public BigInteger Round()
{
BigRational r = this + new BigRational(BigInteger.One, new BigInteger(2));
if (r.Denominator == BigInteger.One)
{
if ((r.Numerator & BigInteger.One) != BigInteger.Zero)
{
return(r.Numerator - BigInteger.One);
}
else
{
return(r.Numerator);
}
}
else
{
return(r.Floor());
}
}
public float GetSingleValue(RoundingMode m)
{
if (this.IsZero)
{
return(0.0f);
}
Tuple <BigRational, int> normalized = Normalize(this);
BigRational frac = normalized.Item1;
int expt = normalized.Item2;
expt += 127;
int loops = 24;
while (expt < 0 && loops > 0)
{
frac /= Two;
expt += 1;
loops -= 1;
}
if (expt <= 0)
{
expt = 0; frac /= Two;
}
if (expt > 254)
{
return((frac < Zero) ? float.NegativeInfinity : float.PositiveInfinity);
}
int bits = (frac * singleFractionScale).RoundingOp(m).GetInt32Value(OverflowBehavior.Saturate);
if (bits < 0)
{
bits = (-bits) | unchecked ((int)0x80000000L);
}
bits &= unchecked ((int)0x807FFFFFL);
bits |= expt << 23;
return(BitConverter.ToSingle(BitConverter.GetBytes(bits), 0));
}
public double GetDoubleValue(RoundingMode m)
{
if (this.IsZero)
{
return(0.0);
}
Tuple <BigRational, int> normalized = Normalize(this);
BigRational frac = normalized.Item1;
int expt = normalized.Item2;
expt += 1023;
int loops = 53;
while (expt < 0 && loops > 0)
{
frac /= Two;
expt += 1;
loops -= 1;
}
if (expt <= 0)
{
expt = 0; frac /= Two;
}
if (expt > 2046)
{
return((frac < Zero) ? double.NegativeInfinity : double.PositiveInfinity);
}
long bits = (frac * doubleFractionScale).RoundingOp(m).GetInt64Value(OverflowBehavior.Saturate);
if (bits < 0)
{
bits = (-bits) | unchecked ((long)0x8000000000000000L);
}
bits &= unchecked ((long)0x800FFFFFFFFFFFFFL);
bits |= (long)expt << 52;
return(BitConverter.Int64BitsToDouble(bits));
}
public override ConvexHull Add(Vertex3 vt)
{
if (this.Line.Contains(vt))
{
BigRational scaledPos = (vt - v1).ScaledLengthAlong(v2 - v1);
if (scaledPos < BigRational.Zero)
{
return(new CH_LineSegment(vt, v2));
}
else if (scaledPos > BigRational.One)
{
return(new CH_LineSegment(v1, vt));
}
else
{
return(this);
}
}
else
{
return(new CH_Polygon(new Vertex3[] { v1, v2, vt }.ToImmutableList()));
}
}
public override PointStatus GetPointStatus(Vertex3 vt)
{
if (v1 == vt || v2 == vt)
{
return(PointStatus.OnCorner);
}
else if (this.Line.Contains(vt))
{
BigRational scaledPos = (vt - v1).ScaledLengthAlong(v2 - v1);
if (scaledPos < BigRational.Zero || scaledPos > BigRational.One)
{
return(PointStatus.Outside);
}
else
{
return(PointStatus.OnEdge);
}
}
else
{
return(PointStatus.Outside);
}
}
public static Vector3 Interpolate(BigRational x1, Vector3 y1, BigRational x2, Vector3 y2, BigRational x3)
{
return(y1 + (y2 - y1) * (x3 - x1) / (x2 - x1));
}
// (y3 - y1) (x3 - x1)
// --------- = ---------
// (y2 - y1) (y2 - y1)
// (x3 - x1)
// y3 = y1 + (y2 - y1) * ---------
// (x2 - x1)
public static BigRational Interpolate(BigRational x1, BigRational y1, BigRational x2, BigRational y2, BigRational x3)
{
return(y1 + (y2 - y1) * (x3 - x1) / (x2 - x1));
}
public Vertex3(BigRational x, BigRational y, BigRational z)
{
this.x = x;
this.y = y;
this.z = z;
}
public Vertex2(BigRational x, BigRational y)
{
this.x = x;
this.y = y;
}
public static Vector2 operator *(BigInteger a, Vector2 b)
{
BigRational aa = new BigRational(a, BigInteger.One);
return(new Vector2(aa * b.x, aa * b.y));
}
public static Vector2 operator *(Vector2 a, BigInteger b)
{
BigRational bb = new BigRational(b, BigInteger.One);
return(new Vector2(a.x * bb, a.y * bb));
}
public Vector2(BigRational x, BigRational y)
{
this.x = x;
this.y = y;
}
public static Vector3 operator /(Vector3 a, BigInteger b)
{
BigRational bb = new BigRational(b, BigInteger.One);
return(new Vector3(a.x / bb, a.y / bb, a.z / bb));
}
public static Tuple <BigRational, int> Normalize(BigRational r)
{
if (r.IsNegative)
{
Tuple <BigRational, int> result = Normalize(-r);
return(new Tuple <BigRational, int>(-result.Item1, result.Item2));
}
Stack <BigRational> powers = new Stack <BigRational>();
Stack <int> exponents = new Stack <int>();
BigRational currentPower;
int currentExponent;
int finalExponent = 0;
if (r < One)
{
currentPower = OneHalf;
currentExponent = -1;
while (r < currentPower)
{
powers.Push(currentPower);
exponents.Push(currentExponent);
currentPower *= currentPower;
currentExponent *= 2;
}
while (powers.Count > 0)
{
currentPower = powers.Pop();
currentExponent = exponents.Pop();
if (r < currentPower)
{
r /= currentPower;
finalExponent += currentExponent;
}
}
}
else
{
currentPower = Two;
currentExponent = 1;
while (r > currentPower)
{
powers.Push(currentPower);
exponents.Push(currentExponent);
currentPower *= currentPower;
currentExponent *= 2;
}
while (powers.Count > 0)
{
currentPower = powers.Pop();
currentExponent = exponents.Pop();
if (r > currentPower)
{
r /= currentPower;
finalExponent += currentExponent;
}
}
}
while (r >= Two)
{
r /= Two;
finalExponent += 1;
}
while (r < One)
{
r *= Two;
finalExponent -= 1;
}
return(new Tuple <BigRational, int>(r, finalExponent));
}
public static BigRational Max(BigRational a, BigRational b)
{
return((a > b) ? a : b);
}
public static BigRational Min(BigRational a, BigRational b)
{
return((a < b) ? a : b);
}