chore: import upstream snapshot with attribution

doc/Makefile

@@ -0,0 +1,225 @@
+# Makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line.
+SPHINXOPTS    = -n -v -v
+SPHINXBUILD   = sphinx-build
+PAPER         =
+BUILDDIR      = _build
+
+# Internal variables.
+PAPEROPT_a4     = -D latex_paper_size=a4
+PAPEROPT_letter = -D latex_paper_size=letter
+ALLSPHINXOPTS   = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) .
+# the i18n builder cannot share the environment and doctrees with the others
+I18NSPHINXOPTS  = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) .
+
+.PHONY: help
+help:
+	@echo "Please use \`make <target>' where <target> is one of"
+	@echo "  html       to make standalone HTML files"
+	@echo "  dirhtml    to make HTML files named index.html in directories"
+	@echo "  singlehtml to make a single large HTML file"
+	@echo "  pickle     to make pickle files"
+	@echo "  json       to make JSON files"
+	@echo "  htmlhelp   to make HTML files and a HTML help project"
+	@echo "  qthelp     to make HTML files and a qthelp project"
+	@echo "  applehelp  to make an Apple Help Book"
+	@echo "  devhelp    to make HTML files and a Devhelp project"
+	@echo "  epub       to make an epub"
+	@echo "  epub3      to make an epub3"
+	@echo "  latex      to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
+	@echo "  latexpdf   to make LaTeX files and run them through pdflatex"
+	@echo "  latexpdfja to make LaTeX files and run them through platex/dvipdfmx"
+	@echo "  text       to make text files"
+	@echo "  man        to make manual pages"
+	@echo "  texinfo    to make Texinfo files"
+	@echo "  info       to make Texinfo files and run them through makeinfo"
+	@echo "  gettext    to make PO message catalogs"
+	@echo "  changes    to make an overview of all changed/added/deprecated items"
+	@echo "  xml        to make Docutils-native XML files"
+	@echo "  pseudoxml  to make pseudoxml-XML files for display purposes"
+	@echo "  linkcheck  to check all external links for integrity"
+	@echo "  doctest    to run all doctests embedded in the documentation (if enabled)"
+	@echo "  coverage   to run coverage check of the documentation (if enabled)"
+	@echo "  dummy      to check syntax errors of document sources"
+
+.PHONY: clean
+clean:
+	rm -rf $(BUILDDIR)/*
+
+.PHONY: html
+html:
+	$(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
+	@echo
+	@echo "Build finished. The HTML pages are in $(BUILDDIR)/html."
+
+.PHONY: dirhtml
+dirhtml:
+	$(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
+	@echo
+	@echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
+
+.PHONY: singlehtml
+singlehtml:
+	$(SPHINXBUILD) -b singlehtml $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml
+	@echo
+	@echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml."
+
+.PHONY: pickle
+pickle:
+	$(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle
+	@echo
+	@echo "Build finished; now you can process the pickle files."
+
+.PHONY: json
+json:
+	$(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json
+	@echo
+	@echo "Build finished; now you can process the JSON files."
+
+.PHONY: htmlhelp
+htmlhelp:
+	$(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp
+	@echo
+	@echo "Build finished; now you can run HTML Help Workshop with the" \
+	      ".hhp project file in $(BUILDDIR)/htmlhelp."
+
+.PHONY: qthelp
+qthelp:
+	$(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp
+	@echo
+	@echo "Build finished; now you can run "qcollectiongenerator" with the" \
+	      ".qhcp project file in $(BUILDDIR)/qthelp, like this:"
+	@echo "# qcollectiongenerator $(BUILDDIR)/qthelp/numexpr3.qhcp"
+	@echo "To view the help file:"
+	@echo "# assistant -collectionFile $(BUILDDIR)/qthelp/numexpr3.qhc"
+
+.PHONY: applehelp
+applehelp:
+	$(SPHINXBUILD) -b applehelp $(ALLSPHINXOPTS) $(BUILDDIR)/applehelp
+	@echo
+	@echo "Build finished. The help book is in $(BUILDDIR)/applehelp."
+	@echo "N.B. You won't be able to view it unless you put it in" \
+	      "~/Library/Documentation/Help or install it in your application" \
+	      "bundle."
+
+.PHONY: devhelp
+devhelp:
+	$(SPHINXBUILD) -b devhelp $(ALLSPHINXOPTS) $(BUILDDIR)/devhelp
+	@echo
+	@echo "Build finished."
+	@echo "To view the help file:"
+	@echo "# mkdir -p $$HOME/.local/share/devhelp/numexpr3"
+	@echo "# ln -s $(BUILDDIR)/devhelp $$HOME/.local/share/devhelp/numexpr3"
+	@echo "# devhelp"
+
+.PHONY: epub
+epub:
+	$(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub
+	@echo
+	@echo "Build finished. The epub file is in $(BUILDDIR)/epub."
+
+.PHONY: epub3
+epub3:
+	$(SPHINXBUILD) -b epub3 $(ALLSPHINXOPTS) $(BUILDDIR)/epub3
+	@echo
+	@echo "Build finished. The epub3 file is in $(BUILDDIR)/epub3."
+
+.PHONY: latex
+latex:
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+	@echo
+	@echo "Build finished; the LaTeX files are in $(BUILDDIR)/latex."
+	@echo "Run \`make' in that directory to run these through (pdf)latex" \
+	      "(use \`make latexpdf' here to do that automatically)."
+
+.PHONY: latexpdf
+latexpdf:
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+	@echo "Running LaTeX files through pdflatex..."
+	$(MAKE) -C $(BUILDDIR)/latex all-pdf
+	@echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
+
+.PHONY: latexpdfja
+latexpdfja:
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+	@echo "Running LaTeX files through platex and dvipdfmx..."
+	$(MAKE) -C $(BUILDDIR)/latex all-pdf-ja
+	@echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
+
+.PHONY: text
+text:
+	$(SPHINXBUILD) -b text $(ALLSPHINXOPTS) $(BUILDDIR)/text
+	@echo
+	@echo "Build finished. The text files are in $(BUILDDIR)/text."
+
+.PHONY: man
+man:
+	$(SPHINXBUILD) -b man $(ALLSPHINXOPTS) $(BUILDDIR)/man
+	@echo
+	@echo "Build finished. The manual pages are in $(BUILDDIR)/man."
+
+.PHONY: texinfo
+texinfo:
+	$(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
+	@echo
+	@echo "Build finished. The Texinfo files are in $(BUILDDIR)/texinfo."
+	@echo "Run \`make' in that directory to run these through makeinfo" \
+	      "(use \`make info' here to do that automatically)."
+
+.PHONY: info
+info:
+	$(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
+	@echo "Running Texinfo files through makeinfo..."
+	make -C $(BUILDDIR)/texinfo info
+	@echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo."
+
+.PHONY: gettext
+gettext:
+	$(SPHINXBUILD) -b gettext $(I18NSPHINXOPTS) $(BUILDDIR)/locale
+	@echo
+	@echo "Build finished. The message catalogs are in $(BUILDDIR)/locale."
+
+.PHONY: changes
+changes:
+	$(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes
+	@echo
+	@echo "The overview file is in $(BUILDDIR)/changes."
+
+.PHONY: linkcheck
+linkcheck:
+	$(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
+	@echo
+	@echo "Link check complete; look for any errors in the above output " \
+	      "or in $(BUILDDIR)/linkcheck/output.txt."
+
+.PHONY: doctest
+doctest:
+	$(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
+	@echo "Testing of doctests in the sources finished, look at the " \
+	      "results in $(BUILDDIR)/doctest/output.txt."
+
+.PHONY: coverage
+coverage:
+	$(SPHINXBUILD) -b coverage $(ALLSPHINXOPTS) $(BUILDDIR)/coverage
+	@echo "Testing of coverage in the sources finished, look at the " \
+	      "results in $(BUILDDIR)/coverage/python.txt."
+
+.PHONY: xml
+xml:
+	$(SPHINXBUILD) -b xml $(ALLSPHINXOPTS) $(BUILDDIR)/xml
+	@echo
+	@echo "Build finished. The XML files are in $(BUILDDIR)/xml."
+
+.PHONY: pseudoxml
+pseudoxml:
+	$(SPHINXBUILD) -b pseudoxml $(ALLSPHINXOPTS) $(BUILDDIR)/pseudoxml
+	@echo
+	@echo "Build finished. The pseudo-XML files are in $(BUILDDIR)/pseudoxml."
+
+.PHONY: dummy
+dummy:
+	$(SPHINXBUILD) -b dummy $(ALLSPHINXOPTS) $(BUILDDIR)/dummy
+	@echo
+	@echo "Build finished. Dummy builder generates no files."

doc/api.rst

@@ -0,0 +1,28 @@
+NumExpr API
+===========
+
+.. automodule:: numexpr
+   :members: evaluate, re_evaluate, disassemble, NumExpr, get_vml_version, set_vml_accuracy_mode, set_vml_num_threads, set_num_threads, detect_number_of_cores, detect_number_of_threads
+
+.. py:attribute:: ncores
+
+    The number of (virtual) cores detected.
+
+.. py:attribute:: nthreads
+
+    The number of threads currently in-use.
+
+.. py:attribute:: MAX_THREADS
+
+    The maximum number of threads, as set by the environment variable ``NUMEXPR_MAX_THREADS``
+
+.. py:attribute:: version
+
+    The version of NumExpr.
+
+
+Tests submodule
+---------------
+
+.. automodule:: numexpr.tests
+   :members: test, print_versions

doc/conf.py

@@ -0,0 +1,356 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+#
+# numexpr documentation build configuration file, created by
+# sphinx-quickstart on Sat Feb  4 17:19:36 2017.
+#
+# This file is execfile()d with the current directory set to its
+# containing dir.
+#
+# Note that not all possible configuration values are present in this
+# autogenerated file.
+#
+# All configuration values have a default; values that are commented out
+# serve to show the default.
+
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+#
+# import os, sys
+# import numexpr
+# module_location = os.path.dirname(numexpr.__file__)
+# sys.path.insert(0, os.path.abspath(module_location))
+
+# -- General configuration ------------------------------------------------
+
+# If your documentation needs a minimal Sphinx version, state it here.
+#
+# needs_sphinx = '1.0'
+
+# Add any Sphinx extension module names here, as strings. They can be
+# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
+# ones.
+extensions = [
+    'sphinx.ext.autodoc',
+    'sphinx.ext.doctest',
+    'sphinx.ext.intersphinx',
+    'sphinx.ext.coverage',
+    'sphinx.ext.todo',
+    'sphinx.ext.imgmath',
+    'sphinx.ext.ifconfig',
+    'sphinx.ext.viewcode',
+    'sphinx.ext.githubpages',
+    'numpydoc',
+]
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# The suffix(es) of source filenames.
+# You can specify multiple suffix as a list of string:
+#
+# source_suffix = ['.rst', '.md']
+source_suffix = '.rst'
+
+# The encoding of source files.
+#
+source_encoding = 'utf-8-sig'
+
+# The master toctree document.
+master_doc = 'index'
+
+# General information about the project.
+project = 'numexpr'
+copyright = '2006 (various)-2023, David M. Cooke, Francesc Alted, and others'
+author = 'David M. Cooke, Francesc Alted, and others'
+
+# The version info for the project you're documenting, acts as replacement for
+# |version| and |release|, also used in various other places throughout the
+# built documents.
+#
+# The short X.Y version.
+version = '2.13'
+# The full version, including alpha/beta/rc tags.
+release = '2.13.dev1'
+
+
+# The language for content autogenerated by Sphinx. Refer to documentation
+# for a list of supported languages.
+#
+# This is also used if you do content translation via gettext catalogs.
+# Usually you set "language" from the command line for these cases.
+language = 'en'
+
+# There are two options for replacing |today|: either, you set today to some
+# non-false value, then it is used:
+#
+# today = ''
+#
+# Else, today_fmt is used as the format for a strftime call.
+#
+# today_fmt = '%B %d, %Y'
+
+# List of patterns, relative to source directory, that match files and
+# directories to ignore when looking for source files.
+# This patterns also effect to html_static_path and html_extra_path
+exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store']
+
+# The reST default role (used for this markup: `text`) to use for all
+# documents.
+#
+# default_role = None
+
+# If true, '()' will be appended to :func: etc. cross-reference text.
+#
+# add_function_parentheses = True
+
+# If true, the current module name will be prepended to all description
+# unit titles (such as .. function::).
+#
+# add_module_names = True
+
+# If true, sectionauthor and moduleauthor directives will be shown in the
+# output. They are ignored by default.
+#
+# show_authors = False
+
+# The name of the Pygments (syntax highlighting) style to use.
+pygments_style = 'sphinx'
+
+# A list of ignored prefixes for module index sorting.
+# modindex_common_prefix = []
+
+# If true, keep warnings as "system message" paragraphs in the built documents.
+# keep_warnings = False
+
+# If true, `todo` and `todoList` produce output, else they produce nothing.
+todo_include_todos = False
+
+
+# -- Options for HTML output ----------------------------------------------
+
+# The theme to use for HTML and HTML Help pages.  See the documentation for
+# a list of builtin themes.
+#
+html_theme = 'default'
+
+# Theme options are theme-specific and customize the look and feel of a theme
+# further.  For a list of options available for each theme, see the
+# documentation.
+#
+# html_theme_options = {}
+
+# Add any paths that contain custom themes here, relative to this directory.
+# html_theme_path = []
+
+# The name for this set of Sphinx documents.
+# "<project> v<release> documentation" by default.
+#
+# html_title = 'numexpr va0'
+
+# A shorter title for the navigation bar.  Default is the same as html_title.
+#
+# html_short_title = None
+
+# The name of an image file (relative to this directory) to place at the top
+# of the sidebar.
+#
+# html_logo = None
+
+# The name of an image file (relative to this directory) to use as a favicon of
+# the docs.  This file should be a Windows icon file (.ico) being 16x16 or 32x32
+# pixels large.
+#
+# html_favicon = None
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']
+
+# Add any extra paths that contain custom files (such as robots.txt or
+# .htaccess) here, relative to this directory. These files are copied
+# directly to the root of the documentation.
+#
+# html_extra_path = []
+
+# If not None, a 'Last updated on:' timestamp is inserted at every page
+# bottom, using the given strftime format.
+# The empty string is equivalent to '%b %d, %Y'.
+#
+# html_last_updated_fmt = None
+
+# If true, SmartyPants will be used to convert quotes and dashes to
+# typographically correct entities.
+#
+# html_use_smartypants = True
+
+# Custom sidebar templates, maps document names to template names.
+#
+# html_sidebars = {}
+
+# Additional templates that should be rendered to pages, maps page names to
+# template names.
+#
+# html_additional_pages = {}
+
+# If false, no module index is generated.
+#
+# html_domain_indices = True
+
+# If false, no index is generated.
+#
+# html_use_index = True
+
+# If true, the index is split into individual pages for each letter.
+#
+# html_split_index = False
+
+# If true, links to the reST sources are added to the pages.
+#
+# html_show_sourcelink = True
+
+# If true, "Created using Sphinx" is shown in the HTML footer. Default is True.
+#
+# html_show_sphinx = True
+
+# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True.
+#
+# html_show_copyright = True
+
+# If true, an OpenSearch description file will be output, and all pages will
+# contain a <link> tag referring to it.  The value of this option must be the
+# base URL from which the finished HTML is served.
+#
+# html_use_opensearch = ''
+
+# This is the file name suffix for HTML files (e.g. ".xhtml").
+# html_file_suffix = None
+
+# Language to be used for generating the HTML full-text search index.
+# Sphinx supports the following languages:
+#   'da', 'de', 'en', 'es', 'fi', 'fr', 'h', 'it', 'ja'
+#   'nl', 'no', 'pt', 'ro', 'r', 'sv', 'tr', 'zh'
+#
+# html_search_language = 'en'
+
+# A dictionary with options for the search language support, empty by default.
+# 'ja' uses this config value.
+# 'zh' user can custom change `jieba` dictionary path.
+#
+# html_search_options = {'type': 'default'}
+
+# The name of a javascript file (relative to the configuration directory) that
+# implements a search results scorer. If empty, the default will be used.
+#
+# html_search_scorer = 'scorer.js'
+
+# Output file base name for HTML help builder.
+htmlhelp_basename = 'numexprdoc'
+
+# -- Options for LaTeX output ---------------------------------------------
+
+latex_elements = {
+     # The paper size ('letterpaper' or 'a4paper').
+     #
+     # 'papersize': 'letterpaper',
+
+     # The font size ('10pt', '11pt' or '12pt').
+     #
+     # 'pointsize': '10pt',
+
+     # Additional stuff for the LaTeX preamble.
+     #
+     # 'preamble': '',
+
+     # Latex figure (float) alignment
+     #
+     # 'figure_align': 'htbp',
+}
+
+# Grouping the document tree into LaTeX files. List of tuples
+# (source start file, target name, title,
+#  author, documentclass [howto, manual, or own class]).
+#latex_documents = [
+#    (master_doc, 'numexpr.tex', 'numexpr Documentation',
+#     'David M. Cooke, Francesc Alted, and others', 'manual'),
+#]
+
+# The name of an image file (relative to this directory) to place at the top of
+# the title page.
+#
+# latex_logo = None
+
+# For "manual" documents, if this is true, then toplevel headings are parts,
+# not chapters.
+#
+# latex_use_parts = False
+
+# If true, show page references after internal links.
+#
+# latex_show_pagerefs = False
+
+# If true, show URL addresses after external links.
+#
+# latex_show_urls = False
+
+# Documents to append as an appendix to all manuals.
+#
+# latex_appendices = []
+
+# It false, will not define \strong, \code, 	itleref, \crossref ... but only
+# \sphinxstrong, ..., \sphinxtitleref, ... To help avoid clash with user added
+# packages.
+#
+# latex_keep_old_macro_names = True
+
+# If false, no module index is generated.
+#
+# latex_domain_indices = True
+
+
+# -- Options for manual page output ---------------------------------------
+
+# One entry per manual page. List of tuples
+# (source start file, name, description, authors, manual section).
+#man_pages = [
+#    (master_doc, 'numexpr', 'numexpr Documentation',
+#     [author], 1)
+#]
+
+# If true, show URL addresses after external links.
+#
+# man_show_urls = False
+
+
+# -- Options for Texinfo output -------------------------------------------
+
+# Grouping the document tree into Texinfo files. List of tuples
+# (source start file, target name, title, author,
+#  dir menu entry, description, category)
+#texinfo_documents = [
+#    (master_doc, 'numexpr', 'numexpr Documentation',
+#     author, 'numexpr', 'One line description of project.',
+#     'Miscellaneous'),
+#]
+
+# Documents to append as an appendix to all manuals.
+#
+# texinfo_appendices = []
+
+# If false, no module index is generated.
+#
+# texinfo_domain_indices = True
+
+# How to display URL addresses: 'footnote', 'no', or 'inline'.
+#
+# texinfo_show_urls = 'footnote'
+
+# If true, do not generate a @detailmenu in the "Top" node's menu.
+#
+# texinfo_no_detailmenu = False
+
+
+# Example configuration for intersphinx: refer to the Python standard library.
+intersphinx_mapping = {'https://docs.python.org/': None}

doc/index.rst

@@ -0,0 +1,27 @@
+.. numexpr documentation master file, created by
+   sphinx-quickstart on Sat Feb  4 17:19:36 2017.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+NumExpr Documentation Reference
+=================================
+
+Contents:
+
+.. toctree::
+   :maxdepth: 2
+
+   intro
+   user_guide
+   vm2
+   mkl
+   api
+   release_notes
+
+
+Indices and tables
+==================
+
+* :ref:`genindex`
+* :ref:`modindex`
+* :ref:`search`

doc/intro.rst

@@ -0,0 +1,95 @@
+How it works
+============
+
+The string passed to :code:`evaluate` is compiled into an object representing the
+expression and types of the arrays used by the function :code:`numexpr`.
+
+The expression is first compiled using Python's :code:`compile` function (this means
+that the expressions have to be valid Python expressions). From this, the
+variable names can be taken. The expression is then evaluated using instances
+of a special object that keep track of what is being done to them, and which
+builds up the parse tree of the expression.
+
+This parse tree is then compiled to a bytecode program, which describes how to
+perform the operation element-wise. The virtual machine uses "vector registers":
+each register is many elements wide (by default 4096 elements). The key to
+NumExpr's speed is handling chunks of elements at a time.
+
+There are two extremes to evaluating an expression elementwise. You can do each
+operation as arrays, returning temporary arrays. This is what you do when you
+use NumPy: :code:`2*a+3*b` uses three temporary arrays as large as :code:`a` or
+:code:`b`. This strategy wastes memory (a problem if your arrays are large),
+and also is not a good use of cache memory: for large arrays, the results of
+:code:`2*a` and :code:`3*b` won't be in cache when you do the add.
+
+The other extreme is to loop over each element, as in::
+
+    for i in xrange(len(a)):
+        c[i] = 2*a[i] + 3*b[i]
+
+This doesn't consume extra memory, and is good for the cache, but, if the
+expression is not compiled to machine code, you will have a big case statement
+(or a bunch of if's) inside the loop, which adds a large overhead for each
+element, and will hurt the branch-prediction used on the CPU.
+
+:code:`numexpr` uses a in-between approach. Arrays are handled as chunks (of
+4096 elements) at a time, using a register machine. As Python code,
+it looks something like this::
+
+    for i in xrange(0, len(a), 256):
+       r0 = a[i:i+128]
+       r1 = b[i:i+128]
+       multiply(r0, 2, r2)
+       multiply(r1, 3, r3)
+       add(r2, r3, r2)
+       c[i:i+128] = r2
+
+(remember that the 3-arg form stores the result in the third argument,
+instead of allocating a new array). This achieves a good balance between
+cache and branch-prediction. And the virtual machine is written entirely in
+C, which makes it faster than the Python above.  Furthermore the virtual machine
+is also multi-threaded, which allows for efficient parallelization of NumPy
+operations.
+
+There is some more information and history at:
+
+http://www.bitsofbits.com/2014/09/21/numpy-micro-optimization-and-numexpr/
+
+Expected performance
+====================
+
+The range of speed-ups for NumExpr respect to NumPy can vary from 0.95x and 20x,
+being 2x, 3x or 4x typical values, depending on the complexity of the
+expression and the internal optimization of the operators used. The strided and
+unaligned case has been optimized too, so if the expression contains such
+arrays, the speed-up can increase significantly. Of course, you will need to
+operate with large arrays (typically larger than the cache size of your CPU)
+to see these improvements in performance.
+
+Here there are some real timings. For the contiguous case::
+
+    In [1]: import numpy as np
+    In [2]: import numexpr as ne
+    In [3]: a = np.random.rand(1e6)
+    In [4]: b = np.random.rand(1e6)
+    In [5]: timeit 2*a + 3*b
+    10 loops, best of 3: 18.9 ms per loop
+    In [6]: timeit ne.evaluate("2*a + 3*b")
+    100 loops, best of 3: 5.83 ms per loop   # 3.2x: medium speed-up (simple expr)
+    In [7]: timeit 2*a + b**10
+    10 loops, best of 3: 158 ms per loop
+    In [8]: timeit ne.evaluate("2*a + b**10")
+    100 loops, best of 3: 7.59 ms per loop   # 20x: large speed-up due to optimised pow()
+
+For unaligned arrays, the speed-ups can be even larger::
+
+    In [9]: a = np.empty(1e6, dtype="b1,f8")['f1']
+    In [10]: b = np.empty(1e6, dtype="b1,f8")['f1']
+    In [11]: a.flags.aligned, b.flags.aligned
+    Out[11]: (False, False)
+    In [12]: a[:] = np.random.rand(len(a))
+    In [13]: b[:] = np.random.rand(len(b))
+    In [14]: timeit 2*a + 3*b
+    10 loops, best of 3: 29.5 ms per loop
+    In [15]: timeit ne.evaluate("2*a + 3*b")
+    100 loops, best of 3: 7.46 ms per loop   # ~ 4x speed-up

doc/make.bat

@@ -0,0 +1,281 @@
+@ECHO OFF
+
+REM Command file for Sphinx documentation
+
+if "%SPHINXBUILD%" == "" (
+	set SPHINXBUILD=sphinx-build
+)
+set BUILDDIR=_build
+set ALLSPHINXOPTS=-d %BUILDDIR%/doctrees %SPHINXOPTS% .
+set I18NSPHINXOPTS=%SPHINXOPTS% .
+if NOT "%PAPER%" == "" (
+	set ALLSPHINXOPTS=-D latex_paper_size=%PAPER% %ALLSPHINXOPTS%
+	set I18NSPHINXOPTS=-D latex_paper_size=%PAPER% %I18NSPHINXOPTS%
+)
+
+if "%1" == "" goto help
+
+if "%1" == "help" (
+	:help
+	echo.Please use `make ^<target^>` where ^<target^> is one of
+	echo.  html       to make standalone HTML files
+	echo.  dirhtml    to make HTML files named index.html in directories
+	echo.  singlehtml to make a single large HTML file
+	echo.  pickle     to make pickle files
+	echo.  json       to make JSON files
+	echo.  htmlhelp   to make HTML files and a HTML help project
+	echo.  qthelp     to make HTML files and a qthelp project
+	echo.  devhelp    to make HTML files and a Devhelp project
+	echo.  epub       to make an epub
+	echo.  epub3      to make an epub3
+	echo.  latex      to make LaTeX files, you can set PAPER=a4 or PAPER=letter
+	echo.  text       to make text files
+	echo.  man        to make manual pages
+	echo.  texinfo    to make Texinfo files
+	echo.  gettext    to make PO message catalogs
+	echo.  changes    to make an overview over all changed/added/deprecated items
+	echo.  xml        to make Docutils-native XML files
+	echo.  pseudoxml  to make pseudoxml-XML files for display purposes
+	echo.  linkcheck  to check all external links for integrity
+	echo.  doctest    to run all doctests embedded in the documentation if enabled
+	echo.  coverage   to run coverage check of the documentation if enabled
+	echo.  dummy      to check syntax errors of document sources
+	goto end
+)
+
+if "%1" == "clean" (
+	for /d %%i in (%BUILDDIR%\*) do rmdir /q /s %%i
+	del /q /s %BUILDDIR%\*
+	goto end
+)
+
+
+REM Check if sphinx-build is available and fallback to Python version if any
+%SPHINXBUILD% 1>NUL 2>NUL
+if errorlevel 9009 goto sphinx_python
+goto sphinx_ok
+
+:sphinx_python
+
+set SPHINXBUILD=python -m sphinx.__init__
+%SPHINXBUILD% 2> nul
+if errorlevel 9009 (
+	echo.
+	echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
+	echo.installed, then set the SPHINXBUILD environment variable to point
+	echo.to the full path of the 'sphinx-build' executable. Alternatively you
+	echo.may add the Sphinx directory to PATH.
+	echo.
+	echo.If you don't have Sphinx installed, grab it from
+	echo.http://sphinx-doc.org/
+	exit /b 1
+)
+
+:sphinx_ok
+
+
+if "%1" == "html" (
+	%SPHINXBUILD% -b html %ALLSPHINXOPTS% %BUILDDIR%/html
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The HTML pages are in %BUILDDIR%/html.
+	goto end
+)
+
+if "%1" == "dirhtml" (
+	%SPHINXBUILD% -b dirhtml %ALLSPHINXOPTS% %BUILDDIR%/dirhtml
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The HTML pages are in %BUILDDIR%/dirhtml.
+	goto end
+)
+
+if "%1" == "singlehtml" (
+	%SPHINXBUILD% -b singlehtml %ALLSPHINXOPTS% %BUILDDIR%/singlehtml
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The HTML pages are in %BUILDDIR%/singlehtml.
+	goto end
+)
+
+if "%1" == "pickle" (
+	%SPHINXBUILD% -b pickle %ALLSPHINXOPTS% %BUILDDIR%/pickle
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished; now you can process the pickle files.
+	goto end
+)
+
+if "%1" == "json" (
+	%SPHINXBUILD% -b json %ALLSPHINXOPTS% %BUILDDIR%/json
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished; now you can process the JSON files.
+	goto end
+)
+
+if "%1" == "htmlhelp" (
+	%SPHINXBUILD% -b htmlhelp %ALLSPHINXOPTS% %BUILDDIR%/htmlhelp
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished; now you can run HTML Help Workshop with the ^
+.hhp project file in %BUILDDIR%/htmlhelp.
+	goto end
+)
+
+if "%1" == "qthelp" (
+	%SPHINXBUILD% -b qthelp %ALLSPHINXOPTS% %BUILDDIR%/qthelp
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished; now you can run "qcollectiongenerator" with the ^
+.qhcp project file in %BUILDDIR%/qthelp, like this:
+	echo.^> qcollectiongenerator %BUILDDIR%\qthelp\numexpr3.qhcp
+	echo.To view the help file:
+	echo.^> assistant -collectionFile %BUILDDIR%\qthelp\numexpr3.ghc
+	goto end
+)
+
+if "%1" == "devhelp" (
+	%SPHINXBUILD% -b devhelp %ALLSPHINXOPTS% %BUILDDIR%/devhelp
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished.
+	goto end
+)
+
+if "%1" == "epub" (
+	%SPHINXBUILD% -b epub %ALLSPHINXOPTS% %BUILDDIR%/epub
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The epub file is in %BUILDDIR%/epub.
+	goto end
+)
+
+if "%1" == "epub3" (
+	%SPHINXBUILD% -b epub3 %ALLSPHINXOPTS% %BUILDDIR%/epub3
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The epub3 file is in %BUILDDIR%/epub3.
+	goto end
+)
+
+if "%1" == "latex" (
+	%SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished; the LaTeX files are in %BUILDDIR%/latex.
+	goto end
+)
+
+if "%1" == "latexpdf" (
+	%SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex
+	cd %BUILDDIR%/latex
+	make all-pdf
+	cd %~dp0
+	echo.
+	echo.Build finished; the PDF files are in %BUILDDIR%/latex.
+	goto end
+)
+
+if "%1" == "latexpdfja" (
+	%SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex
+	cd %BUILDDIR%/latex
+	make all-pdf-ja
+	cd %~dp0
+	echo.
+	echo.Build finished; the PDF files are in %BUILDDIR%/latex.
+	goto end
+)
+
+if "%1" == "text" (
+	%SPHINXBUILD% -b text %ALLSPHINXOPTS% %BUILDDIR%/text
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The text files are in %BUILDDIR%/text.
+	goto end
+)
+
+if "%1" == "man" (
+	%SPHINXBUILD% -b man %ALLSPHINXOPTS% %BUILDDIR%/man
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The manual pages are in %BUILDDIR%/man.
+	goto end
+)
+
+if "%1" == "texinfo" (
+	%SPHINXBUILD% -b texinfo %ALLSPHINXOPTS% %BUILDDIR%/texinfo
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The Texinfo files are in %BUILDDIR%/texinfo.
+	goto end
+)
+
+if "%1" == "gettext" (
+	%SPHINXBUILD% -b gettext %I18NSPHINXOPTS% %BUILDDIR%/locale
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The message catalogs are in %BUILDDIR%/locale.
+	goto end
+)
+
+if "%1" == "changes" (
+	%SPHINXBUILD% -b changes %ALLSPHINXOPTS% %BUILDDIR%/changes
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.The overview file is in %BUILDDIR%/changes.
+	goto end
+)
+
+if "%1" == "linkcheck" (
+	%SPHINXBUILD% -b linkcheck %ALLSPHINXOPTS% %BUILDDIR%/linkcheck
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Link check complete; look for any errors in the above output ^
+or in %BUILDDIR%/linkcheck/output.txt.
+	goto end
+)
+
+if "%1" == "doctest" (
+	%SPHINXBUILD% -b doctest %ALLSPHINXOPTS% %BUILDDIR%/doctest
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Testing of doctests in the sources finished, look at the ^
+results in %BUILDDIR%/doctest/output.txt.
+	goto end
+)
+
+if "%1" == "coverage" (
+	%SPHINXBUILD% -b coverage %ALLSPHINXOPTS% %BUILDDIR%/coverage
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Testing of coverage in the sources finished, look at the ^
+results in %BUILDDIR%/coverage/python.txt.
+	goto end
+)
+
+if "%1" == "xml" (
+	%SPHINXBUILD% -b xml %ALLSPHINXOPTS% %BUILDDIR%/xml
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The XML files are in %BUILDDIR%/xml.
+	goto end
+)
+
+if "%1" == "pseudoxml" (
+	%SPHINXBUILD% -b pseudoxml %ALLSPHINXOPTS% %BUILDDIR%/pseudoxml
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. The pseudo-XML files are in %BUILDDIR%/pseudoxml.
+	goto end
+)
+
+if "%1" == "dummy" (
+	%SPHINXBUILD% -b dummy %ALLSPHINXOPTS% %BUILDDIR%/dummy
+	if errorlevel 1 exit /b 1
+	echo.
+	echo.Build finished. Dummy builder generates no files.
+	goto end
+)
+
+:end

doc/mkl.rst

@@ -0,0 +1,167 @@
+NumExpr with Intel MKL
+======================
+
+Numexpr has support for Intel's VML (included in Intel's MKL) in order to
+accelerate the evaluation of transcendental functions on Intel CPUs.  Here it
+is a small example on the kind of improvement you may get by using it.
+
+A first benchmark
+-----------------
+
+Firstly, we are going to exercise how MKL performs when computing a couple of
+simple expressions.  One is a pure algebraic one: :code:`2*y + 4*x` and the other
+contains transcendental functions: :code:`sin(x)**2 + cos(y)**2`.
+
+For this, we are going to use this worksheet_.  I (Francesc Alted) ran this
+benchmark on a Intel Xeon E3-1245 v5 @ 3.50GHz. Here are the results when
+not using MKL::
+
+    NumPy version: 1.11.1
+    Time for an algebraic expression:     0.168 s / 6.641 GB/s
+    Time for a transcendental expression: 1.945 s / 0.575 GB/s
+    Numexpr version: 2.6.1. Using MKL: False
+    Time for an algebraic expression:     0.058 s / 19.116 GB/s
+    Time for a transcendental expression: 0.283 s / 3.950 GB/s
+
+
+And now, using MKL::
+
+    NumPy version: 1.11.1
+    Time for an algebraic expression:     0.169 s / 6.606 GB/s
+    Time for a transcendental expression: 1.943 s / 0.575 GB/s
+    Numexpr version: 2.6.1. Using MKL: True
+    Time for an algebraic expression:     0.058 s / 19.153 GB/s
+    Time for a transcendental expression: 0.075 s / 14.975 GB/s
+
+
+As you can see, numexpr using MKL can be up to 3.8x faster for the case of the
+transcendental expression.  Also, you can notice that the pure algebraic
+expression is not accelerated at all.  This is completely expected, as the
+MKL is offering accelerations for CPU bounded functions (sin, cos, tan, exp,
+log, sinh...) and not pure multiplications or adds.
+
+Finally, note how numexpr+MKL can be up to 26x faster than using a pure NumPy
+solution.  And this was using a processor with just four physical cores; you
+should expect more speedup as you throw more cores at that.
+
+.. _worksheet: https://github.com/pydata/numexpr/blob/master/bench/vml_timing2.py
+
+More benchmarks (older)
+-----------------------
+
+Numexpr & VML can both use several threads for doing computations.  Let's see
+how performance improves by using 1 or 2 threads on a 2-core Intel CPU (Core2
+E8400 @ 3.00GHz).
+
+Using 1 thread
+^^^^^^^^^^^^^^
+
+Here we have some benchmarks on the improvement of speed that Intel's VML can
+achieve.  First, look at times by some easy expression containing sine and
+cosine operations *without* using VML::
+
+    In [17]: ne.use_vml
+    Out[17]: False
+
+    In [18]: x = np.linspace(-1, 1, 1e6)
+
+    In [19]: timeit np.sin(x)**2+np.cos(x)**2
+    10 loops, best of 3: 43.1 ms per loop
+
+    In [20]: ne.set_num_threads(1)
+    Out[20]: 2
+
+    In [21]: timeit ne.evaluate('sin(x)**2+cos(x)**2')
+    10 loops, best of 3: 29.5 ms per loop
+
+
+and now using VML::
+
+    In [37]: ne.use_vml
+    Out[37]: True
+
+    In [38]: x = np.linspace(-1, 1, 1e6)
+
+    In [39]: timeit np.sin(x)**2+np.cos(x)**2
+    10 loops, best of 3: 42.8 ms per loop
+
+    In [40]: ne.set_num_threads(1)
+    Out[40]: 2
+
+    In [41]: timeit ne.evaluate('sin(x)**2+cos(x)**2')
+    100 loops, best of 3: 19.8 ms per loop
+
+Hey, VML can accelerate computations by a 50% using a single CPU.  That's great!
+
+Using 2 threads
+^^^^^^^^^^^^^^^
+
+First, look at the time of the non-VML numexpr when using 2 threads::
+
+    In [22]: ne.set_num_threads(2)
+    Out[22]: 1
+
+    In [23]: timeit ne.evaluate('sin(x)**2+cos(x)**2')
+    100 loops, best of 3: 15.3 ms per loop
+
+OK.  We've got an almost perfect 2x improvement in speed with regard to the 1
+thread case.  Let's see about the VML-powered numexpr version::
+
+    In [43]: ne.set_num_threads(2)
+    Out[43]: 1
+
+    In [44]: timeit ne.evaluate('sin(x)**2+cos(x)**2')
+    100 loops, best of 3: 12.2 ms per loop
+
+Ok, that's about 1.6x improvement over the 1 thread VML computation, and
+still a 25% of improvement over the non-VML version.  Good, native numexpr
+multithreading code really looks very efficient!
+
+Numexpr native threading code vs VML's one
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+You may already know that both numexpr and Intel's VML do have support for
+multithreaded computations, but you might be curious about which one is more
+efficient, so here it goes a hint.  First, using the VML multithreaded
+implementation::
+
+    In [49]: ne.set_vml_num_threads(2)
+
+    In [50]: ne.set_num_threads(1)
+    Out[50]: 1
+
+    In [51]: ne.set_vml_num_threads(2)
+
+    In [52]: timeit ne.evaluate('sin(x)**2+cos(x)**2')
+    100 loops, best of 3: 16.8 ms per loop
+
+and now, using the native numexpr threading code::
+
+    In [53]: ne.set_num_threads(2)
+    Out[53]: 1
+
+    In [54]: ne.set_vml_num_threads(1)
+
+    In [55]: timeit ne.evaluate('sin(x)**2+cos(x)**2')
+    100 loops, best of 3: 12 ms per loop
+
+
+This means that numexpr's native multithreaded code is about 40% faster than
+VML's for this case.  So, in general, you should use the former with numexpr
+(and this is the default actually).
+
+Mixing numexpr's and VML multithreading capabilities
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Finally, you might be tempted to use both multithreading codes at the same
+time, but you will be deceived about the improvement in performance::
+
+    In [57]: ne.set_vml_num_threads(2)
+
+    In [58]: timeit ne.evaluate('sin(x)**2+cos(x)**2')
+    100 loops, best of 3: 17.7 ms per loop
+
+Your code actually performs much worse.  That's normal too because you are
+trying to run 4 threads on a 2-core CPU.  For CPUs with many cores, you may
+want to try with different threading configurations, but as a rule of thumb,
+numexpr's one will generally win.

doc/release_notes.rst

@@ -0,0 +1,4 @@
+Release Notes
+=============
+
+.. include:: ../RELEASE_NOTES.rst

doc/requirements.txt

@@ -0,0 +1,4 @@
+sphinx == 6.2.1
+numpy >= 1.13.3
+sphinx-rtd-theme == 1.2.2
+numpydoc == 1.5.0

doc/user_guide.rst

@@ -0,0 +1,340 @@
+NumExpr User Guide
+==================
+
+The NumExpr package supplies routines for the fast evaluation of
+array expressions elementwise by using a vector-based virtual
+machine.
+
+Using it is simple::
+
+    >>> import numpy as np
+    >>> import numexpr as ne
+    >>> a = np.arange(10)
+    >>> b = np.arange(0, 20, 2)
+    >>> c = ne.evaluate('2*a + 3*b')
+    >>> c
+    array([ 0,  8, 16, 24, 32, 40, 48, 56, 64, 72])
+
+
+It is also possible to use NumExpr to validate an expression::
+
+    >>> ne.validate('2*a + 3*b')
+
+which returns `None` on success or raises an exception on invalid inputs.
+
+and it can also re_evaluate an expression::
+
+    >>> b = np.arange(0, 40, 4)
+    >>> ne.re_evaluate()
+
+Building
+--------
+
+*NumExpr* requires Python_ 3.7 or greater, and NumPy_ 1.13 or greater.  It is
+built in the standard Python way:
+
+.. code-block:: bash
+
+    $ pip install .
+
+You must have a C-compiler (i.e. MSVC Build tools on Windows and GCC on Linux) installed.
+
+Then change to a directory that is not the repository directory (e.g. `/tmp`) and
+test :code:`numexpr` with:
+
+.. code-block:: bash
+
+    $ python -c "import numexpr; numexpr.test()"
+
+.. _Python: http://python.org
+.. _NumPy: http://numpy.scipy.org
+
+
+Enabling Intel VML support
+--------------------------
+
+Starting from release 1.2 on, numexpr includes support for Intel's VML
+library.  This allows for better performance on Intel architectures,
+mainly when evaluating transcendental functions (trigonometrical,
+exponential, ...). It also enables numexpr using several CPU cores.
+
+If you have Intel's MKL (the library that embeds VML), just copy the
+:code:`site.cfg.example` that comes in the distribution to :code:`site.cfg` and
+edit the latter giving proper directions on how to find your MKL
+libraries in your system.  After doing this, you can proceed with the
+usual building instructions listed above.  Pay attention to the
+messages during the building process in order to know whether MKL has
+been detected or not.  Finally, you can check the speed-ups on your
+machine by running the :code:`bench/vml_timing.py` script (you can play with
+different parameters to the :code:`set_vml_accuracy_mode()` and
+:code:`set_vml_num_threads()` functions in the script so as to see how it would
+affect performance).
+
+Threadpool Configuration
+------------------------
+
+Threads are spawned at import-time, with the number being set by the environment
+variable ``NUMEXPR_MAX_THREADS``. The default maximum thread count is **64**.
+There is no advantage to spawning more threads than the number of virtual cores
+available on the computing node. Practically NumExpr scales at large thread
+count (`> 8`) only on very large matrices (`> 2**22`). Spawning large numbers
+of threads is not free, and can increase import times for NumExpr or packages
+that import it such as Pandas or PyTables.
+
+If desired, the number of threads in the pool used can be adjusted via an
+environment variable, ``NUMEXPR_NUM_THREADS`` (preferred) or ``OMP_NUM_THREADS``.
+Typically only setting ``NUMEXPR_MAX_THREADS`` is sufficient; the number of
+threads used can be adjusted dynamically via ``numexpr.set_num_threads(int)``.
+The number of threads can never exceed that set by ``NUMEXPR_MAX_THREADS``.
+
+If the user has not configured the environment prior to importing NumExpr, info
+logs will be generated, and the initial number of threads *that are used*_ will
+be set to the number of cores detected in the system or 8, whichever is *less*.
+
+Usage::
+
+    import os
+    os.environ['NUMEXPR_MAX_THREADS'] = '16'
+    os.environ['NUMEXPR_NUM_THREADS'] = '8'
+    import numexpr as ne
+
+Usage Notes
+-----------
+
+`NumExpr`'s principal routine is::
+
+    evaluate(ex, local_dict=None, global_dict=None, optimization='aggressive', truediv='auto')
+
+where :code:`ex` is a string forming an expression, like :code:`"2*a+3*b"`.  The
+values for :code:`a` and :code:`b` will by default be taken from the calling
+function's frame (through the use of :code:`sys._getframe()`).
+Alternatively, they can be specified using the :code:`local_dict` or
+:code:`global_dict` arguments, or passed as keyword arguments.
+
+The :code:`optimization` parameter can take the values :code:`'moderate'`
+or :code:`'aggressive'`.  :code:`'moderate'` means that no optimization is made
+that can affect precision at all.  :code:`'aggressive'` (the default) means that
+the expression can be rewritten in a way that precision *could* be affected, but
+normally very little.  For example, in :code:`'aggressive'` mode, the
+transformation :code:`x~**3` -> :code:`x*x*x` is made, but not in
+:code:`'moderate'` mode.
+
+The `truediv` parameter specifies whether the division is a 'floor division'
+(False) or a 'true division' (True).  The default is the value of
+`__future__.division` in the interpreter.  See PEP 238 for details.
+
+Expressions are cached, so reuse is fast.  Arrays or scalars are
+allowed for the variables, which must be of type 8-bit boolean (bool),
+32-bit signed integer (int), 64-bit signed integer (long),
+double-precision floating point number (float), 2x64-bit,
+double-precision complex number (complex) or raw string of bytes
+(str).  If they are not in the previous set of types, they will be
+properly upcasted for internal use (the result will be affected as
+well).  The arrays must all be the same size.
+
+
+Datatypes supported internally
+------------------------------
+
+*NumExpr* operates internally only with the following types:
+
+    * 8-bit boolean (bool)
+    * 32-bit signed integer (int or int32)
+    * 64-bit signed integer (long or int64)
+    * 32-bit single-precision floating point number (float or float32)
+    * 64-bit, double-precision floating point number (double or float64)
+    * 2x64-bit, double-precision complex number (complex or complex128)
+    * Raw string of bytes (str in Python 2.7, bytes in Python 3+, numpy.str in both cases)
+
+If the arrays in the expression does not match any of these types,
+they will be upcasted to one of the above types (following the usual
+type inference rules, see below).  Have this in mind when doing
+estimations about the memory consumption during the computation of
+your expressions.
+
+Also, the types in NumExpr conditions are somewhat stricter than those
+of Python.  For instance, the only valid constants for booleans are
+:code:`True` and :code:`False`, and they are never automatically cast to integers.
+
+
+Casting rules
+-------------
+
+Casting rules in NumExpr follow closely those of *NumPy*.  However, for
+implementation reasons, there are some known exceptions to this rule,
+namely:
+
+    * When an array with type :code:`int8`, :code:`uint8`, :code:`int16` or
+      :code:`uint16` is used inside NumExpr, it is internally upcasted to an
+      :code:`int` (or :code:`int32` in NumPy notation).
+    * When an array with type :code:`uint32` is used inside NumExpr, it is
+      internally upcasted to a :code:`long` (or :code:`int64` in NumPy notation).
+    * A floating point function (e.g. :code:`sin`) acting on :code:`int8` or
+      :code:`int16` types returns a :code:`float64` type, instead of the
+      :code:`float32` that is returned by NumPy functions.  This is mainly due
+      to the absence of native :code:`int8` or :code:`int16` types in NumExpr.
+    * In operations implying a scalar and an array, the normal rules of casting
+      are used in NumExpr, in contrast with NumPy, where array types takes
+      priority.  For example, if :code:`a` is an array of type :code:`float32`
+      and :code:`b` is an scalar of type :code:`float64` (or Python :code:`float`
+      type, which is equivalent), then :code:`a*b` returns a :code:`float64` in
+      NumExpr, but a :code:`float32` in NumPy (i.e. array operands take priority
+      in determining the result type).  If you need to keep the result a
+      :code:`float32`, be sure you use a :code:`float32` scalar too.
+
+
+Supported operators
+-------------------
+
+*NumExpr* supports the set of operators listed below:
+
+    * Bitwise and logical operators (and, or, not, xor): :code:`&, |, ~, ^`
+    * Comparison operators: :code:`<, <=, ==, !=, >=, >`
+    * Unary arithmetic operators: :code:`-`
+    * Binary arithmetic operators: :code:`+, -, *, /, //, **, %, <<, >>`
+
+
+Supported functions
+-------------------
+
+The next are the current supported set:
+
+    * :code:`where(bool, number1, number2): number` -- number1 if the bool condition
+      is true, number2 otherwise.
+    * :code:`{isinf, isnan, isfinite}(float|complex): bool` -- returns element-wise True
+      for ``inf`` or ``NaN``, ``NaN``, not ``inf`` respectively.
+    * :code:`signbit(float|complex): bool` -- returns element-wise True if signbit is set
+      False otherwise.
+    * :code:`{sin,cos,tan}(float|complex): float|complex` -- trigonometric sine,
+      cosine or tangent.
+    * :code:`{arcsin,arccos,arctan}(float|complex): float|complex` -- trigonometric
+      inverse sine, cosine or tangent.
+    * :code:`arctan2(float1, float2): float` -- trigonometric inverse tangent of
+      float1/float2.
+    * :code:`hypot(float1, float2): float` -- Euclidean distance between float1, float2
+    * :code:`nextafter(float1, float2): float` -- next representable floating-point value after
+      float1 in direction of float2
+    * :code:`copysign(float1, float2): float` -- return number with magnitude of float1 and
+      sign of float2
+    * :code:`{maximum,minimum}(float1, float2): float` -- return max/min of float1, float2
+    * :code:`{sinh,cosh,tanh}(float|complex): float|complex` -- hyperbolic sine,
+      cosine or tangent.
+    * :code:`{arcsinh,arccosh,arctanh}(float|complex): float|complex` -- hyperbolic
+      inverse sine, cosine or tangent.
+    * :code:`{log,log10,log1p,log2}(float|complex): float|complex` -- natural, base-10 and
+      log(1+x) logarithms.
+    * :code:`{exp,expm1}(float|complex): float|complex` -- exponential and exponential
+      minus one.
+    * :code:`sqrt(float|complex): float|complex` -- square root.
+    * :code:`trunc(float): float` -- round towards zero
+    * :code:`round(float|complex|int): float|complex|int` -- round to nearest integer (`rint`)
+    * :code:`sign(float|complex|int): float|complex|int` -- return -1, 0, +1 depending on sign
+    * :code:`abs(float|complex|int): float|complex|int`  -- absolute value.
+    * :code:`conj(complex): complex` -- conjugate value.
+    * :code:`{real,imag}(complex): float` -- real or imaginary part of complex.
+    * :code:`complex(float, float): complex` -- complex from real and imaginary
+      parts.
+    * :code:`contains(np.str, np.str): bool` -- returns True for every string in :code:`op1` that
+      contains :code:`op2`.
+
+Notes
+-----
+
+    * :code:`abs()` for complex inputs returns a :code:`complex` output too.  This is a
+      departure from NumPy where a :code:`float` is returned instead.  However,
+      NumExpr is not flexible enough yet so as to allow this to happen.
+      Meanwhile, if you want to mimic NumPy behaviour, you may want to select the
+      real part via the :code:`real` function (e.g. :code:`real(abs(cplx))`) or via the
+      :code:`real` selector (e.g. :code:`abs(cplx).real`).
+
+More functions can be added if you need them. Note however that NumExpr 2.6 is
+in maintenance mode and a new major revision is under development.
+
+Supported reduction operations
+------------------------------
+
+The next are the current supported set:
+
+  * :code:`sum(number, axis=None)`: Sum of array elements over a given axis.
+    Negative axis are not supported.
+  * :code:`prod(number, axis=None)`: Product of array elements over a given axis.
+    Negative axis are not supported.
+
+*Note:* because of internal limitations, reduction operations must appear the
+last in the stack.  If not, it will be issued an error like::
+
+    >>> ne.evaluate('sum(1)*(-1)')
+    RuntimeError: invalid program: reduction operations must occur last
+
+General routines
+----------------
+
+  * :code:`evaluate(expression, local_dict=None, global_dict=None,
+    optimization='aggressive', truediv='auto')`:  Evaluate a simple array
+    expression element-wise.  See examples above.
+  * :code:`re_evaluate(local_dict=None)`:  Re-evaluate the last array expression
+    without any check.  This is meant for accelerating loops that are re-evaluating
+    the same expression repeatedly without changing anything else than the operands.
+    If unsure, use evaluate() which is safer.
+  * :code:`test()`:  Run all the tests in the test suite.
+  * :code:`print_versions()`:  Print the versions of software that numexpr relies on.
+  * :code:`set_num_threads(nthreads)`: Sets a number of threads to be used in operations.
+    Returns the previous setting for the number of threads.  See note below to see
+    how the number of threads is set via environment variables.
+
+    If you are using VML, you may want to use *set_vml_num_threads(nthreads)* to
+    perform the parallel job with VML instead.  However, you should get very
+    similar performance with VML-optimized functions, and VML's parallelizer
+    cannot deal with common expressions like `(x+1)*(x-2)`, while NumExpr's
+    one can.
+
+  * :code:`detect_number_of_cores()`: Detects the number of cores on a system.
+
+
+Intel's VML specific support routines
+-------------------------------------
+
+When compiled with Intel's VML (Vector Math Library), you will be able
+to use some additional functions for controlling its use. These are:
+
+  * :code:`set_vml_accuracy_mode(mode)`:  Set the accuracy for VML operations.
+
+    The :code:`mode` parameter can take the values:
+
+    - :code:`'low'`: Equivalent to VML_LA - low accuracy VML functions are called
+    - :code:`'high'`: Equivalent to VML_HA - high accuracy VML functions are called
+    - :code:`'fast'`: Equivalent to VML_EP - enhanced performance VML functions are called
+
+    It returns the previous mode.
+
+    This call is equivalent to the :code:`vmlSetMode()` in the VML library. See:
+
+    http://www.intel.com/software/products/mkl/docs/webhelp/vml/vml_DataTypesAccuracyModes.html
+
+    for more info on the accuracy modes.
+
+  * :code:`set_vml_num_threads(nthreads)`: Suggests a maximum number of
+    threads to be used in VML operations.
+
+    This function is equivalent to the call
+    :code:`mkl_domain_set_num_threads(nthreads, MKL_VML)` in the MKL library.
+    See:
+
+    http://www.intel.com/software/products/mkl/docs/webhelp/support/functn_mkl_domain_set_num_threads.html
+
+    for more info about it.
+
+  * :code:`get_vml_version()`:  Get the VML/MKL library version.
+
+
+Authors
+-------
+
+.. include:: ../AUTHORS.txt
+
+License
+-------
+
+NumExpr is distributed under the MIT_ license.
+
+.. _MIT: http://www.opensource.org/licenses/mit-license.php

doc/vm2.rst

@@ -0,0 +1,128 @@
+Performance of the Virtual Machine in NumExpr2.0
+================================================
+
+Numexpr 2.0 leverages a new virtual machine completely based on the new ndarray
+iterator introduced in NumPy 1.6.  This represents a nice combination of the
+advantages of using the new iterator, while retaining the ability to avoid
+copies in memory as well as the multi-threading capabilities of the previous
+virtual machine (1.x series).
+
+The increased performance of the new virtual machine can be seen in several
+scenarios, like:
+
+  * *Broadcasting*.  Expressions containing arrays that needs to be broadcasted,
+    will not need additional memory (i.e. they will be broadcasted on-the-fly).
+  * *Non-native dtypes*.  These will be translated to native dtypes on-the-fly,
+    so there is not need to convert the whole arrays first.
+  * *Fortran-ordered arrays*.  The new iterator will find the best path to
+    optimize operations on such arrays, without the need to transpose them first.
+
+There is a drawback though: performance with small arrays suffers a bit because
+of higher set-up times for the new virtual machine.  See below for detailed
+benchmarks.
+
+Some benchmarks for best-case scenarios
+---------------------------------------
+
+Here you have some benchmarks of some scenarios where the new virtual machine
+actually represents an advantage in terms of speed (also memory, but this is
+not shown here).  As you will see, the improvement is notable in many areas,
+ranging from 3x to 6x faster operations.
+
+Broadcasting
+^^^^^^^^^^^^
+
+    >>> a = np.arange(1e3)
+    >>> b = np.arange(1e6).reshape(1e3, 1e3)
+
+    >>> timeit ne.evaluate("a*(b+1)")   # 1.4.2
+    100 loops, best of 3: 16.4 ms per loop
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 2.0
+    100 loops, best of 3: 5.2 ms per loop
+
+
+Non-native types
+^^^^^^^^^^^^^^^^
+
+    >>> a = np.arange(1e6, dtype=">f8")
+    >>> b = np.arange(1e6, dtype=">f8")
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 1.4.2
+    100 loops, best of 3: 17.2 ms per loop
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 2.0
+    100 loops, best of 3: 6.32 ms per loop
+
+
+Fortran-ordered arrays
+^^^^^^^^^^^^^^^^^^^^^^
+
+    >>> a = np.arange(1e6).reshape(1e3, 1e3).copy('F')
+    >>> b = np.arange(1e6).reshape(1e3, 1e3).copy('F')
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 1.4.2
+    10 loops, best of 3: 32.8 ms per loop
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 2.0
+    100 loops, best of 3: 5.62 ms per loop
+
+
+
+Mix of 'non-native' arrays, Fortran-ordered, and using broadcasting
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+    >>> a = np.arange(1e3, dtype='>f8').copy('F')
+    >>> b = np.arange(1e6, dtype='>f8').reshape(1e3, 1e3).copy('F')
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 1.4.2
+    10 loops, best of 3: 21.2 ms per loop
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 2.0
+    100 loops, best of 3: 5.22 ms per loop
+
+
+Longer setup-time
+^^^^^^^^^^^^^^^^^
+
+The only drawback of the new virtual machine is during the computation of
+small arrays::
+
+    >>> a = np.arange(10)
+    >>> b = np.arange(10)
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 1.4.2
+    10000 loops, best of 3: 22.1 µs per loop
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 2.0
+    10000 loops, best of 3: 30.6 µs per loop
+
+
+i.e. the new virtual machine takes a bit more time to set-up (around 8 µs in
+this machine).  However, this should be not too important because for such a
+small arrays NumPy is always a better option::
+
+    >>> timeit c = a*(b+1)
+    100000 loops, best of 3: 4.16 µs per loop
+
+
+And for arrays large enough the difference is negligible::
+
+    >>> a = np.arange(1e6)
+    >>> b = np.arange(1e6)
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 1.4.2
+    100 loops, best of 3: 5.77 ms per loop
+
+    >>> timeit ne.evaluate("a*(b+1)")  # 2.0
+    100 loops, best of 3: 5.77 ms per loop
+
+
+Conclusion
+----------
+
+The new virtual machine introduced in numexpr 2.0 brings more performance in
+many different scenarios (broadcast, non-native dtypes, Fortran-orderd arrays),
+while it shows slightly worse performance for small arrays.  However, as
+numexpr is more geared to compute large arrays, the new virtual machine should
+be good news for numexpr users in general.