Common Subexpression Elimination and C Code Generation

This repository provides a small MATLAB utility for performing common subexpression elimination (CSE) on symbolic expressions and emitting equivalent MATLAB and C code.

Files

• cse.m
  Core function. Takes a symbolic expression (scalar, vector, or matrix) and returns:

  • MATLAB code with factored powers and extracted common subexpressions
  • C code using double / double _Complex

• cse_print.m
  Convenience wrapper around cse that prints MATLAB and C code for quick inspection.

• test_cse.m
  Simple smoke tests covering scalars, vectors, matrices, complex expressions, and cell input.

Requirements

• MATLAB
• Symbolic Math Toolbox

Tested with recent MATLAB versions, but the code is mostly standard Symbolic Toolbox API.

Usage

Basic

syms a b c x
expr = a*x^2 + b*x^2 + c;

[m_code, c_code] = cse(expr);

disp(m_code);
disp(c_code);

Using cse_print

syms a b c x
expr = a*x^2 + b*x^2 + c;

cse_print(expr);

Example output:

--- MATLAB code ---
x_2 = x*x;
expr = c + x_2*(a + b);

--- C code ---
double x_2 = x*x;
double expr = c+x_2*(a+b);

Vectors and matrices

syms a b c x
A = [a*x, b; c, b + a*x];

cse_print(A);

Example output (MATLAB):

tmp1 = a*x;
A = [ ...
  tmp1, b; ...
  c, b + tmp1
];

Function signature

[m_code, c_code] = cse(r, tmp_name, ncse, max_power)

• r – symbolic expression, vector/matrix, string, or cell of strings
• tmp_name – prefix for temporaries (default: 'tmp')
• ncse – max number of CSE iterations (default: 10)
• max_power – max power to extract as a separate temp (default: 10)

Output:

• m_code – MATLAB code as a single string with newlines
• c_code – C code as a single string with newlines

Code generation details

• A preprocessing step applies simplify(collect(r)) to expose algebraic structure for CSE.
• Powers of symbols (x^2, a^3, etc.) are optionally extracted into temps (x_2, a_3, …) up to max_power.
• CSE is done via subexpr and only eliminates structurally identical subexpressions.
• C code:
  • Uses double by default and promotes to double _Complex when needed.
  • Flattens vectors/matrices to 1D arrays using MATLAB’s column-major linear indexing (A(:) order).

Running tests

From MATLAB:

test_cse;

This prints the original symbolic expression and the generated MATLAB and C code for several test cases.