_Exp(Digits @base, Digits exp, int expDigitN, Digits answer)
{
int expBitNUsed = Digits.SigBitN(exp, expDigitN);
ushort[] widthCutoffs = new ushort[] { 6, 24, 80, 240, 672 };
Digits basepower = answer;
int bucketWidth = 1;
while (
bucketWidth < 5 && widthCutoffs[bucketWidth - 1] < expBitNUsed
)
{
bucketWidth++;
}
Modular.ValidateData(@base, _mod, _digitN);
UInt32 bucketMask = (1U << bucketWidth) - 1;
UInt32 maxBucket = bucketMask;
Digits bucketData = new Digits((int)(_digitN * maxBucket));
Temps2000 temps = new Temps2000();
temps._modulus = this;
temps._bucket[0] = null;
Modular.Add(_one, _one, bucketData, _mod, _digitN);
bool base2 = Digits.Compare(@base, bucketData, _digitN) == 0;
if (base2 && expBitNUsed != 0)
{
int shiftMax
= Digit.BitN * _digitN > 1024 ? 1024 : Digit.BitN * _digitN;
int highExponBitN = 0;
bool bighBitNProcessed = false;
Digits temp = bucketData;
for (int i = expBitNUsed; i-- != 0;)
{
Digit expBit = Digits.GetBit(exp, i);
if (bighBitNProcessed)
{
_Mul(temp, temp, temp);
if (expBit != 0)
{
Modular.Add(temp, temp, temp, _mod, _digitN);
}
}
else
{
highExponBitN = (int)(2 * highExponBitN + expBit);
if (i == 0 || 2 * highExponBitN >= shiftMax)
{
bighBitNProcessed = true;
_Shift(_one, highExponBitN, temp);
}
}
}
temps._bucket[1] = temp;
Debug.Assert(bighBitNProcessed, "internal error");
}
else
{
UInt32 ibucket;
for (ibucket = 1; ibucket <= maxBucket; ibucket++)
{
Digits bloc = bucketData
+ (int)(_digitN
* (ibucket
- 1
+ ((ibucket & 1) == 0 ? maxBucket : 0))
/ 2);
temps._bucket[ibucket] = bloc;
temps._bucketBusy[ibucket] = false;
bloc._Set(_one, _digitN);
}
basepower._Set(@base, _digitN);
Digit carried = 0;
int ndoubling = 0;
for (int i = 0; i != expBitNUsed; i++)
{
Digit bitNow = Digits.GetBit(exp, i);
Debug.Assert(carried >> bucketWidth + 2 == 0
, "internal error");
if (bitNow != 0)
{
while (ndoubling >= bucketWidth + 1)
{
if ((carried & 1) != 0)
{
ibucket = carried & bucketMask;
carried -= ibucket;
temps._modulus
._BucketMul(ibucket, basepower, temps);
}
temps._modulus._BasePowerSquaring(basepower);
carried /= 2;
ndoubling--;
}
carried |= 1U << ndoubling;
}
ndoubling++;
}
while (carried != 0)
{
bool squareNow = false;
if (carried <= maxBucket)
{
ibucket = carried;
}
else if ((carried & 1) == 0)
{
squareNow = true;
}
else if (carried <= 3 * maxBucket)
{
ibucket = maxBucket;
}
else
{
Debug.Assert(false, "untested code");
ibucket = carried & bucketMask;
}
if (squareNow)
{
carried /= 2;
temps._modulus._BasePowerSquaring(basepower);
}
else
{
carried -= ibucket;
temps._modulus._BucketMul(ibucket, basepower, temps);
}
}
for (ibucket = maxBucket; ibucket >= 2; ibucket--)
{
if (temps._bucketBusy[ibucket])
{
bool found = false;
UInt32 jbucket, jbucketMax, kbucket;
Digits bloci;
if ((ibucket & 1) == 0)
{
jbucketMax = ibucket / 2;
}
else
{
jbucketMax = 1;
}
for (
jbucket = ibucket >> 1;
jbucket != ibucket && !found;
jbucket++
)
{
if (temps._bucketBusy[jbucket])
{
jbucketMax = jbucket;
found = temps._bucketBusy[ibucket - jbucket];
}
}
jbucket = jbucketMax;
kbucket = ibucket - jbucket;
bloci = temps._bucket[ibucket];
temps._modulus._BucketMul(jbucket, bloci, temps);
temps._modulus._BucketMul(kbucket, bloci, temps);
}
}
}
answer._Set(temps._bucket[1], _digitN);
}