/// <summary>Compute bits of Pi in the local machine.</summary>
public static double ComputePi(long b)
{
double pi = 0;
foreach (Bellard.Parameter p in Bellard.Parameter.Values())
{
pi = Modular.AddMod(pi, new Bellard.Sum(b, p, 1, null).GetValue());
}
return(pi);
}
// N'
// R - 1
/// <summary>Set the modular and initialize this object.</summary>
internal virtual Montgomery Set(long n)
{
if (n % 2 != 1)
{
throw new ArgumentException("n % 2 != 1, n=" + n);
}
N = n;
R = long.HighestOneBit(n) << 1;
NI = R - Modular.ModInverse(N, R);
R1 = R - 1;
s = long.NumberOfTrailingZeros(R);
return(this);
}
/// <summary>
/// Compute the value using
/// <see cref="Montgomery.Mod(long)"/>
/// .
/// </summary>
internal virtual double Compute_montgomery()
{
long e = E.value;
long n = N.value;
double s = 0;
for (; e > E.limit; e += E.delta)
{
s = Modular.AddMod(s, montgomery.Set(n).Mod(e) / (double)n);
n += N.delta;
}
return(s);
}
/// <summary>
/// Compute the value using
/// <see cref="Modular.Mod(long, long)"/>
/// .
/// </summary>
internal virtual double Compute_modular()
{
long e = E.value;
long n = N.value;
double s = 0;
for (; e > E.limit; e += E.delta)
{
s = Modular.AddMod(s, Modular.Mod(e, n) / (double)n);
n += N.delta;
}
return(s);
}
internal virtual double Compute_modPow()
{
long e = E.value;
long n = N.value;
double s = 0;
for (; e > E.limit; e += E.delta)
{
s = Modular.AddMod(s, Two.ModPow(BigInteger.ValueOf(e), BigInteger.ValueOf(n)) /
n);
n += N.delta;
}
return(s);
}
/// <summary>get the value of sigma</summary>
public virtual double GetValue()
{
if (sigma.GetValue() == null)
{
double d = 0;
for (int i = 0; i < parts.Length; i++)
{
d = Modular.AddMod(d, parts[i].Compute());
}
sigma.SetValue(d);
}
double s = Modular.AddMod(sigma.GetValue(), tail.Compute());
return(parameter.isplus ? s : -s);
}
/// <summary>
/// <inheritDoc/>
///
/// </summary>
public virtual Summation GetElement()
{
if (sigma.GetValue() == null)
{
int i = 0;
double d = 0;
for (; i < parts.Length && parts[i].GetValue() != null; i++)
{
d = Modular.AddMod(d, parts[i].GetValue());
}
if (i == parts.Length)
{
sigma.SetValue(d);
}
}
return(sigma);
}
/// <summary>
/// <inheritDoc/>
///
/// </summary>
public virtual Org.Apache.Hadoop.Examples.PI.Math.Summation Combine(Org.Apache.Hadoop.Examples.PI.Math.Summation
that)
{
if (this.N.delta != that.N.delta || this.E.delta != that.E.delta)
{
throw new ArgumentException("this.N.delta != that.N.delta || this.E.delta != that.E.delta"
+ ",\n this=" + this + ",\n that=" + that);
}
if (this.E.limit == that.E.value && this.N.limit == that.N.value)
{
double v = Modular.AddMod(this.value, that.value);
Org.Apache.Hadoop.Examples.PI.Math.Summation s = new Org.Apache.Hadoop.Examples.PI.Math.Summation
(new ArithmeticProgression(N.symbol, N.value, N.delta, that.N.limit), new ArithmeticProgression
(E.symbol, E.value, E.delta, that.E.limit));
s.SetValue(v);
return(s);
}
return(null);
}
/// <summary>Compute bits of Pi from the results.</summary>
public static double ComputePi <T>(long b, IDictionary <Bellard.Parameter, T> results
)
where T : Container <Summation>
{
if (results.Count != Bellard.Parameter.Values().Length)
{
throw new ArgumentException("m.size() != Parameter.values().length" + ", m.size()="
+ results.Count + "\n m=" + results);
}
double pi = 0;
foreach (Bellard.Parameter p in Bellard.Parameter.Values())
{
Summation sigma = results[p].GetElement();
Bellard.Sum s = new Bellard.Sum(b, p, 1, null);
s.SetValue(sigma);
pi = Modular.AddMod(pi, s.GetValue());
}
return(pi);
}
internal static void ModBenchmarks()
{
Util.Timer t = new Util.Timer(false);
t.Tick("modBenchmarks()");
long[][][] en = GenerateEN(10000, 10);
t.Tick("generateEN");
for (int i = 0; i < en.Length; i++)
{
long n = en[i][0][0];
for (int j = 1; j < en[i].Length; j++)
{
long e = en[i][j][0];
long answer = en[i][j][1];
long s = Modular.Mod(e, n);
if (s != answer)
{
NUnit.Framework.Assert.AreEqual("e=" + e + ", n=" + n + ", answer=" + answer + " but s="
+ s, answer, s);
}
}
}
t.Tick("Modular.mod");
TestModular.Montgomery2 m2 = new TestModular.Montgomery2();
for (int i_1 = 0; i_1 < en.Length; i_1++)
{
long n = en[i_1][0][0];
m2.Set(n);
for (int j = 1; j < en[i_1].Length; j++)
{
long e = en[i_1][j][0];
long answer = en[i_1][j][1];
long s = m2.Mod(e);
if (s != answer)
{
NUnit.Framework.Assert.AreEqual("e=" + e + ", n=" + n + ", answer=" + answer + " but s="
+ s, answer, s);
}
}
}
t.Tick("montgomery.mod");
for (int i_2 = 0; i_2 < en.Length; i_2++)
{
long n = en[i_2][0][0];
m2.Set(n);
for (int j = 1; j < en[i_2].Length; j++)
{
long e = en[i_2][j][0];
long answer = en[i_2][j][1];
long s = m2.Mod2(e);
if (s != answer)
{
NUnit.Framework.Assert.AreEqual("e=" + e + ", n=" + n + ", answer=" + answer + " but s="
+ s, answer, s);
}
}
}
t.Tick("montgomery.mod2");
for (int i_3 = 0; i_3 < en.Length; i_3++)
{
long n = en[i_3][0][0];
BigInteger N = BigInteger.ValueOf(n);
for (int j = 1; j < en[i_3].Length; j++)
{
long e = en[i_3][j][0];
long answer = en[i_3][j][1];
long s = Two.ModPow(BigInteger.ValueOf(e), N);
if (s != answer)
{
NUnit.Framework.Assert.AreEqual("e=" + e + ", n=" + n + ", answer=" + answer + " but s="
+ s, answer, s);
}
}
}
t.Tick("BigInteger.modPow(e, n)");
}