void AlgebraicSieve(BigInteger[] algebraicElements, BigInteger b, SieveOptions options)
{
for (int i = 0; i < options.AlgebraicFactorbase.Elements.Count; i++)
{
var currentPair = options.AlgebraicFactorbase.Elements[i];
var startPoint = (options.LowerBound + b * currentPair.Item1) % currentPair.Item2;
if (startPoint <= 0)
{
startPoint = -startPoint;
}
else
{
startPoint = currentPair.Item2 - startPoint;
}
var prime = (long)currentPair.Item2;
for (long j = (long)startPoint; j < options.IntervalLength; j += prime)
{
while (algebraicElements[j] % prime == 0 && algebraicElements[j] != 0)
{
algebraicElements[j] /= prime;
}
}
}
}
public List <Pair> Sieve(long pairsCount, SieveOptions options)
{
var result = new List <Pair>();
var intervalLength = (long)(options.UpperBound - options.LowerBound);
for (BigInteger b = 1; b < 100; b++)
{
Console.Write("\r {0}/{1} [b={2}]", result.Count, pairsCount, b);
var rationalElements = new BigInteger[intervalLength];
var norms = new BigInteger[intervalLength];
InitSieve(rationalElements, norms, b, options);
RationalSieve(rationalElements, b, options);
AlgebraicSieve(norms, b, options);
for (long i = 0; i < intervalLength; i++)
{
if (BigInteger.Abs(rationalElements[i]) == 1 && (BigInteger.Abs(norms[i]) == 1))
{
var firstComponent = options.LowerBound + i;
var secondComponent = b;
var d = BigInteger.GreatestCommonDivisor(firstComponent, secondComponent);
if (d == 1)
{
result.Add(new Pair(firstComponent, secondComponent));
}
if (result.Count == pairsCount)
{
Console.Write("\r {0}/{1}", result.Count, pairsCount);
return(result);
}
}
}
}
return(result);
}
void AlgebraicSieve(double[] elements, BigInteger b, SieveOptions options)
{
for (int i = 0; i < options.AlgebraicFactorbase.Elements.Count; i++)
{
var currentPair = options.AlgebraicFactorbase.Elements[i];
var startPoint = (options.LowerBound + b * currentPair.Item1) % currentPair.Item2;
if (startPoint <= 0)
{
startPoint = -startPoint;
}
else
{
startPoint = currentPair.Item2 - startPoint;
}
var log = BigInteger.Log(currentPair.Item2);
var prime = (long)currentPair.Item2;
for (long j = (long)startPoint; j < options.IntervalLength; j += prime)
{
elements[j] += log;
}
}
}
void InitSieve(BigInteger[] rationalElements, BigInteger[] norms, BigInteger b, SieveOptions options)
{
var a = options.LowerBound;
var normCalculator = new FirstDegreeElementsNormCalculator(options.Polynomial, b);
for (var i = 0; i < rationalElements.Length; i++)
{
rationalElements[i] = a + b * options.IntegerRoot;
norms[i] = normCalculator.CalculateNorm(a);
a++;
}
}
public List <Pair> Sieve(long pairsCount, SieveOptions options)
{
var result = new List <Pair>();
var intervalLength = (int)(options.UpperBound - options.LowerBound);
var fudge = 0.7;
var smoothTester = new SmoothTester();
for (int b = 1; true; b++)
{
var norm = new FirstDegreeElementsNormCalculator(options.Polynomial, b);
var rationalSmoothBound = fudge * BigInteger.Log(b * options.IntegerRoot);
var rationalElements = new double[intervalLength];
var algebraicElements = new double[intervalLength];
RationalSieve(rationalElements, b, options);
AlgebraicSieve(algebraicElements, b, options);
if (b % 2 == 0)
{
for (int i = (options.LowerBound % 2 == 0?1:0); i < intervalLength; i += 2)
{
if (rationalElements[i] >= rationalSmoothBound)
{
var firstComponent = options.LowerBound + i;
var secondComponent = b;
var algebraicSmoothBound = fudge *
BigInteger.Log(BigInteger.Abs(norm.CalculateNorm(firstComponent)));
if (algebraicElements[i] >= algebraicSmoothBound)
{
if (BigInteger.GreatestCommonDivisor(firstComponent, secondComponent) != 1)
{
continue;
}
if (smoothTester.IsSmoothOverRationalFactorbase(firstComponent, secondComponent,
options.IntegerRoot, options.RationalFactorbase))
{
if (smoothTester.IsSmoothOverAlgebraicFactorbase(firstComponent, secondComponent,
options.Polynomial, options.AlgebraicFactorbase))
{
result.Add(new Pair(firstComponent, secondComponent));
}
}
}
}
}
}
else
{
for (int i = 0; i < intervalLength; i++)
{
if (rationalElements[i] >= rationalSmoothBound)
{
var firstComponent = options.LowerBound + i;
var secondComponent = b;
var algebraicSmoothBound = fudge *
BigInteger.Log(BigInteger.Abs(norm.CalculateNorm(firstComponent)));
if (algebraicElements[i] >= algebraicSmoothBound)
{
if (BigInteger.GreatestCommonDivisor(firstComponent, secondComponent) != 1)
{
continue;
}
if (smoothTester.IsSmoothOverRationalFactorbase(firstComponent, secondComponent,
options.IntegerRoot, options.RationalFactorbase))
{
if (smoothTester.IsSmoothOverAlgebraicFactorbase(firstComponent, secondComponent,
options.Polynomial, options.AlgebraicFactorbase))
{
result.Add(new Pair(firstComponent, secondComponent));
}
}
}
}
}
}
Console.Write("\r{0}/{1} [b={2}] ", result.Count, pairsCount, b);
if (result.Count >= pairsCount)
{
break;
}
}
Console.WriteLine();
Console.WriteLine();
return(result);
}