Arbitrary-precision integers (included)
You are encouraged to solve this task according to the task description, using any language you may know.
Using the in-built capabilities of your language, calculate the integer value of:
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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
- Long multiplication
- Exponentiation order
- exponentiation operator
- Exponentiation with infix operators in (or operating on) the base
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))- Output:
5^4^3^2 = 62060698786608744707...92256259918212890625 and has 183231 digits
8th
200000 n#
5 4 3 2 bfloat ^ ^ ^
"%.0f" s:strfmt
dup s:len . " digits" . cr
dup 20 s:lsub . "..." . 20 s:rsub . cr
- Output:
183231 digits 62060698786608744707...92256259918212890625
ACL2
(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)))))
- Output:
62060698786608744707 ... 92256259918212890625 (183231 digits)
Ada
Using GMP, Ada bindings provided in GNATColl
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;
- Output:
Size is: 183231 62060698786608744707.....92256259918212890625
ALGOL 68
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- Output:
First 20 digits: 62060698786608744707 Last 20 digits: 92256259918212890625 Number of digits: 183231
Alore
def Main()
var len as Int
var result as Str
result = Str(5**4**3**2)
len = result.length()
Print(len)
Print(result[:20])
Print(result[len-20:])
endArturo
num: to :string 5^4^3^2
print [first.n: 20 num ".." last.n: 20 num "=>" size num "digits"]
- Output:
62060698786608744707 .. 92256259918212890625 => 183231 digits
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
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
Bracmat
At the prompt type the following one-liner:
{?} @(5^4^3^2:?first [20 ? [-21 ?last [?length)&str$(!first "..." !last "\nlength " !length)
{!} 62060698786608744707...92256259918212890625
length 183231
S 2,46 secC
#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;
}
- Output:
GMP says size is: 183231 size really is 183231 Digits: 62060698786608744707...92256259918212890625
OpenSSL is about 17 times slower than GMP (on one computer), but still fast enough for this small task.
/* 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;
}
- 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.
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);
}
}
- Output:
n = 5^4^3^2 n = 62060698786608744707...92256259918212890625 n digits = 183231
C++
To compile link with GMP -lgmp
#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;
}
- Output:
62060698786608744707...92256259918212890625
Ceylon
Be sure to import ceylon.whole in your module.ceylon file.
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``");
}
- 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
(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)"))
- Output:
output> 62060698786608744707..92256259918212890625 (183231 digits)
Redefining exp as follows speeds up the calculation of big about a hundred times:
(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))))
CLU
This program uses the bigint type that is supplied with Portable CLU, in
misc.lib. The program must be merged with that library in order to work.
The type is not included in the CLU specification, however it is included as a library with the reference implementation.
start_up = proc ()
% Get bigint versions of 5, 4, 3 and 2
five: bigint := bigint$i2bi(5)
four: bigint := bigint$i2bi(4)
three: bigint := bigint$i2bi(3)
two: bigint := bigint$i2bi(2)
% Calculate 5**4**3**2
huge_no: bigint := five ** four ** three ** two
% Turn answer into string
huge_str: string := bigint$unparse(huge_no)
% Scan for first digit (the string will have some leading whitespace)
i: int := 1
while huge_str[i] = ' ' do i := i + 1 end
po: stream := stream$primary_output()
stream$putl(po, "First 20 digits: "
|| string$substr(huge_str, i, 20))
stream$putl(po, "Last 20 digits: "
|| string$substr(huge_str, string$size(huge_str)-19, 20))
stream$putl(po, "Amount of digits: "
|| int$unparse(string$size(huge_str) - i + 1))
end start_up- Output:
First 20 digits: 62060698786608744707 Last 20 digits: 92256259918212890625 Amount of digits: 183231
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.
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.
- 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]
(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)))
- Output:
62060698786608744707...92256259918212890625, length 183231
Crystal
require "big"
z = (BigInt.new(5) ** 4 ** 3 ** 2).to_s
zSize = z.size
puts "5**4**3**2 = #{z[0, 20]} .. #{z[zSize-20, 20]} and has #{zSize} digits"
- Output:
5**4**3**2 = 62060698786608744707 .. 92256259918212890625 and it has 183231 digits
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);
}
- 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.
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}');
- Output:
First twenty: 62060698786608744707 Last twenty: 92256259918212890625 Number of digits: 183231
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- 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
Thanks for Rudy Velthuis, BigIntegers Library [2].
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.
- Output:
5^4^3^2 = 62060698786608744707...92256259918212890625 (183231 digits)
E
E implementations are required to support arbitrary-size integers transparently.
? 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: 183231EchoLisp
;; 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
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
- Output:
Length: 183231 Prefix:62060698786608744707 Suffix:92256259918212890625
Emacs Lisp
As of Emacs 27.1, bignums are supported via GMP. However, there is a configurable limit on the maximum bignum size. If the limit is exceeded, an overflow error is raised.
(let* ((integer-width (* 65536 16)) ; raise bignum limit from 65536 bits to avoid overflow error
(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))
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.
(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))
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.
-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]).
- 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
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
Factor
Factor has built-in bignum support. Operations on integers overflow to bignums.
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 ;
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.
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:
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
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.
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
62060698786608744707 92256259918212890625
FreeBASIC
freebasic has it's own gmp static library. Here, a power function operates via a string and uinteger.
#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
- 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.
a = 5^4^3^2
as = "$a" // Coerce to string
println["Length=" + length[as] + ", " + left[as,20] + "..." + right[as,20]]This prints Length=183231, 62060698786608744707...92256259918212890625
FutureBasic
Translated from c
Thanks, Ken
/*
Uses GMP for Multiple Precision Arithmetic
Install GMP using terminal and Homebrew command, "brew install gmp"
before running this app in FutureBasic.
Homebrew available here, https://brew.sh
*/
include "NSLog.incl"
void local fn GMPoutput
CFStringRef sourcePath = fn StringByAppendingPathComponent( @"/tmp/", @"temp.m" )
CFStringRef executablePath = fn StringByAppendingPathComponent( @"/tmp/", @"temp" )
CFStringRef gmpStr = @"#import <Foundation/Foundation.h>\n#import <gmp.h>\n¬
int main(int argc, const char * argv[]) {\n¬
@autoreleasepool {\n¬
mpz_t a;\n¬
mpz_init_set_ui(a, 5);\n¬
mpz_pow_ui(a, a, 1 << 18);\n¬
size_t len = mpz_sizeinbase(a, 10);\n¬
printf(\"GMP says size is: %zu\\n\", len);\n¬
char *s = mpz_get_str(0, 10, a);\n¬
size_t trueLen = strlen(s);\n¬
printf(\" Actual size is: %zu\\n\", trueLen);\n¬
printf(\"First & Last 20 digits: %.20s…%s\\n\", s, s + trueLen - 20);\n¬
}\n¬
return 0;\n¬
}"
fn StringWriteToURL( gmpStr, fn URLFileURLWithPath( sourcePath ), YES, NSUTF8StringEncoding, NULL )
TaskRef task = fn TaskInit
TaskSetExecutableURL( task, fn URLFileURLWithPath( @"usr/bin/clang" ) )
CFArrayRef arguments = @[@"-o", executablePath, sourcePath, @"-lgmp", @"-fobjc-arc"]
TaskSetArguments( task, arguments )
PipeRef pipe = fn PipeInit
TaskSetStandardInput( task, pipe )
fn TaskLaunch( task, NULL )
TaskWaitUntilExit( task )
if ( fn TaskTerminationStatus( task ) == 0 )
TaskRef executionTask = fn TaskInit
TaskSetExecutableURL( executionTask, fn URLFileURLWithPath( executablePath ) )
PipeRef executionPipe = fn PipeInit
TaskSetStandardOutput( executionTask, executionPipe )
FileHandleRef executionFileHandle = fn PipeFileHandleForReading( executionPipe )
fn TaskLaunch( executionTask, NULL )
TaskWaitUntilExit( executionTask )
CFDataRef outputData = fn FileHandleReadDataToEndOfFile( executionFileHandle, NULL )
CFStringRef outputStr = fn StringWithData( outputData, NSUTF8StringEncoding )
NSLog( @"%@", outputStr )
else
alert 1,, @"GMP required but not installed"
end if
fn FileManagerRemoveItemAtURL( fn URLFileURLWithPath( sourcePath ) )
fn FileManagerRemoveItemAtURL( fn URLFileURLWithPath( executablePath ) )
end fn
fn GMPoutput
HandleEvents- Output:
GMP says size is: 183231 Actual size is: 183231 First & Last 20 digits: 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.
In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.
Solution
In the following script, the result is converted to a string, in order to calculate its size, and its first/last digits.
_01.png)
_02.png)
GAP
n:=5^(4^(3^2));;
s := String(n);;
m := Length(s);
# 183231
s{[1..20]};
# "62060698786608744707"
s{[m-19..m]};
# "92256259918212890625"
Go
Using math/big's
Int.Exp.
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:],
)
}
- Output:
5^(4^(3^2)) has 183231 digits: 62060698786608744707 ... 92256259918212890625
Golfscript
5 4 3 2??? # Calculate 5^(4^(3^2))
`.. # Convert to string and make two copies
20<p # Print the first 20 digits
-20>p # Print the last 20 digits
,p # Print the lengthThe p command prints the top element from the stack, so the output of this program is just three lines:
"62060698786608744707" "92256259918212890625" 183231
Groovy
Solution:
def bigNumber = 5G ** (4 ** (3 ** 2))
Test:
def bigString = bigNumber.toString()
assert bigString[0..<20] == "62060698786608744707"
assert bigString[-20..-1] == "92256259918212890625"
println bigString.size()
- Output:
183231
Haskell
Haskell comes with built-in support for arbitrary precision integers. The type of arbitrary precision integers is Integer.
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")
- Output:
5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits
Hoon
=+ big=(pow 5 (pow 4 (pow 3 2)))
=+ digits=(lent (skip <big> |=(a/* ?:(=(a '.') & |))))
[digits (div big (pow 10 (sub digits 20))) (mod big (pow 10 20))]- 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.
- 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.
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
Java
Java library's BigInteger class provides support for arbitrary precision integers.
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);
}
}
- 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.
>>> const y = (5n**4n**3n**2n).toString();
>>> console.log(`5**4**3**2 = ${y.slice(0,20)}...${y.slice(-20)} and has ${y.length} digits`);
5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digitsjq
Works with gojq, the Go implementation of jq
There is a BigInt.jq library for jq, but gojq, the Go implementation of jq, supports unbounded-precision integer arithmetic, so the output shown below is that produced by gojq.
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
5|power(4|power(3|power(2))) | tostring
| .[:20], .[-20:], length- 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.
julia> @elapsed bigstr = string(BigInt(5)^4^3^2)
0.017507363
julia> length(bigstr)
183231
julia> bigstr[1:20]
"62060698786608744707"
julia> bigstr[end-19:end]
"92256259918212890625"
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
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 $len digits")
}
- Output:
5^4^3^2 = 62060698786608744707...92256259918212890625 and has 183231 digits
Lambdatalk
Just using Javascript's BigInt
{def N {BI.** 5 {BI.** 4 {BI.** 3 2}}}} -> N
length: {def L {W.length {N}}} -> L = 183231
20 first digits: {W.slice 0 20 {N}} -> 62060698786608744707
20 last digits: {W.slice -20 {L} {N}} -> 92256259918212890625
langur
Arbitrary precision is native in langur.
val xs = string(5 ^ 4 ^ 3 ^ 2)
writeln len(xs), " digits"
if len(xs) > 39 and s2s(xs, 1..20) == "62060698786608744707" and
s2s(xs, -20 .. -1) == "92256259918212890625" {
writeln "SUCCESS"
}- Output:
183231 digits SUCCESS
Lasso
Interestingly, we have to define our own method for integer powers.
define integer->pow(factor::integer) => {
#factor <= 0
? return 0
local(retVal) = 1
loop(#factor) => { #retVal *= self }
return #retVal
}
local(bigint) = string(5->pow(4->pow(3->pow(2))))
#bigint->sub(1,20) + ` ... ` + #bigint->sub(#bigint->size - 19)
"\n"
`Number of digits: ` + #bigint->size
- Output:
62060698786608744707 ... 92256259918212890625 Number of digits: 183231
Liberty BASIC
Interestingly this takes a LONG time in LB.
It takes however only seconds in RunBASIC, which is written by the same author, shares most of LB's syntax, and is based on later Smalltalk implementation.
Note the brackets are needed to enforce the desired order of exponentiating.
a$ = str$( 5^(4^(3^2)))
print len( a$)
print left$( a$, 20); "......"; right$( a$, 20)- 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)
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))
- Output:
62060698786608744707...92256259918212890625 (183231 digits)
Maple
Maple supports large integer arithmetic natively.
> n := 5^(4^(3^2)):
> length( n ); # number of digits
183231
> s := convert( n, 'string' ):
> s[ 1 .. 20 ], s[ -20 .. -1 ]; # extract first and last twenty digits
"62060698786608744707", "92256259918212890625"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.
> interface( elisiondigitsbefore = 20, elisiondigitsafter = 20 ):
> 5^(4^(3^2)):
62060698786608744707[...183191 digits...]92256259918212890625Mathematica / Wolfram Language
Mathematica can handle arbitrary precision integers on almost any size without further declarations. To view only the first and last twenty digits:
s:=ToString[5^4^3^2];
Print[StringTake[s,20]<>"..."<>StringTake[s,-20]<>" ("<>ToString@StringLength@s<>" digits)"];
- Output:
62060698786608744707...92256259918212890625 (183231 digits)
MATLAB
Using the Variable Precision Integer library this task is accomplished thusly:
>> answer = vpi(5)^(vpi(4)^(vpi(3)^vpi(2)));
>> numDigits = order(answer) + 1
numDigits =
183231
>> [sprintf('%d',leadingdigit(answer,20)) '...' sprintf('%d',trailingdigit(answer,20))]
%First and Last 20 Digits
ans =
62060698786608744707...92256259918212890625
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 */
Nanoquery
Integer values are arbitrary-precision by default in 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"- Output:
The first twenty digits are 62060698786608744707 The last twenty digits are 92256259918212890625 These digits are correct. The result is 183231 digits long
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");
}
}
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))))
- Output:
The result has: 183231 digits First 20 digits: 62060698786608744707 Last 20 digits: 92256259918212890625
NetRexx
Using Java's BigInteger Class
/* 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
- Output:
Run time in seconds: 6.696671
Expected result: 62060698786608744707...92256259918212890625
Actual result: 62060698786608744707...92256259918212890625
digits: 183231
Result confirmed
Using Java's BigDecimal Class
/* 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
- 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
/* 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"
- Output:
Run time in seconds: 719.660995
Expected result: 62060698786608744707...92256259918212890625
Actual result: 62060698786608744707...92256259918212890625
digits: 183231
Result confirmed
Nim
import bigints
var x = 5.pow 4.pow 3.pow 2
var s = $x
echo s[0..19]
echo s[s.high - 19 .. s.high]
echo s.len
Output:
62060698786608744707 92256259918212890625 183231
OCaml
open Num
open Str
open String
let () =
let answer = (Int 5) **/ (Int 4) **/ (Int 3) **/ (Int 2) in
let answer_string = string_of_num answer in
Printf.printf "has %d digits: %s ... %s\n"
(length answer_string)
(first_chars answer_string 20)
(last_chars answer_string 20)
A more readable program can be obtained using Delimited Overloading:
let () =
let answer = Num.(5**4**3**2) in
let s = Num.(to_string answer) in
Printf.printf "has %d digits: %s ... %s\n"
(String.length s) (Str.first_chars s 20) (Str.last_chars s 20)
- Output:
has 183231 digits: 62060698786608744707 ... 92256259918212890625
Oforth
Oforth handles arbitrary precision integers :
import: mapping
5 4 3 2 pow pow pow >string dup left( 20 ) . dup right( 20 ) . size .- Output:
62060698786608744707 92256259918212890625 183231
Ol
(define x (expt 5 (expt 4 (expt 3 2))))
(print
(div x (expt 10 (- (log 10 x) 20)))
"..."
(mod x (expt 10 20)))
(print "totally digits: " (log 10 x))
- Output:
62060698786608744707...92256259918212890625 totally digits: 183231
ooRexx
--REXX program to show arbitrary precision integers.
numeric digits 200000
check = '62060698786608744707...92256259918212890625'
start = .datetime~new
n = 5 ** (4 ** (3**2))
time = .datetime~new - start
say 'elapsed time for the calculation:' time
say
sampl = left(n, 20)"..."right(n, 20)
say ' check:' check
say 'Sample:' sampl
say 'digits:' length(n)
say
if check=sampl then say 'passed!'
else say 'failed!'
- Output:
prompt$ rexx rexx-arbitrary.rexx elapsed time for the calculation: 00:00:45.373140 check: 62060698786608744707...92256259918212890625 Sample: 62060698786608744707...92256259918212890625 digits: 183231 passed!
Oz
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)"}- 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:
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- 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).
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)]- Output:
[6.20606987866087447074832055728 E183230, Mod(92256259918212890625, 100000000000000000000), 183231]
Pascal
FreePascal comes with a header unit for gmp. Starting from the C program, this is a Pascal version:
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.
- Output:
GMP says size is: 183231 Actual size is: 183231 Digits: 62060698786608744707...92256259918212890625
PascalABC.NET
begin
var result: string := power(5bi, integer(power(4, power(3, 2)))).tostring;
result[1:21].Println;
result[result.Length - 19:].Println;
result.Length.Println;
end.
- Output:
62060698786608744707 92256259918212890625 183231
Perl
Perl's Math::BigInt core module handles big integers:
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));
You can enable "transparent" big integer support by enabling the bigint pragma:
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));
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:
$ time perl transparent-bigint.pl
5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits
1m4.28s real 1m4.30s user 0m0.00s system
Phix
with javascript_semantics include mpfr.e atom t0 = time() mpz res = mpz_init() mpz_ui_pow_ui(res,5,power(4,power(3,2))) string s = mpz_get_short_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.
<?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));
?>
- 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).
Picat
main =>
X = to_string(5**4**3**2),
Y = len(X),
println("Result: "),
print("Number of digits: "), println(Y),
println("First 20 digits: " ++ X[1..20]),
println("Last 20 digits: " ++ X[Y-19..Y]).PicoLisp
(let L (chop (** 5 (** 4 (** 3 2))))
(prinl (head 20 L) "..." (tail 20 L))
(length L) )- Output:
62060698786608744707...92256259918212890625 -> 183231
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
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
$BigNumberString.Length
- Output:
62060698786608744707...92256259918212890625 183231
Processing
import java.math.BigInteger;
// Variable definitions
BigInteger _5, _4, powResult;
_5 = BigInteger.valueOf(5);
_4 = BigInteger.valueOf(4);
//calculations
powResult = _5.pow(_4.pow(9).intValueExact());
String powStr = powResult.toString();
int powLen = powStr.length();
String powStrStart = powStr.substring(0, 20);
String powStrEnd = powStr.substring(powLen - 20);
//output
System.out.printf("5**4**3**2 = %s...%s and has %d digits%n", powStrStart, powStrEnd, powLen);
- Output:
5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits
Prolog
task(Length) :-
N is 5^4^3^2,
number_codes(N, Codes),
append(`62060698786608744707`, _, Codes),
append(_, `92256259918212890625`, Codes),
length(Codes, Length).
Query like so:
?- task(N).
N = 183231 ;
false.
PureBasic
PureBasic has in its current version (today 4.50) no internal support for large numbers, but there are several free libraries for this.
Using Decimal.pbi, e.g. the same included library as in Long multiplication#PureBasic, this task is solved as below.
IncludeFile "Decimal.pbi"
;- Declare the variables that will be used
Define.Decimal *a
Define n, L$, 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$+"and the result is "+digits+" digits long."
MessageRequester("Arbitrary-precision integers, PureBasic",out$)
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.
>>> 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
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.
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")
- Output:
first 20 digits: 62060698786608744707 last 20 digits: 92256259918212890625 number of digits: 183231
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))
- Output:
Got 183231 digits 62060698786608744707 ... 92256259918212890625
Raku
(formerly Perl 6)
given [**] 5, 4, 3, 2 {
use Test;
ok /^ 62060698786608744707 <digit>* 92256259918212890625 $/,
'5**4**3**2 has expected first and last twenty digits';
printf 'This number has %d digits', .chars;
}
- Output:
ok 1 - 5**4**3**2 has expected first and last twenty digits This number 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)
/*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. */
- output:
check: 62060698786608744707...92256259918212890625 sample: 62060698786608744707...92256259918212890625 digits: 183231 passed!
automatic setting of decimal digits
/*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. */
- output is the same as the 1st REXX version.
Ruby
Ruby comes with built-in support for arbitrary precision integers.
y = ( 5**4**3**2 ).to_s
puts "5**4**3**2 = #{y[0..19]}...#{y[-20..-1]} and has #{y.length} digits"
- Output:
5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits
Run BASIC
x$ = str$( 5^(4^(3^2)))
print "Length:";len( x$)
print left$( x$, 20); "......"; right$( x$, 20)- 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.
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);
}
- Output:
Number of digits: 183231 First and last digits: "62060698786608744707".."92256259918212890625"
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;- 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.
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>
Scheme
R4RS and R5RS encourage, and R6RS requires, that exact integers be of arbitrary precision.
(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)
- Output:
5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits
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;- Output:
5**4**3**2 = 62060698786608744707...92256259918212890625 decimal digits: 183231
Sidef
var x = 5**(4**(3**2))
var y = x.to_s
printf("5**4**3**2 = %s...%s and has %i digits\n", y.first(20), y.last(20), y.len)
- Output:
5**4**3**2 = 62060698786608744707...92256259918212890625 and has 183231 digits
SIMPOL
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.
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 sSmalltalk
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:
|num|
num := (5 raisedTo: (4 raisedTo: (3 raisedTo: 2))) asString.
Transcript
show: (num first: 20), '...', (num last: 20); cr;
show: 'digits: ', num size asString.
On a Transcript window:
62060698786608744707...92256259918212890625 digits: 183231
And a more advanced one:
|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.
- Output:
'62060698786608744707...92256259918212890625 digits: 183231'
Note 1) should work in all Smalltalk dialects; tried in Smalltalk/X and VisualWorks.
SPL
t = #.str(5^(4^(3^2)))
n = #.size(t)
#.output(n," digits")
#.output(#.mid(t,1,20),"...",#.mid(t,n-19,20))- Output:
183231 digits 62060698786608744707...92256259918212890625
Standard ML
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;
it took too long to run
mLite
mLite does not have a logarithm function so one was constructed (see fun log10)
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;
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.
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"
}
- Output:
5**4**3**2 has 183231 digits Value starts with 62060698786608744707, ends with 92256259918212890625
Transd
#lang transd
MainModule: {
_start:(λ locals: a BigLong(5) ss StringStream() s ""
(textout to: ss (pow a (pow 4 (pow 3 2))))
(= s (str ss))
(with len (size s)
(lout "The number of digits is: " len)
(lout (sub s 0 20) " ... " (sub s (- len 20))))
)
}
- Output:
The number of digits is: 183231 62060698786608744707 ... 92256259918212890625
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)- 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
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<i>)
end for
# get the last twenty digits
for (set i (- (size xstr) 20)) (< i (size xstr)) (inc i)
set last (+ last xstr<i>)
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 ifOutput
- 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.
#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_>With this calculation taking about a day to run, correct results are attainable but not performant.
62060698786608744707...92256259918212890625 length: 183231
Visual Basic .NET
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.
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
- 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.
V (Vlang)
import math.big
import math
fn main() {
mut x := u32(math.pow(3,2))
x = u32(math.pow(4,x))
mut y := big.integer_from_int(5)
y = y.pow(x)
str := y.str()
println("5^(4^(3^2)) has $str.len digits: ${str[..20]} ... ${str[str.len-20..]}")
}- Output:
5^(4^(3^2)) has 183231 digits: 62060698786608744707 ... 9225625991821289062
Wren
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])")
- Output:
5 ^ 4 ^ 3 ^ 2 has 183,231 digits. The first twenty are : 62060698786608744707 and the last twenty are : 92256259918212890625
Zig
const std = @import("std");
const bigint = std.math.big.int.Managed;
pub fn main() !void {
var a = try bigint.initSet(std.heap.c_allocator, 5);
try a.pow(&a, try std.math.powi(u32, 4, try std.math.powi(u32, 3, 2)));
defer a.deinit();
var as = try a.toString(std.heap.c_allocator, 10, .lower);
defer std.heap.c_allocator.free(as);
std.debug.print("{s}...{s}\n", .{ as[0..20], as[as.len - 20 ..] });
std.debug.print("{} digits\n", .{as.len});
}
- Output:
62060698786608744707...92256259918212890625 183231 digits
zkl
Using the GNU big num library:
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,*]);- Output:
183,231 62060698786608744707...92256259918212890625
Categories:
- Programming Tasks
- Arbitrary precision
- 11l
- 8th
- ACL2
- Ada
- GMP
- ALGOL 68
- Alore
- Arturo
- Bc
- Bracmat
- C
- OpenSSL
- C sharp
- C++
- Boost-Multiprecision (GMP Backend)
- Ceylon
- Clojure
- CLU
- COBOL
- Common Lisp
- Crystal
- D
- Dart
- Dc
- Delphi
- System.SysUtils
- Velthuis.BigIntegers
- E
- EchoLisp
- Elixir
- Emacs Lisp
- Calc
- Erlang
- F Sharp
- Factor
- Forth
- The Forth Scientific Library
- Fortran
- FreeBASIC
- Frink
- FutureBasic
- Fōrmulæ
- GAP
- Go
- Golfscript
- Groovy
- Haskell
- Hoon
- Icon
- Unicon
- J
- Java
- JavaScript
- Jq
- Julia
- Klong
- Kotlin
- Lambdatalk
- Langur
- Lasso
- Liberty BASIC
- Lua
- Maple
- Mathematica
- Wolfram Language
- MATLAB
- Maxima
- Nanoquery
- Nemerle
- NewLisp
- NetRexx
- Nim
- Bigints
- OCaml
- Oforth
- Ol
- OoRexx
- Oz
- PARI/GP
- Pascal
- Math
- PascalABC.NET
- Perl
- Phix
- Phix/basics
- Phix/mpfr
- PHP
- Picat
- PicoLisp
- Pike
- PowerShell
- Processing
- Prolog
- PureBasic
- Python
- Quackery
- R
- Racket
- Raku
- REXX
- Ruby
- Run BASIC
- Rust
- Sather
- Scala
- Scheme
- Seed7
- Sidef
- SIMPOL
- SIMPOL examples needing attention
- Examples needing attention
- Smalltalk
- SPL
- Standard ML
- Stata
- Tcl
- Transd
- TXR
- Ursa
- Ursala
- Visual Basic .NET
- System.Numerics
- V (Vlang)
- Wren
- Wren-fmt
- Wren-big
- Zig
- Zkl
- AutoHotkey/Omit
- AWK/Omit
- Batch File/Omit
- BBC BASIC/Omit
- Brainf***/Omit
- PostScript/Omit
- SAS/Omit
- Scratch/Omit
- Sed/Omit
- ZX Spectrum Basic/Omit
- Pages with math errors
- Pages with math render errors