/// <summary>
/// b^x를 반환함
/// </summary>
/// <param name="b">b ≥ 0인 배정밀도 부동 소수점 숫자</param>
/// <param name="x"></param>
/// <returns></returns>
public static double Power(double b, double x)
{
if (b == 1 || x == 0)
{
return(1);
}
if (b < 0)
{
return(Double.NaN);
}
if (x == 1)
{
return(b);
}
double res = 1;
int a = (int)Math.Round(x);
double p = 1;
double r = (x - a) * Logarithm.Log(b);
for (int n = 1; n <= Factorial.Expanded; ++n)
{
p *= r;
res += p * Factorial.Get(n);
}
return(IntPow(b, a) * res);
}
private static double T2(double x)
{
double res = 0;
double r = x * x;
double cur = x;
for (int i = 1; i <= Factorial.Expanded; i += 2)
{
if (i != 1)
{
cur *= r;
}
res += ((i - 1) % 4 == 0 ? 1 : -1) * cur * Factorial.Get(i);
}
return(res);
}
private static double T1(double x)
{
double res = 0;
double r = (x + Math.PI * 0.5) * (x + Math.PI * 0.5);
double cur = 1;
for (int i = 0; i <= Factorial.Expanded; i += 2)
{
if (i != 0)
{
cur *= r;
}
res += (i % 4 == 0 ? -1 : 1) * cur * Factorial.Get(i);
}
return(res);
}
/// <summary>
/// <see cref="Math.E"/>^x를 반환함
/// </summary>
/// <returns></returns>
public static double Exp(double x)
{
if (x == 0)
{
return(1);
}
if (x == 1)
{
return(Math.E);
}
double res = 1;
int a = (int)Math.Round(x);
double p = 1;
double r = x - a;
for (int n = 1; n <= Factorial.Expanded; ++n)
{
p *= r;
res += p * Factorial.Get(n);
}
return(IntPow(Math.E, a) * res);
}