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//! `Evaluator` is a `TokensReducer`, it takes token in RPN form //! and evaluates its Polynomial value. use super::*; use polynomial::{Polynomial, PolynomialError}; use std::collections::BTreeMap; use std::fmt; /// Pointer to function processing `Polynomial` arguments. /// /// Such function takes a defined number of Polynomial /// arguments and transform them into a single Polynomial /// value. It is used to implement operators and other /// functions in the evaluator. pub type FunctionHandle = Box<Fn(Vec<Polynomial>) -> Result<Polynomial, EvaluationError>>; /// Definition of function with its arity. /// /// A function is used to implement operators and other /// functions in the evaluator. Each function consist /// of `FunctionHandle` which process arguments into a single /// `Polynomial` value. /// /// A function handle is guaranteed to receive a defined /// number of arguments, as this is checked during the /// evaluation (there is no need checking arity of arguments /// in the handler). pub struct Function { arity: usize, handle: FunctionHandle } /// Debug formatter for `Function` impl fmt::Debug for Function { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { write!(f, "Function(arity: {}, handle: ?)", self.arity) } } impl Function { /// Creates a new function with given arity and handler. /// /// Handler can be a pointer to a closure or a function. /// A function handler is guaranteed to receive required /// number of arguments when called. /// /// # Examples /// /// ``` /// # use xxcalc::polynomial_calculator::functions; /// # use xxcalc::evaluator::Function; /// # use xxcalc::polynomial::Polynomial; /// let f_a = Function::new(2, Box::new(functions::addition)); /// let f_b = Function::new(0, Box::new(|args| { /// return Ok(Polynomial::constant(42.0)); /// })); /// ``` pub fn new(a: usize, h: FunctionHandle) -> Function { Function { arity: a, handle: h } } } /// Evaluator takes `Tokens` in Reverse Polish Notation and evaluates /// them using defined functions and constants into a sngle Polynomial /// value. /// /// Evaluator stores registered functions (with their arity) between /// multiple executions. There is no difference between an operator /// and a function call. Additionaly constants can be registered. /// Both identifiers are kept in binary tree, so their retrieval /// is relatively quick. Symbols used for functions or constants /// must be unique, a function with no arguments can replace a /// constant, however its value may change. /// /// # Examples /// /// ``` /// # use xxcalc::tokenizer::Tokenizer; /// # use xxcalc::parser::{Parser, Operator, OperatorAssociativity}; /// # use xxcalc::evaluator::{Evaluator, Function}; /// # use xxcalc::polynomial::Polynomial; /// # use xxcalc::{StringProcessor, TokensProcessor, TokensReducer}; /// let mut tokenizer = Tokenizer::default(); /// let mut parser = Parser::default(); /// let mut evaluator = Evaluator::default(); /// /// parser.register_operator('+', Operator::new(1, OperatorAssociativity::Left)); /// evaluator.register_function("+", Function::new(2, Box::new(|args| { /// // not a production code, just a sample /// Ok(args[0].clone() + args[1].clone()) /// }))); /// /// let parsed = parser.process(tokenizer.process("2+2")).unwrap(); /// assert_eq!(evaluator.process(parsed), Ok(Polynomial::constant(4.0))); /// ``` /// /// # Extending /// /// One can directly register functions or constants with the evaluator, /// or embed the evalutor in another `TokensReducer` which will add these /// handlers by default. pub struct Evaluator { functions: BTreeMap<String, Function>, constants: BTreeMap<String, Polynomial> } /// Creates a new default Evaluator. /// /// Such evaluator is not aware of any functions or constants. /// One must define functions before being able to evaluate /// operators or other calls. impl Default for Evaluator { fn default() -> Evaluator { Evaluator::new() } } /// This is a main processing unit in the evaluator. It takes /// tokens in Reverse Polish Notation and evaluates them into /// a single `Polynomial` value. /// /// Before evaluating functions, operators or constants they /// must be registered, as evaluator has no knowledge what to /// do with the arguments and how to reduce them into a single /// value. Operators and functions are actualy the same thing, /// except that operators always require two arguments. /// /// A traditional stack based postfix evaluation algorithm is /// used (it computes the result in a linear time). Numbers and /// constants are put on a stack, until a operator or a function /// call is required. Such call takes off appropriate number of /// arguments from the stack and calls the function handler /// with these arguments. Result of such evaluation is put back /// on the stack. In the end last value on the stack is returned /// as the result of the evaluation. /// /// # Errors /// /// A `PolynomialError` is returned when underlying function handler returns /// an error (it may happen as a result of converting non constant to float, /// division by zero of polynomials or division of polynomials with wrong /// degree). /// /// A `MultipleExpressions` error is returned when there are multiple tokens /// left on the stack. It is causes by providing to many arguments to a /// function or giving too many expressions. /// /// ``` /// # use xxcalc::tokenizer::Tokenizer; /// # use xxcalc::parser::{Parser, Operator, OperatorAssociativity}; /// # use xxcalc::evaluator::{Evaluator, Function}; /// # use xxcalc::polynomial::Polynomial; /// # use xxcalc::{StringProcessor, TokensProcessor, TokensReducer, EvaluationError}; /// let mut tokenizer = Tokenizer::default(); /// let mut parser = Parser::default(); /// let mut evaluator = Evaluator::default(); /// /// { /// let parsed = parser.process(tokenizer.process("2, 2")).unwrap(); /// assert_eq!(evaluator.process(parsed).unwrap_err(), EvaluationError::MultipleExpressions); /// } /// /// evaluator.register_function("foo", Function::new(1, Box::new(|args| { /// Ok(Polynomial::constant(42.0)) /// }))); /// /// { /// let parsed = parser.process(tokenizer.process("foo(2, 2)")).unwrap(); /// assert_eq!(evaluator.process(parsed).unwrap_err(), EvaluationError::MultipleExpressions); /// } /// ``` /// /// An `ArgumentMissing` error is returned when number of tokens on a stack /// is less than required arity of given functions. The error contains /// required arity and position of error. /// /// ``` /// # use xxcalc::tokenizer::Tokenizer; /// # use xxcalc::parser::{Parser, Operator, OperatorAssociativity}; /// # use xxcalc::evaluator::{Evaluator, Function}; /// # use xxcalc::polynomial::Polynomial; /// # use xxcalc::{StringProcessor, TokensProcessor, TokensReducer, EvaluationError}; /// let mut tokenizer = Tokenizer::default(); /// let mut parser = Parser::default(); /// let mut evaluator = Evaluator::default(); /// /// parser.register_operator('+', Operator::new(1, OperatorAssociativity::Left)); /// evaluator.register_function("+", Function::new(2, Box::new(|args| { /// // not a production code, just a sample /// Ok(args[0].clone() + args[1].clone()) /// }))); /// /// { /// let parsed = parser.process(tokenizer.process("2+2+")).unwrap(); /// assert_eq!(evaluator.process(parsed).unwrap_err(), EvaluationError::ArgumentMissing(String::from("+"), 2, 3)); /// } /// /// evaluator.register_function("foo", Function::new(1, Box::new(|args| { /// Ok(Polynomial::constant(42.0)) /// }))); /// /// { /// let parsed = parser.process(tokenizer.process("foo()")).unwrap(); /// assert_eq!(evaluator.process(parsed).unwrap_err(), EvaluationError::ArgumentMissing(String::from("foo"), 1, 0)); /// } /// ``` /// /// An `UnknownSymbol` error is returned when an operator or identifier token is /// encountered with a name of unregistered function or constant. Each operator, /// function and constant need to be registered before it can be evaluated. /// /// ``` /// # use xxcalc::tokenizer::Tokenizer; /// # use xxcalc::parser::{Parser, Operator, OperatorAssociativity}; /// # use xxcalc::evaluator::{Evaluator, Function}; /// # use xxcalc::polynomial::Polynomial; /// # use xxcalc::{StringProcessor, TokensProcessor, TokensReducer, EvaluationError}; /// let mut tokenizer = Tokenizer::default(); /// let mut parser = Parser::default(); /// let mut evaluator = Evaluator::default(); /// /// parser.register_operator('+', Operator::new(1, OperatorAssociativity::Left)); /// /// { /// let parsed = parser.process(tokenizer.process("2+2")).unwrap(); /// assert_eq!(evaluator.process(parsed).unwrap_err(), EvaluationError::UnknownSymbol(String::from("+"), 1)); /// } /// /// { /// let parsed = parser.process(tokenizer.process("foo(1)")).unwrap(); /// assert_eq!(evaluator.process(parsed).unwrap_err(), EvaluationError::UnknownSymbol(String::from("foo"), 0)); /// } /// /// { /// let parsed = parser.process(tokenizer.process("pi")).unwrap(); /// assert_eq!(evaluator.process(parsed).unwrap_err(), EvaluationError::UnknownSymbol(String::from("pi"), 0)); /// } /// ``` impl TokensReducer for Evaluator { fn process(&self, tokens: &Tokens) -> Result<Polynomial, EvaluationError> { let mut stack: Vec<Polynomial> = Vec::with_capacity(2); for &(position, ref token) in &tokens.tokens { match *token { Token::Number(x) => stack.push(Polynomial::constant(x)), Token::Operator(x) => { let result = self.call_function(&x.to_string(), position, &mut stack)?; stack.push(result); }, Token::Identifier(idx) => { let x = tokens.identifiers.get(idx).unwrap(); if let Some(constant) = self.constants.get(x) { stack.push(constant.clone()); continue; } let result = self.call_function(&x, position, &mut stack)?; stack.push(result); }, _ => unreachable!() } } if stack.len() == 1 { Ok(stack.pop().unwrap()) } else { Err(EvaluationError::MultipleExpressions) } } } impl Evaluator { /// Creates an empty Evaluator with no defined symbols. pub fn new() -> Evaluator { Evaluator { functions: BTreeMap::new(), constants: BTreeMap::new() } } /// Registers a function with its name. /// /// Each function (or an operator) must have a registered function /// handle which takes arguments (or operands) and evaluate them /// into a single value Polynomial. /// /// If a function with the same name has been registered, previously /// registered function is returned, however the name of the function /// cannot collide with an already registered constant. /// /// # Examples /// /// ``` /// # use xxcalc::tokenizer::Tokenizer; /// # use xxcalc::parser::{Parser, Operator, OperatorAssociativity}; /// # use xxcalc::evaluator::{Evaluator, Function}; /// # use xxcalc::polynomial::Polynomial; /// # use xxcalc::{StringProcessor, TokensProcessor, TokensReducer, EvaluationError}; /// let mut tokenizer = Tokenizer::default(); /// let mut parser = Parser::default(); /// let mut evaluator = Evaluator::default(); /// /// parser.register_operator('+', Operator::new(1, OperatorAssociativity::Left)); /// /// { /// let parsed = parser.process(tokenizer.process("2+2")).unwrap(); /// assert_eq!(evaluator.process(parsed), Err(EvaluationError::UnknownSymbol(String::from("+"), 1))); /// } /// /// evaluator.register_function("+", Function::new(2, Box::new(|args| { /// // not a production code, just a sample /// Ok(args[0].clone() + args[1].clone()) /// }))); /// /// { /// let parsed = parser.process(tokenizer.process("2+2")).unwrap(); /// assert_eq!(evaluator.process(parsed), Ok(Polynomial::constant(4.0))); /// } /// ``` /// /// # Errors /// /// A ConflictingName error is returned when name of the function collides /// with previously registered constant. /// /// ``` /// # use xxcalc::evaluator::{Evaluator, Function}; /// # use xxcalc::polynomial::Polynomial; /// # use xxcalc::{StringProcessor, TokensProcessor, TokensReducer, EvaluationError}; /// let mut evaluator = Evaluator::default(); /// /// evaluator.register_constant("foo", Polynomial::constant(42.0)); /// let result = evaluator.register_function("foo", Function::new(1, Box::new(|args| { /// Ok(args[0].clone()) /// }))); /// /// assert_eq!(result.unwrap_err(), EvaluationError::ConflictingName(String::from("foo"))); /// ``` pub fn register_function(&mut self, name: &str, function: Function) -> Result<Option<Function>, EvaluationError> { if self.constants.contains_key(name) { return Err(EvaluationError::ConflictingName(name.to_string())); } Ok(self.functions.insert(name.to_string(), function)) } /// Registers a Polynomial constant with its name. /// /// An identifier with given name is replaced with the constant value /// when it is encountered during evaluation process. // /// If a constant with the same name has been registered, previously /// registered constant is returned, however the name of the constant /// cannot collide with an already registered function. /// /// # Examples /// /// ``` /// # use xxcalc::tokenizer::Tokenizer; /// # use xxcalc::parser::{Parser, Operator, OperatorAssociativity}; /// # use xxcalc::evaluator::{Evaluator, Function}; /// # use xxcalc::polynomial::Polynomial; /// # use xxcalc::{StringProcessor, TokensProcessor, TokensReducer, EvaluationError}; /// let mut tokenizer = Tokenizer::default(); /// let mut parser = Parser::default(); /// let mut evaluator = Evaluator::default(); /// /// { /// let parsed = parser.process(tokenizer.process("foo")).unwrap(); /// assert_eq!(evaluator.process(parsed), Err(EvaluationError::UnknownSymbol(String::from("foo"), 0))); /// } /// /// evaluator.register_constant("foo", Polynomial::constant(42.0)); /// /// { /// let parsed = parser.process(tokenizer.process("foo")).unwrap(); /// assert_eq!(evaluator.process(parsed), Ok(Polynomial::constant(42.0))); /// } /// ``` /// /// # Errors /// /// A ConflictingName error is returned when name of the constant collides /// with previously registered function. /// /// ``` /// # use xxcalc::evaluator::{Evaluator, Function}; /// # use xxcalc::polynomial::Polynomial; /// # use xxcalc::{StringProcessor, TokensProcessor, TokensReducer, EvaluationError}; /// let mut evaluator = Evaluator::default(); /// /// evaluator.register_function("foo", Function::new(1, Box::new(|args| { /// Ok(args[0].clone()) /// }))); /// let result = evaluator.register_constant("foo", Polynomial::constant(42.0)); /// /// assert_eq!(result.unwrap_err(), EvaluationError::ConflictingName(String::from("foo"))); /// ``` pub fn register_constant(&mut self, name: &str, constant: Polynomial) -> Result<Option<Polynomial>, EvaluationError> { if self.functions.contains_key(name) { return Err(EvaluationError::ConflictingName(name.to_string())); } Ok(self.constants.insert(name.to_string(), constant)) } #[inline(always)] fn call_function(&self, name: &str, position: usize, stack: &mut Vec<Polynomial>) -> Result<Polynomial, EvaluationError> { if let Some(function) = self.functions.get(name) { if stack.len() >= function.arity { let stack_len = stack.len(); let args: Vec<Polynomial> = stack.split_off(stack_len - function.arity); (function.handle)(args) } else { Err(EvaluationError::ArgumentMissing(name.to_owned(), function.arity, position)) } } else { Err(EvaluationError::UnknownSymbol(name.to_owned(), position)) } } } /// Encloses `PolynomialError` into an `EvaluationError` impl From<PolynomialError> for EvaluationError { fn from(e: PolynomialError) -> EvaluationError { EvaluationError::PolynomialError(e) } } #[cfg(test)] #[allow(unused_must_use)] mod tests { use TokensReducer; use TokensProcessor; use StringProcessor; use EvaluationError; use evaluator::{Evaluator, Function}; use parser::{Parser, Operator, OperatorAssociativity}; use tokenizer::*; use polynomial::*; #[test] fn test_symbol_registration() { let mut evaluator = Evaluator::new(); assert!(evaluator.register_constant("foo", Polynomial::constant(1.0)).is_ok()); assert!(evaluator.register_constant("foo", Polynomial::constant(2.0)).is_ok()); assert!(evaluator.register_function("foo", Function::new(1, Box::new(|_| Err(EvaluationError::MultipleExpressions)))).is_err()); assert!(evaluator.register_function("bar", Function::new(1, Box::new(|_| Err(EvaluationError::MultipleExpressions)))).is_ok()); assert!(evaluator.register_constant("bar", Polynomial::constant(3.0)).is_err()); } pub fn addition(args: Vec<Polynomial>) -> Result<Polynomial, EvaluationError> { Ok(args[0].clone() + args[1].clone()) } pub fn subtraction(args: Vec<Polynomial>) -> Result<Polynomial, EvaluationError> { Ok(args[0].clone() - args[1].clone()) } pub fn multiplication(args: Vec<Polynomial>) -> Result<Polynomial, EvaluationError> { Ok(args[0].clone() * args[1].clone()) } #[test] fn test_operators() { let mut evaluator = Evaluator::new(); let mut parser = Parser::new(); parser.register_operator('+', Operator::new(1, OperatorAssociativity::Left)); evaluator.register_function("+", Function::new(2, Box::new(addition))); parser.register_operator('-', Operator::new(1, OperatorAssociativity::Left)); evaluator.register_function("-", Function::new(2, Box::new(subtraction))); parser.register_operator('*', Operator::new(5, OperatorAssociativity::Left)); evaluator.register_function("*", Function::new(2, Box::new(multiplication))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("2+4")).unwrap()), Ok(Polynomial::constant(6.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("2*4")).unwrap()), Ok(Polynomial::constant(8.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("2+4*6")).unwrap()), Ok(Polynomial::constant(26.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("2*4+6")).unwrap()), Ok(Polynomial::constant(14.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("(2+4)*6")).unwrap()), Ok(Polynomial::constant(36.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("2+-4")).unwrap()), Ok(Polynomial::constant(-2.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("2--4")).unwrap()), Ok(Polynomial::constant(6.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("2++4")).unwrap()), Ok(Polynomial::constant(6.0))); } #[test] fn test_constants() { let mut evaluator = Evaluator::new(); let mut parser = Parser::new(); assert_eq!(evaluator.process(parser.process(tokenize_ref!("foo")).unwrap()), Err(EvaluationError::UnknownSymbol("foo".to_string(), 0))); evaluator.register_constant("foo", Polynomial::constant(123.0)); assert_eq!(evaluator.process(parser.process(tokenize_ref!("foo")).unwrap()), Ok(Polynomial::constant(123.0))); } #[test] fn test_functions() { let mut evaluator = Evaluator::new(); let mut parser = Parser::new(); parser.register_operator('+', Operator::new(1, OperatorAssociativity::Left)); evaluator.register_function("+", Function::new(2, Box::new(addition))); parser.register_operator('-', Operator::new(1, OperatorAssociativity::Left)); evaluator.register_function("-", Function::new(2, Box::new(subtraction))); parser.register_operator('*', Operator::new(5, OperatorAssociativity::Left)); evaluator.register_function("*", Function::new(2, Box::new(multiplication))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("double(2)")).unwrap()), Err(EvaluationError::UnknownSymbol("double".to_string(), 0))); evaluator.register_function("double", Function::new(1, Box::new(|args|{ Ok(args[0].clone() * Polynomial::constant(2.0)) }))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("double(2)")).unwrap()), Ok(Polynomial::constant(4.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("double(4*-0.5)")).unwrap()), Ok(Polynomial::constant(-4.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("double()")).unwrap()), Err(EvaluationError::ArgumentMissing("double".to_string(), 1, 0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("double(1, 2)")).unwrap()), Err(EvaluationError::MultipleExpressions)); } #[test] fn test_functions_no_arguments() { let mut evaluator = Evaluator::new(); let mut parser = Parser::new(); parser.register_operator('*', Operator::new(5, OperatorAssociativity::Left)); evaluator.register_function("*", Function::new(2, Box::new(multiplication))); evaluator.register_function("unit", Function::new(0, Box::new(|_|{ Ok(Polynomial::constant(1.0)) }))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("unit()")).unwrap()), Ok(Polynomial::constant(1.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("unit")).unwrap()), Ok(Polynomial::constant(1.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("unit*2")).unwrap()), Ok(Polynomial::constant(2.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("2unit")).unwrap()), Ok(Polynomial::constant(2.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("unit(2)")).unwrap()), Err(EvaluationError::MultipleExpressions)); } #[test] fn test_functions_multiple_arguments() { let mut evaluator = Evaluator::new(); let mut parser = Parser::new(); parser.register_operator('*', Operator::new(5, OperatorAssociativity::Left)); evaluator.register_function("*", Function::new(2, Box::new(multiplication))); evaluator.register_function("mod", Function::new(2, Box::new(|args|{ Ok(Polynomial::constant(args[0].clone().as_f64()? % args[1].clone().as_f64()?)) }))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("mod(17, 4)")).unwrap()), Ok(Polynomial::constant(1.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("mod(1)")).unwrap()), Err(EvaluationError::ArgumentMissing("mod".to_string(), 2, 0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("mod(1, 2, 3)")).unwrap()), Err(EvaluationError::MultipleExpressions)); } #[test] fn test_multiple_expression() { let evaluator = Evaluator::new(); let mut parser = Parser::new(); assert_eq!(evaluator.process(parser.process(tokenize_ref!("2, 2")).unwrap()), Err(EvaluationError::MultipleExpressions)); } #[test] fn test_polynomials() { let mut evaluator = Evaluator::new(); let mut parser = Parser::new(); parser.register_operator('+', Operator::new(1, OperatorAssociativity::Left)); evaluator.register_function("+", Function::new(2, Box::new(addition))); parser.register_operator('*', Operator::new(5, OperatorAssociativity::Left)); evaluator.register_function("*", Function::new(2, Box::new(multiplication))); evaluator.register_constant("x", Polynomial::linear(0.0, 1.0)); assert_eq!(evaluator.process(parser.process(tokenize_ref!("x")).unwrap()), Ok(Polynomial::linear(0.0, 1.0))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("x*x")).unwrap()), Ok(Polynomial::new(&[0.0, 0.0, 1.0]))); assert_eq!(evaluator.process(parser.process(tokenize_ref!("x+x")).unwrap()), evaluator.process(parser.process(tokenize_ref!("2x")).unwrap())); } }