void _Shift(Digits a, int n, Digits b)
{
if (a != b)
{
b._Set(a, _digitN);
}
Modular.ValidateData(a, _mod, _digitN);
if (n < 0 && (_mod[0] & 1) == 0)
{
throw new ArgumentException();
}
while (n > 0)
{
int shiftNow = n > Digit.BitN ? Digit.BitN : n;
Digit carryOut = Digits.ShiftLost(b, shiftNow, b, _digitN)
, qest = _leftRecip
.EstQuotient(carryOut
, b[_digitN - 1]
, _digitN >= 2 ? b[_digitN - 2] : 0);
carryOut -= Digits.Decumulate(_mod, qest, b, _digitN);
if (carryOut != 0 || Digits.Compare(b, _mod, _digitN) >= 0)
{
carryOut -= Digits.Sub(b, _mod, b, _digitN);
}
Debug.Assert(carryOut == 0, "internal error");
n -= shiftNow;
}
while (n < 0)
{
int shiftNow = -n > Digit.BitN ? Digit.BitN : -n;
Digit mul = unchecked (0 - _rightRecip * b[0])
& Digit.MaxValue >> Digit.BitN - shiftNow
, carry = Digits.Accumulate(_mod, mul, b, _digitN)
, lowBitNLost = Digits.ShiftLost(b, -shiftNow, b, _digitN);
b[_digitN - 1] |= carry << Digit.BitN - shiftNow;
Debug.Assert(lowBitNLost == 0, "internal error");
n += shiftNow;
}
}
internal static void Div(
UInt64 num
, Digit denom
, Reciprocal recip
, out Digit q
, out Digit r
)
{
Digit numHi = Hi(num)
, numLo = Lo(num)
, qEst = Digit.MaxValue - recip.EstQuotient(numHi, numLo, 0);
UInt64 rEst = unchecked (
((UInt64)(numHi - denom) << Digit.BitN | numLo)
+ (UInt64)qEst * denom
);
q = unchecked ((Digit)(Hi(rEst) - qEst));
r = unchecked (Lo(rEst) + (denom & Hi(rEst)));
Digit qq, rr;
Div(num, denom, out qq, out rr);
Debug.Assert(qq == q && rr == r, "internal error");
}