mathpad/MathPad/MPExpressionEvaluator.m

//
//  MPExpressionEvaluator.m
//  MathPad
//
//  Created by Kim Wittenburg on 31.08.14.
//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
//

#import "MPExpressionEvaluator.h"
#import "MPExpression.h"
#import "MPFunction.h"
#import "MPMathRules.h"
#import "MPToken.h"
#import "MPFunction+MPToken.h"
#import "MPTokenStream.h"

#import "MPEvaluationContext.h"
#import "MPPowerFunction.h"



@interface MPExpressionEvaluator ()
@property (readwrite, nonatomic, copy) NSString *definedVariable;


- (void)setError:(MPParseError *)error;

@end

@implementation MPExpressionEvaluator {
    MPParseError *__autoreleasing *_error;
    MPTokenStream *tokenStream;
}

- (id)initWithExpression:(MPExpression *)expression
{
    self = [super init];
    if (self) {
        _expression = expression;
    }
    return self;
}

#pragma mark Evaluating Expressions
- (void)setError:(MPParseError *)error
{
    if (_error) {
        error.pathToExpression = self.expression.indexPath;
        *_error = error;
    }
}

- (MPTerm *)parseExpectingVariable:(BOOL)flag
                             error:(MPParseError *__autoreleasing *)error
{
    _error = error;
    tokenStream = [[MPTokenStream alloc] initWithTokens:[self.expression allItemsInReferenceFrame:MPTokenReferenceFrame]];
    if (!tokenStream.hasMoreTokens) {
        self.error = MPParseError(NSMakeRange(0, 0), @"Empty Expression");
        return nil;
    }
    
    // Variable Definition
    if (flag) {
        MPToken *variableToken = [tokenStream nextToken];
        MPToken *equalsToken = [tokenStream nextTokenOfType:MPEqualsToken];
        
        if (variableToken.tokenType != MPVariableToken) {
            self.error = MPParseError(variableToken.range, @"Expected Variable Definition.");
            return nil;
        }
        if (equalsToken.tokenType != MPEqualsToken) {
            self.error = MPParseError(equalsToken.range, @"Expected \"=\".");
            return nil;
        }
        self.definedVariable = variableToken.stringValue;
    }
    
    BOOL isAtBeginning = YES;
    NSMutableArray *summands = [[NSMutableArray alloc] init];
    NSMutableArray *currentSummand = [[NSMutableArray alloc] init];
    
    while (tokenStream.hasMoreTokens) {
        MPToken *multiplicationToken = [tokenStream nextTokenOfType:MPMultiplicationSymbolToken];
        MPToken *operatorToken = [tokenStream nextTokenOfType:MPOperatorListToken];
        NSRange valueRange;
        MPTerm *value = [self nextValue:&valueRange];
        
        if (multiplicationToken) {
            if (isAtBeginning) {
                self.error = MPParseError(multiplicationToken.range, @"Unexpected Symbol. Expected Number.");
                return nil;
            }
            if (operatorToken) {
                if (operatorToken.numberOfOperators > [[MPMathRules sharedRules] maximumOperatorChainLengthInMultiplication]) {
                    self.error = MPParseError(operatorToken.range, @"Too many operators in multiplication");
                    return nil;
                }
                [currentSummand addObject:[[MPTerm alloc] initWithNumber:operatorToken.operatorValue]];
            }
            if (value) {
                [currentSummand addObject:value];
            } else {
                return nil;
            }
        } else {
            if (operatorToken) {
                if (operatorToken.numberOfOperators > [[MPMathRules sharedRules] maximumOperatorChainLength]) {
                    self.error = MPParseError(operatorToken.range, @"Too many operators.");
                    return nil;
                }
                [summands addObject:[[MPTerm alloc] initWithFactors:currentSummand.copy]];
                currentSummand = [[NSMutableArray alloc] init];
                [currentSummand addObject:[[MPTerm alloc] initWithNumber:operatorToken.operatorValue]];
                if (value) {
                    [currentSummand addObject:value];
                } else {
                    return nil;
                }
            } else if (!value) {
                return nil;
            } else if (isAtBeginning || [[MPMathRules sharedRules] allowsImplicitMultiplication]) {
                [currentSummand addObject:value];
            } else {
                self.error = MPParseError(NSMakeRange(valueRange.location, 0), @"Implicit Multiplication not allowed here");
                return nil;
            }
        }
        
        isAtBeginning = NO;
    }
    [summands addObject:[[MPTerm alloc] initWithFactors:currentSummand.copy]];
    return [[MPTerm alloc] initWithSummands:summands.copy];
}

- (MPTerm *)nextValue:(NSRangePointer)range
{
    MPToken *token = [tokenStream nextToken];
    if (range) {
        *range = token.range;
    }
    switch (token.tokenType) {
        case MPNumberToken:
        {
            return [self decoratedTerm:[[MPTerm alloc] initWithNumber:token.number]];
        }
            
        case MPVariableToken:
        {
            if(![[MPEvaluationContext sharedContext] isVariableDefined:token.variable]) {
                self.error = MPParseError(token.range, @"Undefined Variable");
                return nil;
            }
            return [self decoratedTerm:[[MPTerm alloc] initWithVariable:token.variable]];
        }
            
        case MPGenericFunctionToken:
        {
            if ([token isKindOfClass:[MPPowerFunction class]]) {
                self.error = MPParseError(NSMakeRange(token.range.location, 0), @"No Base for Power");
                return nil;
            }
            return [self decoratedTerm:[((MPFunction *)token) parseWithError:_error]];
        }
            
        case MPSinToken:
        {
            BOOL inverse = [self inverseFunction];
            NSRange sinTermRange;
            MPTerm *sinTerm = [self nextValue:&sinTermRange];
            if (!sinTerm) {
                if (range) {
                    *range = NSUnionRange(token.range, sinTermRange);
                }
                return nil;
            }
            return inverse ? [[MPTerm alloc] initWithInverseSinOfTerm:sinTerm] : [[MPTerm alloc] initWithSinOfTerm:sinTerm];
        }
            
        case MPCosToken:
        {
            BOOL inverse = [self inverseFunction];
            NSRange cosTermRange;
            MPTerm *cosTerm = [self nextValue:&cosTermRange];
            if (!cosTerm) {
                if (range) {
                    *range = NSUnionRange(token.range, cosTermRange);
                }
                return nil;
            }
            return inverse ? [[MPTerm alloc] initWithInverseCosOfTerm:cosTerm] : [[MPTerm alloc] initWithCosOfTerm:cosTerm];
        }
            
        case MPTanToken:
        {
            BOOL inverse = [self inverseFunction];
            NSRange tanTermRange;
            MPTerm *tanTerm = [self nextValue:&tanTermRange];
            if (!tanTerm) {
                if (range) {
                    *range = NSUnionRange(token.range, tanTermRange);
                }
                return nil;
            }
            return inverse ? [[MPTerm alloc] initWithInverseTanOfTerm:tanTerm] : [[MPTerm alloc] initWithTanOfTerm:tanTerm];
        }

        case MPEOFToken:
        {
            self.error = MPParseError(token.range, @"Unexpected End. Expected Number.");
            return nil;
        }
            
        default:
        {
            self.error = MPParseError(token.range, @"Unexpected Symbol. Expected Number.");
            return nil;
        }
    }
}

- (MPTerm *)decoratedTerm:(MPTerm *)term
{
    MPTerm *decoratedTerm = term;
    MPToken *facultyToken = [tokenStream nextTokenOfType:MPFactorialToken];
    if (facultyToken) {
        decoratedTerm = [[MPTerm alloc] initWithFactorialOfTerm:term];
    }
    MPToken *powerToken = [tokenStream nextTokenOfType:MPGenericFunctionToken];
    if ([powerToken isKindOfClass:[MPPowerFunction class]]) {
        MPPowerFunction *powerFunction = (MPPowerFunction *)powerToken;
        powerFunction.baseTerm = decoratedTerm;
        return [powerFunction parseWithError:_error];
    } else if (powerToken) {
        tokenStream.currentTokenIndex--;
    }
    return decoratedTerm;
}

- (BOOL)inverseFunction
{
    MPToken *powerToken = [tokenStream nextTokenOfType:MPGenericFunctionToken];
    if ([powerToken isKindOfClass:[MPPowerFunction class]]) {
        MPPowerFunction *powerFunction = (MPPowerFunction *)powerToken;
        if (powerFunction.exponentExpression.countElements == 1) {
            id<MPExpressionElement> element = [powerFunction.exponentExpression elementAtIndex:0];
            if ([element isString]) {
                NSString *exponent = [[((NSString *)element) componentsSeparatedByCharactersInSet:[NSCharacterSet whitespaceAndNewlineCharacterSet]] componentsJoinedByString:@""];
                if ([exponent isEqualToString:@"-1"]) {
                    return YES;
                }
            }
        }
    }
    if(powerToken) {
        tokenStream.currentTokenIndex--;
    }
    return NO;
}

@end