Introducing the muparserx math parser library

The evaluation of a mathematical expression is a standard task required in many applications. It can be solved by either using a standard math expression parser such as muparser or by embedding a scripting language such as Lua. There are however some limitations: Although muparser is pretty fast it will only work with scalar values and although Lua is very flexible it does neither support binary operators for arrays nor complex numbers. So if you need a math expression parser with support for arrays, matrices and strings muparserx may be able to help you. It was originally based on the original muparser engine but has since evolved into a standalone project with a completely new parsing engine.

Parser	Data types				Precision	User defined operators			User defined functions		Localization	Licence	Performance (Expr. per second)
	complex	scalar	string	vector		Binary	Postfix	Infix	Strings as parameters	Arbitrary number of parameters
muparser	(1)		(2)		double							MIT	~ 10.000.000
muparserSSE					float					max. 10		MIT	~ 20.000.000
muparserX					double							BSD New	~ 1.600.000

Overview

• Supported data types: double, integer, complex, boolean, string, array
• Extensible with custom operators (binary, infix or postfix)
• Extensible with custom functions with an arbitrary number of function arguments
• Support for an unlimited number of variables and constants
• No limit on expression complexity
• Reads binary, hexadecimal, complex, integer and string values from expressions and can be extended to read user defined values as well.
• Supports a large variety of predefined operators, functions and constants.
• Written in standard compliant C++ code with no external dependencies.

Features

By default the parser supports the following mathematical constants:

• The eulerian number with: e = 2.718281828459045235360287
• Pi with pi = 3.141592653589793238462643
• The imaginary unit with: i = sqrt(-1)

Binary and ternary operators

• Standard operators: +, -, *, /, ^
• Assignment operators: =, +=, -=, *=, /=
• Logical operators: and, or, xor, ==, !=, >, <, <=, >=
• Bit manipulation: &, |, <<, >>
• String concatenation: //
• if then else conditionals with lazy evaluation: ?:

Postfix Operators

• Unit postfixes (nano, micro, milli, kilo, giga, mega): n, mu, m, k, G, M
• Transpose operator: '

Infix Operators

• Sign operator and type conversions: -, (float), (int)

Special Operators

• Multidimensional index operator: a[1,2]
• Ternary if-then-else operator: (a<b) ? c:d
• In-place array creation: {1,2,3}

Predefined Functions

• Standard functions abs, sin, cos, tan, sinh, cosh, tanh, ln, log, log10, exp, sqrt
• Unlimited number of arguments: min, max, sum
• String functions: str2dbl, strlen, toupper
• Complex functions: real, imag, conj, arg, norm
• Array functions: sizeof, eye, ones, zeros

Sample expressions

The next table shows samples of expressions that can be evaluated using muparserx:

Expression	Result	Explanation
"hello"=="world"	false	Comparing strings
"hello "//"world"	"hello world"	String concatanation operator
sin(a+8i)	...	Support for a variety of predefined functions working with complex numbers.
va[3]+vb[5]	...	Support for array variables
va[3]=9	...	Assignment operator in combination with indexed access to a vector
toupper("hello"//"world")	"HELLOWORLD"	Transforming a concatenated string to uppercase.
#010010	18	Interpreting binary values
0x1eff	7935	Interpreting hex values
#10>0x1eff	false	Comparing binary and hex values
1+2-3*4/5^6	2.99923	The standard operators
a = ((a<b) ? 10 : -10)	10 or -10 depending on a and b	Ternary operator for if-then-else conditionals

You might also like:

muparser - Fast Math Parser Library

muparserSSE - A Math Expression Compiler

A Comparison of Numeric Integration Schemes