MEL

Math Expression Library

const auto val = mel::Eval<double>("sqrt(pow(3,2) + pow(4,2)");

MEL is a small (~500 loc) header-only C++11 library to parse strings into math expression objects that can be evaluated at runtime, by substituting symbols (e.g. x) by runtime values. It can be used, for example, to implement user-defined functions (UDF) in a larger code, in a self-contained way.

Usage

The two main functions of the library are Parse and Eval.

• Parse creates an expression object (a tree) for an input string and extracts the symbols into a container, a symbol is a sub-string that cannot be split into more math operations, or interpreted directly as a number. The type (float, double, etc.) for such constants is a template parameter of the function.
• Eval evaluates an expression tree, the mapping from symbol to value can be specified in two ways, either via a string -> value functor (3 argument version), or more efficiently via a index -> value functor (2 argument version). In the latter, "index" is the position of a symbol in the list of symbols created by Parse. The return type for Eval is a template parameter, and can be different from the one used in Parse (provided the latter can be converted into the former).

Note: A single-argument overload of Eval is provided for expressions without symbols, it evaluates a string directly (i.e. parses and evaluates). This is a convenience function, it is not efficient when the expression needs to be evaluated multiple times. An additional convenience function, Print, can be used to visualize the expression trees produced by Parse.

Example 1

Symbols as strings.

#include <cmath>
#include <map>
#include "mel.hpp"

const std::string expr = "a + \"const b\" * x + c*pow(x,2)";
std::vector<std::string> symbols;
const auto tree = mel::Parse<double>(expr, symbols);

// Assign values to symbols.
std::map<std::string, double> values = {{"a", 1}, {"\"const b\"", -1}, {"c", 0.5}, {"x", 0}};
auto symbol_to_val = [&values](const std::string& s) {
  return values.at(s);
};

// Evaluate for different values of x.
for (double x = 0; x <= 10; x += 0.1) {
  values.at("x") = x;
  std::cout << mel::Eval<double>(tree, symbols, symbol_to_val) << '\n';
}

Example 2

Symbols as indices.

#include <cmath>
#include <vector>
#include "mel.hpp"

const std::string expr = "a + \"const b\" * x + c*pow(x,2)";
std::vector<std::string> symbols;
const auto tree = mel::Parse<double>(expr, symbols);

// Assign values to symbol indices, here we know the order is "a", "const b", "x", "c",
// but in a real application this process of (efficiently) mapping symbol indices
// to indices of recognized symbols (by the app using MEL) can be more involved.
std::vector<double> values = {1, -1, 0, 0.5};
auto idx_to_val = [&values](int i) {
  return values[i];
};

// Evaluate for different values of x.
for (double x = 0; x <= 10; x += 0.1) {
  values[2] = x;
  std::cout << mel::Eval<double>(tree, idx_to_val) << '\n';
}

Default math functions and customization

In the default configuration, MEL parses the four arithmetic operations (+-*/), power and trigonometric functions from cmath, log, exp, fabs, fmin, and fmax. If the type used for Eval only supports simple arithmetic, the macro MEL_ONLY_ARITHMETIC_OPS can be defined before including mel.hpp. The macros MEL_SUPPORTED_FUNCTIONS, MEL_FUNCTION_CODES, and MEL_FUNCTION_IMPLEMENTATIONS, can be used to fully customize the supported math functions, see definitions.hpp for instructions.

Note: MEL can only handle functions of 1 or 2 arguments, with a single return value.

Performance

MEL expressions are between 1 and 100 times slower to evaluate than native C++ (a few benchmarks are included in tests.hpp) The best-case scenario is for expressions that use a large number of functions (pow, exp, etc.) relative to the number of symbols, or when the expression is evaluated in a bandwidth-bound context. The worst-case scenario is for expressions with many repeated symbols (which implies common sub expressions that are not optimized in MEL) used in a compute-bound context.

Note: To achieve good performance, the expression trees have a maximum number of nodes (constants, symbols, or operations) defined at compile-time. The default value is 255 (~4KB trees with up to 64bit constants) and can be overriden with macro MEL_MAX_TREE_SIZE.

License

LGPL-3.0