after the necessary research has been conducted. Unit tests have been updated to cover a greater range of integer values to test for this problem. Platforms using compilers other than GCC were not affected by this, as they did not use SIMD anyway. The main effect of this present change is that some calculations may be slower for some array types. The problem with GCC generating incorrect SIMD instructions in some circumstances is apparently a known (but obscure) issue. This will be avoided in future releases by sticking with manual SIMD built-ins. Some source code files have updated date stamps in this release but no substantive code changes due to the template system used to auto-generate code.
  • 5.0.0 - The main focus of this release has been adding SIMD
    acceleration support to the ARMv7 platform (e.g. Raspberry Pi 3). Also added SIMD support to ‘lshift’ and ‘rshift’ on x86-64 and ARM. Changed arrayparamsbase to fix compiler warning on newer versions of GCC, but no change in actual operation. Updated supported OS versions tested, and added OpenBSD to supported platform list.
  • 4.3.1 - Numerous performance inprovements through the use of SIMD
    acceleration in many functions. See the documentation to see which functions are affected. Restrictions on the use of non-finite data in parameters has been relaxed where possible. Repeat now allows non-finite data as fill values. For findindices, if no matches are found the result code is now 0 (zero) instead of -1.
  • 4.2.0 - Added fma function. This has no equivalent in the Python
    standard library but is equivalent to x * y + z. Also changed list of supported platforms to update FreeBSD to version 12 and added Centos 7.
  • 4.1.0 - Added isfinite function.
  • 4.0.1 - Repeat upload to synchronise source and Windows binary “wheel”
    version. PyPI was not happy with the previous attempt.
  • 4.0.0 - Major revision with many changes. Amap, starmap, and acalc were
    replaced with new individual functions. This change was made to provides a simpler and more consistent interface which is tailored to the individual function rather than attempting to make one parameter format fit all. The “disovfl” parameter has been named to “matherrors” in order to better reflect that it encompasses more than just integer overflow. Support for the “bytes” type has been removed. The Raspberry Pi has been added as a supported platform.
  • 3.1.0 - Added log2 to amap, amapi, and acalc.
  • 3.0.0 - Changed package format to “Wheel” files. No functional changes.
  • 2.1.1 - Fixed missing header files in PyPI package. No functional changes.
  • 2.0.0 - Many changes. Updated MS Windows support to 3.6 and latest compiler.
    This in turn brought the Windows version up to feature parity with the other versions. Changed supported MS Windows version from 32 bit to 64 bit. Added SIMD support for some functions which provided a significant performance for those affected. Updated supported versions of Debian and FreeBSD to current releases.
  • 1.1.0 - Added support for math constants math.pi and math.e.
  • 1.0.0 - First release.

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