C#，数值计算——多项式微分（Binomial Deviates）的计算方法与源程序
1 文本格式
using System;
namespace Legalsoft.Truffer
{
///
/// 二项式偏差
/// Binomial Deviates
///
public class Binomialdev : Ran
{
private double pp { get; set; }
private double p { get; set; }
private double pb { get; set; }
private double expnp { get; set; }
private double np { get; set; }
private double glnp { get; set; }
private double plog { get; set; }
private double pclog { get; set; }
private double sq { get; set; }
private int n { get; set; }
private int swch { get; set; }
private ulong uz { get; set; }
private ulong uo { get; set; }
private ulong unfin { get; set; }
private ulong diff { get; set; }
private ulong rltp { get; set; }
private int[] pbits { get; set; } = new int[5];
private double[] cdf { get; set; } = new double[64];
private double[] logfact { get; set; } = new double[1024];
public Binomialdev(int nn, double ppp, ulong i) : base(i)
{
this.pp = ppp;
this.n = nn;
pb = p = (pp <= 0.5 ? pp : 1.0 - pp);
if (n <= 64)
{
uz = 0;
uo = 0xffffffffffffffffL;
rltp = 0;
for (int j = 0; j < 5; j++)
{
pbits[j] = 1 & ((int)(pb *= 2.0));
}
pb -= Math.Floor(pb);
swch = 0;
}
else if (n * p < 30.0)
{
cdf[0] = Math.Exp(n * Math.Log(1 - p));
for (int j = 1; j < 64; j++)
{
cdf[j] = cdf[j - 1] + Math.Exp(Globals.gammln(n + 1.0) - Globals.gammln(j + 1.0) - Globals.gammln(n - j + 1.0) + j * Math.Log(p) + (n - j) * Math.Log(1.0 - p));
}
swch = 1;
}
else
{
np = n * p;
glnp = Globals.gammln(n + 1.0);
plog = Math.Log(p);
pclog = Math.Log(1.0 - p);
sq = Math.Sqrt(np * (1.0 - p));
if (n < 1024)
{
for (int j = 0; j <= n; j++)
{
logfact[j] = Globals.gammln(j + 1.0);
}
}
swch = 2;
}
}
public int dev()
{
int k;
if (swch == 0)
{
unfin = uo;
for (int j = 0; j < 5; j++)
{
diff = unfin & (int64() ^ (pbits[j] > 0 ? uo : uz));
if (pbits[j] > 0)
{
rltp |= diff;
}
else
{
rltp = rltp & ~diff;
}
unfin = unfin & ~diff;
}
k = 0;
for (int j = 0; j < n; j++)
{
if ((unfin & 1) > 0)
{
if (doub() < pb)
{
++k;
}
}
else
{
if ((rltp & 1) > 0)
{
++k;
}
}
unfin >>= 1;
rltp >>= 1;
}
}
else if (swch == 1)
{
double y = doub();
int kl = -1;
k = 64;
while (k - kl > 1)
{
int km = (kl + k) / 2;
if (y < cdf[km])
{
k = km;
}
else
{
kl = km;
}
}
}
else
{
for (; ; )
{
double u = 0.645 * doub();
double v = -0.63 + 1.25 * doub();
double v2 = Globals.SQR(v);
if (v >= 0.0)
{
if (v2 > 6.5 * u * (0.645 - u) * (u + 0.2))
{
continue;
}
}
else
{
if (v2 > 8.4 * u * (0.645 - u) * (u + 0.1))
{
continue;
}
}
k = (int)(Math.Floor(sq * (v / u) + np + 0.5));
if (k < 0 || k > n)
{
continue;
}
double u2 = Globals.SQR(u);
if (v >= 0.0)
{
if (v2 < 12.25 * u2 * (0.615 - u) * (0.92 - u))
{
break;
}
}
else
{
if (v2 < 7.84 * u2 * (0.615 - u) * (1.2 - u))
{
break;
}
}
double b = sq * Math.Exp(glnp + k * plog + (n - k) * pclog - (n < 1024 ? logfact[k] + logfact[n - k] : Globals.gammln(k + 1.0) + Globals.gammln(n - k + 1.0)));
if (u2 < b)
{
break;
}
}
}
if (p != pp)
{
k = n - k;
}
return k;
}
}
}
2 代码格式
using System;
namespace Legalsoft.Truffer
{
///
/// 二项式偏差
/// Binomial Deviates
///
public class Binomialdev : Ran
{
private double pp { get; set; }
private double p { get; set; }
private double pb { get; set; }
private double expnp { get; set; }
private double np { get; set; }
private double glnp { get; set; }
private double plog { get; set; }
private double pclog { get; set; }
private double sq { get; set; }
private int n { get; set; }
private int swch { get; set; }
private ulong uz { get; set; }
private ulong uo { get; set; }
private ulong unfin { get; set; }
private ulong diff { get; set; }
private ulong rltp { get; set; }
private int[] pbits { get; set; } = new int[5];
private double[] cdf { get; set; } = new double[64];
private double[] logfact { get; set; } = new double[1024];
public Binomialdev(int nn, double ppp, ulong i) : base(i)
{
this.pp = ppp;
this.n = nn;
pb = p = (pp <= 0.5 ? pp : 1.0 - pp);
if (n <= 64)
{
uz = 0;
uo = 0xffffffffffffffffL;
rltp = 0;
for (int j = 0; j < 5; j++)
{
pbits[j] = 1 & ((int)(pb *= 2.0));
}
pb -= Math.Floor(pb);
swch = 0;
}
else if (n * p < 30.0)
{
cdf[0] = Math.Exp(n * Math.Log(1 - p));
for (int j = 1; j < 64; j++)
{
cdf[j] = cdf[j - 1] + Math.Exp(Globals.gammln(n + 1.0) - Globals.gammln(j + 1.0) - Globals.gammln(n - j + 1.0) + j * Math.Log(p) + (n - j) * Math.Log(1.0 - p));
}
swch = 1;
}
else
{
np = n * p;
glnp = Globals.gammln(n + 1.0);
plog = Math.Log(p);
pclog = Math.Log(1.0 - p);
sq = Math.Sqrt(np * (1.0 - p));
if (n < 1024)
{
for (int j = 0; j <= n; j++)
{
logfact[j] = Globals.gammln(j + 1.0);
}
}
swch = 2;
}
}
public int dev()
{
int k;
if (swch == 0)
{
unfin = uo;
for (int j = 0; j < 5; j++)
{
diff = unfin & (int64() ^ (pbits[j] > 0 ? uo : uz));
if (pbits[j] > 0)
{
rltp |= diff;
}
else
{
rltp = rltp & ~diff;
}
unfin = unfin & ~diff;
}
k = 0;
for (int j = 0; j < n; j++)
{
if ((unfin & 1) > 0)
{
if (doub() < pb)
{
++k;
}
}
else
{
if ((rltp & 1) > 0)
{
++k;
}
}
unfin >>= 1;
rltp >>= 1;
}
}
else if (swch == 1)
{
double y = doub();
int kl = -1;
k = 64;
while (k - kl > 1)
{
int km = (kl + k) / 2;
if (y < cdf[km])
{
k = km;
}
else
{
kl = km;
}
}
}
else
{
for (; ; )
{
double u = 0.645 * doub();
double v = -0.63 + 1.25 * doub();
double v2 = Globals.SQR(v);
if (v >= 0.0)
{
if (v2 > 6.5 * u * (0.645 - u) * (u + 0.2))
{
continue;
}
}
else
{
if (v2 > 8.4 * u * (0.645 - u) * (u + 0.1))
{
continue;
}
}
k = (int)(Math.Floor(sq * (v / u) + np + 0.5));
if (k < 0 || k > n)
{
continue;
}
double u2 = Globals.SQR(u);
if (v >= 0.0)
{
if (v2 < 12.25 * u2 * (0.615 - u) * (0.92 - u))
{
break;
}
}
else
{
if (v2 < 7.84 * u2 * (0.615 - u) * (1.2 - u))
{
break;
}
}
double b = sq * Math.Exp(glnp + k * plog + (n - k) * pclog - (n < 1024 ? logfact[k] + logfact[n - k] : Globals.gammln(k + 1.0) + Globals.gammln(n - k + 1.0)));
if (u2 < b)
{
break;
}
}
}
if (p != pp)
{
k = n - k;
}
return k;
}
}
}