/// <summary>
/// Calculates a product of a two ALong instances, a.k.a "School" method (very slow)
/// </summary>
/// <param name="num1">Multiplicand</param>
/// <param name="num2">Multiplier</param>
/// <returns>Product of num1 and num2.</returns>
//TODO: replace with Karatsuba, Schönhage–Strassen or Knuth. (Fast Fourier transform?).
//TODO: use base of size of Int32 to "shorten" sizes of numbers within multiplication speed being kept.
public static ALong Mul(ALong num1, ALong num2)
{
var result = new ALong(0);
if (num1 == 0 || num2 == 0)
{
return(result);
}
var carry = 0;
for (int i = 0; i < num1.Length(); i++)
{
var n1 = num1.GetRNumAtIndex(i);
var res = String.Empty;
var n2len = num2.Length();
carry = 0;
for (int k = 0; k < n2len; k++)
{
var n2 = num2.GetRNumAtIndex(k);
var ns = n1 * n2 + carry;
carry = ns / 10;
res = (ns % 10) + res;
if (k == n2len - 1 && carry > 0)
{
res = carry.ToString() + res;
}
}
var mulres = new ALong(res);
mulres.MulBase(i);
result += mulres;
}
if (num1.IsNegative != num2.IsNegative)
{
result.SetNegative(true);
}
return(result);
}
/// <summary>
/// Calculates a quotient and remainder of division of a two ALong instances.
/// </summary>
/// <param name="num1">Divident</param>
/// <param name="num2">Divisor</param>
/// <returns>A Tuple of Quotient and Remainder.</returns>
public static Tuple <ALong, ALong> Divide(ALong num1, ALong num2)
{
var num2a = Abs(num2);
if (num2a < Int32.MaxValue)
{
return(DivInt(num1, num2.ToString().ToInt()));
}
if (num2 == 0)
{
throw new ArgumentException("Division by zero");
}
if (num1 == 0)
{
return(new Tuple <ALong, ALong>(new ALong(0), new ALong(0)));
}
var num1a = Abs(num1);
if (num1a == num2a)
{
return(new Tuple <ALong, ALong>(new ALong(1).SetNegative(num1.IsNegative != num2.IsNegative), new ALong(0)));
}
if (num1a < num2a)
{
return(new Tuple <ALong, ALong>(new ALong(0), new ALong(num1)));
}
var b = 10; // base
var down = new ALong(0);
// Get upper limit
var up = new ALong(b);
while (num1a > num2a * up)
{
up = up * b;
}
// Divide
while (up - down > 1)
{
var cur = (down + up) / 2;
var c = num2a * (cur);
if (c < num1a)
{
down = cur; continue;
}
if (c > num1a)
{
up = cur; continue;
}
if (c == num1a)
{
down = cur; up = cur; continue;
}
}
var remainder = num1a - down * num2a;
down.SetNegative(num1.IsNegative != num2.IsNegative);
remainder.SetNegative(num1.IsNegative);
return(new Tuple <ALong, ALong>(down, remainder));
}