pye

pyeda

Python EDA

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Copyright (c) 2012, Chris Drake All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * 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. 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 HOLDER 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.

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Python Electronic Design Automation


PyEDA is a Python library for electronic design automation.

Read the docs! <http://pyeda.rtfd.org>_

.. image:: https://travis-ci.org/cjdrake/pyeda.png?branch=master :target: https://travis-ci.org/cjdrake/pyeda

Features

  • Symbolic Boolean algebra with a selection of function representations:

    • Logic expressions
    • Truth tables, with three output states (0, 1, "don't care")
    • Reduced, ordered binary decision diagrams (ROBDDs)
  • SAT solvers:

    • Backtracking
    • PicoSAT <http://fmv.jku.at/picosat>_
  • Espresso <http://embedded.eecs.berkeley.edu/pubs/downloads/espresso/index.htm>_ logic minimization

  • Formal equivalence

  • Multi-dimensional bit vectors

  • DIMACS CNF/SAT parsers

  • Logic expression parser

Download

Bleeding edge code::

$ git clone git://github.com/cjdrake/pyeda.git

For release tarballs and zipfiles, visit PyEDA's page at the Cheese Shop <https://pypi.python.org/pypi/pyeda>_.

Installation

Latest release version using pip <http://www.pip-installer.org/en/latest>_::

$ pip3 install pyeda

Installation from the repository::

$ python3 setup.py install

Note that you will need to have Python headers and libraries in order to compile the C extensions. For MacOS, the standard Python installation should have everything you need. For Linux, you will probably need to install the Python3 "development" package.

For Debian-based systems (eg Ubuntu, Mint)::

$ sudo apt-get install python3-dev

For RedHat-based systems (eg RHEL, Centos)::

$ sudo yum install python3-devel

For Windows, just grab the binaries from Christoph Gohlke's excellent pythonlibs page <http://www.lfd.uci.edu/~gohlke/pythonlibs/>_.

Logic Expressions

Invoke your favorite Python terminal, and invoke an interactive pyeda session::

from pyeda.inter import *

Create some Boolean expression variables::

a, b, c, d = map(exprvar, "abcd")

Construct Boolean functions using overloaded Python operators: ~ (NOT), | (OR), ^ (XOR), & (AND), >> (IMPLIES)::

f0 = ~a & b | c & ~d f1 = a >> b f2 = ~a & b | a & ~b f3 = ~a & ~b | a & b f4 = ~a & ~b & ~c | a & b & c f5 = a & b | ~a & c

Construct Boolean functions using standard function syntax::

f10 = Or(And(Not(a), b), And(c, Not(d))) f11 = Implies(a, b) f12 = Xor(a, b) f13 = Xnor(a, b) f14 = Equal(a, b, c) f15 = ITE(a, b, c) f16 = Nor(a, b, c) f17 = Nand(a, b, c)

Construct Boolean functions using higher order operators::

OneHot(a, b, c) And(Or(~a, ~b), Or(~a, ~c), Or(~b, ~c), Or(a, b, c)) OneHot0(a, b, c) And(Or(~a, ~b), Or(~a, ~c), Or(~b, ~c)) Majority(a, b, c) Or(And(a, b), And(a, c), And(b, c)) AchillesHeel(a, b, c, d) And(Or(a, b), Or(c, d))

Investigate a function's properties::

f0.support frozenset({a, b, c, d}) f0.inputs (a, b, c, d) f0.top a f0.degree 4 f0.cardinality 16 f0.depth 2

Convert expressions to negation normal form (NNF), with only OR/AND and literals::

f11.to_nnf() Or(~a, b) f12.to_nnf() Or(And(~a, b), And(a, ~b)) f13.to_nnf() Or(And(~a, ~b), And(a, b)) f14.to_nnf() Or(And(~a, ~b, ~c), And(a, b, c)) f15.to_nnf() Or(And(a, b), And(~a, c)) f16.to_nnf() And(~a, ~b, ~c) f17.to_nnf() Or(~a, ~b, ~c)

Restrict a function's input variables to fixed values, and perform function composition::

f0.restrict({a: 0, c: 1}) Or(b, ~d) f0.compose({a: c, b: ~d}) Or(And(~c, ~d), And(c, ~d))

Test function formal equivalence::

f2.equivalent(f12) True f4.equivalent(f14) True

Investigate Boolean identities::

Double complement

~~a a

Idempotence

a | a a And(a, a) a

Identity

Or(a, 0) a And(a, 1) a

Dominance

Or(a, 1) 1 And(a, 0) 0

Commutativity

(a | b).equivalent(b | a) True (a & b).equivalent(b & a) True

Associativity

Or(a, Or(b, c)) Or(a, b, c) And(a, And(b, c)) And(a, b, c)

Distributive

(a | (b & c)).to_cnf() And(Or(a, b), Or(a, c)) (a & (b | c)).to_dnf() Or(And(a, b), And(a, c))

De Morgan's

Not(a | b).to_nnf() And(~a, ~b) Not(a & b).to_nnf() Or(~a, ~b)

Perform Shannon expansions::

a.expand(b) Or(And(a, ~b), And(a, b)) (a & b).expand([c, d]) Or(And(a, b, ~c, ~d), And(a, b, ~c, d), And(a, b, c, ~d), And(a, b, c, d))

Convert a nested expression to disjunctive normal form::

f = a & (b | (c & d)) f.depth 3 g = f.to_dnf() g Or(And(a, b), And(a, c, d)) g.depth 2 f.equivalent(g) True

Convert between disjunctive and conjunctive normal forms::

f = ~a & ~b & c | ~a & b & ~c | a & ~b & ~c | a & b & c g = f.to_cnf() h = g.to_dnf() g And(Or(a, b, c), Or(a, ~b, ~c), Or(~a, b, ~c), Or(~a, ~b, c)) h Or(And(~a, ~b, c), And(~a, b, ~c), And(a, ~b, ~c), And(a, b, c))

Multi-Dimensional Bit Vectors

Create some four-bit vectors, and use slice operators::

A = exprvars('a', 4) B = exprvars('b', 4) A farray([a[0], a[1], a[2], a[3]]) A[2:] farray([a[2], a[3]]) A[-3:-1] farray([a[1], a[2]])

Perform bitwise operations using Python overloaded operators: ~ (NOT), | (OR), & (AND), ^ (XOR)::

~A farray([~a[0], ~a[1], ~a[2], ~a[3]]) A | B farray([Or(a[0], b[0]), Or(a[1], b[1]), Or(a[2], b[2]), Or(a[3], b[3])]) A & B farray([And(a[0], b[0]), And(a[1], b[1]), And(a[2], b[2]), And(a[3], b[3])]) A ^ B farray([Xor(a[0], b[0]), Xor(a[1], b[1]), Xor(a[2], b[2]), Xor(a[3], b[3])])

Reduce bit vectors using unary OR, AND, XOR::

A.uor() Or(a[0], a[1], a[2], a[3]) A.uand() And(a[0], a[1], a[2], a[3]) A.uxor() Xor(a[0], a[1], a[2], a[3])

Create and test functions that implement non-trivial logic such as arithmetic::

from pyeda.logic.addition import * S, C = ripple_carry_add(A, B)

Note "1110" is LSB first. This says: "7 + 1 = 8".

S.vrestrict({A: "1110", B: "1000"}).to_uint() 8

Other Function Representations

Consult the documentation <http://pyeda.rtfd.org>_ for information about truth tables, and binary decision diagrams. Each function representation has different trade-offs, so always use the right one for the job.

PicoSAT SAT Solver C Extension

PyEDA includes an extension to the industrial-strength PicoSAT <http://fmv.jku.at/picosat>_ SAT solving engine.

Use the satisfy_one method to finding a single satisfying input point::

f = OneHot(a, b, c) f.satisfy_one() {a: 0, b: 0, c: 1}

Use the satisfy_all method to iterate through all satisfying input points::

list(f.satisfy_all()) [{a: 0, b: 0, c: 1}, {a: 0, b: 1, c: 0}, {a: 1, b: 0, c: 0}]

For more interesting examples, see the following documentation chapters:

  • Solving Sudoku <http://pyeda.readthedocs.org/en/latest/sudoku.html>_
  • All Solutions to the Eight Queens Puzzle <http://pyeda.readthedocs.org/en/latest/queens.html>_

Espresso Logic Minimization C Extension

PyEDA includes an extension to the famous Espresso library for the minimization of two-level covers of Boolean functions.

Use the espresso_exprs function to minimize multiple expressions::

f1 = Or(~a & ~b & ~c, ~a & ~b & c, a & ~b & c, a & b & c, a & b & ~c) f2 = Or(~a & ~b & c, a & ~b & c) f1m, f2m = espresso_exprs(f1, f2) f1m Or(And(~a, ~b), And(a, b), And(~b, c)) f2m And(~b, c)

Use the espresso_tts function to minimize multiple truth tables::

X = exprvars('x', 4) f1 = truthtable(X, "0000011111------") f2 = truthtable(X, "0001111100------") f1m, f2m = espresso_tts(f1, f2) f1m Or(x[3], And(x[0], x[2]), And(x[1], x[2])) f2m Or(x[2], And(x[0], x[1]))

Execute Unit Test Suite

If you have Nose <http://nose.readthedocs.org/en/latest>_ installed, run the unit test suite with the following command::

$ make test

If you have Coverage <https://pypi.python.org/pypi/coverage>_ installed, generate a coverage report (including HTML) with the following command::

$ make cover

Perform Static Lint Checks

If you have Pylint <http://www.pylint.org>_ installed, perform static lint checks with the following command::

$ make lint

Build the Documentation

If you have Sphinx <http://sphinx-doc.org>_ installed, build the HTML documentation with the following command::

$ make html

Python Versions Supported

PyEDA is developed using Python 3.3+. It is NOT compatible with Python 2.7, or Python 3.2.

Citations

I recently discovered that people actually use this software in the real world. Feel free to send me a pull request if you would like your project listed here as well.

  • A Model-Based Approach for Reliability Assessment in Component-Based Systems <https://www.phmsociety.org/sites/phmsociety.org/files/phm_submission/2014/phmc_14_025.pdf>_
  • bunsat <http://www.react.uni-saarland.de/tools/bunsat>, used for the SAT paper Fast DQBF Refutation <http://www.react.uni-saarland.de/publications/sat14.pdf>
  • Solving Logic Riddles with PyEDA <http://nicky.vanforeest.com/misc/pyeda/puzzle.html>_
  • Input-Aware Implication Selection Scheme Utilizing ATPG for Efficient Concurrent Error Detection <https://www.mdpi.com/2079-9292/7/10/258>_
  • Generation Methodology for Good-Enough Approximate Modules of ATMR <https://www.dropbox.com/s/dx307ml5qlxn49z/electronicstestingppr.pdf>_
  • Effect of FPGA Circuit Implementation on Error Detection Using Logic Implication Checking <https://www.dropbox.com/s/brwjnrqdlvkuxxe/08491817.pdf>_

Presentations

  • Video from SciPy 2015 <https://www.youtube.com/watch?v=cljDuK0ouRs>_

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