eBinarySplitting.frink


// Program to calculate e using binary splitting.  This is very much
// faster than the simple method used in e.frink.
//
// See:
//    http://numbers.computation.free.fr/Constants/Algorithms/splitting.html
//    http://www.ginac.de/CLN/binsplit.pdf

digits = 10000
setPrecision[digits+3]

sum = 0

// Find number of terms to calculate.  ln[x!] = ln[1] + ln[2] + ... + ln[x]
k = 1;
logFactorial = 0.;
logMax = digits * ln[10]
while (logFactorial < logMax)
{
   logFactorial = logFactorial + ln[k];
   k = k + 1;
}

println["k=$k"]

start = now[];
e = 1 + P[0,k]/Q[0,k]
end = now[];

println["Calculation complete."]

println[e]                      // Rational number
println[1. * e]                 // Force to floating-point

println["Time is " + (end-start)]

P[a,b] :=
{
   if (b-a) == 1
      return 1
   m = (a+b) div 2
   r = P[a,m] Q[m,b] + P[m,b]
   return r
}

Q[a,b] :=
{
   if (b-a) == 1
      return b
   m = (a+b) div 2
   return Q[a,m] Q[m,b]
}


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This is a program written in the programming language Frink.
For more information, view the Frink Documentation or see More Sample Frink Programs.

Alan Eliasen was born 14705 days, 19 hours, 50 minutes ago.