public void SieveMethodTest()
{
var algebraicFactorbase = new AlgebraicFactorbase(new List <Pair>()
{
new Pair(0, 2),
new Pair(6, 7),
new Pair(13, 17),
new Pair(11, 23),
new Pair(26, 29),
new Pair(18, 31),
new Pair(19, 41),
new Pair(13, 43),
new Pair(1, 53),
new Pair(46, 61),
new Pair(2, 67),
new Pair(6, 67),
new Pair(44, 67),
new Pair(50, 73),
new Pair(23, 79),
new Pair(47, 79),
new Pair(73, 79),
new Pair(28, 89),
new Pair(62, 89),
new Pair(73, 89),
new Pair(28, 97),
new Pair(87, 101),
new Pair(47, 103)
});
var rationalFactorbase = new RationalFactorbase(new List <Pair>()
{
new Pair(1, 2),
new Pair(1, 3),
new Pair(1, 5),
new Pair(3, 7),
new Pair(9, 11),
new Pair(5, 13),
new Pair(14, 17),
new Pair(12, 19),
new Pair(8, 23),
new Pair(2, 29),
});
var polynomial = new Polynomial(new BigInteger[] { 8, 29, 15, 1 });
var root = 31;
var options = new SieveOptions(1000, -1000, algebraicFactorbase, rationalFactorbase, polynomial, root);
var sieveAlgorithm = new SimpleSieveAlgorithm();
var result = sieveAlgorithm.Sieve(40, options);
var smoothTester = new SmoothTester();
foreach (var pair in result)
{
Assert.IsTrue(smoothTester.IsSmoothOverRationalFactorbase(pair.Item1, pair.Item2, root, rationalFactorbase));
Assert.IsTrue(smoothTester.IsSmoothOverAlgebraicFactorbase(pair.Item1, pair.Item2, polynomial, algebraicFactorbase));
}
}
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);
}
