XXCalc

XXCalc is a scientific calculator interpreting an infix notation with basic solving capabilities. It is written in C++ and it is meant to be quick, robust, embeddable and easily extentable.

>>> (3+(4-1))*5
30
>>> 2 * x + 0.5 = 1
x=0.25
>>> 2x + 1 = 2(1-x)
x=0.25
>>> (x^3+2x-1)^3
x^9+6x^7-3x^6+12x^5-12x^4+11x^3-12x^2+6x-1
>>> bind(ans, 1)
8

Features

The main program xxcalc is a command line linear solver capable of:

• addition, subtraction, multiplication, division and exponentiation of polynomials,
• supporting of nested parentheses,
• solving linear equations,
• supporting pi and e constants,
• supporting log10(number), log(number, base) functions,
• evaluating polynomials using bind(expression, value),
• reporting variety of errors to user.

This program can perform arithmetic operations on polynomials of any degree (as long as a result of the operation is still a polynomial). However, solving is implemented only for linear equations (polynomials of degree 1 at most).

If libreadline is installed, command line interface is a bit interactive and supports history, otherwise a basic standard input and output methods are used.

Build instructions

In order to build the program following requirements must be satisfied:

• compiler of C++11 standard (clang or gcc),
• CMake 3.0+ build tool,
• git client (for unit test library),
• optionally libreadline for pretty input.

The project uses cmake build scripts, however usage of them can be simplified - assuming the dependencies are satisfied, ./build.sh will compile the program into bin directory.

Basis of operation

The solver is split into multiple extensible functional units. The user can embed the solver into his own program and modify its behaviour on variety of levels.

The very first step is a Tokenizer - it takes an input as a text string and performs tokenization (lexing) process. Tokens are smallest complete pieces detected in the input, such as operators, numbers (including scientfic notation), identifiers or parentheses. Such tokenized input is given to a Parser - the parser transforms the input from common infix form into Reverse Polish Notation using the linear time Shunting Yard algorithm. The input obeys rules of associativity and precedence for operators, which must be registered beforehand. Using xxcalc-debug one can observe output of tokenizer and parser.

Parsed tokens in RPN form are evaluated using a Evaluator. Evaluator takes the input and transforms it into computed value. The evaluator support constants and multiple argument functions. The basic unit of data used in computations is a Value which represents a polynomial. This allows to do complex symbolic operations with ease and abstracts other parts of software from the implementation of these operations. The value is a well designed class with support for many operators, which makes interaction with this type a comfortable operation.

Initially the evaluator has no defined functions or constants. A PolynomialCalculator is providing basic arithmetic operations, log functions and some constants - they are registered with the parser and the evaluator. A constant x represents a polynomial of degree 1 and coefficient 1 which makes inputting polynomials a familiar experience.

A LinearSolver extends the polynomial calculator with a basic solving capabilities. A new operator = is defined with the lowest precedence - it takes its operands and using basic arithmetic operations extracts value of the symbol x in a linear expression. This value is returned as the output of = operation. This makes the implementation very clean and readable as there is no difference between common computation or solving expressions.

Unit testing

The project is heavily unit tested using Catch unit test framework. Unit test can be executed using xxcalc-test. The library is automatically downloaded with a CMake build script.

Authors

• Amadeusz Juskowiak juskowiak@amdeusz.me