private static Q NRoot(Q number, Z root)
{
Q epsilon;
if (constants.ContainsKey("$epsilon"))
epsilon = constants["$epsilon"];
else
epsilon = Q.One / Q.Pow(constants["$output_base"], constants["$precision"].GetWholePart());
// pick 2 as first approximation
Q guess;
Q nextGuess = 2;
do
{
guess = nextGuess;
Q part = Q.Pow(guess, root - 1);
nextGuess = guess - (part * guess - number) / (root * part);
} while (Q.Abs(nextGuess - guess) > epsilon);
return nextGuess;
}
private static Z RoundWhole(Q fraction)
{
return (fraction.Numerator + fraction.Denominator / 2) / fraction.Denominator;
}
private static Q ParseNum(string num, Q _base, Dictionary<string, Q> vars)
{
if (num.Contains("jostein"))
{
Console.WriteLine("U FRIKIN FAGITT U FUKING THINK U KNO MATHS???");
RektForm f = new RektForm();
f.ShowDialog();
return Z.Parse("11111111111111111111111");
}
if (num.StartsWith("root"))
{
string param1 = num.Substring(4).Split(',')[0];
string param2 = num.Substring(4).Split(',')[1];
Q p1 = ParseExpression(param1, _base, vars);
Q p2 = ParseExpression(param2, _base, vars);
return NRoot(p1, p2.GetWholePart());
}
if (string.IsNullOrWhiteSpace(num))
return Q.Zero;
if (vars.ContainsKey(num))
return vars[num];
if (constants.ContainsKey(num))
return constants[num];
string digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".Remove((int)Ceiling(_base));
int sign = 1;
if (num.StartsWith("-"))
{
sign = -1;
num = num.Remove(0, 1);
}
int i;
i = num.IndexOfAny(new char[] { ',', '.' });
if (i == -1)
i = num.Length;
else
num = num.Remove(i, 1);
int pow = i - 1;
Q magnitude = Q.Pow(_base, pow);
Q number = Q.Zero;
foreach (char c in num)
{
int val = digits.IndexOf(c);
if (val == -1)
{
Console.WriteLine("Unknown digit {0} in base {1}", c, NumToString(_base, 10));
return Q.Zero;
}
else
{
number += val * magnitude;
magnitude /= _base; // pow--
}
}
return number * sign;
}
private static Z Ceiling(Q fraction)
{
return (fraction.Numerator + fraction.Denominator - 1) / fraction.Denominator;
}
private static Q ParseExpression(string expr, Q _base, Dictionary<string, Q> vars = null)
{
if (vars == null)
vars = new Dictionary<string, BigRational>();
int i;
i = expr.IndexOf(":=");
if (i != -1)
{
string vn = expr.Remove(i).Trim();
Q value = ParseExpression(expr.Substring(i + 2), 10);
if (constants.ContainsKey(vn))
constants[vn] = value;
else
constants.Add(vn, value);
return value;
}
i = expr.LastIndexOf("(");
if (i != -1)
{
int l = expr.Substring(i).IndexOf(")");
if (l == -1)
{
Console.WriteLine("Missing end paranthesis");
l = expr.Length - i;
expr = expr + ")";
}
Q prnt = ParseExpression(expr.Substring(i + 1, l - 1), _base, vars);
string vname = "$v" + vars.Count; // Name of variable
vars.Add(vname, prnt);
expr = expr.Remove(i, l + 1);
expr = expr.Insert(i, vname);
return ParseExpression(expr, _base, vars);
}
i = expr.IndexOf("+");
if (i != -1)
{
Q left = ParseExpression(expr.Remove(i), _base, vars);
Q rght = ParseExpression(expr.Substring(i + 1), _base, vars);
return left + rght;
}
i = expr.IndexOf("-");
if (i != -1)
{
Q left = ParseExpression(expr.Remove(i), _base, vars);
Q rght = ParseExpression(expr.Substring(i + 1), _base, vars);
return left - rght;
}
i = expr.IndexOf("*");
if (i != -1)
{
Q left = ParseExpression(expr.Remove(i), _base, vars);
Q rght = ParseExpression(expr.Substring(i + 1), _base, vars);
return left * rght;
}
i = expr.IndexOf("/");
if (i != -1)
{
Q left = ParseExpression(expr.Remove(i), _base, vars);
Q rght = ParseExpression(expr.Substring(i + 1), _base, vars);
if (rght == Q.Zero)
{
Console.WriteLine("ERROR - DIVIDE BY ZERO NOT POSSIBLE WITHOUT AN ACTIVATED DIVISION SIGIL");
return Q.Zero;
}
return left / rght;
}
i = expr.IndexOf("^");
if (i != -1)
{
Q left = ParseExpression(expr.Remove(i), _base, vars);
Q rght = ParseExpression(expr.Substring(i + 1), _base, vars);
if (left == Q.Zero && rght.Sign < 0)
return ParseExpression("0/0", _base, vars);
left = Q.Pow(left, rght.Numerator);
return NRoot(left, rght.Denominator); // left^(x/y) = root(left^x, y)
/*
left = Q.Pow(left, rght.Numerator);
return NRoot(left, rght.Denominator);
*/
}
// No operators - just parse number
return ParseNum(expr, _base, vars);
}
private static string NumToString(Q input, Q toBase)
{
if (constants["$frac"] == Q.Zero || input.Denominator == 1) // Either is frac false or denominator > 1
{
StringBuilder sb = new StringBuilder();
char[] digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZÆØÅ".ToCharArray();
int sign = input.Sign;
if (input < 0)
input = -input;
int pow = 0; // Number of digits to the left of decimal separator
while (input / Q.Pow(toBase, pow + 1) >= Q.One)
pow++;
Z precision = -constants["$precision"].GetWholePart();
Q divisor = Q.Pow(toBase, pow);
for (int p = pow; p > precision; p--)
{
Z coefficient = (input / divisor).GetWholePart(); // Take the quotient
input -= coefficient * divisor; // Leaves only remainder
sb.Append(digits[(int)coefficient]);
divisor /= toBase;
}
sb.Insert(pow + 1, '.');
if (sign < 0)
sb.Insert(0, '-');
string res = sb.ToString().TrimEnd('0').TrimEnd('.');
return res;
}
else
{
return NumToString(input.Numerator, toBase) + "/" + NumToString(input.Denominator, toBase);
}
}