/// <summary>
/// Compares 2 <see cref="IntX" /> objects.
/// Returns "-2" if any argument is null, "-1" if <paramref name="int1" /> < <paramref name="int2" />,
/// "0" if equal and "1" if >.
/// </summary>
/// <param name="int1">First big integer.</param>
/// <param name="int2">Second big integer.</param>
/// <param name="throwNullException">Raises or not <see cref="NullReferenceException" />.</param>
/// <returns>Comparsion result.</returns>
/// <exception cref="ArgumentNullException"><paramref name="int1" /> or <paramref name="int2" /> is a null reference and <paramref name="throwNullException" /> is set to true.</exception>
static public int Cmp(IntX int1, IntX int2, bool throwNullException)
{
// If one of the operands is null, throw exception or return -2
bool isNull1 = ReferenceEquals(int1, null);
bool isNull2 = ReferenceEquals(int2, null);
if (isNull1 || isNull2)
{
if (throwNullException)
{
throw new ArgumentNullException(isNull1 ? "int1" : "int2", Strings.CantBeNullCmp);
}
else
{
return(isNull1 && isNull2 ? 0 : -2);
}
}
// Compare sign
if (int1._negative && !int2._negative)
{
return(-1);
}
if (!int1._negative && int2._negative)
{
return(1);
}
// Compare presentation
return(DigitOpHelper.Cmp(int1._digits, int1._length, int2._digits, int2._length) * (int1._negative ? -1 : 1));
}
/// <summary>
/// Converts digits from internal representaion into given base.
/// </summary>
/// <param name="digits">Big integer digits.</param>
/// <param name="length">Big integer length.</param>
/// <param name="numberBase">Base to use for output.</param>
/// <param name="outputLength">Calculated output length (will be corrected inside).</param>
/// <returns>Conversion result (later will be transformed to string).</returns>
override public uint[] ToString(uint[] digits, uint length, uint numberBase, ref uint outputLength)
{
uint[] outputArray = base.ToString(digits, length, numberBase, ref outputLength);
// Maybe base method already converted this number
if (outputArray != null)
{
return(outputArray);
}
// Create an output array for storing of number in other base
outputArray = new uint[outputLength + 1];
// Make a copy of initial data
uint[] digitsCopy = new uint[length];
Array.Copy(digits, digitsCopy, length);
// Calculate output numbers by dividing
uint outputIndex;
for (outputIndex = 0; length > 0; ++outputIndex)
{
length = DigitOpHelper.DivMod(digitsCopy, length, numberBase, digitsCopy, out outputArray[outputIndex]);
}
outputLength = outputIndex;
return(outputArray);
}
/// <summary>
/// Subtracts two big integers.
/// </summary>
/// <param name="int1">First big integer.</param>
/// <param name="int2">Second big integer.</param>
/// <returns>Resulting big integer.</returns>
static public IntX Sub(IntX int1, IntX int2)
{
// Process zero values in special way
if (int1._length == 0)
{
return(new IntX(int2._digits, true));
}
if (int2._length == 0)
{
return(new IntX(int1));
}
// Determine lower big int (without sign)
IntX smallerInt;
IntX biggerInt;
int compareResult = DigitOpHelper.Cmp(int1._digits, int1._length, int2._digits, int2._length);
if (compareResult == 0)
{
return(new IntX()); // integers are equal
}
if (compareResult < 0)
{
smallerInt = int1;
biggerInt = int2;
}
else
{
smallerInt = int2;
biggerInt = int1;
}
// Create new big int object
IntX newInt = new IntX(biggerInt._length, ReferenceEquals(int1, smallerInt) ^ int1._negative);
// Do actual subtraction
newInt._length = DigitOpHelper.Sub(
biggerInt._digits,
biggerInt._length,
smallerInt._digits,
smallerInt._length,
newInt._digits);
// Normalization may be needed
newInt.TryNormalize();
return(newInt);
}
/// <summary>
/// Adds two big integers.
/// </summary>
/// <param name="int1">First big integer.</param>
/// <param name="int2">Second big integer.</param>
/// <returns>Resulting big integer.</returns>
/// <exception cref="ArgumentException"><paramref name="int1" /> or <paramref name="int2" /> is too big for add operation.</exception>
static public IntX Add(IntX int1, IntX int2)
{
// Process zero values in special way
if (int2._length == 0)
{
return(new IntX(int1));
}
if (int1._length == 0)
{
IntX x = new IntX(int2);
x._negative = int1._negative; // always get sign of the first big integer
return(x);
}
// Determine big int with lower length
IntX smallerInt;
IntX biggerInt;
DigitHelper.GetMinMaxLengthObjects(int1, int2, out smallerInt, out biggerInt);
// Check for add operation possibility
if (biggerInt._length == uint.MaxValue)
{
throw new ArgumentException(Strings.IntegerTooBig);
}
// Create new big int object of needed length
IntX newInt = new IntX(biggerInt._length + 1, int1._negative);
// Do actual addition
newInt._length = DigitOpHelper.Add(
biggerInt._digits,
biggerInt._length,
smallerInt._digits,
smallerInt._length,
newInt._digits);
// Normalization may be needed
newInt.TryNormalize();
return(newInt);
}
/// <summary>
/// Shifts <see cref="IntX" /> object.
/// Determines which operation to use basing on shift sign.
/// </summary>
/// <param name="intX">Big integer.</param>
/// <param name="shift">Bits count to shift.</param>
/// <param name="toLeft">If true the shifting to the left.</param>
/// <returns>Bitwise shift operation result.</returns>
/// <exception cref="ArgumentNullException"><paramref name="intX" /> is a null reference.</exception>
static public IntX Sh(IntX intX, long shift, bool toLeft)
{
// Exceptions
if (ReferenceEquals(intX, null))
{
throw new ArgumentNullException("intX", Strings.CantBeNullOne);
}
// Zero can't be shifted
if (intX._length == 0)
{
return(new IntX());
}
// Can't shift on zero value
if (shift == 0)
{
return(new IntX(intX));
}
// Determine real bits count and direction
ulong bitCount;
bool negativeShift;
DigitHelper.ToUInt64WithSign(shift, out bitCount, out negativeShift);
toLeft ^= negativeShift;
// Get position of the most significant bit in intX and amount of bits in intX
int msb = Bits.Msb(intX._digits[intX._length - 1]);
ulong intXBitCount = (ulong)(intX._length - 1) * Constants.DigitBitCount + (ulong)msb + 1UL;
// If shifting to the right and shift is too big then return zero
if (!toLeft && bitCount >= intXBitCount)
{
if (intX.Negative)
{
return(-1);
}
return(new IntX());
}
// Calculate new bit count
ulong newBitCount = toLeft ? intXBitCount + bitCount : intXBitCount - bitCount;
// If shifting to the left and shift is too big to fit in big integer, throw an exception
if (toLeft && newBitCount > Constants.MaxBitCount)
{
throw new ArgumentException(Strings.IntegerTooBig, "intX");
}
// Get exact length of new big integer (no normalize is ever needed here).
// Create new big integer with given length
uint newLength = (uint)(newBitCount / Constants.DigitBitCount + (newBitCount % Constants.DigitBitCount == 0 ? 0UL : 1UL));
IntX newInt = new IntX(newLength, intX._negative);
// Get full and small shift values
uint fullDigits = (uint)(bitCount / Constants.DigitBitCount);
int smallShift = (int)(bitCount % Constants.DigitBitCount);
// We can just copy (no shift) if small shift is zero
if (smallShift == 0)
{
if (toLeft)
{
Array.Copy(intX._digits, 0, newInt._digits, fullDigits, intX._length);
}
else
{
Array.Copy(intX._digits, fullDigits, newInt._digits, 0, newLength);
}
}
else
{
// Do copy with real shift in the needed direction
if (toLeft)
{
DigitOpHelper.Shr(intX._digits, 0, intX._length, newInt._digits, fullDigits + 1, Constants.DigitBitCount - smallShift, false);
}
else
{
// If new result length is smaller then original length we shouldn't lose any digits
if (newLength < intX._length)
{
newLength++;
}
DigitOpHelper.Shr(intX._digits, fullDigits, newLength, newInt._digits, 0, smallShift, fullDigits + newLength > intX._length);
}
}
if (!toLeft && intX.Negative)
{
return(~-newInt);
}
return(newInt);
}
/// <summary>
/// Divides one <see cref="IntX" /> by another.
/// </summary>
/// <param name="int1">First big integer.</param>
/// <param name="int2">Second big integer.</param>
/// <param name="modRes">Remainder big integer.</param>
/// <param name="resultFlags">Which operation results to return.</param>
/// <returns>Divident big integer.</returns>
/// <exception cref="ArgumentNullException"><paramref name="int1" /> or <paramref name="int2" /> is a null reference.</exception>
/// <exception cref="DivideByZeroException"><paramref name="int2" /> equals zero.</exception>
virtual public IntX DivMod(IntX int1, IntX int2, out IntX modRes, DivModResultFlags resultFlags)
{
// Null reference exceptions
if (ReferenceEquals(int1, null))
{
throw new ArgumentNullException("int1", Strings.CantBeNull);
}
else if (ReferenceEquals(int2, null))
{
throw new ArgumentNullException("int2", Strings.CantBeNull);
}
// Check if int2 equals zero
if (int2._length == 0)
{
throw new DivideByZeroException();
}
// Get flags
bool divNeeded = (resultFlags & DivModResultFlags.Div) != 0;
bool modNeeded = (resultFlags & DivModResultFlags.Mod) != 0;
// Special situation: check if int1 equals zero; in this case zero is always returned
if (int1._length == 0)
{
modRes = modNeeded ? new IntX() : null;
return(divNeeded ? new IntX() : null);
}
// Special situation: check if int2 equals one - nothing to divide in this case
if (int2._length == 1 && int2._digits[0] == 1)
{
modRes = modNeeded ? new IntX() : null;
return(divNeeded ? int2._negative ? -int1 : +int1 : null);
}
// Get resulting sign
bool resultNegative = int1._negative ^ int2._negative;
// Check if int1 > int2
int compareResult = DigitOpHelper.Cmp(int1._digits, int1._length, int2._digits, int2._length);
if (compareResult < 0)
{
modRes = modNeeded ? new IntX(int1) : null;
return(divNeeded ? new IntX() : null);
}
else if (compareResult == 0)
{
modRes = modNeeded ? new IntX() : null;
return(divNeeded ? new IntX(resultNegative ? -1 : 1) : null);
}
//
// Actually divide here (by Knuth algorithm)
//
// Prepare divident (if needed)
IntX divRes = null;
if (divNeeded)
{
divRes = new IntX(int1._length - int2._length + 1U, resultNegative);
}
// Prepare mod (if needed)
if (modNeeded)
{
modRes = new IntX(int1._length + 1U, int1._negative);
}
else
{
modRes = null;
}
// Call procedure itself
uint modLength = int1._length;
uint divLength = DivMod(
int1._digits,
modNeeded ? modRes._digits : null,
ref modLength,
int2._digits,
null,
int2._length,
divNeeded ? divRes._digits : null,
resultFlags,
compareResult);
// Maybe set new lengths and perform normalization
if (divNeeded)
{
divRes._length = divLength;
divRes.TryNormalize();
}
if (modNeeded)
{
modRes._length = modLength;
modRes.TryNormalize();
}
// Return div
return(divRes);
}
/// <summary>
/// Divides two big integers.
/// Also modifies <paramref name="digitsPtr1" /> and <paramref name="length1"/> (it will contain remainder).
/// </summary>
/// <param name="digitsPtr1">First big integer digits.</param>
/// <param name="digitsBufferPtr1">Buffer for first big integer digits. May also contain remainder.</param>
/// <param name="length1">First big integer length.</param>
/// <param name="digitsPtr2">Second big integer digits.</param>
/// <param name="digitsBufferPtr2">Buffer for second big integer digits. Only temporarily used.</param>
/// <param name="length2">Second big integer length.</param>
/// <param name="digitsResPtr">Resulting big integer digits.</param>
/// <param name="resultFlags">Which operation results to return.</param>
/// <param name="cmpResult">Big integers comparsion result (pass -2 if omitted).</param>
/// <returns>Resulting big integer length.</returns>
virtual unsafe public uint DivMod(
uint *digitsPtr1,
uint *digitsBufferPtr1,
ref uint length1,
uint *digitsPtr2,
uint *digitsBufferPtr2,
uint length2,
uint *digitsResPtr,
DivModResultFlags resultFlags,
int cmpResult)
{
// Base implementation covers some special cases
bool divNeeded = (resultFlags & DivModResultFlags.Div) != 0;
bool modNeeded = (resultFlags & DivModResultFlags.Mod) != 0;
//
// Special cases
//
// Case when length1 == 0
if (length1 == 0)
{
return(0);
}
// Case when both lengths are 1
if (length1 == 1 && length2 == 1)
{
if (divNeeded)
{
*digitsResPtr = *digitsPtr1 / *digitsPtr2;
if (*digitsResPtr == 0)
{
length2 = 0;
}
}
if (modNeeded)
{
*digitsBufferPtr1 = *digitsPtr1 % *digitsPtr2;
if (*digitsBufferPtr1 == 0)
{
length1 = 0;
}
}
return(length2);
}
// Compare digits first (if was not previously compared)
if (cmpResult == -2)
{
cmpResult = DigitOpHelper.Cmp(digitsPtr1, length1, digitsPtr2, length2);
}
// Case when first value is smaller then the second one - we will have remainder only
if (cmpResult < 0)
{
// Maybe we should copy first digits into remainder (if remainder is needed at all)
if (modNeeded)
{
DigitHelper.DigitsBlockCopy(digitsPtr1, digitsBufferPtr1, length1);
}
// Zero as division result
return(0);
}
// Case when values are equal
if (cmpResult == 0)
{
// Maybe remainder must be marked as empty
if (modNeeded)
{
length1 = 0;
}
// One as division result
if (divNeeded)
{
*digitsResPtr = 1;
}
return(1);
}
// Case when second length equals to 1
if (length2 == 1)
{
// Call method basing on fact if div is needed
uint modRes;
if (divNeeded)
{
length2 = DigitOpHelper.DivMod(digitsPtr1, length1, *digitsPtr2, digitsResPtr, out modRes);
}
else
{
modRes = DigitOpHelper.Mod(digitsPtr1, length1, *digitsPtr2);
}
// Maybe save mod result
if (modNeeded)
{
if (modRes != 0)
{
length1 = 1;
*digitsBufferPtr1 = modRes;
}
else
{
length1 = 0;
}
}
return(length2);
}
// This is regular case, not special
return(uint.MaxValue);
}
/// <summary>
/// Parses provided string representation of <see cref="IntX" /> object.
/// </summary>
/// <param name="value">Number as string.</param>
/// <param name="startIndex">Index inside string from which to start.</param>
/// <param name="endIndex">Index inside string on which to end.</param>
/// <param name="numberBase">Number base.</param>
/// <param name="charToDigits">Char->digit dictionary.</param>
/// <param name="digitsRes">Resulting digits.</param>
/// <returns>Parsed integer length.</returns>
override unsafe public uint Parse(string value, int startIndex, int endIndex, uint numberBase, IDictionary <char, uint> charToDigits, uint[] digitsRes)
{
uint newLength = base.Parse(value, startIndex, endIndex, numberBase, charToDigits, digitsRes);
// Maybe base method already parsed this number
if (newLength != 0)
{
return(newLength);
}
// Check length - maybe use classic parser instead
uint initialLength = (uint)digitsRes.LongLength;
if (initialLength < Constants.FastParseLengthLowerBound || initialLength > Constants.FastParseLengthUpperBound)
{
return(_classicParser.Parse(value, startIndex, endIndex, numberBase, charToDigits, digitsRes));
}
uint valueLength = (uint)(endIndex - startIndex + 1);
uint digitsLength = 1U << Bits.CeilLog2(valueLength);
// Prepare array for digits in other base
uint[] valueDigits = ArrayPool <uint> .Instance.GetArray(digitsLength);
// This second array will store integer lengths initially
uint[] valueDigits2 = ArrayPool <uint> .Instance.GetArray(digitsLength);
fixed(uint *valueDigitsStartPtr = valueDigits, valueDigitsStartPtr2 = valueDigits2)
{
// In the string first digit means last in digits array
uint *valueDigitsPtr = valueDigitsStartPtr + valueLength - 1;
uint *valueDigitsPtr2 = valueDigitsStartPtr2 + valueLength - 1;
// Reverse copy characters into digits
fixed(char *valueStartPtr = value)
{
char *valuePtr = valueStartPtr + startIndex;
char *valueEndPtr = valuePtr + valueLength;
for (; valuePtr < valueEndPtr; ++valuePtr, --valueDigitsPtr, --valueDigitsPtr2)
{
// Get digit itself - this call will throw an exception if char is invalid
*valueDigitsPtr = StrRepHelper.GetDigit(charToDigits, *valuePtr, numberBase);
// Set length of this digit (zero for zero)
*valueDigitsPtr2 = *valueDigitsPtr == 0U ? 0U : 1U;
}
}
// We have retrieved lengths array from pool - it needs to be cleared before using
DigitHelper.SetBlockDigits(valueDigitsStartPtr2 + valueLength, digitsLength - valueLength, 0);
// Now start from the digit arrays beginning
valueDigitsPtr = valueDigitsStartPtr;
valueDigitsPtr2 = valueDigitsStartPtr2;
// Current multiplier (classic or fast) will be used
IMultiplier multiplier = MultiplyManager.GetCurrentMultiplier();
// Here base in needed power will be stored
IntX baseInt = null;
// Temporary variables used on swapping
uint[] tempDigits;
uint * tempPtr;
// Variables used in cycle
uint *ptr1, ptr2, valueDigitsPtrEnd;
uint loLength, hiLength;
// Outer cycle instead of recursion
for (uint innerStep = 1, outerStep = 2; innerStep < digitsLength; innerStep <<= 1, outerStep <<= 1)
{
// Maybe baseInt must be multiplied by itself
baseInt = baseInt == null ? numberBase : baseInt * baseInt;
// Using unsafe here
fixed(uint *baseDigitsPtr = baseInt._digits)
{
// Start from arrays beginning
ptr1 = valueDigitsPtr;
ptr2 = valueDigitsPtr2;
// vauleDigits array end
valueDigitsPtrEnd = valueDigitsPtr + digitsLength;
// Cycle thru all digits and their lengths
for (; ptr1 < valueDigitsPtrEnd; ptr1 += outerStep, ptr2 += outerStep)
{
// Get lengths of "lower" and "higher" value parts
loLength = *ptr2;
hiLength = *(ptr2 + innerStep);
if (hiLength != 0)
{
// We always must clear an array before multiply
DigitHelper.SetBlockDigits(ptr2, outerStep, 0U);
// Multiply per baseInt
hiLength = multiplier.Multiply(
baseDigitsPtr,
baseInt._length,
ptr1 + innerStep,
hiLength,
ptr2);
}
// Sum results
if (hiLength != 0 || loLength != 0)
{
*ptr1 = DigitOpHelper.Add(
ptr2,
hiLength,
ptr1,
loLength,
ptr2);
}
else
{
*ptr1 = 0U;
}
}
}
// After inner cycle valueDigits will contain lengths and valueDigits2 will contain actual values
// so we need to swap them here
tempDigits = valueDigits;
valueDigits = valueDigits2;
valueDigits2 = tempDigits;
tempPtr = valueDigitsPtr;
valueDigitsPtr = valueDigitsPtr2;
valueDigitsPtr2 = tempPtr;
}
}
// Determine real length of converted number
uint realLength = valueDigits2[0];
// Copy to result
Array.Copy(valueDigits, digitsRes, realLength);
// Return arrays to pool
ArrayPool <uint> .Instance.AddArray(valueDigits);
ArrayPool <uint> .Instance.AddArray(valueDigits2);
return(realLength);
}
