public static Rational ContinuedFraction(double x)
{
Debug.Assert(0 <= x && x < 1.0);
int scale = 1;
while (x < 0.5)
{
x *= 2.0;
scale *= 2;
}
var a = new List<int>();
while (x > 1e-6 && a.Count < 10)
{
var r = 1.0 / x;
int a1 = (int)r;
x = r - a1;
a.Add(a1);
}
Debug.Print("cfrac [{0}]", string.Join(", ", a));
var rat = new Rational(0, 1);
for (int i = a.Count-1; i >= 0; --i)
{
rat = a[i] + rat;
rat = rat.Reciprocal();
}
rat = rat / scale;
Debug.Print("crat: {0}", rat);
return rat;
}
/// <summary>
/// Determine whether <paramref name="instr"/> is a match for
/// the pattern that is a constant division
/// </summary>
/// <remarks>
/// The pattern is:
/// <code>
/// hi:lo = r * const
/// hi = slice(hi:lo) (alias)
/// hi = hi >> shift (optional)
/// </code>
/// This transformation must be carried out before value propagation
/// pushes the shift inside other operations.
/// </remarks>
/// <param name="instr"></param>
/// <returns></returns>
public bool Match(Instruction instr)
{
Assignment ass;
SequenceStorage dst;
BinaryExpression bin;
Constant cRight;
// Look for hi:lo = a * C
if (!instr.As(out ass) ||
!ass.Dst.Storage.As(out dst) ||
!ass.Src.As(out bin) ||
!(bin.Operator is IMulOperator) ||
!bin.Right.As(out cRight) ||
ass.Dst.DataType.Size <= bin.Left.DataType.Size)
{
return false;
}
this.idOrig = ass.Dst;
this.idDst = FindAlias(ass.Dst, dst.Head);
if (idDst == null)
return false;
var best = FindBestRational(cRight.ToUInt32());
// There may be a subsequent SAR / SHR to increase
// the divisor.
var idSlice = idDst;
Constant rShift = null;
if (idSlice != null)
{
rShift = FindShiftUse(idSlice);
if (rShift != null)
{
best = best / (1 << rShift.ToInt32());
}
}
this.bestRational = best;
this.dividend = bin.Left;
return true;
}