// this algorithm is very inefficient
public static decimal Ln(decimal v)
{
if (v <= 0M)
{
throw new ArgumentOutOfRangeException("v");
}
// algorithm is based on area hyperbolic tangent
// https://en.wikipedia.org/wiki/Logarithm
decimal x = 0;
decimal t = (v - 1M) / (v + 1M);
decimal tMul = t * t;
for (int i = 0; i < 1000 * 1000 * 1000; ++i)
{
decimal diff = 2M / (i * 2 + 1M) * t;
if (WWDecimalMath.IsExtremelySmall(diff))
{
break;
}
x += diff;
t *= tMul;
//Console.WriteLine(" {0} {1}", i, x);
}
return(x);
}
public override string ToString()
{
if (WWDecimalMath.IsExtremelySmall(imaginary))
{
return(string.Format("{0:0.#######}", real));
}
if (WWDecimalMath.IsExtremelySmall(real))
{
return(string.Format("{0:0.#######}i", imaginary));
}
return(string.Format("{0:0.#######} {1:+0.#######;-0.#######}i", real, imaginary));
}
private void FftStageN(int stageNr, WWDecimalComplex[] x, WWDecimalComplex[] y)
{
/*
* stage0: 2つの入力データにバタフライ演算 (length=8の時) 4回 (nRepeat=4, nSubRepeat=2)
* y[0] = x[0] + w_n^(0*4) * x[1]
* y[1] = x[0] + w_n^(1*4) * x[1]
*
* y[2] = x[2] + w_n^(0*4) * x[3]
* y[3] = x[2] + w_n^(1*4) * x[3]
*
* y[4] = x[4] + w_n^(0*4) * x[5]
* y[5] = x[4] + w_n^(1*4) * x[5]
*
* y[6] = x[6] + w_n^(0*4) * x[7]
* y[7] = x[6] + w_n^(1*4) * x[7]
*/
/*
* stage1: 4つの入力データにバタフライ演算 (length=8の時) 2回 (nRepeat=2, nSubRepeat=4)
* y[0] = x[0] + w_n^(0*2) * x[2]
* y[1] = x[1] + w_n^(1*2) * x[3]
* y[2] = x[0] + w_n^(2*2) * x[2]
* y[3] = x[1] + w_n^(3*2) * x[3]
*
* y[4] = x[4] + w_n^(0*2) * x[6]
* y[5] = x[5] + w_n^(1*2) * x[7]
* y[6] = x[4] + w_n^(2*2) * x[6]
* y[7] = x[5] + w_n^(3*2) * x[7]
*/
/*
* stage2: 8つの入力データにバタフライ演算 (length=8の時) 1回 (nRepeat=1, nSubRepeat=8)
* y[0] = x[0] + w_n^(0*1) * x[4]
* y[1] = x[1] + w_n^(1*1) * x[5]
* y[2] = x[2] + w_n^(2*1) * x[6]
* y[3] = x[3] + w_n^(3*1) * x[7]
* y[4] = x[0] + w_n^(4*1) * x[4]
* y[5] = x[1] + w_n^(5*1) * x[5]
* y[6] = x[2] + w_n^(6*1) * x[6]
* y[7] = x[3] + w_n^(7*1) * x[7]
*/
/*
* stageN:
*/
int nRepeat = Pow2(mNumStage - stageNr - 1);
int nSubRepeat = mNumPoints / nRepeat;
var t = new WWDecimalComplex();
for (int i = 0; i < nRepeat; ++i)
{
int offsBase = i * nSubRepeat;
bool allZero = true;
for (int j = 0; j < nSubRepeat / 2; ++j)
{
int offs = offsBase + (j % (nSubRepeat / 2));
if (!WWDecimalMath.IsExtremelySmall(x[offs].Magnitude()))
{
allZero = false;
break;
}
if (!WWDecimalMath.IsExtremelySmall(x[offs + nSubRepeat / 2].Magnitude()))
{
allZero = false;
break;
}
}
if (allZero)
{
for (int j = 0; j < nSubRepeat / 2; ++j)
{
y[j + offsBase].Set(0, 0);
}
}
else
{
for (int j = 0; j < nSubRepeat; ++j)
{
int offs = offsBase + (j % (nSubRepeat / 2));
y[j + offsBase].CopyFrom(x[offs]);
t.CopyFrom(mWn[j * nRepeat]);
t.Mul(x[offs + nSubRepeat / 2]);
y[j + offsBase].Add(t);
}
}
}
}