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Description:

arrayfunc 8.5.2

Authors:
Michael Griffin

Version:
8.5.2 for 2023-10-05
Copyright:
2014 - 2023
License:
This document may be distributed under the Apache 2.0 License.

Language:
Python 3.6 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/
If you are installing on an ARM platform such as the Raspberry Pi, see the
installation notes at the end before attempting to install from PyPI using PIP.

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)

pow2
x * x or math.pow(x, 2)

pow3
x * x * x or math.pow(x, 3)

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
Hardware
Bits
Compiler
Python Version

Debian 12
i686
32
GCC
3.11.2

Debian 12
x86_64
64
GCC
3.11.2

Ubuntu 22.04
x86_64
64
GCC
3.10.12

Ubuntu 23.04
x86_64
64
GCC
3.11.4

opensuse-leap 15.4
x86_64
64
GCC
3.6.15

almalinux 9.2
x86_64
64
GCC
3.9.16

alpine 3.18.4
i686
32
GCC
3.11.6

FreeBSD 13.2
amd64
64
Clang
3.9.18

OpenBSD 7.3
amd64
64
Clang
3.10.13

MS Windows 10
AMD64
64
MSC
3.12.0

MS Windows 11
AMD64
64
MSC
3.12.0

Raspbian 11
armv7l
32
GCC
3.9.2

Ubuntu 22.04
aarch64
64
GCC
3.10.12

amd64 is another name for x86_64 and does not indicate the CPU brand.
armv7l is 32 bit ARM. The test hardware is a Raspberry Pi 3.
aarch64 is 64 bit ARM. The test hardware is a Raspberry Pi 4.

The Rasberry Pi 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 4 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
# Force install from PyPI source instead of using a binary wheel.
pip3 install --user --force-reinstall --no-binary=:all: arrayfunc
# Install from a local copy of the source package (Linux).
pip3 install --no-index --find-links=. arrayfunc
# Install a local package as a user package.
pip3 install --user --no-index --find-links=. arrayfunc
# Windows, FreeBSD, and OpenBSD seems to use "pip" instead
# of "pip3" for some reason.
pip install arrayfunc
Newer versions of OpenBSD and FreeBSD will not install this package correctly
when running setup.py directly. Use pip to install, even for local package
installs. Testing of this package has been changed to use only pip (or pip3)
in order to provide a common testing method for all platforms. Testing using
setup.py directly is no longer done.
Recent versions of PyPI seem to be building their own binary wheels for some
platforms using their own infrastruction. This may result in an invalid ARM
binary on Raspberry Pi.
If you have difficulties, then either download the tar.gz version and install
it locally (see the above instructions for a local install). Alternatively,
see the above example for how to force a binary install instead of using a
wheel. There is also a bash script called “setupuser.sh” which will call setup.
py directly with the appropriate parameters.
The setup.py file has platform detection code which it uses to pass the
correct flags to the C compiler. For ARM, this includes the CPU type. If you
are using an ARM CPU type which is not recognized then setup.py may not
compile in SIMD features. You can experiment with modifying setup.py to add
new ARM models, but be sure that anything you try is compatible with the
existing ones.

Installing on Linux with PIP and PEP-668
PEP-668 (PEPs describe changes to Python) introduced a new feature which can
affect how packages are installed with PIP. If PIP is configured to be
EXTERNALLY-MANAGED it will refuse to install a package outside of a virtual
environment.
The intention of this is to prevent conflicts between packages which are
installed using the system package manager, and ones which are installed using
PIP.
Linux distros which are affeced by this include the latest versions of Debian
and Ubuntu.
As this package is a library which is intended to be used by other
applications, there is no one right way to install it, whether inside or
outside of a virtual environment. Review the options available with PIP to see
what is suitable for your application.
For testing purposes this package was installed by setting the environment
variable PIP_BREAK_SYSTEM_PACKAGES to “1”, which effectively disables this
feature in PIP.
example:
export PIP_BREAK_SYSTEM_PACKAGES=1

Release History

8.5.2 - Update to testing and support. There were no code changes.
Python version on Windows 10 and 11 was updated to version 12.

8.5.1 - Update to testing and support. There were no code. changes.
Ubuntu version updated to 23.04. AlmaLinux updated to 9.1.
Alpine Linux updated to 3.17.3. FreeBSD updated to 13.2.
OpenBSD updated to 7.3.
On Ubuntu 23.04, the installation method has changed due to how
PEP-668 was implemented by Debian and how this affects “pip”.
Some other distros may experience the same problems if they made
the same changes. See the README.TxT for details.

8.5.0 - Added pyproject.toml file to satisfy Python 3.11 requirements.
Updated build scripts to use python3 -m build instead of calling
setup.py directly. Test targets were updated, Ubuntu 20.04 was
dropped, Ubuntu 22.10 was added, FreeBSD python version upgraded
to 3.9, OpenBSD upgraded to 7.2, Windows 10 Python upgraded to 3.11,
Windows 11 Python upgraded to 3.11. Removed duplicate assignment in
parameter parsing return data in arrayparams_asum.c.
Added __version__ attribute to allow checking package version
number at run time. Added version unit test. Updated setup.py
and other files to allow the version number to be automatically
updated from a single source at build time.

8.4.1 - Minor bug fix for asum for unsigned integer SIMD on ARM. This
corrects the function return type for SIMD operations on ARM.
No incorrect behaviour was found in the original, but this change
was made to ensure correctness.

8.4.0 - Major performance improvements for asum through the use of SIMD and
other optimizations.

8.3.0 - Fixed the effects of an apparent compiler bug affecting 32 bit
x86 only for function asum. Tested and verified on 32 bit Debian
and 32 bit Alpine. This would in a few very specific circumstances
result in the sum of a float array (array code ‘f’) exceeding
the valid range for a float instead of returning infinity. The
fix forces the result to infinity in these cases. Also tested
with new releases of Alma 9 and Alpine 3.16.

8.2.0 - Update to testing and support. Tested with new releases of Ubuntu
22.04 and OpenBSD 7.1. Changed “simdsupport” to also report the
architecture the binary was compiled for. “Simdsupport” is only
used for testing and benchmarking and is not a stable part of
the release.

8.1.2 - Bump to correct minor documentation error in README.rst.

8.1.1 - Update to testing and support. Raspberry Pi 32 bit OS updated to
version 2022-04-04. Update to setup.py to improve ARM version
detection.

8.1.0 - Update to testing and support. Centos has been replaced by
AlmaLinux due to Red Hat ending long term support for Centos.
No actual code changes.

8.0.1 - Technical bump to version number to include update information.

8.0.0 - Performance improvements in add, sub, mul, neg, abs, ceil, floor,
trunc, sqrt, degrees, radians. Asum will now use error checking
with floating point SIMD by default where available. Benchmarks
and unit tests have been updated accordingly.

7.2.0 - Performance improvements in asum and pow. Asum will now use error
checking with floating point SIMD on x86_64 by default. Pow has
special cases for powers of 2 and 3 on integer arrays which allow
for much greater performance. Pow will now raise a value error
exception if an attempt to raise to a negative number. This makes it
it more compatible with Python. New functions pow2 and pow3 added
which raise array values to powers of 2 and 3 respectively. These
have additional optimisations beyond pow, particularly with floating
point arrays. Benchmarks for add, floordiv, mod, mul, pow, sub, and
truediv have been changed to make them run the expanded range of
tests much faster.

7.1.0 - This is a bugfix release to correct mod, mul, and pow. This affects
integer overflow checking at extremes, particularly with the greatest
magnitude negative number on signed arrays. Certain combinations of
numbers may have produced an overflow error when the result was at
the negative margin of the numeric range (e.g. -128 for array type
‘b’ when -2 is raised to the power of 7). The errors have been fixed,
including adding special cases. Also, when 1 or -1 was raised to a
very large power this would cause the algorithm to work for a very
long time to produce an answer (e.g. 1 to the power of 4 billion).
This is now detected and a special case added to short circuit the
calculation to produce the answer. The unit tests for these and
related functions have been updated to include a much wider range
of test data.

7.0.0 - Major speed improvements to add, sub, mul, abs, neg using SIMD with
overflow checking on integer array types. SIMD is now active as the
default on integer arrays with smaller word sizes for these
functions. Major speed improvements on x86 for lshift and rshift by
adding SIMD support to addition integer array types. This was already
present on ARM. Added benchmark for “convert” (this was missing).
Debian test platforms were updated to latest versions (11).

6.2.0 - Updated benchmarks to make each one a separate file. Centos and
OpenSuse test platforms updated to latest versions.

6.1.1 - Documentation updated and version number bumped to reflect testing
with Ubuntu 21.04, FreeBSD 13.0, and OpenBSD 6.9. No code changes.

6.1.0 - Changed convguardbands to narrow -ve guard bands by 1 to handle
LLVM warning. Changed setup.py to detect Raspberry Pi 4 and set the
compiler args accordingly. Added support for Pi 4. Dropped testing
of 64 bit mode on Pi 3.

6.0.1 - Documentation updated to reflect testing with the release version
of Ubuntu 20.04 ARM (Rasberry Pi), Ubuntu 2010 (x86-64), OpenBSD 6.8,
and Python 3.9 on Windows. No code changes and no change in version
number.

6.0.0 - Documentation updated to reflect testing with the release version
of Ubuntu 20.04. No code changes and no change in version number.

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.