Arbitrary-precision integers (included)

Using the in-built capabilities of your language, calculate the integer value of:

         $5^{4^{3^{2}}}$

Confirm that the first and last twenty digits of the answer are:

     62060698786608744707...92256259918212890625

Find and show the number of decimal digits in the answer.

Note:

Do not submit an implementation of arbitrary precision arithmetic. The intention is to show the capabilities of the language as supplied. If a language has a single, overwhelming, library of varied modules that is endorsed by its home site – such as CPAN for Perl or Boost for C++ – then that may be used instead.
Strictly speaking, this should not be solved by fixed-precision numeric libraries where the precision has to be manually set to a large value; although if this is the only recourse then it may be used with a note explaining that the precision must be set manually to a large enough value.

Related tasks

11l

Translation of: Python

<lang 11l>V y = String(BigInt(5) ^ 4 ^ 3 ^ 2) print(‘5^4^3^2 = #....#. and has #. digits’.format(y[0.<20], y[(len)-20..], y.len))</lang>

Output:

5^4^3^2 = 62060698786608744707...92256259918212890625 and has 183231 digits

8th

<lang forth> 200000 n# 5 4 3 2 bfloat ^ ^ ^ "%.0f" s:strfmt dup s:len . " digits" . cr dup 20 s:lsub . "..." . 20 s:rsub . cr </lang>

Output:

183231 digits
62060698786608744707...92256259918212890625

ACL2

<lang Lisp>(in-package "ACL2")

(include-book "arithmetic-3/floor-mod/floor-mod" :dir :system)

(set-print-length 0 state)

(defun arbitrary-precision ()

  (declare (xargs :mode :program))
  (let* ((x (expt 5 (expt 4 (expt 3 2))))
         (s (mv-let (col str)
                    (fmt1-to-string "~xx" 
                                    (list (cons #\x x))
                                    0)
               (declare (ignore col))
               str)))
        (cw "~s0 ... ~x1 (~x2 digits)~%"
            (subseq s 0 20)
            (mod x (expt 10 20))
            (1- (length s)))))</lang>

Output:

62060698786608744707 ... 92256259918212890625 (183231 digits)

Ada

Library: GMP

Using GMP, Ada bindings provided in GNATColl

<lang Ada>with Ada.Text_IO; use Ada.Text_IO; with GNATCOLL.GMP; use GNATCOLL.GMP; with GNATCOLL.GMP.Integers; use GNATCOLL.GMP.Integers; procedure ArbitraryInt is

  type stracc is access String;
  BigInt : Big_Integer;
  len : Natural;
  str : stracc;

begin

  Set (BigInt, 5);
  Raise_To_N (BigInt, Unsigned_Long (4**(3**2)));
  str := new String'(Image (BigInt));
  len := str'Length;
  Put_Line ("Size is:"& Natural'Image (len));
  Put_Line (str (1 .. 20) & "....." & str (len - 19 .. len));

end ArbitraryInt;</lang>

Output:

Size is: 183231
62060698786608744707.....92256259918212890625

ALGOL 68

<lang algol68> BEGIN COMMENT

  The task specifies

  "Strictly speaking, this should not be solved by fixed-precision
  numeric libraries where the precision has to be manually set to a
  large value; although if this is the only recourse then it may be
  used with a note explaining that the precision must be set manually
  to a large enough value."

  Now one should always speak strictly, especially to animals and
  small children and, strictly speaking, Algol 68 Genie requires that
  a non-default numeric precision for a LONG LONG INT be specified by
  "precision=<integral denotation>" either in a source code PRAGMAT
  or as a command line argument.  However, that specification need
  not be made manually.  This snippet of code outputs an appropriate
  PRAGMAT

  printf (($gg(0)xgl$, "PR precision=",

ENTIER (1.0 + log (5) * 4^(3^(2))), "PR"));

  and the technique shown in the "Call a foreign-language function"
  task used to write, compile and run an Algol 68 program in which
  the precision is programmatically determined.

  The default stack size on this machine is also inadequate but twice
  the default is sufficient.  The PRAGMAT below can be machine
  generated with

  printf (($gg(0)xgl$, "PR stack=", 2 * system stack size, "PR"));

COMMENT

  PR precision=183231 PR
  PR stack=16777216 PR
  INT digits = ENTIER (1.0 + log (5) * 4^(3^(2))), exponent = 4^(3^2);
  LONG LONG INT big = LONG LONG 5^exponent;
  printf (($gxg(0)l$, " First 20 digits:", big % LONG LONG 10 ^ (digits - 20)));
  printf (($gxg(0)l$, "  Last 20 digits:", big MOD LONG LONG 10 ^ 20));
  printf (($gxg(0)l$, "Number of digits:", digits))

END

</lang>

Output:

 First 20 digits: 62060698786608744707
  Last 20 digits: 92256259918212890625
Number of digits: 183231

bc

<lang bc>/* 5432.bc */

y = 5 ^ 4 ^ 3 ^ 2 c = length(y) " First 20 digits: "; y / (10 ^ (c - 20)) " Last 20 digits: "; y % (10 ^ 20) "Number of digits: "; c quit</lang>

Output:

$ time bc 5432.bc  
 First 20 digits: 62060698786608744707
  Last 20 digits: 92256259918212890625
Number of digits: 183231
    0m24.81s real     0m24.81s user     0m0.00s system

At the prompt type the following one-liner: <lang bracmat>{?} @(5^4^3^2:?first [20 ? [-21 ?last [?length)&str$(!first "..." !last "\nlength " !length) {!} 62060698786608744707...92256259918212890625 length 183231

   S   2,46 sec</lang>

C

Library: GMP

<lang c>#include <gmp.h>

include <stdio.h>
include <string.h>

int main() { mpz_t a; mpz_init_set_ui(a, 5); mpz_pow_ui(a, a, 1 << 18); /* 2**18 == 4**9 */

int len = mpz_sizeinbase(a, 10); printf("GMP says size is: %d\n", len);

/* because GMP may report size 1 too big; see doc */ char *s = mpz_get_str(0, 10, a); printf("size really is %d\n", len = strlen(s)); printf("Digits: %.20s...%s\n", s, s + len - 20);

// free(s); /* we could, but we won't. we are exiting anyway */ return 0; }</lang>

Output:

GMP says size is: 183231
size really is 183231
Digits: 62060698786608744707...92256259918212890625

Library: OpenSSL

OpenSSL is about 17 times slower than GMP (on one computer), but still fast enough for this small task. <lang c>/* 5432.c */

include <openssl/bn.h> /* BN_*() */
include <openssl/err.h> /* ERR_*() */
include <stdlib.h> /* exit() */
include <stdio.h> /* fprintf() */
include <string.h> /* strlen() */

void fail(const char *message) { fprintf(stderr, "%s: error 0x%08lx\n", ERR_get_error()); exit(1); }

int main() { BIGNUM two, three, four, five; BIGNUM answer; BN_CTX *context; size_t length; char *string;

context = BN_CTX_new(); if (context == NULL) fail("BN_CTX_new");

/* answer = 5 ** 4 ** 3 ** 2 */ BN_init(&two); BN_init(&three); BN_init(&four); BN_init(&five); if (BN_set_word(&two, 2) == 0 || BN_set_word(&three, 3) == 0 || BN_set_word(&four, 4) == 0 || BN_set_word(&five, 5) == 0) fail("BN_set_word"); BN_init(&answer); if (BN_exp(&answer, &three, &two, context) == 0 || BN_exp(&answer, &four, &answer, context) == 0 || BN_exp(&answer, &five, &answer, context) == 0) fail("BN_exp");

/* string = decimal answer */ string = BN_bn2dec(&answer); if (string == NULL) fail("BN_bn2dec");

length = strlen(string); printf(" First 20 digits: %.20s\n", string); if (length >= 20) printf(" Last 20 digits: %.20s\n", string + length - 20); printf("Number of digits: %zd\n", length);

OPENSSL_free(string); BN_free(&answer); BN_free(&five); BN_free(&four); BN_free(&three); BN_free(&two); BN_CTX_free(context);

return 0; }</lang>

Output:

$ make LDLIBS=-lcrypto 5432 
cc -O2 -pipe    -o 5432 5432.c -lcrypto
$ time ./5432 
 First 20 digits: 62060698786608744707
  Last 20 digits: 92256259918212890625
Number of digits: 183231
    0m1.30s real     0m1.30s user     0m0.00s system

C#

System.Numerics.BigInteger was added in C# 4. The exponent of BigInteger.Pow() is limited to a 32-bit signed integer, which is not a problem in this specific task.

Works with: C# version 4+

<lang csharp>using System; using System.Diagnostics; using System.Linq; using System.Numerics;

static class Program {

   static void Main() {
       BigInteger n = BigInteger.Pow(5, (int)BigInteger.Pow(4, (int)BigInteger.Pow(3, 2)));
       string result = n.ToString();

       Debug.Assert(result.Length == 183231);
       Debug.Assert(result.StartsWith("62060698786608744707"));
       Debug.Assert(result.EndsWith("92256259918212890625"));

       Console.WriteLine("n = 5^4^3^2");
       Console.WriteLine("n = {0}...{1}", 
           result.Substring(0, 20),
           result.Substring(result.Length - 20, 20)
           );

       Console.WriteLine("n digits = {0}", result.Length);
   }

}</lang>

Output:

n = 5^4^3^2
n = 62060698786608744707...92256259918212890625
n digits = 183231

C++

Library: Boost-Multiprecision (GMP Backend)

To compile link with GMP -lgmp <lang cpp>#include <iostream>

include <boost/multiprecision/gmp.hpp>
include <string>

namespace mp = boost::multiprecision;

int main(int argc, char const *argv[]) {

   // We could just use (1 << 18) instead of tmpres, but let's point out one
   // pecularity with gmp and hence boost::multiprecision: they won't accept
   // a second mpz_int with pow(). Therefore, if we stick to multiprecision
   // pow we need to convert_to<uint64_t>().
   uint64_t tmpres = mp::pow(mp::mpz_int(4)
                           , mp::pow(mp::mpz_int(3)
                                   , 2).convert_to<uint64_t>()
                                     ).convert_to<uint64_t>();
   mp::mpz_int res = mp::pow(mp::mpz_int(5), tmpres);
   std::string s = res.str();
   std::cout << s.substr(0, 20) 
             << "..."
             << s.substr(s.length() - 20, 20) << std::endl;
   return 0;

} </lang>

Output:

62060698786608744707...92256259918212890625

Ceylon

Be sure to import ceylon.whole in your module.ceylon file. <lang ceylon>import ceylon.whole {

   wholeNumber,
   two

}

shared void run() {

   value five = wholeNumber(5);
   value four = wholeNumber(4);
   value three = wholeNumber(3);

   value bigNumber = five ^ four ^ three ^ two;

   value firstTwenty = "62060698786608744707";
   value lastTwenty =  "92256259918212890625";
   value bigString = bigNumber.string;

   "The number must start with ``firstTwenty`` and end with ``lastTwenty``"
   assert(bigString.startsWith(firstTwenty), bigString.endsWith(lastTwenty));

   value bigSize = bigString.size;
   print("The first twenty digits are ``bigString[...19]``");
   print("The last twenty digits are ``bigString[(bigSize - 20)...]``");
   print("The number of digits in 5^4^3^2 is ``bigSize``");

}</lang>

Output:

The first twenty digits are 62060698786608744707
The last twenty digits are 92256259918212890625
The number of digits in 5^4^3^2 is 183231

Clojure

<lang clojure>(defn exp [n k] (reduce * (repeat k n)))

(def big (->> 2 (exp 3) (exp 4) (exp 5))) (def sbig (str big))

(assert (= "62060698786608744707" (.substring sbig 0 20))) (assert (= "92256259918212890625" (.substring sbig (- (count sbig) 20)))) (println (count sbig) "digits")

(println (str (.substring sbig 0 20) ".." (.substring sbig (- (count sbig) 20))) (str "(" (count sbig) " digits)"))</lang>

Output:

output> 62060698786608744707..92256259918212890625 (183231 digits)

Redefining exp as follows speeds up the calculation of big about a hundred times: <lang clojure>(defn exp [n k]

 (cond
   (zero? (mod k 2)) (recur (* n n) (/ k 2))
   (zero? (mod k 3)) (recur (* n n n) (/ k 3))
   :else (reduce * (repeat k n))))</lang>

COBOL

This entry might be pushing the limits of the spirit of the task. COBOL does not have arbitrary-precision integers in the spec, but it does mandate a precision of some 1000 digits with intermediate results, from 10^-999 through 10^1000, for purposes of rounding financially sound decimal arithmetic. GnuCOBOL uses libgmp or equivalent to meet and surpass this requirement, but this precision is not exposed to general programming in the language. The capabilities are included in the GnuCOBOL implementation run-time support, but require access to some of the opaque features of libgmp for use in this task.

This listing includes a few calculations, 12345**9 is an example that demonstrates the difference between the library's view of certain string lengths and a native C view of the data.

Works with: GnuCOBOL

Library: GMP

<lang COBOL> identification division.

      program-id. arbitrary-precision-integers.
      remarks. Uses opaque libgmp internals that are built into libcob.

      data division.
      working-storage section.
      01 gmp-number.
         05 mp-alloc          usage binary-long.
         05 mp-size           usage binary-long.
         05 mp-limb           usage pointer.
      01 gmp-build.
         05 mp-alloc          usage binary-long.
         05 mp-size           usage binary-long.
         05 mp-limb           usage pointer.

      01 the-int              usage binary-c-long unsigned.
      01 the-exponent         usage binary-c-long unsigned.
      01 valid-exponent       usage binary-long value 1.
         88 cant-use          value 0 when set to false 1.

      01 number-string        usage pointer.
      01 number-length        usage binary-long.

      01 window-width         constant as 20.
      01 limit-width          usage binary-long.       
      01 number-buffer        pic x(window-width) based.
      
      procedure division.
      arbitrary-main.

     *> calculate 10 ** 19
      perform initialize-integers.
      display "10 ** 19        : " with no advancing
      move 10 to the-int
      move 19 to the-exponent
      perform raise-pow-accrete-exponent
      perform show-all-or-portion
      perform clean-up

     *> calculate 12345 ** 9
      perform initialize-integers.
      display "12345 ** 9      : " with no advancing
      move 12345 to the-int
      move 9 to the-exponent
      perform raise-pow-accrete-exponent
      perform show-all-or-portion
      perform clean-up

     *> calculate 5 ** 4 ** 3 ** 2
      perform initialize-integers.
      display "5 ** 4 ** 3 ** 2: " with no advancing
      move 3 to the-int
      move 2 to the-exponent
      perform raise-pow-accrete-exponent
      move 4 to the-int
      perform raise-pow-accrete-exponent
      move 5 to the-int
      perform raise-pow-accrete-exponent
      perform show-all-or-portion
      perform clean-up
      goback.
     *> **************************************************************

      initialize-integers.
      call "__gmpz_init" using gmp-number returning omitted
      call "__gmpz_init" using gmp-build returning omitted
      .

      raise-pow-accrete-exponent.
     *> check before using previously overflowed exponent intermediate
      if cant-use then
          display "Error: intermediate overflow occured at "
                  the-exponent upon syserr
          goback
      end-if
      call "__gmpz_set_ui" using gmp-number by value 0
          returning omitted
      call "__gmpz_set_ui" using gmp-build by value the-int
          returning omitted
      call "__gmpz_pow_ui" using gmp-number gmp-build
          by value the-exponent
          returning omitted
      call "__gmpz_set_ui" using gmp-build by value 0
          returning omitted
      call "__gmpz_get_ui" using gmp-number returning the-exponent
      call "__gmpz_fits_ulong_p" using gmp-number
          returning valid-exponent
      .

     *> get string representation, base 10
      show-all-or-portion.
      call "__gmpz_sizeinbase" using gmp-number
          by value 10
          returning number-length
      display "GMP length: " number-length ", " with no advancing

      call "__gmpz_get_str" using null by value 10
          by reference gmp-number
          returning number-string
      call "strlen" using by value number-string
          returning number-length
      display "strlen: " number-length

     *> slide based string across first and last of buffer
      move window-width to limit-width
      set address of number-buffer to number-string
      if number-length <= window-width then
          move number-length to limit-width
          display number-buffer(1:limit-width)
      else
          display number-buffer with no advancing
          subtract window-width from number-length
          move function max(0, number-length) to number-length
          if number-length <= window-width then
              move number-length to limit-width
          else
              display "..." with no advancing
          end-if
          set address of number-buffer up by
              function max(window-width, number-length)
          display number-buffer(1:limit-width)
      end-if
      .

      clean-up.
      call "free" using by value number-string returning omitted
      call "__gmpz_clear" using gmp-number returning omitted
      call "__gmpz_clear" using gmp-build returning omitted
      set address of number-buffer to null
      set cant-use to false
      .

      end program arbitrary-precision-integers.

</lang>

Output:

prompt$ cobc -xj arbitrary-integer.cob
10 ** 19        : GMP length: +0000000020, strlen: +0000000020
10000000000000000000
12345 ** 9      : GMP length: +0000000038, strlen: +0000000037
6659166111488656281486807152009765625
5 ** 4 ** 3 ** 2: GMP length: +0000183231, strlen: +0000183231
62060698786608744707...92256259918212890625

Common Lisp

Common Lisp has arbitrary precision integers, inherited from MacLisp: "[B]ignums—arbitrary precision integer arithmetic—were added [to MacLisp] in 1970 or 1971 to meet the needs of Macsyma users." [Evolution of Lisp [1], 2.2.2] <lang lisp>(let ((s (format () "~s" (expt 5 (expt 4 (expt 3 2))))))

 (format t "~a...~a, length ~a" (subseq s 0 20) 
         (subseq s (- (length s) 20)) (length s)))</lang>

Output:

62060698786608744707...92256259918212890625, length 183231

D

<lang d>void main() {

 import std.stdio, std.bigint, std.conv;

 auto s = text(5.BigInt ^^ 4 ^^ 3 ^^ 2);
 writefln("5^4^3^2 = %s..%s (%d digits)", s[0..20], s[$-20..$], s.length);

}</lang>

Output:

5^4^3^2 = 62060698786608744707..92256259918212890625 (183231 digits)

With dmd about 0.55 seconds compilation time (-release -noboundscheck) and about 3.3 seconds run time.

Dart

Originally Dart's integral type int supported arbitrary length integers, but this is no longer the case; Dart now supports integral type BigInt. <lang dart>import 'dart:math' show pow;

int fallingPowers(int base) =>

   base == 1 ? 1 : pow(base, fallingPowers(base - 1));

void main() {

 final exponent = fallingPowers(4),
     s = BigInt.from(5).pow(exponent).toString();
 print('First twenty:     ${s.substring(0, 20)}');
 print('Last twenty:      ${s.substring(s.length - 20)}');
 print('Number of digits: ${s.length}');

</lang>

Output:

First twenty:     62060698786608744707
Last twenty:      92256259918212890625
Number of digits: 183231

dc

Translation of: bc

<lang dc>[5432.dc]sz

5 4 3 2 ^ ^ ^ sy [y = 5 ^ 4 ^ 3 ^ 2]sz ly Z sc [c = length of y]sz [ First 20 digits: ]P ly 10 lc 20 - ^ / p sz [y / (10 ^ (c - 20))]sz [ Last 20 digits: ]P ly 10 20 ^ % p sz [y % (10 ^ 20)]sz [Number of digits: ]P lc p sz</lang>

Output:

$ time dc 5432.dc                                                              
 First 20 digits: 62060698786608744707
  Last 20 digits: 92256259918212890625
Number of digits: 183231
    0m24.80s real     0m24.81s user     0m0.00s system

Delphi

Library: System.SysUtils

Library: Velthuis.BigIntegers

Thanks for Rudy Velthuis, BigIntegers Library [2].

<lang Delphi> program Arbitrary_precision_integers;

{$APPTYPE CONSOLE}

uses

 System.SysUtils,
 Velthuis.BigIntegers;

var

 value: BigInteger;
 result: string;

begin

 value := BigInteger.pow(3, 2);
 value := BigInteger.pow(4, value.AsInteger);
 value := BigInteger.pow(5, value.AsInteger);
 result := value.tostring;
 Write('5^4^3^2 = ');
 Write(result.substring(0, 20), '...');
 Write(result.substring(result.length - 20, 20));
 Writeln(' (', result.Length,' digits)');
 readln;

end.</lang>

Output:

5^4^3^2 = 62060698786608744707...92256259918212890625 (183231 digits)

E

E implementations are required to support arbitrary-size integers transparently. <lang e>? def value := 5**(4**(3**2)); null ? def decimal := value.toString(10); null ? decimal(0, 20)

value: "62060698786608744707"

? decimal(decimal.size() - 20)

value: "92256259918212890625"

? decimal.size()

value: 183231</lang>

EchoLisp

to save space and time, we do'nt stringify Ω = 5^4^3^2 , but directly extract tail and head and number of decimal digits

(lib 'bigint) ;; arbitrary size integers

(define e10000 (expt 10 10000)) ;; 10^10000

(define (last-n big (n 20)) (string-append "..." (number->string (modulo big (expt 10 n)))))

(define (first-n big (n 20)) (while (> big e10000) (set! big (/ big e10000))) ;; cut 10000 digits at a time (string-append (take (number->string big) n) "..."))

faster than directly using (number-length big)

(define (digits big (digits 0)) (while (> big e10000) (set! big (/ big e10000)) (set! digits (1+ digits))) (+ (* digits 10000) (number-length big)))

(define Ω (expt 5 (expt 4 (expt 3 2))))

(last-n Ω )

   → "...92256259918212890625"

(first-n Ω )

   → "62060698786608744707..."

(digits Ω )

   → 183231

</lang>

Elixir

Translation of: Erlang

<lang elixir>defmodule Arbitrary do

 def pow(_,0), do: 1
 def pow(b,e) when e > 0, do: pow(b,e,1)
 
 defp pow(b,1,acc), do: acc * b
 defp pow(b,p,acc) when rem(p,2)==0, do: pow(b*b,div(p,2),acc)
 defp pow(b,p,acc), do: pow(b,p-1,acc*b)
 
 def test do
   s = pow(5,pow(4,pow(3,2))) |> to_string
   l = String.length(s)
   prefix = String.slice(s,0,20)
   suffix = String.slice(s,-20,20)
   IO.puts "Length: #{l}\nPrefix:#{prefix}\nSuffix:#{suffix}"
 end

end Arbitrary.test</lang>

Output:

Length: 183231
Prefix:62060698786608744707
Suffix:92256259918212890625

Emacs Lisp

GMP

As of Emacs 27.1, bignums are supported via GMP.

<lang lisp>(let* ((integer-width (* 65536 16)) ; raise bignum limit from 65536 bits

      (answer (number-to-string (expt 5 (expt 4 (expt 3 2)))))
      (length (length answer)))
 (message "%s has %d digits"

(if (> length 40) (format "%s...%s" (substring answer 0 20) (substring answer (- length 20) length)) answer) length))</lang>

Calc

Emacs versions older than 27.1 do not support bignums, but include Calc, a library that implements big integers. The calc-eval function takes an algebraic formula in a string, and returns the result in a string.

Library: Calc

<lang lisp>(let* ((answer (calc-eval "5**4**3**2"))

      (length (length answer)))
 (message "%s has %d digits"

(if (> length 40) (format "%s...%s" (substring answer 0 20) (substring answer (- length 20) length)) answer) length))</lang>

This implementation is very slow; one computer, running GNU Emacs 23.4.1, needed about seven minutes to find the answer.

Output:

62060698786608744707...92256259918212890625 has 183231 digits

Erlang

Erlang supports arbitrary precision integers. However, the math:pow function returns a float. This implementation includes an implementation of pow for integers with exponent greater than 0. <lang erlang> -module(arbitrary). -compile([export_all]).

pow(B,E) when E > 0 ->

   pow(B,E,1).

pow(_,0,_) -> 0; pow(B,1,Acc) -> Acc * B; pow(B,P,Acc) when P rem 2 == 0 ->

   pow(B*B,P div 2, Acc);

pow(B,P,Acc) ->

   pow(B,P-1,Acc*B).

test() ->

   I = pow(5,pow(4,pow(3,2))),   
   S = integer_to_list(I),
   L = length(S),
   Prefix = lists:sublist(S,20),
   Suffix = lists:sublist(S,L-19,20),
   io:format("Length: ~b~nPrefix:~s~nSuffix:~s~n",[L,Prefix,Suffix]).

</lang>

Output:

23> arbitrary:test().

Length: 183231
Prefix:62060698786608744707
Suffix:92256259918212890625
ok

F#

You can specifiy arbitrary-precision integers (bigint or System.Numeric.BigInteger) in F# by postfixing the number with the letter 'I'. While '**' is the power function, two things should be noted:

bigint does not support raising to a power of a bigint
The int type does not support the power method

<lang fsharp>let () =

   let answer = 5I **(int (4I ** (int (3I ** 2))))
   let sans = answer.ToString()
   printfn "Length = %d, digits %s ... %s" sans.Length (sans.Substring(0,20)) (sans.Substring(sans.Length-20))

Length = 183231, digits 62060698786608744707 ... 92256259918212890625</lang>

Factor

Factor has built-in bignum support. Operations on integers overflow to bignums. <lang factor>USING: formatting kernel math.functions math.parser sequences ; IN: rosettacode.bignums

test-bignums ( -- )

   5 4 3 2 ^ ^ ^ number>string
   [ 20 head ] [ 20 tail* ] [ length ] tri
   "5^4^3^2 is %s...%s and has %d digits\n" printf ;</lang>

It prints: 5^4^3^2 is 62060698786608744707...92256259918212890625 and has 183231 digits

Forth

ANS Forth has no in-built facility for arbitrarily-sized numbers, but libraries are available.

Works with: ANS Forth

Library: The Forth Scientific Library

Here is a solution using The Forth Scientific Library, available here.

The big.fth needs to be patched to allow printing of numbers with more than 256 digits. Note that this restriction is only on the printing routines, as the size of numbers handled by the library is only limited by the available memory.

The patch is:

388c388
< CREATE big_string 256 CHARS ALLOT
---
> CREATE big_string 500000 CHARS ALLOT
394c394
<   big_string 256 CHARS + bighld ! ;  \ Haydon p 67
---
>   big_string 500000 CHARS + bighld ! ;  \ Haydon p 67
403c403
<   big_string 256 CHARS +     \ One past end of string
---
>   big_string 500000 CHARS +  \ One past end of string

Here is the solution:

<lang forth>INCLUDE big.fth

big_digit_pointer *exp \ iteration counter big_digit_pointer *base \ point to base of number being exponentiated

big_digit_pointer *0 \ store 0 big_digit_pointer *1 \ store 1 big_digit_pointer *result \ point to result of exponentiation big_digit_pointer *temp \ point to temporary result

big-- ( addr-n -- )

   DUP 0 *1 big-                   ( addr-n addr-n-1 ) \ decrement value
   SWAP DUP @ ABS 1+ CELLS MOVE    ( ) \ overwrite addr-n with addr-n-1

big> ( addr1 addr2 -- flag )

   2DUP big< >R                    ( addr1 addr2 ) ( R: flag1 )
   big=                            ( flag2 ) ( R: flag1 )
   R> OR 0=                        ( ! <= )

big^ ( addr-base addr-exp - addr )

   to_pointer *exp
   to_pointer *base

   HERE 1 , 0 , to_pointer *0      \ create limit value for counter
   HERE 1 , 1 , to_pointer *1      \ create subtraend for counter
   HERE 1 , 1 , to_pointer *result \ create result = 1
   BEGIN
       0 *exp 0 *0 big>            ( flag ) \ loop while exp > 0
       0 *exp big--                \ prepare for next iteration
   WHILE
       0 *result 0 *base big* 
       to_pointer *temp            \ temp = result * base

       0 *temp 0 *result 
       reposition                  \ move [temp,HERE[ to [result,result+size[
   REPEAT
   0 *result 0 *0 
   reposition                      \ overwrite *0 with result
   0 *0                            \ and return its address

big-show ( addr -- )

   \ show first 20 and last 20 digits of the big number
   <big# big#s #big>               ( addr n )  \ returns string
   DUP . ."  digits" CR            \ show number of digits
   DUP 50 > IF
       OVER 20 TYPE ." ..."        \ show first 20 digits
       + 20 - 20 TYPE CR           \ show last 20 digits
   ELSE
       TYPE CR
   THEN

\ compute 5^(4^(3^2)) big 5 big 4 big 3 big 2 big^ big^ big^ big-show CR</lang>

and the output:

183231  digits
62060698786608744707...92256259918212890625

Fortran

Modern Fortran has no in-built facility for arbitrarily-sized numbers, but libraries are available.

FM library

Here is a solution using David M. Smith's FM library, available here.

<lang fortran>program bignum

   use fmzm
   implicit none
   type(im) :: a
   integer :: n
   
   call fm_set(50)
   a = to_im(5)**(to_im(4)**(to_im(3)**to_im(2)))
   n = to_int(floor(log10(to_fm(a))))
   call im_print(a / to_im(10)**(n - 19))
   call im_print(mod(a, to_im(10)**20))

end program</lang>

62060698786608744707
92256259918212890625

FreeBASIC

freebasic has it's own gmp static library. Here, a power function operates via a string and uinteger. <lang FreeBASIC>#Include once "gmp.bi" Dim Shared As Zstring * 100000000 outtext

Function Power(number As String,n As Uinteger) As String'automate precision

   #define dp 3321921
   Dim As __mpf_struct _number,FloatAnswer
   Dim As Ulongint ln=Len(number)*(n)*4
   If ln>dp Then ln=dp
   mpf_init2(@FloatAnswer,ln)
   mpf_init2(@_number,ln)
   mpf_set_str(@_number,number,10)
   mpf_pow_ui(@Floatanswer,@_number,n)
   gmp_sprintf( @outtext,"%." & Str(n) & "Ff",@FloatAnswer )
   Var outtxt=Trim(outtext)
   If Instr(outtxt,".") Then outtxt= Rtrim(outtxt,"0"):outtxt=Rtrim(outtxt,".")
   Return Trim(outtxt)

End Function

Extern gmp_version Alias "__gmp_version" As Zstring Ptr Print "GMP version ";*gmp_version Print

var ans=power("5",(4^(3^2))) Print Left(ans,20) + " ... "+Right(ans,20) Print "Number of digits ";Len(ans) Sleep</lang>

Output:

GMP version 5.1.1

62060698786608744707 ... 92256259918212890625
Number of digits  183231

Frink

Frink has built-in arbitrary-precision integers and all operations automatically promote to arbitrary precision when needed.

Fun Fact: The drastically faster arbitrary-precision integer operations that landed in Java 8 (for much faster multiplication, exponentiation, and toString) were taken from Frink's implementation and contributed to Java. Another fun fact is that it took employees from Java 11 years to integrate the improvements. <lang frink>a = 5^4^3^2 as = "$a" // Coerce to string println["Length=" + length[as] + ", " + left[as,20] + "..." + right[as,20]]</lang> This prints Length=183231, 62060698786608744707...92256259918212890625

Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.

In this page you can see the program(s) related to this task and their results.

GAP

<lang gap>n:=5^(4^(3^2));; s := String(n);; m := Length(s);

183231

s{[1..20]};

"62060698786608744707"

s{[m-19..m]};

"92256259918212890625"</lang>

Go

Using math/big's Int.Exp. <lang go>package main

import ( "fmt" "math/big" )

func main() { x := big.NewInt(2) x = x.Exp(big.NewInt(3), x, nil) x = x.Exp(big.NewInt(4), x, nil) x = x.Exp(big.NewInt(5), x, nil) str := x.String() fmt.Printf("5^(4^(3^2)) has %d digits: %s ... %s\n", len(str), str[:20], str[len(str)-20:], ) }</lang>

Output:

5^(4^(3^2)) has 183231 digits: 62060698786608744707 ... 92256259918212890625

Golfscript

<lang golfscript>5 4 3 2??? # Calculate 5^(4^(3^2)) `.. # Convert to string and make two copies

20

p # Print the last 20 digits ,p # Print the length</lang> The p command prints the top element from the stack, so the output of this program is just three lines:

"62060698786608744707"
"92256259918212890625"
183231

Groovy

Solution: <lang groovy>def bigNumber = 5G ** (4 ** (3 ** 2))</lang> Test: <lang groovy>def bigString = bigNumber.toString()

assert bigString[0..<20] == "62060698786608744707" assert bigString[-20..-1] == "92256259918212890625"

println bigString.size()</lang>

Output:

Haskell

Haskell comes with built-in support for arbitrary precision integers. The type of arbitrary precision integers is Integer. <lang haskell>main :: IO () main = do

 let y = show (5 ^ 4 ^ 3 ^ 2)
 let l = length y
 putStrLn
   ("5**4**3**2 = " ++
    take 20 y ++ "..." ++ drop (l - 20) y ++ " and has " ++ show l ++ " digits")</lang>

Output:

5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits

Hoon

<lang Hoon> =+ big=(pow 5 (pow 4 (pow 3 2))) =+ digits=(lent (skip |=(a/* ?:(=(a '.') & |)))) [digits (div big (pow 10 (sub digits 20))) (mod big (pow 10 20))] </lang>

Output:

[183.231 62.060.698.786.608.744.707 92.256.259.918.212.890.625]

As of 23 July 2016, the standard library lacks a base-10 logarithm, so the length is computed by pretty-printing the number and counting the length of the resulting string without grouping dots.

Icon and Unicon

Both Icon and Unicon have built-in support for bignums.

Note: It takes far longer to convert the result to a string than it does to do the computation itself. <lang icon>procedure main()

   x := 5^4^3^2
   write("done with computation")
   x := string(x)
   write("5 ^ 4 ^ 3 ^ 2 has ",*x," digits")
   write("The first twenty digits are ",x[1+:20])
   write("The last twenty digits are  ",x[0-:20])

end</lang>

Sample run:

->ap
done with computation
5 ^ 4 ^ 3 ^ 2 has 183231 digits
The first twenty digits are 62060698786608744707
The last twenty digits are  92256259918212890625
->

J

J has built-in support for extended precision integers. See also J:Essays/Extended Precision Functions. <lang j> Pow5432=: 5^4^3^2x

  Pow5432=: ^/ 5 4 3 2x                    NB. alternate J solution
  # ": Pow5432                             NB. number of digits

183231

  20 ({. , '...' , -@[ {. ]) ": Pow5432    NB. 20 first & 20 last digits

62060698786608744707...92256259918212890625</lang>

Java

Java library's BigInteger class provides support for arbitrary precision integers. <lang java>import java.math.BigInteger;

class IntegerPower {

   public static void main(String[] args) {
       BigInteger power = BigInteger.valueOf(5).pow(BigInteger.valueOf(4).pow(BigInteger.valueOf(3).pow(2).intValueExact()).intValueExact());
       String str = power.toString();
       int len = str.length();
       System.out.printf("5**4**3**2 = %s...%s and has %d digits%n",
               str.substring(0, 20), str.substring(len - 20), len);
   }

}</lang>

Output:

5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits

JavaScript

The ECMA-262 JavaScript standard now defines a BigInt [3] type for for abitrary precision integers.

BigInt is already implemented by Chrome and Firefox, but not yet by Explorer or Safari. <lang javacript>>>> const y = (5n**4n**3n**2n).toString(); >>> console.log(`5**4**3**2 = ${y.slice(0,20)}...${y.slice(-20)} and has ${y.length} digits`); 5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits</lang>

jq

Works with gojq, the Go implementation of jq

There is a BigInt.jq library for jq, but gojq, the Go implementation of jq, supports unbounded-precision integer arithmetic, so the output shown below is that produced by gojq. <lang jq> def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);

Output:

62060698786608744707
92256259918212890625
183231

Julia

Julia includes built-in support for arbitrary-precision arithmetic using the GMP (integer) and GNU MPFR (floating-point) libraries, wrapped by the built-in BigInt and BigFloat types, respectively.

<lang julia>julia> @elapsed bigstr = string(BigInt(5)^4^3^2) 0.017507363

julia> length(bigstr) 183231

julia> bigstr[1:20] "62060698786608744707"

julia> bigstr[end-20:end] "892256259918212890625"</lang>

Klong

   n::$5^4^3^2
   .p("5^4^3^2 = ",(20#n),"...",((-20)#n)," and has ",($#n)," digits")

Output:

5^4^3^2 = 62060698786608744707...92256259918212890625 and has 183231 digits

Kotlin

Translation of: Java

<lang scala>import java.math.BigInteger

fun main(args: Array<String>) {

   val x = BigInteger.valueOf(5).pow(Math.pow(4.0, 3.0 * 3.0).toInt())
   val y = x.toString()
   val len = y.length
   println("5^4^3^2 = ${y.substring(0, 20)}...${y.substring(len - 20)} and has $len digits")

}</lang>

Output:

5^4^3^2 = 62060698786608744707...92256259918212890625 and has 183231 digits

Lasso

Interestingly, we have to define our own method for integer powers. <lang lasso>define integer->pow(factor::integer) => {

   #factor <= 0
       ? return 0

   local(retVal) = 1
   
   loop(#factor) => { #retVal *= self }

   return #retVal

}

local(bigint) = string(5->pow(4->pow(3->pow(2))))

bigint->sub(1,20) + ` ... ` + #bigint->sub(#bigint->size - 19)

"\n" `Number of digits: ` + #bigint->size</lang>

Output:

62060698786608744707 ... 92256259918212890625
Number of digits: 183231

Liberty BASIC

Interestingly this takes a LONG time in LB.

It takes however only seconds in RunBASIC, which is written by the same author, shares most of LB's syntax, and is based on later Smalltalk implementation.

Note the brackets are needed to enforce the desired order of exponentiating. <lang lb>a$ = str$( 5^(4^(3^2))) print len( a$) print left$( a$, 20); "......"; right$( a$, 20)</lang>

Output:

183231
62060698786608744707......92256259918212890625

Lua

Pure/native off-the-shelf Lua does not include support for arbitrary-precision arithmetic. However, there are a number of optional libraries that do, including several from an author of the language itself - one of which this example will use. (citing the "..may be used instead" allowance) <lang lua>bc = require("bc") -- since 5$=5^4$, and IEEE754 can handle 4$, this would be sufficient: -- n = bc.pow(bc.new(5), bc.new(4^3^2)) -- but for this task: n = bc.pow(bc.new(5), bc.pow(bc.new(4), bc.pow(bc.new(3), bc.new(2)))) s = n:tostring() print(string.format("%s...%s (%d digits)", s:sub(1,20), s:sub(-20,-1), #s))</lang>

Output:

62060698786608744707...92256259918212890625 (183231 digits)

Maple

Maple supports large integer arithmetic natively. <lang Maple> > n := 5^(4^(3^2)): > length( n ); # number of digits

> s := convert( n, 'string' ): > s[ 1 .. 20 ], s[ -20 .. -1 ]; # extract first and last twenty digits

            "62060698786608744707", "92256259918212890625"

</lang> In the Maple graphical user interface it is also possible to set things up so that only (say) the first and last 20 digits of a large integer are displayed explicitly. This is done as follows. <lang Maple> > interface( elisiondigitsbefore = 20, elisiondigitsafter = 20 ): > 5^(4^(3^2)):

            62060698786608744707[...183191 digits...]92256259918212890625

</lang>

Mathematica / Wolfram Language

Mathematica can handle arbitrary precision integers on almost any size without further declarations. To view only the first and last twenty digits: <lang Mathematica>s:=ToString[5^4^3^2]; Print[StringTake[s,20]<>"..."<>StringTake[s,-20]<>" ("<>ToString@StringLength@s<>" digits)"];</lang>

Output:

62060698786608744707...92256259918212890625 (183231 digits)

MATLAB

Using the Variable Precision Integer library this task is accomplished thusly: <lang MATLAB>>> answer = vpi(5)^(vpi(4)^(vpi(3)^vpi(2))); >> numDigits = order(answer) + 1

numDigits =

>> [sprintf('%d',leadingdigit(answer,20)) '...' sprintf('%d',trailingdigit(answer,20))] %First and Last 20 Digits

ans =

62060698786608744707...92256259918212890625</lang>

Maxima

<lang maxima>block([s, n], s: string(5^4^3^2), n: slength(s), print(substring(s, 1, 21), "...", substring(s, n - 19)), n); /* 62060698786608744707...92256259918212890625 183231 */</lang>

Nanoquery

Integer values are arbitrary-precision by default in Nanoquery. <lang Nanoquery>value = str(5^(4^(3^2)))

first20 = value.substring(0,20) last20 = value.substring(len(value) - 20)

println "The first twenty digits are " + first20 println "The last twenty digits are " + last20

if (first20 = "62060698786608744707") && (last20 = "92256259918212890625") println "\nThese digits are correct.\n" end

println "The result is " + len(str(value)) + " digits long"</lang>

Output:

The first twenty digits are 62060698786608744707
The last twenty digits are 92256259918212890625

These digits are correct.

The result is 183231 digits long

Nemerle

Translation of: C#

<lang Nemerle>using System.Console; using System.Numerics; using System.Numerics.BigInteger;

module BigInt {

   Main() : void
   {
       def n = Pow(5, Pow(4, Pow(3, 2) :> int) :> int).ToString();
       def len = n.Length;
       def first20 = n.Substring(0, 20);
       def last20 = n.Substring(len - 20, 20);
       
       assert (first20 == "62060698786608744707", "High order digits are incorrect");
       assert (last20 == "92256259918212890625", "Low order digits are incorrect");
       assert (len == 183231, "Result contains wrong number of digits");
       
       WriteLine("Result: {0} ... {1}", first20, last20);
       WriteLine($"Length of result: $len digits");
   }

}</lang> Output:

Result: 62060698786608744707 ... 92256259918212890625
Length of result: 183231 digits

=

NewLisp

No built-in big integer exponentiation

(define (exp-big x n) (setq x (bigint x)) (let (y 1L) (if (= n 0) 1L (while (> n 1) (if (odd? n) (setq y (* x y))) (setq x (* x x) n (/ n 2))) (* x y))))

task

(define (test) (local (res) ; drop the "L" at the end (setq res (0 (- (length res) 1) (string (exp-big 5 (exp-big 4 (exp-big 3 2)))))) (println "The result has: " (length res) " digits") (println "First 20 digits: " (0 20 res)) (println "Last 20 digits: " (-20 20 res)))) </lang>

Output:

The result has:  183231 digits
First 20 digits: 62060698786608744707
Last 20 digits:  92256259918212890625

NetRexx

Using Java's BigInteger Class

<lang NetRexx>/* NetRexx */

options replace format comments java crossref savelog symbols

import java.math.BigInteger

numeric digits 30 -- needed to report the run-time

nanoFactor = 10 ** 9

t1 = System.nanoTime x = BigInteger.valueOf(5) x = x.pow(BigInteger.valueOf(4).pow(BigInteger.valueOf(3).pow(2).intValue()).intValue()) n = Rexx(x.toString) t2 = System.nanoTime td = t2 - t1 say "Run time in seconds:" td / nanoFactor say

check = "62060698786608744707...92256259918212890625" sample = n.left(20)"..."n.right(20)

say "Expected result:" check say " Actual result:" sample say " digits:" n.length say

if check = sample then

 say "Result confirmed"

else

 say "Result does not satisfy test"

return</lang>

Output:

Run time in seconds: 6.696671 
 
Expected result: 62060698786608744707...92256259918212890625 
  Actual result: 62060698786608744707...92256259918212890625 
         digits: 183231 
 
Result confirmed

Using Java's BigDecimal Class

<lang NetRexx>/* NetRexx */

options replace format comments java crossref savelog symbols

import java.math.BigDecimal

numeric digits 30 -- needed to report the run-time

nanoFactor = 10 ** 9

t1 = System.nanoTime x = BigDecimal.valueOf(5) x = x.pow(BigDecimal.valueOf(4).pow(BigDecimal.valueOf(3).pow(2).intValue()).intValue()) n = Rexx(x.toString) t2 = System.nanoTime td = t2 - t1 say "Run time in seconds:" td / nanoFactor say

check = "62060698786608744707...92256259918212890625" sample = n.left(20)"..."n.right(20)

say "Expected result:" check say " Actual result:" sample say " digits:" n.length say

if check = sample then

 say "Result confirmed"

else

 say "Result does not satisfy test"

return</lang>

Output:

Run time in seconds: 7.103424 
 
Expected result: 62060698786608744707...92256259918212890625 
  Actual result: 62060698786608744707...92256259918212890625 
         digits: 183231 
 
Result confirmed

Using NetRexx Built-In Math

Like Rexx, NetRexx comes with built-in support for numbers that can be manually set to very large values of precision. Compared to the two methods shown above however, the performance is extremely poor.

Note

Translation of: REXX

<lang NetRexx>/* NetRexx */

options replace format comments java crossref savelog symbols

/* precision must be set manually */

numeric digits 190000

nanoFactor = 10 ** 9

t1 = System.nanoTime n = 5 ** (4 ** (3 ** 2)) t2 = System.nanoTime td = t2 - t1 say "Run time in seconds:" td / nanoFactor say

check = "62060698786608744707...92256259918212890625" sample = n.left(20)"..."n.right(20)

say "Expected result:" check say " Actual result:" sample say " digits:" n.length say

if check = sample then

 say "Result confirmed"

else

 say "Result does not satisfy test"</lang>

Output:

Run time in seconds: 719.660995

Expected result: 62060698786608744707...92256259918212890625
  Actual result: 62060698786608744707...92256259918212890625
         digits: 183231

Result confirmed

Nim

Library: bigints

<lang nim>import bigints

var x = 5.pow 4.pow 3.pow 2 var s = $x

echo s[0..19] echo s[s.high - 19 .. s.high] echo s.len</lang> Output:

62060698786608744707
92256259918212890625
183231

OCaml

<lang ocaml>open Num open Str open String

let () =

 let answer = (Int 5) **/ (Int 4) **/ (Int 3) **/ (Int 2) in
 let answer_string = string_of_num answer in
 Printf.printf "has %d digits: %s ... %s\n"
               (length answer_string)
               (first_chars answer_string 20)
               (last_chars answer_string 20)</lang>

A more readable program can be obtained using Delimited Overloading: <lang ocaml>let () =

 let answer = Num.(5**4**3**2) in
 let s = Num.(to_string answer) in
 Printf.printf "has %d digits: %s ... %s\n"
   (String.length s) (Str.first_chars s 20) (Str.last_chars s 20)</lang>

Output:

has 183231 digits: 62060698786608744707 ... 92256259918212890625

Oforth

Oforth handles arbitrary precision integers :

<lang Oforth>import: mapping

5 4 3 2 pow pow pow >string dup left( 20 ) . dup right( 20 ) . size . </lang>

Output:

62060698786608744707 92256259918212890625 183231

Ol

<lang scheme> (define x (expt 5 (expt 4 (expt 3 2)))) (print

  (div x (expt 10 (- (log 10 x) 20)))
  "..."
  (mod x (expt 10 20)))

(print "totally digits: " (log 10 x)) </lang>

Output:

62060698786608744707...92256259918212890625
totally digits: 183231

ooRexx

Translation of: REXX

<lang ooRexx> --REXX program to show arbitrary precision integers. numeric digits 200000 check = '62060698786608744707...92256259918212890625'

start = .datetime~new n = 5 ** (4 ** (3**2)) time = .datetime~new - start say 'elapsed time for the calculation:' time say sampl = left(n, 20)"..."right(n, 20)

say ' check:' check say 'Sample:' sampl say 'digits:' length(n) say

if check=sampl then say 'passed!'

              else say 'failed!'

</lang>

Output:

prompt$ rexx rexx-arbitrary.rexx
elapsed time for the calculation: 00:00:45.373140

 check: 62060698786608744707...92256259918212890625
Sample: 62060698786608744707...92256259918212890625
digits: 183231

passed!

Oz

<lang oz>declare

 Pow5432 = {Pow 5 {Pow 4 {Pow 3 2}}}
 S = {Int.toString Pow5432}
 Len = {Length S}

in

 {System.showInfo
  {List.take S 20}#"..."#
  {List.drop S Len-20}#" ("#Len#" Digits)"}</lang>

Output:

62060698786608744707...92256259918212890625 (183231 Digits)

PARI/GP

PARI/GP natively supports integers of arbitrary size, so one could just use N=5^4^3^2. But this would be foolish (using a lot of unneeded memory) if the task is to get just the number of, and the first and last twenty digits. The number of and the leading digits are given as 1 + the integer part, resp. 10^(fractional part + offset), of the logarithm to base 10 (not as log(N) with N=A^B, but as B*log(A); one needs at least 20 correct decimals of the log, on 64 bit machines the default precision is 39 digits, but on 32 bit architecture one should set default(realprecision,30) to be on the safe side). To get the trailing digits, one would use modular exponentiation which is also built-in and very efficient even for extremely huge exponents: <lang parigp>num_first_last_digits(a=5,b=4^3^2,n=20)={ my(L = b*log(a)/log(10), m=Mod(a,10^n)^b); [L\1+1, 10^frac(L)\10^(1-n), lift(m)] \\ where x\y = floor(x/y) but more efficient } print("Length, first and last 20 digits of 5^4^3^2: ", num_first_last_digits()) \\ uses default values a=5, b=4^3^2, n=20</lang>

Output:

Length, first and last 20 digits of 5^4^3^2: [183231, 62060698786608744707, 92256259918212890625]

If an integer is already given, then logint(N,10)+1 is the most efficient way to get its number of digits.

An alternate but much slower method for counting decimal digits is #Str(n). Note that sizedigit is not exact—in particular, it may be off by one (thus the function below). <lang parigp>digits(x)={ my(s=sizedigit(x)-1); if(x<10^s,s,s+1) };

N=5^(4^(3^2)); [precision(N*1.,20), Mod(N,10^20), digits(N)]</lang>

Output:

[6.20606987866087447074832055728 E183230, Mod(92256259918212890625, 100000000000000000000), 183231]

Pascal

Works with: Free_Pascal

Library: math

Library: GMP

FreePascal comes with a header unit for gmp. Starting from the C program, this is a Pascal version: <lang pascal>program GMP_Demo;

uses

 math, gmp;

var

 a:   mpz_t;
 out: pchar;
 len: longint;
 i:   longint;

begin

 mpz_init_set_ui(a, 5);
 mpz_pow_ui(a, a, 4 ** (3 ** 2));
 len := mpz_sizeinbase(a, 10);
 writeln('GMP says size is: ', len);
 out := mpz_get_str(NIL, 10, a);
 writeln('Actual size is:   ', length(out));
 write('Digits: ');
 for i := 0 to 19 do
   write(out[i]);
 write ('...');
 for i := len - 20 to len do
   write(out[i]);
 writeln;

end.</lang>

Output:

GMP says size is: 183231
Actual size is:   183231
Digits: 62060698786608744707...92256259918212890625

Perl

Perl's Math::BigInt core module handles big integers: <lang perl>use Math::BigInt; my $x = Math::BigInt->new('5') ** Math::BigInt->new('4') ** Math::BigInt->new('3') ** Math::BigInt->new('2'); my $y = "$x"; printf("5**4**3**2 = %s...%s and has %i digits\n", substr($y,0,20), substr($y,-20), length($y));</lang> You can enable "transparent" big integer support by enabling the bigint pragma: <lang perl>use bigint; my $x = 5**4**3**2; my $y = "$x"; printf("5**4**3**2 = %s...%s and has %i digits\n", substr($y,0,20), substr($y,-20), length($y));</lang>

Math::BigInt is very slow. Perl 5.10 was about 120 times slower than Ruby 1.9.2 (on one computer); Perl used more than one minute, but Ruby used less than one second.

Output:

<lang perl>$ time perl transparent-bigint.pl 5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits

   1m4.28s real     1m4.30s user     0m0.00s system</lang>

Phix

Library: Phix/basics

Library: Phix/mpfr

include mpfr.e
atom t0 = time()
mpz res = mpz_init()
mpz_ui_pow_ui(res,5,power(4,power(3,2)))
string s = shorten(mpz_get_str(res)),
       e = elapsed(time()-t0)
printf(1,"5^4^3^2 = %s (%s)\n", {s,e})

Output:

5^4^3^2 = 62060698786608744707...92256259918212890625 (183,231 digits) (0.1s)

PHP

PHP has two separate arbitrary-precision integer services.

The first is the BC library.[4] It represents the integers as strings, so may not be very efficient. The advantage is that it is more likely to be included with PHP. <lang php><?php $y = bcpow('5', bcpow('4', bcpow('3', '2'))); printf("5**4**3**2 = %s...%s and has %d digits\n", substr($y,0,20), substr($y,-20), strlen($y)); ?></lang>

Output:

5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits

The second is the GMP library.[5] It represents the integers as an opaque type, so may be faster. However, it is less likely to be compiled into your version of PHP (it isn't compiled into mine).

PicoLisp

<lang PicoLisp>(let L (chop (** 5 (** 4 (** 3 2))))

  (prinl (head 20 L) "..." (tail 20 L))
  (length L) )</lang>

Output:

62060698786608744707...92256259918212890625
-> 183231

Pike

<lang Pike>> string res = (string)pow(5,pow(4,pow(3,2))); > res[..19] == "62060698786608744707"; Result: 1 > res[<19..] == "92256259918212890625"; Result: 1 > sizeof(result); Result: 183231</lang>

PowerShell

<lang PowerShell># Perform calculation $BigNumber = [BigInt]::Pow( 5, [BigInt]::Pow( 4, [BigInt]::Pow( 3, 2 ) ) )

Display first and last 20 digits

$BigNumberString = [string]$BigNumber $BigNumberString.Substring( 0, 20 ) + "..." + $BigNumberString.Substring( $BigNumberString.Length - 20, 20 )

Display number of digits

$BigNumberString.Length</lang>

Output:

62060698786608744707...92256259918212890625
183231

Prolog

Works with: SWI-Prolog version 6.6

<lang prolog> task(Length) :-

   N is 5^4^3^2,

   number_codes(N, Codes),
   append(`62060698786608744707`, _,  Codes),
   append(_, `92256259918212890625`, Codes),
   
   length(Codes, Length).

</lang>

Query like so:

<lang prolog> ?- task(N). N = 183231 ; false. </lang>

PureBasic

PureBasic has in its current version (today 4.50) no internal support for large numbers, but there are several free libraries for this.

Using Decimal.pbi, e.g. the same included library as in Long multiplication#PureBasic, this task is solved as below. <lang PureBasic>IncludeFile "Decimal.pbi"

- Declare the variables that will be used

Define.Decimal *a Define n, L$, R$, out$, digits.s

- 4^3^2 is withing 32 bit range, so normal procedures can be used

n=Pow(4,Pow(3,2))

- 5^n is larger then 31^2, so the same library call as in the "Long multiplication" task is used

a=PowerDecimal(IntegerToDecimal(5),IntegerToDecimal(n))

- Convert the large number into a string & present the results

out$=DecimalToString(*a) L$ = Left(out$,20) R$ = Right(out$,20) digits=Str(Len(out$)) out$="First 20 & last 20 chars of 5^4^3^2 are;"+#CRLF$+L$+#CRLF$+R$+#CRLF$ out$+"and the result is "+digits+" digits long."

MessageRequester("Arbitrary-precision integers, PureBasic",out$)</lang>

Python

Python comes with built-in support for arbitrary precision integers. The type of arbitrary precision integers is long in Python 2.x (overflowing operations on int's are automatically converted into long's), and int in Python 3.x. <lang python>>>> y = str( 5**4**3**2 ) >>> print ("5**4**3**2 = %s...%s and has %i digits" % (y[:20], y[-20:], len(y))) 5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits</lang>

Quackery

As a dialogue in the Quackery shell. (REPL)

 > quackery

Welcome to Quackery.

Enter "leave" to leave the shell.

/O> 5 4 3 2 ** ** **
... number$ dup 20 split swap echo$
... say "..." -20 split echo$ drop cr
... size echo say " digits" cr
... 
62060698786608744707...92256259918212890625
183231 digits

Stack empty.

/O>

R

R does not come with built-in support for arbitrary precision integers, but it can be implemented with the GMP library (there is also an interface to bc). <lang R>library(gmp) large=pow.bigz(5,pow.bigz(4,pow.bigz(3,2))) largestr=as.character(large) cat("first 20 digits:",substr(largestr,1,20),"\n",

   "last 20 digits:",substr(largestr,nchar(largestr)-19,nchar(largestr)),"\n",
   "number of digits: ",nchar(largestr),"\n")</lang>

Output:

first 20 digits: 62060698786608744707 
 last 20 digits: 92256259918212890625 
 number of digits:  183231

Racket

<lang Racket>#lang racket

(define answer (number->string (foldr expt 1 '(5 4 3 2)))) (define len (string-length answer))

(printf "Got ~a digits~n" len) (printf "~a ... ~a~n"

       (substring answer 0 20)
       (substring answer (- len 20) len))

</lang>

Output:

Got 183231 digits
62060698786608744707 ... 92256259918212890625

Raku

(formerly Perl 6)

Works with: Rakudo version 2015.12

<lang perl6>given ~[**] 5, 4, 3, 2 {

  say "5**4**3**2 = {.substr: 0,20}...{.substr: *-20} and has {.chars} digits";

}</lang>

Output:

5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits

REXX

REXX comes with built-in support for fixed precision integers that can be manually set to a large value of precision (digits).
Most REXXes have a practical limit of around eight million bytes, but that is mostly an underlying limitation of addressing virtual storage.

manual setting of decimal digits

Note: both REXX versions (below) don't work with:

PC/REXX
Personal REXX

as those REXX versions have a practical maximum of around 3,700 or less for numeric digits (officially, it's 4K).

The 3,700 limit is based on the setting of RXISA, program size, and the amount of storage used by REXX variables.

Both (below) REXX programs have been tested with:

PC/REXX (can't execute correctly)
Personal REXX (can't execute correctly)
Regina REXX
R4
ROO
ooRexx (tested by Walter Pachl)

<lang rexx>/*REXX program calculates and demonstrates arbitrary precision numbers (using powers). */ numeric digits 200000 /*two hundred thousand decimal digits. */

   # = 5 ** (4 ** (3 ** 2) )                    /*calculate multiple exponentiations.  */

true=62060698786608744707...92256259918212890625 /*what answer is supposed to look like.*/ rexx= left(#, 20)'...'right(#, 20) /*the left and right 20 decimal digits.*/

say ' true:' true /*show what the "true" answer is. */ say ' REXX:' rexx /* " " " REXX " " */ say 'digits:' length(#) /* " " " length of answer is. */ say if true == rexx then say 'passed!' /*either it passed, ··· */

                 else say 'failed!'             /*    or it didn't.                    */
                                                /*stick a fork in it,  we're all done. */</lang>

output:

 check: 62060698786608744707...92256259918212890625
sample: 62060698786608744707...92256259918212890625
digits: 183231

passed!

automatic setting of decimal digits

<lang rexx>/*REXX program calculates and demonstrates arbitrary precision numbers (using powers). */ numeric digits 5 /*just use enough digits for 1st time. */

                 #=5** (4** (3** 2) )           /*calculate multiple exponentiations.  */

parse var # 'E' pow . /*POW might be null, so N is OK. */

if pow\== then do /*general case: POW might be < zero.*/

                 numeric digits  abs(pow) + 9   /*recalculate with more decimal digits.*/
                 #=5** (4** (3** 2) )           /*calculate multiple exponentiations.  */
                 end                            /* [↑]  calculation is the real McCoy. */

true=62060698786608744707...92256259918212890625 /*what answer is supposed to look like.*/ rexx= left(#, 20)'...'right(#, 20) /*the left and right 20 decimal digits.*/

say ' true:' true /*show what the "true" answer is. */ say ' REXX:' rexx /* " " " REXX " " */ say 'digits:' length(#) /* " " " length of answer is. */ say if true == rexx then say 'passed!' /*either it passed, ··· */

                 else say 'failed!'             /*    or it didn't.                    */
                                                /*stick a fork in it,  we're all done. */</lang>

output is the same as the 1^st REXX version.

Ruby

Ruby comes with built-in support for arbitrary precision integers.

<lang ruby>irb(main):001:0> y = ( 5**4**3**2 ).to_s puts "5**4**3**2 = #{y[0..19]}...#{y[-20..-1]} and has #{y.length} digits" </lang>

Output:

5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits

Run BASIC

<lang runbasic>x$ = str$( 5^(4^(3^2))) print "Length:";len( x$) print left$( x$, 20); "......"; right$( x$, 20)</lang>

Output:

Length:183231
62060698786608744707......92256259918212890625

Rust

This is accomplished via the `num` crate. This used to be part of the standard library, but was relegated to an external crate when Rust hit 1.0. It is still owned and maintained by members of the Rust core team and is the de-facto library for numerical generics and arbitrary precision arithmetic.

<lang rust>extern crate num; use num::bigint::BigUint; use num::FromPrimitive; use num::pow::pow;

fn main() {

   let big = BigUint::from_u8(5).unwrap();
   let answer_as_string = format!("{}", pow(big,pow(4,pow(3,2))));
   
     // The rest is output formatting.
   let first_twenty: String = answer_as_string.chars().take(20).collect();
   let last_twenty_reversed: Vec<char> = answer_as_string.chars().rev().take(20).collect();
   let last_twenty: String = last_twenty_reversed.into_iter().rev().collect();
   println!("Number of digits: {}", answer_as_string.len());
   println!("First and last digits: {:?}..{:?}", first_twenty, last_twenty);

}</lang>

Output:

Number of digits: 183231
First and last digits: "62060698786608744707".."92256259918212890625"

Sather

<lang sather>class MAIN is

 main is
   r:INTI;
   p1 ::= "62060698786608744707";
   p2 ::= "92256259918212890625";

   -- computing 5^(4^(3^2)), it could be written
   -- also e.g. (5.inti)^((4.inti)^((3.inti)^(2.inti)))
   r  := (3.pow(2)).inti;
   r  := (4.inti).pow(r);
   r  := (5.inti).pow(r);

   sr ::= r.str; -- string rappr. of the number
   if sr.head(p1.size) = p1
      and sr.tail(p2.size) = p2 then
        #OUT + "result is ok..\n";
   else
        #OUT + "oops\n";
   end;
   #OUT + "# of digits: " + sr.size + "\n";
 end;

end;</lang>

Output:

result is ok..
# of digits: 183231

Scala

Scala does not come with support for arbitrary precision integers powered to arbitrary precision integers, except if performed on a module. It can use arbitrary precision integers in other ways, including powering them to 32-bits integers. <lang scala>scala> BigInt(5) modPow (BigInt(4) pow (BigInt(3) pow 2).toInt, BigInt(10) pow 20) res21: scala.math.BigInt = 92256259918212890625

scala> (BigInt(5) pow (BigInt(4) pow (BigInt(3) pow 2).toInt).toInt).toString res22: String = 6206069878660874470748320557284679309194219265199117173177383244 78446890420544620839553285931321349485035253770303663683982841794590287939217907 89641300156281305613064874236198955114921296922487632406742326659692228562195387 46210423235340883954495598715281862895110697243759768434501295076608139350684049 01191160699929926568099301259938271975526587719565309995276438998093283175080241 55833224724855977970015112594128926594587205662421861723789001208275184293399910 13912158886504596553858675842231519094813553261073608575593794241686443569888058 92732524316323249492420512640962691673104618378381545202638771401061171968052873 21414945463925055899307933774904078819911387324217976311238875802878310483037255 33789567769926391314746986316354035923183981697660495275234703657750678459919... scala> res22 take 20 res23: String = 62060698786608744707

scala> res22 length res24: Int = 183231

scala> </lang>

Scheme

R⁴RS and R⁵RS encourage, and R⁶RS requires, that exact integers be of arbitrary precision. <lang scheme>(define x (expt 5 (expt 4 (expt 3 2)))) (define y (number->string x)) (define l (string-length y)) (display (string-append "5**4**3**2 = " (substring y 0 20) "..." (substring y (- l 20) l) " and has " (number->string l) " digits")) (newline)</lang>

Output:

5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits

Seed7

<lang seed7>$ include "seed7_05.s7i";

 include "bigint.s7i";

const proc: main is func

 local
   var bigInteger: fiveToThePowerOf262144 is 5_ ** 4 ** 3 ** 2;
   var string: numberAsString is str(fiveToThePowerOf262144);
 begin
   writeln("5**4**3**2 = " <& numberAsString[..20] <&
           "..." <& numberAsString[length(numberAsString) - 19 ..]);
   writeln("decimal digits: " <& length(numberAsString));
 end func;</lang>

Output:

5**4**3**2 = 62060698786608744707...92256259918212890625
decimal digits: 183231

Sidef

<lang ruby>var x = 5**(4**(3**2)); var y = x.to_s; printf("5**4**3**2 = %s...%s and has %i digits\n", y.ft(0,19), y.ft(-20), y.len);</lang>

Output:

5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits

SIMPOL

This example is incomplete. Number of digits in result not given. Please ensure that it meets all task requirements and remove this message.

SIMPOL supports arbitrary precision integers powered to arbitrary precision integers. This is the only integer data type in SIMPOL. SIMPOL supports conversion from its integer data type to other formats when calling external library functions. <lang simpol>constant FIRST20 "62060698786608744707" constant LAST20 "92256259918212890625"

function main()

 integer i
 string s, s2

 i = .ipower(5, .ipower(4, .ipower(3, 2)))
 s2 = .tostr(i, 10)
 if .lstr(s2, 20) == FIRST20 and .rstr(s2, 20) == LAST20
   s = "Success! The integer matches both the first 20 and the last 20 digits. There are " + .tostr(.len(s2), 10) + " digits in the result.{d}{a}"
 else
   s = ""
   if .lstr(s2, 20) != FIRST20 
     s = "Failure! The first 20 digits are: " + .lstr(s2, 20) + " but they should be: " + FIRST20 + "{d}{a}"
   end if
   if .rstr(s2, 20) != LAST20 
     s = s + "Failure! The first 20 digits are: " + .lstr(s2, 20) + " but they should be: " + LAST20 + "{d}{a}"
   end if
 end if

end function s</lang>

Smalltalk

This code in Squeak Smalltalk ¹ returns a string containing the first 20 digits, last 20 digits and length of the result.

A very simple approach: <lang smalltalk>|num| num := (5 raisedTo: (4 raisedTo: (3 raisedTo: 2))) asString. Transcript

  show: (num first: 20), '...', (num last: 20); cr;
  show: 'digits: ', num size asString.</lang>

On a Transcript window:

62060698786608744707...92256259918212890625
digits: 183231

And a more advanced one: <lang smalltalk>|num numstr| num := (2 to: 5) fold: [:exp :base| base raisedTo: exp]. numstr := num asString. '<1s>...<2s> digits:<3p>'

  expandMacrosWith: (numstr first: 20)
  with: (numstr last: 20)
  with: numstr size.</lang>

Output:

'62060698786608744707...92256259918212890625  digits: 183231'

Note 1) should work in all Smalltalk dialects; tried in Smalltalk/X and VisualWorks.

SPL

<lang spl>t = #.str(5^(4^(3^2))) n = #.size(t)

.output(n," digits")
.output(#.mid(t,1,20),"...",#.mid(t,n-19,20))</lang>

Output:

183231 digits
62060698786608744707...92256259918212890625

Standard ML

<lang sml>let

 val answer = IntInf.pow (5, IntInf.toInt (IntInf.pow (4, IntInf.toInt (IntInf.pow (3, 2)))))
 val s = IntInf.toString answer
 val len = size s

in

 print ("has " ^ Int.toString len ^ " digits: " ^
        substring (s, 0, 20) ^ " ... " ^
        substring (s, len-20, 20) ^ "\n")

end;</lang> it took too long to run

mLite

mLite does not have a logarithm function so one was constructed (see fun log10) <lang sml> fun ntol (0, x) = if len x < 1 then [0] else x

      | (n, x) = ntol (n div 10, (n mod 10) :: x)
      | n      = ntol (n, [])

and powers_of_10 9 = 1000000000

              | 8 = 100000000
              | 7 = 10000000
              | 6 = 1000000
              | 5 = 100000
              | 4 = 10000
              | 3 = 1000
              | 2 = 100
              | 1 = 10
              | 0 = 1

and size (c, 0) = c

      | (c, n > 9999999999) = size (c + 10, trunc (n / 10000000000))
      | (c, n)              = size (c +  1, trunc (n / 10))
      | n                   = size (     0, trunc (n / 10))

and makeVisible L = map (fn x = if int x then chr (x + 48) else x) L and log10 (n, 0, x) = ston ` implode ` makeVisible ` rev x

       | (n, c, x) =
           let val n' = n^10;
             val size_n' = size n'
           in 
             log10 (n' / powers_of_10 size_n', c - 1, size_n' :: x)

end

       | (n, c) =
           let
             val size_n = size n
           in
             log10 (n / 10^size_n, c, #"." :: rev (ntol size_n) @ [])
           end

val fourThreeTwo = 4^3^2; val fiveFourThreeTwo = 5^fourThreeTwo;

val digitCount = trunc (log10(5,6) * fourThreeTwo + 0.5); print "Count = "; println digitCount;

val end20 = fiveFourThreeTwo mod (10^20); print "End 20 = "; println end20;

val top20 = fiveFourThreeTwo div (10^(digitCount - 20)); print "Top 20 = "; println top20; </lang> Output

 Count = 183231
 End 20 = 92256259918212890625
 Top 20 = 62060698786608744707

Took 1 hour and 9 minutes to run (AMD A6, Windows 10)

Stata

Stata does not have builtin support for arbitrary-precision integers. However, since version 16 Stata has builtin support for Python, so arbitrary-precision integers are readily available from a Python prompt within Stata.

Tcl

Tcl supports arbitrary precision integers (and an exponentiation operator) from 8.5 onwards.

Works with: Tcl version 8.5

<lang tcl>set bigValue [expr {5**4**3**2}] puts "5**4**3**2 has [string length $bigValue] digits" if {[string match "62060698786608744707*92256259918212890625" $bigValue]} {

   puts "Value starts with 62060698786608744707, ends with 92256259918212890625"

} else {

   puts "Value does not match 62060698786608744707...92256259918212890625"

}</lang>

Output:

5**4**3**2 has 183231 digits
Value starts with 62060698786608744707, ends with 92256259918212890625

TXR

<lang txr>@(bind (f20 l20 ndig)

      @(let* ((str (tostring (expt 5 4 3 2)))
              (len (length str)))
         (list [str :..20] [str -20..:] len)))

@(bind f20 "62060698786608744707") @(bind l20 "92256259918212890625") @(output) @f20...@l20 ndigits=@ndig @(end)</lang>

Output:

62060698786608744707...92256259918212890625
ndigits=183231

Ursa

The Ursa standard library provides the module unbounded_int which contains the definition of the unbounded_int type. In Cygnus/X Ursa, unbounded_int is essentially a wrapper for java.math.BigInteger

Usage

<lang ursa>import "unbounded_int" decl unbounded_int x x.set ((x.valueof 5).pow ((x.valueof 4).pow ((x.valueof 3).pow 2)))

decl string first last xstr set xstr (string x)

get the first twenty digits

decl int i for (set i 0) (< i 20) (inc i) set first (+ first xstr) end for

get the last twenty digits
for (set i (- (size xstr) 20)) (< i (size xstr)) (inc i) set last (+ last xstr) end for
out "the first and last digits of 5^(4^(3^2)) are " first "..." console out last " (the result was " (size xstr) " digits long)" endl endl console
if (and (and (= first "62060698786608744707") (= last "92256259918212890625")) (= (size xstr) 183231)) out "(pass)" endl console else out "FAIL" endl console end if</lang>
Output

Output:
the first and last digits of 5^(4^(3^2)) are 62060698786608744707...92256259918212890625 (the result was 183231 digits long) (pass)
Ursala
There are no infix arithmetic operators in the language, but there is a power function in the bcd library, which is part of the standard distribution from the home site.
There is no distinction between ordinary and arbitrary precision integers, but the binary converted decimal representation used here is more efficient than the usual binary representation in calculations that would otherwise be dominated by the conversion to decimal output. <lang Ursala>#import std
import nat

import bcd
show+
main = <.@ixtPX take/$20; ^|T/~& '...'--@x,'length: '--@h+ %nP+ length@t>@h %vP power=> <5_,4_,3_,2_></lang> With this calculation taking about a day to run, correct results are attainable but not performant.
62060698786608744707...92256259918212890625 length: 183231
Visual Basic .NET
Translation of: C#
Library: System.Numerics
Addressing the issue of the BigInteger.Pow() function having the exponent value limited to Int32.MaxValue (2147483647), here are a couple of alternative implementations using a BigInteger for the exponent. <lang vbnet>Imports System.Console Imports BI = System.Numerics.BigInteger
Module Module1
Dim Implems() As String = {"Built-In", "Recursive", "Iterative"}, powers() As Integer = {5, 4, 3, 2}
Function intPowR(val As BI, exp As BI) As BI If exp = 0 Then Return 1 Dim ne As BI, vs As BI = val * val If exp.IsEven Then ne = exp >> 1 : Return If (ne > 1, intPowR(vs, ne), vs) ne = (exp - 1) >> 1 : Return If (ne > 1, intPowR(vs, ne), vs) * val End Function
Function intPowI(val As BI, exp As BI) As BI intPowI = 1 : While (exp > 0) : If Not exp.IsEven Then intPowI *= val val *= val : exp >>= 1 : End While End Function
Sub DoOne(title As String, p() As Integer) Dim st As DateTime = DateTime.Now, res As BI, resStr As String Select Case (Array.IndexOf(Implems, title)) Case 0 : res = BI.Pow(p(0), CInt(BI.Pow(p(1), CInt(BI.Pow(p(2), p(3)))))) Case 1 : res = intPowR(p(0), intPowR(p(1), intPowR(p(2), p(3)))) Case Else : res = intPowI(p(0), intPowI(p(1), intPowI(p(2), p(3)))) End Select : resStr = res.ToString() Dim et As TimeSpan = DateTime.Now - st Debug.Assert(resStr.Length = 183231) Debug.Assert(resStr.StartsWith("62060698786608744707")) Debug.Assert(resStr.EndsWith("92256259918212890625")) WriteLine("n = {0}", String.Join("^", powers)) WriteLine("n = {0}...{1}", resStr.Substring(0, 20), resStr.Substring(resStr.Length - 20, 20)) WriteLine("n digits = {0}", resStr.Length) WriteLine("{0} elasped: {1} milliseconds." & vblf, title, et.TotalMilliseconds) End Sub
Sub Main() For Each itm As String in Implems : DoOne(itm, powers) : Next If Debugger.IsAttached Then Console.ReadKey() End Sub
End Module</lang>

Output:
n = 5^4^3^2 n = 62060698786608744707...92256259918212890625 n digits = 183231 Built-In elasped: 2487.4002 milliseconds. n = 5^4^3^2 n = 62060698786608744707...92256259918212890625 n digits = 183231 Recursive elasped: 2413.0434 milliseconds. n = 5^4^3^2 n = 62060698786608744707...92256259918212890625 n digits = 183231 Iterative elasped: 2412.5477 milliseconds.

Remarks: Not much difference in execution times for three methods. But the exponents are relatively small. If one does need to evaluate an exponent greater than Int32.MaxValue, the execution time will be measured in hours.

Wren
Library: Wren-fmt
Library: Wren-big
<lang ecmascript>import "/fmt" for Fmt import "/big" for BigInt
var p = BigInt.three.pow(BigInt.two) p = BigInt.four.pow(p) p = BigInt.five.pow(p) var s = p.toString Fmt.print("5 ^ 4 ^ 3 ^ 2 has $,d digits.\n", s.count) System.print("The first twenty are : %(s[0..19])") System.print("and the last twenty are : %(s[-20..-1])")</lang>

Output:
5 ^ 4 ^ 3 ^ 2 has 183,231 digits. The first twenty are : 62060698786608744707 and the last twenty are : 92256259918212890625
zig
<lang zig>const std = @import("std"); const bigint = std.math.big.int.Managed;
pub fn main() !void {
var gpa = std.heap.GeneralPurposeAllocator(.{}){}; const allocator = &gpa.allocator; defer _ = gpa.deinit();
var a = try bigint.initSet(allocator, 5); try a.pow(a.toConst(), try std.math.powi(u32, 4, try std.math.powi(u32, 3, 2))); defer a.deinit();
var as = try a.toString(allocator, 10, false); defer allocator.free(as);
std.debug.print("{s}...{s}\n", .{ as[0..20], as[as.len - 20 ..] }); std.debug.print("{} digits\n", .{as.len});
}</lang>

Output:
62060698786608744707...92256259918212890625 183231 digits
zkl
Using the GNU big num library: <lang zkl>var BN=Import("zklBigNum"); n:=BN(5).pow(BN(4).pow(BN(3).pow(2))); s:=n.toString(); "%,d".fmt(s.len()).println(); println(s[0,20],"...",s[-20,*]);</lang>

Output:
183,231 62060698786608744707...92256259918212890625