/// <summary>
/// Calculates a quotient and remainder of division of an ALong instance and integer.
/// </summary>
/// <param name="num1">Divident</param>
/// <param name="num2">Divisor</param>
/// <returns>A Tuple of Quotient and Remainder.</returns>
public static Tuple <ALong, ALong> DivInt(ALong num1, int num2)
{
if (num2 == 0)
{
throw new ArgumentException("Division by zero");
}
if (num1 == 0)
{
return(new Tuple <ALong, ALong>(new ALong(0), new ALong(0)));
}
if (num1 == num2)
{
return(new Tuple <ALong, ALong>(new ALong(1), new ALong(0)));
}
if (Abs(num1) < Math.Abs(num2))
{
return(new Tuple <ALong, ALong>(new ALong(0), new ALong(num1)));
}
var strres = "";
string divident = "";
var dividentInt = 0L;
var divisor = Math.Abs(num2);
int remainder = 0;
for (int i = 0; i < num1.Length(); i++)
{
divident += num1.Num[i];
dividentInt = divident.ToLong();
if (dividentInt < divisor)
{
if (strres != "")
{
strres += "0";
}
continue;
}
var res = dividentInt / divisor;
strres += res;
divident = (dividentInt - res * divisor).ToString();
}
remainder = divident.ToInt();
return(new Tuple <ALong, ALong>(new ALong(strres).SetNegative(num1.IsNegative != num2 < 0), new ALong(num1.IsNegative ? remainder * -1 : remainder)));
}
/// <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 Summary of a two ALong absolute values, a.k.a "School" method.
/// </summary>
/// <param name="num1">First addend</param>
/// <param name="num2">Second addend</param>
/// <returns>ALong instance representing a sum of two addends.</returns>
private static ALong AbsSum(ALong num1, ALong num2)
{
var result = String.Empty;
int carry = 0;
var max = Math.Max(num1.Length(), num2.Length());
for (int i = 0; i < max; i++)
{
var n1 = num1.GetRNumAtIndex(i);
var n2 = num2.GetRNumAtIndex(i);
var ns = n1 + n2 + carry;
carry = 0;
if (ns >= 10)
{
ns = ns - 10; carry = 1;
}
result = ns.ToString() + result;
if (i == max - 1 && carry > 0)
{
result = carry.ToString() + result;
}
}
return(new ALong(result));
}