arythemetic_expressions_parser_kharchenko_kma

overview

this project implements a command-line parser for simple arithmetic expressions and handles expressions as such:

• basic arythmetics: +, -, *, /
• nested brackets: ((...))
• negative numbers: -x or expressions like -(1+2)
• special functions: log(x) for natural logarithm and sqrt(x) for square root
• basic arythemetics inside special functions (log and sqrt): log(10 + 5), sqrt(2 + 7)
• sequences of basic arythemetics: ((2 + 3) * 4)
• log is a natural logorythm (ln)

the parser evaluates input expressions and returns the result

technical description

parsing process

1. preprocessing:

   • remove outer brackets
   • handle minus at the beginning of expressions: -(...)
   • validate balanced brackets; invalid expressions get rejected

2. expression evaluation:

   • if the expression is a single number, it is returned as a result
   • if the expression contains arythmetic operators:
     • operators * and / are evaluated first
     • operators + and - are evaluated afterwards
   • brackets are recursively evaluated from inner to outer

3. special functions:

   • natural logarythm (log(x)):
     • evaluated only if x > 0, else -> error
     • returns ln(x) using f64::ln()
   • square root (sqrt(x)):
     • evaluated only if x >= 0, else -> error
     • returns sqrt(x) using f64::sqrt()

4. error handling:

   • expressions are validated for:
     • balanced brackets
     • valid numeric parsing
     • division by zero
     • domain errors for log and sqrt
     • acceptable characters (no random strings allowed)
   • invalid expressions returns ParseError::InvalidExpression

grammar overview

1. text explanation

• expression ::= Term { ("+" | "-") Term }

• term ::= Factor { ("*" | "/") Factor }

• factor ::= Number | "(" Expression ")" | Function | "-" Factor

• function ::= "log" "(" Expression ")" | "sqrt" "(" Expression ")"

  • Expression — any expression, which may be calculated by the program
  • Term — multiplication/division
  • Factor — the number, inner expression or a function
  • Function — log or sqrt

2. the tree on the example of an expression sqrt(2 + 3) * 4

        (*)
       /   \
    sqrt     4
     |
     (+)
    /   \
   2     3

link to crates.io : https://crates.io/crates/arythemetic_expressions_parser_kharchenko_kma