piChudnovsky.frink

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/** Program to calculate pi to a large number of digits using the Chudnovsky
    algorithm with binary splitting.

    see:
     http://numbers.computation.free.fr/Constants/Algorithms/splitting.html

    This program is a testbed for timing the performance of this algorithm and
    prints extraneous output.  If you want a quieter, cached version that you
    can use in your own library, see pi.frink instead. */


//input["Hit Enter. "]    // This is so we can attach jvirtualvm profiler.

use karatsuba.frink

digits = million

if length[ARGS] >= 1
   digits = eval[ARGS@0]

digitsPerIteration = 14.1816474627254776555

// Find number of terms to calculate
k = floor[digits/digitsPerIteration]

setPrecision[digits+3]

println["Calculating $digits digits."]
//println["k=$k"]

start1 = now[];

// pi = p[0,k] * (C/D) * sqrt[C] / (q[0,k] + A * p)
p = p[0,k]
q = q[0,k]
end = now[];

//println["p is $p: " + factor[p]]
//println["q is $q: " /* + factor[abs[q]]*/]

println["Time spent in binary splitting: " + format[end-start1, "s", 3]];

start = now[];
sqC = karatsubaSqrt[640320, digits+2, true]
end = now[];
println["Time spent in square root: " + format[end-start, "s", 3]];

start = now[];
piprime = p * 53360 / (q + 13591409 * p)
pi = piprime * sqC
end = now[];
println["Time spent in combining operations " + format[end-start, "s", 3]]


println["Calculation complete."]

setPrecision[digits]
start = now[]
value = 1. * pi
end = now[]
println["Time spent in floating-point calculation: " + format[end-start, "s", 3]]

start = now[]
println[value]
end = now[]
println["Time spent in printing: " + format[end-start, "s", 3]]

end = now[]

println["Total time is " + format[end-start1, "s", 3]]

//sqrtPi = sqrt[pi, digits]
//println["Square root of pi is:"]
//println[sqrtPi]
//println[sqrtPi^2 - pi]


q[a,b] :=
{
   if (b-a)==1
   {
      result = (-1)^b * g[a,b] * (13591409 + 545140134 b)
//      println["q[$a,$b]=" + factor[abs[result]]]
      return result
   }

   m = (a+b) div 2
//   println["m=$m"]
   r = q[a,m] p[m,b] + q[m,b] g[a,m]
//   println["q[$a,$b]=" + factor[abs[r]]]
//   println["r=$r"]
   return r
}

p[a,b] :=
{
   if (b-a) == 1
   {
      result = 10939058860032000 b^3  // Constant is C^3/24
//      println["p[$a,$b]=" + factor[result]]
      return result
   }
   m = (a+b) div 2
   result = p[a,m] p[m,b]
//   println["p[$a,$b]=" + factor[result]]
   return result
}

g[a,b] :=
{
   if (b-a) == 1
   {
      result = (6b-5)(2b-1)(6b-1)
//      println["g[$a,$b]=" + factor[result]]
      return result
   }
   m = (a+b) div 2
   result = g[a,m] g[m,b]
//   println["g[$a,$b]=" + factor[result]]
   return result
}


View or download piChudnovsky.frink in plain text format


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 18012 days, 11 hours, 33 minutes ago.