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BigCFloat.m
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BigCFloat.m
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// ##############################################################
// BigCFloat.m
// BigFloat Implementation
//
// Created by Matt Gallagher on Sat Apr 19 2003.
// Copyright (c) 2003 Matt Gallagher. All rights reserved.
// ##############################################################
#import "BigCFloat.h"
//
// About BigCFloat
//
// BigCFloat extends the BigFloat implementation to span the complex domain.
// Not much more complicated than that.
//
// Unless you really want strictly real numbers I actually recommend you use this
// class instead of BigFloat as it smooths over a few glitches in the real domain
// Taylor Series for trigonometric functions.
//
@implementation BigCFloat
#pragma mark
#pragma mark ### Constructors ###
//
// init
//
// Wrapper that adds complex number support around the base class
//
- (instancetype)init
{
self = [super init];
if (self)
{
bcf_imaginary = [[BigFloat alloc] init];
bcf_has_imaginary = NO;
}
return self;
}
//
// initWithReal
//
// Init real and imaginary parts. You can validly pass nil instead of zero.
//
- (instancetype)initWithReal:(BigFloat *)realPart imaginary:(BigFloat *)imaginaryPart
{
self = [super init];
if (self)
{
if (!realPart) realPart = [BigFloat bigFloatWithInt:0 radix:bf_radix];
if (!imaginaryPart) imaginaryPart = [BigFloat bigFloatWithInt:0 radix:bf_radix];
[super assign:realPart];
if ([imaginaryPart isKindOfClass:[BigCFloat class]])
{
BigCFloat *cnum = (BigCFloat *)imaginaryPart;
bcf_imaginary = [cnum realPartCopy];
}
else
{
bcf_imaginary = [imaginaryPart copy];
}
bcf_has_imaginary = ![bcf_imaginary isZero];
if ([bcf_imaginary radix] != bf_radix)
[bcf_imaginary convertToRadix:bf_radix];
}
return self;
}
//
// initWithMagnitude
//
// Initialisation in polar coordinates.
//
- (instancetype)initWithMagnitude:(BigFloat *)r angle:(BigFloat *)theta
{
self = [super init];
if (self)
{
BigFloat *realPart;
BigFloat *imaginaryPart;
if ([theta isKindOfClass:[BigCFloat class]])
{
BigCFloat *cnum = (BigCFloat *)theta;
imaginaryPart = [cnum realPartCopy];
realPart = [cnum realPartCopy];
}
else
{
imaginaryPart = [theta copy];
realPart = [theta copy];
}
[realPart cosWithTrigMode:BF_radians inv:NO hyp:NO];
[super assign:r];
[super multiplyBy:realPart];
[imaginaryPart sinWithTrigMode:BF_radians inv:NO hyp:NO];
[imaginaryPart multiplyBy:r];
bcf_imaginary = [[BigFloat alloc] init];
[bcf_imaginary assign:imaginaryPart];
if ([bcf_imaginary radix] != bf_radix)
[bcf_imaginary convertToRadix:bf_radix];
bcf_has_imaginary = ![imaginaryPart isZero];
}
return self;
}
//
// initWithInt
//
// Wrapper that adds complex number support around the base class
//
- (instancetype)initWithInt:(signed int)newValue radix:(unsigned short)newRadix
{
self = [super initWithInt:newValue radix:newRadix];
if (self)
{
bcf_imaginary = [BigFloat bigFloatWithInt:0 radix:newRadix];
bcf_has_imaginary = NO;
}
return self;
}
//
// initWithDouble
//
// Wrapper that adds complex number support around the base class
//
- (instancetype)initWithDouble:(double)newValue radix:(unsigned short)newRadix
{
self = [super initWithDouble:newValue radix:newRadix];
if (self)
{
bcf_imaginary = [BigFloat bigFloatWithInt:0 radix:newRadix];
bcf_has_imaginary = NO;
}
return self;
}
//
// initWithString
//
// Wrapper that adds complex number support around the base class
// Note: we assume an exponent of 'e' where base 15 and higher numbers use character 'E'.
//
- (instancetype)initWithString:(NSString *)newValue radix:(unsigned short)newRadix {
self = [super initWithInt:0 radix:newRadix];
if (self && newValue.length > 0) {
// break apart the string into real and imaginary pieces
NSCharacterSet *signChars = [NSCharacterSet characterSetWithCharactersInString:@"+-"];
NSMutableString *number = [NSMutableString stringWithString:@""];
NSString *inumber = @"";
char ch = [newValue characterAtIndex:0];
// remove leading sign -- if any
if ([signChars characterIsMember:ch]) { [number appendFormat:@"%c", ch]; newValue = [newValue substringFromIndex:1]; }
NSRange range = [newValue rangeOfCharacterFromSet:signChars];
if (range.length > 0) {
// check if this is an exponent
NSRange expRange = [newValue rangeOfString:@"e"];
if (expRange.length > 0 && expRange.location == range.location-1) {
// search beyond the exponent
range.location++; range.length = newValue.length - range.location;
range = [newValue rangeOfCharacterFromSet:signChars options:0 range:range];
if (range.length > 0) {
// This is likely the start of the second number
[number appendString:[newValue substringToIndex:range.location-1]];
inumber = [newValue substringFromIndex:range.location];
} else {
// Only one number exists
if ([newValue hasSuffix:@"i"]) {
inumber = [NSString stringWithFormat:@"%@%@", number, newValue]; // transfer the sign
number = [NSMutableString stringWithString:@""]; // clear the real part
} else {
number = [NSMutableString stringWithFormat:@"%@%@", number, newValue]; // copy the number
}
}
} else {
// This is the start of the second number
[number appendString:[newValue substringToIndex:range.location-1]];
inumber = [newValue substringFromIndex:range.location];
}
} else {
// only one number exists
if ([newValue hasSuffix:@"i"]) {
inumber = [NSString stringWithFormat:@"%@%@", number, newValue]; // transfer the sign
number = [NSMutableString stringWithString:@""]; // clear the real part
} else {
number = [NSMutableString stringWithFormat:@"%@%@", number, newValue]; // copy the number
}
}
self = [super initWithString:number radix:newRadix];
inumber = [inumber stringByReplacingOccurrencesOfString:@"i" withString:@""]; // remove the "i"
bcf_imaginary = [BigFloat bigFloatWithString:inumber radix:newRadix];
bcf_has_imaginary = ![bcf_imaginary isZero];
}
return self;
}
//
// initPiWithRadix
//
// Wrapper that adds complex number support around the base class
//
- (instancetype)initPiWithRadix:(unsigned short)newRadix
{
self = [super initPiWithRadix:newRadix];
if (self)
{
bcf_imaginary = [BigFloat bigFloatWithInt:0 radix:newRadix];
bcf_has_imaginary = NO;
}
return self;
}
//
// initWithCoder
//
// Wrapper that adds complex number support around the base class
//
- (instancetype)initWithCoder:(NSCoder *)coder
{
self = [super initWithCoder:coder];
bcf_imaginary = [coder decodeObjectForKey:@"BCFImaginary"];
bcf_has_imaginary = [coder decodeBoolForKey:@"BCFHasImaginary"];
return self;
}
//
// encodeWithCoder
//
// Wrapper that adds complex number support around the base class
//
- (void)encodeWithCoder:(NSCoder *)coder
{
[super encodeWithCoder:coder];
[coder encodeObject:bcf_imaginary forKey:@"BCFImaginary"];
[coder encodeBool:bcf_has_imaginary forKey:@"BCFHasImaginary"];
}
//
// copyWithZone
//
// Wrapper that adds complex number support around the base class
//
- (id)copyWithZone:(NSZone*)zone
{
BigCFloat *copy;
copy = [[BigCFloat allocWithZone:zone] init];
[copy assign:self];
[copy->bcf_imaginary assign:self->bcf_imaginary];
copy->bcf_has_imaginary = self->bcf_has_imaginary;
return copy;
}
//
// bigFloatWithReal
//
// Returns an autoreleased complex number initialised with given real and imaginary
//
+ (BigCFloat*)bigFloatWithReal:(BigFloat *)realPart imaginary:(BigFloat *)imaginaryPart
{
return [[BigCFloat alloc] initWithReal:realPart imaginary:imaginaryPart];
}
//
// bigFloatWithMagnitude
//
// Returns an autoreleased complex number initialised with given polar coordinates
//
+ (BigCFloat*)bigFloatWithMagnitude:(BigFloat *)r angle:(BigFloat *)theta
{
return [[BigCFloat alloc] initWithMagnitude:r angle:theta];
}
//
// bigFloatWithInt
//
// Wrapper that adds complex number support around the base class
//
+ (BigCFloat*)bigFloatWithInt:(signed int)newValue radix:(unsigned short)newRadix
{
return [[BigCFloat alloc] initWithInt:newValue radix:newRadix];
}
//
// bigFloatWithDouble
//
// Wrapper that adds complex number support around the base class
//
+ (BigCFloat*)bigFloatWithDouble:(double)newValue radix:(unsigned short)newRadix
{
return [[BigCFloat alloc] initWithDouble:newValue radix:newRadix];
}
//
// bigFloatWithString
//
// Wrapper that adds complex number support around the base class
//
+ (BigCFloat*)bigFloatWithString:(NSString *)newValue radix:(unsigned short)newRadix {
return [[BigCFloat alloc] initWithString:newValue radix:newRadix];
}
//
// piWithRadix
//
// Wrapper that adds complex number support around the base class
//
+ (BigCFloat*)piWithRadix:(unsigned short)newRadix
{
return [[BigCFloat alloc] initPiWithRadix:newRadix];
}
+ (BigCFloat *)one {
return [BigCFloat bigFloatWithInt:1 radix:10];
}
+ (BigCFloat *)zero {
return [BigCFloat bigFloatWithInt:0 radix:10];
}
+ (BigCFloat *)i; {
return [BigCFloat bigFloatWithReal:[BigCFloat bigFloatWithInt:0 radix:10] imaginary:[BigCFloat bigFloatWithInt:1 radix:10]];
}
#pragma mark
#pragma mark ### Complex Functions ###
//
// realPartCopy
//
// Returns a copy of the real part of the number
//
- (BigFloat *)realPartCopy
{
return [super copyWithZone:nil];
}
//
// realPart
//
// Returns an autoreleased copy of the real part of the number
//
- (BigFloat *)realPart
{
return [self realPartCopy];
}
//
// imaginaryPartCopy
//
// Returns a copy of the imaginary part of the number
//
- (BigFloat *)imaginaryPartCopy;
{
return [bcf_imaginary copyWithZone:nil];
}
//
// imaginaryPart
//
// Returns an autoreleased copy of the imaginary part of the number
//
- (BigFloat *)imaginaryPart;
{
return [self imaginaryPartCopy];
}
//
// magnitudeCopy
//
// Calculates the magnitude and returns a copy of it
//
- (BigFloat *)magnitudeCopy
{
BigFloat *magnitude;
BigFloat *imSquared;
if (!bcf_has_imaginary)
{
magnitude = [super copyWithZone:nil];
[magnitude abs];
return magnitude;
}
magnitude = [super copyWithZone:nil];
[magnitude multiplyBy:magnitude];
imSquared = [bcf_imaginary copy];
[imSquared multiplyBy:imSquared];
[magnitude add:imSquared];
[magnitude sqrt];
return magnitude;
}
//
// magnitude
//
// Calculates the magnitude and returns it
//
- (BigFloat *)magnitude
{
return [self magnitudeCopy];
}
//
// angleCopy
//
// Calculates the angle (phase) and returns a copy of it
//
- (BigFloat *)angleCopy
{
BigFloat *angle;
BigFloat *magnitude;
if (!bcf_has_imaginary)
{
if (bf_is_negative)
return [[BigFloat alloc] initPiWithRadix:bf_radix];
else
return [BigFloat bigFloatWithInt:0 radix:bf_radix];
}
angle = [bcf_imaginary copy];
magnitude = [self magnitudeCopy];
[angle divideBy:magnitude];
[angle sinWithTrigMode:BF_radians inv:YES hyp:NO];
if (bf_is_negative)
{
BigFloat *piMinusAngle;
BigFloat *minusOne;
minusOne = [BigFloat bigFloatWithInt:-1 radix:bf_radix];
piMinusAngle = [minusOne copy];
[piMinusAngle cosWithTrigMode:BF_radians inv:YES hyp:NO];
if ([bcf_imaginary isNegative])
{
[piMinusAngle multiplyBy:minusOne];
}
[piMinusAngle subtract:angle];
[angle assign:piMinusAngle];
}
return angle;
}
//
// angle
//
// Calculates the angle (phase)
//
- (BigFloat *)angle
{
return [self angleCopy];
}
//
// conjugate
//
// Changes the sign of the imaginary part
//
- (void)conjugate
{
BigFloat *minusOne;
if (!bcf_has_imaginary) return;
minusOne = [BigFloat bigFloatWithInt:-1 radix:bf_radix];
[bcf_imaginary multiplyBy:minusOne];
}
//
// hasImaginary
//
// Returns whether the number has an imaginary component
//
- (BOOL)hasImaginary
{
return bcf_has_imaginary;
}
//
// imaginaryHasExponent
//
// Returns whether the imaginary component has an exponent
//
- (BOOL)imaginaryHasExponent
{
return bcf_has_imaginary && [bcf_imaginary hasExponent];
}
#pragma mark
#pragma mark ### Public Utility Functions ###
//
// appendDigit
//
// Wrapper that adds complex number support around the base class
//
- (BOOL)appendDigit:(short)digit useComplement:(int)complement
{
if (digit == L'i')
{
bcf_has_imaginary = YES;
return YES;
}
if (bcf_has_imaginary)
{
return [bcf_imaginary appendDigit:digit useComplement:complement];
}
return [super appendDigit:digit useComplement:complement];
}
//
// appendExpDigit
//
// Wrapper that adds complex number support around the base class
//
- (void)appendExpDigit:(short)digit
{
if (bcf_has_imaginary)
{
[bcf_imaginary appendExpDigit:digit];
return;
}
[super appendExpDigit:digit];
}
//
// deleteDigit
//
// Wrapper that adds complex number support around the base class
//
- (void)deleteDigitUseComplement:(int)complement
{
if (bcf_has_imaginary)
{
[bcf_imaginary deleteDigitUseComplement:complement];
if ([bcf_imaginary isZero] && [bcf_imaginary getUserPoint] == 0)
{
bcf_has_imaginary = NO;
}
return;
}
[super deleteDigitUseComplement:complement];
}
//
// deleteExpDigit
//
// Wrapper that adds complex number support around the base class
//
- (void)deleteExpDigit
{
if (bcf_has_imaginary)
{
[bcf_imaginary deleteExpDigit];
return;
}
[super deleteExpDigit];
}
//
// convertToRadix
//
// Wrapper that adds complex number support around the base class
//
- (void)convertToRadix:(unsigned short)newRadix
{
BigFloat *real = [self realPart];
[real convertToRadix:newRadix];
[super assign:real];
[bcf_imaginary convertToRadix:newRadix];
}
//
// radix
//
// Wrapper that adds complex number support around the base class
//
- (unsigned short)radix
{
return [super radix];
}
//
// isValid
//
// Wrapper that adds complex number support around the base class
//
- (BOOL)isValid
{
return bf_is_valid && [bcf_imaginary isValid];
}
//
// isZero
//
// Wrapper that adds complex number support around the base class
//
- (BOOL)isZero
{
return [super isZero] && [bcf_imaginary isZero];
}
//
// setUserPoint
//
// Wrapper that adds complex number support around the base class
//
- (void)setUserPoint:(int)pointLocation
{
if (bcf_has_imaginary)
{
[bcf_imaginary setUserPoint:pointLocation];
return;
}
[super setUserPoint:pointLocation];
}
//
// getUserPoint
//
// Wrapper that adds complex number support around the base class
//
- (int)getUserPoint
{
if (bcf_has_imaginary)
{
return [bcf_imaginary getUserPoint];
}
return [super getUserPoint];
}
//
// compareWith
//
// Wrapper that adds complex number support around the base class
//
- (NSComparisonResult)compareWith:(BigFloat*)num
{
NSComparisonResult real_result;
NSComparisonResult im_result;
// We're actually comparing with another BigCFloat
if ([num isKindOfClass:[BigCFloat class]])
{
BigCFloat *cnum = (BigCFloat *)num;
real_result = [[self realPart] compareWith:[cnum realPart]];
im_result = [bcf_imaginary compareWith:cnum->bcf_imaginary];
if (real_result == NSOrderedSame && im_result == NSOrderedSame)
{
return NSOrderedSame;
}
else if (real_result == NSOrderedSame)
{
return im_result;
}
else if (im_result == NSOrderedSame)
{
return real_result;
}
return NSOrderedAscending;
}
real_result = [[self realPart] compareWith:num];
if (bcf_has_imaginary && real_result == NSOrderedSame)
{
if ([bcf_imaginary isNegative])
return NSOrderedAscending;
else
return NSOrderedDescending;
}
else if (bcf_has_imaginary)
{
return NSOrderedAscending;
}
return real_result;
}
//
// duplicate
//
// Wrapper that adds complex number support around the base class
//
- (BigFloat*)duplicate
{
return [self copy];
}
//
// assign
//
// Wrapper that adds complex number support around the base class
//
- (void)assign:(BigFloat*)newValue
{
if ([newValue isKindOfClass:[BigCFloat class]])
{
BigCFloat *cvalue = (BigCFloat*)newValue;
[super assign:cvalue];
[bcf_imaginary assign:cvalue->bcf_imaginary];
bcf_has_imaginary = [cvalue hasImaginary];
return;
}
if (bcf_has_imaginary)
{
bcf_imaginary = [[BigFloat alloc] initWithInt:0 radix:bf_radix];
bcf_has_imaginary = NO;
}
[super assign:newValue];
}
//
// abs
//
// Wrapper that adds complex number support around the base class
//
- (void)abs
{
if (bcf_has_imaginary)
{
BigFloat *magnitude = [self magnitudeCopy];
[self assign:magnitude];
return;
}
[super abs];
}
#pragma mark
#pragma mark ### Arithmetic Functions ###
//
// add
//
// Wrapper that adds complex number support around the base class
//
- (void)add:(BigFloat*)num
{
BigFloat *real = [self realPart];
[real add:num];
[super assign:real];
if ([num isKindOfClass:[BigCFloat class]])
{
BigCFloat *cnum = (BigCFloat *)num;
if ([cnum hasImaginary])
{
[bcf_imaginary add:cnum->bcf_imaginary];
if ([bcf_imaginary isZero])
bcf_has_imaginary = NO;
else
bcf_has_imaginary = YES;
}
}
}
//
// subtract
//
// Wrapper that adds complex number support around the base class
//
- (void)subtract:(BigFloat*)num
{
BigFloat *real = [self realPart];
[real subtract:num];
[super assign:real];
if ([num isKindOfClass:[BigCFloat class]])
{
BigCFloat *cnum = (BigCFloat *)num;
if ([cnum hasImaginary])
{
[bcf_imaginary subtract:cnum->bcf_imaginary];
if ([bcf_imaginary isZero])
bcf_has_imaginary = NO;
else
bcf_has_imaginary = YES;
}
}
}
//
// multiplyBy
//
// Wrapper that adds complex number support around the base class
//
- (void)multiplyBy:(BigFloat*)num
{
BigFloat *real;
if ([num isKindOfClass:[BigCFloat class]] && [(BigCFloat *)num hasImaginary])
{
BigCFloat *cnum = (BigCFloat *)num;
BigFloat *firstTerm;
BigFloat *secondTerm;
BigFloat *imaginary;
firstTerm = [self realPartCopy];
[firstTerm multiplyBy:[cnum realPart]];
secondTerm = [self imaginaryPartCopy];
[secondTerm multiplyBy:cnum->bcf_imaginary];
[firstTerm subtract:secondTerm];
real = [firstTerm copy];
firstTerm = [self imaginaryPartCopy];
[firstTerm multiplyBy:[cnum realPart]];
secondTerm = [self realPartCopy];
[secondTerm multiplyBy:cnum->bcf_imaginary];
[firstTerm add:secondTerm];
imaginary = [firstTerm copy];
[self assign:real];
[bcf_imaginary assign:imaginary];
bcf_has_imaginary = ![bcf_imaginary isZero];
return;
}
real = [self realPart];
[real multiplyBy:num];
[super assign:real];
if (bcf_has_imaginary)
{
[bcf_imaginary multiplyBy: num];
bcf_has_imaginary = ![bcf_imaginary isZero];
}
}
//
// divideBy
//
// Wrapper that adds complex number support around the base class
//
- (void)divideBy:(BigFloat*)num
{
BigFloat *real;
if ([num isKindOfClass:[BigCFloat class]] && [(BigCFloat *)num hasImaginary])
{
BigCFloat *cnum = (BigCFloat *)num;
BigFloat *firstTerm;
BigFloat *secondTerm;
BigFloat *denominator;
BigFloat *imaginary;
firstTerm = [cnum realPartCopy];
[firstTerm multiplyBy:firstTerm];
secondTerm = [cnum imaginaryPartCopy];
[secondTerm multiplyBy:secondTerm];
[firstTerm add:secondTerm];
denominator = [firstTerm copy];
firstTerm = [self realPartCopy];
[firstTerm multiplyBy:[cnum realPart]];
secondTerm = [self imaginaryPartCopy];
[secondTerm multiplyBy:cnum->bcf_imaginary];
[firstTerm add:secondTerm];
[firstTerm divideBy:denominator];
real = [firstTerm copy];
firstTerm = [self imaginaryPartCopy];
[firstTerm multiplyBy:[cnum realPart]];
secondTerm = [self realPartCopy];
[secondTerm multiplyBy:cnum->bcf_imaginary];
[firstTerm subtract:secondTerm];
[firstTerm divideBy:denominator];
imaginary = [firstTerm copy];
[self assign:real];
[bcf_imaginary assign:imaginary];
bcf_has_imaginary = ![bcf_imaginary isZero];
return;
}
real = [self realPart];
[real divideBy:num];
[super assign:real];
if (bcf_has_imaginary)
{
[bcf_imaginary divideBy: num];
bcf_has_imaginary = ![bcf_imaginary isZero];
}
}
//
// moduloBy
//
// Wrapper that adds complex number support around the base class
//
- (void)moduloBy:(BigFloat*)num
{
BigCFloat *cnum;
BigCFloat *quotient;
if (![num isKindOfClass:[BigCFloat class]] || ![(BigCFloat *)num hasImaginary])
{
if (!bcf_has_imaginary)
{
// if there are no imaginary parts then just do the super's work
[super moduloBy:num];
}
// otherwise promote to a Complex number
cnum = [[BigCFloat alloc] init];
[cnum assign:num];
}
else
{
cnum = (BigCFloat *)num;
}
// x % y = (x - (int(x/y) * y))
quotient = [self copy];
[quotient divideBy:cnum];
[quotient wholePart];
[quotient multiplyBy:cnum];
[self subtract:quotient];
}
#pragma mark
#pragma mark ### Extended Mathematics Functions ###
//
// powerOfE
//
// Wrapper that adds complex number support around the base class
//
- (void)powerOfE
{
BigFloat *realPart;
BigFloat *cosPart;
BigFloat *sinPart;
if (!bf_is_valid)
return;
if (bcf_has_imaginary)
{
realPart = [self realPartCopy];
cosPart = [self imaginaryPartCopy];
sinPart = [self imaginaryPartCopy];
[cosPart cosWithTrigMode:BF_radians inv:NO hyp:NO];
[sinPart sinWithTrigMode:BF_radians inv:NO hyp:NO];
[realPart powerOfE];
[self assign:realPart];
[self multiplyBy:cosPart];