mathpad/MathPad/MPExpression.m

//
//  MPExpression.m
//  MathPad
//
//  Created by Kim Wittenburg on 17.04.14.
//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
//

#import "MPExpression.h"
#import "MPFunction.h"
#import "MPException.h"

NSString *MPAdditionOperator = @"+";
NSString *MPSubtractionOperator = @"-";
NSString *MPMultiplicationOperator = @"*";
NSString *MPDivisionOperator = @"/";

@interface MPExpression (MPExpressionPrivate)

- (NSInteger)lengthOfSymbol:(id)symbol;
- (void)validateSymbols:(NSArray *)symbols;
- (NSArray *)repairedSymbols:(NSArray *)symbols; // Merges subsequent strings
- (void)repairSymbols:(NSMutableArray *)symbols;
- (void)getSplitOffset:(out NSUInteger *)offset inSymbolAtIndex:(out NSUInteger *)symbolIndex forSplitLocation:(NSUInteger)loc;

@end

@implementation MPExpression {
    @package
    __strong NSArray *_symbols;
    NSInteger _length;
}

#pragma mark Creation Methods

- (instancetype)initWithSymbols:(NSArray *)symbols
{
    [self validateSymbols:symbols];
    self = [super init];
    if (self) {
        symbols = [self repairedSymbols:symbols];
        _symbols = [[NSArray alloc] initWithArray:symbols
                                        copyItems:YES];
    }
    return self;
}

#pragma mark Primitive Methods

- (NSUInteger)numberOfSymbols
{
    return [_symbols count];
}

- (id)symbolAtIndex:(NSUInteger)index
{
    return _symbols[index];
}

- (double)doubleValue
{
#warning Unimplemented Method
    return 0;
}

#pragma mark - NSCopying

- (id)copyWithZone:(NSZone *)zone
{
    MPExpression *copy = [[MPExpression allocWithZone:zone] initWithSymbols:_symbols];
    return copy;
}

#pragma mark - NSMutableCopying

- (id)mutableCopyWithZone:(NSZone *)zone
{
    MPMutableExpression *mutableCopy = [[MPMutableExpression allocWithZone:zone] initWithSymbols:_symbols];
    return mutableCopy;
}

#pragma mark - NSCoding

- (id)initWithCoder:(NSCoder *)aDecoder
{
    // TODO: Test Coding
    return [self initWithSymbols:[aDecoder decodeObject]];
}

- (void)encodeWithCoder:(NSCoder *)aCoder
{
    [aCoder encodeObject:_symbols];
}

@end

@implementation MPExpression (MPExpressionPrivate)

- (NSInteger)lengthOfSymbol:(id)symbol
{
    if ([symbol isKindOfClass:[NSString class]]) {
        return [symbol length];
    }
    return 1;
}

// TODO: Deal with subsequent strings
- (void)validateSymbols:(NSArray *)symbols
{
    for (id symbol in symbols) {
        if (!([symbol isKindOfClass:[NSString class]]
              || [symbol isKindOfClass:[MPFunction class]])) {
            @throw [NSException exceptionWithName:MPIllegalSymbolException
                                           reason:@"Only NSString and MPFunction objects are valid symbols."
                                         userInfo:@{MPIllegalSymbolExceptionSymbolKey: symbol}];
        }
    }
}

// TODO: Deal with empty strings
- (NSArray *)repairedSymbols:(NSArray *)symbols
{
    NSMutableArray *mutableSymbols = [symbols mutableCopy];
    [self repairSymbols:mutableSymbols];
    return [mutableSymbols copy];
}

- (void)repairSymbols:(NSMutableArray *)symbols
{
    for (NSInteger index = 1; index < symbols.count; index++) {
        id last = symbols[index-1];
        id current = symbols[index];
        if ([last isKindOfClass:[NSString class]] && [current isKindOfClass:[NSString class]]) {
            NSString *new = [NSString stringWithFormat:@"%@%@", last, current];
            [symbols replaceObjectAtIndex:index-1 withObject:new];
            [symbols removeObjectAtIndex:index];
            index--;
        }
    }
}

- (void)getSplitOffset:(out NSUInteger *)offset inSymbolAtIndex:(out NSUInteger *)symbolIndex forSplitLocation:(NSUInteger)loc
{
    NSUInteger length = 0;
    NSUInteger index = 0;
    NSUInteger symbolLength = 0;
    for (id symbol in _symbols) {
        symbolLength = [self lengthOfSymbol:symbol];
        length += symbolLength;
        if (length >= loc) {
            break;
        }
        index++;
    }
    *offset = symbolLength - (length - loc);
    *symbolIndex = index;
}

@end

@implementation MPExpression (MPExpressionExtensionMethods)

+ (NSArray *)operators
{
    return @[MPAdditionOperator, MPSubtractionOperator, MPMultiplicationOperator, MPDivisionOperator];
}

#pragma mark Creation Methods

- (instancetype)init
{
    return [self initWithSymbols:@[]];
}

- (instancetype)initWithString:(NSString *)aString
{
    return [self initWithSymbols:@[aString]];
}

- (instancetype)initWithFunction:(MPFunction *)aFunction
{
    return [self initWithSymbols:@[aFunction]];
}

+ (instancetype)expression
{
    return [[self alloc] init];
}

+ (instancetype)expressionWithString:(NSString *)aString
{
    return [[self alloc] initWithString:aString];
}

+ (instancetype)expressionWithFunction:(MPFunction *)aFunction
{
    return [[self alloc] initWithFunction:aFunction];
}

+ (instancetype)expressionWithSymbols:(NSArray *)symbols
{
    return [[self alloc] initWithSymbols:symbols];
}

#pragma mark Working with Expressions

- (NSUInteger)length
{
    if (_length == 0) {
        for (id symbol in _symbols) {
            _length += [self lengthOfSymbol:symbol];
        }
    }
    return _length;
}

- (MPExpression *)subexpressionFromIndex:(NSUInteger)from
{
    return [self subexpressionWithRange:NSMakeRange(from, [self length] - from)];
}

- (MPExpression *)subexpressionToIndex:(NSUInteger)to
{
    return [self subexpressionWithRange:NSMakeRange(0, to)];
}

- (MPExpression *)subexpressionWithRange:(NSRange)range
{
    if (NSMaxRange(range) > self.length) {
        @throw [NSException exceptionWithName:NSRangeException reason:@"Range outside bounds of expression." userInfo:nil];
    }
    if (range.location == self.length || NSMaxRange(range) == 0 || range.length == 0) {
        // Speed this up
        return [[MPExpression alloc] init];
    }
    NSUInteger startOffset;
    NSUInteger startSymbolIndex;
    [self getSplitOffset:&startOffset inSymbolAtIndex:&startSymbolIndex forSplitLocation:range.location];
    id startSymbol = _symbols[startSymbolIndex];
    if (startOffset == [self lengthOfSymbol:startSymbol]) {
        startOffset = 0;
        startSymbolIndex++;
        startSymbol = _symbols[startSymbolIndex];
    } else if ([startSymbol isKindOfClass:[NSString class]]) {
        startSymbol = [startSymbol substringFromIndex:startOffset];
    }
    NSUInteger endOffset;
    NSUInteger endSymbolIndex;
    [self getSplitOffset:&endOffset inSymbolAtIndex:&endSymbolIndex forSplitLocation:NSMaxRange(range)];
    id endSymbol = _symbols[endSymbolIndex];
    if ([endSymbol isKindOfClass:[NSString class]]) {
        endSymbol = [endSymbol substringToIndex:endOffset];
        
    }
    
    NSMutableArray *symbols = [[NSMutableArray alloc] initWithCapacity:endSymbolIndex-startSymbolIndex+1];
    [symbols addObject:startSymbol];
    if (endSymbolIndex > startSymbolIndex + 1) {
        NSInteger restLength = endSymbolIndex - startSymbolIndex - 1;
        [symbols addObjectsFromArray:[_symbols subarrayWithRange:NSMakeRange(startSymbolIndex+1, restLength)]];
    }
    if (endSymbolIndex > startSymbolIndex) {
        [symbols addObject:endSymbol];
    } else if (endSymbolIndex == startSymbolIndex && [startSymbol isKindOfClass:[NSString class]]) {
        NSString *result = [_symbols[startSymbolIndex] substringWithRange:NSMakeRange(startOffset, endOffset-startOffset)];
        [symbols replaceObjectAtIndex:0 withObject:result];
    }
    return [[MPExpression alloc] initWithSymbols:symbols];
}

- (BOOL)isEqual:(id)object
{
    if (self == object) {
        return YES;
    }
    if (object == nil) {
        return NO;
    }
    if (![object isKindOfClass:[MPExpression class]]) {
        return NO;
    }
    return [self isEqualToExpression:(MPExpression *)object];
}

- (BOOL)isEqualToExpression:(MPExpression *)anExpression
{
    // TODO: Use ->_symbols or .symbols
    return [_symbols isEqualToArray:anExpression->_symbols];
}

- (MPExpression *)expressionByAppendingString:(NSString *)aString
{
    return [self expressionByAppendingSymbols:@[aString]];
}

- (MPExpression *)expressionByAppendingFunction:(MPFunction *)aFunction
{
    return [self expressionByAppendingSymbols:@[aFunction]];
}

- (MPExpression *)expressionByAppendingExpression:(MPExpression *)anExpression
{
    return [self expressionByAppendingSymbols:anExpression.symbols];
}

- (MPExpression *)expressionByAppendingSymbols:(NSArray *)symbols
{
    return [[MPExpression alloc] initWithSymbols:[_symbols arrayByAddingObjectsFromArray:symbols]];
}

#pragma mark Evaluating Expressions

- (float)floatValue
{
    return (float)[self doubleValue];
}

- (int)intValue
{
    return (int)[self doubleValue];
}

- (NSInteger)integerValue
{
    return (NSInteger)[self doubleValue];
}

- (long long)longLongValue
{
    return (long long)[self doubleValue];
}

#pragma mark Querying an Expression's Contents

- (NSArray *)symbols
{
    // _symbols is immutable so it is ok to just return it instead of making a copy
    return _symbols;
}

- (NSString *)description
{
    NSMutableString *description = [[NSMutableString alloc] init];
    NSUInteger index = 0;
    for (id symbol in _symbols) {
        if ([symbol isKindOfClass:[NSString class]]) {
            NSMutableString *correctedSymbol = [[symbol stringByTrimmingCharactersInSet:[NSCharacterSet whitespaceAndNewlineCharacterSet]] mutableCopy];
            // Prefix operator
            if (symbol != _symbols[0]) {
                unichar prefix = [correctedSymbol characterAtIndex:0];
                if ([[NSCharacterSet decimalDigitCharacterSet] characterIsMember:prefix]) {
                    [correctedSymbol insertString:@"*" atIndex:0];
                }
            }
            // Suffix operator
            if (symbol != [_symbols lastObject]) {
                unichar suffix = [correctedSymbol characterAtIndex:correctedSymbol.length-1];
                if ([[NSCharacterSet decimalDigitCharacterSet] characterIsMember:suffix]) {
                    [correctedSymbol appendString:@"*"];
                }
            }
            [description appendString:correctedSymbol];
        } else if (index > 0 && [_symbols[index-1] isKindOfClass:[MPFunction class]]) {
            [description appendFormat:@"*%@", [symbol description]];
        } else {
            [description appendString:[symbol description]];
        }
        index++;
    }
    return description;
}

- (NSUInteger)hash
{
    return [_symbols hash];
}

@end

@implementation MPMutableExpression

- (instancetype)initWithSymbols:(NSArray *)symbols
{
    [self validateSymbols:symbols];
    self = [super initWithSymbols:nil];
    if (self) {
        symbols = [self repairedSymbols:symbols];
        _symbols = [[NSMutableArray alloc] initWithArray:symbols copyItems:YES];
    }
    return self;
}

- (NSArray *)symbols
{
    // Return an immutable array:
    return [_symbols copy];
}

- (void)replaceSymbolsInRange:(NSRange)range withSymbols:(NSArray *)symbols
{
    if (NSMaxRange(range) > self.length) {
        @throw [NSException exceptionWithName:NSRangeException reason:@"Range out of bounds of expression." userInfo:nil];
    }
    [self validateSymbols:symbols];
    
    // Locate the position, split the symbols
    NSUInteger startIndex;
    [self splitSymbolsAtLocation:range.location insertionIndex:&startIndex];
    
    // Perform the deletion
    if (range.length > 0) {
        NSUInteger endIndex;
        [self splitSymbolsAtLocation:NSMaxRange(range) insertionIndex:&endIndex];
        NSMutableIndexSet *indexes = [[NSMutableIndexSet alloc] init];
        for (NSUInteger index = startIndex; index < endIndex; index++) {
            [indexes addIndex:index];
        }
        [(NSMutableArray *)_symbols removeObjectsAtIndexes:indexes];
    }
    
    // Perform the insertion
    if (symbols.count > 0) {
        NSArray *newSymbols = [[NSArray alloc] initWithArray:symbols copyItems:YES];
        [(NSMutableArray *)_symbols replaceObjectsInRange:NSMakeRange(startIndex, 0) withObjectsFromArray:newSymbols];
    }
    
    // Revalidate structure and invalidate length
    [self repairSymbols:(NSMutableArray *)_symbols];
    _length = 0;
}

- (void)splitSymbolsAtLocation:(NSUInteger)loc insertionIndex:(out NSUInteger *)insertionIndex
{
    NSUInteger splitSymbolIndex;
    NSUInteger splitOffset;
    [self getSplitOffset:&splitOffset inSymbolAtIndex:&splitSymbolIndex forSplitLocation:loc];
    id splitSymbol = _symbols[splitSymbolIndex];
    NSInteger splitSymbolLength = [self lengthOfSymbol:splitSymbol];
    if (splitOffset == splitSymbolLength) {
        splitOffset = 0;
        splitSymbolIndex++;
    }
    if (splitOffset != 0) {
        NSString *leftPart = [splitSymbol substringToIndex:splitOffset];
        NSString *rightPart = [splitSymbol substringFromIndex:splitOffset];
        [(NSMutableArray *)_symbols replaceObjectAtIndex:splitSymbolIndex withObject:leftPart];
        splitSymbolIndex++;
        [(NSMutableArray *)_symbols insertObject:rightPart atIndex:splitSymbolIndex];
    }
    *insertionIndex = splitSymbolIndex;
}

@end

@implementation MPMutableExpression (MPMutableExpressionExtensionMethods)

- (void)insertString:(NSString *)aString atIndex:(NSUInteger)loc
{
    [self insertSymbols:@[aString] atIndex:loc];
}

- (void)insertFunction:(MPFunction *)aFunction atIndex:(NSUInteger)loc
{
    [self insertSymbols:@[aFunction] atIndex:loc];
}

- (void)insertExpression:(MPExpression *)anExpression atIndex:(NSUInteger)loc
{
    [self insertSymbols:anExpression.symbols atIndex:loc];
}

- (void)insertSymbols:(NSArray *)symbols atIndex:(NSUInteger)loc
{
    [self replaceSymbolsInRange:NSMakeRange(loc, 0)
                    withSymbols:symbols];
}

- (void)deleteSymbolsInRange:(NSRange)range
{
    [self replaceSymbolsInRange:range
                    withSymbols:@[]];
}

- (void)appendString:(NSString *)aString
{
    [self appendSymbols:@[aString]];
}

- (void)appendFunction:(MPFunction *)aFunction
{
    [self appendSymbols:@[aFunction]];
}

- (void)appendExpression:(MPExpression *)anExpression
{
    [self appendSymbols:anExpression.symbols];
}

- (void)appendSymbols:(NSArray *)symbols
{
    [self replaceSymbolsInRange:NSMakeRange(self.length, 0)
                    withSymbols:symbols];
}

- (void)setString:(NSString *)aString
{
    [self setSymbols:@[aString]];
}

- (void)setFunction:(MPFunction *)aFunction
{
    [self setSymbols:@[aFunction]];
}

- (void)setExpression:(MPExpression *)anExpression
{
    [self setSymbols:anExpression.symbols];
}

- (void)setSymbols:(NSArray *)symbols
{
    [self replaceSymbolsInRange:NSMakeRange(0, self.length)
                    withSymbols:symbols];
}

@end