/// <summary>
/// Returns a specified big integer raised to the specified power.
/// </summary>
/// <param name="value">Number to raise.</param>
/// <param name="power">Power.</param>
/// <param name="multiplyMode">Multiply mode set explicitly.</param>
/// <returns>Number in given power.</returns>
/// <exception cref="ArgumentNullException"><paramref name="value" /> is a null reference.</exception>
static public IntX Pow(IntX value, uint power, MultiplyMode multiplyMode)
{
// Exception
if (ReferenceEquals(value, null))
{
throw new ArgumentNullException("value");
}
// Return one for zero pow
if (power == 0)
{
return(1);
}
// Return the number itself from a power of one
if (power == 1)
{
return(new IntX(value));
}
// Return zero for a zero
if (value._length == 0)
{
return(new IntX());
}
// Get first one bit
int msb = Bits.Msb(power);
// Get multiplier
IMultiplier multiplier = MultiplyManager.GetMultiplier(multiplyMode);
// Do actual raising
IntX res = value;
for (uint powerMask = 1U << (msb - 1); powerMask != 0; powerMask >>= 1)
{
// Always square
res = multiplier.Multiply(res, res);
// Maybe mul
if ((power & powerMask) != 0)
{
res = multiplier.Multiply(res, value);
}
}
return(res);
}
/// <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 unsafe 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);
}
// Check length - maybe use classic converter instead
if (length < Constants.FastConvertLengthLowerBound || length > Constants.FastConvertLengthUpperBound)
{
return(_classicStringConverter.ToString(digits, length, numberBase, ref outputLength));
}
int resultLengthLog2 = Bits.CeilLog2(outputLength);
uint resultLength = 1U << resultLengthLog2;
// Create and initially fill array for transofmed numbers storing
uint[] resultArray = ArrayPool <uint> .Instance.GetArray(resultLength);
Array.Copy(digits, resultArray, length);
// Create and initially fill array with lengths
uint[] resultArray2 = ArrayPool <uint> .Instance.GetArray(resultLength);
resultArray2[0] = length;
IMultiplier multiplier = MultiplyManager.GetCurrentMultiplier();
IDivider divider = DivideManager.GetCurrentDivider();
// Generate all needed pows of numberBase in stack
Stack baseIntStack = new Stack(resultLengthLog2);
IntX baseInt = null;
for (int i = 0; i < resultLengthLog2; ++i)
{
baseInt = baseInt == null ? numberBase : multiplier.Multiply(baseInt, baseInt);
baseIntStack.Push(baseInt);
}
// Create temporary buffer for second digits when doing div operation
uint[] tempBuffer = new uint[baseInt._length];
// We will use unsafe code here
fixed(uint *resultPtr1Const = resultArray, resultPtr2Const = resultArray2, tempBufferPtr = tempBuffer)
{
// Results pointers which will be modified (on swap)
uint *resultPtr1 = resultPtr1Const;
uint *resultPtr2 = resultPtr2Const;
// Temporary variables used on swapping
uint[] tempArray;
uint * tempPtr;
// Variables used in cycle
uint *ptr1, ptr2, ptr1end;
uint loLength;
// Outer cycle instead of recursion
for (uint innerStep = resultLength >> 1, outerStep = resultLength; innerStep > 0; innerStep >>= 1, outerStep >>= 1)
{
// Prepare pointers
ptr1 = resultPtr1;
ptr2 = resultPtr2;
ptr1end = resultPtr1 + resultLength;
// Get baseInt from stack and fix it too
baseInt = (IntX)baseIntStack.Pop();
fixed(uint *baseIntPtr = baseInt._digits)
{
// Cycle thru all digits and their lengths
for (; ptr1 < ptr1end; ptr1 += outerStep, ptr2 += outerStep)
{
// Divide ptr1 (with length in *ptr2) by baseIntPtr here.
// Results are stored in ptr2 & (ptr2 + innerStep), lengths - in *ptr1 and (*ptr1 + innerStep)
loLength = *ptr2;
*(ptr1 + innerStep) = divider.DivMod(
ptr1,
ptr2,
ref loLength,
baseIntPtr,
tempBufferPtr,
baseInt._length,
ptr2 + innerStep,
DivModResultFlags.Div | DivModResultFlags.Mod,
-2);
*ptr1 = loLength;
}
}
// After inner cycle resultArray will contain lengths and resultArray2 will contain actual values
// so we need to swap them here
tempArray = resultArray;
resultArray = resultArray2;
resultArray2 = tempArray;
tempPtr = resultPtr1;
resultPtr1 = resultPtr2;
resultPtr2 = tempPtr;
}
// Retrieve real output length
outputLength = DigitHelper.GetRealDigitsLength(resultArray2, outputLength);
// Create output array
outputArray = new uint[outputLength];
// Copy each digit but only if length is not null
fixed(uint *outputPtr = outputArray)
{
for (uint i = 0; i < outputLength; ++i)
{
if (resultPtr2[i] != 0)
{
outputPtr[i] = resultPtr1[i];
}
}
}
}
// Return temporary arrays to pool
ArrayPool <uint> .Instance.AddArray(resultArray);
ArrayPool <uint> .Instance.AddArray(resultArray2);
return(outputArray);
}
/// <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);
}
