Integer long division: Difference between revisions

Line 94:

1/5261 (Period 1052) = 0.̅0̅0̅0̅1̅9̅0̅0̅7̅7̅9̅3̅1̅9̅5̅2̅1̅0̅0̅3̅6̅1̅1̅4̅8̅0̅7̅0̅7̅0̅8̅9̅9̅0̅6̅8̅6̅1̅8̅1̅3̅3̅4̅3̅4̅7̅0̅8̅2̅3̅0̅3̅7̅4̅4̅5̅3̅5̅2̅5̅9̅4̅5̅6̅3̅7̅7̅1̅1̅4̅6̅1̅6̅9̅9̅2̅9̅6̅7̅1̅1̅6̅5̅1̅7̅7̅7̅2̅2̅8̅6̅6̅3̅7̅5̅2̅1̅3̅8̅3̅7̅6̅7̅3̅4̅4̅6̅1̅1̅2̅9̅0̅6̅2̅9̅1̅5̅7̅9̅5̅4̅7̅6̅1̅4̅5̅2̅1̅9̅5̅4̅0̅0̅1̅1̅4̅0̅4̅6̅7̅5̅9̅1̅7̅1̅2̅6̅0̅2̅1̅6̅6̅8̅8̅8̅4̅2̅4̅2̅5̅3̅9̅4̅4̅1̅1̅7̅0̅8̅8̅0̅0̅6̅0̅8̅2̅4̅9̅3̅8̅2̅2̅4̅6̅7̅2̅1̅1̅5̅5̅6̅7̅3̅8̅2̅6̅2̅6̅8̅7̅7̅0̅1̅9̅5̅7̅8̅0̅2̅6̅9̅9̅1̅0̅6̅6̅3̅3̅7̅1̅9̅8̅2̅5̅1̅2̅8̅3̅0̅2̅6̅0̅4̅0̅6̅7̅6̅6̅7̅7̅4̅3̅7̅7̅4̅9̅4̅7̅7̅2̅8̅5̅6̅8̅7̅1̅3̅1̅7̅2̅4̅0̅0̅6̅8̅4̅2̅8̅0̅5̅5̅5̅0̅2̅7̅5̅6̅1̅3̅0̅0̅1̅3̅3̅0̅5̅4̅5̅5̅2̅3̅6̅6̅4̅7̅0̅2̅5̅2̅8̅0̅3̅6̅4̅9̅4̅9̅6̅2̅9̅3̅4̅8̅0̅3̅2̅6̅9̅3̅4̅0̅4̅2̅9̅5̅7̅6̅1̅2̅6̅2̅1̅1̅7̅4̅6̅8̅1̅6̅1̅9̅4̅6̅3̅9̅8̅0̅2̅3̅1̅8̅9̅5̅0̅7̅6̅9̅8̅1̅5̅6̅2̅4̅4̅0̅6̅0̅0̅6̅4̅6̅2̅6̅4̅9̅6̅8̅6̅3̅7̅1̅4̅1̅2̅2̅7̅9̅0̅3̅4̅4̅0̅4̅1̅0̅5̅6̅8̅3̅3̅3̅0̅1̅6̅5̅3̅6̅7̅8̅0̅0̅7̅9̅8̅3̅2̅7̅3̅1̅4̅1̅9̅8̅8̅2̅1̅5̅1̅6̅8̅2̅1̅8̅9̅6̅9̅7̅7̅7̅6̅0̅8̅8̅1̅9̅6̅1̅6̅0̅4̅2̅5̅7̅7̅4̅5̅6̅7̅5̅7̅2̅7̅0̅4̅8̅0̅8̅9̅7̅1̅6̅7̅8̅3̅8̅8̅1̅3̅9̅1̅3̅7̅0̅4̅6̅1̅8̅8̅9̅3̅7̅4̅6̅4̅3̅6̅0̅3̅8̅7̅7̅5̅8̅9̅8̅1̅1̅8̅2̅2̅8̅4̅7̅3̅6̅7̅4̅2̅0̅6̅4̅2̅4̅6̅3̅4̅0̅9̅9̅9̅8̅0̅9̅9̅2̅2̅0̅6̅8̅0̅4̅7̅8̅9̅9̅6̅3̅8̅8̅5̅1̅9̅2̅9̅2̅9̅1̅0̅0̅9̅3̅1̅3̅8̅1̅8̅6̅6̅5̅6̅5̅2̅9̅1̅7̅6̅9̅6̅2̅5̅5̅4̅6̅4̅7̅4̅0̅5̅4̅3̅6̅2̅2̅8̅8̅5̅3̅8̅3̅0̅0̅7̅0̅3̅2̅8̅8̅3̅4̅8̅2̅2̅2̅7̅7̅1̅3̅3̅6̅2̅4̅7̅8̅6̅1̅6̅2̅3̅2̅6̅5̅5̅3̅8̅8̅7̅0̅9̅3̅7̅0̅8̅4̅2̅0̅4̅5̅2̅3̅8̅5̅4̅7̅8̅0̅4̅5̅9̅9̅8̅8̅5̅9̅5̅3̅2̅4̅0̅8̅2̅8̅7̅3̅9̅7̅8̅3̅3̅1̅1̅1̅5̅7̅5̅7̅4̅6̅0̅5̅5̅8̅8̅2̅9̅1̅1̅9̅9̅3̅9̅1̅7̅5̅0̅6̅1̅7̅7̅5̅3̅2̅7̅8̅8̅4̅4̅3̅2̅6̅1̅7̅3̅7̅3̅1̅2̅2̅9̅8̅0̅4̅2̅1̅9̅7̅3̅0̅0̅8̅9̅3̅3̅6̅6̅2̅8̅0̅1̅7̅4̅8̅7̅1̅6̅9̅7̅3̅9̅5̅9̅3̅2̅3̅3̅2̅2̅5̅6̅2̅2̅5̅0̅5̅2̅2̅7̅1̅4̅3̅1̅2̅8̅6̅8̅2̅7̅5̅9̅9̅3̅1̅5̅7̅1̅9̅4̅4̅4̅9̅7̅2̅4̅3̅8̅6̅9̅9̅8̅6̅6̅9̅4̅5̅4̅4̅7̅6̅3̅3̅5̅2̅9̅7̅4̅7̅1̅9̅6̅3̅5̅0̅5̅0̅3̅7̅0̅6̅5̅1̅9̅6̅7̅3̅0̅6̅5̅9̅5̅7̅0̅4̅2̅3̅8̅7̅3̅7̅8̅8̅2̅5̅3̅1̅8̅3̅8̅0̅5̅3̅6̅0̅1̅9̅7̅6̅8̅1̅0̅4̅9̅2̅3̅0̅1̅8̅4̅3̅7̅5̅5̅9̅3̅9̅9̅3̅5̅3̅7̅3̅5̅0̅3̅1̅3̅6̅2̅8̅5̅8̅7̅7̅2̅0̅9̅6̅5̅5̅9̅5̅8̅9̅4̅3̅1̅6̅6̅6̅9̅8̅3̅4̅6̅3̅2̅1̅9̅9̅2̅0̅1̅6̅7̅2̅6̅8̅5̅8̅0̅1̅1̅7̅8̅4̅8̅3̅1̅7̅8̅1̅0̅3̅0̅2̅2̅2̅3̅9̅1̅1̅8̅0̅3̅8̅3̅9̅5̅7̅4̅2̅2̅5̅4̅3̅2̅4̅2̅7̅2̅9̅5̅1̅9̅1̅0̅2̅8̅3̅2̅1̅6̅1̅1̅8̅6̅0̅8̅6̅2̅9̅5̅3̅8̅1̅1̅0̅6̅2̅5̅3̅5̅6̅3̅9̅6̅1̅2̅2̅4̅1̅0̅1̅8̅8̅1̅7̅7̅1̅5̅2̅6̅3̅2̅5̅7̅9̅3̅5̅7̅5̅3̅6̅5̅9

</pre>

=={{header|Nim}}==

<lang Nim>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"</lang>

<pre>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</pre>

=={{header|Phix}}==