Square root by hand: Difference between revisions

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m (→‎{{header|REXX}}: adjusted program to show one exactly less decimal digit in the answer (result).)
m (→‎{{header|Wren}}: Minor tidy)
 
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{{draft task}}
Create a program that will calculate n digits of the square root of a number.
 
;Task:
The program should continue forever (or until the number of digits is specified) calculating and outputting each decimal digit in succession. The program should be a "spigot algorithm" generating the digits of the number sequentially from left to right providing increasing precision as the algorithm proceeds.
Create a program that will calculate   '''n'''   decimal digits of the square root of a non─negative number.
 
 
The program should continue forever (or until the number of digits is specified) calculating and outputting each decimal digit in succession.
 
The program should be a "spigot algorithm" generating the digits of the number sequentially from left to right providing increasing precision as the algorithm proceeds.
<br><br>
 
=={{header|Arturo}}==
{{trans|Nim}}
<syntaxhighlight lang="rebol">i: 2
j: to :integer sqrt 2.0
k: new j
d: new j
n: new 500
n0: n
 
while ø [
prints d
i: (i - k * d) * 100
k: new 20 * j
d: new 1
while [d =< 10][
if i < d * k+d [
dec 'd
break
]
inc 'd
]
j: d + j*10
'k + d
if n0 > 0 -> dec 'n
if n=0 -> break
]
 
print ""</syntaxhighlight>
 
{{out}}
 
<pre>14142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372</pre>
 
=={{header|C#|CSharp}}==
{{Trans|Visual Basic .NET}}
{{libheader|System.Numerics}}
<langsyntaxhighlight lang="csharp">using System;
using static System.Math;
using static System.Console;
Line 28 ⟶ 67:
if (n0 > 0) WriteLine("\nTime taken for {0} digits: {1}", n0, DateTime.Now - st); }
 
}</langsyntaxhighlight>{{out}}<pre style="height:32ex; overflow:scroll; white-space:pre-wrap;">14142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372
Time taken for 500 digits: 00:00:00.0092331
</pre>
 
=={{header|D}}==
{{trans|C#}}
<syntaxhighlight lang="d">import std.bigint;
import std.math;
import std.stdio;
 
void main() {
BigInt i = 2;
BigInt j = cast(long) floor(sqrt(cast(real) 2.0));
BigInt k = j;
BigInt d = j;
int n = 500;
int n0 = n;
do {
write(d);
i = (i - k * d) * 100;
k = 20 * j;
for (d = 1; d <= 10; d++) {
if ((k + d) * d > i) {
d -= 1;
break;
}
}
j = j * 10 + d;
k += d;
if (n0 > 0) {
n--;
}
} while (n > 0);
}</syntaxhighlight>
{{out}}
<pre>14142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372</pre>
 
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
// Square Root of n 'By Hand' (n as bigint >= 1). Nigel Galloway: October 14th., 2020
let rec fN n g=match n/100I with i when i=0I->(n%100I)::g |i->fN i ((n%100I)::g)
let fG n g=[9I.. -1I..0I]|>Seq.map(fun g->(g,g*(20I*n+g)))|>Seq.find(fun(_,n)->n<=g)
let fL(n,g,l)=let c,n=match n with []->(g*100I,[]) |_->((List.head n)+g*100I,List.tail n)
let x,y=fG l c in Some(int x,(n,c-y,l*10I+x))
let sR n g l=Seq.unfold fL (fN n [],0I,0I)|>Seq.take l|>Seq.iteri(fun i n->printf "%s%d" (if i=(g+1)/2 then "." else "") n); printfn "\n"
 
sR 2I 1 480; sR 1089I 2 8
</syntaxhighlight>
{{out}}
<pre>
1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871
 
3.3000000
</pre>
 
=={{header|Go}}==
{{trans|Visual Basic .NET}}
The original has been adjusted in a similar fashion to the Wren entry to deal with non-integer cases.
<lang go>package main
<syntaxhighlight lang="go">package main
 
import (
Line 46 ⟶ 137:
var hundred = big.NewInt(100)
 
func sqrt(n int64float64, limit int) {
iif := big.NewInt(n) < 0 {
log.Fatal("Number cannot be negative")
}
count := 0
for n != math.Trunc(n) {
n *= 100
count--
}
i := big.NewInt(int64(n))
j := new(big.Int).Sqrt(i)
count += len(j.String())
k := new(big.Int).Set(j)
d := new(big.Int).Set(j)
t := new(big.Int)
digits := 0
var sb strings.Builder
for digits < limit {
fmtsb.PrintWriteString(d.String())
t.Mul(k, d)
i.Sub(i, t)
Line 74 ⟶ 175:
digits = digits + 1
}
root := strings.TrimRight(sb.String(), "0")
fmt.Println()
if len(root) == 0 {
root = "0"
}
if count > 0 {
root = root[0:count] + "." + root[count:]
} else if count == 0 {
root = "0." + root
} else {
root = "0." + strings.Repeat("0", -count) + root
}
root = strings.TrimSuffix(root, ".")
fmt.Println(root)
}
 
func main() {
numbers := []float64{2, 0.2, 10.89, 625, 0.0001}
sqrt(2, 480) // enough for demo purposes
digits := []int{500, 80, 8, 8, 8}
}</lang>
for i, n := range numbers {
fmt.Printf("First %d significant digits (at most) of the square root of %g:\n", digits[i], n)
sqrt(n, digits[i])
fmt.Println()
}
}</syntaxhighlight>
 
{{out}}
<pre style="height:22ex72ex; overflow:scroll; white-space:pre-wrap;">
First 500 significant digits (at most) of the square root of 2:
141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372
 
First 80 significant digits (at most) of the square root of 0.2:
0.44721359549995793928183473374625524708812367192230514485417944908210418512756097
 
First 8 significant digits (at most) of the square root of 10.89:
3.3
 
First 8 significant digits (at most) of the square root of 625:
25
 
First 8 significant digits (at most) of the square root of 0.0001:
0.01
</pre>
=={{header|FreeBASIC}}==
{{libheader|GMP}}
<syntaxhighlight lang="freebasic">' version 20-12-2020
' compile with: fbc -s console
 
#Include Once "gmp.bi"
=={{header|Phix}}==
...whereas this <i>is</i> a spigot algorithm<i>!</i>
<lang Phix>-- based on https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Decimal_(base_10)
function bcd_sub(string a,b)
-- returns "a"-"b", coping with different lengths
-- (assumes a>=b, which it always will be here,
--- protected as it is by the bcd_le(b,a) call.)
integer c = 0, d = length(a)-length(b)
if d<0 then a = repeat('0',-d)&a
elsif d>0 then b = repeat('0', d)&b end if
for i=length(a) to 1 by -1 do
d = a[i]-b[i]-c
c = d<0
a[i] = d+c*10+'0'
end for
a = trim_head(a,"0") -- (note: "" equ "0")
return a
end function
 
Dim As Integer dec_p, i, x, n1, n2, r , guess
function bcd_xp20x(string p, integer x)
Dim As String number = "2", square_root, p1, p2
-- returns x*(p*20+x)
Dim As ZString Ptr zstr
integer c = 0, d, m = 1
' remove space(s) and leading 0's
p &= x+'0'
number = LTrim(Trim(number), "0")
for i=length(p) to 1 by -1 do
dec_p = InStr(number, ".")
d = (p[i]-'0')*m*x+c
Print "Square Root of "; number; " = ";
p[i] = remainder(d,10)+'0'
square_root = "Square Root of " + number + " = "
c = floor(d/10)
m = 2
end for
if c then
p = (remainder(c,10)+'0')&p
c = floor(c/10)
if c then ?9/0 end if -- loop rqd?
end if
return p
end function
 
' remove the decimal point and make number an even length string
function bcd_le(string a,b)
If dec_p = 0 Then
-- returns a<=b numerically, taking care of different lengths
If (Len(number) And 1) = 1 Then number = "0" + number
integer d = length(a)-length(b)
ifdec_p d<0= thenLen(number) + 1
Else
a = repeat('0',-d)&a
number = RTrim(number, "0")
elsif d>0 then
If dec_p <> 1 b = repeat('0',d)&bThen
p1 = Left(number, dec_p -1)
end if
If (Len(p1) And 1) = 1 Then p1 = "0" + p1
return a<=b
End If
end function
p2 = Mid(number, dec_p +1)
If (Len(p2) And 1) = 1 Then p2 = p2 + "0"
number = p1 + p2
End If
 
dec_p = dec_p Shr 1
function spigot_sqrt(string s, integer maxlen=50)
i = 1
-- returns the square root of a positive string number to any precision
 
if find('-',s) or s="" then ?9/0 end if
' handle zero's and find first non zero digit(s) of the root
integer dot = find('.',s)
' can be done with integers
if dot=0 then dot = length(s)+1 end if
Do
if remainder(dot,2)=0 then s = "0"&s end if
dotn1 += 1Val(Mid(number, i, 2))
 
string res = "", p = "", c = ""
integerIf in1 = 10 Then
n2 = 0
while true do -- (until (i>length && carry=0) or > maxlen)
Else
if (i<=length(s) and s[i]='.')
orFor (ix >length(s)= and0 dot)To then9
resIf &=x "."* x > n1 Then Exit For
dot = 0Next
n2 = x i +=- 1
endr if= n1 - (n2 * n2)
End If
c &= iff(i<=length(s)?s[i]:'0') &
 
iff(i<length(s)?s[i+1]:'0')
If dec_p for x=9 to 0 by -1 doThen
Print string y = bcd_xp20x(p,x)".";
square_root += if bcd_le(y,c) then"."
End If
c = bcd_sub(c,y)
 
res &= x+'0'
Print Str(n2); : square_root += Str(n2)
p &= x+'0'
dec_p -= exit1
n2 += end ifn2
i += 2
if x=0 then ?9/0 end if -- (sanity check)
 
end for
Loop Until n1 <> 0
i += 2
 
if (c="" and i>length(s)) or length(res)>maxlen then exit end if
' handle the rest of the number string
end while
' starting with GMP integers
return res
Dim As Mpz_ptr t1_, t2_, t3_, t4_, n2_, r_ , guess_
end function
t1_ = Allocate(Len(__Mpz_struct)) : Mpz_init(t1_)
?spigot_sqrt("152.2756")
t2_ = Allocate(Len(__Mpz_struct)) : Mpz_init(t2_)
?spigot_sqrt("15241.383936")
t3_ = Allocate(Len(__Mpz_struct)) : Mpz_init(t3_)
string r = spigot_sqrt("2",500)
t4_ = Allocate(Len(__Mpz_struct)) : Mpz_init(t4_)
puts(1,join_by(r,1,100,""))</lang>
n2_ = Allocate(Len(__Mpz_struct)) : Mpz_init(n2_)
r_ = Allocate(Len(__Mpz_struct)) : Mpz_init(r_)
guess_ = Allocate(Len(__Mpz_struct)) : Mpz_init(guess_)
 
mpz_set_ui(n2_, n2)
mpz_set_ui(r_, r)
 
For x = i To Len(number)-1 Step 2
mpz_mul_ui(t1_, r_, 10)
i = Val(Mid(number, x, 1))
mpz_add_ui(t1_, t1_, i)
 
If mpz_cmp_ui(t1_, 0) = 0 Or mpz_cmp_ui(n2_, 0) = 0 Then
mpz_set_ui(guess_, 0)
Else
mpz_fdiv_q(guess_, t1_, n2_)
If mpz_cmp_ui(guess_, 9) > 0 Then mpz_set_ui(guess_, 9)
End If
 
mpz_mul_ui(t1_, r_, 100)
i = Val(Mid(number, x, 2))
mpz_add_ui(t1_, t1_, i)
mpz_mul_ui(t3_, n2_, 10)
 
If mpz_cmp_ui(n2_, 0) = 0 Then
mpz_set_ui(guess_, 0)
Else
While mpz_cmp_ui(guess_, 0) <> 0
mpz_add(t4_, t3_, guess_)
mpz_mul(t4_, t4_, guess_)
If mpz_cmp(t4_, t1_) <= 0 Then Exit While
mpz_sub_ui(guess_, guess_, 1)
Beep
Wend
End If
 
mpz_sub(r_, t1_, t4_)
mpz_add(t3_, t3_, guess_)
mpz_add(n2_, t3_, guess_)
 
If dec_p = 0 Then
Print ".";
square_root += "."
End If
 
zstr = mpz_get_str(0, 10, guess_)
Print *zstr; : square_root += *zstr
dec_p -= 1
Next
 
' last posible position of decimal point
If dec_p = 0 And r <> 0 Then
Print ".";
square_root += "."
End If
' if r = then stop
If mpz_cmp_ui(r_, 0) <> 0 Then
 
' stop if any key is pressed
While Inkey <> "" : Wend
While Inkey = ""
mpz_mul_ui(t1_, r_, 10)
mpz_fdiv_q(guess_, t1_, n2_)
If mpz_cmp_ui(guess_, 9) > 0 Then mpz_set_ui(guess_, 9)
mpz_mul_ui(t1_, r_, 100)
mpz_mul_ui(t3_, n2_, 10)
 
Do
mpz_add(t4_, t3_, guess_)
mpz_mul(t4_, t4_, guess_)
If mpz_cmp(t4_, t1_) <= 0 Then Exit Do
mpz_sub_ui(guess_, guess_, 1)
Loop
 
mpz_sub(r_, t1_, t4_)
mpz_add(t3_, t3_, guess_)
mpz_add(n2_, t3_, guess_)
zstr = mpz_get_str(0, 10, guess_)
Print *zstr; : square_root += *zstr
 
Wend
 
End If
Print
 
/' remove this line to save the square root to a file
x = FreeFile
Open "square_root_by_hand.txt" For Output As #x
Print #x, square_root
Close
'/
 
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End</syntaxhighlight>
{{out}}
<pre style="height:30ex; overflow:scroll; white-space:pre-wrap;">Square Root of 2 = 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572735013846230912297024924836055850737212644121497099935831413222665927505592755799950501152782060571470109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989687253396546331808829640620615258352395054745750287759961729835575220337531857011354374603408498847160386899970699004815030544027790316454247823068492936918621580578463111596668713013015618568987237235288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162075847492265722600208558446652145839889394437092659180031138824646815708263010059485870400318648034219489727829064104507263688131373985525611732204024509122770022694112757362728049573810896750401836986836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112024944134172853147810580360337107730918286931471017111168391658172688941975871658215212822951848847208969463386289156288276595263514054226765323969461751129160240871551013515045538128756005263146801712740265396947024030051749531886292563138518816347800156936917688185237868405228783762938921430065586956868596459515550164472450983689603688732311438941557665104088391429233811320605243362948531704991577175622854974143899918802176243096520656421182731672625753959471725593463723863226148274262220867115583959992652117625269891754098815934864008345708518147223181420407042650905653233339843645786579679651926729239987536661721598257886026336361782749599421940377775368142621773879919455139723127406689832998989538672882285637869774966251996658352577619893932284534473569479496295216889148549253890475582883452609652409654288939453864662574492755638196441031697983306185201937938494005715633372054806854057586799967012137223947582142630658513221740883238294728761739364746783743196000159218880734785761725221186749042497736692920731109636972160893370866115673458533483329525467585164471075784860246360083444911481858765555428645512331421992631133251797060843655970435285641008791850076036100915946567067688360557174007675690509613671940132493560524018599910506210816359772643138060546701029356997104242510578174953105725593498445112692278034491350663756874776028316282960553242242695753452902883876844642917328277088831808702533985233812274999081237189254072647536785030482159180188616710897286922920119759988070381854333253646021108229927929307287178079988809917674177410898306080032631181642798823117154363869661702999934161614878686018045505553986913115186010386375325004558186044804075024119518430567453368361367459737442398855328517930896037389891517319587413442881784212502191695187559344438739618931454999990610758704909026088351763622474975785885836803745793115733980209998662218694992259591327642361941059210032802614987456659968887406795616739185957288864247346358588686449682238600698335264279905628316561391394255764906206518602164726303336297507569787060660685649816009271870929215313236828135698893709741650447459096053747279652447709409924123871061447054398674364733847745481910087288622214958952959118789214917983398108378827815306556231581036064867587303601450227320882935134138722768417667843690529428698490838455744579409598626074249954916802853077398938296036213353987532050919989360751390644449576845699347127636450716327915470159773354863893942325727754003826027478567417258095141630715959784981800944356037939098559016827215403458158152100493666295344882710729239660232163823826661262683050257278116945103537937156882336593229782319298606467978986409208560955814261436363100461559433255047449397593399912541953230093217530447653396470662761166175351875464620967634558738616488019884849747926404506544489691004079421181692579685756378488149898641685499491635761448404702103398921534237703723335311564594438970365316672194904935188290580630740134686264167247011065346349391640714628556798017793381442404526913706660977763878486623800339232437047411533187253190601916599645538115788841380843323210533767461812178014296092832411362752540887372905129407339479433061943956936702079429515878228349321931666411130154959469837897767434443539337709957134988407890850815892366070088658105470949790465722988880892461282816013133701029080290999745647849581545614648715516390502419857906131093458783306200262207372471676685455499904994085710809925759928893236615438271955005781625133038153146577907926868500806984428479152424275441026805756321565322061885751225113063937025362927161968251259192025216058701189596732244239267423734490764646727375347964598819149807931718002423855453886038368310800779182466462754117444250018727779518164383451463461299020763343017968554385631667723518389336667042222110939144930287963812839889311731308430042125550185498506529455637766031461255909104611384768282359592477228629042642736163264585443392877263860343149804896397363329754885925681149296836126725898573833216436663487023477302610106130507298611534129948808774473111229542652751653665911730142360626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=={{header|J}}==
<syntaxhighlight lang=J>srdig=: {{
if. x > 1{9!:36'' do. 9!:37]x 1}9!:36'' end.
<.@%:y*10^2x*need+x-#":<.@%:y*10^2x*need=.0>.x-#":<.@%:y=.x:y
}}</syntaxhighlight>
 
Example use: x digits of the square root of y:
<syntaxhighlight lang=J> 1000 srdig 2
1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572735013846230912297024924836055850737212644121497099935831413222665927505592755799950501152782060571470109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989687253396546331808829640620615258352395054745750287759961729835575220337531857011354374603408498847160386899970699004815030544027790316454247823068492936918621580578463111596668713013015618568987237235288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162075847492265722600208558446652145839889394437092659180031138824646815708263010059485870400318648034219489727829064104507263688131373985525611732204024509122770022694112757362728049573810896750401836986836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112024944134172853147810580360337107730918286931471017111168391658172688941975871658215212822951848847
1000 srdig 0.2
4472135954999579392818347337462552470881236719223051448541794490821041851275609798828828816757564549939016352301547567008506535448894147727172720243066905417733556346383758331622553290645279713161071522700835067570006846784828128884172865078194505185254457752599034804881363223551817818996984742781459457796964177283085379788198263387154039497357768850179508265912366353842999954849603060868230071915336665024997630356278816001124841710487084471112212612685640468186663965867919492704542402683499228405271809475771008779374122271320091514279913191133913835129156443905000121078462468010018573529751059444113532507332148971707010524661356989266844484635274554053264815360208886631651467011786196272452686397372943893979940361637904852891924069044282384465825196392651622208340991614096240806911989887013711103711145024777283310020524872625142048899237578849365806808949432230911446403475353180921837059151207155968796108310761558128787279446057512125998964427704354697184907030242092691110081414455744
1000 srdig 3
1732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248575675626141415406703029969945094998952478811655512094373648528093231902305582067974820101084674923265015312343266903322886650672254668921837971227047131660367861588019049986537379859389467650347506576050756618348129606100947602187190325083145829523959832997789824508288714463832917347224163984587855397667958063818353666110843173780894378316102088305524901670023520711144288695990956365797087168498072899493296484283020786408603988738697537582317317831395992983007838702877053913369563312103707264019249106768231199288375641141422016742752102372994270831059898459475987664288897796147837958390228854852903576033852808064381972344661059689722872865264153822664698420021195484155278441181286534507035191650016689294415480846071277143999762926834629577438361895110127148638746976545982451788550975379013880664961911962222957110555242923723192197738262561631468842032853716682938649611917049738836395495938
</syntaxhighlight>
 
=={{header|Java}}==
{{trans|D}}
<syntaxhighlight lang="java">import java.math.BigInteger;
 
public class SquareRoot {
public static final BigInteger ONE_HUNDRED = BigInteger.valueOf(100);
public static final BigInteger TWENTY = BigInteger.valueOf(20);
 
public static void main(String[] args) {
var i = BigInteger.TWO;
var j = BigInteger.valueOf((long) Math.floor(Math.sqrt(2.0)));
var k = j;
var d = j;
int n = 500;
int n0 = n;
do {
System.out.print(d);
i = i.subtract(k.multiply(d)).multiply(ONE_HUNDRED);
k = TWENTY.multiply(j);
for (d = BigInteger.ONE; d.compareTo(BigInteger.TEN) <= 0; d = d.add(BigInteger.ONE)) {
if (k.add(d).multiply(d).compareTo(i) > 0) {
d = d.subtract(BigInteger.ONE);
break;
}
}
j = j.multiply(BigInteger.TEN).add(d);
k = k.add(d);
if (n0 > 0) {
n--;
}
} while (n > 0);
System.out.println();
}
}</syntaxhighlight>
{{out}}
<pre>14142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372</pre>
 
=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
 
'''Works with gojq, the Go implementation of jq'''
 
The program presented here can readily be changed into a "spigot" by
changing the `until (.digits >= $limit; ...)` loop into a `while (true; ...)` loop, and replacing the post-loop lines to emit `.d`. The unneeded variables can likewise be easily eliminated.
 
gojq supports unbounded-precision integer arithmetic, and is therefore
used for this task.
 
'''Helper functions'''
<syntaxhighlight lang="jq"># Integer division
def idivide($j):
. as $i
| ($i % $j) as $mod
| ($i - $mod) / $j ;
 
# Integer sqrt
# input should be a non-negative integer for accuracy
# but may be any non-negative finite number
def isqrt:
def irt:
. as $x
| 1 | until(. > $x; . * 4) as $q
| {$q, $x, r: 0}
| until( .q <= 1;
.q |= idivide(4)
| .t = .x - .r - .q
| .r |= idivide(2)
| if .t >= 0
then .x = .t
| .r += .q
else .
end)
| .r ;
if type == "number" and (isinfinite|not) and (isnan|not) and . >= 0
then irt
else "isqrt requires a non-negative integer for accuracy" | error
end ;
</syntaxhighlight>
'''sqrt'''
<syntaxhighlight lang="jq">def sqrt_by_hand($limit):
. as $n
| if $n < 0 then "sqrt_by_hand: input cannot be negative." | error
else {count: 0, $n}
| until( .n | . == floor;
.n *= 100
| .count += -1 )
| .i = (.n|tostring|tonumber) # ensure .i is an integer
| .j = (.i|isqrt)
| .count = (.count + (.j|tostring|length))
| .k = .j
| .d = .j
| .digits = 0
| .root = ""
| until (.digits >= $limit;
.root = (.root + (.d|tostring))
| .i = ((.i - .k*.d) * 100)
| .k = (.j * 20)
| .d = 1
| .stop = false
| until ((.d > 10) or .stop;
if (.k + .d)*.d > .i
then .d += -1
| .stop = true
else .d += 1
end )
| .j = (.j*10 + .d)
| .k = (.k + .d)
| .digits += 1 )
| .root |= sub("0+$"; "")
| if .root == "" then .root = "0" else . end
| if .count > 0
then .root = .root[0:.count] + "." + .root[.count:]
elif .count == 0
then .root = "0." + .root
else .root = "0." + ("0" * (-.count)) + .root
end
| if .root[-1:] == "."
then .root |= .[:-1]
else .
end
| .root
end ;
[2, 0.2, 10.89, 625, 0.0001] as $numbers
| [500, 80, 8, 8, 8] as $digits
| range (0; $numbers|length) as $i
| $numbers[$i]
| "First \($digits[$i]) significant digits (at most) of the square root of \(.):",
sqrt_by_hand($digits[$i]),
""</syntaxhighlight>
{{out}}
<pre>
First 500 significant digits (at most) of the square root of 2:
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372
 
First 80 significant digits (at most) of the square root of 0.2:
0.44721359549995793928183473374625524708812367192230514485417944908210418512756097
 
First 8 significant digits (at most) of the square root of 10.89:
3.3
 
First 8 significant digits (at most) of the square root of 625:
25
 
First 8 significant digits (at most) of the square root of 0.0001:
0.01
</pre>
 
=={{header|Julia}}==
Uses channels to iterate the spigot flow.
<syntaxhighlight lang="julia">function sqrt_spigot(number::Integer, places=0, limit=10000, bufsize=32)
spigot = Channel{Char}(bufsize)
 
""" Mark off pairs of digits, starting from the decimal point, working left. """
function markoff(n)
d = digits(n)
pairs, len = Vector{BigInt}[], length(d)
if isodd(len)
push!(pairs, [pop!(d)])
len -= 1
end
for i in len-1:-2:1
push!(pairs, [d[i], d[i+1]])
end
places = length(pairs) - div(places , 2)
return pairs
end
 
""" look at first digit(s) and find largest i such that i^2 < that number """
function firststep!(pairs)
curnum = evalpoly(BigInt(10), popfirst!(pairs))
i = BigInt(findlast(x -> x * x <= curnum, 0:9) - 1)
put!(spigot, Char('0' + i))
return pairs, [i], curnum - i * i
end
 
"""
What is the largest number d that we can put in the units and also multiply times
the divisor such that the result is still be less than or equal to what we have?
"""
function nextstep!(pairs, founddigits, remain)
divisor = evalpoly(BigInt(10), founddigits) * 2
remwithnext = remain * 100 + evalpoly(BigInt(10), popfirst!(pairs))
d = BigInt(findlast(x -> x * (divisor * 10 + x) <= remwithnext, 0:9) - 1)
remain = remwithnext - (divisor * 10 + d) * d
pushfirst!(founddigits, d)
put!(spigot, Char('0' + d))
return pairs, founddigits, remain
end
 
""" start the process of adding digits to the channel """
function longhand_sqrt(n)
p = markoff(n)
if places <= 0 # 0 <= n < 1, such as 0.00144
put!(spigot, '0')
put!(spigot, '.')
for i in places:1:-1
put!(spigot, '0')
end
end
pairs, founddigits, remain = firststep!(p)
for _ in 1:limit
if isempty(pairs) # more zeros for part right of decimal point
push!(pairs, [0, 0], [0, 0], [0, 0], [0, 0])
end
(places -= 1) == 0 && put!(spigot, '.')
pairs, founddigits, remain = nextstep!(pairs, founddigits, remain)
end
end
 
@async(longhand_sqrt(number))
 
# return the channel from which to take! digits.
return spigot
end
 
function sqrt_spigot(str::String, lm=10000, bsiz=32)
str = lowercase(str)
if occursin("e", str)
str, exdig = split(str, "e")
extra = parse(Int, exdig)
!occursin(".", str) && (str *= '.')
else
extra = 0
end
if occursin(".", str)
if str[1] == '.'
str = '0' * str
elseif str[end] == str
str = str * '0'
end
s1, s2 = split(str, ".")
if extra < 0 # negative exponent, so rewrite call in non-exponential form
pos = length(s1) + extra
if pos < 0
str = "0." * "0"^(-pos) * s1 * s2
else
str = s1[1:end-pos] * "." * s1[end-pos+1:end] * s2
end
return sqrt_spigot(str, lm, bsiz)
end
b1, b2, places = parse(BigInt, s1), parse(BigInt, s2), length(s2)
if extra > 0
b1 *= BigInt(10)^extra
b2 *= BigInt(10)^extra
end
if isodd(places)
n = b1 * BigInt(10)^(places + 1) + b2 * 10
places += 1
else
n = b1 * BigInt(10)^places + b2
end
return sqrt_spigot(n, places, lm, bsiz)
else
return sqrt_spigot(parse(BigInt, str), 0, lm, bsiz)
end
end
 
sqrt_spigot(number::Real; l=10000, b=32) = sqrt_spigot("$number", l, b)
 
function testspigotsqrt(arr)
for num in arr
spigot = sqrt_spigot(num)
println("The square root of $num is:")
for i in 1:500
print(take!(spigot))
i % 50 == 0 && println()
end
println()
end
end
 
testspigotsqrt([2, 0.2, 0, 00.0001, 10.89, 144e-6, 2.0e4, 0.00000009, 1.44e+04, 1.44e-32])
</syntaxhighlight>{{out}}
<pre>
The square root of 2.0 is:
1.414213562373095048801688724209698078569671875376
94807317667973799073247846210703885038753432764157
27350138462309122970249248360558507372126441214970
99935831413222665927505592755799950501152782060571
47010955997160597027453459686201472851741864088919
86095523292304843087143214508397626036279952514079
89687253396546331808829640620615258352395054745750
28775996172983557522033753185701135437460340849884
71603868999706990048150305440277903164542478230684
92936918621580578463111596668713013015618568987237
 
The square root of 0.2 is:
0.447213595499957939281834733746255247088123671922
30514485417944908210418512756097988288288167575645
49939016352301547567008506535448894147727172720243
06690541773355634638375833162255329064527971316107
15227008350675700068467848281288841728650781945051
85254457752599034804881363223551817818996984742781
45945779696417728308537978819826338715403949735776
88501795082659123663538429999548496030608682300719
15336665024997630356278816001124841710487084471112
21261268564046818666396586791949270454240268349922
 
The square root of 0.0 is:
0.000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
 
The square root of 0.0001 is:
0.010000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
 
The square root of 10.89 is:
3.300000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
 
The square root of 0.000144 is:
0.012000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
 
The square root of 20000.0 is:
141.4213562373095048801688724209698078569671875376
94807317667973799073247846210703885038753432764157
27350138462309122970249248360558507372126441214970
99935831413222665927505592755799950501152782060571
47010955997160597027453459686201472851741864088919
86095523292304843087143214508397626036279952514079
89687253396546331808829640620615258352395054745750
28775996172983557522033753185701135437460340849884
71603868999706990048150305440277903164542478230684
92936918621580578463111596668713013015618568987237
 
The square root of 9.0e-8 is:
0.000300000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
 
The square root of 14400.0 is:
120.0000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
 
The square root of 1.44e-32 is:
0.000000000000000120000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
</pre>
 
=={{header|Kotlin}}==
{{trans|java}}
<syntaxhighlight lang="scala">import java.math.BigInteger
import kotlin.math.floor
import kotlin.math.sqrt
 
val ONE_HUNDRED: BigInteger = BigInteger.valueOf(100)
val TWENTY: BigInteger = BigInteger.valueOf(20)
 
fun main() {
var i = BigInteger.TWO
var j = BigInteger.valueOf(floor(sqrt(2.0)).toLong())
var k = j
var d = j
var n = 500
val n0 = n
do {
print(d)
i = i.subtract(k.multiply(d)).multiply(ONE_HUNDRED)
k = TWENTY.multiply(j)
d = BigInteger.ONE
while (d <= BigInteger.TEN) {
if (k.add(d).multiply(d) > i) {
d = d.subtract(BigInteger.ONE)
break
}
d = d.add(BigInteger.ONE)
}
j = j.multiply(BigInteger.TEN).add(d)
k = k.add(d)
if (n0 > 0) {
n--
}
} while (n > 0)
println()
}</syntaxhighlight>
{{out}}
<pre>14142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372</pre>
 
=={{header|Nim}}==
{{trans|Kotlin}}
{{libheader|bignum}}
<syntaxhighlight lang="nim">import math
import bignum
 
var
i = newInt(2)
j = newInt(sqrt(2.0).int)
k, d = j
n = 500
let n0 = n
while true:
stdout.write d
i = (i - k * d) * 100
k = 20 * j
d = newInt(1)
while d <= 10:
if (k + d) * d > i:
dec d, 1
break
inc d, 1
j = j * 10 + d
inc k, d
if n0 > 0: dec n
if n == 0: break</syntaxhighlight>
 
{{out}}
<pre>14142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372</pre>
 
=={{header|Perl}}==
{{trans|Raku}}
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
 
sub integral { my($n) = @_; (length($n) % 2 != 0 ? '0' . $n : $n) =~ /../g }
sub fractional { my($n) = @_; (length($n) % 2 == 0 ? $n . '0' : $n) =~ /../g }
 
sub SpigotSqrt {
my($in) = @_;
 
my(@dividends, @fractional, $dividend, $quotient, $remainder, $accum);
my $d = 9;
my $D = '';
my $dot = 0;
 
if ($in == int $in) {
@dividends = integral($in);
} else {
@dividends = integral($in =~ /(.*)\./);
@fractional = fractional($in =~ /\.(.*)/);
}
$dividend = shift @dividends;
 
while () {
until ( ( $remainder = $dividend - ($D.$d) * $d ) >= 0) { $d-- }
 
$accum .= $d;
$quotient .= $d;
unless (@dividends) {
last if $remainder == 0 and $quotient != 0 and !@fractional;
unless ($dot) { $accum .= '.' and $dot = 1 }
if (@fractional) {
push @dividends, @fractional;
@fractional = ();
} else {
push @dividends, '00';
}
}
$dividend = $remainder . shift @dividends;
$D = 2 * $quotient;
$d = 9
}
return $accum;
}
 
say "The square root of $_ is " . SpigotSqrt $_ for < 25 0.0625 152.2756 >;</syntaxhighlight>
{{out}}
<pre>The square root of 25 is 5
The square root of 0.0625 is 0.25
The square root of 152.2756 is 12.34</pre>
 
=={{header|Phix}}==
Based on https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Decimal_(base_10)<br>
The use of string inputs helps guarantee perfect accuracy.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"0.8.2"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">bcd</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">op</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- first, take care of different lengths</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)-</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">d</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)&</span><span style="color: #000000;">a</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)&</span><span style="color: #000000;">b</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">op</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"le"</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">b</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">op</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"sub"</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- return "a"-"b" (as a string)
-- (assumes a&gt;=b, which it always will be here,
--- protected as it is by a bcd(b,a,"le") call.)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">c</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span>
<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">+</span><span style="color: #000000;">c</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">trim_head</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (note: "" equ "0")</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">a</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- unknown op</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">bcd_xp20x</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- returns x*(p*20+x)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">p</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">m</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">c</span>
<span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)+</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)+</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)&</span><span style="color: #000000;">p</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- loop rqd?</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">p</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">spigot_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">maxlen</span><span style="color: #0000FF;">=</span><span style="color: #000000;">50</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- returns the square root of a positive string number to any precision</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">or</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #008000;">""</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">dot</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'.'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">dot</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">dot</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dot</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"0"</span><span style="color: #0000FF;">&</span><span style="color: #000000;">s</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">dot</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (until (i&gt;length && carry=0) or &gt; maxlen)</span>
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'.'</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span> <span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #000000;">dot</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">"."</span>
<span style="color: #000000;">dot</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">&=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]:</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">&</span>
<span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]:</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">9</span> <span style="color: #008080;">to</span> <span style="color: #000000;">0</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bcd_xp20x</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">bcd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"le"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bcd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"sub"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">p</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- (sanity check)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #008000;">""</span> <span style="color: #008080;">and</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)></span><span style="color: #000000;">maxlen</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">spigot_test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">maxlen</span><span style="color: #0000FF;">=</span><span style="color: #000000;">50</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"Square root%s of %s:%s %s\n"</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">spigot_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">maxlen</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">fnd</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">lf</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)>=</span><span style="color: #000000;">maxlen</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">fnd</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" (first %d digits)"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxlen</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">lf</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"\n "</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">trim_tail</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n "</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">fnd</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lf</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"152.2756"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"15241.383936"</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"0.2"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">80</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"10.89"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"625"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0.0001"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0.00000009"</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"20000"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">99</span><span style="color: #0000FF;">},{</span><span style="color: #008000;">"2"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500</span><span style="color: #0000FF;">}}</span>
<span style="color: #7060A8;">papply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #000000;">spigot_test</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<small>(the final "2" was re-joined up by hand)</small>
<pre>
Square root of 152.2756: 12.34
"12.34"
Square root of 15241.383936: 123.456
"123.456"
Square root (first 80 digits) of 0.2:
1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157
0.4472135954999579392818347337462552470881236719223051448541794490821041851275609
2735013846230912297024924836055850737212644121497099935831413222665927505592755799950501152782060571
Square root of 10.89: 3.3
4701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079
Square root of 625: 25
8968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884
Square root of 0: 0
71603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372
Square root of 0.0001: 0.01
Square root of 0.00000009: 0.0003
Square root (first 99 digits) of 20000:
141.421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157
Square root (first 500 digits) of 2:
1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157
2735013846230912297024924836055850737212644121497099935831413222665927505592755799950501152782060571
4701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079
8968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884
71603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372
</pre>
stress test?:
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.0"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (mpfr_set_default_prec[ision] has been renamed)</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #7060A8;">mpfr_set_default_precision</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 100 d.p precision</span>
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">pi</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">mpfr_const_pi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ps</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">rs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">spigot_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ps</span><span style="color: #0000FF;">,</span><span style="color: #000000;">102</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (&lt;=101 is not enough)</span>
<span style="color: #7060A8;">mpfr_set_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rs</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">rs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Pi (builtin) vs spigot_sqrt(pi) squared:\n %s\n %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">ps</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rs</span><span style="color: #0000FF;">})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Pi (builtin) vs spigot_sqrt(pi) squared:
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170680
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170680
</pre>
 
=={{header|Racket}}==
 
{{trans|D}} (but with variable I, not constant 2)
 
<syntaxhighlight lang="racket">#lang racket
 
(define (square-root-by-hand I digits-remaining)
(define j (integer-sqrt I))
(define (loop d i j k n need-dot?)
(display d)
(when need-dot? (display "."))
(flush-output)
(let* ((i (* 100 (- i (* k d))))
(k (* 10 I j))
(d (sub1 (for/first ((d (in-range 1 11)) #:when (> (* d (+ k d)) i)) d))))
(unless (or (zero? i) (and n (zero? n)))
(loop d i (+ (* 10 j) d) (+ k d) (and n (sub1 n)) #f))))
(loop j I j j digits-remaining #t)
(newline))
 
(square-root-by-hand 2 1000)
(square-root-by-hand 256 100)
(square-root-by-hand 144 #f)</syntaxhighlight>
 
{{out}}
 
<pre>1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372352885092648612494977154218334204285686060146824720771435854874155657069677653720226485447015858801620758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342194897278290641045072636881313739855256117322040245091227700226941127573627280495738108967504018369868368450725799364729060762996941380475654823728997180326802474420629269124859052181004459842150591120249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
16.
12.</pre>
 
=={{header|Raku}}==
Implemented a [https://www.wikihow.com/Calculate-a-Square-Root-by-Hand#Finding-Square-Roots-Manually long division algorithm.].
<syntaxhighlight lang="raku" line># 20201023 Raku programming solution
 
sub integral (Str $in) { # prepend '0' if length is odd
given $in { .chars mod 2 ?? ('0'~$_).comb(2) !! .comb(2) }
}
 
sub fractional (Str $in) { # append '0' if length is odd
given $in { .chars mod 2 ?? ($_~'0').comb(2) !! .comb(2) }
}
 
sub SpigotSqrt ($in) {
 
my @dividends, my @fractional; # holds digital duos
my $d = 9; # unit digit part of divisors & running answer
my $D = ''; # tens+ digit part of divisors
my $dot_printed = False;
my $dividend; my $quotient = ''; my $remainder;
 
return "Sorry, minimum charge is $0⁺" if $in ≤ 0;
 
if $in.narrow ~~ Int { # integer
@dividends = integral($in.Str)
} else {
given split(/\./, $in.Str) { # floating point
@dividends = integral(@_[0]);
@fractional = fractional(@_[1]);
}
}
 
$dividend = shift @dividends;
 
loop {
until ( $remainder = $dividend - ($D~$d) * $d ) ≥ 0 {
$d-- # keep trying till the max divisor is found
}
print $d; # running answer
$quotient ~= $d;
unless @dividends.Bool {
last if ( $remainder == 0 and $quotient != 0 and !@fractional.Bool );
unless $dot_printed { print '.' and $dot_printed = True }
if @fractional.Bool { # happen only once
@dividends.append: @fractional;
@fractional = (); # retired
} else {
@dividends.append: '00';
}
}
$dividend = $remainder.Str ~ shift @dividends;
$D = 2*$quotient;
$d = 9
}
}
 
#`[ matches result from https://stackoverflow.com/a/28152047/3386748
for <99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999982920000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000726067> { # ]
for < 25 0.0625 152.2756 13579.02468 > {
say "The square root of $_ is";
SpigotSqrt $_ ; print "\n";
}</syntaxhighlight>
{{out}}
<pre>The square root of 25 is
5
The square root of 0.0625 is
0.25
The square root of 152.2756 is
12.34
The square root of 13579.02468 is
116.5290722523782903561833846788464631805119729204989141878325473726703822155976113726101636833624692173783050112427274490403132495026916228339453686341013613481116569793281525666303293666139135373395664751766204609166006753350008676787108560810713189340122619853015331030735400702976991920098868235804433621649473896395145322270105611438518020713137788187701241059921153133101219142225340975562189465283743880315403123043908068827985609461380033349440281928044661628680849458194668644072518779930532625670101046028192429778354952392572052578927533919600336446165970115867463651405291843435779882540897283554569528134419570259054368204716277521872340583781499813500950876849873104131526244245476070417915^C</pre>
 
=={{header|REXX}}==
This REXX version also handles non-negative numbers less than unity, &nbsp; and may suppress superfluous trailing zeros.
 
It also handles the placing of a decimal point &nbsp; (if needed).
<langsyntaxhighlight lang="rexx">/*REXX program computes the square root by the old "by pen─n'─paper" (hand) method.*/
signal on halt /*handle the case of user interrupt. */
parse arg xx digs . /*obtain optional arguments from the CL*/
if xx=='' | xx=="," then xx= 2 /*Not specified? Then use the default.*/
if digs=='' | digs=="," then digs= 400500 /* " " " " " " */
numeric digits digs + digs % 2 /*ensure enough decimal digits for calc*/
call sqrtHand xx, digs /*invoke the function for sqrt by hand.*/
Line 201 ⟶ 1,174:
return r /*R is the integer square root of Z. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrtHandspit: parse arg x@; call charout ,places @; parse valueif iSqrt(x)#<9 with jthen 1s= ks 1 ?|| /*j,@ k, ? iSqrt(x)/*show one character*/
if @==. then do; ##= ## + 1; L= 0; end; return /*handle dec. point.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrtHand: parse arg x 1 ox,##; parse value iSqrt(x) with j 1 k 1 ? /*j, k, ? ≡ iSqrt(x)*/
if ?==0 then ?= /*handle the case of sqrt < 1. */
if j*j=x then do; say j; return; end end /*have we found the exact sqrt?*/
L= length(?) /*L: used to place dec. point.*/
if L==0 then call charout , . do; #= 0; call spit .; end /*handle dec. point for iX < 1. */
s= do spit=1 for places /*S: partial square root. .*/
do call#=1 charout ,until #==##; call spit ? /*spit out a single digit->term*/
if L>0 then do;call spit . call charout , .; L= 0; end /*process dec.the decimal point. */
if ?==''#<9 then ?= 0 if datatype(s, 'N') then if s*s=ox then leave /*ensure theexact√ ? is a valid dig.*/
if x?=='' (x -then k*?)= 0 /*ensure 100; ?= 1 is a valid digit.*/
kx= j(x - k*?) * 100; ?= 201
k= j * do while ?<=1020
if (k + ?)*? > x then do; while ?<= ? - 1; leave; end10
if (k + ?)*? > x then do; ?= ? - 1; leave; else ?= ? + 1end
end /*while else ?≤10*/= ? + 1
j= ? + j end /*while*10/
kj= ? + kj*10
k= end? + /*spit*/k
return< end /*#*/lang>
return</syntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605
1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157
5850737212644121497099935831413222665927505592755799950501152782060571470109559971605970274534596862014728517418640889198609552329
2735013846230912297024924836055850737212644121497099935831413222665927505592755799950501152782060571
2304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746
4701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079
0340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
8968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884
7160386899970699004815030544027790316454247823068492936918621580578463111596668713013015618568987237
2
</pre>
{{out|output|text=&nbsp; when using the inputs of: &nbsp; &nbsp; <tt> .92 &nbsp; 80 </tt>}}
<pre>
.44721359549995793928183473374625524708812367192230514485417944908210418512756097
.9486832980505137995996680633298155601158665417975650480572514558377783315917714
</pre>
{{out|output|text=&nbsp; when using the inputs of: &nbsp; &nbsp; <tt> 10.89 &nbsp; 80 </tt>}}
<pre>
3.3
</pre>
{{out|output|text=&nbsp; when using the inputs of: &nbsp; &nbsp; <tt> 625 </tt>}}
Line 237 ⟶ 1,216:
25
</pre>
 
=={{header|Smalltalk}}==
{{trans|Visual Basic .NET}}
Smalltalk has builtin arbitrary precision integer arithmetic.
{{works with|Smalltalk/X}}
<syntaxhighlight lang="smalltalk">|i j k d n n0 t|
i := 2.
j := 2 sqrt floor.
k := j.
d := j.
Stdout nextPutAll:'Number of digits: '.
n := n0 := Integer readFrom:Stdin onError:[ 'bad input' printCR. ^ self].
t := Time millisecondsToRun:[
[
Stdout print:d.
i := (i - (k * d)) * 100.
k := 20 * j.
d := 1.
[:exit |
[d <= 10] whileTrue:[
((k + d) * d) > i ifTrue:[
d := d - 1.
exit value.
].
d := d + 1.
].
] valueWithExit.
j := (j * 10) + d.
k := k + d.
n := n-1.
] doWhile:[n > 0].
].
Stdout print: e'\nTime taken for {n0} digits: {t}ms\n'.</syntaxhighlight>
{{out}}
<pre>Number of digits: 500
14142135623730950488016887242096980785696718753769480731766797379907324784621070
38850387534327641572735013846230912297024924836055850737212644121497099935831413
22266592750559275579995050115278206057147010955997160597027453459686201472851741
86408891986095523292304843087143214508397626036279952514079896872533965463318088
296406206152583523950547457502877599617298355752203375318570113543746034084988
471603868999706990048150305440277903164542478230684929369186215805784631115966
687130130156185689872372
Time taken for 500 digits: 8ms</pre>
 
=={{header|Visual Basic .NET}}==
{{libheader|System.Numerics}}
This is "spigot like", but not a true spigot, just an implementation of the "by hand" method of computing the square root, in this case, of two.<langsyntaxhighlight lang="vbnet">Imports System.Math, System.Console, BI = System.Numerics.BigInteger
 
Module Module1
Line 260 ⟶ 1,282:
If n0 > 0 Then WriteLine (VbLf & "Time taken for {0} digits: {1}", n0, DateTime.Now - st)
End Sub
End Module</langsyntaxhighlight>{{out}}Execute without any command line parameters for it to run until it crashes (due to BigInteger variables eating up available memory).
 
Output with command line parameter of 500:<pre style="height:32ex; overflow:scroll; white-space:pre-wrap;">14142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372
Time taken for 500 digits: 00:00:00.0263710</pre>
 
=={{header|V (Vlang)}}==
{{trans|Wren}}
{{libheader|math.big}}
The translation is clearer than the original thanks the infix operators of the math.big lib in Vlang
<syntaxhighlight lang="v (vlang)">import math
import math.big
import strings
 
fn sqrt(n f64, limit int) string {
one := big.from_int(1)
ten := big.from_int(10)
twenty := big.from_int(20)
hundred := big.from_int(100)
 
mut n0 := n
if n0 < 0.0 {
panic('Number cannot be negative')
}
mut count := 0
for n0 != math.trunc(n0) {
n0 *= 100
count--
}
mut i := big.from_int(int(n0))
mut j := i.isqrt()
count += j.str().len
mut k := j.clone()
mut d := j.clone()
mut digits := 0
mut sb := ''
for digits < limit {
sb += d.str()
i = (i - k * d) * hundred
k = j * twenty
d = one
for big.cmp(d, ten) <= 0 {
if big.cmp((k + d) * d, i) > 0 {
d.dec()
break
}
d.inc()
}
j = j * ten + d
k = k + d
digits++
}
 
mut root := sb.trim_right('0')
if root.len == 0 {
root = '0'
}
if count > 0 {
root = root[0..count] + '.' + root[count..]
} else if count == 0 {
root = '0.' + root
} else {
root = '0.' + strings.repeat(`0`, -count) + root
}
root = root.trim_suffix('.')
if root.len > limit && root.contains('.') {
l := root.after_char(`.`)
if l.len > limit {
root = root[0..(root.len - (l.len - limit))]
}
}
return root
}
 
fn main() {
numbers := [f64(2), 0.2, 10.89, 625, 0.0001]
digits := [500, 80, 8, 8, 8]
for i, n in numbers {
println('First ${digits[i]} significant digits (at most) of the square root of $n:')
println(sqrt(n, digits[i]))
}
}</syntaxhighlight>
{{out}}With this version the result of sqrt(2) is erroneous from index 310. There is a problem in the math.big library which uses the tiny-bignum that hat limited capabilities.
=== Other version using v-gmp Module ===
This version gives the correct results
<syntaxhighlight lang="v (vlang)">import math
import gmp
import strings
 
fn sqrt(n f64, limit int) string {
one := gmp.from_i64(1)
ten := gmp.from_i64(10)
twenty := gmp.from_i64(20)
hundred := gmp.from_i64(100)
 
mut n0 := f64(n)
if n0 < 0 {
panic('Number cannot be negative')
}
mut count := 0
for n0 != math.trunc(n0) {
n0 *= 100
count--
}
mut i := gmp.from_f64(n0)
mut j := i.isqrt()
count += j.str().len
mut k := j.clone()
mut d := j.clone()
mut digits := 0
mut root := ''
for digits < limit {
root += d.str()
i = (i - k * d) * hundred
k = j * twenty
d = one.clone()
for gmp.cmp(d, ten) <= 0 {
if gmp.cmp((k + d) * d, i) > 0 {
d.dec()
break
}
d.inc()
}
j = j * ten + d
k = k + d
digits++
}
 
root = root.trim_right('0')
if root.len == 0 {
root = '0'
}
if count > 0 {
root = root[0..count] + '.' + root[count..]
} else if count == 0 {
root = '0.' + root
} else {
root = '0.' + strings.repeat(`0`, -count) + root
}
root = root.trim_suffix('.')
return root
}
 
fn main() {
numbers := [f64(2), 0.2, 10.89, 625, 0.0001]
digits := [500, 80, 8, 8, 8]
for i, n in numbers {
println('First ${digits[i]} significant digits (at most) of the square root of $n:')
println(sqrt(n, digits[i]))
}
}</syntaxhighlight>
{{out}}<pre style="height:32ex; overflow:scroll; white-space:pre-wrap;>First 500 significant digits (at most) of the square root of 2:
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372
First 80 significant digits (at most) of the square root of 0.2:
0.44721359549995793928183473374625524708812367192230514485417944908210418512756097
First 8 significant digits (at most) of the square root of 10.89:
3.3
First 8 significant digits (at most) of the square root of 625:
25
First 8 significant digits (at most) of the square root of 0.0001:
0.01</pre>
 
=={{header|Wren}}==
{{trans|Visual Basic .NET}}
{{libheader|Wren-big}}
The original has been adjusted to deal with any non-negative number, not just integers. Where appropriate a decimal point and leading zero(s) have been added but don't count towards the required number of digits. Trailing zeros do count but have been trimmed off for display purposes.
<lang ecmascript>import "/big" for BigInt
<syntaxhighlight lang="wren">import "./big" for BigInt
 
var sqrt = Fn.new { |n, limit|
if (n < 0) Fiber.abort("Number cannot be negative.")
var count = 0
while (!n.isInteger) {
n = n * 100
count = count - 1
}
var i = BigInt.new(n)
var j = i.isqrt
count = count + j.toString.count
var k = j
var d = j
var digits = 0
var root = ""
while (digits < limit) {
System.write(root = root + d).toString
i = (i - k*d) * 100
k = j * 20
Line 292 ⟶ 1,479:
digits = digits + 1
}
Systemroot = root.printtrimEnd("0")
if (root == "") root = "0"
if (count > 0) {
root = root[0...count] + "." + root[count..-1]
} else if (count == 0) {
root = "0." + root
} else {
root = "0." + ("0" * (-count)) + root
}
if (root[-1] == ".") root = root[0..-2]
System.print(root)
}
 
var numbers = [2, 0.2, 10.89, 625, 0.0001]
sqrt.call(2, 480) // enough for demo purposes</lang>
var digits = [500, 80, 8, 8, 8]
var i = 0
for (n in numbers) {
System.print("First %(digits[i]) significant digits (at most) of the square root of %(n):")
sqrt.call(n, digits[i])
System.print()
i = i + 1
}</syntaxhighlight>
 
{{out}}
<pre style="height:22ex72ex; overflow:scroll; white-space:pre-wrap;">
First 500 significant digits (at most) of the square root of 2:
141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372
 
First 80 significant digits (at most) of the square root of 0.2:
0.44721359549995793928183473374625524708812367192230514485417944908210418512756097
 
First 8 significant digits (at most) of the square root of 10.89:
3.3
 
First 8 significant digits (at most) of the square root of 625:
25
 
First 8 significant digits (at most) of the square root of 0.0001:
0.01
</pre>
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