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).
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
Common Lisp
<lang 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)
() ))
</lang>
- Output:
($/ 1 149) 00067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651 148
Julia
<lang julia>function f2d(numr, denr)
dpart, remainders, r = "", Dict{BigInt, Int}(), BigInt(numr) % denr while (r != 0) && !haskey(remainders, r) remainders[r] = length(dpart) r *= 10 partrem, r = divrem(r, denr) dpart *= string(partrem) end return r == 0 ? (0, 0) : (dpart[remainders[r]+1:end], remainders[r])
end
overline(s) = mapreduce(c -> "\u0305" * c, *, s)
testpairs = [(0, 1), (1, 1), (1, 3), (1, 7), (-83, 60), (1, 17), (10, 13), (3227, 555),
(5^21, Int128(2)^63), (1, 149), (1, 5261)]
function testrepeatingdecimals()
for (numr, denr) in testpairs n = numr < 0 ? -numr : numr repeated, extra = f2d(n, denr) if repeated == 0 println(lpad("$numr/$denr", 36), " (Period 0) = ", BigFloat(numr)/denr) else prefix, suffix = split(string(BigFloat(numr) / denr)[begin:end-2], ".") println(lpad("$numr/$denr", 36), " (Period ", rpad("$(length(repeated)))", 6), " = $prefix.$(suffix[begin:extra])$(overline(repeated))") end end
end
testrepeatingdecimals()
</lang>
- 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
<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>
- 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
<lang perl>use strict; use warnings;
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}, 0, '{'; $fraction .= '}'; $period, $negative . $fraction
}
printf "%10s Period is %5d : %s\n", $_, long_division split '/'
for <0/1 1/1 1/5 1/3 -1/3 1/7 -83/60 1/17 10/13 3227/555 1/149></lang>
- Output:
0/1 Period is 0 : 0 1/1 Period is 0 : 1 1/5 Period is 0 : 0.2 1/3 Period is 1 : 0.{3} -1/3 Period is 1 : -0.{3} 1/7 Period is 6 : 0.{142857} -83/60 Period is 3 : -1.38{3} 1/17 Period is 16 : 0.{0588235294117647} 10/13 Period is 6 : 0.{769230} 3227/555 Period is 4 : 5.8{144} 1/149 Period is 148 : 0.{0067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651}
Phix
Translation of the python code linked to by the Wren entry, modified to cope with negatives.
with javascript_semantics procedure test(sequence s) atom {n,d} = s, {numr,denr} = {abs(n),abs(d)}, c = 10*remainder(numr,denr) string sgn = iff(sign(n)*sign(d)=-1?"-":""), q = sprintf("%s%d.",{sgn,floor(numr/denr)}), digits = "" while c and c<denr do c *= 10 q &= '0' end while integer passed = new_dict() while getd_index(c,passed)=NULL do integer digit = floor(c/denr) assert(digit>=0 and digit<=9) digits &= '0'+digit setd(c,length(digits),passed) c = 10*remainder(c,denr) end while integer pc = getd(c,passed) destroy_dict(passed) q &= digits[1..pc-1] digits = digits[pc..$] 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:
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. <lang perl6>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
}</lang>
- 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
Wren
This is based on the Python code here. <lang ecmascript>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")
}</lang>
- 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