# Integer long division

Write a function that prints the result of the division of two positive integers with infinite precision (only limited by the available memory), stopping before the period starts repeating itself. Return also the length of this period (0 if there is no period).

Integer long division is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Demonstrate it with the division 1/149, whose result is 0.0067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651, where the last 148 digits repeat endlessly.

The result could be stored as a string or simply output to the screen.
Note that the division of any two integers will always produce a period, but if the numerator is an exact multiple of the denominator, or if the denominator contains only the factors 2 and 5, the period will be 0. In the remaining cases, these possible 2's and 5's of the denominator produce a leading number of digits in the quotient, but have no effect on the period.

References

Related

## C++

Library: GMP
```#include <gmpxx.h>

#include <iomanip>
#include <iostream>
#include <map>
#include <string>

using big_int = mpz_class;

std::pair<std::string, size_t> divide(const big_int& n, const big_int& d) {
assert(n >= 0);
assert(d > 0);
std::string result = big_int(n / d).get_str();
result += '.';
big_int c = 10 * (n % d);
size_t digits = 0;
std::map<big_int, size_t> seen;
while (seen.count(c) == 0) {
if (c == 0) {
if (result.back() == '.')
result.pop_back();
return {result, 0};
}
seen[c] = digits++;
if (c < d) {
result += '0';
c *= 10;
} else {
result += big_int(c / d).get_str();
c = 10 * (c % d);
}
}
return {result, digits - seen[c]};
}

int main() {
big_int test[][2] = {
{0, 1},   {1, 1},    {1, 5},
{1, 3},   {1, 7},    {83, 60},
{1, 17},  {10, 13},  {3227, 555},
{1, 149}, {1, 5261}, {476837158203125, big_int("9223372036854775808")}};
for (auto [n, d] : test) {
auto [result, period] = divide(n, d);
std::string str = n.get_str();
str += '/';
str += d.get_str();
std::string repetend = result.substr(result.size() - period);
if (repetend.size() > 30)
repetend.replace(15, repetend.size() - 30, "...");
result.resize(result.size() - period);
std::cout << std::setw(35) << str << " = " << result;
if (period != 0)
std::cout << '{' << repetend << "} (period " << period << ')';
std::cout << '\n';
}
}
```
Output:
```                                0/1 = 0
1/1 = 1
1/5 = 0.2
1/3 = 0.{3} (period 1)
1/7 = 0.{142857} (period 6)
83/60 = 1.38{3} (period 1)
1/17 = 0.{0588235294117647} (period 16)
10/13 = 0.{769230} (period 6)
3227/555 = 5.8{144} (period 3)
1/149 = 0.{006711409395973...087248322147651} (period 148)
1/5261 = 0.{000190077931952...263257935753659} (period 1052)
476837158203125/9223372036854775808 = 0.000051698788284564229679463043254372678347863256931304931640625
```

## Common Lisp

```(defun \$/ (a b)
"Divide a/b with infinite precision printing each digit as it is calculated and return the period length"
; (\$/ 1 17) => 588235294117647 ; 16
(assert (and (integerp a) (integerp b) (not (zerop b))))
(do* (c
(i0 (1+ (max (factor-multiplicity b 2) (factor-multiplicity b 5)))) ; the position which marks the beginning of the period
(r a (* 10 r)) ; remainder
(i 0 (1+ i)) ; iterations counter
(rem (if (= i i0) r -1) (if (= i i0) r rem)) ) ; the first remainder against which to check for repeating remainders
((and (= r rem) (not (= i i0))) (- i i0))
(multiple-value-setq (c r) (floor r b))
(princ c) ))

(defun factor-multiplicity (n factor)
"Return how many times the factor is contained in n"
; (factor-multiplicity 12 2) => 2
(do* ((i 0 (1+ i))
(n (/ n factor) (/ n factor)) )
((not (integerp n)) i)
() ))
```
Output:
```(\$/ 1 149)
00067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651
148
```

## jq

Works with gojq, the Go implementation of jq

gojq supports unbounded-precision integer arithmetic, which makes light work of the task.

This entry uses the "(repetend)" convention (e.g. 1/3 => 0.(3)), partly because the Unicode "overline" might not display properly. In case the overline style is preferred, simply use the following function in the obvious way:

```# "\u0305"
def overline: explode | map(., 773) | implode;```
```# To take advantage of gojq's support for accurate integer division:
def idivide(\$j):
. as \$i
| (\$i % \$j) as \$mod
| (\$i - \$mod) / \$j ;

# If \$m >= 0, \$n > 0 then emit [ s, repetend ]
# where s is the string representation of \$m/\$n (possibly including trailing dots);
#       repetend is a string giving the repeating part of the decimal if any.
#
def integer_division(\$m; \$n):
if \$m < 0 then "numerator must not be negative" | error
elif \$n <= 0 then "denominator must be positive" | error
else (\$m | idivide(\$n) | tostring + ".") as \$quotient
|  {c: ((\$m % \$n) * 10), \$quotient }
| until (.c <= 0 or .c >= \$n;  .c *= 10 | .quotient += "0")
| . + { digits: "", passed: {}, i: 0, emit: false }
| until (.emit;
(.c | tostring) as \$cs
| if .passed|has(\$cs)
then .quotient = .quotient + .digits[: .passed[\$cs]]
| .emit = {quotient, repetend: .digits[.passed[\$cs] :] }
else .q = (.c | idivide(\$n))
| .r = .c % \$n
| .passed[\$cs] = .i
| .digits += (.q|tostring)
| .i += 1
| .c = .r * 10
end
)
end
| .emit
# move zeros from the tail of .repetend if possible
| until ( .repetend[-1:] != "0" or .quotient[-1:] != "0";
.quotient   |= .[:-1]
| .repetend |= "0" + .[:-1] )
| if .repetend != "0" and (.repetend|length > 0)
then [.quotient + "(" + .repetend + ")", .repetend]
else [(.quotient | sub("[.]\$"; "")),
(.repetend | if . == "0" then "" else . end)]
end ;

def examples:
[0, 1], [1, 1], [1, 3], [1, 7], [83,60], [1, 17], [10, 13], [3227, 555],
[476837158203125, 9223372036854775808],
[1, 149], [1, 5261]
;

examples as [\$a, \$b]
| (integer_division(\$a; \$b)) as [\$s, \$r]
|"\(\$a)/\(\$b) = \(\$s)",
"Repetend is \(\$r)",
"Period is \(\$r|length)\n" ;

Output:
```0/1 = 0
Repetend is
Period is 0

1/1 = 1
Repetend is
Period is 0

1/3 = 0.(3)
Repetend is 3
Period is 1

1/7 = 0.(142857)
Repetend is 142857
Period is 6

83/60 = 1.38(3)
Repetend is 3
Period is 1

1/17 = 0.(0588235294117647)
Repetend is 0588235294117647
Period is 16

10/13 = 0.(769230)
Repetend is 769230
Period is 6

3227/555 = 5.8(144)
Repetend is 144
Period is 3

476837158203125/9223372036854775808 = 0.000051698788284564229679463043254372678347863256931304931640625
Repetend is
Period is 0

1/149 = 0.(0067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651)
Repetend is 0067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651
Period is 148

1/5261 = 0.(00019007793195210036114807070899068618133434708230374453525945637711461699296711651777228663752138376734461129062915795476145219540011404675917126021668884242539441170880060824938224672115567382626877019578026991066337198251283026040676677437749477285687131724006842805550275613001330545523664702528036494962934803269340429576126211746816194639802318950769815624406006462649686371412279034404105683330165367800798327314198821516821896977760881961604257745675727048089716783881391370461889374643603877589811822847367420642463409998099220680478996388519292910093138186656529176962554647405436228853830070328834822277133624786162326553887093708420452385478045998859532408287397833111575746055882911993917506177532788443261737312298042197300893366280174871697395932332256225052271431286827599315719444972438699866945447633529747196350503706519673065957042387378825318380536019768104923018437559399353735031362858772096559589431666983463219920167268580117848317810302223911803839574225432427295191028321611860862953811062535639612241018817715263257935753659)
Repetend is 00019007793195210036114807070899068618133434708230374453525945637711461699296711651777228663752138376734461129062915795476145219540011404675917126021668884242539441170880060824938224672115567382626877019578026991066337198251283026040676677437749477285687131724006842805550275613001330545523664702528036494962934803269340429576126211746816194639802318950769815624406006462649686371412279034404105683330165367800798327314198821516821896977760881961604257745675727048089716783881391370461889374643603877589811822847367420642463409998099220680478996388519292910093138186656529176962554647405436228853830070328834822277133624786162326553887093708420452385478045998859532408287397833111575746055882911993917506177532788443261737312298042197300893366280174871697395932332256225052271431286827599315719444972438699866945447633529747196350503706519673065957042387378825318380536019768104923018437559399353735031362858772096559589431666983463219920167268580117848317810302223911803839574225432427295191028321611860862953811062535639612241018817715263257935753659
Period is 1052
```

## Julia

```function f2d(numr, denr)
dpart, remainders, r = "", Dict{BigInt, Int}(), BigInt(numr) % denr
while (r != 0) && !haskey(remainders, r)
remainders[r] = length(dpart)
r *= 10
partrem, r = divrem(r, denr)
dpart *= string(partrem)
end
return r == 0 ? (0, 0) : (dpart[remainders[r]+1:end], remainders[r])
end

overline(s) = mapreduce(c -> "\u0305" * c, *, s)

testpairs =  [(0, 1), (1, 1), (1, 3), (1, 7), (-83, 60), (1, 17), (10, 13), (3227, 555),
(5^21, Int128(2)^63), (1, 149), (1, 5261)]

function testrepeatingdecimals()
for (numr, denr) in testpairs
n = numr < 0 ? -numr : numr
repeated, extra = f2d(n, denr)
if repeated == 0
println(lpad("\$numr/\$denr", 36), "  (Period 0)     = ", BigFloat(numr)/denr)
else
prefix, suffix = split(string(BigFloat(numr) / denr)[begin:end-2], ".")
" = \$prefix.\$(suffix[begin:extra])\$(overline(repeated))")
end
end
end

testrepeatingdecimals()
```
Output:
```
0/1  (Period 0)     = 0.0
1/1  (Period 0)     = 1.0
1/3  (Period 1)     = 0.̅3
1/7  (Period 6)     = 0.̅1̅4̅2̅8̅5̅7
-83/60  (Period 1)     = -1.38̅3
1/17  (Period 16)    = 0.̅0̅5̅8̅8̅2̅3̅5̅2̅9̅4̅1̅1̅7̅6̅4̅7
10/13  (Period 6)     = 0.̅7̅6̅9̅2̅3̅0
3227/555  (Period 3)     = 5.8̅1̅4̅4
476837158203125/9223372036854775808  (Period 0)     = 5.1698788284564229679463043254372678347863256931304931640625e-05
1/149  (Period 148)   = 0.̅0̅0̅6̅7̅1̅1̅4̅0̅9̅3̅9̅5̅9̅7̅3̅1̅5̅4̅3̅6̅2̅4̅1̅6̅1̅0̅7̅3̅8̅2̅5̅5̅0̅3̅3̅5̅5̅7̅0̅4̅6̅9̅7̅9̅8̅6̅5̅7̅7̅1̅8̅1̅2̅0̅8̅0̅5̅3̅6̅9̅1̅2̅7̅5̅1̅6̅7̅7̅8̅5̅2̅3̅4̅8̅9̅9̅3̅2̅8̅8̅5̅9̅0̅6̅0̅4̅0̅2̅6̅8̅4̅5̅6̅3̅7̅5̅8̅3̅8̅9̅2̅6̅1̅7̅4̅4̅9̅6̅6̅4̅4̅2̅9̅5̅3̅0̅2̅0̅1̅3̅4̅2̅2̅8̅1̅8̅7̅9̅1̅9̅4̅6̅3̅0̅8̅7̅2̅4̅8̅3̅2̅2̅1̅4̅7̅6̅5̅1
1/5261  (Period 1052)  = 0.̅0̅0̅0̅1̅9̅0̅0̅7̅7̅9̅3̅1̅9̅5̅2̅1̅0̅0̅3̅6̅1̅1̅4̅8̅0̅7̅0̅7̅0̅8̅9̅9̅0̅6̅8̅6̅1̅8̅1̅3̅3̅4̅3̅4̅7̅0̅8̅2̅3̅0̅3̅7̅4̅4̅5̅3̅5̅2̅5̅9̅4̅5̅6̅3̅7̅7̅1̅1̅4̅6̅1̅6̅9̅9̅2̅9̅6̅7̅1̅1̅6̅5̅1̅7̅7̅7̅2̅2̅8̅6̅6̅3̅7̅5̅2̅1̅3̅8̅3̅7̅6̅7̅3̅4̅4̅6̅1̅1̅2̅9̅0̅6̅2̅9̅1̅5̅7̅9̅5̅4̅7̅6̅1̅4̅5̅2̅1̅9̅5̅4̅0̅0̅1̅1̅4̅0̅4̅6̅7̅5̅9̅1̅7̅1̅2̅6̅0̅2̅1̅6̅6̅8̅8̅8̅4̅2̅4̅2̅5̅3̅9̅4̅4̅1̅1̅7̅0̅8̅8̅0̅0̅6̅0̅8̅2̅4̅9̅3̅8̅2̅2̅4̅6̅7̅2̅1̅1̅5̅5̅6̅7̅3̅8̅2̅6̅2̅6̅8̅7̅7̅0̅1̅9̅5̅7̅8̅0̅2̅6̅9̅9̅1̅0̅6̅6̅3̅3̅7̅1̅9̅8̅2̅5̅1̅2̅8̅3̅0̅2̅6̅0̅4̅0̅6̅7̅6̅6̅7̅7̅4̅3̅7̅7̅4̅9̅4̅7̅7̅2̅8̅5̅6̅8̅7̅1̅3̅1̅7̅2̅4̅0̅0̅6̅8̅4̅2̅8̅0̅5̅5̅5̅0̅2̅7̅5̅6̅1̅3̅0̅0̅1̅3̅3̅0̅5̅4̅5̅5̅2̅3̅6̅6̅4̅7̅0̅2̅5̅2̅8̅0̅3̅6̅4̅9̅4̅9̅6̅2̅9̅3̅4̅8̅0̅3̅2̅6̅9̅3̅4̅0̅4̅2̅9̅5̅7̅6̅1̅2̅6̅2̅1̅1̅7̅4̅6̅8̅1̅6̅1̅9̅4̅6̅3̅9̅8̅0̅2̅3̅1̅8̅9̅5̅0̅7̅6̅9̅8̅1̅5̅6̅2̅4̅4̅0̅6̅0̅0̅6̅4̅6̅2̅6̅4̅9̅6̅8̅6̅3̅7̅1̅4̅1̅2̅2̅7̅9̅0̅3̅4̅4̅0̅4̅1̅0̅5̅6̅8̅3̅3̅3̅0̅1̅6̅5̅3̅6̅7̅8̅0̅0̅7̅9̅8̅3̅2̅7̅3̅1̅4̅1̅9̅8̅8̅2̅1̅5̅1̅6̅8̅2̅1̅8̅9̅6̅9̅7̅7̅7̅6̅0̅8̅8̅1̅9̅6̅1̅6̅0̅4̅2̅5̅7̅7̅4̅5̅6̅7̅5̅7̅2̅7̅0̅4̅8̅0̅8̅9̅7̅1̅6̅7̅8̅3̅8̅8̅1̅3̅9̅1̅3̅7̅0̅4̅6̅1̅8̅8̅9̅3̅7̅4̅6̅4̅3̅6̅0̅3̅8̅7̅7̅5̅8̅9̅8̅1̅1̅8̅2̅2̅8̅4̅7̅3̅6̅7̅4̅2̅0̅6̅4̅2̅4̅6̅3̅4̅0̅9̅9̅9̅8̅0̅9̅9̅2̅2̅0̅6̅8̅0̅4̅7̅8̅9̅9̅6̅3̅8̅8̅5̅1̅9̅2̅9̅2̅9̅1̅0̅0̅9̅3̅1̅3̅8̅1̅8̅6̅6̅5̅6̅5̅2̅9̅1̅7̅6̅9̅6̅2̅5̅5̅4̅6̅4̅7̅4̅0̅5̅4̅3̅6̅2̅2̅8̅8̅5̅3̅8̅3̅0̅0̅7̅0̅3̅2̅8̅8̅3̅4̅8̅2̅2̅2̅7̅7̅1̅3̅3̅6̅2̅4̅7̅8̅6̅1̅6̅2̅3̅2̅6̅5̅5̅3̅8̅8̅7̅0̅9̅3̅7̅0̅8̅4̅2̅0̅4̅5̅2̅3̅8̅5̅4̅7̅8̅0̅4̅5̅9̅9̅8̅8̅5̅9̅5̅3̅2̅4̅0̅8̅2̅8̅7̅3̅9̅7̅8̅3̅3̅1̅1̅1̅5̅7̅5̅7̅4̅6̅0̅5̅5̅8̅8̅2̅9̅1̅1̅9̅9̅3̅9̅1̅7̅5̅0̅6̅1̅7̅7̅5̅3̅2̅7̅8̅8̅4̅4̅3̅2̅6̅1̅7̅3̅7̅3̅1̅2̅2̅9̅8̅0̅4̅2̅1̅9̅7̅3̅0̅0̅8̅9̅3̅3̅6̅6̅2̅8̅0̅1̅7̅4̅8̅7̅1̅6̅9̅7̅3̅9̅5̅9̅3̅2̅3̅3̅2̅2̅5̅6̅2̅2̅5̅0̅5̅2̅2̅7̅1̅4̅3̅1̅2̅8̅6̅8̅2̅7̅5̅9̅9̅3̅1̅5̅7̅1̅9̅4̅4̅4̅9̅7̅2̅4̅3̅8̅6̅9̅9̅8̅6̅6̅9̅4̅5̅4̅4̅7̅6̅3̅3̅5̅2̅9̅7̅4̅7̅1̅9̅6̅3̅5̅0̅5̅0̅3̅7̅0̅6̅5̅1̅9̅6̅7̅3̅0̅6̅5̅9̅5̅7̅0̅4̅2̅3̅8̅7̅3̅7̅8̅8̅2̅5̅3̅1̅8̅3̅8̅0̅5̅3̅6̅0̅1̅9̅7̅6̅8̅1̅0̅4̅9̅2̅3̅0̅1̅8̅4̅3̅7̅5̅5̅9̅3̅9̅9̅3̅5̅3̅7̅3̅5̅0̅3̅1̅3̅6̅2̅8̅5̅8̅7̅7̅2̅0̅9̅6̅5̅5̅9̅5̅8̅9̅4̅3̅1̅6̅6̅6̅9̅8̅3̅4̅6̅3̅2̅1̅9̅9̅2̅0̅1̅6̅7̅2̅6̅8̅5̅8̅0̅1̅1̅7̅8̅4̅8̅3̅1̅7̅8̅1̅0̅3̅0̅2̅2̅2̅3̅9̅1̅1̅8̅0̅3̅8̅3̅9̅5̅7̅4̅2̅2̅5̅4̅3̅2̅4̅2̅7̅2̅9̅5̅1̅9̅1̅0̅2̅8̅3̅2̅1̅6̅1̅1̅8̅6̅0̅8̅6̅2̅9̅5̅3̅8̅1̅1̅0̅6̅2̅5̅3̅5̅6̅3̅9̅6̅1̅2̅2̅4̅1̅0̅1̅8̅8̅1̅7̅7̅1̅5̅2̅6̅3̅2̅5̅7̅9̅3̅5̅7̅5̅3̅6̅5̅9
```

## Nim

Translation of: Wren
Library: bignum
```import strformat, strutils, tables
import bignum

proc divide(m, n: Int): tuple[repr: string; cycle: string; period: int] =
doAssert m >= 0, "m must not be negative."
doAssert n > 0, "n must be positive."

var quotient = &"{m div n}."
var c = m mod n * 10
var zeros = 0
while c > 0 and c < n:
c *= 10
quotient &= '0'
inc zeros

var digits = ""
var passed: Table[string, int]
var i = 0
while true:
let cs = \$c
if cs in passed:
let idx = passed[cs]
let prefix = digits[0..<idx]
var cycle = digits[idx..^1]
var repr = &"{quotient}{prefix}({cycle})"
repr = repr.replace("(0)", "").strip(leading = false, trailing = true, {'.'})
let index = repr.find('(')
if index < 0: return (repr, "", 0)
repr = repr.multiReplace(("(", ""), (")", ""))
for _ in 1..zeros:
if cycle[^1] == '0':
repr.setLen(repr.len - 1)
cycle = '0' & cycle[0..^2]
else:
break
return (repr & "...", cycle, cycle.len)

let q = c div n
let r = c mod n
passed[cs] = i
digits &= \$q
inc i
c = r * 10

const Tests = [("0", "1"), ("1", "1"), ("1", "3"), ("1", "7"),
("83","60"), ("1", "17"), ("10", "13"), ("3227", "555"),
("476837158203125", "9223372036854775808"), ("1", "149"), ("1", "5261")]

for test in Tests:
let a = newInt(test[0])
let b = newInt(test[1])
let (repr, cycle, period) = divide(a, b)
echo &"{a}/{b} = {repr}"
echo &"Cycle is <{cycle}>"
echo &"Period is {period}\n"
```
Output:
```0/1 = 0
Cycle is <>
Period is 0

1/1 = 1
Cycle is <>
Period is 0

1/3 = 0.3...
Cycle is <3>
Period is 1

1/7 = 0.142857...
Cycle is <142857>
Period is 6

83/60 = 1.383...
Cycle is <3>
Period is 1

1/17 = 0.0588235294117647...
Cycle is <0588235294117647>
Period is 16

10/13 = 0.769230...
Cycle is <769230>
Period is 6

3227/555 = 5.8144...
Cycle is <144>
Period is 3

476837158203125/9223372036854775808 = 0.000051698788284564229679463043254372678347863256931304931640625
Cycle is <>
Period is 0

1/149 = 0.0067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651...
Cycle is <0067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651>
Period is 148

1/5261 = 0.00019007793195210036114807070899068618133434708230374453525945637711461699296711651777228663752138376734461129062915795476145219540011404675917126021668884242539441170880060824938224672115567382626877019578026991066337198251283026040676677437749477285687131724006842805550275613001330545523664702528036494962934803269340429576126211746816194639802318950769815624406006462649686371412279034404105683330165367800798327314198821516821896977760881961604257745675727048089716783881391370461889374643603877589811822847367420642463409998099220680478996388519292910093138186656529176962554647405436228853830070328834822277133624786162326553887093708420452385478045998859532408287397833111575746055882911993917506177532788443261737312298042197300893366280174871697395932332256225052271431286827599315719444972438699866945447633529747196350503706519673065957042387378825318380536019768104923018437559399353735031362858772096559589431666983463219920167268580117848317810302223911803839574225432427295191028321611860862953811062535639612241018817715263257935753659...
Cycle is <00019007793195210036114807070899068618133434708230374453525945637711461699296711651777228663752138376734461129062915795476145219540011404675917126021668884242539441170880060824938224672115567382626877019578026991066337198251283026040676677437749477285687131724006842805550275613001330545523664702528036494962934803269340429576126211746816194639802318950769815624406006462649686371412279034404105683330165367800798327314198821516821896977760881961604257745675727048089716783881391370461889374643603877589811822847367420642463409998099220680478996388519292910093138186656529176962554647405436228853830070328834822277133624786162326553887093708420452385478045998859532408287397833111575746055882911993917506177532788443261737312298042197300893366280174871697395932332256225052271431286827599315719444972438699866945447633529747196350503706519673065957042387378825318380536019768104923018437559399353735031362858772096559589431666983463219920167268580117848317810302223911803839574225432427295191028321611860862953811062535639612241018817715263257935753659>
Period is 1052```

## Perl

```use strict;
use warnings;
use utf8;
binmode(STDOUT, ':utf8');

sub long_division {
my(\$n, \$d) = @_;
my %seen;

my(\$numerator,\$denominator) = (abs \$n, abs \$d);
my \$negative = (\$n < 0 xor \$d < 0) ? '-' : '';

my \$fraction = sprintf '%d.', \$numerator / \$denominator;
my \$position = length \$fraction;
\$numerator %= \$denominator;
while (!\$seen{\$numerator}) {
return 0, \$fraction =~ s/\.\$//r unless \$numerator;
\$seen{\$numerator} = \$position;
\$fraction  .= int 10 * \$numerator / \$denominator;
\$numerator  =     10 * \$numerator % \$denominator;
\$position++;
}

my \$period = length(\$fraction) - \$seen{\$numerator};
substr(\$fraction, \$seen{\$numerator}+(2*\$_)+1, 0, "\N{COMBINING OVERLINE}") for 0 .. \$period-1;
\$period, \$negative . \$fraction
}

printf "%10s Period is %5d : %s\n", \$_, long_division split '/'
for <0/1 1/1 1/5 1/3 -1/3 1/7 -83/60 1/17 10/13 3227/555 1/149>
```
Output:
```                                0/1 Period is     0 : 0
1/1 Period is     0 : 1
1/5 Period is     0 : 0.2
1/3 Period is     1 : 0.3̅
-1/3 Period is     1 : -0.3̅
1/7 Period is     6 : 0.1̅4̅2̅8̅5̅7̅
-83/60 Period is     1 : -1.383̅
1/17 Period is    16 : 0.0̅5̅8̅8̅2̅3̅5̅2̅9̅4̅1̅1̅7̅6̅4̅7̅
10/13 Period is     6 : 0.7̅6̅9̅2̅3̅0̅
3227/555 Period is     3 : 5.81̅4̅4̅
476837158203125/9223372036854775808 Period is     0 : 0.0000516987882845642321427703791414387524127960205078125
1/149 Period is   148 : 0.0̅0̅6̅7̅1̅1̅4̅0̅9̅3̅9̅5̅9̅7̅3̅1̅5̅4̅3̅6̅2̅4̅1̅6̅1̅0̅7̅3̅8̅2̅5̅5̅0̅3̅3̅5̅5̅7̅0̅4̅6̅9̅7̅9̅8̅6̅5̅7̅7̅1̅8̅1̅2̅0̅8̅0̅5̅3̅6̅9̅1̅2̅7̅5̅1̅6̅7̅7̅8̅5̅2̅3̅4̅8̅9̅9̅3̅2̅8̅8̅5̅9̅0̅6̅0̅4̅0̅2̅6̅8̅4̅5̅6̅3̅7̅5̅8̅3̅8̅9̅2̅6̅1̅7̅4̅4̅9̅6̅6̅4̅4̅2̅9̅5̅3̅0̅2̅0̅1̅3̅4̅2̅2̅8̅1̅8̅7̅9̅1̅9̅4̅6̅3̅0̅8̅7̅2̅4̅8̅3̅2̅2̅1̅4̅7̅6̅5̅1̅```

## Phix

Translation of the Python code linked to by the Wren entry, modified to cope with negatives.

```with javascript_semantics
procedure test(sequence s)
atom {n,d} = s,
{numr,denr} = {abs(n),abs(d)},
c = 10*remainder(numr,denr)
string sgn = iff(sign(n)*sign(d)=-1?"-":""),
q = sprintf("%s%d.",{sgn,floor(numr/denr)}),
digits = ""
while c and c<denr do
c *= 10
q &= '0'
end while
integer passed = new_dict()
while getd_index(c,passed)=NULL do
integer digit = floor(c/denr)
assert(digit>=0 and digit<=9)
digits &= '0'+digit
setd(c,length(digits),passed)
c = 10*remainder(c,denr)
end while
integer pc = getd(c,passed)
destroy_dict(passed)
q &= digits[1..pc-1]
digits = digits[pc..\$]
if digits="0" then
q = trim_tail(q,'.')
else
while digits[\$] = q[\$] do
{digits,q} = {q[\$]&digits[1..\$-1],q[1..\$-1]}
end while
integer ld = length(digits)
if ld>20 then digits[11..-11] = "..." end if
q = sprintf("%s{%s} (period %d)",{q,digits,ld})
end if
string nod = sprintf("%d/%d",{n,d})
printf(1,"%40s = %s\n",{nod,q})
end procedure

constant tests = {{0,1},{1,1},{1,3},{-1,3},{1,-3},{-1,-3},{-17,2},{177,16},
{1,7},{-83,60},{1,17},{10,13},{3227,555},{1,149},{1,5261},
{476837158203125,9223372036854775808}}[1..\$-(machine_bits()=32)]
papply(tests,test)
```
Output:

The results below are on 64 bit, not surprisingly the last example is inaccurate past 16 significant digits on 32 bit (ditto p2js), and hence omitted.

```                                     0/1 = 0
1/1 = 1
1/3 = 0.{3} (period 1)
-1/3 = -0.{3} (period 1)
1/-3 = -0.{3} (period 1)
-1/-3 = 0.{3} (period 1)
-17/2 = -8.5
177/16 = 11.0625
1/7 = 0.{142857} (period 6)
-83/60 = -1.38{3} (period 1)
1/17 = 0.{0588235294117647} (period 16)
10/13 = 0.{769230} (period 6)
3227/555 = 5.8{144} (period 3)
1/149 = 0.{0067114093...8322147651} (period 148)
1/5261 = 0.{0001900779...7935753659} (period 1052)
476837158203125/9223372036854775808 = 0.000051698788284564229679463043254372678347863256931304931640625
```

## Raku

It's a built-in.

```for 0/1, 1/1, 1/3, 1/7, -83/60, 1/17, 10/13, 3227/555, 5**21/2**63, 1/149, 1/5261 -> \$rat {
printf "%35s - Period is %-5s: %s%s\n", \$rat.nude.join('/'), .[1].chars, .[0], (.[1].comb Z~ "\c[COMBINING OVERLINE]" xx *).join
given \$rat.base-repeating
}
```
Output:
```                                0/1 - Period is 0    : 0
1/1 - Period is 0    : 1
1/3 - Period is 1    : 0.3̅
1/7 - Period is 6    : 0.1̅4̅2̅8̅5̅7̅
-83/60 - Period is 1    : -1.383̅
1/17 - Period is 16   : 0.0̅5̅8̅8̅2̅3̅5̅2̅9̅4̅1̅1̅7̅6̅4̅7̅
10/13 - Period is 6    : 0.7̅6̅9̅2̅3̅0̅
3227/555 - Period is 3    : 5.81̅4̅4̅
476837158203125/9223372036854775808 - Period is 0    : 0.000051698788284564229679463043254372678347863256931304931640625
1/149 - Period is 148  : 0.0̅0̅6̅7̅1̅1̅4̅0̅9̅3̅9̅5̅9̅7̅3̅1̅5̅4̅3̅6̅2̅4̅1̅6̅1̅0̅7̅3̅8̅2̅5̅5̅0̅3̅3̅5̅5̅7̅0̅4̅6̅9̅7̅9̅8̅6̅5̅7̅7̅1̅8̅1̅2̅0̅8̅0̅5̅3̅6̅9̅1̅2̅7̅5̅1̅6̅7̅7̅8̅5̅2̅3̅4̅8̅9̅9̅3̅2̅8̅8̅5̅9̅0̅6̅0̅4̅0̅2̅6̅8̅4̅5̅6̅3̅7̅5̅8̅3̅8̅9̅2̅6̅1̅7̅4̅4̅9̅6̅6̅4̅4̅2̅9̅5̅3̅0̅2̅0̅1̅3̅4̅2̅2̅8̅1̅8̅7̅9̅1̅9̅4̅6̅3̅0̅8̅7̅2̅4̅8̅3̅2̅2̅1̅4̅7̅6̅5̅1̅
1/5261 - Period is 1052 : 0.0̅0̅0̅1̅9̅0̅0̅7̅7̅9̅3̅1̅9̅5̅2̅1̅0̅0̅3̅6̅1̅1̅4̅8̅0̅7̅0̅7̅0̅8̅9̅9̅0̅6̅8̅6̅1̅8̅1̅3̅3̅4̅3̅4̅7̅0̅8̅2̅3̅0̅3̅7̅4̅4̅5̅3̅5̅2̅5̅9̅4̅5̅6̅3̅7̅7̅1̅1̅4̅6̅1̅6̅9̅9̅2̅9̅6̅7̅1̅1̅6̅5̅1̅7̅7̅7̅2̅2̅8̅6̅6̅3̅7̅5̅2̅1̅3̅8̅3̅7̅6̅7̅3̅4̅4̅6̅1̅1̅2̅9̅0̅6̅2̅9̅1̅5̅7̅9̅5̅4̅7̅6̅1̅4̅5̅2̅1̅9̅5̅4̅0̅0̅1̅1̅4̅0̅4̅6̅7̅5̅9̅1̅7̅1̅2̅6̅0̅2̅1̅6̅6̅8̅8̅8̅4̅2̅4̅2̅5̅3̅9̅4̅4̅1̅1̅7̅0̅8̅8̅0̅0̅6̅0̅8̅2̅4̅9̅3̅8̅2̅2̅4̅6̅7̅2̅1̅1̅5̅5̅6̅7̅3̅8̅2̅6̅2̅6̅8̅7̅7̅0̅1̅9̅5̅7̅8̅0̅2̅6̅9̅9̅1̅0̅6̅6̅3̅3̅7̅1̅9̅8̅2̅5̅1̅2̅8̅3̅0̅2̅6̅0̅4̅0̅6̅7̅6̅6̅7̅7̅4̅3̅7̅7̅4̅9̅4̅7̅7̅2̅8̅5̅6̅8̅7̅1̅3̅1̅7̅2̅4̅0̅0̅6̅8̅4̅2̅8̅0̅5̅5̅5̅0̅2̅7̅5̅6̅1̅3̅0̅0̅1̅3̅3̅0̅5̅4̅5̅5̅2̅3̅6̅6̅4̅7̅0̅2̅5̅2̅8̅0̅3̅6̅4̅9̅4̅9̅6̅2̅9̅3̅4̅8̅0̅3̅2̅6̅9̅3̅4̅0̅4̅2̅9̅5̅7̅6̅1̅2̅6̅2̅1̅1̅7̅4̅6̅8̅1̅6̅1̅9̅4̅6̅3̅9̅8̅0̅2̅3̅1̅8̅9̅5̅0̅7̅6̅9̅8̅1̅5̅6̅2̅4̅4̅0̅6̅0̅0̅6̅4̅6̅2̅6̅4̅9̅6̅8̅6̅3̅7̅1̅4̅1̅2̅2̅7̅9̅0̅3̅4̅4̅0̅4̅1̅0̅5̅6̅8̅3̅3̅3̅0̅1̅6̅5̅3̅6̅7̅8̅0̅0̅7̅9̅8̅3̅2̅7̅3̅1̅4̅1̅9̅8̅8̅2̅1̅5̅1̅6̅8̅2̅1̅8̅9̅6̅9̅7̅7̅7̅6̅0̅8̅8̅1̅9̅6̅1̅6̅0̅4̅2̅5̅7̅7̅4̅5̅6̅7̅5̅7̅2̅7̅0̅4̅8̅0̅8̅9̅7̅1̅6̅7̅8̅3̅8̅8̅1̅3̅9̅1̅3̅7̅0̅4̅6̅1̅8̅8̅9̅3̅7̅4̅6̅4̅3̅6̅0̅3̅8̅7̅7̅5̅8̅9̅8̅1̅1̅8̅2̅2̅8̅4̅7̅3̅6̅7̅4̅2̅0̅6̅4̅2̅4̅6̅3̅4̅0̅9̅9̅9̅8̅0̅9̅9̅2̅2̅0̅6̅8̅0̅4̅7̅8̅9̅9̅6̅3̅8̅8̅5̅1̅9̅2̅9̅2̅9̅1̅0̅0̅9̅3̅1̅3̅8̅1̅8̅6̅6̅5̅6̅5̅2̅9̅1̅7̅6̅9̅6̅2̅5̅5̅4̅6̅4̅7̅4̅0̅5̅4̅3̅6̅2̅2̅8̅8̅5̅3̅8̅3̅0̅0̅7̅0̅3̅2̅8̅8̅3̅4̅8̅2̅2̅2̅7̅7̅1̅3̅3̅6̅2̅4̅7̅8̅6̅1̅6̅2̅3̅2̅6̅5̅5̅3̅8̅8̅7̅0̅9̅3̅7̅0̅8̅4̅2̅0̅4̅5̅2̅3̅8̅5̅4̅7̅8̅0̅4̅5̅9̅9̅8̅8̅5̅9̅5̅3̅2̅4̅0̅8̅2̅8̅7̅3̅9̅7̅8̅3̅3̅1̅1̅1̅5̅7̅5̅7̅4̅6̅0̅5̅5̅8̅8̅2̅9̅1̅1̅9̅9̅3̅9̅1̅7̅5̅0̅6̅1̅7̅7̅5̅3̅2̅7̅8̅8̅4̅4̅3̅2̅6̅1̅7̅3̅7̅3̅1̅2̅2̅9̅8̅0̅4̅2̅1̅9̅7̅3̅0̅0̅8̅9̅3̅3̅6̅6̅2̅8̅0̅1̅7̅4̅8̅7̅1̅6̅9̅7̅3̅9̅5̅9̅3̅2̅3̅3̅2̅2̅5̅6̅2̅2̅5̅0̅5̅2̅2̅7̅1̅4̅3̅1̅2̅8̅6̅8̅2̅7̅5̅9̅9̅3̅1̅5̅7̅1̅9̅4̅4̅4̅9̅7̅2̅4̅3̅8̅6̅9̅9̅8̅6̅6̅9̅4̅5̅4̅4̅7̅6̅3̅3̅5̅2̅9̅7̅4̅7̅1̅9̅6̅3̅5̅0̅5̅0̅3̅7̅0̅6̅5̅1̅9̅6̅7̅3̅0̅6̅5̅9̅5̅7̅0̅4̅2̅3̅8̅7̅3̅7̅8̅8̅2̅5̅3̅1̅8̅3̅8̅0̅5̅3̅6̅0̅1̅9̅7̅6̅8̅1̅0̅4̅9̅2̅3̅0̅1̅8̅4̅3̅7̅5̅5̅9̅3̅9̅9̅3̅5̅3̅7̅3̅5̅0̅3̅1̅3̅6̅2̅8̅5̅8̅7̅7̅2̅0̅9̅6̅5̅5̅9̅5̅8̅9̅4̅3̅1̅6̅6̅6̅9̅8̅3̅4̅6̅3̅2̅1̅9̅9̅2̅0̅1̅6̅7̅2̅6̅8̅5̅8̅0̅1̅1̅7̅8̅4̅8̅3̅1̅7̅8̅1̅0̅3̅0̅2̅2̅2̅3̅9̅1̅1̅8̅0̅3̅8̅3̅9̅5̅7̅4̅2̅2̅5̅4̅3̅2̅4̅2̅7̅2̅9̅5̅1̅9̅1̅0̅2̅8̅3̅2̅1̅6̅1̅1̅8̅6̅0̅8̅6̅2̅9̅5̅3̅8̅1̅1̅0̅6̅2̅5̅3̅5̅6̅3̅9̅6̅1̅2̅2̅4̅1̅0̅1̅8̅8̅1̅7̅7̅1̅5̅2̅6̅3̅2̅5̅7̅9̅3̅5̅7̅5̅3̅6̅5̅9̅```

## RPL

Works with: HP version 48
Translation of: Nim
```« DUP2 /
IF DUP FP THEN
IP "." +  ROT ROT   @ HP49+: add R→I after IP
ABS SWAP ABS OVER MOD 10 * { }
→ quotient n c passed
« ""
WHILE c DUP n < AND REPEAT
10 'c' STO*
'quotient' "0" STO+
END
WHILE passed c POS NOT REPEAT
'passed' c STO+
c n / IP +   @ HP49+: replace / IP by IQUOT
c n MOD 10 * 'c' STO
END
passed c POS DUP2 1 SWAP 1 - SUB
quotient SWAP + ROT ROT
OVER SIZE SUB
IF DUP "0" == THEN DROP "" END
»
ELSE →STR ROT ROT DROP2 "" END
» 'LDIV' STO      @ ( m n → "quotient.prefix" "repetend" )

« DUP2 "/" SWAP + + " = " + ROT ROT
LDIV
IF DUP SIZE THEN ")" + SWAP "(" + SWAP + ELSE DROP END
+
» 'VUDIV' STO     @ @ ( m n → "m/n = quotient.prefix(repetend)" )
```
```-3227 555 VUDIV
355 113 VUDIV
```
Output:
```
2: "-3227/555 = -5.8(144)"
1: 355/113 = 3.(1415929203539823008849557522123893805309734513274336283185840707964601769911504424778761061946902654867256637168)
```

## V (Vlang)

Translation of: wren
```import math.big

const big_ten = big.integer_from_int(10)

fn divide(m big.Integer, n big.Integer) ?[]string {
if m < big.zero_int {
return error('m must not be negative')
}
if n <= big.zero_int {
return error('n must be positive')
}
mut quotient := '\${(m/n)}.'
mut c := (m % n) * big_ten
mut zeros := 0
for c > big.zero_int && c < n {
c = c * big_ten
quotient = quotient + "0"
zeros ++
}
mut digits := ""
mut passed := map[string]int{}//string:int
mut i := 0
for {
mut cs := c.str()
if cs in passed {
prefix := digits[0..passed[cs]]
mut repetend := digits[passed[cs]..digits.len]
mut result := '\$quotient\${prefix}(\${repetend})'
result = result.replace("(0)", "").trim_right(".")
index := result.index("(") or {-1}
if index == -1 {
return [result, "", '0']
}
result = result.replace("(", "").replace(")", "")
for _ in 0..zeros {
if repetend[repetend.len-1] == 0 {
result = result[0..result.len-1]
repetend = "0" + repetend[0..result.len-1]
} else {
break
}
}
return [result + "....", repetend, repetend.len.str()]
}
q := c / n
r := c % n
passed[cs] = i
digits += q.str()
i++
c = r * big_ten
}
return ['FAIL','','']
}

fn main(){
for test in [[0, 1], [1, 1], [1, 3], [1, 7], [83,60], [1, 17], [10, 13], [3227, 555],
[476837158203125, 9223372036854775808], [1, 149], [1, 5261]] {
a := big.integer_from_i64(test[0])
b := big.integer_from_i64(test[1])
res := divide(a,b) or {['Need positive numbers','','']}
println('\$a/\$b = \${res[0]}')
println("repetend is '\${res[1]}'")
println('period is \${res[2]}\n')
}
}```
Output:
`Similar as wren entry`

## Wren

This is based on the Python code here.

```import "./big" for BigInt

var divide = Fn.new { |m, n|
if (m < 0) Fiber.abort("m must not be negative")
if (n <= 0) Fiber.abort("n must be positive.")
var quotient = (m/n).toString + "."
var c = (m % n) * 10
var zeros = 0
while (c > 0 && c < n) {
c = c * 10
quotient = quotient + "0"
zeros = zeros + 1
}
var digits = ""
var passed = {}
var i = 0
while (true) {
var cs = c.toString
if (passed.containsKey(cs)) {
var prefix = digits[0...passed[cs]]
var repetend = digits[passed[cs]..-1]
var result = quotient + prefix + "(" + repetend + ")"
result = result.replace("(0)", "").trimEnd(".")
var index = result.indexOf("(")
if (index == -1) return [result, "", 0]
result = result.replace("(", "").replace(")", "")
for (i in 0...zeros) {
if (repetend[-1] == "0") {
result = result[0..-2]
repetend = "0" + repetend[0..-2]
} else break
}
return [result + "....", repetend, repetend.count]
}
var q = c / n
var r = c % n
passed[cs] = i
digits = digits + q.toString
i = i + 1
c = r * 10
}
}

var tests = [
[0, 1], [1, 1], [1, 3], [1, 7], [83,60], [1, 17], [10, 13], [3227, 555],
[476837158203125, "9223372036854775808"], [1, 149], [1, 5261]
]
for (test in tests) {
var a = BigInt.new(test[0])
var b = BigInt.new(test[1])
var res = divide.call(a, b)
System.print("%(a)/%(b) = %(res[0])")
System.print("Repetend is '%(res[1])'")
System.print("Period is %(res[2])\n")
}
```
Output:
```0/1 = 0
Repetend is ''
Period is 0

1/1 = 1
Repetend is ''
Period is 0

1/3 = 0.3....
Repetend is '3'
Period is 1

1/7 = 0.142857....
Repetend is '142857'
Period is 6

83/60 = 1.383....
Repetend is '3'
Period is 1

1/17 = 0.0588235294117647....
Repetend is '0588235294117647'
Period is 16

10/13 = 0.769230....
Repetend is '769230'
Period is 6

3227/555 = 5.8144....
Repetend is '144'
Period is 3

476837158203125/9223372036854775808 = 0.000051698788284564229679463043254372678347863256931304931640625
Repetend is ''
Period is 0

1/149 = 0.0067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651....
Repetend is '0067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651'
Period is 148

1/5261 = 0.00019007793195210036114807070899068618133434708230374453525945637711461699296711651777228663752138376734461129062915795476145219540011404675917126021668884242539441170880060824938224672115567382626877019578026991066337198251283026040676677437749477285687131724006842805550275613001330545523664702528036494962934803269340429576126211746816194639802318950769815624406006462649686371412279034404105683330165367800798327314198821516821896977760881961604257745675727048089716783881391370461889374643603877589811822847367420642463409998099220680478996388519292910093138186656529176962554647405436228853830070328834822277133624786162326553887093708420452385478045998859532408287397833111575746055882911993917506177532788443261737312298042197300893366280174871697395932332256225052271431286827599315719444972438699866945447633529747196350503706519673065957042387378825318380536019768104923018437559399353735031362858772096559589431666983463219920167268580117848317810302223911803839574225432427295191028321611860862953811062535639612241018817715263257935753659....
Repetend is '00019007793195210036114807070899068618133434708230374453525945637711461699296711651777228663752138376734461129062915795476145219540011404675917126021668884242539441170880060824938224672115567382626877019578026991066337198251283026040676677437749477285687131724006842805550275613001330545523664702528036494962934803269340429576126211746816194639802318950769815624406006462649686371412279034404105683330165367800798327314198821516821896977760881961604257745675727048089716783881391370461889374643603877589811822847367420642463409998099220680478996388519292910093138186656529176962554647405436228853830070328834822277133624786162326553887093708420452385478045998859532408287397833111575746055882911993917506177532788443261737312298042197300893366280174871697395932332256225052271431286827599315719444972438699866945447633529747196350503706519673065957042387378825318380536019768104923018437559399353735031362858772096559589431666983463219920167268580117848317810302223911803839574225432427295191028321611860862953811062535639612241018817715263257935753659'
Period is 1052
```