public static BigInteger ModPow(BigInteger value, BigInteger exponent, BigInteger modulus)
{
if (exponent.Sign < 0)
{
throw new ArgumentOutOfRangeException(nameof(exponent));
}
value.AssertValid();
exponent.AssertValid();
modulus.AssertValid();
bool trivialValue = value._bits == null;
bool trivialExponent = exponent._bits == null;
bool trivialModulus = modulus._bits == null;
if (trivialModulus)
{
uint bits = trivialValue && trivialExponent?BigIntegerCalculator.Pow(NumericsHelpers.Abs(value._sign), NumericsHelpers.Abs(exponent._sign), NumericsHelpers.Abs(modulus._sign)) :
trivialValue?BigIntegerCalculator.Pow(NumericsHelpers.Abs(value._sign), exponent._bits, NumericsHelpers.Abs(modulus._sign)) :
trivialExponent?BigIntegerCalculator.Pow(value._bits, NumericsHelpers.Abs(exponent._sign), NumericsHelpers.Abs(modulus._sign)) :
BigIntegerCalculator.Pow(value._bits, exponent._bits, NumericsHelpers.Abs(modulus._sign));
return(value._sign < 0 && !exponent.IsEven ? -1 * bits : bits);
}
else
{
uint[] bits = trivialValue && trivialExponent?BigIntegerCalculator.Pow(NumericsHelpers.Abs(value._sign), NumericsHelpers.Abs(exponent._sign), modulus._bits) :
trivialValue?BigIntegerCalculator.Pow(NumericsHelpers.Abs(value._sign), exponent._bits, modulus._bits) :
trivialExponent?BigIntegerCalculator.Pow(value._bits, NumericsHelpers.Abs(exponent._sign), modulus._bits) :
BigIntegerCalculator.Pow(value._bits, exponent._bits, modulus._bits);
return(new BigInteger(bits, value._sign < 0 && !exponent.IsEven));
}
}
private static bool NumberToBigInteger(ref BigNumberBuffer number, out BigInteger result)
{
int currentBufferSize = 0;
int totalDigitCount = 0;
int numberScale = number.scale;
const int MaxPartialDigits = 9;
const uint TenPowMaxPartial = 1000000000;
int[]? arrayFromPoolForResultBuffer = null;
if (numberScale < 0)
{
result = default;
return(false);
}
try
{
if (number.digits.Length <= s_naiveThreshold)
{
return(Naive(ref number, out result));
}
else
{
return(DivideAndConquer(ref number, out result));
}
}
finally
{
if (arrayFromPoolForResultBuffer != null)
{
ArrayPool <int> .Shared.Return(arrayFromPoolForResultBuffer);
}
}
bool Naive(ref BigNumberBuffer number, out BigInteger result)
{
Span <uint> stackBuffer = stackalloc uint[BigIntegerCalculator.StackAllocThreshold];
Span <uint> currentBuffer = stackBuffer;
uint partialValue = 0;
int partialDigitCount = 0;
foreach (ReadOnlyMemory <char> digitsChunk in number.digits.GetChunks())
{
if (!ProcessChunk(digitsChunk.Span, ref currentBuffer))
{
result = default;
return(false);
}
}
if (partialDigitCount > 0)
{
MultiplyAdd(ref currentBuffer, s_uint32PowersOfTen[partialDigitCount], partialValue);
}
result = NumberBufferToBigInteger(currentBuffer, number.sign);
return(true);
bool ProcessChunk(ReadOnlySpan <char> chunkDigits, ref Span <uint> currentBuffer)
{
int remainingIntDigitCount = Math.Max(numberScale - totalDigitCount, 0);
ReadOnlySpan <char> intDigitsSpan = chunkDigits.Slice(0, Math.Min(remainingIntDigitCount, chunkDigits.Length));
bool endReached = false;
// Storing these captured variables in locals for faster access in the loop.
uint _partialValue = partialValue;
int _partialDigitCount = partialDigitCount;
int _totalDigitCount = totalDigitCount;
for (int i = 0; i < intDigitsSpan.Length; i++)
{
char digitChar = chunkDigits[i];
if (digitChar == '\0')
{
endReached = true;
break;
}
_partialValue = _partialValue * 10 + (uint)(digitChar - '0');
_partialDigitCount++;
_totalDigitCount++;
// Update the buffer when enough partial digits have been accumulated.
if (_partialDigitCount == MaxPartialDigits)
{
MultiplyAdd(ref currentBuffer, TenPowMaxPartial, _partialValue);
_partialValue = 0;
_partialDigitCount = 0;
}
}
// Check for nonzero digits after the decimal point.
if (!endReached)
{
ReadOnlySpan <char> fracDigitsSpan = chunkDigits.Slice(intDigitsSpan.Length);
for (int i = 0; i < fracDigitsSpan.Length; i++)
{
char digitChar = fracDigitsSpan[i];
if (digitChar == '\0')
{
break;
}
if (digitChar != '0')
{
return(false);
}
}
}
partialValue = _partialValue;
partialDigitCount = _partialDigitCount;
totalDigitCount = _totalDigitCount;
return(true);
}
}
bool DivideAndConquer(ref BigNumberBuffer number, out BigInteger result)
{
Span <uint> currentBuffer;
int[]? arrayFromPoolForMultiplier = null;
try
{
totalDigitCount = Math.Min(number.digits.Length - 1, numberScale);
int bufferSize = (totalDigitCount + MaxPartialDigits - 1) / MaxPartialDigits;
Span <uint> buffer = new uint[bufferSize];
arrayFromPoolForResultBuffer = ArrayPool <int> .Shared.Rent(bufferSize);
Span <uint> newBuffer = MemoryMarshal.Cast <int, uint>(arrayFromPoolForResultBuffer).Slice(0, bufferSize);
newBuffer.Clear();
// Separate every MaxPartialDigits digits and store them in the buffer.
// Buffers are treated as little-endian. That means, the array { 234567890, 1 }
// represents the number 1234567890.
int bufferIndex = bufferSize - 1;
uint currentBlock = 0;
int shiftUntil = (totalDigitCount - 1) % MaxPartialDigits;
int remainingIntDigitCount = totalDigitCount;
foreach (ReadOnlyMemory <char> digitsChunk in number.digits.GetChunks())
{
ReadOnlySpan <char> digitsChunkSpan = digitsChunk.Span;
ReadOnlySpan <char> intDigitsSpan = digitsChunkSpan.Slice(0, Math.Min(remainingIntDigitCount, digitsChunkSpan.Length));
for (int i = 0; i < intDigitsSpan.Length; i++)
{
char digitChar = intDigitsSpan[i];
Debug.Assert(char.IsDigit(digitChar));
currentBlock *= 10;
currentBlock += unchecked ((uint)(digitChar - '0'));
if (shiftUntil == 0)
{
buffer[bufferIndex] = currentBlock;
currentBlock = 0;
bufferIndex--;
shiftUntil = MaxPartialDigits;
}
shiftUntil--;
}
remainingIntDigitCount -= intDigitsSpan.Length;
Debug.Assert(0 <= remainingIntDigitCount);
ReadOnlySpan <char> fracDigitsSpan = digitsChunkSpan.Slice(intDigitsSpan.Length);
for (int i = 0; i < fracDigitsSpan.Length; i++)
{
char digitChar = fracDigitsSpan[i];
if (digitChar == '\0')
{
break;
}
if (digitChar != '0')
{
result = default;
return(false);
}
}
}
Debug.Assert(currentBlock == 0);
Debug.Assert(bufferIndex == -1);
int blockSize = 1;
arrayFromPoolForMultiplier = ArrayPool <int> .Shared.Rent(blockSize);
Span <uint> multiplier = MemoryMarshal.Cast <int, uint>(arrayFromPoolForMultiplier).Slice(0, blockSize);
multiplier[0] = TenPowMaxPartial;
// This loop is executed ceil(log_2(bufferSize)) times.
while (true)
{
// merge each block pairs.
// When buffer represents:
// | A | B | C | D |
// Make newBuffer like:
// | A + B * multiplier | C + D * multiplier |
for (int i = 0; i < bufferSize; i += blockSize * 2)
{
Span <uint> curBuffer = buffer.Slice(i);
Span <uint> curNewBuffer = newBuffer.Slice(i);
int len = Math.Min(bufferSize - i, blockSize * 2);
int lowerLen = Math.Min(len, blockSize);
int upperLen = len - lowerLen;
if (upperLen != 0)
{
Debug.Assert(blockSize == lowerLen);
Debug.Assert(blockSize == multiplier.Length);
Debug.Assert(multiplier.Length == lowerLen);
BigIntegerCalculator.Multiply(multiplier, curBuffer.Slice(blockSize, upperLen), curNewBuffer.Slice(0, len));
}
long carry = 0;
int j = 0;
for (; j < lowerLen; j++)
{
long digit = (curBuffer[j] + carry) + curNewBuffer[j];
curNewBuffer[j] = unchecked ((uint)digit);
carry = digit >> 32;
}
if (carry != 0)
{
while (true)
{
curNewBuffer[j]++;
if (curNewBuffer[j] != 0)
{
break;
}
j++;
}
}
}
Span <uint> tmp = buffer;
buffer = newBuffer;
newBuffer = tmp;
blockSize *= 2;
if (bufferSize <= blockSize)
{
break;
}
newBuffer.Clear();
int[]? arrayToReturn = arrayFromPoolForMultiplier;
arrayFromPoolForMultiplier = ArrayPool <int> .Shared.Rent(blockSize);
Span <uint> newMultiplier = MemoryMarshal.Cast <int, uint>(arrayFromPoolForMultiplier).Slice(0, blockSize);
newMultiplier.Clear();
BigIntegerCalculator.Square(multiplier, newMultiplier);
multiplier = newMultiplier;
if (arrayToReturn is not null)
{
ArrayPool <int> .Shared.Return(arrayToReturn);
}
}
// shrink buffer to the currently used portion.
// First, calculate the rough size of the buffer from the ratio that the number
// of digits follows. Then, shrink the size until there is no more space left.
// The Ratio is calculated as: log_{2^32}(10^9)
const double digitRatio = 0.934292276687070661;
currentBufferSize = Math.Min((int)(bufferSize * digitRatio) + 1, bufferSize);
Debug.Assert(buffer.Length == currentBufferSize || buffer[currentBufferSize] == 0);
while (0 < currentBufferSize && buffer[currentBufferSize - 1] == 0)
{
currentBufferSize--;
}
currentBuffer = buffer.Slice(0, currentBufferSize);
result = NumberBufferToBigInteger(currentBuffer, number.sign);
}
finally
{
if (arrayFromPoolForMultiplier != null)
{
ArrayPool <int> .Shared.Return(arrayFromPoolForMultiplier);
}
}
return(true);
}
BigInteger NumberBufferToBigInteger(Span <uint> currentBuffer, bool signa)
{
int trailingZeroCount = numberScale - totalDigitCount;
while (trailingZeroCount >= MaxPartialDigits)
{
MultiplyAdd(ref currentBuffer, TenPowMaxPartial, 0);
trailingZeroCount -= MaxPartialDigits;
}
if (trailingZeroCount > 0)
{
MultiplyAdd(ref currentBuffer, s_uint32PowersOfTen[trailingZeroCount], 0);
}
int sign;
uint[]? bits;
if (currentBufferSize == 0)
{
sign = 0;
bits = null;
}
else if (currentBufferSize == 1 && currentBuffer[0] <= int.MaxValue)
{
sign = (int)(signa ? -currentBuffer[0] : currentBuffer[0]);
bits = null;
}
else
{
sign = signa ? -1 : 1;
bits = currentBuffer.Slice(0, currentBufferSize).ToArray();
}
return(new BigInteger(sign, bits));
}
// This function should only be used for result buffer.
void MultiplyAdd(ref Span <uint> currentBuffer, uint multiplier, uint addValue)
{
Span <uint> curBits = currentBuffer.Slice(0, currentBufferSize);
uint carry = addValue;
for (int i = 0; i < curBits.Length; i++)
{
ulong p = (ulong)multiplier * curBits[i] + carry;
curBits[i] = (uint)p;
carry = (uint)(p >> 32);
}
if (carry == 0)
{
return;
}
if (currentBufferSize == currentBuffer.Length)
{
int[]? arrayToReturn = arrayFromPoolForResultBuffer;
arrayFromPoolForResultBuffer = ArrayPool <int> .Shared.Rent(checked (currentBufferSize * 2));
Span <uint> newBuffer = MemoryMarshal.Cast <int, uint>(arrayFromPoolForResultBuffer);
currentBuffer.CopyTo(newBuffer);
currentBuffer = newBuffer;
if (arrayToReturn != null)
{
ArrayPool <int> .Shared.Return(arrayToReturn);
}
}
currentBuffer[currentBufferSize] = carry;
currentBufferSize++;
}
}
