2

For teaching purposes, how would you write a "julian" Julia 1.0+ code to print the first 2,000 digits of pi past the decimal point? The result, in the Julia REPL, should match this pi website.

The expected output is:

julia> include("solution.jl")
Pi to 2,000 digits to right of decimal point is:
3.
14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999837297804995105973173281609631859
50244594553469083026425223082533446850352619311881
71010003137838752886587533208381420617177669147303
59825349042875546873115956286388235378759375195778
18577805321712268066130019278766111959092164201989
38095257201065485863278865936153381827968230301952
03530185296899577362259941389124972177528347913151
55748572424541506959508295331168617278558890750983
81754637464939319255060400927701671139009848824012
85836160356370766010471018194295559619894676783744
94482553797747268471040475346462080466842590694912
93313677028989152104752162056966024058038150193511
25338243003558764024749647326391419927260426992279
67823547816360093417216412199245863150302861829745
55706749838505494588586926995690927210797509302955
32116534498720275596023648066549911988183479775356
63698074265425278625518184175746728909777727938000
81647060016145249192173217214772350141441973568548
16136115735255213347574184946843852332390739414333
45477624168625189835694855620992192221842725502542
56887671790494601653466804988627232791786085784383
82796797668145410095388378636095068006422512520511
73929848960841284886269456042419652850222106611863
06744278622039194945047123713786960956364371917287
46776465757396241389086583264599581339047802759009
Julia Learner
  • 2,106
  • 7
  • 25

2 Answers2

2

The surprising key to solving this question with very little code, to a relative newcomer to Julia, like myself, and maybe someone else, is that the pi constant in Julia is not hard-coded to some number of digits, like many other languages. In Julia, the pi constant "changes" its precision, based on the underlying precision of the current operation, e.g., Julia's current BigFloat precision in this example.

So if we set the BigFloat precision to 2,001 decimal digits and do a BigFloat outcome operation with pi, we should get the desired answer.

The simplest way to do this operation, that I am aware of, is to just change pi to the BigFloat type. This will result in an outcome type of BigFloat, as shown by this code.

julia> VERSION
v"1.1.0"

julia> typeof(BigFloat(pi))  # big"1" * pi also works
BigFloat

The original question can be solved with this method, as shown by the code below. Note that using 2,002 vs. 2,001 decimal digits in the setprecision input calculation, may not be needed, but I used at least one extra digit as a "guard" digit, for any potential rounding.

setprecision(Int(ceil(log2(10) * 2002))) do
    pi_str = string(BigFloat(pi))[1:3+1999]
    digits_str = pi_str[3:3+1999]
    println("Pi to 2,000 digits to right of decimal point is:")
    println(pi_str[1:2])
    for start in 1:50:1951
        println(digits_str[start:start+49])
    end
end

I find it remarkable that Julia can solve this problem with so little code! I also tried this for 10,000 digits past the decimal point, and it worked great.

Here is the output:

julia> include("solution.jl")
Pi to 2,000 digits to right of decimal point is:
3.
14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999837297804995105973173281609631859
50244594553469083026425223082533446850352619311881
71010003137838752886587533208381420617177669147303
59825349042875546873115956286388235378759375195778
18577805321712268066130019278766111959092164201989
38095257201065485863278865936153381827968230301952
03530185296899577362259941389124972177528347913151
55748572424541506959508295331168617278558890750983
81754637464939319255060400927701671139009848824012
85836160356370766010471018194295559619894676783744
94482553797747268471040475346462080466842590694912
93313677028989152104752162056966024058038150193511
25338243003558764024749647326391419927260426992279
67823547816360093417216412199245863150302861829745
55706749838505494588586926995690927210797509302955
32116534498720275596023648066549911988183479775356
63698074265425278625518184175746728909777727938000
81647060016145249192173217214772350141441973568548
16136115735255213347574184946843852332390739414333
45477624168625189835694855620992192221842725502542
56887671790494601653466804988627232791786085784383
82796797668145410095388378636095068006422512520511
73929848960841284886269456042419652850222106611863
06744278622039194945047123713786960956364371917287
46776465757396241389086583264599581339047802759009
Julia Learner
  • 2,106
  • 7
  • 25
  • I am not sure how this teaches the calculation of pi-digits. I would rather say this is a simple demonstration of how Julia handles some irrational constants without rounding. – hckr Feb 13 '19 at 10:59
  • @hckr You are correct. The teaching here is not about the calculation of pi, but about how the irrational type in Julia works, in contrast to many other languages. – Julia Learner Feb 14 '19 at 01:50
  • @hckr Based on your comment, I removed the word "calculate" from the title of the question.and the first sentence. I think that more accurately explains that this method show how to "print" pi, rather than "calculate" pi. Thanks for clarification. – Julia Learner Feb 14 '19 at 17:08
1

Here is the short code to print out Pi. It is in a file called "pi_print.jl" and it contains the actual ALGORITHM for calculating the digits of Pi using bigint.

function main()
    firsttime_flag = true
    counter = 2000
    (k, a, b, a1, b1) = (BigInt(2), BigInt(4), BigInt(1), BigInt(12), BigInt(4))
    while counter > 0
        (p, q, k) = (k*k, BigInt(2)*k+BigInt(1), k+BigInt(1))
        (a, b, a1, b1) = (a1, b1, p*a+q*a1, p*b+q*b1)
        (d,d1) = ( div(a,b),div(a1,b1) )
        while d == d1 && counter > 0
            if firsttime_flag
                firsttime_flag = false
                println("Pi to 2,000 digits to the right of decimal point is:")
                write(stdout,string(d))
                println(".")
            else
                write(stdout,string(d))
                counter = counter - 1
            end
            (a,a1) = ( BigInt(10) * (a % b), BigInt(10) * (a1 % b1) )
            (d,d1) = ( div(a,b),div(a1,b1) )
        end
    end
end

main()

Here is the output (which I have truncated)

$ julia pi_print.jl 
Pi to 2,000 digits to the right of decimal point is:
3.
1415926535897932384626433832795028841971693993751058209749445923078164
0628620899862141592653589793238462643383279502884197169399375105820974
...

using REPL

$ julia
               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.0.3 (2018-12-18)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

julia> include("pi_print.jl")
Pi to 2,000 digits to the right of decimal point is:
3.
1415926535897932384626433832795028841971693993751058209749445923078164062862
0899862803482534211706798214808651328230664709384460955058223172535940812848
1117450284102701938521105559644622948954930381964428810975665933446128475648
2337867831652712019091456485669234603486104543266482133936072602491412737245
8700660631558817488152092096282925409171536436789259036001133053054882046652
1384146951941511609433057270365759591953092186117381932611793105118548074462
3799627495673518857527248912279381830119491298336733624406566430860213949463
9522473719070217986094370277053921717629317675238467481846766940513200056812
7145263560827785771342757789609173637178721468440901224953430146549585371050
7922796892589235420199561121290219608640344181598136297747713099605187072113
4999999837297804995105973173281609631859502445945534690830264252230825334468
5035261931188171010003137838752886587533208381420617177669147303598253490428
7554687311595628638823537875937519577818577805321712268066130019278766111959
0921642019893809525720106548586327886593615338182796823030195203530185296899
5773622599413891249721775283479131515574857242454150695950829533116861727855
8890750983817546374649393192550604009277016711390098488240128583616035637076
6010471018194295559619894676783744944825537977472684710404753464620804668425
9069491293313677028989152104752162056966024058038150193511253382430035587640
2474964732639141992726042699227967823547816360093417216412199245863150302861
8297455570674983850549458858692699569092721079750930295532116534498720275596
0236480665499119881834797753566369807426542527862551818417574672890977772793
8000816470600161452491921732172147723501414419735685481613611573525521334757
4184946843852332390739414333454776241686251898356948556209921922218427255025
4256887671790494601653466804988627232791786085784383827967976681454100953883
7863609506800642251252051173929848960841284886269456042419652850222106611863
0674427862203919494504712371378696095636437191728746776465757396241389086583
264599581339047802759009
Steven Siew
  • 778
  • 5
  • 9