/// <summary>
/// Returns 2 raised to the specified power.
/// </summary>
public static Fix32 Pow2(this Fix32 xx)
{
#if USE_DOUBLES
return(Math.Pow(2, x.ToDouble()).ToFix32());
#endif
Fix32 x = xx;
if ((int)x == 0)
{
return(Fix32.One);
}
// Avoid negative arguments by exploiting that exp(-x) = 1/exp(x).
bool neg = (int)x < 0;
if (neg)
{
x = x.Neg();
}
if ((int)x == (int)Fix32.One)
{
return(neg ? Fix32.One.Div(Fix32.Two) : Fix32.Two); // Can be cached
}
if ((int)x >= (int)Fix32.Log2Max)
{
return(neg ? Fix32.One.Div(Fix32.MaxValue) : Fix32.MaxValue); // Can be cached
}
if ((int)x <= (int)Fix32.Log2Min)
{
return(neg ? Fix32.MaxValue : Fix32.Zero);
}
/*
* The algorithm is based on the power series for exp(x):
* http://en.wikipedia.org/wiki/Exponential_function#Formal_definition
*
* From term n, we get term n+1 by multiplying with x/n.
* When the sum term drops to zero, we can stop summing.
*/
int integerPart = x.Floor().ToInt();
// Take fractional part of exponent
x = (Fix32)((uint)x & FRACTIONAL_MASK);
Fix32 result = Fix32.One;
Fix32 term = Fix32.One;
Fix32 i = Fix32.One;
while ((int)term != 0)
{
term = x.Mul(term).Mul(Fix32.Ln2.Div(i));
result = result.Add(term);
i = i.AddFast(Fix32.One);
}
result = (Fix32)((int)result << integerPart);
if (neg)
{
result = Fix32.One.Div(result);
}
return(result);
}
/// <summary>
/// Returns the arctan of of the specified number, calculated using Euler series
/// </summary>
public static Fix32 Atan(this Fix32 zz)
{
#if USE_DOUBLES
return(Math.Atan(z.ToDouble()).ToFix32());
#endif
Fix32 z = zz;
if ((int)z == 0)
{
return(Fix32.Zero);
}
// Force positive values for argument
// Atan(-z) = -Atan(z).
bool neg = ((int)z < 0);
if (neg)
{
z = z.Neg();
}
Fix32 result;
if ((int)z == (int)Fix32.One)
{
result = Fix32.PiOver4;
}
else
{
bool invert = (int)z > (int)Fix32.One;
if (invert)
{
z = Fix32.One.Div(z);
}
result = Fix32.One;
Fix32 term = Fix32.One;
Fix32 zSq = z.Mul(z);
Fix32 zSq2 = zSq.Mul(Fix32.Two);
Fix32 zSqPlusOne = zSq.Add(Fix32.One);
Fix32 zSq12 = zSqPlusOne.Mul(Fix32.Two);
Fix32 dividend = zSq2;
Fix32 divisor = zSqPlusOne.Mul(Fix32.Three);
for (int i = 2; i < 30; i++)
{
term = term.Mul(dividend.Div(divisor));
result = result.Add(term);
dividend = dividend.Add(zSq2);
divisor = divisor.Add(zSq12);
if ((int)term == 0)
{
break;
}
}
result = result.Mul(z).Div(zSqPlusOne);
if (invert)
{
result = Fix32.PiOver2.Sub(result);
}
}
if (neg)
{
result = result.Neg();
}
return(result);
}