/// <summary>
/// Create a fixed-int number from parts. For example, to create 1.5 pass in 1 and 500.
/// </summary>
/// <param name="PreDecimal">The number above the decimal. For 1.5, this would be 1.</param>
/// <param name="PostDecimal">The number below the decimal, to three digits.
/// For 1.5, this would be 500. For 1.005, this would be 5.</param>
/// <returns>A fixed-int representation of the number parts</returns>
public static FInt FromParts(int PreDecimal, int PostDecimal) {
FInt f = new FInt(PreDecimal);
if (PostDecimal != 0)
f.RawValue += (new FInt(PostDecimal) / 1000).RawValue;
return f;
}
public FInt LengthSquared(out FInt i)
{
FInt.Multiply(ref X, ref X, out scratch1);
FInt.Multiply(ref Y, ref Y, out scratch2);
FInt.Add(ref scratch1, ref scratch2, out i);
return i;
}
public static void Divide(ref FInt one, ref FInt other, out FInt dest) {
dest.RawValue = (one.RawValue << SHIFT_AMOUNT) / (other.RawValue);
}
public static void Multiply(ref FInt one, ref FInt other, out FInt dest) {
dest.RawValue = (one.RawValue * other.RawValue) >> SHIFT_AMOUNT;
}
public static FInt Abs(FInt F) {
if (F < 0)
return F.Inverse;
else
return F;
}
public static FInt PIOver180F = PI / (FInt)180; //PI / 180
#endregion
#region Sqrt
public static FInt Sqrt(FInt f, int NumberOfIterations) {
if (f.RawValue < 0) //NaN in Math.Sqrt
throw new ArithmeticException("Input Error");
if (f.RawValue == 0)
return (FInt)0;
FInt k = f + FInt.OneF >> 1;
for (int i = 0; i < NumberOfIterations; i++)
k = (k + (f / k)) >> 1;
if (k.RawValue < 0)
throw new ArithmeticException("Overflow");
else
return k;
}
public static FInt Atan2(FInt F1, FInt F2) {
if (F2.RawValue == 0 && F1.RawValue == 0)
return (FInt)0;
FInt result = (FInt)0;
if (F2 > 0)
result = Atan(F1 / F2);
else if (F2 < 0) {
if (F1 >= 0)
result = (PI - Atan(Abs(F1 / F2)));
else
result = (PI - Atan(Abs(F1 / F2))).Inverse;
} else
result = (F1 >= 0 ? PI : PI.Inverse) / new FInt(2, true);
return result;
}
public static FInt Tan(FInt i) {
return Sin(i) / Cos(i);
}
public static FInt Asin(FInt F) {
bool isNegative = F < 0;
F = Abs(F);
if (F > FInt.OneF)
throw new ArithmeticException("Bad Asin Input:" + F.ToDouble());
FInt f1 = mul(mul(mul(mul(new FInt(145103 >> FInt.SHIFT_AMOUNT, false), F) -
new FInt(599880 >> FInt.SHIFT_AMOUNT, false), F) +
new FInt(1420468 >> FInt.SHIFT_AMOUNT, false), F) -
new FInt(3592413 >> FInt.SHIFT_AMOUNT, false), F) +
new FInt(26353447 >> FInt.SHIFT_AMOUNT, false);
FInt f2 = PI / new FInt(2, true) - (Sqrt(FInt.OneF - F) * f1);
return isNegative ? f2.Inverse : f2;
}
private static FInt mul(FInt F1, FInt F2) {
return F1 * F2;
}
public static FInt Cos(FInt i) {
return Sin(i + new FInt(6435, false));
}
private static FInt sin_lookup(FInt i, FInt j) {
if (j > 0 && j < new FInt(10, false) && i < new FInt(90, false))
return new FInt(SIN_TABLE[i.RawValue], false) +
((new FInt(SIN_TABLE[i.RawValue + 1], false) - new FInt(SIN_TABLE[i.RawValue], false)) /
new FInt(10, false)) * j;
else
return new FInt(SIN_TABLE[i.RawValue], false);
}
public static FInt Sin(FInt i) {
FInt j = (FInt)0;
for (; i < 0; i += new FInt(25736, false))
;
if (i > new FInt(25736, false))
i %= new FInt(25736, false);
FInt k = (i * new FInt(10, false)) / new FInt(714, false);
if (i != 0 && i != new FInt(6434, false) && i != new FInt(12868, false) &&
i != new FInt(19302, false) && i != new FInt(25736, false))
j = (i * new FInt(100, false)) / new FInt(714, false) - k * new FInt(10, false);
if (k <= new FInt(90, false))
return sin_lookup(k, j);
if (k <= new FInt(180, false))
return sin_lookup(new FInt(180, false) - k, j);
if (k <= new FInt(270, false))
return sin_lookup(k - new FInt(180, false), j).Inverse;
else
return sin_lookup(new FInt(360, false) - k, j).Inverse;
}
public static FInt Sqrt(FInt f) {
byte numberOfIterations = 8;
if (f.RawValue > 0x64000)
numberOfIterations = 12;
if (f.RawValue > 0x3e8000)
numberOfIterations = 16;
return Sqrt(f, numberOfIterations);
}
public PVector2(FInt x, FInt y)
{
X = x;
Y = y;
}
public static FInt Atan(FInt F) {
return Asin(F / Sqrt(FInt.OneF + (F * F)));
}
public static void Multiply(ref PVector2 v, ref FInt i, out PVector2 o)
{
FInt.Multiply(ref v.X, ref i, out o.X);
FInt.Multiply(ref v.Y, ref i, out o.Y);
}
public static void Sub(ref FInt one, ref FInt other, out FInt dest) {
dest.RawValue = (one.RawValue - other.RawValue);
}