Download or view piChudnovskyNew.frink in plain text format
/** 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.
This is a new version that's intended to be used with Frink: The Next
Generation. It uses mostly fast floating-point algorithms.
See: https://frinklang.org/experimental.html
*/
//input["Hit Enter. "] // This is so we can attach jvirtualvm profiler.
//use sqrtWayne.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["Time spent in binary splitting: " + format[end-start1, "s", 3]];
start = now[];
sqC = sqrt[640320, digits+2]
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]]
q[a,b] :=
{
if (b-a)==1
return (-1)^b * g[a,b] * (13591409 + 545140134 b)
m = (a+b) div 2
return q[a,m] p[m,b] + q[m,b] g[a,m]
}
p[a,b] :=
{
if (b-a) == 1
return 10939058860032000 b^3 // Constant is C^3/24
m = (a+b) div 2
return p[a,m] p[m,b]
}
g[a,b] :=
{
if (b-a) == 1
return (6b-5)(2b-1)(6b-1)
m = (a+b) div 2
return g[a,m] g[m,b]
}
Download or view piChudnovskyNew.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 19972 days, 8 hours, 18 minutes ago.