Steady squares is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Euler Project #284

The 3-digit number 376 in the decimal numbering system is an example of numbers with the special property that its square ends with the same digits: 376*376 = 141376. Let's call a number with this property a steady square. Find steady squares under 10.000

## ALGOL 68

Using the observation that the final digit must be 1, 5 or 6 (See Talk page).

```BEGIN # find some steady squares - numbers whose squares end in the number    #
# e.g. 376^2 = 141 376                                                  #
INT max number    = 10 000; # maximum number we will consider             #
INT power of ten := 10;
[]INT last digit = ( 1, 5, 6 );
FOR n FROM 0 BY 10 TO max number DO
IF n = power of ten THEN
# the number of digits just increased                             #
power of ten *:= 10
FI;
FOR d FROM LWB last digit TO UPB last digit DO
INT nd = n + last digit[ d ];
INT n2 = nd * nd;
IF n2 MOD power of ten = nd THEN
# have a steady square                                        #
print( ( whole( nd, -5 ), "^2 = ", whole( n2, 0 ), newline ) )
FI
OD
OD
END```
Output:
```    1^2 = 1
5^2 = 25
6^2 = 36
25^2 = 625
76^2 = 5776
376^2 = 141376
625^2 = 390625
9376^2 = 87909376
```

## AWK

```# syntax: GAWK -f STEADY_SQUARES.AWK
BEGIN {
start = 1
stop = 999999
for (i=start; i<=stop; i++) {
n = i ^ 2
if (n ~ (i "\$")) {
printf("%6d^2 = %12d\n",i,n)
count++
}
}
printf("\nSteady squares %d-%d: %d\n",start,stop,count)
exit(0)
}
```
Output:
```     1^2 =            1
5^2 =           25
6^2 =           36
25^2 =          625
76^2 =         5776
376^2 =       141376
625^2 =       390625
9376^2 =     87909376
90625^2 =   8212890625
109376^2 =  11963109376
890625^2 = 793212890625

Steady squares 1-999999: 11
```

## BASIC

### ASIC

Compile with the Extended math option.

Translation of: C
```REM Steady squares
FOR I = 1 TO 9999
N = I
IF Steady <> 0 THEN
PRINT I;
PRINT " ^ 2 = ";
II& = I * I
PRINT II&
ENDIF
NEXT I
END

REM Result: Steady = 1 if N * N is steady; Steady = 0 otherwise.
D = N
WHILE D <> 0
D = D / 10
WEND
NNModMask& = N * N
IF NNModMask& = N THEN
ELSE
ENDIF
RETURN
```
Output:
```     1 ^ 2 =            1
5 ^ 2 =           25
6 ^ 2 =           36
25 ^ 2 =          625
76 ^ 2 =         5776
376 ^ 2 =       141376
625 ^ 2 =       390625
9376 ^ 2 =     87909376
```

### FreeBASIC

```function numdig( byval n as uinteger ) as uinteger
'number of decimal digits in n
dim as uinteger d=0
while n
d+=1
n\=10
wend
return d
end function

function is_steady_square( n as const uinteger ) as boolean
dim as integer n2 = n^2
if n2 mod 10^numdig(n) = n then return true else return false
end function

for i as uinteger = 1 to 10000
if is_steady_square(i) then print using "####^2 = ########";i;i^2
next i
```
Output:
```   1^2 =        1
5^2 =       25
6^2 =       36
25^2 =      625
76^2 =     5776
376^2 =   141376
625^2 =   390625
9376^2 = 87909376
```

### GW-BASIC

```10 FOR N = 1 TO 10000
20 M\$ = STR\$(N)
30 M2#=N*N
40 M\$ = RIGHT\$(M\$,LEN(M\$)-1)
50 N2\$ = STR\$(M2#)
60 A = LEN(M\$)
70 IF RIGHT\$(N2\$,A)= M\$ THEN PRINT M\$,N2\$
80 NEXT N
```
Output:
```1              1
5              25
6              36
25             625
76             5776
376            141376
625            390625
9376           87909376
```

### Liberty BASIC

Translation of: C
Works with: Just BASIC version any
```rem Steady squares
for i = 1 to 9999
print using("####",i); " ^ 2 = "; using("########", i * i)
end if
next i
end

d = n
while d <> 0
d = int(d / 10)
wend
isSteady = ((n * n) mod mask = n)
end function```
Output:
```   1 ^ 2 =        1
5 ^ 2 =       25
6 ^ 2 =       36
25 ^ 2 =      625
76 ^ 2 =     5776
376 ^ 2 =   141376
625 ^ 2 =   390625
9376 ^ 2 = 87909376
```

### Tiny BASIC

Because TinyBASIC is limited to signed 16-bit integers, we need to perform the squaring by repeated addition and then take modulus. That makes for a pretty inefficient solution.

```REM  N = THE NUMBER TO BE SQUARED
REM  D = 10^THE NUMBER OF DIGITS IN N
REM  M = THE SQUARE OF N, MODULO D
REM  T = TEMP COPY OF N

LET N = 1
LET D = 10
10 IF N > 9 THEN LET D = 100
IF N > 99 THEN LET D = 1000
IF N > 999 THEN LET D = 10000
LET M = 0
LET T = N
20 LET M = M + N
LET M = M - (M/D)*D
LET T = T - 1
IF T > 0 THEN GOTO 20
rem PRINT N, "  ", M
IF M  = N THEN PRINT N
LET N = N + 1
IF N < 10000 THEN GOTO 10
END```
Output:
```
1
5
6
25
76
376
625

9376```

## C

```#include <stdio.h>
#include <stdbool.h>

{
int mask = 1;
for (int d = n; d != 0; d /= 10)
return (n * n) % mask == n;
}

int main()
{
for (int i = 1; i < 10000; i++)
printf("%4d^2 = %8d\n", i, i * i);
return 0;
}
```
Output:
```   1^2 =        1
5^2 =       25
6^2 =       36
25^2 =      625
76^2 =     5776
376^2 =   141376
625^2 =   390625
9376^2 = 87909376```

## CLU

```n_digits = proc (n: int) returns (int)
i: int := 0
while n>0 do
i := i+1
n := n/10
end
return(i)
end n_digits

steady = proc (n: int) returns (bool)
sq: int := n ** 2
return (sq // 10**n_digits(n) = n)

start_up = proc ()
po: stream := stream\$primary_output()
for i: int in int\$from_to(1, 10000) do
if ~steady(i) then continue end
stream\$putright(po, int\$unparse(i), 4)
stream\$puts(po, "^2 = ")
stream\$putright(po, int\$unparse(i**2), 8)
stream\$putl(po, "")
end
end start_up```
Output:
```   1^2 =        1
5^2 =       25
6^2 =       36
25^2 =      625
76^2 =     5776
376^2 =   141376
625^2 =   390625
9376^2 = 87909376```

## Draco

```proc nonrec steady(ulong n) bool:
while mask <= n do mask := mask * 10 od;
n*n % mask = n
corp

proc nonrec main() void:
word i;
for i from 1 upto 10000 do
writeln(i:4, "^2 = ", make(i,ulong)*i:8)
fi
od
corp```
Output:
```   1^2 =        1
5^2 =       25
6^2 =       36
25^2 =      625
76^2 =     5776
376^2 =   141376
625^2 =   390625
9376^2 = 87909376```

## F#

### The Function

Implements No Search Required. large values may be produced using only integers.

```// Steady Squares. Nigel Galloway: December 21st., 2021
let fN g=let n=List.fold2(fun z n g->z+n*g) 0L g (g|>List.rev) in (n,g)
let five,six=(5L,[|0L..9L|]),(6L,[|0L;9L;8L;7L;6L;5L;4L;3L;2L;1L|])
let stdySq(g0,N)=let rec fG n (g,l)=seq{let i=Array.item(int((n+g)%10L)) N in yield i; yield! (fG((n+g+2L*g0*i)/10L)(fN(i::l)))}
seq{yield g0; yield! fG(g0*g0/10L)(0L,[])}
```

### Some Examples

```stdySq six|>Seq.take 80|>Seq.rev|>Seq.iter(printf "%d");printfn ""
stdySq five|>Seq.take 80|>Seq.rev|>Seq.iter(printf "%d");printfn ""
```
Output:
```61490109937833490419136188999442576576769103890995893380022607743740081787109376
38509890062166509580863811000557423423230896109004106619977392256259918212890625
```
Confirming Phix's example for 999 digits (in 11 thousands of sec).
```stdySq six|>Seq.skip 920|>Seq.take 79|>Seq.rev|>Seq.iter(printf "%d");printfn "..."
```
Output:
```7218745998663099139651109156359761242340631780203738180821664795072958006751247...
Real: 00:00:00.011
```
9999 digits
```stdySq six|>Seq.skip 9920|>Seq.take 79|>Seq.rev|>Seq.iter(printf "%d");printfn "...";;
```
Output:
```8908826164991254342660560818535016604238201034937718562215376152130910068662033...
Real: 00:00:00.330
```
If you have 57secs to spare then do 99999 digits, I leave it to the faithless to prove that this a Steady Square.
```stdySq six|>Seq.skip 99920|>Seq.take 79|>Seq.rev|>Seq.iter(printf "%d");printfn "...";;
```
Output:
```2755643458676224038154570844433833690960332159243668007360724907611570195135435...
Real: 00:00:57.520
```

## Factor

Only checking numbers that end with 1, 5, and 6. See Talk:Steady_Squares for more details.

Works with: Factor version 0.99 2021-06-02
```USING: formatting kernel math math.functions
math.functions.integer-logs prettyprint sequences
tools.memory.private ;

: steady? ( n -- ? )
[ sq ] [ integer-log10 1 + 10^ mod ] [ = ] tri ;

1000 <iota> { 1 5 6 } [
[ 10 * ] dip + dup steady?
[ dup sq commas "%4d^2 = %s\n" printf ] [ drop ] if
] cartesian-each
```
Output:
```   1^2 = 1
5^2 = 25
6^2 = 36
25^2 = 625
76^2 = 5,776
376^2 = 141,376
625^2 = 390,625
9376^2 = 87,909,376
```

## Fermat

```Func Isstead( n ) =
m:=n;
d:=1;
while m>0 do
d:=d*10;
m:=m\10;
od;
if n^2|d=n then Return(1) else Return(0) fi.;

for i = 1 to 9999 do
if Isstead(i) then !!(i,'^2 = ',i^2) fi;
od;```
Output:
``` 1^2 =  1
5^2 =  25
6^2 =  36
25^2 =  625
76^2 =  5776
376^2 =  141376
625^2 =  390625
9376^2 =  87909376
```

## Go

Translation of: Wren
Library: Go-rcu
```package main

import (
"fmt"
"rcu"
"strconv"
"strings"
)

func contains(list []int, s int) bool {
for _, e := range list {
if e == s {
return true
}
}
return false
}

func main() {
fmt.Println("Steady squares under 10,000:")
finalDigits := []int{1, 5, 6}
for i := 1; i < 10000; i++ {
if !contains(finalDigits, i%10) {
continue
}
sq := i * i
sqs := strconv.Itoa(sq)
is := strconv.Itoa(i)
if strings.HasSuffix(sqs, is) {
fmt.Printf("%5s -> %10s\n", rcu.Commatize(i), rcu.Commatize(sq))
}
}
}
```
Output:
```Steady squares under 10,000:
1 ->          1
5 ->         25
6 ->         36
25 ->        625
76 ->      5,776
376 ->    141,376
625 ->    390,625
9,376 -> 87,909,376
```

```import Control.Monad (join)
import Data.List (isSuffixOf)

--------------- NUMBERS WITH STEADY SQUARES --------------

p :: Int -> Bool
p = isSuffixOf . show <*> (show . join (*))

--------------------------- TEST -------------------------
main :: IO ()
main =
print \$
takeWhile (< 10000) \$ filter p [0 ..]
```
Output:
`[0,1,5,6,25,76,376,625,9376]`

or retaining the string pair when the test succeeds:

```import Control.Monad (join)
import Data.Bifunctor (bimap)
import Data.List (isSuffixOf)

---------------------- STEADY NUMBERS --------------------

steadyPair :: Int -> [(String, String)]
[ (s, s2)
| let (s, s2) = join bimap show (n, n * n),
s `isSuffixOf` s2
]

--------------------------- TEST -------------------------
main :: IO ()
main =
( \xs ->
let (w, w2) = join bimap length (last xs)
in mapM_
( putStrLn . uncurry ((<>) . (<> " -> "))
. bimap
(justifyRight w ' ')
(justifyRight w2 ' ')
)
xs
)
\$ [0 .. 10000] >>= steadyPair

------------------------- GENERIC ------------------------

justifyRight :: Int -> Char -> String -> String
justifyRight n c = (drop . length) <*> (replicate n c <>)
```
Output:
```   0 ->        0
1 ->        1
5 ->       25
6 ->       36
25 ->      625
76 ->     5776
376 ->   141376
625 ->   390625
9376 -> 87909376```

or obtaining the squares by addition, rather than multiplication:

```import Control.Monad (join)
import Data.Bifunctor (bimap)
import Data.List (isSuffixOf)

--------------- NUMBERS WITH STEADY SQUARES --------------

steadyPair :: Int -> Int -> [(Int, (String, String))]
steadyPair a b =
[ (a, ab)
| let ab = join bimap show (a, b),
uncurry isSuffixOf ab
]

--------------------------- TEST -------------------------
main :: IO ()
main =
putStrLn \$
unlines
( uncurry ((<>) . (<> " -> ")) . snd
<\$> takeWhile
((10000 >) . fst)
( concat \$
zipWith
[0 ..]
(scanl (+) 0 [1, 3 ..])
)
)
```
Output:
```0 -> 0
1 -> 1
5 -> 25
6 -> 36
25 -> 625
76 -> 5776
376 -> 141376
625 -> 390625
9376 -> 87909376```

## J

Implementation:
```issteady=: {{ Y-:N{.":*:y[N=.-#Y=.":y }}"0
```
```   I.issteady i.1e4
0 1 5 6 25 76 376 625 9376
```
Note that for larger values we would want to take advantage of the suffix characteristics of these numbers (a multi-digit steady square would have a suffix which is a steady square).

## JavaScript

### Procedural

Translation of: TypeScript
Translation of: C
```// Steady squares

// Result: true if n * n is steady; false otherwise.
var mask = 1;
for (var d = n; d != 0; d = Math.floor(d / 10))
return (n * n) % mask == n;
}

for (var i = 1; i < 10000; i++)
console.log(i.toString().padStart(4, ' ') + "^2 = " +
(i * i).toString().padStart(8, ' '));
```
Output:
```   1^2 =        1
5^2 =       25
6^2 =       36
25^2 =      625
76^2 =     5776
376^2 =   141376
625^2 =   390625
9376^2 = 87909376
```

### Functional

```(() => {
"use strict";

// ----------------- STEADY SQUARES ------------------

// isSteady :: Int -> Bool
const isSteady = n =>

// steadyPair :: Int -> [(String, String)]
const steadyPair = n => {
// An empty list if n is not steady, otherwise a
// list containing a tuple of (n, n^2) strings.
const
s = `\${n}`,
s2 = `\${n ** 2}`;

return s2.endsWith(s) ? [
[s, s2]
] : [];
};

// ---------------------- TESTS ----------------------
const main = () => {
const
range = enumFromTo(0)(1E4),
[w, w2] = pairs[pairs.length - 1]
.map(x => x.length);

return [

pairs.map(([n, n2]) => {
const
square = n2.padStart(w2, " ");

return `\${steady} -> \${square}`;
})
.join("\n")
]
.join("\n\n");
};

// --------------------- GENERIC ---------------------

// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m =>
n => Array.from({
length: 1 + n - m
}, (_, i) => m + i);

// MAIN ---
return main();
})();
```
Output:
```0, 1, 5, 6, 25, 76, 376, 625, 9376

0 ->        0
1 ->        1
5 ->       25
6 ->       36
25 ->      625
76 ->     5776
376 ->   141376
625 ->   390625
9376 -> 87909376```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

```# Input: an upper bound, or null for infinite
range(0; . // infinite)
| tostring as \$i
| select( .*. | tostring | endswith(\$i));

10000
Output:
```0
1
5
6
25
76
376
625
9376
```

## Julia

```issteadysquare(n) = (s = "\$n"; s == "\$(n * n)"[end+1-length(s):end])

println(filter(issteadysquare, 1:10000)) # [1, 5, 6, 25, 76, 376, 625, 9376]
```

```            NORMAL MODE IS INTEGER
VECTOR VALUES FMT = \$I4,7H **2 = ,I8*\$
THROUGH LOOP, FOR I=1, 1, I.G.10000
SQ = I*I
PRINT FORMAT FMT, I, SQ
END OF CONDITIONAL
LOOP        CONTINUE
END OF PROGRAM```
Output:
```   1**2 =        1
5**2 =       25
6**2 =       36
25**2 =      625
76**2 =     5776
376**2 =   141376
625**2 =   390625
9376**2 = 87909376```

## Perl

```#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Steady_Squares
use warnings;

(\$_ ** 2) =~ /\$_\$/ and printf "%5d  %d\n", \$_, \$_ ** 2 for 1 .. 10000;
```
Output:
```    1  1
5  25
6  36
25  625
76  5776
376  141376
625  390625
9376  87909376
```

## Phix

A number n ending in 2,3,4,7,8, or 9 will have a square ending in 4,9,6,9,4 or 1 respectively.
Further a number ending in k 0s will have a square ending in 2*k 0s, and hence always fail, so all possible candidates must end in 1, 5, or 6.
Further, the square of any k-digit number n will end in the same k-1 digits as the square of the number formed from the last k-1 digits of n,
in other words every successful 3-digit n must end with one of the previously successful answers (maybe zero padded), and so on for 4 digits, etc.
I stopped after 8 digits to avoid the need to fire up gmp. Finishes near-instantly, of course.

```with javascript_semantics
sequence success = {1,5,6}  -- (as above)
atom p10 = 10
for digits=2 to 8 do
for d=1 to 9 do
for i=1 to length(success) do
atom cand = d*p10+success[i]
if remainder(cand*cand,p10*10)=cand then
success &= cand
end if
end for
end for
p10 *= 10
end for
printf(1,"%d such numbers < 100,000,000 found:\n",length(success))
for i=1 to length(success) do
atom si = success[i]
printf(1,"%,11d^2 = %,21d\n",{si,si*si})
end for
```
Output:
```15 such numbers < 100,000,000 found:
1^2 =                     1
5^2 =                    25
6^2 =                    36
25^2 =                   625
76^2 =                 5,776
376^2 =               141,376
625^2 =               390,625
9,376^2 =            87,909,376
90,625^2 =         8,212,890,625
109,376^2 =        11,963,109,376
890,625^2 =       793,212,890,625
2,890,625^2 =     8,355,712,890,625
7,109,376^2 =    50,543,227,109,376
12,890,625^2 =   166,168,212,890,625
87,109,376^2 = 7,588,043,387,109,376
```

### mpz (super fast to 1000 digits)

Obsessed with the idea the series could in fact be finite, I wheeled out gmp anyway... As per the talk page, it turns out that all steady squares (apart from 1) are in fact on a 5-chain and a 6-chain, which carry on forever. The following easily finishes in less than a second.

```with javascript_semantics
include mpfr.e
constant limit = 1000
sequence success = {"1","5","6"}    -- (as above)
sequence squared = {"1","25","36"}  -- (kiss)
integer count = 3
mpz ch5 = mpz_init(5),  -- the 5-chain
ch6 = mpz_init(6),  -- the 6-chain
p10 = mpz_init(10),
{d10,sqr,r10,t10,cand} = mpz_inits(5), ch
for digits=2 to limit-1 do
for d=1 to 9 do
ch = ch5
mpz_mul_si(d10,p10,d)
mpz_mul_si(t10,p10,10)
for chain=5 to 6 do
mpz_mul(sqr,cand,cand)
mpz_fdiv_r(r10,sqr,t10)
if mpz_cmp(cand,r10)=0 then
count += 1
if digits<=12 or digits>=limit-3 then
success = append(success,shorten(mpz_get_str(cand)))
squared = append(squared,shorten(mpz_get_str(sqr)))
end if
mpz_set(ch,cand)
end if
ch = ch6
end for
end for
mpz_mul_si(p10,p10,10)
end for
printf(1,"%d steady squares < 1e%d found:\n",{count,limit})
for i=1 to length(success) do
printf(1,"%13s^2 = %25s\n",{success[i],squared[i]})
end for
```

No doubt you could significantly improve that by replacing the mul/div with mpz_powm_ui(r10, cand, 2, t10) and o/c not even trying to print any of the silly-length numbers.

Output:
```1783 steady squares < 1e1000 found:
1^2 =                         1
5^2 =                        25
6^2 =                        36
25^2 =                       625
76^2 =                      5776
376^2 =                    141376
625^2 =                    390625
9376^2 =                  87909376
90625^2 =                8212890625
109376^2 =               11963109376
890625^2 =              793212890625
2890625^2 =             8355712890625
7109376^2 =            50543227109376
12890625^2 =           166168212890625
87109376^2 =          7588043387109376
212890625^2 =         45322418212890625
787109376^2 =        619541169787109376
1787109376^2 =       3193759921787109376
8212890625^2 =      67451572418212890625
18212890625^2 =     331709384918212890625
81787109376^2 =    6689131260081787109376
918212890625^2 =  843114912509918212890625
18745998663099139651...07743740081787109376 (997 digits)^2 = 35141246587691473110...07743740081787109376 (1,993 digits)
81254001336900860348...92256259918212890625 (997 digits)^2 = 66022127332570868008...92256259918212890625 (1,994 digits)
21874599866309913965...07743740081787109376 (998 digits)^2 = 47849811931116570591...07743740081787109376 (1,995 digits)
78125400133690086034...92256259918212890625 (998 digits)^2 = 61035781460491829128...92256259918212890625 (1,996 digits)
27812540013369008603...92256259918212890625 (999 digits)^2 = 77353738199525217326...92256259918212890625 (1,997 digits)
72187459986630991396...07743740081787109376 (999 digits)^2 = 52110293793214504525...07743740081787109376 (1,998 digits)
```

Note that should this produce two steady squares of the same length that begin with the same digit, the one that ends in 5 would be shown first, even if it is numerically after then one that ends in 6, not that there are any such < 1e1000. In other words add a flag that effectively swaps the `ch = ch5` and `ch = ch6` lines.

### No Search Required using strings

```with javascript_semantics
atom t0 = time()
constant limit = 9999
sequence fivesix = {"5","6"} -- (held backwards)
for chain=5 to 6 do
string f56 = fivesix[chain-4]
integer d0 = f56[1]-'0', d = 0, n = floor(d0*d0/10),
dn = iff(chain=6?10-n:n)
f56 &= dn+'0'
for digit=2 to limit-1 do
n = floor((n+d+2*dn*d0)/10)
d = 0
for j=2 to digit do
d += (f56[j]-'0')*(f56[-j+1]-'0')
end for
dn = remainder(n+d,10)
if chain=6 and dn then dn=10-dn end if
f56 &= dn+'0'
end for
fivesix[chain-4] = f56
end for
integer count = 1
printf(1,"%13s\n",{"1"})
for d=1 to limit do
sequence r = {}
for j=1 to 2 do
string fj = fivesix[j]
if fj[d]!='0' then
count += 1
if d<=12 then
r &= {sprintf("%13s",{reverse(fj[1..d])})}
elsif d=999 or d=9999 then
r &= {sprintf("%s...%s (%d digits)",{reverse(fj[d-19..d]),reverse(fj[1..20]),d})}
end if
end if
end for
if length(r)>1 and r[2]<r[1] then r = reverse(r) end if
for i=1 to length(r) do
printf(1,"%s\n",{r[i]})
end for
end for
printf(1,"%d steady squares < 1e%d found\n",{count,limit+1})
?elapsed(time()-t0)
```
Output:
```            1
5
6
25
76
376
625
9376
90625
109376
890625
2890625
7109376
12890625
87109376
212890625
787109376
1787109376
8212890625
18212890625
81787109376
918212890625
27812540013369008603...92256259918212890625 (999 digits)
72187459986630991396...07743740081787109376 (999 digits)
10911738350087456573...92256259918212890625 (9999 digits)
89088261649912543426...07743740081787109376 (9999 digits)
18069 steady squares < 1e10000 found
"4.0s"
```

Unfortunately it is not particularly fast, 7mins on a 10 year old i3 for 99,999 digits, with results that match F#. Then again, I suppose it is a near-perfect candidate for my (far future) plans to boost performance in version 2... Perhaps more for my future benefit than anyone else's, if we replace the `for j=2 to digit do` loop with:

```        #ilASM{
mov esi,[f56]
mov edx,[digit]
mov ecx,1
shl esi,2
sub edx,1
xor eax,eax
xor edi,edi
@@:
mov al,[esi+ecx]
mov bl,[esi+edx]
sub al,'0'
sub bl,'0'
mul bl
xor eax,eax
sub edx,1
cmp edx,1
jge @b
mov [d],edi
xor ebx,ebx
}
```

we get the above plus

```27556434586762240381...07743740081787109376 (99999 digits)
72443565413237759618...92256259918212890625 (99999 digits)
179886 steady squares < 1e100000 found
"12.2s"
```

Which is a whopping 35-fold speedup, so obviously all I need to do is make the compiler emit similarly efficient code...

## Python

### Procedural

```print("working...")
print("Steady squares under 10.000 are:")
limit = 10000

for n in range(1,limit):
nstr = str(n)
nlen = len(nstr)
square = str(pow(n,2))
rn = square[-nlen:]
if nstr == rn:
print(str(n) + " " + str(square))

print("done...")
```
Output:
```working...
Steady squares under 10.000 are:
1 1
5 25
6 36
25 625
76 5776
376 141376
625 390625
9376 87909376
done...```

### Functional

```'''Steady squares'''

from itertools import chain

# steadyPair :: Int -> [(String, String)]
'''An empty list if x^2 is not suffixed, in decimal,
by the decimal digits of x. Otherwise a list
containing a tuple of the decimal strings of (x, x^2)
'''
s, s2 = str(x), str(x**2)

return [(s, s2)] if s2.endswith(s) else []

# ------------------------ TESTS -------------------------
# main :: IO ()
def main():
'''Roots of numbers with steady squares up to 10000
'''
ns = range(1, 1 + 10000)
w, w2 = (len(x) for x in xs[-1])

print([n for n in ns if steadyPair(n)])
print()
print(
'\n'.join([
f'{s.rjust(w, " ")} -> {s2.rjust(w2, " ")}'
for (s, s2) in xs
])
)

# ----------------------- GENERIC ------------------------

# concatMap :: (a -> [b]) -> [a] -> [b]
def concatMap(f):
'''A concatenated list over which a function has been
mapped.
The list monad can be derived by using a function f
which wraps its output in a list, (using an empty
list to represent computational failure).
'''
def go(xs):
return list(chain.from_iterable(map(f, xs)))
return go

# MAIN ---
if __name__ == '__main__':
main()
```
Output:
```[1, 5, 6, 25, 76, 376, 625, 9376]

1 ->        1
5 ->       25
6 ->       36
25 ->      625
76 ->     5776
376 ->   141376
625 ->   390625
9376 -> 87909376```

Or, defining the squares as an additive accumulation:

```'''Steady Squares'''

from itertools import accumulate, chain, count, takewhile
from operator import add

def main():
'''Numbers up to 10000 which have steady squares'''
print(
'\n'.join(
f'{a} -> {b}' for (a, b) in takewhile(
lambda ab: 10000 > ab[0],
enumerate(
accumulate(
chain([0], count(1, 2)),
)
)
) if str(b).endswith(str(a))
)
)

# MAIN ---
if __name__ == '__main__':
main()
```
Output:
```0 -> 0
1 -> 1
5 -> 25
6 -> 36
25 -> 625
76 -> 5776
376 -> 141376
625 -> 390625
9376 -> 87909376```

## Raku

```.say for ({\$++²}…*).kv.grep( {\$^v.ends-with: \$^k} )[1..10]
```
Output:
```(1 1)
(5 25)
(6 36)
(25 625)
(76 5776)
(376 141376)
(625 390625)
(9376 87909376)
(90625 8212890625)
(109376 11963109376)```

## REXX

```/* REXX */
Numeric Digits 50
Call time 'R'
n=1000000000
Say 'Steady squares below' n
Do i=1 To n
c=right(i,1)
If pos(c,'156')>0 Then Do
i2=i*i
If right(i2,length(i))=i Then
Say right(i,length(n)) i2
End
End
Say time('E')
```
Output:
```Steady squares below 1000000000
1 1
5 25
6 36
25 625
76 5776
376 141376
625 390625
9376 87909376
90625 8212890625
109376 11963109376
890625 793212890625
2890625 8355712890625
7109376 50543227109376
12890625 166168212890625
87109376 7588043387109376
212890625 45322418212890625
787109376 619541169787109376
468.422000```

## Ring

```see "working..." +nl
see "Steady squatres under 10.000 are:" + nl
limit = 10000

for n = 1 to limit
nstr = string(n)
len = len(nstr)
square = pow(n,2)
rn = right(string(square),len)
if nstr = rn
see "" + n + " -> " + square + nl
ok
next

see "done..." +nl```
Output:
```working...
Steady numbers under 10.000 are:
1 -> 1
5 -> 25
6 -> 36
25 -> 625
76 -> 5776
376 -> 141376
625 -> 390625
9376 -> 87909376
done...
```

## TypeScript

Translation of: C
```// Steady squares

function steady(n: number): bool {
// Result: true if n * n is steady; false otherwise.
var mask = 1;
for (var d = n; d != 0; d = Math.floor(d / 10))
return (n * n) % mask == n;
}

for (var i = 1; i < 10000; i++)
console.log(i.toString().padStart(4, ' ') + "^2 = " +
(i * i).toString().padStart(8, ' '));
```
Output:
```   1^2 =        1
5^2 =       25
6^2 =       36
25^2 =      625
76^2 =     5776
376^2 =   141376
625^2 =   390625
9376^2 = 87909376
```

## Wren

Library: Wren-fmt

Although it hardly matters for a small range such as this, one can cut down the numbers to be examined by observing that a steady square must end in 1, 5 or 6.

```import "./fmt" for Fmt

System.print("Steady squares under 10,000:")
var finalDigits = [1, 5, 6]
for (i in 1..9999) {
if (!finalDigits.contains(i % 10)) continue
var sq = i * i
if (sq.toString.endsWith(i.toString)) Fmt.print("\$,5d -> \$,10d", i, sq)
}
```
Output:
```Steady squares under 10,000:
1 ->          1
5 ->         25
6 ->         36
25 ->        625
76 ->      5,776
376 ->    141,376
625 ->    390,625
9,376 -> 87,909,376
```

## XPL0

```int  N, P;
[for N:= 0 to 10000-1 do
[P:= 1;
repeat P:= P*10 until P>N;
if rem(N*N/P) = N then
[IntOut(0, N);
Text(0, "^^2 = ");
IntOut(0, N*N);
CrLf(0);
];
];
]```
Output:
```0^2 = 0
1^2 = 1
5^2 = 25
6^2 = 36
25^2 = 625
76^2 = 5776
376^2 = 141376
625^2 = 390625
9376^2 = 87909376
```

## Yabasic

```// Rosetta Code problem: http://rosettacode.org/wiki/Steady_squares
// by Galileo, 04/2022

for i = 1 to 10000
r\$ = str\$(i^2, "%9.f")
if i = val(right\$(r\$, len(str\$(i)))) print i, "\t=", r\$
next```
Output:
```1       =        1
5       =       25
6       =       36
25      =      625
76      =     5776
376     =   141376
625     =   390625
9376    = 87909376
---Program done, press RETURN---```