/// <summary>
/// Constructs a BigInt from a string, using the specified precision and base
/// </summary>
/// <param name="init"></param>
/// <param name="precision"></param>
/// <param name="numberBase"></param>
public BigInt(string init, PrecisionSpec precision, int numberBase)
{
InitFromString(init, precision, numberBase);
}
private void Init(PrecisionSpec mantissaPrec)
{
int mbWords = ((mantissaPrec.NumBits) >> 5);
if ((mantissaPrec.NumBits & 31) != 0) mbWords++;
int newManBits = mbWords << 5;
//For efficiency, we just use a 32-bit exponent
exponent = 0;
mantissa = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));
//scratch = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));
}
/// <summary>
/// Get e to the indicated precision
/// </summary>
/// <param name="precision">The preicision to perform the calculation to</param>
/// <returns>e (the number for which the d/dx(e^x) = e^x)</returns>
public static BigFloat GetE(PrecisionSpec precision)
{
if (eCache == null || eCache.mantissa.Precision.NumBits < precision.NumBits)
{
CalculateEOnly(precision.NumBits);
//CalculateFactorials(precision.NumBits);
}
BigFloat ret = new BigFloat(precision);
ret.Assign(eCache);
return ret;
}
/// <summary>
/// Constructs a BigFloat from a BigInt, using the specified precision
/// </summary>
/// <param name="value"></param>
/// <param name="mantissaPrec"></param>
public BigFloat(BigInt value, PrecisionSpec mantissaPrec)
{
if (value.IsZero())
{
Init(mantissaPrec);
SetZero();
return;
}
mantissa = new BigInt(value, mantissaPrec);
exponent = BigInt.GetMSB(value);
mantissa.Normalise();
}
/// <summary>
/// Copy Constructor - constructs a new BigFloat with the specified precision, copying the old one.
///
/// The value is rounded towards zero in the case where precision is decreased. The Round() function
/// should be used beforehand if a correctly rounded result is required.
/// </summary>
/// <param name="value"></param>
/// <param name="mantissaPrec"></param>
public BigFloat(BigFloat value, PrecisionSpec mantissaPrec)
{
Init(mantissaPrec);
exponent = value.exponent;
if (mantissa.AssignHigh(value.mantissa)) exponent++;
}
/// <summary>
/// Uses the Gauss-Legendre formula for pi
/// Taken from http://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_algorithm
/// </summary>
/// <param name="numBits"></param>
private static void CalculatePi(int numBits)
{
int bits = numBits + 32;
//Precision extend taken out.
PrecisionSpec normalPres = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);
PrecisionSpec extendedPres = new PrecisionSpec(bits, PrecisionSpec.BaseType.BIN);
if (scratch.Precision.NumBits != bits)
{
scratch = new BigInt(extendedPres);
}
//a0 = 1
BigFloat an = new BigFloat(1, extendedPres);
//b0 = 1/sqrt(2)
BigFloat bn = new BigFloat(2, extendedPres);
bn.Sqrt();
bn.exponent--;
//to = 1/4
BigFloat tn = new BigFloat(1, extendedPres);
tn.exponent -= 2;
int pn = 0;
BigFloat anTemp = new BigFloat(extendedPres);
int iteration = 0;
int cutoffBits = numBits >> 5;
for (iteration = 0; ; iteration++)
{
//Save a(n)
anTemp.Assign(an);
//Calculate new an
an.Add(bn);
an.exponent--;
//Calculate new bn
bn.Mul(anTemp);
bn.Sqrt();
//Calculate new tn
anTemp.Sub(an);
anTemp.mantissa.SquareHiFast(scratch);
anTemp.exponent += anTemp.exponent + pn + 1 - anTemp.mantissa.Normalise();
tn.Sub(anTemp);
anTemp.Assign(an);
anTemp.Sub(bn);
if (anTemp.exponent < -(bits - cutoffBits)) break;
//New pn
pn++;
}
an.Add(bn);
an.mantissa.SquareHiFast(scratch);
an.exponent += an.exponent + 1 - an.mantissa.Normalise();
tn.exponent += 2;
an.Div(tn);
pi = new BigFloat(an, normalPres);
piBy2 = new BigFloat(pi);
piBy2.exponent--;
twoPi = new BigFloat(pi, normalPres);
twoPi.exponent++;
piRecip = new BigFloat(an.Reciprocal(), normalPres);
twoPiRecip = new BigFloat(piRecip);
twoPiRecip.exponent--;
//1/3 is going to be useful for sin.
threeRecip = new BigFloat((new BigFloat(3, extendedPres)).Reciprocal(), normalPres);
}
/// <summary>
/// Constructs a BigFloat from a 64-bit integer
/// </summary>
/// <param name="value"></param>
/// <param name="mantissaPrec"></param>
public BigFloat(Int64 value, PrecisionSpec mantissaPrec)
{
int mbWords = ((mantissaPrec.NumBits) >> 5);
if ((mantissaPrec.NumBits & 31) != 0) mbWords++;
int newManBits = mbWords << 5;
//For efficiency, we just use a 32-bit exponent
exponent = 0;
UInt64 uValue;
if (value < 0)
{
if (value == Int64.MinValue)
{
uValue = 0x80000000;
}
else
{
uValue = (UInt64)(-value);
}
}
else
{
uValue = (UInt64)value;
}
mantissa = new BigInt(value, new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));
//scratch = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));
int bit = BigInt.GetMSB(uValue);
if (bit == -1) return;
int shift = mantissa.Precision.NumBits - (bit + 1);
if (shift > 0)
{
mantissa.LSH(shift);
}
else
{
mantissa.SetHighDigit((uint)(uValue >> (-shift)));
}
exponent = bit;
}
//*************** Utility Functions **************
/// <summary>
/// Casts a BigInt to the new precision provided.
/// Note: This will return the input if the precision already matches.
/// </summary>
/// <param name="input"></param>
/// <param name="precision"></param>
/// <returns></returns>
public static BigInt CastToPrecision(BigInt input, PrecisionSpec precision)
{
if (input.pres == precision) return input;
return new BigInt(input, precision);
}
/// <summary>
/// GetSDTMultiplicityResult() calculates Singles, Doubles, and Triples rates plus related metadata.
///
/// This utility method works for both Slow- and Fast-Background Multiplicity Analyzers.
///
/// Note that the input parameter "accidentalsHistogram" need not be normalized,
/// and that a normalized-accidentals distribution will be included in output and will be valid
/// for both slow and fast accidentals.
///
/// </summary>
/// <param name="realsPlusAccidentalsHistogram"> The histogram of gate populations. </param>
/// <param name="accidentalsHistogram"> The histogram of gate populations - NOT NORMALIZED. </param>
/// <param name="wasFastAccidentals"> true or false. Affects how PTsingles are calculated, etc. </param>
/// <param name="multiplicityGateWidth"> as a UInt64, in 100-nanosecond tics. </param>
/// <param name="multiplicityDeadDelay"> as a UInt64, in 100-nanosecond tics. </param>
/// <param name="accidentalsDelay"> as a UInt64, in 100-nanosecond tics. </param>
/// <param name="deadTimeCoeffTinNanoSecs"> as a double, in nanoseconds. </param>
/// <param name="deadTimeCoeffAinMicroSecs"> as a double, in microseconds. </param>
/// <param name="deadTimeCoeffBinPicoSecs"> as a double, in picoseconds. </param>
/// <param name="deadTimeCoeffCinNanoSecs"> as a double, in nanoseconds. </param>
/// <param name="totalMeasurementTime"> as a double, in seconds. </param>
/// <param name="normedAccidentalsHistogram"> UInt64[]. </param>
/// <returns></returns>
public MultiplicityResult GetSDTMultiplicityResult(UInt64[] realsPlusAccidentalsHistogram,
UInt64[] accidentalsHistogram,
Boolean wasFastAccidentals,
UInt64 multiplicityGateWidth,
UInt64 multiplicityDeadDelay,
UInt64 accidentalsDelay,
double deadTimeCoeffTinNanoSecs,
double deadTimeCoeffAinMicroSecs,
double deadTimeCoeffBinPicoSecs,
double deadTimeCoeffCinNanoSecs,
double totalMeasurementTime,
UInt64[] normedAccidentalsHistogram = null)
{
MultiplicityResult result;
double phi;
double gateInSeconds;
UInt32 biggestKey, biggestAKey;
int arrayLength;
double[] alpha;
double[] beta;
BigFloat[] α = new BigFloat[0], β = new BigFloat[0];
result = new MultiplicityResult();
if (wasFastAccidentals == true)
{
result.isSlowBackground = false;
}
else
{
result.isSlowBackground = true;
}
//store parameters
result.multiplicityGateWidth = multiplicityGateWidth;
result.multiplicityDeadDelay = multiplicityDeadDelay;
result.accidentalsDelay = accidentalsDelay;
result.deadTimeCoefficientTinNanoSecs = deadTimeCoeffTinNanoSecs;
result.deadTimeCoefficientAinMicroSecs = deadTimeCoeffAinMicroSecs;
result.deadTimeCoefficientBinPicoSecs = deadTimeCoeffBinPicoSecs;
result.deadTimeCoefficientCinNanoSecs = deadTimeCoeffCinNanoSecs;
//copy the real-plus-accidental multiplicity histogram
biggestKey = 0;
arrayLength = realsPlusAccidentalsHistogram.Length;
for (int i = 0; i < arrayLength; i++)
{
if (realsPlusAccidentalsHistogram[i] > 0)
{
result.realPlusAccidentalDistribution.Add((UInt64)i, realsPlusAccidentalsHistogram[i]);
biggestKey = (UInt32)i;
}
}
result.maxRABin = biggestKey;
//copy the accidental-only histogram
biggestAKey = 0;
arrayLength = accidentalsHistogram.Length;
for (int i = 0; i < arrayLength; i++)
{
if (accidentalsHistogram[i] > 0)
{
result.accidentalDistribution.Add((UInt32)i, accidentalsHistogram[i]);
biggestAKey = (UInt32)i;
}
}
result.maxABin = biggestAKey;
//************************************************************
//Normalize the AccidentalDistribution,
//scaling the FastBackgroundAnalysis result in proportion
//to the number of Real+Accidental gate
UInt64 numAccidentalGates = 0;
UInt64 numRealPlusAccidentalGates = 0;
foreach (KeyValuePair<UInt64, UInt64> pair in result.realPlusAccidentalDistribution)
{
numRealPlusAccidentalGates += pair.Value;
}
// compute the normalization param and recompute the unnormalizaed array from this one (code does not seem to work JFL)
if (normedAccidentalsHistogram != null)
{
for (int i = 0; i < normedAccidentalsHistogram.Length; i++)
{
if (normedAccidentalsHistogram[i] > 0)
{
result.normalizedAccidentalDistribution.Add((UInt32)i, normedAccidentalsHistogram[i]);
}
}
UInt64 numNAccidentalGates = 0;
foreach (ulong no in normedAccidentalsHistogram)
{
numNAccidentalGates += no;
}
double denormalizingRatio;
UInt64 denormalizedRate;
denormalizingRatio = ((double)numNAccidentalGates) / ((double)numRealPlusAccidentalGates);
result.accidentalDistribution.Clear();
foreach (KeyValuePair<UInt64, UInt64> pair in result.normalizedAccidentalDistribution)
{
denormalizedRate = (UInt64)(pair.Value * denormalizingRatio);
result.accidentalDistribution.Add(pair.Key, denormalizedRate);
biggestAKey = (UInt32)pair.Key;
}
result.maxABin = biggestAKey;
foreach (KeyValuePair<UInt64, UInt64> pair in result.accidentalDistribution)
{
numAccidentalGates += pair.Value;
}
}
else
{
foreach (KeyValuePair<UInt64, UInt64> pair in result.accidentalDistribution)
{
numAccidentalGates += pair.Value;
}
double normalizingRatio;
UInt64 normalizedRate;
normalizingRatio = ((double)numRealPlusAccidentalGates) / ((double)numAccidentalGates);
result.normalizedAccidentalDistribution.Clear();
foreach (KeyValuePair<UInt64, UInt64> pair in result.accidentalDistribution)
{
normalizedRate = (UInt64)(pair.Value * normalizingRatio);
result.normalizedAccidentalDistribution.Add(pair.Key, normalizedRate);
}
}
//*** END Normalizing the AccidentalDistribution *************
//store the bigger key...
if (biggestAKey > biggestKey)
{
biggestKey = biggestAKey;
}
if (biggestKey < 2)
{
biggestKey = 2; //...minimum size for data-output arrays...
}
alpha = new double[biggestKey + 1];
beta = new double[biggestKey + 1];
gateInSeconds = ((double)multiplicityGateWidth) * this.ticSizeInSeconds;
phi = (deadTimeCoeffTinNanoSecs / 1E9) / gateInSeconds;
bool standard = true; // dev note: this toggle signals use of BigNum when FP overflow is detected
int axover = 0, bxover = 0;
//calculate the alphas
alpha[0] = 0.0;
alpha[1] = 1.0;
for (int n = 2; n <= biggestKey; n++)
{
if (phi > 1e-20)
{
alpha[n] = 1.0;
if (standard)
{
for (int k = 0; k <= (n - 2); k++)
{
double alphaCoeff;
alphaCoeff = this.binomialCoefficient((n - 1), (k + 1))
* Math.Pow((double)(k + 1), (double)k)
* Math.Pow(phi, (double)k)
/ (Math.Pow((1.0 - ((k + 1) * phi)), (double)(k + 2)));
alpha[n] += alphaCoeff;
if (Double.IsInfinity(alpha[n]) || Double.IsNaN(alpha[n]))
{
result.warnings.Add("Overflow alpha at n = " + n + ", k = " + k);
alpha[n] = 0;
axover = n;
standard = false; k = n; n = n - 1; // redo the loop
α = new BigFloat[biggestKey + 1];
}
}
}
else
{
// INCCCycleConditioning.calc_alpha_beta
PrecisionSpec ps128 = new PrecisionSpec(128, PrecisionSpec.BaseType.BIN);
BigFloat one = new BigFloat(1, ps128);
BigFloat combination;
BigFloat sum;
double raise1, power1, power2;
double log1, log2, log3;
BigFloat exp1, exp2, exp3;
/* calculate alpha array */
sum = new BigFloat(0, ps128);
for (int k = 0; k <= (n - 2); k++)
{
combination = new BigFloat(binomialCoefficient((n - 1), (k + 1)), ps128);
raise1 = (double)(k + 1);
power1 = (double)k;
power2 = (double)(k + 2);
log1 = Math.Log(raise1);
log2 = Math.Log(phi);
log3 = Math.Log(1.0 - raise1 * phi);
exp1 = BigFloat.Exp(new BigFloat(log1 * power1, ps128));
exp2 = BigFloat.Exp(new BigFloat(log2 * power1, ps128));
exp3 = BigFloat.Exp(new BigFloat(log3 * power2, ps128));
sum += combination * exp1 * exp2 / exp3;
}
α[n] = new BigFloat(one + sum, ps128);
}
}
else
{
alpha[n] = 1.0;
}
}
//calculate the betas
standard = true;
beta[0] = 0.0;
beta[1] = 0.0;
beta[2] = alpha[2] - 1.0;
for (int n = 3; n <= biggestKey; n++)
{
if (phi > 1e-20)
{
beta[n] = alpha[n] - 1.0;
if (standard)
{
for (int k = 0; k <= (n - 3); k++)
{
double betaCoeff;
betaCoeff = this.binomialCoefficient((n - 1), (k + 2))
* (k + 1)
* Math.Pow((double)(k + 2), (double)k)
* Math.Pow(phi, (double)k)
/ (Math.Pow((1.0 - ((k + 2) * phi)), (double)(k + 3)));
beta[n] += betaCoeff;
if (Double.IsInfinity(beta[n]) || Double.IsNaN(beta[n]))
{
result.warnings.Add("Overflow beta at n = " + n + ", k = " + k);
beta[n] = 0;
bxover = n;
standard = false; k = n; n = n - 1; // redo the loop
β = new BigFloat[biggestKey + 1];
}
}
}
else
{
PrecisionSpec ps128 = new PrecisionSpec(128, PrecisionSpec.BaseType.BIN);
BigFloat one = new BigFloat(1, ps128);
BigFloat combination;
BigFloat sum;
double raise1, power1, power2;
double log1, log2, log3;
BigFloat exp1, exp2, exp3;
sum = new BigFloat(0, ps128);
for (int k = 0; k <= n - 3; k++)
{
combination = new BigFloat(binomialCoefficient((n - 1), (k + 2)), ps128);
raise1 = (double)(k + 2);
power1 = (double)k;
power2 = (double)(k + 3);
log1 = Math.Log(raise1);
log2 = Math.Log(phi);
log3 = Math.Log(1.0 - raise1 * phi);
exp1 = BigFloat.Exp(new BigFloat(log1 * power1, ps128));
exp2 = BigFloat.Exp(new BigFloat(log2 * power1, ps128));
exp3 = BigFloat.Exp(new BigFloat(log3 * power2, ps128));
sum += combination * (new BigFloat(k + 1, ps128)) * exp1 * exp2 / exp3;
}
β[n] = α[n] - one + sum;
}
}
else
{
beta[n] = 0.0;
}
}
//store the alpha and beta coefficients
result.alpha = new double[biggestKey + 1];
result.beta = new double[biggestKey + 1];
for (int i = 0; i <= biggestKey; i++)
{
result.alpha[i] = alpha[i];
result.beta[i] = beta[i];
}
double lastGoodD = 0;
for (int i = axover; axover > 0 && i <= biggestKey; i++)
{
double d;
bool good = Double.TryParse(α[i].ToString(), System.Globalization.NumberStyles.Any, System.Globalization.CultureInfo.InvariantCulture.NumberFormat, out d); // what to do when it is really larger than a double?
if (!good)
{
result.alpha[i] = lastGoodD;
result.warnings.Add(String.Format("α[{0}] conversion failed on {1}", i, α[i].ToString()));
}
else
{
lastGoodD = d;
result.alpha[i] = d;
}
}
for (int i = bxover; bxover > 0 && i <= biggestKey; i++)
{
double d;
bool good = Double.TryParse(β[i].ToString(), System.Globalization.NumberStyles.Any, System.Globalization.CultureInfo.InvariantCulture.NumberFormat, out d);
if (!good)
{
result.beta[i] = lastGoodD;
result.warnings.Add(String.Format("β[{0}] conversion failed on {1}", i, β[i].ToString())); // URGENT: alpha/beta arrays are to be transformed from doubles to BigFloat types when this conversion happens to overflow
}
else
{
lastGoodD = d;
result.beta[i] = d;
}
}
//NOTE: in the following calculations,
//variables named RAxxx refer to "Reals Plus Accidentals" phenomena, and
//variables named Axxx refer to "Accidentals" phenomena (such as, fast-background counting)
//calculate the factorial moments
double RAfactorialMoment0, RAfactorialMoment1, RAfactorialMoment2, RAfactorialMoment3;
double AfactorialMoment0, AfactorialMoment1, AfactorialMoment2, AfactorialMoment3;
double RAfactorialMomentAlpha1, AfactorialMomentAlpha1;
double RAfactorialMomentBeta2, AfactorialMomentBeta2;
RAfactorialMoment0 = 0.0;
RAfactorialMoment1 = 0.0;
RAfactorialMoment2 = 0.0;
RAfactorialMoment3 = 0.0;
AfactorialMoment0 = 0.0;
AfactorialMoment1 = 0.0;
AfactorialMoment2 = 0.0;
AfactorialMoment3 = 0.0;
RAfactorialMomentAlpha1 = 0.0;
AfactorialMomentAlpha1 = 0.0;
RAfactorialMomentBeta2 = 0.0;
AfactorialMomentBeta2 = 0.0;
for (int i = 0; i <= biggestKey; i++)
{
UInt64 gateCount;
int j = i + 1;
int k = i + 2;
int L = i + 3;
if (result.realPlusAccidentalDistribution.TryGetValue((UInt64)i, out gateCount))
{
RAfactorialMoment0 += (double)gateCount;
}
if (result.accidentalDistribution.TryGetValue((UInt64)i, out gateCount))
{
AfactorialMoment0 += gateCount;
}
if (j <= biggestKey)
{
if (result.realPlusAccidentalDistribution.TryGetValue((UInt64)j, out gateCount))
{
RAfactorialMoment1 += (double)(((UInt64)j) * gateCount);
RAfactorialMomentAlpha1 += alpha[j] * ((double)gateCount);
}
if (result.accidentalDistribution.TryGetValue((UInt64)j, out gateCount))
{
AfactorialMoment1 += (double)(((UInt64)j) * gateCount);
AfactorialMomentAlpha1 += alpha[j] * ((double)gateCount);
}
}
if (k <= biggestKey)
{
if (result.realPlusAccidentalDistribution.TryGetValue((UInt32)k, out gateCount))
{
RAfactorialMoment2 += (double)(((UInt64)(k * (k - 1) / 2)) * gateCount);
RAfactorialMomentBeta2 += beta[k] * ((double)gateCount);
}
if (result.accidentalDistribution.TryGetValue((UInt32)k, out gateCount))
{
AfactorialMoment2 += (double)(((UInt64)(k * (k - 1) / 2)) * gateCount);
AfactorialMomentBeta2 += beta[k] * ((double)gateCount);
}
}
if (L <= biggestKey)
{
if (result.realPlusAccidentalDistribution.TryGetValue((UInt32)L, out gateCount))
{
RAfactorialMoment3 += ((double)(((UInt64)(L * (L - 1) * (L - 2))) * gateCount)) / 6.0;
}
if (result.accidentalDistribution.TryGetValue((UInt32)L, out gateCount))
{
AfactorialMoment3 += ((double)(((UInt64)(L * (L - 1) * (L - 2))) * gateCount)) / 6.0;
}
}
}
//store the factorial moments
result.RAfactorialMoment0 = RAfactorialMoment0;
result.RAfactorialMoment1 = RAfactorialMoment1;
result.RAfactorialMoment2 = RAfactorialMoment2;
result.RAfactorialMoment3 = RAfactorialMoment3;
result.AfactorialMoment0 = AfactorialMoment0;
result.AfactorialMoment1 = AfactorialMoment1;
result.AfactorialMoment2 = AfactorialMoment2;
result.AfactorialMoment3 = AfactorialMoment3;
//NOTE: in the following calculations,
//variables named PTxxx refer to "Pulse Triggered" phenomena, and
//variables named RTxxx refer to "Regularly Triggered" phenomena (such as, fast-background counting)
//penultimately, use all this to calculate the SDT rates
double PTsingles, RTsingles, normRAfactorialMoment1, normRAfactorialMoment2;
double normRAfactorialMomentAlpha1, normRAfactorialMomentBeta2;
double normAfactorialMoment0, normAfactorialMoment1, normAfactorialMoment2, normAfactorialMoment3;
double normAfactorialMomentAlpha1, normAfactorialMomentBeta2;
if (wasFastAccidentals)
{
PTsingles = RAfactorialMoment0;
double gateFactor = numAccidentalGates / Math.Floor(totalMeasurementTime / (multiplicityGateWidth * this.ticSizeInSeconds));
RTsingles = AfactorialMoment1 / gateFactor;
normRAfactorialMoment1 = RAfactorialMoment1 / PTsingles;
normRAfactorialMoment2 = RAfactorialMoment2 / PTsingles;
//NOT USED: double normRAfactorialMoment3 = RAfactorialMoment3 / PTsingles;
normRAfactorialMomentAlpha1 = RAfactorialMomentAlpha1 / PTsingles;
normRAfactorialMomentBeta2 = RAfactorialMomentBeta2 / PTsingles;
normAfactorialMoment0 = AfactorialMoment0 / numAccidentalGates;
normAfactorialMoment1 = AfactorialMoment1 / numAccidentalGates;
normAfactorialMoment2 = AfactorialMoment2 / numAccidentalGates;
normAfactorialMoment3 = AfactorialMoment3 / numAccidentalGates;
normAfactorialMomentAlpha1 = AfactorialMomentAlpha1 / numAccidentalGates;
normAfactorialMomentBeta2 = AfactorialMomentBeta2 / numAccidentalGates;
}
else
{
PTsingles = AfactorialMoment0; //XXX SHOULDN'T THIS BE RAfactorialMoment0 not AfactorialMoment0???, answer, no, the two values should be the same, RA and A of 0 are identical for "slow"
RTsingles = AfactorialMoment0;
normRAfactorialMoment1 = RAfactorialMoment1 / PTsingles;
normRAfactorialMoment2 = RAfactorialMoment2 / PTsingles;
//NOT USED: double normRAfactorialMoment3 = RAfactorialMoment3 / PTsingles;
normRAfactorialMomentAlpha1 = RAfactorialMomentAlpha1 / PTsingles;
normRAfactorialMomentBeta2 = RAfactorialMomentBeta2 / PTsingles;
normAfactorialMoment0 = AfactorialMoment0 / RTsingles;
normAfactorialMoment1 = AfactorialMoment1 / RTsingles;
normAfactorialMoment2 = AfactorialMoment2 / RTsingles;
normAfactorialMoment3 = AfactorialMoment3 / RTsingles;
normAfactorialMomentAlpha1 = AfactorialMomentAlpha1 / RTsingles;
normAfactorialMomentBeta2 = AfactorialMomentBeta2 / RTsingles;
}
double RTdoubles = (0.5 / (multiplicityGateWidth * this.ticSizeInSeconds)) * ((2.0 * normAfactorialMoment2) - Math.Pow(normAfactorialMoment1, 2.0));
double RTtriples = (0.16667 / (multiplicityGateWidth * this.ticSizeInSeconds))
* ((6.0 * normAfactorialMoment3) - (6.0 * normAfactorialMoment1 * normAfactorialMoment2) + (2.0 * Math.Pow(normAfactorialMoment1, 3)));
double PTdoubles = PTsingles * (normRAfactorialMoment1 - normAfactorialMoment1);
double PTtriples;
double PTtriplesDTcoef;
if (AfactorialMoment0 != 0.0)
{
PTtriples = PTsingles * ((normRAfactorialMoment2 - normAfactorialMoment2)
- ((normAfactorialMoment1 / normAfactorialMoment0)
* (normRAfactorialMoment1 - normAfactorialMoment1)));
PTtriplesDTcoef = PTsingles * ((normRAfactorialMomentBeta2 - normAfactorialMomentBeta2)
- ((normAfactorialMomentAlpha1 / normAfactorialMoment0)
* (normRAfactorialMomentAlpha1 - normAfactorialMomentAlpha1)));
}
else
{
PTtriples = 0.0;
PTtriplesDTcoef = 0.0;
}
if (totalMeasurementTime > 1E-12)
{
PTsingles /= totalMeasurementTime;
PTdoubles /= totalMeasurementTime;
PTtriples /= totalMeasurementTime;
PTtriplesDTcoef /= totalMeasurementTime;
}
else
{
PTsingles = 0.0;
PTdoubles = 0.0;
PTtriples = 0.0;
PTtriplesDTcoef = 0.0;
}
//store the SDT rates
result.singlesRatePerSecond = PTsingles;
result.doublesRatePerSecond = PTdoubles;
result.triplesRatePerSecond = PTtriples;
//now that rates are calculated, calculate the dead-time corrections
// dead time correction coefficients for RT rates (INCC as well as H&C)
// determined experimentally using D/T ratio - see analysisComparison/triplesDeadTime.xls
// the best fit (poly3) used to reproduce the trend
// note: valid only for sources in the range of ~100n/s - ~500,000 n/s
/** NOT USED ***
double DTcoeffT0_RT = 3.42854465;
double DTcoeffT1_RT = 3.35351651E-6;
double DTcoeffT2_RT = -5.83706327E-12;
double DTcoeffT3_RT = 2.03604973E-17;
***************/
// dead time correction coefficients for PT rates with background calculated using H&C consecutive gates
// determined experimentally using D/T ratio - see analysisComparison/triplesDeadTime.xls
// the best fit (poly3) used to reproduce the trend
// note: valid only for sources in the range of ~100n/s - ~500,000 n/s
/** NOT USED ***
double DTcoeffT0_PT = 2.78760077;
double DTcoeffT1_PT = 2.86078894E-6;
double DTcoeffT2_PT = -8.21994836E-12;
double DTcoeffT3_PT = 9.45195862E-17;
***************/
/** NOT USED ***
double DTcoeffA_RT = 0.2063; // these values were determined using two source method
double DTcoeffB_RT = 0.04256;
***************/
double DTcoeffA = deadTimeCoeffAinMicroSecs;
double DTcoeffB = deadTimeCoeffBinPicoSecs;
double DTcoeffC = deadTimeCoeffCinNanoSecs;
double DTcoeffT = deadTimeCoeffTinNanoSecs;
double exponent = ((DTcoeffA / 1E6) + ((DTcoeffB / 1E12) * PTsingles)) * PTsingles;
double PTsinglesDTcorr = PTsingles * Math.Exp(exponent / 4.0);
double PTdoublesDTcorr = PTdoubles * Math.Exp(exponent);
double PTtriplesDTcorr = PTtriplesDTcoef * Math.Exp((DTcoeffT / 1E9) * PTsingles);
/** NOT USED ***
double RTsinglesDTcorr = RTsingles * Math.Exp(( ((DTcoeffA/1E6) + ((DTcoeffB/1E12)*RTsingles)) *RTsingles)/4.0);
double RTdoublesDTcorr = RTdoubles * Math.Exp( ((DTcoeffA_RT/1E6) + ((DTcoeffB_RT/1E12)*RTsingles)) *RTsingles);
double RTtriplesDTcorr = RTtriples* (( (DTcoeffT3_RT*Math.Pow(RTsingles,3))
+ (DTcoeffT2_RT*Math.Pow(RTsingles,2))
+ (DTcoeffT1_RT*RTsingles)
+ DTcoeffT0_RT)
/DTcoeffT0_RT);
***************/
//store the dead-time corrected values
result.deadTimeCorrectedSinglesRate = PTsinglesDTcorr;
result.deadTimeCorrectedDoublesRate = PTdoublesDTcorr;
result.deadTimeCorrectedTriplesRate = PTtriplesDTcorr;
//Calculate the Dytlewski Dead-Time-Corrected Rates, based upon
//N. Dytlewski, Dead-time corrections for multiplicity counters,
//Nuclear Instruments and Methods in Physics Research A305(1991)492-494
double P03, P02, P13, P12, P23;
P03 = Math.Pow((1.0 - (2.0 * phi)), 3.0);
P02 = Math.Pow((1.0 - phi), 2.0);
P13 = (2.0 * Math.Pow((1.0 - phi), 3.0)) - (2.0 * P03);
P12 = 1.0 - P02;
P23 = 1.0 + P03 - (2.0 * Math.Pow((1.0 - phi), 3.0));
result.dytlewskiDeadTimeCorrectedTriplesRate = PTtriples / P03;
//Martyn made me do it. hn 2.6.2015
result.deadTimeCorrectedTriplesRate = result.dytlewskiDeadTimeCorrectedTriplesRate;
result.dytlewskiDeadTimeCorrectedDoublesRate = (PTdoubles / P02) + ((PTtriples * P13) / (P02 * P03));
result.dytlewskiDeadTimeCorrectedSinglesRate = PTsingles + ((P12 * PTdoubles) / P02) + (PTtriples * (((P12 * P13) / (P02 * P03)) - (P23 / P03)));
return (result);
}
/// <summary>
/// Constructs a BigInt from an Int32
/// </summary>
/// <param name="input"></param>
/// <param name="precision"></param>
public BigInt(Int32 input, PrecisionSpec precision)
{
Init(precision);
if (input < 0)
{
sign = true;
if (input == Int32.MinValue)
{
digitArray[0] = 0x80000000;
}
else
{
digitArray[0] = (UInt32)(-input);
}
}
else
{
digitArray[0] = ((UInt32)input);
}
}
/// <summary>
/// Constructs a BigInt from a UInt32
/// </summary>
/// <param name="input"></param>
/// <param name="precision"></param>
public BigInt(Int64 input, PrecisionSpec precision)
{
Init(precision);
if (input < 0) sign = true;
digitArray[0] = (UInt32)(input & 0xffffffff);
if (digitArray.Length >= 2)
{
if (input == Int64.MinValue)
{
digitArray[1] = 0x80000000;
}
else
{
digitArray[1] = (UInt32)((input >> 32) & 0x7fffffff);
}
}
}
/// <summary>
/// Constructs a BigInt from a UInt64
/// </summary>
/// <param name="input"></param>
/// <param name="precision"></param>
public BigInt(UInt64 input, PrecisionSpec precision)
{
Init(precision);
digitArray[0] = (UInt32)(input & 0xffffffff);
if (digitArray.Length > 1) digitArray[1] = (UInt32)(input >> 32);
}
/// <summary>
/// Constructs a BigInt from a UInt32
/// </summary>
/// <param name="input"></param>
/// <param name="precision"></param>
public BigInt(UInt32 input, PrecisionSpec precision)
{
Init(precision);
digitArray[0] = input;
}
/// <summary>
/// Constructs a bigint from the input, matching the new precision provided
/// </summary>
public BigInt(BigInt input, PrecisionSpec precision)
{
//Casts the input to the new precision.
Init(precision);
int Min = (input.digitArray.Length < digitArray.Length) ? input.digitArray.Length : digitArray.Length;
for (int i = 0; i < Min; i++)
{
digitArray[i] = input.digitArray[i];
}
sign = input.sign;
}
private static void CalculateFactorials(int numBits)
{
System.Collections.Generic.List<BigFloat> list = new System.Collections.Generic.List<BigFloat>(64);
System.Collections.Generic.List<BigFloat> list2 = new System.Collections.Generic.List<BigFloat>(64);
PrecisionSpec extendedPrecision = new PrecisionSpec(numBits + 1, PrecisionSpec.BaseType.BIN);
PrecisionSpec normalPrecision = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);
BigFloat factorial = new BigFloat(1, extendedPrecision);
BigFloat reciprocal;
//Calculate e while we're at it
BigFloat e = new BigFloat(1, extendedPrecision);
list.Add(new BigFloat(factorial, normalPrecision));
for (int i = 1; i < Int32.MaxValue; i++)
{
BigFloat number = new BigFloat(i, extendedPrecision);
factorial.Mul(number);
if (factorial.exponent > numBits) break;
list2.Add(new BigFloat(factorial, normalPrecision));
reciprocal = factorial.Reciprocal();
e.Add(reciprocal);
list.Add(new BigFloat(reciprocal, normalPrecision));
}
//Set the cached static values.
inverseFactorialCache = list.ToArray();
factorialCache = list2.ToArray();
invFactorialCutoff = numBits;
eCache = new BigFloat(e, normalPrecision);
eRCPCache = new BigFloat(e.Reciprocal(), normalPrecision);
}
//************************** Conversions *************************
/// <summary>
/// Converts a BigFloat to an BigInt with the specified precision
/// </summary>
/// <param name="n1">The number to convert</param>
/// <param name="precision">The precision to convert it with</param>
/// <param name="round">Do we round the number if we are truncating the mantissa?</param>
/// <returns></returns>
public static BigInt ConvertToInt(BigFloat n1, PrecisionSpec precision, bool round)
{
BigInt ret = new BigInt(precision);
int numBits = n1.mantissa.Precision.NumBits;
int shift = numBits - (n1.exponent + 1);
BigFloat copy = new BigFloat(n1);
bool inc = false;
//Rounding
if (copy.mantissa.Precision.NumBits > ret.Precision.NumBits)
{
inc = true;
for (int i = copy.exponent + 1; i <= ret.Precision.NumBits; i++)
{
if (copy.mantissa.GetBitFromTop(i) == 0)
{
inc = false;
break;
}
}
}
if (shift > 0)
{
copy.mantissa.RSH(shift);
}
else if (shift < 0)
{
copy.mantissa.LSH(-shift);
}
ret.Assign(copy.mantissa);
if (inc) ret.Increment();
return ret;
}
private static void CalculateEOnly(int numBits)
{
PrecisionSpec extendedPrecision = new PrecisionSpec(numBits + 1, PrecisionSpec.BaseType.BIN);
PrecisionSpec normalPrecision = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);
int iExponent = (int)(Math.Sqrt(numBits));
BigFloat factorial = new BigFloat(1, extendedPrecision);
BigFloat constant = new BigFloat(1, extendedPrecision);
constant.exponent -= iExponent;
BigFloat numerator = new BigFloat(constant);
BigFloat reciprocal;
//Calculate the 2^iExponent th root of e
BigFloat e = new BigFloat(1, extendedPrecision);
int i;
for (i = 1; i < Int32.MaxValue; i++)
{
BigFloat number = new BigFloat(i, extendedPrecision);
factorial.Mul(number);
reciprocal = factorial.Reciprocal();
reciprocal.Mul(numerator);
if (-reciprocal.exponent > numBits) break;
e.Add(reciprocal);
numerator.Mul(constant);
System.GC.Collect();
}
for (i = 0; i < iExponent; i++)
{
numerator.Assign(e);
e.Mul(numerator);
}
//Set the cached static values.
eCache = new BigFloat(e, normalPrecision);
eRCPCache = new BigFloat(e.Reciprocal(), normalPrecision);
}
/// <summary>
/// Constructs a BigFloat of the required precision
///
/// Sets the value to zero
/// </summary>
/// <param name="mantissaPrec"></param>
public BigFloat(PrecisionSpec mantissaPrec)
{
Init(mantissaPrec);
}
/// <summary>
/// Calculates the odd reciprocals of the natural numbers (for atan series)
/// </summary>
/// <param name="numBits"></param>
/// <param name="terms"></param>
private static void CalculateReciprocals(int numBits, int terms)
{
int bits = numBits + 32;
PrecisionSpec extendedPres = new PrecisionSpec(bits, PrecisionSpec.BaseType.BIN);
PrecisionSpec normalPres = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);
System.Collections.Generic.List<BigFloat> list = new System.Collections.Generic.List<BigFloat>(terms);
for (int i = 0; i < terms; i++)
{
BigFloat term = new BigFloat(i*2 + 1, extendedPres);
list.Add(new BigFloat(term.Reciprocal(), normalPres));
}
reciprocals = list.ToArray();
}
/// <summary>
/// Constructs a big float from a UInt32 to the required precision
/// </summary>
/// <param name="value"></param>
/// <param name="mantissaPrec"></param>
public BigFloat(UInt32 value, PrecisionSpec mantissaPrec)
{
int mbWords = ((mantissaPrec.NumBits) >> 5);
if ((mantissaPrec.NumBits & 31) != 0) mbWords++;
int newManBits = mbWords << 5;
//For efficiency, we just use a 32-bit exponent
exponent = 0;
mantissa = new BigInt(value, new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));
//scratch = new BigInt(mantissa.Precision);
int bit = BigInt.GetMSB(value);
if (bit == -1) return;
int shift = mantissa.Precision.NumBits - (bit + 1);
mantissa.LSH(shift);
exponent = bit;
}
/// <summary>
/// Constructs a BigFloat from a 64-bit unsigned integer
/// </summary>
/// <param name="value"></param>
/// <param name="mantissaPrec"></param>
public BigFloat(UInt64 value, PrecisionSpec mantissaPrec)
{
int mbWords = ((mantissaPrec.NumBits) >> 5);
if ((mantissaPrec.NumBits & 31) != 0) mbWords++;
int newManBits = mbWords << 5;
//For efficiency, we just use a 32-bit exponent
exponent = 0;
int bit = BigInt.GetMSB(value);
mantissa = new BigInt(value, new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));
//scratch = new BigInt(mantissa.Precision);
int shift = mantissa.Precision.NumBits - (bit + 1);
if (shift > 0)
{
mantissa.LSH(shift);
}
else
{
mantissa.SetHighDigit((uint)(value >> (-shift)));
}
exponent = bit;
}
private void Exp(int numBits)
{
if (IsSpecialValue)
{
if (SpecialValue == SpecialValueType.ZERO)
{
//e^0 = 1
exponent = 0;
mantissa.SetHighDigit(0x80000000);
}
else if (SpecialValue == SpecialValueType.INF_MINUS)
{
//e^-inf = 0
SetZero();
}
return;
}
PrecisionSpec prec = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);
numBits = prec.NumBits;
if (scratch.Precision.NumBits != prec.NumBits)
{
scratch = new BigInt(prec);
}
if (inverseFactorialCache == null || invFactorialCutoff < numBits)
{
CalculateFactorials(numBits);
}
//let x = 1 * 'this'.mantissa (i.e. 1 <= x < 2)
//exp(2^n * x) = e^(2^n * x) = (e^x)^2n = exp(x)^2n
int oldExponent = 0;
if (exponent > -4)
{
oldExponent = exponent + 4;
exponent = -4;
}
BigFloat thisSave = new BigFloat(this, prec);
BigFloat temp = new BigFloat(1, prec);
BigFloat temp2 = new BigFloat(this, prec);
BigFloat res = new BigFloat(1, prec);
int length = inverseFactorialCache.Length;
int iterations;
for (int i = 1; i < length; i++)
{
//temp = x^i
temp.Mul(thisSave);
temp2.Assign(inverseFactorialCache[i]);
temp2.Mul(temp);
if (temp2.exponent < -(numBits + 4)) { iterations = i; break; }
res.Add(temp2);
}
//res = exp(x)
//Now... x^(2^n) = (x^2)^(2^(n - 1))
for (int i = 0; i < oldExponent; i++)
{
res.mantissa.SquareHiFast(scratch);
int shift = res.mantissa.Normalise();
res.exponent = res.exponent << 1;
res.exponent += 1 - shift;
}
//Deal with +/- inf
if (res.exponent == Int32.MaxValue)
{
res.mantissa.Zero();
}
Assign(res);
}
/// <summary>
/// Construct a BigFloat from a double-precision floating point number
/// </summary>
/// <param name="value"></param>
/// <param name="mantissaPrec"></param>
public BigFloat(double value, PrecisionSpec mantissaPrec)
{
if (value == 0.0)
{
Init(mantissaPrec);
return;
}
bool sign = (value < 0) ? true : false;
long bits = BitConverter.DoubleToInt64Bits(value);
// Note that the shift is sign-extended, hence the test against -1 not 1
int valueExponent = (int)((bits >> 52) & 0x7ffL);
long valueMantissa = bits & 0xfffffffffffffL;
//The mantissa is stored with the top bit implied.
valueMantissa = valueMantissa | 0x10000000000000L;
//The exponent is biased by 1023.
exponent = valueExponent - 1023;
//Round the number of bits to the nearest word.
int mbWords = ((mantissaPrec.NumBits) >> 5);
if ((mantissaPrec.NumBits & 31) != 0) mbWords++;
int newManBits = mbWords << 5;
mantissa = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));
//scratch = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));
if (newManBits >= 64)
{
//The mantissa is 53 bits now, so add 11 to put it in the right place.
mantissa.SetHighDigits(valueMantissa << 11);
}
else
{
//To get the top word of the mantissa, shift up by 11 and down by 32 = down by 21
mantissa.SetHighDigit((uint)(valueMantissa >> 21));
}
mantissa.Sign = sign;
}
/// <summary>
/// Calculates ln(2) and returns -10^(n/2 + a bit) for reuse, using the AGM method as described in
/// http://lacim.uqam.ca/~plouffe/articles/log2.pdf
/// </summary>
/// <param name="numBits"></param>
/// <returns></returns>
private static void CalculateLog2(int numBits)
{
//Use the AGM method formula to get log2 to N digits.
//R(a0, b0) = 1 / (1 - Sum(2^-n*(an^2 - bn^2)))
//log(1/2) = R(1, 10^-n) - R(1, 10^-n/2)
PrecisionSpec normalPres = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);
PrecisionSpec extendedPres = new PrecisionSpec(numBits + 1, PrecisionSpec.BaseType.BIN);
BigFloat a0 = new BigFloat(1, extendedPres);
BigFloat b0 = TenPow(-(int)((double)((numBits >> 1) + 2) * 0.302), extendedPres);
BigFloat pow10saved = new BigFloat(b0);
BigFloat firstAGMcacheSaved = new BigFloat(extendedPres);
//save power of 10 (in normal precision)
pow10cache = new BigFloat(b0, normalPres);
ln2cache = R(a0, b0);
//save the first half of the log calculation
firstAGMcache = new BigFloat(ln2cache, normalPres);
firstAGMcacheSaved.Assign(ln2cache);
b0.MulPow2(-1);
ln2cache.Sub(R(a0, b0));
//Convert to log(2)
ln2cache.mantissa.Sign = false;
//Save magic constant for newton log
//First guess in range 1 <= x < 2 is x0 = ln2 * (x - 1) + C
logNewtonConstant = new BigFloat(ln2cache);
logNewtonConstant.Mul(new BigFloat(3, extendedPres));
logNewtonConstant.exponent--;
logNewtonConstant.Sub(new BigFloat(1, extendedPres));
logNewtonConstant = new BigFloat(logNewtonConstant, normalPres);
//Save the inverse.
log2ecache = new BigFloat(ln2cache);
log2ecache = new BigFloat(log2ecache.Reciprocal(), normalPres);
//Now cache log10
//Because the log functions call this function to the precision to which they
//are called, we cannot call them without causing an infinite loop, so we need
//to inline the code.
log10recip = new BigFloat(10, extendedPres);
{
int power2 = log10recip.exponent + 1;
log10recip.exponent = -1;
//BigFloat res = new BigFloat(firstAGMcache);
BigFloat ax = new BigFloat(1, extendedPres);
BigFloat bx = new BigFloat(pow10saved);
bx.Mul(log10recip);
BigFloat r = R(ax, bx);
log10recip.Assign(firstAGMcacheSaved);
log10recip.Sub(r);
ax.Assign(ln2cache);
ax.Mul(new BigFloat(power2, log10recip.mantissa.Precision));
log10recip.Add(ax);
}
log10recip = log10recip.Reciprocal();
log10recip = new BigFloat(log10recip, normalPres);
//Trim to n bits
ln2cache = new BigFloat(ln2cache, normalPres);
}
/// <summary>
/// Constructs a BigFloat from a string
/// </summary>
/// <param name="value"></param>
/// <param name="mantissaPrec"></param>
public BigFloat(string value, PrecisionSpec mantissaPrec)
{
Init(mantissaPrec);
PrecisionSpec extendedPres = new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN);
BigFloat ten = new BigFloat(10, extendedPres);
BigFloat iPart = new BigFloat(extendedPres);
BigFloat fPart = new BigFloat(extendedPres);
BigFloat tenRCP = ten.Reciprocal();
if (value.Contains(System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NaNSymbol))
{
SetNaN();
return;
}
else if (value.Contains(System.Globalization.CultureInfo.CurrentCulture.NumberFormat.PositiveInfinitySymbol))
{
SetInfPlus();
return;
}
else if (value.Contains(System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NegativeInfinitySymbol))
{
SetInfMinus();
return;
}
string decimalpoint = System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator;
char[] digitChars = { '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', ',', '.' };
//Read in the integer part up the the decimal point.
bool sign = false;
value = value.Trim();
int i = 0;
if (value.Length > i && value[i] == '-')
{
sign = true;
i++;
}
if (value.Length > i && value[i] == '+')
{
i++;
}
for ( ; i < value.Length; i++)
{
//break on decimal point
if (value[i] == decimalpoint[0]) break;
int digit = Array.IndexOf(digitChars, value[i]);
if (digit < 0) break;
//Ignore place separators (assumed either , or .)
if (digit > 9) continue;
if (i > 0) iPart.Mul(ten);
iPart.Add(new BigFloat(digit, extendedPres));
}
//If we've run out of characters, assign everything and return
if (i == value.Length)
{
iPart.mantissa.Sign = sign;
exponent = iPart.exponent;
if (mantissa.AssignHigh(iPart.mantissa)) exponent++;
return;
}
//Assign the characters after the decimal point to fPart
if (value[i] == '.' && i < value.Length - 1)
{
BigFloat RecipToUse = new BigFloat(tenRCP);
for (i++; i < value.Length; i++)
{
int digit = Array.IndexOf(digitChars, value[i]);
if (digit < 0) break;
BigFloat temp = new BigFloat(digit, extendedPres);
temp.Mul(RecipToUse);
RecipToUse.Mul(tenRCP);
fPart.Add(temp);
}
}
//If we're run out of characters, add fPart and iPart and return
if (i == value.Length)
{
iPart.Add(fPart);
iPart.mantissa.Sign = sign;
exponent = iPart.exponent;
if (mantissa.AssignHigh(iPart.mantissa)) exponent++;
return;
}
if (value[i] == '+' || value[i] == '-') i++;
if (i == value.Length)
{
iPart.Add(fPart);
iPart.mantissa.Sign = sign;
exponent = iPart.exponent;
if (mantissa.AssignHigh(iPart.mantissa)) exponent++;
return;
}
//Look for exponential notation.
if ((value[i] == 'e' || value[i] == 'E') && i < value.Length - 1)
{
//Convert the exponent to an int.
int exp;
try
{
exp = System.Convert.ToInt32(new string(value.ToCharArray(i + 1, value.Length - (i + 1))));
}
catch (Exception)
{
iPart.Add(fPart);
iPart.mantissa.Sign = sign;
exponent = iPart.exponent;
if (mantissa.AssignHigh(iPart.mantissa)) exponent++;
return;
}
//Raise or lower 10 to the power of the exponent
BigFloat acc = new BigFloat(1, extendedPres);
BigFloat temp = new BigFloat(1, extendedPres);
int powerTemp = exp;
BigFloat multiplierToUse;
if (exp < 0)
{
multiplierToUse = new BigFloat(tenRCP);
powerTemp = -exp;
}
else
{
multiplierToUse = new BigFloat(ten);
}
//Fast power function
while (powerTemp != 0)
{
temp.Mul(multiplierToUse);
multiplierToUse.Assign(temp);
if ((powerTemp & 1) != 0)
{
acc.Mul(temp);
}
powerTemp >>= 1;
}
iPart.Add(fPart);
iPart.Mul(acc);
iPart.mantissa.Sign = sign;
exponent = iPart.exponent;
if (mantissa.AssignHigh(iPart.mantissa)) exponent++;
return;
}
iPart.Add(fPart);
iPart.mantissa.Sign = sign;
exponent = iPart.exponent;
if (mantissa.AssignHigh(iPart.mantissa)) exponent++;
}
private static BigFloat TenPow(int power, PrecisionSpec precision)
{
BigFloat acc = new BigFloat(1, precision);
BigFloat temp = new BigFloat(1, precision);
int powerTemp = power;
BigFloat multiplierToUse = new BigFloat(10, precision);
if (power < 0)
{
multiplierToUse = multiplierToUse.Reciprocal();
powerTemp = -power;
}
//Fast power function
while (powerTemp != 0)
{
temp.Mul(multiplierToUse);
multiplierToUse.Assign(temp);
if ((powerTemp & 1) != 0)
{
acc.Mul(temp);
}
powerTemp >>= 1;
}
return acc;
}
//******************** Mathematical Constants *******************
/// <summary>
/// Gets pi to the indicated precision
/// </summary>
/// <param name="precision">The precision to perform the calculation to</param>
/// <returns>pi (the ratio of the area of a circle to its diameter)</returns>
public static BigFloat GetPi(PrecisionSpec precision)
{
if (pi == null || precision.NumBits <= pi.mantissa.Precision.NumBits)
{
CalculatePi(precision.NumBits);
}
BigFloat ret = new BigFloat (precision);
ret.Assign(pi);
return ret;
}
private static BigFloat R(BigFloat a0, BigFloat b0)
{
//Precision extend taken out.
int bits = a0.mantissa.Precision.NumBits;
PrecisionSpec extendedPres = new PrecisionSpec(bits, PrecisionSpec.BaseType.BIN);
BigFloat an = new BigFloat(a0, extendedPres);
BigFloat bn = new BigFloat(b0, extendedPres);
BigFloat sum = new BigFloat(extendedPres);
BigFloat term = new BigFloat(extendedPres);
BigFloat temp1 = new BigFloat(extendedPres);
BigFloat one = new BigFloat(1, extendedPres);
int iteration = 0;
for (iteration = 0; ; iteration++)
{
//Get the sum term for this iteration.
term.Assign(an);
term.Mul(an);
temp1.Assign(bn);
temp1.Mul(bn);
//term = an^2 - bn^2
term.Sub(temp1);
//term = 2^(n-1) * (an^2 - bn^2)
term.exponent += iteration - 1;
sum.Add(term);
if (term.exponent < -(bits - 8)) break;
//Calculate the new AGM estimates.
temp1.Assign(an);
an.Add(bn);
//a(n+1) = (an + bn) / 2
an.MulPow2(-1);
//b(n+1) = sqrt(an*bn)
bn.Mul(temp1);
bn.Sqrt();
}
one.Sub(sum);
one = one.Reciprocal();
return new BigFloat(one, a0.mantissa.Precision);
}
/// <summary>
/// Newton's method reciprocal, fastest for larger precisions over 15,000 bits.
/// </summary>
/// <returns>The reciprocal 1/this</returns>
public BigFloat ReciprocalNewton()
{
if (mantissa.IsZero())
{
exponent = Int32.MaxValue;
return null;
}
bool oldSign = mantissa.Sign;
int oldExponent = exponent;
//Kill exponent for now (will re-institute later)
exponent = 0;
bool topBit = mantissa.IsTopBitOnlyBit();
PrecisionSpec curPrec = new PrecisionSpec(32, PrecisionSpec.BaseType.BIN);
BigFloat reciprocal = new BigFloat(curPrec);
BigFloat constant2 = new BigFloat(curPrec);
BigFloat temp = new BigFloat(curPrec);
BigFloat thisPrec = new BigFloat(this, curPrec);
reciprocal.exponent = 1;
reciprocal.mantissa.SetHighDigit(3129112985u);
constant2.exponent = 1;
constant2.mantissa.SetHighDigit(0x80000000u);
//D is deliberately left negative for all the following operations.
thisPrec.mantissa.Sign = true;
//Initial estimate.
reciprocal.Add(thisPrec);
//mantissa.Sign = false;
//Shift down into 0.5 < this < 1 range
thisPrec.mantissa.RSH(1);
//Iteration.
int accuracyBits = 2;
int mantissaBits = mantissa.Precision.NumBits;
//Each iteration is a pass of newton's method for RCP.
//The is a substantial optimisation to be done here...
//You can double the number of bits for the calculations
//at each iteration, meaning that the whole process only
//takes some constant multiplier of the time for the
//full-scale multiplication.
while (accuracyBits < mantissaBits)
{
//Increase the precision as needed
if (accuracyBits >= curPrec.NumBits / 2)
{
int newBits = curPrec.NumBits * 2;
if (newBits > mantissaBits) newBits = mantissaBits;
curPrec = new PrecisionSpec(newBits, PrecisionSpec.BaseType.BIN);
reciprocal = new BigFloat(reciprocal, curPrec);
constant2 = new BigFloat(curPrec);
constant2.exponent = 1;
constant2.mantissa.SetHighDigit(0x80000000u);
temp = new BigFloat(temp, curPrec);
thisPrec = new BigFloat(this, curPrec);
thisPrec.mantissa.Sign = true;
thisPrec.mantissa.RSH(1);
}
//temp = Xn
temp.exponent = reciprocal.exponent;
temp.mantissa.Assign(reciprocal.mantissa);
//temp = -Xn * D
temp.Mul(thisPrec);
//temp = -Xn * D + 2 (= 2 - Xn * D)
temp.Add(constant2);
//reciprocal = X(n+1) = Xn * (2 - Xn * D)
reciprocal.Mul(temp);
accuracyBits *= 2;
}
//'reciprocal' is now the reciprocal of the shifted down, zero-exponent mantissa of 'this'
//Restore the mantissa.
//mantissa.LSH(1);
exponent = oldExponent;
//mantissa.Sign = oldSign;
if (topBit)
{
reciprocal.exponent = -(oldExponent);
}
else
{
reciprocal.exponent = -(oldExponent + 1);
}
reciprocal.mantissa.Sign = oldSign;
return reciprocal;
}
/// <summary>
/// Constructs a bigint from the string, with the desired precision, using base 10
/// </summary>
/// <param name="init"></param>
/// <param name="precision"></param>
public BigInt(string init, PrecisionSpec precision)
{
InitFromString(init, precision, 10);
}
