public static void Demo()
{
var v1 = new RationalTypes.Rational(1561384532, 456456378);
var v2 = new RationalTypes.Rational(789, 756);
Print(v1);
Print(v2);
Print(v1 + v2);
Print(v1 - v2);
Print(v1 * v2);
Print(v1 / v2);
}
public static Rational Evaluate(string expression)
{
if (expression.Length == 0)
{
throw new Exception("No content.");
}
if (expression[0] == '*' || expression[0] == '/')
{
throw new Exception("Invalid beginning.");
}
if (expression[expression.Length - 1] == '*' ||
expression[expression.Length - 1] == '/' ||
expression[expression.Length - 1] == '-' ||
expression[expression.Length - 1] == '+')
{
throw new Exception("Invalid ending.");
}
bool wasNumber = false;
List <Element> elements = new List <Element>();
for (int i = 0; i < expression.Length;)
{
switch (expression[i])
{
case '(':
{
i++;
StringBuilder builder = new StringBuilder();
int indent = 1;
while (i < expression.Length)
{
if (expression[i] == ')')
{
indent--; if (indent == 0)
{
break;
}
}
else if (expression[i] == '(')
{
indent++;
}
builder.Append(expression[i++]);
}
i++;
elements.Add(new Element {
Type = ElType.Numeric, value = Evaluate(builder.ToString())
});
wasNumber = false;
break;
}
case '+':
case '-':
elements.Add(new Element {
Type = ElType.Sign, value = expression[i]
});
i++;
wasNumber = false;
break;
case '*':
i++; wasNumber = false;
break;
case '/':
elements.Add(new Element {
Type = ElType.Div
});
i++;
wasNumber = false;
break;
case ' ':
i++; break;
default:
{
StringBuilder builder = new StringBuilder();
while (i < expression.Length &&
expression[i] != '+' &&
expression[i] != '-' &&
expression[i] != '*' &&
expression[i] != '/' &&
expression[i] != '(' &&
expression[i] != ')' &&
expression[i] != ' ')
{
builder.Append(expression[i++]);
}
if (wasNumber)
{
throw new Exception("Repeating numerics.");
}
elements.Add(new Element {
Type = ElType.Numeric, value = Rational.Parse(builder.ToString())
});
wasNumber = true;
break;
}
}
}
Rational value = (Rational)0;
Rational mulvalue = (Rational)0;
SByte sign = 1;
for (int i = 0; i < elements.Count;)
{
switch (elements[i].Type)
{
case ElType.Sign:
value += mulvalue;
mulvalue = (Rational)0;
if (sign != 0 && i > 0)
{
throw new Exception("Repeating signs.");
}
if ((char)elements[i].value == '-')
{
sign = -1;
}
else if ((char)elements[i].value == '+')
{
sign = 1;
}
i++;
break;
case ElType.Numeric:
mulvalue += (Rational)elements[i].value * sign;
if (sign == 0)
{
mulvalue *= (Rational)elements[i].value;
}
sign = 0;
i++;
break;
case ElType.Mul:
mulvalue *= (Rational)elements[i + 1].value;
i += 2;
break;
case ElType.Div:
if (elements[i + 1].Type != ElType.Numeric)
{
throw new Exception("Repeating operators.");
}
mulvalue /= (Rational)elements[i + 1].value;
i += 2;
break;
}
}
value += mulvalue;
return(value);
}
public Rational Pow(Rational Exponent)
{
if (Exponent <= 0 && this == 0)
{
throw new DivideByZeroException();
}
else if (Exponent == 0)
{
if (this == 0)
{
throw new DivideByZeroException();
}
return((Rational)1);
}
else if (this == 0)
{
return((Rational)0);
}
else if (this < 0 && (Exponent.Denominator & 1) == 0)
{
throw new ComplexResultException();
}
long l = 0, r = Math.Abs(Numerator); long i = (Math.Abs(Numerator) + 1) / 2;
long _n = 0, _d = 0;
while (l < r)
{
try
{
if (Utility.Pow(i, Exponent.Denominator) > Math.Abs(Numerator))
{
r = i - 1;
}
else if (Utility.Pow(i, Exponent.Denominator) < Math.Abs(Numerator))
{
l = i;
}
else
{
_n = i; break;
}
}
catch
{ r = i - 1; }
finally
{ i = (l + r + 1) / 2; }
}
if (_n == 0)
{
throw new IrrationalResultException();
}
l = 0; r = Denominator; i = (Denominator + 1) / 2;
while (l < r)
{
try
{
if (Utility.Pow(i, Exponent.Denominator) > Denominator)
{
r = i - 1;
}
else if (Utility.Pow(i, Exponent.Denominator) < Denominator)
{
l = i;
}
else
{
_d = i; break;
}
}
catch
{ r = i - 1; }
finally
{ i = (l + r + 1) / 2; }
}
if (_d == 0)
{
throw new IrrationalResultException();
}
var res = new Rational(Utility.Pow(Sgn * _n, Math.Abs(Exponent.Numerator)), Utility.Pow(_d, Math.Abs(Exponent.Numerator)));
if (Exponent > 0)
{
return(res);
}
else
{
return(res.Inverse);
}
}
static void Print(RationalTypes.Rational r)
{
Console.WriteLine(String.Concat(r.ToString(), "\t", r.ToSignedString(), "\t", r.DecimalApproximation));
}