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# Magic squares of doubly even order

Magic squares of doubly even order
You are encouraged to solve this task according to the task description, using any language you may know.

A magic square is an   N×N  square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column,   and   both diagonals are equal to the same sum   (which is called the magic number or magic constant).

A magic square of doubly even order has a size that is a multiple of four   (e.g.     4, 8, 12).

This means that the subsquares also have an even size, which plays a role in the construction.

 1 2 62 61 60 59 7 8 9 10 54 53 52 51 15 16 48 47 19 20 21 22 42 41 40 39 27 28 29 30 34 33 32 31 35 36 37 38 26 25 24 23 43 44 45 46 18 17 49 50 14 13 12 11 55 56 57 58 6 5 4 3 63 64

Create a magic square of   8 × 8.

## 11l

Translation of: Java
`F magicSquareDoublyEven(n)   V bits = 1001'0110'0110'1001b   V size = n * n   V mult = n I/ 4    V result = [[0] * n] * n   V i = 0   L(r) 0 .< n      L(c) 0 .< n         V bitPos = c I/ mult + (r I/ mult) * 4         result[r][c] = I (bits [&] (1 << bitPos)) != 0 {i + 1} E size - i         i++   R result V n = 8L(row) magicSquareDoublyEven(n)   L(x) row      print(‘#2 ’.format(x), end' ‘’)   print()print("\nMagic constant: "((n * n + 1) * n I/ 2))`
Output:
``` 1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

Magic constant: 260
```

## 360 Assembly

Translation of: Java
`*        Magic squares of doubly even order  01/03/2017MAGICSDB CSECT         USING  MAGICSDB,R13         B      72(R15)            skip save area         DC     17F'0'             save area         STM    R14,R12,12(R13)         ST     R13,4(R15)         ST     R15,8(R13)         LR     R13,R15            end of prolog         SR     R8,R8              k=0         LA     R6,0               i=0       DO WHILE=(C,R6,LE,=A(N-1))  do i=0 to n-1         MVC    PG,=CL80' '          clear buffer         LA     R9,PG                pgi=0         LA     R7,0                 j=0       DO WHILE=(C,R7,LE,=A(N-1))    do j=0 to n-1         LR     R4,R7                  j         SRDA   R4,32                  >>r5         D      R4,MULT                /mult         LR     R2,R5                  r2=j/mult         LR     R4,R6                  i         SRDA   R4,32                  >>r5         D      R4,MULT                /mult         SLA    R5,2                   r5=(i/mult)*4         AR     R2,R5                  bitpos=j/mult+(i/mult)*4         STC    R2,XSLL+3              number_of_shift=bitpos         L      R5,=F'1'               1         EX     0,XSLL                 r5=1<<bitpos  (SLL R5,bitpos)         L      R4,BITS                bits         NR     R4,R5                  bits and (1<<bitpos)       IF LTR,R4,NZ,R4 THEN            if (bits and (1<<bitpos))<>0         LA     R10,1(R8)                x=k+1       ELSE     ,                      else         L      R10,SIZE                 size         SR     R10,R8                   x=size-k       ENDIF    ,                      endif         XDECO  R10,XDEC               edit x         MVC    0(4,R9),XDEC+8         output x         LA     R9,4(R9)               pgi+=4         LA     R8,1(R8)               k++         LA     R7,1(R7)               j++       ENDDO    ,                    enddo j         XPRNT  PG,L'PG              print buffer         LA     R6,1(R6)             i++       ENDDO    ,                  enddo i         MVC    PG,=CL80'magic constant='         L      R1,=A((N*N+1)*N/2) magicnum=(n*n+1)*n/2         XDECO  R1,XDEC            edit magicnum         MVC    PG+15(4),XDEC+8    output magicnum         XPRNT  PG,L'PG            print buffer         L      R13,4(0,R13)       epilog         LM     R14,R12,12(R13)         XR     R15,R15            rc=0         BR     R14                exitXSLL     SLL    R5,0               shift left logicalN        EQU    8                  <= input value nSIZE     DC     A(N*N)             size=n*nMULT     DC     A(N/4)             mult=n/4  (multiple of 4)BITS     DC     XL2'0000',BL2'1001011001101001'  patternPG       DS     CL80               bufferXDEC     DS     CL12               temp for xdeco         YREGS         END    MAGICSDB`
Output:
```   1   2  62  61  60  59   7   8
9  10  54  53  52  51  15  16
48  47  19  20  21  22  42  41
40  39  27  28  29  30  34  33
32  31  35  36  37  38  26  25
24  23  43  44  45  46  18  17
49  50  14  13  12  11  55  56
57  58   6   5   4   3  63  64
magic constant= 260
```

## ALGOL 60

Works with: A60
`begin	comment Magic squares of doubly even order - 10/02/2021;    integer array pattern[1:4,1:4];	integer n, r, c, s, m, i, b, t;	n:=8;	for r:=1 step 1 until 4 do		for c:=1 step 1 until 4 do			pattern[r,c]:=if 				((c=1 or c=4) and (r=1 or r=4)) or				((c=2 or c=3) and (r=2 or r=3)) then 1 else 0;	s:=n*n;  m:=n div 4;	outstring(1,"magic square -- n ="); outinteger(1,n); outstring(1,"\n");	i:=0;	for r:=1 step 1 until n do begin		for c:=1 step 1 until n do begin			b:=pattern[(r-1) div m+1,(c-1) div m+1];			if b=1 then t:=i+1 else t:=s-i;			if t less 10 then outstring(1," ");			outinteger(1,t);			i:=i+1		end;		outstring(1,"\n")	end;	outstring(1,"magic constant ="); outinteger(1,(s+1)*n div 2)end `
Output:
```magic square -- n = 8
1   2  62  61  60  59   7   8
9  10  54  53  52  51  15  16
48  47  19  20  21  22  42  41
40  39  27  28  29  30  34  33
32  31  35  36  37  38  26  25
24  23  43  44  45  46  18  17
49  50  14  13  12  11  55  56
57  58   6   5   4   3  63  64
magic constant = 260
```

## AppleScript

Translation of: JavaScript
`-- MAGIC SQUARE OF DOUBLY EVEN ORDER ----------------------------------------- -- magicSquare :: Int -> [[Int]]on magicSquare(n)    if n mod 4 > 0 then        {}    else        set sqr to n * n         set maybePowerOfTwo to asPowerOfTwo(sqr)        if maybePowerOfTwo is not missing value then             -- For powers of 2, the (append not) 'magic' series directly            -- yields the truth table that we need            set truthSeries to magicSeries(maybePowerOfTwo)        else            -- where n is not a power of 2, we can replicate a            -- minimum truth table, horizontally and vertically             script scale                on |λ|(x)                    replicate(n / 4, x)                end |λ|            end script             set truthSeries to ¬                flatten(scale's |λ|(map(scale, splitEvery(4, magicSeries(4)))))        end if         set limit to sqr + 1        script inOrderOrReversed            on |λ|(x, i)                cond(x, i, limit - i)            end |λ|        end script         -- Taken directly from an integer series  [1..sqr] where True        -- and from the reverse of that series where False        splitEvery(n, map(inOrderOrReversed, truthSeries))    end ifend magicSquare -- magicSeries :: Int -> [Bool]on magicSeries(n)    script boolToggle        on |λ|(x)            not x        end |λ|    end script     if n ≤ 0 then        {true}    else        set xs to magicSeries(n - 1)        xs & map(boolToggle, xs)    end ifend magicSeries  -- TEST ----------------------------------------------------------------------on run     formattedTable(magicSquare(8)) end run -- formattedTable :: [[Int]] -> Stringon formattedTable(lstTable)    set n to length of lstTable    set w to 2.5 * n    "magic(" & n & ")" & linefeed & wikiTable(lstTable, ¬        false, "text-align:center;width:" & ¬        w & "em;height:" & w & "em;table-layout:fixed;")end formattedTable -- wikiTable :: [Text] -> Bool -> Text -> Texton wikiTable(lstRows, blnHdr, strStyle)    script fWikiRows        on |λ|(lstRow, iRow)            set strDelim to cond(blnHdr and (iRow = 0), "!", "|")            set strDbl to strDelim & strDelim            linefeed & "|-" & linefeed & strDelim & space & ¬                intercalate(space & strDbl & space, lstRow)        end |λ|    end script     linefeed & "{| class=\"wikitable\" " & ¬        cond(strStyle ≠ "", "style=\"" & strStyle & "\"", "") & ¬        intercalate("", ¬            map(fWikiRows, lstRows)) & linefeed & "|}" & linefeedend wikiTable  -- GENERIC FUNCTIONS --------------------------------------------------------- -- asPowerOfTwo :: Int -> maybe Inton asPowerOfTwo(n)    if not isPowerOf(2, n) then        missing value    else        set strCMD to ("echo 'l(" & n as string) & ")/l(2)' | bc -l"        (do shell script strCMD) as integer    end ifend asPowerOfTwo -- concatMap :: (a -> [b]) -> [a] -> [b]on concatMap(f, xs)    script append        on |λ|(a, b)            a & b        end |λ|    end script     foldl(append, {}, map(f, xs))end concatMap -- cond :: Bool -> a -> a -> aon cond(bool, f, g)    if bool then        f    else        g    end ifend cond -- flatten :: Tree a -> [a]on flatten(t)    if class of t is list then        concatMap(my flatten, t)    else        t    end ifend flatten -- foldl :: (a -> b -> a) -> a -> [b] -> aon foldl(f, startValue, xs)    tell mReturn(f)        set v to startValue        set lng to length of xs        repeat with i from 1 to lng            set v to |λ|(v, item i of xs, i, xs)        end repeat        return v    end tellend foldl -- intercalate :: Text -> [Text] -> Texton intercalate(strText, lstText)    set {dlm, my text item delimiters} to {my text item delimiters, strText}    set strJoined to lstText as text    set my text item delimiters to dlm    return strJoinedend intercalate -- isPowerOf :: Int -> Int -> Boolon isPowerOf(k, n)    set v to k    script remLeft        on |λ|(x)            x mod v is not 0        end |λ|    end script     script integerDiv        on |λ|(x)            x div v        end |λ|    end script     |until|(remLeft, integerDiv, n) = 1end isPowerOf -- map :: (a -> b) -> [a] -> [b]on map(f, xs)    tell mReturn(f)        set lng to length of xs        set lst to {}        repeat with i from 1 to lng            set end of lst to |λ|(item i of xs, i, xs)        end repeat        return lst    end tellend map  -- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Scripton mReturn(f)    if class of f is script then        f    else        script            property |λ| : f        end script    end ifend mReturn -- Egyptian multiplication - progressively doubling a list, appending-- stages of doubling to an accumulator where needed for binary -- assembly of a target length -- replicate :: Int -> a -> [a]on replicate(n, a)    set out to {}    if n < 1 then return out    set dbl to {a}     repeat while (n > 1)        if (n mod 2) > 0 then set out to out & dbl        set n to (n div 2)        set dbl to (dbl & dbl)    end repeat    return out & dblend replicate -- splitAt :: Int -> [a] -> ([a],[a])on splitAt(n, xs)    if n > 0 and n < length of xs then        if class of xs is text then            {items 1 thru n of xs as text, items (n + 1) thru -1 of xs as text}        else            {items 1 thru n of xs, items (n + 1) thru -1 of xs}        end if    else        if n < 1 then            {{}, xs}        else            {xs, {}}        end if    end ifend splitAt -- splitEvery :: Int -> [a] -> [[a]]on splitEvery(n, xs)    if length of xs ≤ n then        {xs}    else        set {gp, t} to splitAt(n, xs)        {gp} & splitEvery(n, t)    end ifend splitEvery -- until :: (a -> Bool) -> (a -> a) -> a -> aon |until|(p, f, x)    set mp to mReturn(p)    set v to x     tell mReturn(f)        repeat until mp's |λ|(v)            set v to |λ|(v)        end repeat    end tell    return vend |until|`
Output:

magic(8)

 1 63 62 4 60 6 7 57 56 10 11 53 13 51 50 16 48 18 19 45 21 43 42 24 25 39 38 28 36 30 31 33 32 34 35 29 37 27 26 40 41 23 22 44 20 46 47 17 49 15 14 52 12 54 55 9 8 58 59 5 61 3 2 64

## AWK

Translation of: C#

Since standard awk does not support bitwise operators, we provide the function countup to do the magic.

`# Usage: GAWK -f MAGIC_SQUARES_OF_DOUBLY_EVEN_ORDER.AWKBEGIN {    n = 8    msquare[0, 0] = 0    if (magicsquaredoublyeven(msquare, n)) {        for (i = 0; i < n; i++) {            for (j = 0; j < n; j++) {                printf("%2d ", msquare[i, j])            }            printf("\n")        }        printf("\nMagic constant: %d\n", (n * n + 1) * n / 2)        exit 1    } else {        exit 0    }}function magicsquaredoublyeven(msquare, n,    size, mult, r, c, i) {    if (n < 4 || n % 4 != 0) {        printf("Base must be a positive multiple of 4.\n")        return 0    }    size = n * n    mult = n / 4 # how many multiples of 4     i = 0    for (r = 0; r < n; r++) {        for (c = 0; c < n; c++) {            msquare[r, c] = countup(r, c, mult) ? i + 1 : size - i            i++        }    }    return 1}function countup(r, c, mult,    pattern, bitpos) {    # Returns 1, if we are in a count-up zone (0 otherwise)    pattern = "1001011001101001"    bitpos =  int(c / mult) + int(r / mult) * 4 + 1    return substr(pattern, bitpos, 1) + 0}`
Output:
``` 1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

Magic constant: 260```

## Befunge

The size, N, is specified by the first value on the stack. The algorithm is loosely based on the Java implementation.

`8>>>v>10p00g:*1-*\110g2*-*+1+.:00g%!9+,:#[email protected]p00:<^:!!-!%3//4g00%g00\!!%3/*:g00*4:::-1<*:`
Output:
```1       2       62      61      60      59      7       8
9       10      54      53      52      51      15      16
48      47      19      20      21      22      42      41
40      39      27      28      29      30      34      33
32      31      35      36      37      38      26      25
24      23      43      44      45      46      18      17
49      50      14      13      12      11      55      56
57      58      6       5       4       3       63      64```

## C

Takes number of rows from command line, prints out usage on incorrect invocation.

` #include<stdlib.h>#include<ctype.h>#include<stdio.h> int** doublyEvenMagicSquare(int n) {	if (n < 4 || n % 4 != 0)		return NULL; 	int bits = 38505;	int size = n * n;	int mult = n / 4,i,r,c,bitPos; 	int** result = (int**)malloc(n*sizeof(int*)); 	for(i=0;i<n;i++)		result[i] = (int*)malloc(n*sizeof(int)); 	for (r = 0, i = 0; r < n; r++) {		for (c = 0; c < n; c++, i++) {			bitPos = c / mult + (r / mult) * 4;			result[r][c] = (bits & (1 << bitPos)) != 0 ? i + 1 : size - i;		}	}	return result;} int numDigits(int n){	int count = 1; 	while(n>=10){		n /= 10;		count++;	} 	return count;} void printMagicSquare(int** square,int rows){	int i,j,baseWidth = numDigits(rows*rows) + 3; 	printf("Doubly Magic Square of Order : %d and Magic Constant : %d\n\n",rows,(rows * rows + 1) * rows / 2); 	for(i=0;i<rows;i++){		for(j=0;j<rows;j++){			printf("%*s%d",baseWidth - numDigits(square[i][j]),"",square[i][j]);		}		printf("\n");	}} int main(int argC,char* argV[]){	int n; 	if(argC!=2||isdigit(argV[1][0])==0)		printf("Usage : %s <integer specifying rows in magic square>",argV[0]);	else{		n = atoi(argV[1]);		printMagicSquare(doublyEvenMagicSquare(n),n);	}	return 0;} `

Invocation and Output :

```C:\rosettaCode>doublyEvenMagicSquare 12
Doubly Magic Square of Order : 12 and Magic Constant : 870

1     2     3   141   140   139   138   137   136    10    11    12
13    14    15   129   128   127   126   125   124    22    23    24
25    26    27   117   116   115   114   113   112    34    35    36
108   107   106    40    41    42    43    44    45    99    98    97
96    95    94    52    53    54    55    56    57    87    86    85
84    83    82    64    65    66    67    68    69    75    74    73
72    71    70    76    77    78    79    80    81    63    62    61
60    59    58    88    89    90    91    92    93    51    50    49
48    47    46   100   101   102   103   104   105    39    38    37
109   110   111    33    32    31    30    29    28   118   119   120
121   122   123    21    20    19    18    17    16   130   131   132
133   134   135     9     8     7     6     5     4   142   143   144
```

## C#

Translation of: Java
`using System; namespace MagicSquareDoublyEven{    class Program    {        static void Main(string[] args)        {            int n = 8;            var result = MagicSquareDoublyEven(n);            for (int i = 0; i < result.GetLength(0); i++)            {                for (int j = 0; j < result.GetLength(1); j++)                    Console.Write("{0,2} ", result[i, j]);                Console.WriteLine();            }            Console.WriteLine("\nMagic constant: {0} ", (n * n + 1) * n / 2);            Console.ReadLine();        }         private static int[,] MagicSquareDoublyEven(int n)        {            if (n < 4 || n % 4 != 0)                throw new ArgumentException("base must be a positive "                        + "multiple of 4");             // pattern of count-up vs count-down zones            int bits = 0b1001_0110_0110_1001;            int size = n * n;            int mult = n / 4;  // how many multiples of 4             int[,] result = new int[n, n];             for (int r = 0, i = 0; r < n; r++)            {                for (int c = 0; c < n; c++, i++)                {                    int bitPos = c / mult + (r / mult) * 4;                    result[r, c] = (bits & (1 << bitPos)) != 0 ? i + 1 : size - i;                }            }            return result;        }    }}`
``` 1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

Magic constant: 260```

## C++

`#include <iostream>#include <sstream>#include <iomanip>using namespace std; class magicSqr{public:     magicSqr( int d ) {        while( d % 4 > 0 ) { d++; }        sz = d;        sqr = new int[sz * sz];        fillSqr();    }    ~magicSqr() { delete [] sqr; }     void display() const {        cout << "Doubly Even Magic Square: " << sz << " x " << sz << "\n";        cout << "It's Magic Sum is: " << magicNumber() << "\n\n";        ostringstream cvr; cvr << sz * sz;        int l = cvr.str().size();         for( int y = 0; y < sz; y++ ) {            int yy = y * sz;            for( int x = 0; x < sz; x++ ) {                cout << setw( l + 2 ) << sqr[yy + x];            }            cout << "\n";        }        cout << "\n\n";    }private:    void fillSqr() {        static const bool tempAll[4][4] = {{ 1, 0, 0, 1 }, { 0, 1, 1, 0 }, { 0, 1, 1, 0 }, { 1, 0, 0, 1 } };        int i = 0;        for( int curRow = 0; curRow < sz; curRow++ ) {            for( int curCol = 0; curCol < sz; curCol++ ) {                sqr[curCol + sz * curRow] = tempAll[curRow % 4][curCol % 4] ? i + 1 : sz * sz - i;                i++;            }        }    }    int magicNumber() const { return sz * ( ( sz * sz ) + 1 ) / 2; }     int* sqr;    int sz;}; int main( int argc, char* argv[] ) {    magicSqr s( 8 );    s.display();    return 0;}`
Output:
```Doubly Even Magic Square: 8 x 8
It's Magic Sum is: 260

1  63  62   4   5  59  58   8
56  10  11  53  52  14  15  49
48  18  19  45  44  22  23  41
25  39  38  28  29  35  34  32
33  31  30  36  37  27  26  40
24  42  43  21  20  46  47  17
16  50  51  13  12  54  55   9
57   7   6  60  61   3   2  64
```

## D

Translation of: Java
`import std.stdio; void main() {    int n=8;    foreach(row; magicSquareDoublyEven(n)) {        foreach(col; row) {            writef("%2s ", col);        }        writeln;    }    writeln("\nMagic constant: ", (n*n+1)*n/2);} int[][] magicSquareDoublyEven(int n) {    import std.exception;    enforce(n>=4 && n%4 == 0, "Base must be a positive multiple of 4");     int bits = 0b1001_0110_0110_1001;    int size = n * n;    int mult = n / 4;  // how many multiples of 4     int[][] result;    result.length = n;    foreach(i; 0..n) {        result[i].length = n;    }     for (int r=0, i=0; r<n; r++) {        for (int c=0; c<n; c++, i++) {            int bitPos = c / mult + (r / mult) * 4;            result[r][c] = (bits & (1 << bitPos)) != 0 ? i + 1 : size - i;        }    }     return result;}`
Output:
``` 1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

Magic constant: 260```

## Elena

Translation of: C#

ELENA 5.0 :

`import system'routines;import extensions;import extensions'routines; MagicSquareDoublyEven(int n){    if(n < 4 || n.mod(4) != 0)        { InvalidArgumentException.new:"base must be a positive multiple of 4".raise() };     int bits := 09669h;    int size := n * n;    int mult := n / 4;     var result := IntMatrix.allocate(n,n);    int i := 0;    for (int r := 0, r < n, r += 1)    {        for(int c := 0, c < n, c += 1, i += 1)        {            int bitPos := c / mult + (r / mult) * 4;             result[r][c] := ((bits && (1 \$shl bitPos)) != 0).iif(i+1,size - i)        }    };     ^ result} public program(){    int n := 8;     console.printLine(MagicSquareDoublyEven(n));     console.printLine().printLine("Magic constant: ",(n * n + 1) * n / 2)}`
Output:
```1,2,62,61,60,59,7,8
9,10,54,53,52,51,15,16
48,47,19,20,21,22,42,41
40,39,27,28,29,30,34,33
32,31,35,36,37,38,26,25
24,23,43,44,45,46,18,17
49,50,14,13,12,11,55,56
57,58,6,5,4,3,63,64

Magic constant: 260
```

## Elixir

`defmodule Magic_square do  def doubly_even(n) when rem(n,4)!=0, do: raise ArgumentError, "must be even, but not divisible by 4."  def doubly_even(n) do    n2 = n * n    Enum.zip(1..n2, make_pattern(n))    |> Enum.map(fn {i,p} -> if p, do: i, else: n2 - i + 1 end)    |> Enum.chunk(n)    |> to_string(n)    |> IO.puts  end   defp make_pattern(n) do    pattern = Enum.reduce(1..4, [true], fn _,acc ->                acc ++ Enum.map(acc, &(!&1))              end) |> Enum.chunk(4)    for i <- 0..n-1, j <- 0..n-1, do: Enum.at(pattern, rem(i,4)) |> Enum.at(rem(j,4))  end   defp to_string(square, n) do    format = String.duplicate("~#{length(to_char_list(n*n))}w ", n) <> "\n"    Enum.map_join(square, fn row ->      :io_lib.format(format, row)    end)  endend Magic_square.doubly_even(8)`
Output:
``` 1 63 62  4  5 59 58  8
56 10 11 53 52 14 15 49
48 18 19 45 44 22 23 41
25 39 38 28 29 35 34 32
33 31 30 36 37 27 26 40
24 42 43 21 20 46 47 17
16 50 51 13 12 54 55  9
57  7  6 60 61  3  2 64
```

## Factor

`USING: arrays combinators.short-circuit formatting frygeneralizations kernel math math.matrices prettyprint sequences;IN: rosetta-code.doubly-even-magic-squares : top?    ( loc n -- ? ) [ second ] dip 1/4 * <  ;: bottom? ( loc n -- ? ) [ second ] dip 3/4 * >= ;: left?   ( loc n -- ? ) [ first  ] dip 1/4 * <  ;: right?  ( loc n -- ? ) [ first  ] dip 3/4 * >= ;: corner? ( loc n -- ? )    {        [ { [ top?    ] [ left?  ] } ]        [ { [ top?    ] [ right? ] } ]        [ { [ bottom? ] [ left?  ] } ]        [ { [ bottom? ] [ right? ] } ]    } [ 2&& ] map-compose 2|| ; : center? ( loc n -- ? )    { [ top? ] [ bottom? ] [ left? ] [ right? ] } [ not ]    map-compose 2&& ; : backward? ( loc n -- ? ) { [ corner? ] [ center? ] } 2|| ;: forward   ( loc n -- m ) [ first2 ] dip * 1 + + ;: backward  ( loc n -- m ) tuck forward [ sq ] dip - 1 + ; : (doubly-even-magic-square) ( n -- matrix )    [ dup 2array matrix-coordinates flip ] [ 3 dupn ] bi    '[ dup _ backward? [ _ backward ] [ _ forward ] if ]    matrix-map ; ERROR: invalid-order order ; : check-order ( n -- )    dup { [ zero? not ] [ 4 mod zero? ] } 1&& [ drop ]    [ invalid-order ] if ; : doubly-even-magic-square ( n -- matrix )    dup check-order (doubly-even-magic-square) ; : main ( -- )    { 4 8 12 } [        dup doubly-even-magic-square dup        [ "Order: %d\n" printf ]        [ simple-table. ]        [ first sum "Magic constant: %d\n\n" printf ] tri*    ] each ; MAIN: main`
Output:
```Order: 4
16 2  3  13
5  11 10 8
9  7  6  12
4  14 15 1
Magic constant: 34

Order: 8
64 63 3  4  5  6  58 57
56 55 11 12 13 14 50 49
17 18 46 45 44 43 23 24
25 26 38 37 36 35 31 32
33 34 30 29 28 27 39 40
41 42 22 21 20 19 47 48
16 15 51 52 53 54 10 9
8  7  59 60 61 62 2  1
Magic constant: 260

Order: 12
144 143 142 4   5   6   7   8   9   135 134 133
132 131 130 16  17  18  19  20  21  123 122 121
120 119 118 28  29  30  31  32  33  111 110 109
37  38  39  105 104 103 102 101 100 46  47  48
49  50  51  93  92  91  90  89  88  58  59  60
61  62  63  81  80  79  78  77  76  70  71  72
73  74  75  69  68  67  66  65  64  82  83  84
85  86  87  57  56  55  54  53  52  94  95  96
97  98  99  45  44  43  42  41  40  106 107 108
36  35  34  112 113 114 115 116 117 27  26  25
24  23  22  124 125 126 127 128 129 15  14  13
12  11  10  136 137 138 139 140 141 3   2   1
Magic constant: 870
```

## FreeBASIC

`' version 18-03-2016' compile with: fbc -s console' doubly even magic square 4, 8, 12, 16... Sub Err_msg(msg As String)    Print msg    Beep : Sleep 5000, 1 : Exit SubEnd Sub Sub de_magicsq(n As UInteger, filename As String = "")     ' filename <> "" then save square in a file    ' filename can contain directory name    ' if filename exist it will be overwriten, no error checking     If n < 4 Then        Err_msg( "Error: n is to small")        Exit Sub    End If     If (n Mod 4) <> 0 Then        Err_msg "Error: not possible to make doubly" + _        " even magic square size " + Str(n)        Exit Sub    End If     Dim As UInteger sq(1 To n, 1 To n)    Dim As UInteger magic_sum = n * (n ^ 2 +1) \ 2    Dim As UInteger q = n \ 4    Dim As UInteger x, y, nr = 1    Dim As String frmt = String(Len(Str(n * n)) +1, "#")     ' set up the square    For y = 1 To n        For x = q +1 To n - q            sq(x,y) = 1        Next    Next    For x = 1 To n        For y = q +1 To n - q            sq(x, y) Xor= 1        Next    Next     ' fill the square    q = n * n +1    For y = 1 To n        For x = 1 To n            If sq(x,y) = 0 Then                sq(x,y) = q - nr            Else                sq(x,y) = nr            End If            nr += 1        Next    Next     ' check columms and rows    For y = 1 To n        nr = 0 : q = 0        For x = 1 To n            nr += sq(x,y)            q += sq(y,x)        Next        If nr <> magic_sum Or q <> magic_sum Then            Err_msg "Error: value <> magic_sum"            Exit Sub        End If    Next     ' check diagonals    nr = 0 : q = 0    For x = 1 To n        nr += sq(x, x)        q += sq(n - x +1, n - x +1)    Next    If nr <> magic_sum Or q <> magic_sum Then        Err_msg "Error: value <> magic_sum"        Exit Sub    End If     ' printing square's on screen bigger when    ' n > 19 results in a wrapping of the line    Print "Single even magic square size: "; n; "*"; n    Print "The magic sum = "; magic_sum    Print    For y = 1 To n        For x = 1 To n            Print Using frmt; sq(x, y);        Next        Print    Next     ' output magic square to a file with the name provided    If filename <> "" Then        nr = FreeFile        Open filename For Output As #nr        Print #nr, "Single even magic square size: "; n; "*"; n        Print #nr, "The magic sum = "; magic_sum        Print #nr,        For y = 1 To n            For x = 1 To n                Print #nr, Using frmt; sq(x,y);            Next            Print #nr,        Next        Close #nr    End If End Sub ' ------=< MAIN >=------ de_magicsq(8, "magic8de.txt") : Print ' empty keyboard bufferWhile Inkey <> "" : WendPrint : Print "hit any key to end program"SleepEnd`
Output:
```Single even magic square size: 8*8
The magic sum = 260

64 63  3  4  5  6 58 57
56 55 11 12 13 14 50 49
17 18 46 45 44 43 23 24
25 26 38 37 36 35 31 32
33 34 30 29 28 27 39 40
41 42 22 21 20 19 47 48
16 15 51 52 53 54 10  9
8  7 59 60 61 62  2  1```

## Go

`package main import (	"fmt"	"log"	"strings") const dimensions int = 8 func setupMagicSquareData(d int) ([][]int, error) {	var output [][]int	if d < 4 || d%4 != 0 {		return [][]int{}, fmt.Errorf("Square dimension must be a positive number which is divisible by 4")	}	var bits uint = 0x9669 // 0b1001011001101001	size := d * d	mult := d / 4	for i, r := 0, 0; r < d; r++ {		output = append(output, []int{})		for c := 0; c < d; i, c = i+1, c+1 {			bitPos := c/mult + (r/mult)*4			if (bits & (1 << uint(bitPos))) != 0 {				output[r] = append(output[r], i+1)			} else {				output[r] = append(output[r], size-i)			}		}	}	return output, nil} func arrayItoa(input []int) []string {	var output []string	for _, i := range input {		output = append(output, fmt.Sprintf("%4d", i))	}	return output} func main() {	data, err := setupMagicSquareData(dimensions)	if err != nil {		log.Fatal(err)	}	magicConstant := (dimensions * (dimensions*dimensions + 1)) / 2	for _, row := range data {		fmt.Println(strings.Join(arrayItoa(row), " "))	}	fmt.Printf("\nMagic Constant: %d\n", magicConstant)} `
Output:
```   1    2   62   61   60   59    7    8
9   10   54   53   52   51   15   16
48   47   19   20   21   22   42   41
40   39   27   28   29   30   34   33
32   31   35   36   37   38   26   25
24   23   43   44   45   46   18   17
49   50   14   13   12   11   55   56
57   58    6    5    4    3   63   64

Magic Constant: 260
```

`import Data.List (transpose, unfoldr, intercalate)import Data.List.Split (chunksOf)import Data.Bool (bool)import Control.Monad (forM_) magicSquare :: Int -> [[Int]]magicSquare n  | rem n 4 > 0 = []  | otherwise =    chunksOf n \$ zipWith (flip (bool =<< (-) limit)) series [1 .. sqr]  where    sqr = n * n    limit = sqr + 1    series      | isPowerOf 2 n = magicSeries \$ floor (logBase 2 (fromIntegral sqr))      | otherwise =        concat . concat . concat . scale \$ scale <\$> chunksOf 4 (magicSeries 4)      where        scale = replicate \$ quot n 4 magicSeries :: Int -> [Bool]magicSeries = (iterate ((++) <*> fmap not) [True] !!) isPowerOf :: Int -> Int -> BoolisPowerOf k n = until ((0 /=) . flip rem k) (`quot` k) n == 1 -- TEST AND DISPLAY FUNCTIONS --------------------------------------------------checked :: [[Int]] -> (Int, Bool)checked square =  let diagonals =        fmap (flip (zipWith (!!)) [0 ..]) . ((:) <*> (return . reverse))      h:t =        sum <\$>        square ++ -- rows        transpose square ++ -- cols        diagonals square -- diagonals  in (h, all (h ==) t) table :: String -> [[String]] -> [String]table delim rows =  let justifyRight c n s = drop (length s) (replicate n c ++ s)  in intercalate delim <\$>     transpose       ((fmap =<< justifyRight ' ' . maximum . fmap length) <\$> transpose rows) main :: IO ()main =  forM_ [4, 8, 16] \$  \n -> do    let test = magicSquare n    putStrLn \$ unlines (table " " (fmap show <\$> test))    print \$ checked test    putStrLn []`
Output:
``` 1 15 14  4
12  6  7  9
8 10 11  5
13  3  2 16

(34,True)

1 63 62  4 60  6  7 57
56 10 11 53 13 51 50 16
48 18 19 45 21 43 42 24
25 39 38 28 36 30 31 33
32 34 35 29 37 27 26 40
41 23 22 44 20 46 47 17
49 15 14 52 12 54 55  9
8 58 59  5 61  3  2 64

(260,True)

1 255 254   4 252   6   7 249 248  10  11 245  13 243 242  16
240  18  19 237  21 235 234  24  25 231 230  28 228  30  31 225
224  34  35 221  37 219 218  40  41 215 214  44 212  46  47 209
49 207 206  52 204  54  55 201 200  58  59 197  61 195 194  64
192  66  67 189  69 187 186  72  73 183 182  76 180  78  79 177
81 175 174  84 172  86  87 169 168  90  91 165  93 163 162  96
97 159 158 100 156 102 103 153 152 106 107 149 109 147 146 112
144 114 115 141 117 139 138 120 121 135 134 124 132 126 127 129
128 130 131 125 133 123 122 136 137 119 118 140 116 142 143 113
145 111 110 148 108 150 151 105 104 154 155 101 157  99  98 160
161  95  94 164  92 166 167  89  88 170 171  85 173  83  82 176
80 178 179  77 181  75  74 184 185  71  70 188  68 190 191  65
193  63  62 196  60 198 199  57  56 202 203  53 205  51  50 208
48 210 211  45 213  43  42 216 217  39  38 220  36 222 223  33
32 226 227  29 229  27  26 232 233  23  22 236  20 238 239  17
241  15  14 244  12 246 247   9   8 250 251   5 253   3   2 256

(2056,True)```

## J

` masksq=: >:@#@, | _1&^ * 1 + [email protected]\$pat4=: ,:(+.|.)=i.4mask=: ,/@(,./"3@\$&pat4)@] ,~ % 4:demsq=: [email protected] `
Output:
```   demsq 8
64  2  3 61 60  6  7 57
9 55 54 12 13 51 50 16
17 47 46 20 21 43 42 24
40 26 27 37 36 30 31 33
32 34 35 29 28 38 39 25
41 23 22 44 45 19 18 48
49 15 14 52 53 11 10 56
8 58 59  5  4 62 63  1
~.(+/,&,+/"1)demsq 128
1048640
```

## Java

`public class MagicSquareDoublyEven {     public static void main(String[] args) {        int n = 8;        for (int[] row : magicSquareDoublyEven(n)) {            for (int x : row)                System.out.printf("%2s ", x);            System.out.println();        }        System.out.printf("\nMagic constant: %d ", (n * n + 1) * n / 2);    }     static int[][] magicSquareDoublyEven(final int n) {        if (n < 4 || n % 4 != 0)            throw new IllegalArgumentException("base must be a positive "                    + "multiple of 4");         // pattern of count-up vs count-down zones        int bits = 0b1001_0110_0110_1001;        int size = n * n;        int mult = n / 4;  // how many multiples of 4         int[][] result = new int[n][n];         for (int r = 0, i = 0; r < n; r++) {            for (int c = 0; c < n; c++, i++) {                int bitPos = c / mult + (r / mult) * 4;                result[r][c] = (bits & (1 << bitPos)) != 0 ? i + 1 : size - i;            }        }        return result;    }}`
``` 1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

Magic constant: 260```

## JavaScript

### ES6

`(() => {    'use strict';     // doublyEvenMagicSquare :: Int -> [[Int]]    const doublyEvenMagicSquare = n =>        0 === n % 4 ? (() => {            const                sqr = n * n,                power = Math.log2(sqr),                scale = replicate(n / 4);            return chunksOf(n)(                map((x, i) => x ? 1 + i : sqr - i)(                    isInt(power) ? truthSeries(power) : (                        compose(                            flatten,                            scale,                            map(scale),                            chunksOf(4)                        )(truthSeries(4))                    )                )            );        })() : undefined;     // truthSeries :: Int -> [Bool]    const truthSeries = n =>        0 >= n ? (            [true]        ) : (() => {            const xs = truthSeries(n - 1);            return xs.concat(xs.map(x => !x));        })();       // TEST -----------------------------------------------    const main = () =>        // Magic squares of orders 4, 8 and 12, with        // checks of row, column and diagonal sums.        intercalate('\n\n')(            map(n => {                const                    lines = doublyEvenMagicSquare(n),                    sums = map(sum)(                        lines.concat(                            transpose(lines)                            .concat(diagonals(lines))                        )                    ),                    total = sums[0];                return unlines([                    "Order: " + str(n),                    "Summing to: " + str(total),                    "Row, column and diagonal sums checked: " +                    str(all(eq(total))(sums)) + '\n',                    unlines(map(compose(                        intercalate('  '),                        map(compose(justifyRight(3)(' '), str))                    ))(lines))                ]);            })([4, 8, 12])        );      // GENERIC FUNCTIONS ----------------------------------     // all :: (a -> Bool) -> [a] -> Bool    const all = p =>        // True if p(x) holds for every x in xs.        xs => xs.every(p);     // chunksOf :: Int -> [a] -> [[a]]    const chunksOf = n => xs =>        enumFromThenTo(0)(n)(            xs.length - 1        ).reduce(            (a, i) => a.concat([xs.slice(i, (n + i))]),            []        );     // compose (<<<) :: (b -> c) -> (a -> b) -> a -> c    const compose = (...fs) =>        x => fs.reduceRight((a, f) => f(a), x);     // diagonals :: [[a]] -> [[a], [a]]    const diagonals = rows =>        // Two diagonal sequences,        // from top left and bottom left        // respectively, of a given matrix.        map(flip(zipWith(index))(            enumFromTo(0)(pred(                0 < rows.length ? (                    rows[0].length                ) : 0            ))        ))([rows, reverse(rows)]);     // enumFromThenTo :: Int -> Int -> Int -> [Int]    const enumFromThenTo = x1 => x2 => y => {        const d = x2 - x1;        return Array.from({            length: Math.floor(y - x2) / d + 2        }, (_, i) => x1 + (d * i));    };     // enumFromTo :: Int -> Int -> [Int]    const enumFromTo = m => n =>        Array.from({            length: 1 + n - m        }, (_, i) => m + i);     // eq (==) :: Eq a => a -> a -> Bool    const eq = a => b => a === b;     // flatten :: NestedList a -> [a]    const flatten = nest => nest.flat(Infinity);     // flip :: (a -> b -> c) -> b -> a -> c    const flip = f =>        x => y => f(y)(x);     // index (!!) :: [a] -> Int -> a    const index = xs => i => xs[i];     // intercalate :: String -> [String] -> String    const intercalate = s =>        xs => xs.join(s);     // isInt :: Int -> Bool    const isInt = x => x === Math.floor(x);     // justifyRight :: Int -> Char -> String -> String    const justifyRight = n => cFiller => s =>        n > s.length ? (            s.padStart(n, cFiller)        ) : s;     // map :: (a -> b) -> [a] -> [b]    const map = f => xs =>        (Array.isArray(xs) ? (            xs        ) : xs.split('')).map(f);     // pred :: Enum a => a -> a    const pred = x => x - 1;     // replicate :: Int -> a -> [a]    const replicate = n => x =>        Array.from({            length: n        }, () => x);     // reverse :: [a] -> [a]    const reverse = xs =>        'string' !== typeof xs ? (            xs.slice(0).reverse()        ) : xs.split('').reverse().join('');     // show :: a -> String    const show = x => JSON.stringify(x);     // str :: a -> String    const str = x => x.toString();     // sum :: [Num] -> Num    const sum = xs => xs.reduce((a, x) => a + x, 0);     // transpose :: [[a]] -> [[a]]    const transpose = xs =>        xs[0].map((_, iCol) => xs.map((row) => row[iCol]));     // unlines :: [String] -> String    const unlines = xs => xs.join('\n');     // zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]    const zipWith = f => xs => ys =>        xs.slice(            0, Math.min(xs.length, ys.length)        ).map((x, i) => f(x)(ys[i]));     // MAIN ------------------------------------------------    return main();})();`
Output:
```Order: 4
Summing to: 34
Row, column and diagonal sums checked: true

1   15   14    4
12    6    7    9
8   10   11    5
13    3    2   16

Order: 8
Summing to: 260
Row, column and diagonal sums checked: true

1   63   62    4   60    6    7   57
56   10   11   53   13   51   50   16
48   18   19   45   21   43   42   24
25   39   38   28   36   30   31   33
32   34   35   29   37   27   26   40
41   23   22   44   20   46   47   17
49   15   14   52   12   54   55    9
8   58   59    5   61    3    2   64

Order: 12
Summing to: 870
Row, column and diagonal sums checked: true

1  143  142    4    5  139  138    8    9  135  134   12
132   14   15  129  128   18   19  125  124   22   23  121
120   26   27  117  116   30   31  113  112   34   35  109
37  107  106   40   41  103  102   44   45   99   98   48
49   95   94   52   53   91   90   56   57   87   86   60
84   62   63   81   80   66   67   77   76   70   71   73
72   74   75   69   68   78   79   65   64   82   83   61
85   59   58   88   89   55   54   92   93   51   50   96
97   47   46  100  101   43   42  104  105   39   38  108
36  110  111   33   32  114  115   29   28  118  119   25
24  122  123   21   20  126  127   17   16  130  131   13
133   11   10  136  137    7    6  140  141    3    2  144```

## Julia

`using Printf function magicsquaredoubleeven(order::Int)    if order % 4 != 0; error("the order must be divisible by 4") end     sqr = Matrix{Int}(order, order)    mul = div(order, 4)    ext = vcat(1:mul, order-mul+1:order)    isext(i::Int, j::Int) = (i in ext) == (j in ext)    boolsqr = collect(isext(i, j) for i in 1:order, j in 1:order)    for i in linearindices(sqr)        if boolsqr[i]; sqr[i] = i end        if !boolsqr[end+1-i]; sqr[end+1-i] = i end    end    return sqrend for n in (4, 8, 12)    magicconst = div(n ^ 3 + n, 2)    sq = magicsquaredoubleeven(n)     println("Order: \$n; magic constant: \$magicconst.\nSquare:")    for r in 1:n, c in 1:n        @printf("%4i", sq[r, c])        if c == n; println() end    end    println()end`
Output:
```Order: 4; magic constant: 34.
Square:
1  12   8  13
15   6  10   3
14   7  11   2
4   9   5  16

Order: 8; magic constant: 260.
Square:
1   9  48  40  32  24  49  57
2  10  47  39  31  23  50  58
62  54  19  27  35  43  14   6
61  53  20  28  36  44  13   5
60  52  21  29  37  45  12   4
59  51  22  30  38  46  11   3
7  15  42  34  26  18  55  63
8  16  41  33  25  17  56  64

Order: 12; magic constant: 870.
Square:
1  13  25 108  96  84  72  60  48 109 121 133
2  14  26 107  95  83  71  59  47 110 122 134
3  15  27 106  94  82  70  58  46 111 123 135
141 129 117  40  52  64  76  88 100  33  21   9
140 128 116  41  53  65  77  89 101  32  20   8
139 127 115  42  54  66  78  90 102  31  19   7
138 126 114  43  55  67  79  91 103  30  18   6
137 125 113  44  56  68  80  92 104  29  17   5
136 124 112  45  57  69  81  93 105  28  16   4
10  22  34  99  87  75  63  51  39 118 130 142
11  23  35  98  86  74  62  50  38 119 131 143
12  24  36  97  85  73  61  49  37 120 132 144```

## Kotlin

Translation of: Java
`// version 1.1.0 fun magicSquareDoublyEven(n: Int): Array<IntArray> {    if ( n < 4 || n % 4 != 0)         throw IllegalArgumentException("Base must be a positive multiple of 4")     // pattern of count-up vs count-down zones    val bits = 0b1001_0110_0110_1001    val size = n * n    val mult = n / 4  // how many multiples of 4     val result = Array(n) { IntArray(n) }    var i = 0    for (r in 0 until n)        for (c in 0 until n) {            val bitPos = c / mult + r / mult * 4            result[r][c] =  if (bits and (1 shl bitPos) != 0) i + 1 else size - i            i++        }    return result}  fun main(args: Array<String>) {    val n = 8    for (ia in magicSquareDoublyEven(n)) {         for (i in ia) print("%2d  ".format(i))        println()    }    println("\nMagic constant \${(n * n + 1) * n / 2}")}`
Output:
``` 1   2  62  61  60  59   7   8
9  10  54  53  52  51  15  16
48  47  19  20  21  22  42  41
40  39  27  28  29  30  34  33
32  31  35  36  37  38  26  25
24  23  43  44  45  46  18  17
49  50  14  13  12  11  55  56
57  58   6   5   4   3  63  64

Magic constant 260
```

## Lua

For all three kinds of Magic Squares(Odd, singly and doubly even)
See Magic_squares/Lua.

## Nim

Translation of: Kotlin
`import bitops, sequtils, strutils type Square = seq[seq[int]] func magicSquareDoublyEven(n: int): Square =  ## Build a magic square of doubly even order.   assert n >= 4 and (n and 3) == 0, "base must be a positive multiple of 4."  result = newSeqWith(n, newSeq[int](n))   const bits = 0b1001_0110_0110_1001  # Pattern of count-up vs count-down zones.  let size = n * n  let mult = n div 4                  # How many multiples of 4.   var i = 0  for r in 0..<n:    for c in 0..<n:      let bitPos = c div mult + r div mult * 4      result[r][c] = if bits.testBit(bitPos): i + 1 else: size - i      inc i  func `\$`(square: Square): string =  ## Return the string representation of a magic square.  let length = len(\$(square.len * square.len))  for row in square:    result.add row.mapIt((\$it).align(length)).join(" ") & '\n'  when isMainModule:  let n = 8  echo magicSquareDoublyEven(n)  echo "Magic constant = ", n * (n * n + 1) div 2`
Output:
``` 1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

Magic constant = 260```

## PARI/GP

A magic one-liner:

`magicsquare(n)=matrix(n,n,i,j,k=i+j*n-n;if(bitand(38505,2^((j-1)%4*4+(i-1)%4)),k,n*n+1-k))`
Output:
```magicsquare(8)

[ 1 56 48 25 33 24 16 57]

[63 10 18 39 31 42 50  7]

[62 11 19 38 30 43 51  6]

[ 4 53 45 28 36 21 13 60]

[ 5 52 44 29 37 20 12 61]

[59 14 22 35 27 46 54  3]

[58 15 23 34 26 47 55  2]

[ 8 49 41 32 40 17  9 64]```

BTW: The bit field number 38505 = 9669h seems to come from hell to do the magic...

## Perl

See Magic squares/Perl for a general magic square generator.

` `

## Phix

Translation of: C++
`constant t = {{1,1,0,0},              {1,1,0,0},              {0,0,1,1},              {0,0,1,1}} function magic_square(integer n)    if n<4 or mod(n,4)!=0 then return false end if    sequence square = repeat(repeat(0,n),n)    integer i = 0    for r=1 to n do        for c=1 to n do            square[r,c] = iff(t[mod(r,4)+1,mod(c,4)+1]?i+1:n*n-i)            i += 1        end for    end for    return squareend function procedure check(sequence sq)    integer n = length(sq)    integer magic = n*(n*n+1)/2    integer bd = 0, fd = 0    for i=1 to length(sq) do        if sum(sq[i])!=magic then ?9/0 end if        if sum(columnize(sq,i))!=magic then ?9/0 end if        bd += sq[i,i]        fd += sq[n-i+1,n-i+1]    end for    if bd!=magic or fd!=magic then ?9/0 end ifend procedure --for i=4 to 16 by 4 dofor i=8 to 8 by 4 do    sequence square = magic_square(i)    printf(1,"maqic square of order %d, sum: %d\n", {i,sum(square[i])})    string fmt = sprintf("%%%dd",length(sprintf("%d",i*i)))    pp(square,{pp_Nest,1,pp_IntFmt,fmt,pp_StrFmt,3,pp_IntCh,false,pp_Pause,0})    check(square)end for`
Output:
```maqic square of order 8, sum: 260
{{ 1,63,62, 4, 5,59,58, 8},
{56,10,11,53,52,14,15,49},
{48,18,19,45,44,22,23,41},
{25,39,38,28,29,35,34,32},
{33,31,30,36,37,27,26,40},
{24,42,43,21,20,46,47,17},
{16,50,51,13,12,54,55, 9},
{57, 7, 6,60,61, 3, 2,64}}
```

## PureBasic

Translation of: FreeBasic
`Procedure.i MagicN(n.i)  ProcedureReturn n*(n*n+1)/2EndProcedure Procedure.i MaxN(mx.i,n.i)  If mx>n : ProcedureReturn mx : Else : ProcedureReturn n : EndIfEndProcedure Procedure.i MaxL(mx.i)  Define.i i  While mx    mx/10 : i+1  Wend  ProcedureReturn iEndProcedure Procedure.b DblEvenMagicSquare(n.i)  Define.i q=n/4, nr=1, x, y, max, spc  Dim sq.i(n,n)   For y=1 To n    For x=q+1 To n-q      sq(x,y)=1    Next  Next   For x=1 To n    For y=q+1 To n-q      sq(x,y) ! 1    Next  Next   q=n*n+1  For y=1 To n    For x=1 To n      If sq(x,y)=0        sq(x,y)=q-nr      Else        sq(x,y)=nr      EndIf      nr+1      max=MaxN(max,sq(x,y))    Next  Next   spc=MaxL(max)+1  For y=n To 1 Step -1    For x=n To 1 Step -1      Print(RSet(Str(sq(x,y)),spc," "))    Next    PrintN("")  Next EndProcedure OpenConsole("Magic-Square-Doubly-Even")Define.i n Repeat  PrintN("Input [4,8,12..n] (0=Exit)")  While (n<4) Or (n%4)    Print(">") : n=Val(Input())    If n=0 : End : EndIf  Wend    PrintN("The magic sum = "+Str(MagicN(n)))  DblEvenMagicSquare(n)    n=0ForEver`
Output:
```Input [4,8,12..n] (0=Exit)
>8
The magic sum = 260

1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

Input [4,8,12..n] (0=Exit)

>```

## Python

### Procedural

` def MagicSquareDoublyEven(order):    sq = [range(1+n*order,order + (n*order)+1) for n in range(order) ]    n1 = order/4    for r in range(n1):        r1 = sq[r][n1:-n1]        r2 = sq[order -r - 1][n1:-n1]        r1.reverse()        r2.reverse()        sq[r][n1:-n1] = r2        sq[order -r - 1][n1:-n1] = r1    for r in range(n1, order-n1):        r1 = sq[r][:n1]        r2 = sq[order -r - 1][order-n1:]        r1.reverse()        r2.reverse()        sq[r][:n1] = r2        sq[order -r - 1][order-n1:] = r1    return sq def printsq(s):    n = len(s)    bl = len(str(n**2))+1    for i in range(n):        print ''.join( [ ("%"+str(bl)+"s")%(str(x)) for x in s[i]] )    print "\nMagic constant = %d"%sum(s[0]) printsq(MagicSquareDoublyEven(8)) `
Output:
```
1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

Magic constant = 260

>>> ```

### Composition of pure functions

Generating test results and a magic square in the form of a wiki table:

Works with: Python version 3.7
`'''Magic squares of doubly even order''' from itertools import chain, repeatfrom functools import reducefrom math import log  # doublyEvenMagicSquare :: Int -> [[Int]]def doublyEvenMagicSquare(n):    '''Magic square of order n'''     # magic :: Int -> [Bool]    def magic(n):        '''Truth-table series'''        if 0 < n:            xs = magic(n - 1)            return xs + [not x for x in xs]        else:            return [True]     sqr = n * n    power = log(sqr, 2)    scale = replicate(n / 4)    return chunksOf(n)([        succ(i) if bln else sqr - i for i, bln in        enumerate(magic(power) if isInteger(power) else (            flatten(scale(                map(scale, chunksOf(4)(magic(4)))            ))        ))    ])  # TEST ----------------------------------------------------# main :: IO()def main():    '''Tests'''     order = 8    magicSquare = doublyEvenMagicSquare(order)     print(        'Row sums: ',        [sum(xs) for xs in magicSquare],        '\nCol sums:',        [sum(xs) for xs in transpose(magicSquare)],        '\n1st diagonal sum:',        sum(magicSquare[i][i] for i in range(0, order)),        '\n2nd diagonal sum:',        sum(magicSquare[i][(order - 1) - i] for i in range(0, order)),        '\n'    )    print(wikiTable({        'class': 'wikitable',        'style': cssFromDict({            'text-align': 'center',            'color': '#605B4B',            'border': '2px solid silver'        }),        'colwidth': '3em'    })(magicSquare))  # GENERIC -------------------------------------------------  # chunksOf :: Int -> [a] -> [[a]]def chunksOf(n):    '''A series of lists of length n,       subdividing the contents of xs.       Where the length of xs is not evenly divible       the final list will be shorter than n.'''    return lambda xs: reduce(        lambda a, i: a + [xs[i:n + i]],        range(0, len(xs), n), []    ) if 0 < n else []  # concatMap :: (a -> [b]) -> [a] -> [b]def concatMap(f):    '''Concatenated list over which a function has been mapped.       The list monad can be derived by using a function f which       wraps its output a in list       (using an empty list to represent computational failure).'''    return lambda xs: list(        chain.from_iterable(            map(f, xs)        )    )  # cssFromDict :: Dict -> Stringdef cssFromDict(dct):    '''CSS string serialized from key values in a Dictionary.'''    return reduce(        lambda a, k: a + k + ':' + dct[k] + '; ', dct.keys(), ''    )  # flatten :: NestedList a -> [a]def flatten(x):    '''A list of atoms resulting from fully flattening       an arbitrarily nested list.'''    return concatMap(flatten)(x) if isinstance(x, list) else [x]  # isInteger :: Num -> Booldef isInteger(n):    '''Divisible by one without remainder ?'''    return 0 == (n - int(n))  # replicate :: Int -> a -> [a]def replicate(n):    '''A list of length n in which every element       has the value x.'''    return lambda x: list(repeat(x, n))  # succ :: Enum a => a -> adef succ(x):    '''The successor of a value. For numeric types, (1 +).'''    return 1 + x if isinstance(x, int) else (        chr(1 + ord(x))    )  # transpose :: Matrix a -> Matrix adef transpose(m):    '''The rows and columns of the argument transposed.       (The matrix containers and rows can be lists or tuples).'''    if m:        inner = type(m[0])        z = zip(*m)        return (type(m))(            map(inner, z) if tuple != inner else z        )    else:        return m  # wikiTable :: Dict -> [[a]] -> Stringdef wikiTable(opts):    '''List of lists rendered as a wiki table string.'''    def colWidth():        return 'width:' + opts['colwidth'] + '; ' if (            'colwidth' in opts        ) else ''     def cellStyle():        return opts['cell'] if 'cell' in opts else ''     return lambda rows: '{| ' + reduce(        lambda a, k: (            a + k + '="' + opts[k] + '" ' if k in opts else a        ),        ['class', 'style'],        ''    ) + '\n' + '\n|-\n'.join(        '\n'.join(            ('|' if (0 != i and ('cell' not in opts)) else (                '|style="' + colWidth() + cellStyle() + '"|'            )) + (                str(x) or ' '            ) for x in row        ) for i, row in enumerate(rows)    ) + '\n|}\n\n'  if __name__ == '__main__':    main()`
Output:
```Row sums:  [260, 260, 260, 260, 260, 260, 260, 260]
Col sums: [260, 260, 260, 260, 260, 260, 260, 260]
1st diagonal sum: 260
2nd diagonal sum: 260 ```
 1 63 62 4 60 6 7 57 56 10 11 53 13 51 50 16 48 18 19 45 21 43 42 24 25 39 38 28 36 30 31 33 32 34 35 29 37 27 26 40 41 23 22 44 20 46 47 17 49 15 14 52 12 54 55 9 8 58 59 5 61 3 2 64

## R

Translation of the magic square code example from Jama, which is released to the public domain. This includes all three cases.

`magic <- function(n) {  if (n %% 2 == 1) {    p <- (n + 1) %/% 2 - 2    ii <- seq(n)    outer(ii, ii, function(i, j) n * ((i + j + p) %% n) + (i + 2 * (j - 1)) %% n + 1)  } else if (n %% 4 == 0) {    p <- n * (n + 1) + 1    ii <- seq(n)    outer(ii, ii, function(i, j) ifelse((i %/% 2 - j %/% 2) %% 2 == 0, p - n * i - j, n * (i - 1) + j))  } else {    p <- n %/% 2    q <- p * p    k <- (n - 2) %/% 4 + 1    a <- Recall(p)    a <- rbind(cbind(a, a + 2 * q), cbind(a + 3 * q, a + q))    ii <- seq(p)    jj <- c(seq(k - 1), seq(length.out=k - 2, to=n))    m <- a[ii, jj]; a[ii, jj] <- a[ii + p, jj]; a[ii + p, jj] <- m    jj <- c(1, k)    m <- a[k, jj]; a[k, jj] <- a[k + p, jj]; a[k + p, jj] <- m    a  }}`

Example

```> magic(8)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,]   64    2    3   61   60    6    7   57
[2,]    9   55   54   12   13   51   50   16
[3,]   17   47   46   20   21   43   42   24
[4,]   40   26   27   37   36   30   31   33
[5,]   32   34   35   29   28   38   39   25
[6,]   41   23   22   44   45   19   18   48
[7,]   49   15   14   52   53   11   10   56
[8,]    8   58   59    5    4   62   63    1```

## Raku

(formerly Perl 6)

See Magic squares/Raku for a general magic square generator.

Output:

With a parameter of 8:

``` 1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

The magic number is 260```

With a parameter of 12:

```  1   2   3 141 140 139 138 137 136  10  11  12
13  14  15 129 128 127 126 125 124  22  23  24
25  26  27 117 116 115 114 113 112  34  35  36
108 107 106  40  41  42  43  44  45  99  98  97
96  95  94  52  53  54  55  56  57  87  86  85
84  83  82  64  65  66  67  68  69  75  74  73
72  71  70  76  77  78  79  80  81  63  62  61
60  59  58  88  89  90  91  92  93  51  50  49
48  47  46 100 101 102 103 104 105  39  38  37
109 110 111  33  32  31  30  29  28 118 119 120
121 122 123  21  20  19  18  17  16 130 131 132
133 134 135   9   8   7   6   5   4 142 143 144

The magic number is 870```

## REXX

"Marked" numbers   (via the   diag   subroutine)   indicate that those (sequentially generated) numbers don't get
swapped   (and thusly, stay in place in the magic square).

`/*REXX program constructs a  magic square  of doubly even sides (a size divisible by 4).*/n= 8;   s= n%4;   L= n%2-s+1;    w= length(n**2) /*size; small sq;  low middle;  # width*/@.= 0;            H= n%2+s                       /*array default;  high middle.         */call gen                                         /*generate a grid in numerical order.  */call diag                                        /*mark numbers on both diagonals.      */call corn                                        /*  "     "    in small corner boxen.  */call midd                                        /*  "     "    in  the middle    "     */call swap                                        /*swap positive numbers with highest #.*/call show                                        /*display the doubly even magic square.*/call sum                                         /*   "     "  magic number for square. */exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/o:    parse arg ?;             return n-?+1      /*calculate the "other" (right) column.*/@:    parse arg x,y;           return abs(@.x.y)diag:      do r=1 for n;  @.r.[email protected](r,r); o=o(r);  @.r.[email protected](r,o);  end;              returnmidd:      do r=L  to H;  do c=L  to H;  @.r.[email protected](r,c);           end;  end;        returngen:  #=0; do r=1 for n;  do c=1  for n; #=#+1;   @.r.c=#;        end;  end;        returnshow: #=0; do r=1 for n;  \$=; do c=1  for n; \$=\$ right(@(r,c),w); end;  say \$; end; returnsum:  #=0; do r=1 for n;  #=#[email protected](r,1);  end;  say;  say 'The magic number is: '   #; returnmax#:      do a=n for n  by -1;  do b=n  for n  by -1;  if @.a.b>0  then return; end;  end/*──────────────────────────────────────────────────────────────────────────────────────*/swap:         do   r=1  for n                do c=1  for n;  if @.r.c<0  then iterate;  call max#  /*find max number.*/                parse value  [email protected].a.b  ([email protected].r.c)    with    @.r.c  @.a.b /*swap two values.*/                end   /*c*/              end     /*r*/;                       return/*──────────────────────────────────────────────────────────────────────────────────────*/corn:         do   r=1  for n;  if r>s & r<=n-s  then iterate   /*"corner boxen", size≡S*/                do c=1  for n;  if c>s & c<=n-s  then iterate;  @.r.c= [email protected](r,c)  /*negate*/                end   /*c*/              end     /*r*/;                       return`
output   when using the default input:
```  1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

The magic number is:  260
```

## Ruby

`def double_even_magic_square(n)  raise ArgumentError, "Need multiple of four" if n%4 > 0  block_size, max = n/4, n*n  pre_pat = [true, false, false, true,             false, true, true, false]  pre_pat += pre_pat.reverse  pattern = pre_pat.flat_map{|b| [b] * block_size} * block_size  flat_ar = pattern.each_with_index.map{|yes, num| yes ? num+1 : max-num}  flat_ar.each_slice(n).to_aend def to_string(square)  n = square.size  fmt = "%#{(n*n).to_s.size + 1}d" * n  square.inject(""){|str,row| str << fmt % row << "\n"}end puts to_string(double_even_magic_square(8))`
Output:
```  1  2 62 61 60 59  7  8
56 55 11 12 13 14 50 49
48 47 19 20 21 22 42 41
25 26 38 37 36 35 31 32
33 34 30 29 28 27 39 40
24 23 43 44 45 46 18 17
16 15 51 52 53 54 10  9
57 58  6  5  4  3 63 64
```

## Rust

`use std::env; fn main() {    let n: usize = match env::args()        .nth(1)        .and_then(|arg| arg.parse().ok())        .ok_or("Please specify the size of the magic square, as a positive multiple of 4.")    {        Ok(arg) if arg >= 4 && arg % 4 == 0 => arg,        Err(e) => panic!(e),        _ => panic!("Argument must be a positive multiple of 4."),    };     let mc = (n * n + 1) * n / 2;    println!("Magic constant: {}\n", mc);    let bits = 0b1001_0110_0110_1001u32;    let size = n * n;    let width = size.to_string().len() + 1;    let mult = n / 4;    let mut i = 0;    for r in 0..n {        for c in 0..n {            let bit_pos = c / mult + (r / mult) * 4;            print!(                "{e:>w\$}",                e = if bits & (1 << bit_pos) != 0 {                    i + 1                } else {                    size - i                },                w = width            );            i += 1;        }        println!();    }}`
Output:
```Magic constant: 260

1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64
```

## Scala

Output:
Best seen running in your browser either by ScalaFiddle (ES aka JavaScript, non JVM) or Scastie (remote JVM).
`object MagicSquareDoublyEven extends App {  private val n = 8   private def magicSquareDoublyEven(n: Int): Array[Array[Int]] = {    require(n >= 4 || n % 4 == 0, "Base must be a positive multiple of 4.")     // pattern of count-up vs count-down zones    val (bits, mult, result, size) = (38505, n / 4, Array.ofDim[Int](n, n), n * n)    var i = 0     for (r <- result.indices; c <- result(0).indices) {      def bitPos = c / mult + (r / mult) * 4       result(r)(c) = if ((bits & (1 << bitPos)) != 0) i + 1 else size - i      i += 1    }    result  }   magicSquareDoublyEven(n).foreach(row => println(row.map(x => f"\$x%2s ").mkString))  println(f"---%nMagic constant: \${(n * n + 1) * n / 2}%d") }`

## Sidef

Translation of: Ruby
`func double_even_magic_square(n) {    assert(n%4 == 0, "Need multiple of four")    var (bsize, max) = (n/4, n*n)    var pre_pat = [true, false, false, true,                   false, true, true, false]    pre_pat += pre_pat.flip    var pattern = (pre_pat.map{|b| bsize.of(b)... } * bsize)    pattern.map_kv{|k,v| v ? k+1 : max-k }.slices(n)} func format_matrix(a) {    var fmt = "%#{a.len**2 -> len}s"    a.map { .map { fmt % _ }.join(' ') }.join("\n")} say format_matrix(double_even_magic_square(8))`
Output:
``` 1  2 62 61 60 59  7  8
56 55 11 12 13 14 50 49
48 47 19 20 21 22 42 41
25 26 38 37 36 35 31 32
33 34 30 29 28 27 39 40
24 23 43 44 45 46 18 17
16 15 51 52 53 54 10  9
57 58  6  5  4  3 63 64
```

## Stata

Translation of: R
`matafunction magic(n) {    if (mod(n,2)==1) {        p = (n+1)/2-2        a = J(n,n,.)        for (i=1; i<=n; i++) {            for (j=1; j<=n; j++) {                a[i,j] = n*mod(i+j+p,n)+mod(i+2*j-2,n)+1            }        }    } else if (mod(n,4)==0) {        p = n^2+n+1        a = J(n,n,.)        for (i=1; i<=n; i++) {            for (j=1; j<=n; j++) {                a[i,j] = mod(floor(i/2)-floor(j/2),2)==0 ? p-n*i-j : n*(i-1)+j            }        }    } else {        p = n/2        q = p*p        k = (n-2)/4+1        a = magic(p)        a = a,a:+2*q\a:+3*q,a:+q        i = 1..p        j = 1..k-1        if (k>2) j = j,n-k+3..n        m = a[i,j]; a[i,j] = a[i:+p,j]; a[i:+p,j] = m        j = 1,k        m = a[k,j]; a[k,j] = a[k:+p,j]; a[k:+p,j] = m    }    return(a)}end`
```. mata magic(8)
1    2    3    4    5    6    7    8
+-----------------------------------------+
1 |  64    2    3   61   60    6    7   57  |
2 |   9   55   54   12   13   51   50   16  |
3 |  17   47   46   20   21   43   42   24  |
4 |  40   26   27   37   36   30   31   33  |
5 |  32   34   35   29   28   38   39   25  |
6 |  41   23   22   44   45   19   18   48  |
7 |  49   15   14   52   53   11   10   56  |
8 |   8   58   59    5    4   62   63    1  |
+-----------------------------------------+```

## VBScript

Translation of: Java
`' Magic squares of doubly even ordern=8  'multiple of 4pattern="1001011001101001"size=n*n: w=len(size)mult=n\4  'how many multiples of 4 wscript.echo "Magic square : " & n & " x " & ni=0For r=0 To n-1	l=""	For c=0 To n-1		bit=Mid(pattern, c\mult+(r\mult)*4+1, 1)		If bit="1" Then t=i+1 Else t=size-i		l=l & Right(Space(w) & t, w) & " "		i=i+1	Next 'c	wscript.echo lNext 'rwscript.echo "Magic constant=" & (n*n+1)*n/2`
Output:
```Magic square : 8 x 8
1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64
Magic constant=260```

## Visual Basic .NET

Translation of: C#
`Module MagicSquares     Function MagicSquareDoublyEven(n As Integer) As Integer(,)        If n < 4 OrElse n Mod 4 <> 0 Then            Throw New ArgumentException("base must be a positive multiple of 4")        End If         'pattern of count-up vs count-down zones        Dim bits = Convert.ToInt32("1001011001101001", 2)        Dim size = n * n        Dim mult As Integer = n / 4 ' how many multiples of 4         Dim result(n - 1, n - 1) As Integer         Dim i = 0        For r = 0 To n - 1            For c = 0 To n - 1                Dim bitPos As Integer = Math.Floor(c / mult) + Math.Floor(r / mult) * 4                Dim test = (bits And (1 << bitPos)) <> 0                If test Then                    result(r, c) = i + 1                Else                    result(r, c) = size - i                End If                 i = i + 1            Next            Console.WriteLine()        Next         Return result    End Function     Sub Main()        Dim n = 8        Dim result = MagicSquareDoublyEven(n)        For i = 0 To result.GetLength(0) - 1            For j = 0 To result.GetLength(1) - 1                Console.Write("{0,2} ", result(i, j))            Next            Console.WriteLine()        Next        Console.WriteLine()        Console.WriteLine("Magic constant: {0} ", (n * n + 1) * n / 2)         Console.ReadLine()    End Sub End Module`
Output:
``` 1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

Magic constant: 260```

## Wren

Translation of: Kotlin
Library: Wren-fmt
`import "/fmt" for Conv, Fmt var magicSquareDoublyEven = Fn.new { |n|    if (n < 4 || n%4 != 0) Fiber.abort("Base must be a positive multiple of 4")     // pattern of count-up vs count-down zones    var bits = Conv.atoi("1001011001101001", 2)    var size = n * n    var mult = (n/4).floor // how many multiples of 4    var result = List.filled(n, null)    for (i in 0...n) result[i] = List.filled(n, 0)    var i = 0    for (r in 0...n) {        for (c in 0...n) {            var bitPos = (c/mult).floor + (r/mult).floor * 4            result[r][c] = ((bits & (1<<bitPos)) != 0) ? i + 1 : size - i            i = i + 1        }    }    return result} var n = 8for (ia in magicSquareDoublyEven.call(n)) {    for (i in ia) Fmt.write("\$2d  ", i)    System.print()}System.print("\nMagic constant %((n * n + 1) * n / 2)")`
Output:
``` 1   2  62  61  60  59   7   8
9  10  54  53  52  51  15  16
48  47  19  20  21  22  42  41
40  39  27  28  29  30  34  33
32  31  35  36  37  38  26  25
24  23  43  44  45  46  18  17
49  50  14  13  12  11  55  56
57  58   6   5   4   3  63  64

Magic constant 260
```

## zkl

Translation of: Java
`class MagicSquareDoublyEven{   fcn init(n){ var result=magicSquareDoublyEven(n) }   fcn toString{      sink,n:=Sink(String),result.len();  // num collumns      fmt:="%2s ";      foreach row in (result)         { sink.write(row.apply('wrap(n){ fmt.fmt(n) }).concat(),"\n") }      sink.write("\nMagic constant: %d".fmt((n*n + 1)*n/2));      sink.close();   }   fcn magicSquareDoublyEven(n){      if (n<4 or n%4!=0 or n>16)	 throw(Exception.ValueError("base must be a positive multiple of 4"));      bits,size,mult:=0b1001011001101001, n*n, n/4;      result:=n.pump(List(),n.pump(List(),0).copy);  // array[n,n] of zero       foreach i in (size){	 bitsPos:=(i%n)/mult + (i/(n*mult)*4);	 value:=(bits.bitAnd((2).pow(bitsPos))) and i+1 or size-i;	 result[i/n][i%n]=value;      }      result;   }}MagicSquareDoublyEven(8).println();`
Output:
``` 1  2 62 61 60 59  7  8
9 10 54 53 52 51 15 16
48 47 19 20 21 22 42 41
40 39 27 28 29 30 34 33
32 31 35 36 37 38 26 25
24 23 43 44 45 46 18 17
49 50 14 13 12 11 55 56
57 58  6  5  4  3 63 64

Magic constant: 260
```