Analytic Expression Format

Introduction

In many cases, the coordinates, the sizes, locations and other numeric values can be represented as real numbers. However, often an analytic expression which is evaluated at runtime is needed. Example use cases are parametric building blocks and compact models describing bulding block performance. Therefore, openEPDA defines a standardized analytic expression format, which can be used anywhere where a numeric value is expected.

Grammar

Informal summary

The expression grammar was chosen to cover a minimum yet set of expressions. It supports standard mathematical operations, basic mathematical functions and variables defined at runtime.

Expressions can include the following items:

  • basic binary arithmetic operations (addition +, subtraction -, multiplication *, division /, exponentiation ^, and modulus %);

  • unary negation -;

  • mathematical functions (1 argument): abs, acos, asin, ceil, cos, cosh, exp, fac, floor, log, log10, sin, sinh, sqrt, tan, tanh;

  • mathematical functions (2 arguments): atan2, pow;

  • constants: e, pi;

  • numbers (as defined in RFC 7159 - The JSON Data Interchange Format, Section 6. Numbers);

  • arbitrary variable identifiers, starting with a letter, and containing small and capital letters [a-zA-Z], digits [0-9], and an underscore _;

  • combinations of the above enclosed in the parentheses ( and ).

Notes:

  • log function stands for natural logarithm.

  • variable identifiers can not be reserved python keywords. See the list here.

Formal description

To be added after the specification and reference implementation is complete.

Evaluation

A result of expression evaluation should be a numeric value. This means that the information required for expression evaluation (such as variable values) should be available prior to evaluation.

A valid expression can be evaluated using the standard python’s eval function. Also, a valid openEPDA expression is possible to evaluate using tinyexpr C parser.

A parser (e.g. to check expression validity) and an evaluator are available in the openepda python package.