AFormula is a library for dynamically calculating the value of mathematical formulas, passed in as strings. It is designed to mirror roughly the API of the muParser library http://muparser.sourceforge.net/ as well as offer me a place to experiment with more advanced formula evaluation techniques such as JIT-compiling formulas.
Support is included for all the standard arithmetic and comparative operators, including <=, >=, !=, ==, <, >, +, -, *, /, and ^ (power). Arbitrary variables may be defined (as pointers to double-values), and the assignment operator (=) may be used to assign values to them. A full suite of builtin functions is supported, including:
- Trigonometry (sin, cos, tan, asin, acos, atan, atan2)
- Hyperbolic trigonometry (sinh, cosh, tanh, asinh, acosh, atanh)
- Exponentials (log2, log10 [= log], ln, exp, sqrt)
- Miscellaneous (sign, rint, abs)
- Logical control (if(x,if-true,if-false))
Finally, the constants 'pi' and 'e' are supported.
The priority of operations is:
= (assignment, lowest) <=, >=, !=, ==, <, > (comparisons) +, - (addition/subtraction) *, / (multiplication/division) ^ (exponentiation)
AFormula is designed to be quite robust to invalid formulas, and is careful to return appropriate errors when necessary.
There are two JIT backends which AFormula can use in order to compile functions on the fly: LLVM and libjit. In general, both should provide roughly the same performance, though there is a performance test included which will benchmark the library and permit selection at runtime.
The Boost C++ Libraries http://www.boost.org are required to build AFormula.
Note that at the time of this writing I was not able to get libjit to compile without a fair bit of hacking around on its source code. I've pushed my changes to an unofficial clone of libjit, available at http://github.com/cpence/libjit.
Neither of these libraries are necessary (the included muParser backend will be built regardless), but they will provide a large speed boost.
Thanks are most obviously due to the author of muParser, Ingo Berg. Without muParser having been written, I never would have been able to start on the project that produced the need for AFormula. muParser, which is licensed under the MIT license, is Copyright (C) 2004-2006 Ingo Berg.
Also, thanks is due to the pair of massively cross-platform JIT compilation libraries, LLVM and libjit, without which a JIT-compilation backend (for something like an order of magnitude of performance) would be impossible.