/// <summary>
/// Performs the division (with remainder) of two long integer numbers.
/// </summary>
/// <param name="one">The first LongInt number.</param>
/// <param name="two">The second LongInt number.</param>
/// <param name="remainder">The reference to contain the remainder.</param>
/// <returns>The result of integral division.</returns>
public static LongInt <B> Div(LongInt <B> one, LongInt <B> two, out LongInt <B> remainder)
{
Contract.Requires <ArgumentNullException>(one != null, "one");
Contract.Requires <ArgumentNullException>(two != null, "two");
Contract.Ensures(Contract.ForAll(Contract.Result <LongInt <B> >().Digits, x => (x >= 0)));
// Проверка на тупые случаи - деление на большее число или деление на единичную цифру.
if (one.Length < two.Length)
{
remainder = one.Clone() as LongInt <B>;
return(new LongInt <B>()); // zero number should be returned
}
if (two.Length == 1)
{
LongInt <B> result = new LongInt <B>(one.Length);
result.Digits.AddRange(new int[one.Length]);
int rem = LongIntegerMethods.DivideByInteger(LongInt <B> .BASE, result.Digits, one.Digits, two[0]);
// Разберемся с negativeness.
remainder = (LongInt <B>)rem; // convert the result to LongInt...
result.Negative = one.Negative ^ two.Negative;
remainder.Negative = one.Negative;
result.DealWithZeroes();
remainder.DealWithZeroes();
return(result);
}
LongInt <B> res = new LongInt <B>();
res.Digits.AddRange(new int[one.Length - two.Length + 1]);
remainder = new LongInt <B>(two.Length);
// ----- big bada-boom!
IList <int> remDigits = LongIntegerMethods.Div(LongInt <B> .BASE, res.Digits, one.Digits, two.Digits);
// --------------------
remainder.Digits.AddRange(remDigits);
// deal with negativeness
res.Negative = one.Negative ^ two.Negative;
remainder.Negative = one.Negative;
// deal with zeroes
res.DealWithZeroes();
remainder.DealWithZeroes();
return(res);
}
public static void baseConvert(IList <int> from, IList <int> to, int fromBase, int newBase)
{
// проверяем, не кратное ли основание
int?power;
if (WhiteMath <int, CalcInt> .IsNaturalIntegerPowerOf(fromBase, newBase, out power) ||
WhiteMath <int, CalcInt> .IsNaturalIntegerPowerOf(newBase, fromBase, out power))
{
convertPowered(from, to, fromBase, newBase, power.Value);
}
// в противном случае - не избежать последовательного деления.
else
{
int k = 0;
IList <int> divide = from;
while (divide.CountSignificant() > 1 || divide[0] > 0)
{
int remainder;
divide = LongIntegerMethods.DivideByInteger(fromBase, divide, newBase, out remainder);
to[k++] = remainder;
}
}
}
// ---------------------------------------------------------------------
private static void MultiplyKaratsuba(int BASE, IList <int> result, IList <int> one, IList <int> two, int dim)
{
int half = dim / 2;
// Отбрасываем при некотором значении
if (dim <= karatsubaCutoffDimension)
{
LongIntegerMethods.MultiplySimple(BASE, result, one, two);
return;
}
ListSegment <int> a = new ListSegment <int>(one, 0, half);
ListSegment <int> b = new ListSegment <int>(one, half, one.Count - half);
ListSegment <int> c = new ListSegment <int>(two, 0, half);
ListSegment <int> d = new ListSegment <int>(two, half, two.Count - half);
int[] ac = new int[dim];
int[] bd = new int[b.Count + d.Count];
int[] abcd = new int[b.Count + d.Count + 2];
MultiplyKaratsuba(BASE, ac, a, c, half);
MultiplyKaratsuba(BASE, bd, b, d, half);
int[] apb = new int[b.Count + 1];
int[] cpd = new int[d.Count + 1];
int[] acpbd = new int[b.Count + d.Count + 2];
LongIntegerMethods.Sum(BASE, apb, a, b);
LongIntegerMethods.Sum(BASE, cpd, c, d);
MultiplyKaratsuba(BASE, abcd, apb, cpd, half);
LongIntegerMethods.Sum(BASE, acpbd, ac, bd);
int[] difference = new int[b.Count + d.Count + 2];
if (LongIntegerMethods.Dif(BASE, difference, abcd, acpbd))
{
Console.WriteLine("Lower-level difference error.");
}
SumPrivate(BASE, result, ac, 0, difference, half);
SumPrivate(BASE, result, result, 0, bd, dim);
return;
}
//---------------------------------------------------------------
//---------------------NUMBER MULTIPLICATION---------------------
//---------------------------------------------------------------
/// <summary>
/// Performs a simple, square-complex multiplication of two LongInt numbers.
/// </summary>
/// <param name="one"></param>
/// <param name="two"></param>
/// <returns></returns>
public static LongInt <B> MultiplySimple(LongInt <B> one, LongInt <B> two)
{
// the resulting number can have double length.
LongInt <B> res = new LongInt <B>(one.Length + two.Length);
res.Digits.AddRange(new int[one.Length + two.Length]);
res.Negative = one.Negative ^ two.Negative;
// The big one
LongIntegerMethods.MultiplySimple(LongInt <B> .BASE, res.Digits, one.Digits, two.Digits);
// Cut the leading zeroes
res.DealWithZeroes();
return(res);
}
/// <summary>
/// Performs the division (with remainder) of two long integer numbers.
/// The method would return the list containing the remainder digits.
/// </summary>
/// <returns>The list containing the remainder digits.</returns>
/// <param name="BASE">The numberic base of the digits, ex. 10 000</param>
/// <param name="result">The digits array to store the result. WARNING! Should be able to store AT LEAST one.Count - two.Count + 1 digits.</param>
/// <param name="one">The digits array containing the first operand.</param>
/// <param name="two">The digits array containing the second operand.</param>
public static IList <int> Div(int BASE, IList <int> result, IList <int> one, IList <int> two)
{
Contract.Requires <ArgumentNullException>(result != null, "result");
Contract.Requires <ArgumentNullException>(one != null, "one");
Contract.Requires <ArgumentNullException>(two != null, "two");
Contract.Requires(Contract.ForAll(one, x => x >= 0)); // first contains only positive digits
Contract.Requires(Contract.ForAll(two, x => x >= 0)); // second contains only positive digits
Contract.Ensures(Contract.Result <IList <int> >() != null); // remainder's not null
Contract.Ensures(Contract.ForAll(Contract.Result <IList <int> >(), x => x >= 0)); // remainder has positive digits
Contract.Ensures(Contract.ForAll(result, x => x >= 0)); // quot has positive digits
// Обнуляем результат
result.FillByAssign(0);
// ------------------
IList <int> u, v;
int uShift, vShift, i;
long temp, temp1, temp2;
int scale;
int qGuess, remainder;
int borrow, carry;
// Проверим, надо ли домножать.
// Если да - увы, надо выделять дополнительную память.
scale = BASE / (two[two.CountSignificant() - 1] + 1);
if (scale > 1)
{
u = new int[one.Count + 2];
v = new int[two.Count + 2];
int[] scaleAr = new int[] { scale };
MultiplySimple(BASE, u, one, scaleAr);
MultiplySimple(BASE, v, two, scaleAr);
}
else
{
// Число будет "портиться", поэтому нужно создать хоть копию.
u = new int[one.CountSignificant() + 1];
General.ServiceMethods.Copy(one, 0, u, 0, u.Count - 1);
// Делитель портиться не будет.
v = two;
}
// ------------
int n = v.CountSignificant();
int m = u.CountSignificant() - n;
// ------------
// Добавлено -1
for (vShift = m, uShift = n + vShift; vShift >= 0; --vShift, --uShift)
{
qGuess = (int)(((long)u[uShift] * BASE + u[uShift - 1]) / v[n - 1]);
remainder = (int)(((long)u[uShift] * BASE + u[uShift - 1]) % v[n - 1]);
while (remainder < BASE)
{
temp2 = (long)v[n - 2] * qGuess;
temp1 = (long)remainder * BASE + u[uShift - 2];
if ((temp2 > temp1) || (qGuess == BASE))
{
--qGuess;
remainder += v[n - 1];
}
else
{
break;
}
}
// Теперь qGuess - правильное частное или на единицу больше q
// Вычесть делитель B, умноженный на qGuess из делимого U,
// начиная с позиции vJ+i
carry = 0; borrow = 0;
// цикл по цифрам two
for (i = 0; i < n; i++)
{
// получить в temp цифру произведения B*qGuess
temp1 = (long)v[i] * qGuess + carry;
carry = (int)(temp1 / BASE);
temp1 -= (long)carry * BASE;
// Сразу же вычесть из U
temp2 = (long)u[i + vShift] - temp1 + borrow;
if (temp2 < 0)
{
u[i + vShift] = (int)(temp2 + BASE);
borrow = -1;
}
else
{
u[i + vShift] = (int)temp2;
borrow = 0;
}
}
// возможно, умноженое на qGuess число B удлинилось.
// Если это так, то после умножения остался
// неиспользованный перенос carry. Вычесть и его тоже.
temp2 = (long)u[i + vShift] - carry + borrow;
if (temp2 < 0)
{
u[i + vShift] = (int)temp2 + BASE;
borrow = -1;
}
else
{
u[i + vShift] = (int)temp2;
borrow = 0;
}
// Прошло ли вычитание нормально ?
if (borrow == 0)
{
// Да, частное угадано правильно
result[vShift] = qGuess;
}
else
{
// Нет, последний перенос при вычитании borrow = -1,
// значит, qGuess на единицу больше истинного частного
result[vShift] = qGuess - 1;
// добавить одно, вычтенное сверх необходимого B к U
carry = 0;
for (i = 0; i < n; i++)
{
temp = (long)u[i + vShift] + v[i] + carry;
if (temp >= BASE)
{
u[i + vShift] = (int)(temp - BASE);
carry = 1;
}
else
{
u[i + vShift] = (int)temp;
carry = 0;
}
}
u[i + vShift] = u[i + vShift] + carry - BASE;
}
// Обновим размер U, который после вычитания мог уменьшиться
// i = u.Length - 1;
// while ((i > 0) && (u[i] == 0))
// u.digits.RemoveAt(i--);
}
// Возвращаем остаток.
// Только надо поделить на scale.
int[] remDigits = new int[u.Count];
LongIntegerMethods.DivideByInteger(BASE, remDigits, u, scale);
return(remDigits);
}
