Python Electronic Design Automation

## Project description

PyEDA is a Python library for electronic design automation. ## 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:
• Espresso logic minimization
• Formal equivalence
• Multi-dimensional bit vectors
• DIMACS CNF/SAT parsers
• Logic expression parser

Bleeding edge code:

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

For release tarballs and zipfiles, visit PyEDA’s page at the Cheese Shop.

## Installation

Latest release version using pip:

```\$ 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.

## 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, a, a, a])
>>> A[2:]
farray([a, a])
>>> A[-3:-1]
farray([a, a])
```

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

```>>> ~A
farray([~a, ~a, ~a, ~a])
>>> A | B
farray([Or(a, b), Or(a, b), Or(a, b), Or(a, b)])
>>> A & B
farray([And(a, b), And(a, b), And(a, b), And(a, b)])
>>> A ^ B
farray([Xor(a, b), Xor(a, b), Xor(a, b), Xor(a, b)])
```

Reduce bit vectors using unary OR, AND, XOR:

```>>> A.uor()
Or(a, a, a, a)
>>> A.uand()
And(a, a, a, a)
>>> A.uxor()
Xor(a, a, a, a)
```

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 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 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:

## 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, And(x, x), And(x, x))
>>> f2m
Or(x, And(x, x))
```

## Execute Unit Test Suite

If you have Nose installed, run the unit test suite with the following command:

```\$ make test
```

If you have Coverage installed, generate a coverage report (including HTML) with the following command:

```\$ make cover
```

## Perform Static Lint Checks

If you have Pylint installed, perform static lint checks with the following command:

```\$ make lint
```

## Build the Documentation

If you have Sphinx 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.

## Project details

This version 0.28.0 0.27.5 0.27.4 0.27.3 0.27.2 0.27.1 0.27.0 0.26.0 0.25.0 0.24.0 0.23.0 0.22.0 0.21.0 0.20.0 0.19.3 0.19.2 0.19.1 0.19.0 0.18.1 0.18.0 0.17.1 0.17.0 0.16.3 0.16.2 0.16.1 0.16.0 0.15.1 0.15.0 0.14.2 0.14.1 0.14.0 0.13.0 0.12.0 0.11.1 0.11.0 0.10.0 0.9.0 0.8.0 0.7.0 0.6.0 0.5.0 0.4.0