public eeListNode(eeObject obj, eeNumber index, eeListNode prev, eeListNode next)
{
this.obj = obj;
this.index = index;
this.prev = prev;
this.next = next;
}
private eeNumber IntegerDivision(eeNumber divisor, out eeNumber mod)
{
// base case
if (this.AbsoluteValue() < divisor.AbsoluteValue())
{
mod = this;
return(new eeNumber(0));
}
Queue <byte> bytesQue = new Queue <byte>(this.bytes); // a queue of the dividend as bytes
List <eeNumber> quotient = new List <eeNumber>(); // quotient
eeNumber divPart = null;
while (bytesQue.Count() > 0)
{
/* Grab the next digit from dividend */
var asList = divPart == null ? new List <byte>() : divPart.bytes.ToList();
var nextByte = bytesQue.Dequeue();
asList.Add(nextByte);
/* Keep grabbing until we run out or need more */
divPart = new eeNumber(asList);
while (bytesQue.Count() != 0 && divPart < divisor)
{
quotient.Add(new eeNumber(0));
asList.Add(bytesQue.Dequeue());
divPart = new eeNumber(asList);
divPart.TrimZeros();
}
divPart.TrimZeros();
/* Divide it and append the division to the quotient */
eeNumber q = new eeNumber(1); // number of times divisor fits into this divPart
while (divisor * q <= divPart)
{
q += ONE;
}
q -= ONE;
quotient.Add(q); // keep track of quotient
/* Figure out the remainder*/
divPart = divPart - (divisor * q);
}
// remainder
mod = divPart;
var intergerQuotient = new eeNumber(quotient);
intergerQuotient.TrimZeros();
return(intergerQuotient);
}
public eeObject this[eeNumber key]
{
get // retrieve
{
return(null);
}
set // assign
{
return;
}
}
// removes the denominator of this number and returns it
private eeNumber PopDenominator()
{
// if not a fraction
if (this.IsInt())
{
return(new eeNumber(1));
}
var den = this.denominator;
this.denominator = null;
return(den);
}
private static eeNumber FromBinary(bool[] bin)
{
var num = new eeNumber(0);
for (int idx = 0; idx < bin.Length; idx++)
{
if (bin[idx])
{
num += new eeNumber((ulong)Math.Pow(2, bin.Length - idx - 1));
}
}
return(num);
}
// returns a copy of this eeNumber
public eeNumber Copy()
{
var copy = new eeNumber(0);
copy.negative = this.negative;
copy.bytes = (byte[])this.bytes.Clone();
if (this.IsFrac())
{
copy.denominator = new eeNumber(0);
copy.denominator.bytes = (byte[])this.denominator.bytes.Clone();
}
return(copy);
}
public static eeNumber RShift(eeNumber num1, eeNumber num2)
{
if (num1.IsFrac() || num2.IsFrac())
{
throw new Exception("Cannot shift a non-int or by a non-int");
}
List <bool> bin1 = num1.ToBinary();
for (eeNumber i = ZERO.Copy(); i < num2; i += ONE)
{
bin1.RemoveAt(bin1.Count() - 1);
}
return(FromBinary(bin1.ToArray()));
}
public void Append(eeObject obj)
{
_count += eeNumber.ONE;
if (LastNode == null) // if this is the second object to enter the list
{
var node = new eeListNode(obj.Copy(), _count.Copy(), HeadNode, null);
LastNode = node;
HeadNode.next = node;
return;
}
var newNode = new eeListNode(obj.Copy(), _count.Copy(), LastNode, null);
this.LastNode.next = newNode;
this.LastNode = newNode;
}
/* https://stackoverflow.com/a/11419400/9628054 */
public static eeNumber Power(eeNumber base_, eeNumber exp)
{
var y = ONE.Copy();
while (true)
{
if ((exp & ONE) != ZERO)
{
y *= base_;
}
exp >>= 1;
if (exp == ZERO)
{
return(y);
}
base_ *= base_;
}
}
// Greatest Common Factor using Euclid's algorithm
public eeNumber GCF(eeNumber prod2_orig)
{
var prod1 = this.Copy().AbsoluteValue();
var prod2 = prod2_orig.Copy().AbsoluteValue();
while (prod1 != ZERO && prod2 != ZERO)
{
if (prod1 > prod2)
{
prod1 %= prod2;
}
else
{
prod2 %= prod1;
}
}
return(prod1 | prod2);
}
private string ApproximateDivision(long accurateTo)
{
if (this.denominator == null)
{
throw new Exception("Cannot approximate division on an integer");
}
eeNumber denom = this.PopDenominator(),
remainder,
integerQuotient = this.IntegerDivision(denom, out remainder);
string approx = integerQuotient.NumeratorToString();
if (remainder == ZERO)
{
return(approx);
}
const string ZEROSTR = "0";
string decimalAprx = "";
// If the dividend is longer than the max accuracy, iterate to that, otherwise, to max accuracy
long c = denom.bytes.LongCount();
if (c > accurateTo)
{
accurateTo += c;
}
for (int i = 1; i <= accurateTo; i++)
{
eeNumber dec = new eeNumber(
remainder.NumeratorToString() + ZEROSTR
);
decimalAprx += dec.IntegerDivision(denom, out eeNumber rem).NumeratorToString();
remainder = rem;
}
decimalAprx = decimalAprx.TrimEnd('0');
this.denominator = denom;
return($"{approx}.{decimalAprx}");
}
public eeNumber Factorial()
{
if (this < ZERO)
{
throw new Exception();
}
else if (this == ZERO)
{
return(ONE.Copy());
}
var sum = ONE.Copy();
for (eeNumber i = this.Copy(); i > ZERO; i -= ONE)
{
sum *= i;
}
return(sum);
}
public static eeNumber LShift(eeNumber num1, eeNumber num2)
{
if (num1.IsFrac() || num2.IsFrac())
{
throw new Exception("Cannot shift a non-int or by a non-int");
}
List <bool> bin1 = num1.ToBinary();
// trim the tail
//for (eeNumber i = ZERO.Copy(); i < num2; i += ONE)
// bin1.RemoveAt(bin1.Count() - 1);
// add to the front
for (eeNumber i = ZERO.Copy(); i < num2; i += ONE)
{
bin1.Add(false);
}
return(FromBinary(bin1.ToArray()));
}
/* Note:
* We cannot use +, - (non-integer), or / operators in this function or it will cause an infinite recursion loop
* We use the IntergerDivision function as a replacement for /
*/
private void Simplify()
{
if (this.IsInt())
{
return;
}
var denom = PopDenominator();
if (this == ZERO || denom == ONE) // if the numerator is zero or denom is 1, return as-is (without denom)
{
return;
}
// if the denominator is a power of 10, leave it as is, as it's easier to deal with.
else if (denom.IsPowerOf10())
{
this.denominator = denom;
return;
}
// use the GCF to simplify
eeNumber gcf = this.GCF(denom);
if (gcf == ONE) // no change needed
{
this.denominator = denom;
}
else
{
var newObj = this.IntegerDivision(gcf, out _);
this.bytes = newObj.bytes;
if (this.denominator != gcf) // if denom won't be 1
{
this.denominator = denom.IntegerDivision(gcf, out _);
}
}
}
public eeNumber(string num)
{
if (num.StartsWith("-")) // If it's negative
{
negative = true;
num = num.Replace("-", "");
}
if (num.Contains('.')) // if it's a decimal/double
{
var split = num.Split('.'); // seperate integer and decimal
// set the denominator
denominator = new eeNumber("1" + new string('0', split[1].Length));
var fracNumerator = new eeNumber(split[1]);
var intPart = new eeNumber(split[0]);
// continue for the numerator normally
num = ((intPart * denominator) + fracNumerator).NumeratorToString();
}
bytes = num.ToCharArray().Select(x => byte.Parse(x.ToString())).ToArray();
}
// Warning: Subtraction will destroy the contents of num2 and set the contents of num1 to the result
// Make sure to pass a copy of num2 if you are keeping its value
public static eeNumber operator -(eeNumber num1_orig, eeNumber num2_orig)
{
eeNumber num1 = num1_orig.Copy(),
num2 = num2_orig.Copy();
// If either number is a fraction, cross multiply
if (num1.IsFrac() || num2.IsFrac())
{
eeNumber frac1 = num1.PopDenominator(),
frac2 = num2.PopDenominator();
num1 *= frac2;
num2 *= frac1;
var ret = (num1 - num2) / (frac1 * frac2);
ret.TrimZeros();
ret.Simplify();
return(ret);
}
// if the two nums are the same
if (num1 == num2)
{
return(ZERO.Copy());
}
// if first num is negative
else if (num1.negative && !num2.negative)
{
// add them then negate it
num1.negative = false;
var sum = num1 + num2;
sum.negative = true;
return(sum);
}
// if second num is negative
else if (num2.negative && !num1.negative)
{
// minus and negatives cancel
num2.negative = false;
return(num1 + num2);
}
// If they're both negative
else if (num1.negative && num2.negative)
{
// Treat this as adding a negative to a positive
num2.negative = false;
return(num1 + num2);
}
// If we're going to get a negative answer
bool negate = false;
if (num2 > num1)
{
// reverse the two
var buf = num1;
num1 = num2;
num2 = buf;
// and negate
negate = true;
}
// Reverse because we're subtracting from right to left.
byte[] l_bytes = num1.bytes.Reverse().ToArray(),
r_bytes = num2.bytes.Reverse().ToArray();
bool carry = false;
int i;
for (i = 0; i < r_bytes.Length; i++)
{
// Account for the previous carry
if (carry)
{
r_bytes[i]++;
carry = false;
}
// Subtract the digits
byte digitDiff;
if (l_bytes[i] < r_bytes[i]) // account for carry
{
digitDiff = (byte)((10 + l_bytes[i]) - r_bytes[i]);
carry = true;
}
else
{
digitDiff = (byte)(l_bytes[i] - r_bytes[i]);
}
// Set the digit
l_bytes[i] = digitDiff;
}
// If there is still carry left
while (carry)
{
// subtract one from the next value
if (l_bytes[i] == 0)
{
l_bytes[i] = 9;
i++;
}
else
{
l_bytes[i] -= 1;
carry = false;
}
}
// Put it in order again
l_bytes = l_bytes.Reverse().ToArray();
num1.bytes = l_bytes;
num1.negative = negate;
num1.TrimZeros();
return(num1);
}
public static eeNumber operator +(eeNumber num1, eeNumber num2)
{
// If either number is a fraction, cross multiply
if (num1.IsFrac() || num2.IsFrac())
{
eeNumber frac1 = num1.PopDenominator(),
frac2 = num2.PopDenominator();
num1 *= frac2;
num2 *= frac1;
var ret = (num1 + num2) / (frac1 * frac2);
ret.TrimZeros();
ret.Simplify();
return(ret);
}
bool negate = false;
// if first num is negative
if (num1.negative && !num2.negative)
{
num1.negative = false;
return(num2 - num1.Copy());
}
// If 2nd num is negative
else if (num2.negative && !num1.negative)
{
num2.negative = false;
return(num1 - num2.Copy());
}
// They're both negative
else if (num1.negative && num2.negative)
{
num1.negative = false;
num2.negative = false;
negate = true;
}
if (num2.bytes.Length > num1.bytes.Length)
{
// switch so that num1 is larger
var buf = num1;
num1 = num2;
num2 = buf;
}
// Reverse because we're adding from right to left.
byte[] lhs = num1.bytes.Reverse().ToArray(),
rhs = num2.bytes.Reverse().ToArray();
int i;
for (i = 0; i < rhs.Length; i++)
{
byte digitSum = (byte)(rhs[i] + lhs[i]);
lhs[i] = digitSum;
}
num1.bytes = lhs.Reverse().ToArray();
num1.CarryOver();
num1.negative = negate;
return(num1);
}
public static eeNumber operator *(eeNumber num1_orig, eeNumber num2_orig)
{
eeNumber num1 = num1_orig.Copy(),
num2 = num2_orig.Copy();
// if either num is 0, return 0
if (num1 == ZERO || num2 == ZERO)
{
return(new eeNumber(0));
}
bool negate = false;
/* first account for negatives */
// if either num is negative
if (num1.negative ^ num2.negative)
{
// set both to non-negative to multiply them
num1.negative = false;
num2.negative = false;
// apply negative afterwards
negate = true;
}
else if (num1.negative && num2.negative)
{
// otherwise, negatives just cancel out
num1.negative = false;
num2.negative = false;
}
eeNumber final;
// if only one num is a fraction
if (num1.IsFrac() ^ num2.IsFrac())
{
eeNumber frac = num1.denominator != null ? num1 : num2,
reg = num1.denominator != null ? num2 : num1;
var den = frac.PopDenominator();
var newNum = (frac * reg) / den;
final = newNum;
}
// if both nums are fractions
else if (num1.IsFrac() && num2.IsFrac())
{
eeNumber frac1 = num1.PopDenominator(),
frac2 = num2.PopDenominator();
final = (num1 * num2) / (frac1 * frac2);
}
// regular nums
else
{
// Reverse because we're going from right to left.
byte[] lhs = num1.bytes.Reverse().ToArray(),
rhs = num2.bytes.Reverse().ToArray();
// new digit
eeNumber finalNum = new eeNumber(0);
// foreach digit in on the top num
for (int i = 0; i < rhs.Length; i++)
{
byte carry = 0;
List <byte> product = new List <byte>();
// foreach digit in the bottom num
for (int j = 0; j < lhs.Length; j++)
{
// multiply them
byte digitProduct = (byte)(lhs[j] * rhs[i]);
if (carry != 0)
{
digitProduct += carry;
carry = 0;
}
if (digitProduct > 9)
{
carry = (byte)(digitProduct / 10);
digitProduct %= 10;
}
product.Add(digitProduct);
}
// If carry is left
if (carry != 0)
{
product.Add(carry);
}
product.Reverse();
// Add the needed amount of trailing zeros for place value
for (int z = 0; z < i; z++)
{
product.Add(0);
}
finalNum += new eeNumber(product.ToArray());
}
final = finalNum;
}
final.negative = negate;
return(final);
}
public static eeNumber operator /(eeNumber num1_orig, eeNumber num2_orig)
{
/* eeNumbers do not perform traditional division. That is only done
* when the number needs to be approximated for a text representation.
* For divison, we always keep the fractional form for arbitrary accuracy.
*/
eeNumber num1 = num1_orig.Copy(),
num2 = num2_orig.Copy();
if (num2 == ZERO)
{
throw new DivisionByZeroError(num1);
}
bool negate = false;
/* first, account for negatives */
// if either num is negative
if (num1.negative ^ num2.negative)
{
// set both to non-negative to multiply them
num1.negative = false;
num2.negative = false;
// apply negative afterwards
negate = true;
}
else if (num1.negative && num2.negative)
{
// otherwise, negatives just cancel out
num1.negative = false;
num2.negative = false;
}
/* then, divide */
bool a = num1.IsFrac(), b = num2.IsFrac();
// frac divided by num
if (a && !b)
{
num1.denominator *= num2;
num1.negative = negate;
num1.Simplify();
return(num1);
}
// num divided by num
else if (!a && !b)
{
// check if right is a factor of left
if (num1 > num2)
{
var m = num1 % num2;
if (m == ZERO)
{
return(num1 % num2);
}
}
num1.denominator = num2;
num1.negative = negate;
num1.Simplify();
return(num1);
}
// num divided by frac
else if (!a && b)
{
eeNumber numerator = num1 * num2.denominator;
eeNumber denominator = num2;
var newNum = numerator / denominator;
newNum.negative = negate;
return(newNum);
}
// frac divided by frac
else
{
var denom1 = num1.PopDenominator();
eeNumber numerator = num1 * num2.PopDenominator();
eeNumber denominator = num2 * denom1;
var newNum = numerator / denominator;
newNum.negative = negate;
return(newNum);
}
}
public static bool operator >(eeNumber num1, eeNumber num2)
{
bool flip = false;
// if at least one number is a fraction
if (num1.IsFrac() || num2.IsFrac())
{
eeNumber numerator1 = num1,
denom1 = num1.PopDenominator(),
numerator2 = num2,
denom2 = num2.PopDenominator();
// cross multiply & compare
return((numerator1 * denom2) > (numerator2 * denom1));
}
// lhs is neg and rhs isn't
else if (num1.negative && !num2.negative)
{
return(false);
}
// lhs isn't neg and rhs is
else if (!num1.negative && num2.negative)
{
return(true);
}
// both negative
else if (num1.negative && num2.negative)
{
/* Copy the numbers, compare the positive ones in the inverse order.
* Simply flipping the comparison without altering the numbers creates an infinite loop
* and removing the negative from the original object could cause damage higher up.
*/
var num1_copy = num1.Copy();
num1_copy.negative = false;
var num2_copy = num2.Copy();
num2_copy.negative = false;
return(num2_copy > num1_copy);
}
// if both are whole numbers, compare digits normally.
byte[] l_bytes = num1.bytes,
r_bytes = num2.bytes;
// If lhs has more digits
if (l_bytes.Length > r_bytes.Length)
{
return(true);
}
// If rhs has more digits
else if (l_bytes.Length < r_bytes.Length)
{
return(false);
}
else // if they have an equal number of digits
{
// iterate through each digit
for (int i = 0; i < l_bytes.Length; i++)
{
// If the lhs digit is greater, return true
if (l_bytes[i] > r_bytes[i])
{
return(true);
}
// If they're the same, move on to the next digit
else if (l_bytes[i] == r_bytes[i])
{
continue;
}
else // if lhs is smaller, return false
{
return(false);
}
}
}
// they're equal
return(false);
}