# Egyptian division

Egyptian division
You are encouraged to solve this task according to the task description, using any language you may know.

Egyptian division is a method of dividing integers using addition and doubling that is similar to the algorithm of Ethiopian multiplication

Algorithm:

Given two numbers where the dividend is to be divided by the divisor:

1. Start the construction of a table of two columns: `powers_of_2`, and `doublings`; by a first row of a 1 (i.e. 2^0) in the first column and 1 times the divisor in the first row second column.
2. Create the second row with columns of 2 (i.e 2^1), and 2 * divisor in order.
3. Continue with successive i’th rows of 2^i and 2^i * divisor.
4. Stop adding rows, and keep only those rows, where 2^i * divisor is less than or equal to the dividend.
5. We now assemble two separate sums that both start as zero, called here answer and accumulator
6. Consider each row of the table, in the reverse order of its construction.
7. If the current value of the accumulator added to the doublings cell would be less than or equal to the dividend then add it to the accumulator, as well as adding the powers_of_2 cell value to the answer.
8. When the first row has been considered as above, then the integer division of dividend by divisor is given by answer.
(And the remainder is given by the absolute value of accumulator - dividend).

Example: 580 / 34

Table creation:

powers_of_2 doublings
1 34
2 68
4 136
8 272
16 544

Initialization of sums:

1 34
2 68
4 136
8 272
16 544
0 0

Considering table rows, bottom-up:

When a row is considered it is shown crossed out if it is not accumulated, or bold if the row causes summations.

1 34
2 68
4 136
8 272
16 544 16 544
1 34
2 68
4 136
8 272 16 544
16 544
1 34
2 68
4 136 16 544
8 272
16 544
1 34
2 68 16 544
4 136
8 272
16 544
1 34 17 578
2 68
4 136
8 272
16 544

So 580 divided by 34 using the Egyptian method is `17` remainder (578 - 580) or `2`.

The task is to create a function that does Egyptian division. The function should
closely follow the description above in using a list/array of powers of two, and
another of doublings.

• Functions should be clear interpretations of the algorithm.
• Use the function to divide 580 by 34 and show the answer here, on this page.

References

## 11l

Translation of: Python
```F egyptian_divmod(dividend, divisor)
assert(divisor != 0)
V (pwrs, dbls) = ([1], [divisor])
L dbls.last <= dividend
pwrs.append(pwrs.last * 2)
dbls.append(pwrs.last * divisor)
V (ans, accum) = (0, 0)
L(pwr, dbl) zip(pwrs[((len)-2 ..).step(-1)], dbls[((len)-2 ..).step(-1)])
I accum + dbl <= dividend
accum += dbl
ans += pwr
R (ans, abs(accum - dividend))

L(i, j) cart_product(0.<13, 1..12)
assert(egyptian_divmod(i, j) == divmod(i, j))
V (i, j) = (580, 34)
V (d, m) = egyptian_divmod(i, j)
print(‘#. divided by #. using the Egyption method is #. remainder #.’.format(i, j, d, m))```
Output:
```580 divided by 34 using the Egyption method is 17 remainder 2
```

## Action!

```TYPE Answer=[CARD result,reminder]

PROC EgyptianDivision(CARD dividend,divisor Answer POINTER res)
DEFINE SIZE="16"
CARD ARRAY powers(SIZE),doublings(SIZE)
CARD power,doubling,accumulator
INT i,count

count=0 power=1 doubling=divisor
WHILE count<SIZE AND doubling<=dividend
DO
powers(count)=power
doublings(count)=doubling
count==+1
power==LSH 1
doubling==LSH 1
OD

i=count-1
res.result=0
accumulator=0
WHILE i>=0
DO
IF accumulator+doublings(i)<=dividend THEN
accumulator==+doublings(i)
res.result==+powers(i)
FI
i==-1
OD
res.reminder=dividend-accumulator
RETURN

PROC Main()
CARD dividend=[580],divisor=[34]

EgyptianDivision(dividend,divisor,res)
PrintF("%U / %U = %U reminder %U",dividend,divisor,res.result,res.reminder)
RETURN```
Output:
```580 / 34 = 17 reminder 2
```

```with Ada.Text_IO;

procedure Egyptian_Division is

procedure Divide  (a : Natural; b : Positive; q, r : out Natural) is
doublings : array (0..31) of Natural;  -- The natural type holds values < 2^32 so no need going beyond
m, sum, last_index_touched : Natural := 0;
begin
for i in doublings'Range loop
m := b * 2**i;
exit when m > a ;
doublings (i) := m;
last_index_touched := i;
end loop;
q := 0;
for i in reverse doublings'First .. last_index_touched loop
m := sum + doublings (i);
if m <= a then
sum := m;
q := q + 2**i;
end if;
end loop;
r := a -sum;
end Divide;

q, r : Natural;
begin
Divide (580,34, q, r);
end Egyptian_Division;
```
Output:
`Quotient= 17 Remainder= 2`

## ALGOL 68

```BEGIN
# performs Egyptian division of dividend by divisor, setting quotient and remainder #
# this uses 32 bit numbers, so a table of 32 powers of 2 should be sufficient       #
# ( divisors > 2^30 will probably overflow - this is not checked here )             #
PROC egyptian division = ( INT dividend, divisor, REF INT quotient, remainder )VOID:
BEGIN
[ 1 : 32 ]INT powers of 2, doublings;
# initialise the powers of 2 and doublings tables #
powers of 2[ 1 ] := 1;
doublings  [ 1 ] := divisor;
INT   table pos  := 1;
WHILE table pos +:= 1;
powers of 2[ table pos ] := powers of 2[ table pos - 1 ] * 2;
doublings  [ table pos ] := doublings  [ table pos - 1 ] * 2;
doublings[ table pos ] <= dividend
DO
SKIP
OD;
# construct the accumulator and answer #
INT accumulator := 0, answer := 0;
WHILE table pos >=1
DO
IF ( accumulator + doublings[ table pos ] ) <= dividend
THEN
accumulator +:= doublings  [ table pos ];
answer      +:= powers of 2[ table pos ]
FI;
table pos -:= 1
OD;
remainder := ABS ( accumulator - dividend )
END # egyptian division # ;

INT quotient, remainder;
egyptian division( 580, 34, quotient, remainder );
print( ( "580 divided by 34 is: ", whole( quotient, 0 ), " remainder: ", whole( remainder, 0 ), newline ) )
END```
Output:
```580 divided by 34 is: 17 remainder: 2
```

## AppleScript

Unfold to derive successively doubled rows, fold to sum quotient and derive remainder

```-- EGYPTIAN DIVISION ------------------------------------

-- eqyptianQuotRem :: Int -> Int -> (Int, Int)
on egyptianQuotRem(m, n)
script expansion
on |λ|(ix)
set {i, x} to ix
if x > m then
Nothing()
else
Just({ix, {i + i, x + x}})
end if
end |λ|
end script

script collapse
on |λ|(ix, qr)
set {i, x} to ix
set {q, r} to qr
if x < r then
{q + i, r - x}
else
qr
end if
end |λ|
end script

return foldr(collapse, {0, m}, ¬
unfoldr(expansion, {1, n}))
end egyptianQuotRem

-- TEST -------------------------------------------------
on run
egyptianQuotRem(580, 34)
end run

-- GENERIC FUNCTIONS ------------------------------------

-- Just :: a -> Maybe a
on Just(x)
{type:"Maybe", Nothing:false, Just:x}
end Just

-- Nothing :: Maybe a
on Nothing()
{type:"Maybe", Nothing:true}
end Nothing

-- foldr :: (a -> b -> b) -> b -> [a] -> b
on foldr(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from lng to 1 by -1
set v to |λ|(item i of xs, v, i, xs)
end repeat
return v
end tell
end foldr

-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn

-- > unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10
-- > [10,9,8,7,6,5,4,3,2,1]
-- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
on unfoldr(f, v)
set xr to {v, v} -- (value, remainder)
set xs to {}
tell mReturn(f)
repeat -- Function applied to remainder.
set mb to |λ|(item 2 of xr)
if Nothing of mb then
exit repeat
else -- New (value, remainder) tuple,
set xr to Just of mb
-- and value appended to output list.
set end of xs to item 1 of xr
end if
end repeat
end tell
return xs
end unfoldr
```
Output:
`{17, 2}`

## Arturo

```egyptianDiv: function [dividend, divisor][
ensure -> and? dividend >= 0
divisor > 0

if dividend < divisor -> return @[0, dividend]

powersOfTwo: new [1]
doublings: new @[divisor]
d: divisor

while [true][
d: 2 * d
if d > dividend -> break
'powersOfTwo ++ 2 * last powersOfTwo
'doublings ++ d
]

accumulator: 0

loop (dec size doublings)..0 'i [
if dividend >= accumulator + doublings\[i] [
accumulator: accumulator + doublings\[i]
if accumulator = dividend -> break
]
]

]

dividend: 580
divisor: 34

[quotient, remainder]: egyptianDiv dividend divisor

print [dividend "divided by" divisor "is" quotient "with remainder" remainder]
```
Output:
`580 divided by 34 is 17 with remainder 2`

## AutoHotkey

```divident := 580
divisor := 34

obj := []	, div := divisor

while (div < divident)
{
obj[2**(A_Index-1)] := div				; obj[powers_of_2] := doublings
div *= 2						; double up
}

while obj.MaxIndex()						; iterate rows "in the reverse order"
{
if (accumulator + obj[obj.MaxIndex()] <= divident)	; If (accumulator + current doubling) <= dividend
{
accumulator += obj[obj.MaxIndex()]		; add current doubling to the accumulator
}
obj.pop()						; remove current row
}
MsgBox % divident "/" divisor " = " answer ( divident-accumulator > 0 ? " r" divident-accumulator : "")
```

Outputs:

`580/34 = 17 r2`

## BASIC

### ANSI BASIC

Translation of: QBasic

But the arrays are subscripted from 0.

Works with: Decimal BASIC
```100 REM Egyptian division
110 DIM Table(0 TO 31, 0 TO 1)
120 LET Dividend = 580
130 LET Divisor = 34
140 REM ** Division
150 LET I = 0
160 LET Table(I, 0) = 1
170 LET Table(I, 1) = Divisor
180 DO WHILE Table(I, 1) < Dividend
190    LET I = I + 1
200    LET Table(I, 0) = Table(I - 1, 0) * 2
210    LET Table(I, 1) = Table(I - 1, 1) * 2
220 LOOP
230 LET I = I - 1
240 LET Answer = Table(I, 0)
250 LET Accumulator = Table(I, 1)
260 DO WHILE I > 0
270    LET I = I - 1
280    IF Table(I, 1) + Accumulator <= Dividend THEN
300       LET Accumulator = Accumulator + Table(I, 1)
310    END IF
320 LOOP
330 REM ** Results
340 PRINT Dividend; "divided by"; Divisor; "using Egytian division";
350 PRINT " returns"; Answer; "remainder"; Dividend - Accumulator
360 END
```
Output:
``` 580 divided by 34 using Egytian division returns 17 remainder 2
```

### Applesoft BASIC

The MSX BASIC solution works without any changes.

### BaCon

```'---Ported from the c code example to BaCon by bigbass

'==================================================================================
FUNCTION EGYPTIAN_DIVISION(long dividend, long divisor, long remainder) TYPE long
'==================================================================================
'--- remainder is the third  parameter, pass 0 if you do not need the remainder

DECLARE powers[64] TYPE long
DECLARE doublings[64] TYPE long

LOCAL i TYPE long

FOR i = 0 TO  63 STEP 1
powers[i] = 1 << i
doublings[i] = divisor << i
IF (doublings[i] > dividend) THEN
BREAK
ENDIF
NEXT

LOCAL accumulator TYPE long
accumulator = 0

WHILE i >= 0
'--- If the current value of the accumulator added to the
'--- doublings cell would be less than or equal to the
'--- dividend then add it to the accumulator
IF (accumulator + doublings[i] <= dividend) THEN
accumulator = accumulator + doublings[i]
ENDIF
DECR i
WEND

IF remainder THEN
remainder = dividend - accumulator
PRINT dividend ," / ", divisor, " = " , answer ," remainder " , remainder

PRINT "Decoded the answer to a standard fraction"
PRINT  (remainder + 0.0 )/ (divisor + 0.0) + answer
PRINT

ELSE
PRINT dividend ," / ", divisor , " = " , answer
ENDIF

ENDFUNCTION

'--- the large number divided by the smaller number
'--- the third argument is 1 if you want to have a remainder
'--- and 0 if you dont want to have a remainder

EGYPTIAN_DIVISION(580,34,1)
EGYPTIAN_DIVISION(580,34,0)

EGYPTIAN_DIVISION(580,34,1)
```

### BASIC256

```arraybase 1
dim table(32, 2)
dividend = 580
divisor = 34

i = 1
table[i, 1] = 1
table[i, 2] = divisor

while table[i, 2] < dividend
i = i + 1
table[i, 1] = table[i -1, 1] * 2
table[i, 2] = table[i -1, 2] * 2
end while
i = i - 1
accumulator = table[i, 2]

while i > 1
i = i - 1
if table[i, 2]+ accumulator <= dividend then
accumulator = accumulator + table[i, 2]
end if
end while

print string(dividend); " divided by "; string(divisor); " using Egytian division";
print " returns "; string(answer); " mod(ulus) "; string(dividend-accumulator)```
Output:
`Same as FreeBASIC entry.`

### Chipmunk Basic

Translation of: QBasic
Works with: Chipmunk Basic version 3.6.4
Works with: QBasic
```100 dim table(32,2)
110 let dividend = 580
120 let divisor = 34
130 let i = 1
140 let table(i,1) = 1
150 let table(i,2) = divisor
160 do while table(i,2) < dividend
170  let i = i+1
180  let table(i,1) = table(i-1,1)*2
190  let table(i,2) = table(i-1,2)*2
200 loop
210 let i = i-1
230 let accumulator = table(i,2)
240 do while i > 1
250  let i = i-1
260  if table(i,2)+accumulator <= dividend then
280   let accumulator = accumulator+table(i,2)
290  endif
300 loop
310 print str\$(dividend);" divided by ";str\$(divisor);" using Egytian division";
320 print " returns ";str\$(answer);" mod(ulus) ";str\$(dividend-accumulator)
330 end
```

### FreeBASIC

```' version 09-08-2017
' compile with: fbc -s console

Data 580, 34

Dim As UInteger dividend, divisor, answer, accumulator, i
ReDim As UInteger table(1 To 32, 1 To 2)

i = 1
table(i, 1) = 1 : table(i, 2) = divisor

While table(i, 2) < dividend
i += 1
table(i, 1) = table(i -1, 1) * 2
table(i, 2) = table(i -1, 2) * 2
Wend

i -= 1
accumulator = table(i, 2)

While i > 1
i -= 1
If table(i,2)+ accumulator <= dividend Then
accumulator += table(i, 2)
End If
Wend

Print Str(dividend); " divided by "; Str(divisor); " using Egytian division";
Print " returns "; Str(answer); " mod(ulus) "; Str(dividend-accumulator)

' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End```
Output:
`580 divided by 34 using Egytian division returns 17 mod(ulus) 2`

### GW-BASIC

Translation of: QBasic
Works with: PC-BASIC version any
Works with: BASICA
Works with: Chipmunk Basic
Works with: QBasic
```100 CLS
110 DIM T(32,2)
120 LET A = 580
130 LET B = 34
140 LET I = 1
150 LET T(I,1) = 1
160 LET T(I,2) = B
170 WHILE T(I,2) < A
180  LET I = I+1
190  LET T(I,1) = T(I-1,1)*2
200  LET T(I,2) = T(I-1,2)*2
210 WEND
220 LET I = I-1
230 LET R = T(I,1)
240 LET S = T(I,2)
250 WHILE I > 1
260  LET I = I-1
270  IF T(I,2)+S <= A THEN LET R = R+T(I,1): LET S = S+T(I,2)
280 WEND
290 PRINT STR\$(A);" divided by ";STR\$(B);" using Egytian division";
300 PRINT " returns ";STR\$(R);" mod(ulus) ";STR\$(A-S)
310 END
```

### Just BASIC

Same code as QBasic

### Minimal BASIC

Translation of: ANSI BASIC
Works with: BASICA
Works with: Commodore BASIC version 3.5
Works with: MSX BASIC version 2.1
```10 REM Egyptian division
20 DIM T(31,1)
30 REM D1 - dividend; D2 - divisor
40 LET D1 = 580
50 LET D2 = 34
60 REM ** Division
70 LET I = 0
80 LET T(I,0) = 1
90 LET T(I,1) = D2
100 IF T(I,1) >= D1 THEN 160
110 LET I = I+1
120 LET T(I,0) = T(I-1,0)*2
130 LET T(I,1) = T(I-1,1)*2
140 GOTO 100
150 REM A - answer; C - accumulator
160 LET I = I-1
170 LET A = T(I,0)
180 LET C = T(I,1)
190 IF I <= 0 THEN 250
200 LET I = I-1
210 IF T(I,1)+C > D1 THEN 190
220 LET A = A+T(I,0)
230 LET C = C+T(I,1)
240 GOTO 190
250 REM ** Results
260 PRINT D1; "divided by"; D2;
270 PRINT "using Egyptian division";
280 PRINT " returns"; A; "remainder"; D1-C
290 END
```
Output:
``` 580 divided by 34 using Egyptian division returns 17 remainder 2
```

### MSX Basic

Works with: MSX BASIC version any
Works with: Applesoft BASIC
Works with: GW-BASIC
Works with: Chipmunk Basic
Works with: QBasic
```110 DIM T(32,2)
120 A = 580
130 B = 34
140 I = 1
150 T(I,1) = 1
160 T(I,2) = B
170 IF T(I,2) < A THEN  I = I+1 :  T(I,1) = T(I-1,1)*2 : T(I,2) = T(I-1,2)*2
180 IF T(I,2) >= A THEN GOTO 200
190 GOTO 170
200 I = I-1
210 R = T(I,1)
220 S = T(I,2)
230 IF I > 1 THEN I = I-1 : IF T(I,2)+S <= A THEN R = R+T(I,1): S = S+T(I,2)
240 IF I <= 1 THEN GOTO 260
250 GOTO 230
260 PRINT STR\$(A);" divided by ";STR\$(B);" using Egytian division";
270 PRINT " returns ";STR\$(R);" mod(ulus) ";STR\$(A-S)
280 END
```

### PureBasic

```OpenConsole()
Dim table.i(32, 2)
dividend.i = 580
divisor.i = 34

i.i = 1
table(i, 1) = 1
table(i, 2) = divisor

While table(i, 2) < dividend
i + 1
table(i, 1) = table(i -1, 1) * 2
table(i, 2) = table(i -1, 2) * 2
Wend
i - 1
accumulator = table(i, 2)

While i > 1
i - 1
If table(i, 2)+ accumulator <= dividend:
accumulator = accumulator + table(i, 2)
EndIf
Wend

Print(Str(dividend) + " divided by " + Str(divisor) + " using Egytian division")
PrintN(" returns " + Str(answer) + " mod(ulus) " + Str(dividend-accumulator))
Input()
CloseConsole()```
Output:
`Same as FreeBASIC entry.`

### QBasic

Works with: QBasic version 1.1
Works with: QuickBasic version 4.5
Works with: Run BASIC
Works with: Just BASIC
Works with: Liberty BASIC
```DIM table(32, 2)
dividend = 580
divisor = 34

i = 1
table(i, 1) = 1
table(i, 2) = divisor

WHILE table(i, 2) < dividend
i = i + 1
table(i, 1) = table(i - 1, 1) * 2
table(i, 2) = table(i - 1, 2) * 2
WEND
i = i - 1
accumulator = table(i, 2)

WHILE i > 1
i = i - 1
IF table(i, 2) + accumulator <= dividend THEN
accumulator = accumulator + table(i, 2)
END IF
WEND

PRINT STR\$(dividend); " divided by "; STR\$(divisor); " using Egytian division";
PRINT " returns "; STR\$(answer); " mod(ulus) "; STR\$(dividend - accumulator)
```
Output:
`Same as FreeBASIC entry.`

### Run BASIC

Same code as QBasic

### True BASIC

```DIM table(32, 2)
LET dividend = 580
LET divisor = 34

LET i = 1
LET table(i, 1) = 1
LET table(i, 2) = divisor

DO WHILE table(i, 2) < dividend
LET i = i+1
LET table(i, 1) = table(i-1, 1)*2
LET table(i, 2) = table(i-1, 2)*2
LOOP
LET i = i-1
LET accumulator = table(i, 2)

DO WHILE i > 1
LET i = i-1
IF table(i, 2)+accumulator <= dividend THEN
LET accumulator = accumulator+table(i, 2)
END IF
LOOP

PRINT STR\$(dividend); " divided by "; STR\$(divisor); " using Egytian division";
PRINT " returns "; STR\$(answer); " mod(ulus) "; STR\$(dividend-accumulator)
END
```
Output:
`Same as FreeBASIC entry.`

### Visual Basic .NET

Translation of: D
```Module Module1

Function EgyptianDivision(dividend As ULong, divisor As ULong, ByRef remainder As ULong) As ULong
Const SIZE = 64
Dim powers(SIZE) As ULong
Dim doublings(SIZE) As ULong
Dim i = 0

While i < SIZE
powers(i) = 1 << i
doublings(i) = divisor << i
If doublings(i) > dividend Then
Exit While
End If
i = i + 1
End While

Dim answer As ULong = 0
Dim accumulator As ULong = 0
i = i - 1
While i >= 0
If accumulator + doublings(i) <= dividend Then
accumulator += doublings(i)
End If
i = i - 1
End While

remainder = dividend - accumulator
End Function

Sub Main(args As String())
If args.Length < 2 Then
Dim name = Reflection.Assembly.GetEntryAssembly().Location
Console.Error.WriteLine("Usage: {0} dividend divisor", IO.Path.GetFileNameWithoutExtension(name))
Return
End If

Dim dividend = CULng(args(0))
Dim divisor = CULng(args(1))
Dim remainder As ULong

Dim ans = EgyptianDivision(dividend, divisor, remainder)
Console.WriteLine("{0} / {1} = {2} rem {3}", dividend, divisor, ans, remainder)
End Sub

End Module
```
Output:
`580 / 34 = 17 rem 2`

### XBasic

Works with: Windows XBasic
```PROGRAM  "Egyptian division"
VERSION  "0.0000"

DECLARE FUNCTION  Entry ()

FUNCTION  Entry ()
DIM T[32,2]
A = 580
B = 34
I = 1
T[I,1] = 1
T[I,2] = B
DO WHILE T[I,2] < A
INC I
T[I,1] = T[I-1,1]*2
T[I,2] = T[I-1,2]*2
LOOP
DEC I
R = T[I,1]
S = T[I,2]
DO WHILE I > 1
DEC I
IF T[I,2]+S <= A THEN
R = R+T[I,1]
S = S+T[I,2]
END IF
LOOP
PRINT A;" divided by";B;" using Egytian division";
PRINT " returns";R;" mod(ulus)"; A-S
END FUNCTION
END PROGRAM
```

### Yabasic

```dim table(32, 2)
dividend = 580
divisor = 34

i = 1
table(i, 1) = 1
table(i, 2) = divisor

while table(i, 2) < dividend
i = i + 1
table(i, 1) = table(i -1, 1) * 2
table(i, 2) = table(i -1, 2) * 2
wend
i = i - 1
accumulator = table(i, 2)

while i > 1
i = i - 1
if table(i, 2)+ accumulator <= dividend then
accumulator = accumulator + table(i, 2)
fi
wend

print str\$(dividend), " divided by ", str\$(divisor), " using Egytian division";
print " returns ", str\$(answer), " mod(ulus) ", str\$(dividend-accumulator)```
Output:
`Same as FreeBASIC entry.`

## C

```#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <assert.h>

uint64_t egyptian_division(uint64_t dividend, uint64_t divisor, uint64_t *remainder) {
// remainder is an out parameter, pass NULL if you do not need the remainder

static uint64_t powers[64];
static uint64_t doublings[64];

int i;

for(i = 0; i < 64; i++) {
powers[i] = 1 << i;
doublings[i] = divisor << i;
if(doublings[i] > dividend)
break;
}

uint64_t accumulator = 0;

for(i = i - 1; i >= 0; i--) {
// If the current value of the accumulator added to the
// doublings cell would be less than or equal to the
// dividend then add it to the accumulator
if(accumulator + doublings[i] <= dividend) {
accumulator += doublings[i];
}
}

if(remainder)
*remainder = dividend - accumulator;
}

void go(uint64_t a, uint64_t b) {
uint64_t x, y;
x = egyptian_division(a, b, &y);
printf("%llu / %llu = %llu remainder %llu\n", a, b, x, y);
assert(a == b * x + y);
}

int main(void) {
go(580, 32);
}
```

## C#

```using System;
using System.Collections;

namespace Egyptian_division
{
class Program
{
public static void Main(string[] args)
{
Console.Clear();
Console.WriteLine();
Console.WriteLine(" Egyptian division ");
Console.WriteLine();
Console.Write(" Enter value of dividend : ");

Console.Write(" Enter value of divisor : ");

Divide(dividend, divisor);

Console.WriteLine();
Console.Write("Press any key to continue . . . ");

}

static void Divide(int dividend, int divisor)
{
//
// Local variable declaration and initialization
//
int result   = 0;
int reminder = 0;

int powers_of_two = 0;
int doublings 	  = 0;

int accumulator = 0;

int two = 2;
int pow = 0;
int row = 0;

//
// Tables declaration
//
ArrayList table_powers_of_two = new ArrayList();
ArrayList table_doublings     = new ArrayList();

//
// Fill and Show table values
//
Console.WriteLine("                           ");
Console.WriteLine(" powers_of_2     doublings ");
Console.WriteLine("                           ");

// Set initial values
powers_of_two = 1;
doublings = divisor;
while( doublings <= dividend )
{
// Set table value

// Show new table row
Console.WriteLine("{0,8}{1,16}",powers_of_two, doublings);

pow++;

powers_of_two = (int)Math.Pow( two, pow );
doublings = powers_of_two * divisor;
}
Console.WriteLine("                           ");

//
// Calculate division and Show table values
//
row = pow - 1;
Console.WriteLine("                                                 ");
Console.WriteLine("                                                 ");
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop + row);

pow--;
while( pow >= 0 && accumulator < dividend )
{
// Get values from tables
doublings = int.Parse(table_doublings[pow].ToString());
powers_of_two = int.Parse(table_powers_of_two[pow].ToString());

if(accumulator + int.Parse(table_doublings[pow].ToString()) <= dividend )
{
// Set new values
accumulator += doublings;

// Show accumulated row values in different collor
Console.ForegroundColor = ConsoleColor.Green;
Console.Write("{0,8}{1,16}",powers_of_two, doublings);
Console.ForegroundColor = ConsoleColor.Green;
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop - 2);
}
else
{
// Show not accumulated row walues
Console.ForegroundColor = ConsoleColor.DarkGray;
Console.Write("{0,8}{1,16}",powers_of_two, doublings);
Console.ForegroundColor = ConsoleColor.Gray;
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop - 2);
}

pow--;
}

Console.WriteLine();
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop + row + 2);
Console.ResetColor();

// Set result and reminder
if( accumulator < dividend )
{
reminder = dividend - accumulator;

Console.WriteLine(" So " + dividend +
" divided by " + divisor +
" using the Egyptian method is \n " + result +
" remainder (" + dividend + " - " + accumulator +
") or " + reminder);
Console.WriteLine();
}
else
{
reminder = 0;

Console.WriteLine(" So " + dividend +
" divided by " + divisor +
" using the Egyptian method is \n " + result +
" remainder " + reminder);
Console.WriteLine();
}
}
}
}
```
Program Input and Output
Instead of bold and strikeout text format, numbers are represented in different color:
```
Egyptian division

Enter value of dividend : 580
Enter value of divisor  : 34

powers_of_2     doublings

1              34
2              68
4             136
8             272
16             544

1              34        17         578
2              68        16         544
4             136        16         544
8             272        16         544
16             544        16         544

So 580 divided by 34 using the Egyptian method is
17 remainder (580 - 578) or 2

Press any key to continue . . .

```

## C++

Translation of: C
```#include <cassert>
#include <iostream>

typedef unsigned long ulong;

/*
* Remainder is an out paramerter. Use nullptr if the remainder is not needed.
*/
ulong egyptian_division(ulong dividend, ulong divisor, ulong* remainder) {
constexpr int SIZE = 64;
ulong powers[SIZE];
ulong doublings[SIZE];
int i = 0;

for (; i < SIZE; ++i) {
powers[i] = 1 << i;
doublings[i] = divisor << i;
if (doublings[i] > dividend) {
break;
}
}

ulong accumulator = 0;

for (i = i - 1; i >= 0; --i) {
/*
* If the current value of the accumulator added to the
* doublings cell would be less than or equal to the
* dividend then add it to the accumulator
*/
if (accumulator + doublings[i] <= dividend) {
accumulator += doublings[i];
}
}

if (remainder) {
*remainder = dividend - accumulator;
}
}

void print(ulong a, ulong b) {
using namespace std;

ulong x, y;
x = egyptian_division(a, b, &y);

cout << a << " / " << b << " = " << x << " remainder " << y << endl;
assert(a == b * x + y);
}

int main() {
print(580, 34);

return 0;
}
```
Output:
`580 / 34 = 17 remainder 2`

## Common Lisp

```(defun egyptian-division (dividend divisor)
(let* ((doublings (reverse (loop for n = divisor then (* 2 n)
until (> n dividend)
collect n)))
(powers-of-two (reverse (loop for n = 1 then (* 2 n)
repeat (length doublings)
collect n))))
(loop
for d in doublings
for p in powers-of-two
with accumulator = 0
when (<= (+ accumulator d) dividend)
(incf accumulator d))))
```
Output:
```CL-USER> (format t "~A/~A = ~{~A~^ remainder ~}~%" 580 34 (multiple-value-list (egyptian-division 580 34)))
580/34 = 17 remainder 2
```

## D

```import std.stdio;

version(unittest) {
// empty
} else {
int main(string[] args) {
import std.conv;

if (args.length < 3) {
stderr.writeln("Usage: ", args[0], " dividend divisor");
return 1;
}

ulong dividend = to!ulong(args[1]);
ulong divisor = to!ulong(args[2]);
ulong remainder;

auto ans = egyptian_division(dividend, divisor, remainder);
writeln(dividend, " / ", divisor, " = ", ans, " rem ", remainder);

return 0;
}
}

ulong egyptian_division(ulong dividend, ulong divisor, out ulong remainder) {
enum SIZE = 64;
ulong[SIZE] powers;
ulong[SIZE] doublings;
int i;

for (; i<SIZE; ++i) {
powers[i] = 1 << i;
doublings[i] = divisor << i;
if (doublings[i] > dividend) {
break;
}
}

ulong accumulator;

for (i=i-1; i>=0; --i) {
if (accumulator + doublings[i] <= dividend) {
accumulator += doublings[i];
}
}

remainder = dividend - accumulator;
}

unittest {
ulong remainder;

assert(egyptian_division(580UL, 34UL, remainder) == 17UL);
assert(remainder == 2);
}
```

## Delphi

Library: System.Math

Thanks for JensBorrisholt [1].

Translation of: C#
```program Egyptian_division;

{\$APPTYPE CONSOLE}

uses
System.SysUtils,
System.Math,
System.Console; //https://github.com/JensBorrisholt/DelphiConsole

type
TIntegerDynArray = TArray<Integer>;

TIntegerDynArrayHelper = record helper for TIntegerDynArray
public
end;

procedure Divide(dividend, divisor: Integer);
var
result, reminder, powers_of_two, doublings, answer, accumulator, two, pow, row: Integer;
table_powers_of_two, table_doublings: TIntegerDynArray;
begin
result := 0;
reminder := 0;
powers_of_two := 0;
doublings := 0;
accumulator := 0;
two := 2;
pow := 0;
row := 0;

writeln('                           ');
writeln(' powers_of_2     doublings ');
writeln('                           ');

powers_of_two := 1;
doublings := divisor;
while doublings <= dividend do
begin

Writeln(Format('%8d %16d', [powers_of_two, doublings]));
Inc(pow);
powers_of_two := Trunc(IntPower(two, pow));
doublings := powers_of_two * divisor;
end;
writeln('                           ');

row := pow - 1;
writeln('                                                 ');
writeln('                                                 ');
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop + row);
Dec(pow);
while (pow >= 0) and (accumulator < dividend) do
begin

doublings := Trunc(table_doublings[pow]);
powers_of_two := Trunc(table_powers_of_two[pow]);
if (accumulator + Trunc(table_doublings[pow])) <= dividend then
begin

accumulator := accumulator + doublings;

Console.ForegroundColor := TConsoleColor.Green;
Write(Format('%8d %16d', [powers_of_two, doublings]));
Console.ForegroundColor := TConsoleColor.Green;
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop - 2);
end
else
begin

Console.ForegroundColor := TConsoleColor.DarkGray;
Write(Format('%8d %16d', [powers_of_two, doublings]));
Console.ForegroundColor := TConsoleColor.Gray;
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop - 2);
end;
Dec(pow);
end;
writeln;
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop + row + 2);
Console.ResetColor();

if accumulator < dividend then
begin
reminder := dividend - accumulator;
Console.WriteLine(' So ' + dividend.ToString + ' divided by ' + divisor.ToString
+ ' using the Egyptian method is '#10' ' + result.ToString +
' remainder (' + dividend.ToString + ' - ' + accumulator.ToString +
') or ' + reminder.ToString);
writeln;
end
else
begin
reminder := 0;
Console.WriteLine(' So ' + dividend.ToString + ' divided by ' + divisor.ToString
+ ' using the Egyptian method is '#10' ' + result.ToString + ' remainder '
+ reminder.ToString);
writeln;
end;
end;

{ TIntegerDynArrayHelper }

begin
SetLength(self, length(self) + 1);
Self[high(self)] := value;
end;

function parseInt(s: string): Integer;
var
c: Char;
s2: string;
begin
s2 := '';
for c in s do
begin
if c in ['0'..'9'] then
s2 := s2 + c;

end;
result := s2.ToInteger();
end;

var
dividend, divisor: Integer;

begin
Console.Clear();
writeln;
writeln(' Egyptian division ');
writeln;
Console.Write(' Enter value of dividend : ');
Console.Write(' Enter value of divisor : ');
Divide(dividend, divisor);
writeln;
Console.Write('Press any key to continue . . . ');
end.
```
Output:
```
Egyptian division

Enter value of dividend : 580
Enter value of divisor : 34

powers_of_2     doublings

1               34
2               68
4              136
8              272
16              544

1               34        17          578
2               68        16          544
4              136        16          544
8              272        16          544
16              544        16          544

So 580 divided by 34 using the Egyptian method is
17 remainder (580 - 578) or 2

Press any key to continue . . .```

## EasyLang

Translation of: Phix
```proc egyptdiv a b . .
p2 = 1
dbl = b
while dbl <= a
p2s[] &= p2
dbls[] &= dbl
dbl *= 2
p2 *= 2
.
for i = len p2s[] downto 1
if acc + dbls[i] <= a
acc += dbls[i]
ans += p2s[i]
.
.
print a & " / " & b & " = " & ans & " R " & abs (acc - a)
.
egyptdiv 580 34```

## Erlang

```-module(egypt).

-export([ediv/2]).

ediv(A, B) ->
{Twos, Ds} = genpowers(A, [1], [B]),
{Quot, C} = accumulate(A, Twos, Ds),
{Quot, abs(C - A)}.

genpowers(A, [_|Ts], [D|Ds]) when D > A -> {Ts, Ds};
genpowers(A, [T|_] = Twos, [D|_] = Ds) -> genpowers(A, [2*T|Twos], [D*2|Ds]).

accumulate(N, Twos, Ds) -> accumulate(N, Twos, Ds, 0, 0).
accumulate(_, [], [], Q, C) -> {Q, C};
accumulate(N, [T|Ts], [D|Ds], Q, C) when (C + D) =< N -> accumulate(N, Ts, Ds, Q+T, C+D);
accumulate(N, [_|Ts], [_|Ds], Q, C) -> accumulate(N, Ts, Ds, Q, C).
```
Output:
```1> egypt:ediv(580,34).
{17,2}
```

## F#

```// A function to perform Egyptian Division: Nigel Galloway August 11th., 2017
let egyptianDivision N G =
let rec fn n g = seq{yield (n,g); yield! fn (n+n) (g+g)}
Seq.foldBack (fun (n,i) (g,e)->if (i<=g) then ((g-i),(e+n)) else (g,e)) (fn 1 G |> Seq.takeWhile(fun (_,g)->g<=N)) (N,0)
```

Which may be used:

```let (n,g) = egyptianDivision 580 34
printfn "580 divided by 34 is %d remainder %d" g n
```
Output:
```580 divided by 34 is 17 remainder 2
```

## Factor

Works with: Factor version 0.98
```USING: assocs combinators formatting kernel make math sequences ;
IN: rosetta-code.egyptian-division

: table ( dividend divisor -- table )
[ [ 2dup >= ] [ dup , 2 * ] while ] { } make 2nip
dup length <iota> [ 2^ ] map zip <reversed> ;

: accum ( a b dividend -- c )
[ 2dup [ first ] bi@ + ] dip < [ [ + ] 2map ] [ drop ] if ;

: ediv ( dividend divisor -- quotient remainder )
{
[ table ]
[ 2drop { 0 0 } ]
[ drop [ accum ] curry reduce first2 swap ]
[ drop - abs ]
} 2cleave ;

580 34 ediv "580 divided by 34 is %d remainder %d\n" printf
```
Output:
```580 divided by 34 is 17 remainder 2
```

## Forth

```variable tab-end

: build ( m n -- )
swap >r  1 swap  \ dividend on ret stack
begin dup r@ <= while
2dup tab-end @ 2!
[ 2 cells ] literal tab-end +!
swap dup +
swap dup +
repeat 2drop rdrop ;

: e/mod ( m n -- q r )
over >r build
0 r>  \ initial quotient = 0, remainder = dividend
pad tab-end @ [ 2 cells ] literal - do
dup i @ >= if
i @ -  swap i cell+ @ +  swap
then
[ -2 cells ] literal +loop ;

: .egypt ( m n -- )
cr 2dup swap . ." divided by " . ." is " e/mod swap . ." remainder " . ;
```
Output:
```580 34 .egypt
580 divided by 34 is 17 remainder 2  ok
```

## Go

Translation of: Kotlin
```package main

import "fmt"

func egyptianDivide(dividend, divisor int) (quotient, remainder int) {
if dividend < 0 || divisor <= 0 {
panic("Invalid argument(s)")
}
if dividend < divisor {
return 0, dividend
}
powersOfTwo := []int{1}
doublings := []int{divisor}
doubling := divisor
for {
doubling *= 2
if doubling > dividend {
break
}
l := len(powersOfTwo)
powersOfTwo = append(powersOfTwo, powersOfTwo[l-1]*2)
doublings = append(doublings, doubling)
}
accumulator := 0
for i := len(doublings) - 1; i >= 0; i-- {
if accumulator+doublings[i] <= dividend {
accumulator += doublings[i]
if accumulator == dividend {
break
}
}
}
}

func main() {
dividend := 580
divisor := 34
quotient, remainder := egyptianDivide(dividend, divisor)
fmt.Println(dividend, "divided by", divisor, "is", quotient, "with remainder", remainder)
}
```
Output:
```580 divided by 34 is 17 with remainder 2
```

## Groovy

Translation of: Java
```class EgyptianDivision {
/**
* Runs the method and divides 580 by 34
*
* @param args not used
*/
static void main(String[] args) {
divide(580, 34)
}

/**
* Divides <code>dividend</code> by <code>divisor</code> using the Egyptian Division-Algorithm and prints the
* result to the console
*
* @param dividend
* @param divisor
*/
static void divide(int dividend, int divisor) {
List<Integer> powersOf2 = new ArrayList<>()
List<Integer> doublings = new ArrayList<>()

//populate the powersof2- and doublings-columns
int line = 0
while ((Math.pow(2, line) * divisor) <= dividend) { //<- could also be done with a for-loop
int powerOf2 = (int) Math.pow(2, line)
line++
}

int accumulator = 0

//Consider the rows in reverse order of their construction (from back to front of the List<>s)
for (int i = powersOf2.size() - 1; i >= 0; i--) {
if (accumulator + doublings.get(i) <= dividend) {
accumulator += doublings.get(i)
}
}

println(String.format("%d, remainder %d", answer, dividend - accumulator))
}
}
```
Output:
`17, remainder 2`

Deriving division from (+) and (-) by unfolding from a seed pair (1, divisor) up to a series of successively doubling pairs, and then refolding that series of 'two column rows' back down to a (quotient, remainder) pair, using (0, dividend) as the initial accumulator value. In other words, taking the divisor as a unit, and deriving the binary composition of the dividend in terms of that unit.

```import Data.List (unfoldr)

egyptianQuotRem :: Integer -> Integer -> (Integer, Integer)
egyptianQuotRem m n =
let expansion (i, x)
| x > m = Nothing
| otherwise = Just ((i, x), (i + i, x + x))
collapse (i, x) (q, r)
| x < r = (q + i, r - x)
| otherwise = (q, r)
in foldr collapse (0, m) \$ unfoldr expansion (1, n)

main :: IO ()
main = print \$ egyptianQuotRem 580 34
```
Output:
`(17,2)`

We can make the process of calculation more visible by adding a trace layer:

```import Data.List (unfoldr)
import Debug.Trace (trace)

egyptianQuotRem :: Int -> Int -> (Int, Int)
egyptianQuotRem m n =
let rows =
unfoldr
(\(i, x) ->
if x > m
then Nothing
else Just ((i, x), (i + i, x + x)))
(1, n)
in trace
(unlines
[ "Number pair unfolded to series of doubling rows:"
, show rows
, "\nRows refolded down to (quot, rem):"
, show (0, m)
])
foldr
(\(i, x) (q, r) ->
if x < r
then trace
(concat
["(+", show i, ", -", show x, ") -> rem ", show (r - x)])
(q + i, r - x)
else (q, r))
(0, m)
rows

main :: IO ()
main = print \$ egyptianQuotRem 580 34
```
Output:
```Number pair unfolded to series of doubling rows:
[(1,34),(2,68),(4,136),(8,272),(16,544)]

Rows refolded down to (quot, rem):
(0,580)

(+16, -544) -> rem 36
(+1, -34) -> rem 2
(17,2)```

Another approach, using lazy lists and foldr:

```doublings = iterate ((+) >>= id)

powers = doublings 1

k n (u, v) (ans, acc)
| v + ans <= n = (v + ans, u + acc)
| otherwise = (ans, acc)

egy n = snd . foldr (k n) (0, 0) . zip powers . takeWhile (<= n) . doublings

main :: IO ()
main = print \$ egy 580 34
```
Output:
`17`

## J

Implementation:

```doublings=:_1 }. (+:@]^:(> {:)^:a: (,~ 1:))
ansacc=: 1 }. (] + [ * {.@[ >: {:@:+)/@([,.doublings)
egydiv=: (0,[)+1 _1*ansacc
```

```   580 doublings 34
1  34
2  68
4 136
8 272
16 544
580 ansacc 34
17 578
580 egydiv 34
17 2
```

Notes: pre When building the doublings table, we don't actually know we've exceeded our numerator until we are done. This would result in an excess row, so we have to explicitly not include that excess row in our `doublings` result.

Our "fold" is actually not directly on the result of doublings - for our fold, we add another column where every value is the numerator. This conveniently makes it available for comparison at every stage of the fold and seems a more concise approach than creating a closure. (We do not include this extra value in our `ansacc` result, of course.)

## Java

```import java.util.ArrayList;
import java.util.List;

public class EgyptianDivision {

/**
* Runs the method and divides 580 by 34
*
* @param args not used
*/
public static void main(String[] args) {

divide(580, 34);

}

/**
* Divides <code>dividend</code> by <code>divisor</code> using the Egyptian Division-Algorithm and prints the
* result to the console
*
* @param dividend
* @param divisor
*/
public static void divide(int dividend, int divisor) {

List<Integer> powersOf2 = new ArrayList<>();
List<Integer> doublings = new ArrayList<>();

//populate the powersof2- and doublings-columns
int line = 0;
while ((Math.pow(2, line) * divisor) <= dividend) { //<- could also be done with a for-loop
int powerOf2 = (int) Math.pow(2, line);
line++;
}

int accumulator = 0;

//Consider the rows in reverse order of their construction (from back to front of the List<>s)
for (int i = powersOf2.size() - 1; i >= 0; i--) {
if (accumulator + doublings.get(i) <= dividend) {
accumulator += doublings.get(i);
}
}

System.out.println(String.format("%d, remainder %d", answer, dividend - accumulator));
}
}
```
Output:
`17, remainder 2`

## JavaScript

### ES6

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

// EGYPTIAN DIVISION --------------------------------

// eqyptianQuotRem :: Int -> Int -> (Int, Int)
const eqyptianQuotRem = (m, n) => {
const expansion = ([i, x]) =>
x > m ? (
Nothing()
) : Just([
[i, x],
[i + i, x + x]
]);
const collapse = ([i, x], [q, r]) =>
x < r ? (
[q + i, r - x]
) : [q, r];
return foldr(
collapse,
[0, m],
unfoldr(expansion, [1, n])
);
};

// TEST ---------------------------------------------

// main :: IO ()
const main = () =>
showLog(
eqyptianQuotRem(580, 34)
);
// -> [17, 2]

// GENERIC FUNCTIONS --------------------------------

// Just :: a -> Maybe a
const Just = x => ({
type: 'Maybe',
Nothing: false,
Just: x
});

// Nothing :: Maybe a
const Nothing = () => ({
type: 'Maybe',
Nothing: true,
});

// flip :: (a -> b -> c) -> b -> a -> c
const flip = f =>
1 < f.length ? (
(a, b) => f(b, a)
) : (x => y => f(y)(x));

// foldr :: (a -> b -> b) -> b -> [a] -> b
const foldr = (f, a, xs) => xs.reduceRight(flip(f), a);

// unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
const unfoldr = (f, v) => {
let
xr = [v, v],
xs = [];
while (true) {
const mb = f(xr[1]);
if (mb.Nothing) {
return xs
} else {
xr = mb.Just;
xs.push(xr[0])
}
}
};

// showLog :: a -> IO ()
const showLog = (...args) =>
console.log(
args
.map(JSON.stringify)
.join(' -> ')
);

// MAIN ---
return main();
})();
```
Output:
`[17,2]`

## jq

Works with: jq

Also works with gojq, the Go implementation of jq, and with fq.

```def egyptianDivide(\$dividend; \$divisor):
if (\$dividend < 0 or \$divisor <= 0) then "egyptianDivide: invalid argument(s)" | error
elif (\$dividend < \$divisor) then [0, \$dividend]
else
{ powersOfTwo: [1],
doublings: [\$divisor],
doubling: (2 * \$divisor)
}
| until(.doubling > \$dividend;
.powersOfTwo += [.powersOfTwo[-1]*2]
| .doublings += [.doubling]
| .doubling *= 2 )
| .accumulator = 0
| .i = (.doublings|length)-1
| until( .i < 0 or .accumulator == \$dividend;
if (.accumulator + .doublings[.i] <= \$dividend)
then .accumulator += .doublings[.i]
else .
end
| .i += -1)
end;

egyptianDivide(\$dividend; \$divisor)
| "\(\$dividend) ÷ \(\$divisor) = \(.[0]) with remainder \(.[1]).";

Output:
```580 ÷ 34 = 17 with remainder 2.
```

## Julia

Works with: Julia version 0.6
```function egyptian_divrem(dividend, divisor)
function row(powers_of2, doublings)
if dividend > doublings
row(2powers_of2, 2doublings)
if accumulator + doublings ≤ dividend
accumulator += doublings
end
end
end
row(1, divisor)
end

egyptian_divrem(580, 34)
```
Output:
`(17, 2)`

## Kotlin

```// version 1.1.4

data class DivMod(val quotient: Int, val remainder: Int)

fun egyptianDivide(dividend: Int, divisor: Int): DivMod {
require (dividend >= 0 && divisor > 0)
if (dividend < divisor) return DivMod(0, dividend)
val powersOfTwo = mutableListOf(1)
val doublings = mutableListOf(divisor)
var doubling = divisor
while (true) {
doubling *= 2
if (doubling > dividend) break
}
var accumulator = 0
for (i in doublings.size - 1 downTo 0) {
if (accumulator + doublings[i] <= dividend) {
accumulator += doublings[i]
if (accumulator == dividend) break
}
}
}

fun main(args: Array<String>) {
val dividend = 580
val divisor = 34
val (quotient, remainder) = egyptianDivide(dividend, divisor)
println("\$dividend divided by \$divisor is \$quotient with remainder \$remainder")
}
```
Output:
```580 divided by 34 is 17 with remainder 2
```

## Lambdatalk

```{def doublings
{def doublings.loop
{lambda {:a :c}
{if {> {A.get 1 {A.last :c}} :a}
then {A.sublast! :c}
else {doublings.loop
:a
{A.addlast! {A.new {* 2 {A.get 0 {A.last :c}}}
{* 2 {A.get 1 {A.last :c}}}} :c}} }}}
{lambda {:a :b}
{doublings.loop :a {A.new {A.new 1 :b}}} }}
-> doublings

divide
-> {def divide
{def divide.loop
{lambda {:a :b :table :last :i}
{if {< {+ :last {A.get 1 {A.get :i :table}}} :a}
then {A.new {+ {* {A.get 0 {A.last :table}} 1} 1}
{- :a {+ :last {A.get 1 {A.get :i :table}}}}}
else {divide.loop :a :b :table :last {- :i 1} }}}}
{lambda {:a :b}
{let { {:a :a} {:b :b}
{:table {doublings :a :b}}
} {divide.loop :a :b :table
{A.get 1 {A.last :table}}
{- {A.length :table} 1} }}}}

{divide 580 34}
-> [17,2]       // 580 = 17*34+2
{divide 100 3}
-> [33,1]       // 100 = 3*33+1
{divide 7 2}
-> [3,1]        //   7 = 2*3+1
```

## Lua

Translation of: Python
```function egyptian_divmod(dividend,divisor)
local pwrs, dbls = {1}, {divisor}
while dbls[#dbls] <= dividend do
table.insert(pwrs, pwrs[#pwrs] * 2)
table.insert(dbls, pwrs[#pwrs] * divisor)
end
local ans, accum = 0, 0

for i=#pwrs-1,1,-1 do
if accum + dbls[i] <= dividend then
accum = accum + dbls[i]
ans = ans + pwrs[i]
end
end

return ans, math.abs(accum - dividend)
end

local i, j = 580, 34
local d, m = egyptian_divmod(i, j)
print(i.." divided by "..j.." using the Egyptian method is "..d.." remainder "..m)
```
Output:
`580 divided by 34 using the Egyptian method is 17 remainder 2`

## Mathematica/Wolfram Language

```ClearAll[EgyptianDivide]
EgyptianDivide[dividend_, divisor_] := Module[{table, i, answer, accumulator},
table = {{1, divisor}};
i = 1;
While[Last[Last[table]] < dividend,
AppendTo[table, 2^i {1, divisor}];
i++
];
table //= Most;
accumulator = 0;
Do[
If[accumulator + t[[2]] <= dividend,
accumulator += t[[2]];
]
,
{t, Reverse@table}
];
]
EgyptianDivide[580, 34]
```
Output:
`{17, 2}`

## Modula-2

```MODULE EgyptianDivision;
FROM FormatString IMPORT FormatString;

PROCEDURE EgyptianDivision(dividend,divisor : LONGCARD; VAR remainder : LONGCARD) : LONGCARD;
CONST
SZ = 64;
VAR
powers,doublings : ARRAY[0..SZ] OF LONGCARD;
i : INTEGER;
BEGIN
FOR i:=0 TO SZ-1 DO
powers[i] := 1 SHL i;
doublings[i] := divisor SHL i;
IF doublings[i] > dividend THEN
BREAK
END
END;

accumulator := 0;
FOR i:=i-1 TO 0 BY -1 DO
IF accumulator + doublings[i] <= dividend THEN
accumulator := accumulator + doublings[i];
END
END;

remainder := dividend - accumulator;
END EgyptianDivision;

VAR
buf : ARRAY[0..63] OF CHAR;
div,rem : LONGCARD;
BEGIN
div := EgyptianDivision(580, 34, rem);
FormatString("580 divided by 34 is %l remainder %l\n", buf, div, rem);
WriteString(buf);

END EgyptianDivision.
```

## Nim

```import strformat

func egyptianDivision(dividend, divisor: int): tuple[quotient, remainder: int] =
if dividend < 0 or divisor <= 0:
raise newException(IOError, "Invalid argument(s)")
if dividend < divisor:
return (0, dividend)

var powersOfTwo: array[sizeof(int) * 8, int]
var doublings: array[sizeof(int) * 8, int]

for i, _ in powersOfTwo:
powersOfTwo[i] = 1 shl i
doublings[i] = divisor shl i
if doublings[i] > dividend:
break

var accumulator = 0
for i in countdown(len(doublings) - 1, 0):
if accumulator + doublings[i] <= dividend:
inc accumulator, doublings[i]
if accumulator == dividend:
break

let dividend = 580
let divisor = 34
var (quotient, remainder) = egyptianDivision(dividend, divisor)
echo fmt"{dividend} divided by {divisor} is {quotient} with remainder {remainder}"
```
Output:
```580 divided by 34 is 17 with remainder 2
```

## OCaml

```let egypt_div x y =
let rec table p d lst =
if d > x
then lst
else table (p + p) (d + d) ((p, d) :: lst)
in
let consider (q, a) (p, d) =
if a + d > x
then q, a
else q + p, a + d
in
List.fold_left consider (0, 0) (table 1 y [])
```
Output:
```# egypt_div 580 34 ;;
- : int * int = (17, 578)
```

## PARI/GP

Translation of: Julia
```myrow(powers_of2, doublings) =
{
if (dividend > doublings,
myrow(2 * powers_of2, 2 * doublings);
if (accumulator + doublings <= dividend,
accumulator += doublings;
);
);
};

egyptian_divrem(dividend, divisor) =
{
accumulator = 0;
myrow(1, divisor);
}

divisor=34;
dividend=580;
print1(egyptian_divrem(dividend, divisor));```
Output:
```[17, 2]
```

## Perl

Translation of: Raku
```sub egyptian_divmod {
my(\$dividend, \$divisor) = @_;
die "Invalid divisor" if \$divisor <= 0;

my @table = (\$divisor);
push @table, 2*\$table[-1] while \$table[-1] <= \$dividend;

my \$accumulator = 0;
for my \$k (reverse 0 .. \$#table) {
next unless \$dividend >= \$table[\$k];
\$accumulator += 1 << \$k;
\$dividend    -= \$table[\$k];
}
\$accumulator, \$dividend;
}

for ([580,34], [578,34], [7532795332300578,235117]) {
my(\$n,\$d) = @\$_;
printf "Egyption divmod %s %% %s = %s remainder %s\n", \$n, \$d, egyptian_divmod( \$n, \$d )
}
```
Output:
```Egyption divmod 580 % 34 = 17 remainder 2
Egyption divmod 578 % 34 = 17 remainder 0
Egyption divmod 7532795332300578 % 235117 = 32038497141 remainder 81```

## Phix

```with javascript_semantics
procedure egyptian_division(integer dividend, divisor)
integer p2 = 1, dbl = divisor, ans = 0, accum = 0
sequence p2s = {}, dbls = {}, args
while dbl<=dividend do
p2s = append(p2s,p2)
dbls = append(dbls,dbl)
dbl += dbl
p2 += p2
end while
for i=length(p2s) to 1 by -1 do
if accum+dbls[i]<=dividend then
accum += dbls[i]
ans += p2s[i]
end if
end for
args = {dividend,divisor,ans,abs(accum-dividend)}
printf(1,"%d divided by %d is: %d remainder %d\n",args)
end procedure

egyptian_division(580,34)
```
Output:
```580 divided by 34 is: 17 remainder 2
```

## PicoLisp

```(seed (in "/dev/urandom" (rd 8)))

(de divmod (Dend Disor)
(cons (/ Dend Disor) (% Dend Disor)) )
(de egyptian (Dend Disor)
(let
(P 0
D Disor
S
(make
(while (>= Dend (setq @@ (+ D D)))
(yoke
(cons
(** 2 (swap 'P (inc P)))
(swap 'D @@) ) ) ) )
P (** 2 P) )
(mapc
'((L)
(and
(>= Dend (+ D (cdr L)))
(inc 'P (car L))
(inc 'D (cdr L)) ) )
S )
(cons P (abs (- Dend D))) ) )
(for N 1000
(let (A (rand 1 1000)  B (rand 1 A))
(test (divmod A B) (egyptian A B)) ) )
(println (egyptian 580 34))```
Output:
`(17 . 2)`

## Prolog

Works with: SWI Prolog
```egyptian_divide(Dividend, Divisor, Quotient, Remainder):-
powers2_multiples(Dividend, [1], Powers, [Divisor], Multiples),
accumulate(Dividend, Powers, Multiples, 0, Quotient, 0, Acc),
Remainder is Dividend - Acc.

powers2_multiples(Dividend, Powers, Powers, Multiples, Multiples):-
Multiples = [M|_],
2 * M > Dividend,
!.
powers2_multiples(Dividend, [Power|P], Powers, [Multiple|M], Multiples):-
Power2 is 2 * Power,
Multiple2 is 2 * Multiple,
powers2_multiples(Dividend, [Power2,Power|P], Powers,
[Multiple2, Multiple|M], Multiples).

accumulate(_, [], [], Ans, Ans, Acc, Acc):-!.
accumulate(Dividend, [P|Powers], [M|Multiples], Ans1, Answer, Acc1, Acc):-
Acc1 + M =< Dividend,
!,
Acc2 is Acc1 + M,
Ans2 is Ans1 + P,
accumulate(Dividend, Powers, Multiples, Ans2, Answer, Acc2, Acc).
accumulate(Dividend, [_|Powers], [_|Multiples], Ans1, Answer, Acc1, Acc):-
accumulate(Dividend, Powers, Multiples, Ans1, Answer, Acc1, Acc).

test_egyptian_divide(Dividend, Divisor):-
egyptian_divide(Dividend, Divisor, Quotient, Remainder),
writef('%w / %w = %w, remainder = %w\n', [Dividend, Divisor,
Quotient, Remainder]).

main:-
test_egyptian_divide(580, 34).
```
Output:
```580 / 34 = 17, remainder = 2
```

## Python

### Idiomatic

```from itertools import product

def egyptian_divmod(dividend, divisor):
assert divisor != 0
pwrs, dbls = [1], [divisor]
while dbls[-1] <= dividend:
pwrs.append(pwrs[-1] * 2)
dbls.append(pwrs[-1] * divisor)
ans, accum = 0, 0
for pwr, dbl in zip(pwrs[-2::-1], dbls[-2::-1]):
if accum + dbl <= dividend:
accum += dbl
ans += pwr
return ans, abs(accum - dividend)

if __name__ == "__main__":
# Test it gives the same results as the divmod built-in
for i, j in product(range(13), range(1, 13)):
assert egyptian_divmod(i, j) == divmod(i, j)
# Mandated result
i, j = 580, 34
print(f'{i} divided by {j} using the Egyption method is %i remainder %i'
% egyptian_divmod(i, j))
```

Sample output

```580 divided by 34 using the Egyption method is 17 remainder 2
```

### Functional

Expressing the summing catamorphism in terms of functools.reduce, and the preliminary expansion (by repeated addition to self) in terms of an unfoldl function, which is dual to reduce, and constructs a list from a seed value.

Multiplication and division operators are both avoided, in the spirit of the Rhind Papyrus derivations of both (*) and (/) from plain addition and subtraction.

Also in deference to the character of the Rhind methods, the (unfoldl) unfolding of the seed values to a list of progressively doubling rows is recursively defined, and mutation operations are avoided. The efficiency of the Egyptian method's exponential expansion means that there is no need here, even with larger numbers, to compress space by using an imperative translation of the higher-order unfold function.

```'''Quotient and remainder of division by the Rhind papyrus method.'''

from functools import reduce

# eqyptianQuotRem :: Int -> Int -> (Int, Int)
def eqyptianQuotRem(m):
'''Quotient and remainder derived by the Eqyptian method.'''

def expansion(xi):
'''Doubled value, and next power of two - both by self addition.'''
x, i = xi
return Nothing() if x > m else Just(
((x + x, i + i), xi)
)

def collapse(qr, ix):
'''Addition of a power of two to the quotient,
and subtraction of a paired value from the remainder.'''
i, x = ix
q, r = qr
return (q + i, r - x) if x < r else qr

return lambda n: reduce(
collapse,
unfoldl(expansion)(
(1, n)
),
(0, m)
)

# ------------------------- TEST --------------------------
# main :: IO ()
def main():
'''Test'''
print(
eqyptianQuotRem(580)(34)
)

# ------------------- GENERIC FUNCTIONS -------------------

# Just :: a -> Maybe a
def Just(x):
'''Constructor for an inhabited Maybe (option type) value.'''
return {'type': 'Maybe', 'Nothing': False, 'Just': x}

# Nothing :: Maybe a
def Nothing():
'''Constructor for an empty Maybe (option type) value.'''
return {'type': 'Maybe', 'Nothing': True}

# unfoldl(lambda x: Just(((x - 1), x)) if 0 != x else Nothing())(10)
# -> [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
# unfoldl :: (b -> Maybe (b, a)) -> b -> [a]
def unfoldl(f):
'''Dual to reduce or foldl.
Where these reduce a list to a summary value, unfoldl
builds a list from a seed value.
Where f returns Just(a, b), a is appended to the list,
and the residual b is used as the argument for the next
application of f.
When f returns Nothing, the completed list is returned.
'''
def go(v):
x, r = v, v
xs = []
while True:
mb = f(x)
if mb.get('Nothing'):
return xs
else:
x, r = mb.get('Just')
xs.insert(0, r)
return xs
return go

# MAIN ----------------------------------------------------
if __name__ == '__main__':
main()
```
Output:
`(17, 2)`

## Quackery

```  [ dup 0 = if
[ \$ "Cannot divide by zero."
fail ]
[] unrot
[ 2dup < not while
rot over swap join
unrot dup + again ]
drop swap
dup size
[] 1 rot times
[ tuck swap join
swap dup + ]
drop
temp put
0 swap
witheach
[ over +
rot 2dup > iff
[ nip swap
0
temp take
i^ poke
temp put ]
else
[ swap rot drop ] ]
- 0 temp take
witheach +
swap ]                         is egyptian ( n n --> n n )

[ over echo
say " divided by "
dup echo
say " is "
egyptian
swap echo
say " remainder "
echo
say "." ]                      is task     ( n n -->     )

Output:
`580 divided by 34 is 17 remainder 2.`

## R

```Egyptian_division <- function(num, den){
pow2 = 0
row = 1

Table = data.frame(powers_of_2 = 2^pow2,
doubling = den)

while(Table\$doubling[nrow(Table)] < num){
row = row + 1
pow2 = pow2 + 1

Table[row, 1] <- 2^pow2
Table[row, 2] <- 2^pow2 * den
}

Table <- Table[-nrow(Table),]
#print(Table) to see the table

accumulator <- 0

for (i in nrow(Table):1) {
if (accumulator + Table\$doubling[i] <= num) {
accumulator <- accumulator + Table\$doubling[i]
}
}

remainder = abs(accumulator - num)

}

Egyptian_division(580, 34)
Egyptian_division(300, 2)
```
Output:
```Answer is 17, remainder 2
```

## Racket

```#lang racket

(define (quotient/remainder-egyptian dividend divisor (trace? #f))
(define table
(for*/list ((power_of_2 (sequence-map (curry expt 2) (in-naturals)))
(doubling (in-value (* divisor power_of_2)))
#:break (> doubling dividend))
(list power_of_2 doubling)))

(when trace?
(displayln "Table\npow_2\tdoubling")
(for ((row table)) (printf "~a\t~a~%" (first row) (second row))))

((row (reverse table))
(acc′ (in-value (+ accumulator (second row)))))
(when trace? (printf "row:~a\tans/acc:~a ~a\t" row answer accumulator))
(cond
[(<= acc′ dividend)
(define ans′ (+ answer (first row)))
(when trace? (printf "~a <= ~a -> ans′/acc′:~a ~a~%" acc′ dividend ans′ acc′))
(values ans′ acc′)]
[else
(when trace? (printf "~a > ~a [----]~%" acc′ dividend))

(module+ test
(require rackunit)
(let-values (([q r] (quotient/remainder-egyptian 580 34)))
(check-equal? q 17)
(check-equal? r 2))

(let-values (([q r] (quotient/remainder-egyptian 192 3)))
(check-equal? q 64)
(check-equal? r 0)))

(module+ main
(quotient/remainder-egyptian 580 34 #t))
```
Output:
```Table
pow_2	doubling
1	34
2	68
4	136
8	272
16	544
row:(16 544)	ans/acc:0 0	544 <= 580 -> ans′/acc′:16 544
row:(8 272)	ans/acc:16 544	816 > 580 [----]
row:(4 136)	ans/acc:16 544	680 > 580 [----]
row:(2 68)	ans/acc:16 544	612 > 580 [----]
row:(1 34)	ans/acc:16 544	578 <= 580 -> ans′/acc′:17 578
17
2```

## Raku

(formerly Perl 6)

Works with: Rakudo version 2017.07

### Normal version

Only works with positive real numbers, not negative or complex.

```sub egyptian-divmod (Real \$dividend is copy where * >= 0, Real \$divisor where * > 0) {
my \$accumulator = 0;
([1, \$divisor], { [.[0] + .[0], .[1] + .[1]] } … ^ *.[1] > \$dividend)
.reverse.map: { \$dividend -= .[1], \$accumulator += .[0] if \$dividend >= .[1] }
\$accumulator, \$dividend;
}

#TESTING
for 580,34, 578,34, 7532795332300578,235117 -> \$n, \$d {
printf "%s divmod %s = %s remainder %s\n",
\$n, \$d, |egyptian-divmod( \$n, \$d )
}
```
Output:
```580 divmod 34 = 17 remainder 2
578 divmod 34 = 17 remainder 0
7532795332300578 divmod 235117 = 32038497141 remainder 81```

### More "Egyptian" version

As a preceding version was determined to be "let's just say ... not Egyptian" we submit an alternate which is hopefully more "Egyptian". Now only handles positive Integers up to 10 million, mostly due to limitations on Egyptian notation for numbers.

Note: if the below is just a mass of "unknown glyph" boxes, try installing Googles free Noto Sans Egyptian Hieroglyphs font.

This is intended to be humorous and should not be regarded as good (or even sane) programming practice. That being said, 𓂽 & 𓂻 really are the ancient Egyptian symbols for addition and subtraction, and the Egyptian number notation is as accurate as possible. Everything else owes more to whimsy than rigor.

```my (\𓄤, \𓄊, \𓎆, \𓄰) = (0, 1, 10, 10e7);
sub infix:<𓂽> { \$^𓃠 + \$^𓃟 }
sub infix:<𓂻> { \$^𓃲 - \$^𓆊 }
sub infix:<𓈝> { \$^𓃕 < \$^𓃢 }
sub 𓁶 (Int \𓆉) {
my \𓁢 = [«'' 𓏺 𓏻 𓏼 𓏽 𓏾 𓏿 𓐀 𓐁 𓐂»], [«'' 𓎆 𓎏 𓎐 𓎑 𓎊 𓎋 𓎌 𓎍 𓎎»],
[«'' 𓍢 𓍣 𓍤 𓍥 𓍦 𓍧 𓍨 𓍩 𓍪»], [«'' 𓆼 𓆽 𓆾 𓆿 𓇀 𓇁 𓇂 𓇃 𓇄»],
[«'' 𓂭 𓂮 𓂯 𓂰 𓂱 𓂲 𓂳 𓂴 𓂵»], ['𓆐' Xx ^𓎆], ['𓁨' Xx ^𓎆];
([~] 𓆉.polymod( 𓎆 xx * ).map( { 𓁢[\$++;\$_] } ).reverse) || '𓄤'
}

sub infix:<𓅓> (Int \$𓂀 is copy where 𓄤 𓂻 𓄊 𓈝 * 𓈝 𓄰, Int \𓌳 where 𓄤 𓈝 * 𓈝 𓄰) {
my \$𓎦 = 𓄤;
([𓄊,𓌳], { [.[𓄤] 𓂽 .[𓄤], .[𓄊] 𓂽 .[𓄊]] } … ^\$𓂀 𓈝 *.[𓄊])
.reverse.map: { \$𓂀 𓂻= .[𓄊], \$𓎦 𓂽= .[𓄤] if .[𓄊] 𓈝 (\$𓂀 𓂽 𓄊) }
\$𓎦, \$𓂀;
}

#TESTING
for 580,34, 578,34, 2300578,23517 -> \𓃾, \𓆙 {
printf "%s divmod %s = %s remainder %s =OR= %s 𓅓 %s = %s remainder %s\n",
𓃾, 𓆙, |(𓃾 𓅓 𓆙), (𓃾, 𓆙, |(𓃾 𓅓 𓆙))».&𓁶;
}
```
Output:
```580 divmod 34 = 17 remainder 2 =OR= 𓍦𓎍 𓅓 𓎐𓏽 = 𓎆𓐀 remainder 𓏻
578 divmod 34 = 17 remainder 0 =OR= 𓍦𓎌𓐁 𓅓 𓎐𓏽 = 𓎆𓐀 remainder 𓄤
2300578 divmod 23517 = 97 remainder 19429 =OR= 𓁨𓁨𓆐𓆐𓆐𓍦𓎌𓐁 𓅓 𓂮𓆾𓍦𓎆𓐀 = 𓎎𓐀 remainder 𓂭𓇄𓍥𓎏𓐂```

## REXX

Only addition and subtraction is used in this version of the Egyptian division method.

```/*REXX program performs division on positive integers using the Egyptian division method*/
numeric digits 1000                              /*support gihugic numbers & be gung-ho.*/
parse arg n d .                                  /*obtain optional arguments from the CL*/
if d=='' | d==","  then do;  n= 580;    d= 34    /*Not specified?  Then use the defaults*/
end
call EgyptDiv n, d                               /*invoke the Egyptian Division function*/
parse var result q r                             /*extract the quotient & the remainder.*/
say n   ' divided by '       d       " is "       q       ' with a remainder of '      r
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
EgyptDiv: procedure;  parse arg num,dem          /*obtain the numerator and denominator.*/
p= 1;                       t= dem     /*initialize the double & power values.*/
do #=1  until t>num      /*construct the power & doubling lists.*/
pow.#= p;     p= p + p   /*build power  entry; bump power value.*/
dbl.#= t;     t= t + t   /*  "  doubling  "  ;   " doubling val.*/
end   /*#*/
acc=0;  ans=0                          /*initialize accumulator & answer to 0 */
do s=#   by -1   for #   /* [↓]  process the table "backwards". */
sum= acc + dbl.s         /*compute the sum (to be used for test)*/
if sum>num  then iterate /*Is sum to big?  Then ignore this step*/
acc= sum                 /*use the "new" sum for the accumulator*/
end   /*s*/
return ans  num-acc                    /*return the answer and the remainder. */
```
output   when using the default inputs:
```580  divided by  34  is  17  with a remainder of  2
```
output   when using the input of:     9876543210111222333444555666777888999   13579
```9876543210111222333444555666777888999  divided by  13579  is  727339510281406755537562093436769  with a remainder of  2748
```

## Ring

```load "stdlib.ring"

table = newlist(32, 2)
dividend = 580
divisor = 34

i = 1
table[i][1] = 1
table[i][2] = divisor

while table[i] [2] < dividend
i = i + 1
table[i][1] = table[i -1] [1] * 2
table[i][2] = table[i -1] [2] * 2
end
i = i - 1
accumulator = table[i][2]

while i > 1
i = i - 1
if table[i][2]+ accumulator <= dividend
accumulator = accumulator + table[i][2]
ok
end

see string(dividend)  + " divided by " + string(divisor) + " using egytian division" + nl
see " returns " + string(answer) + " mod(ulus) " + string(dividend-accumulator)```

Output:

```580 divided by 34 using egytian division
returns 17 mod(ulus) 2
```

## Ruby

```def egyptian_divmod(dividend, divisor)
table = [[1, divisor]]
table << table.last.map{|e| e*2} while table.last.first * 2 <= dividend
table.reverse_each do |pow, double|
if accumulator + double <= dividend
accumulator += double
end
end
end

puts "Quotient = %s Remainder = %s" % egyptian_divmod(580, 34)
```
Output:
```Quotient = 17 Remainder = 2
```

## Rust

```fn egyptian_divide(dividend: u32, divisor: u32) -> (u32, u32) {
let dividend = dividend as u64;
let divisor = divisor as u64;

let pows = (0..32).map(|p| 1 << p);
let doublings = (0..32).map(|p| divisor << p);

.zip(pows)
.rev()
.skip_while(|(i, _)| i > &dividend )
.fold((0, 0), |(answer, sum), (double, power)| {
if sum + double < dividend {
(answer + power, sum + double)
} else {
}
});

(answer as u32, (dividend - sum) as u32)
}

fn main() {
let (div, rem) = egyptian_divide(580, 34);
println!("580 divided by 34 is {} remainder {}", div, rem);
}
```
Output:
`580 divided by 34 is 17 remainder 2`

## Scala

Output:

Best seen running in your browser either by ScalaFiddle (ES aka JavaScript, non JVM) or Scastie (remote JVM).

```object EgyptianDivision extends App {

private def divide(dividend: Int, divisor: Int): Unit = {
val powersOf2, doublings = new collection.mutable.ListBuffer[Integer]

//populate the powersof2- and doublings-columns
var line = 0
while ((math.pow(2, line) * divisor) <= dividend) {
val powerOf2 = math.pow(2, line).toInt
powersOf2 += powerOf2
doublings += (powerOf2 * divisor)
line += 1
}

//Consider the rows in reverse order of their construction (from back to front of the List)
var i = powersOf2.size - 1
for (i <- powersOf2.size - 1 to 0 by -1)
if (accumulator + doublings(i) <= dividend) {
accumulator += doublings(i)
}

}

divide(580, 34)

}
```

## Sidef

Translation of: Ruby
```func egyptian_divmod(dividend, divisor) {
var table = [[1, divisor]]
table << table[-1].map{|e| 2*e } while (2*table[-1][0] <= dividend)
var (answer, accumulator) = (0, 0)
table.reverse.each { |pair|
var (pow, double) = pair...
if (accumulator + double <= dividend) {
accumulator += double
}
}
}

say ("Quotient = %s Remainder = %s" % egyptian_divmod(580, 34))
```
Output:
```Quotient = 17 Remainder = 2
```

## Swift

```extension BinaryInteger {
@inlinable
public func egyptianDivide(by divisor: Self) -> (quo: Self, rem: Self) {
let table =
(0...).lazy
.map({i -> (Self, Self) in
let power = Self(2).power(Self(i))

return (power, power * divisor)
})
.prefix(while: { \$0.1 <= self })
.reversed()

let (answer, acc) = table.reduce((Self(0), Self(0)), {cur, row in
let ((ans, acc), (power, doubling)) = (cur, row)

return acc + doubling <= self ? (ans + power, doubling + acc) : cur
})

}

@inlinable
public func power(_ n: Self) -> Self {
return stride(from: 0, to: n, by: 1).lazy.map({_ in self }).reduce(1, *)
}
}

let dividend = 580
let divisor = 34
let (quo, rem) = dividend.egyptianDivide(by: divisor)

print("\(dividend) divided by \(divisor) = \(quo) rem \(rem)")
```
Output:
`580 divided by 34 = 17 rem 2`

## Tailspin

```templates egyptianDivision
def dividend: \$(1);
def divisor: \$(2);
def table: [ { powerOf2: 1"1", doubling: (\$divisor)"1" } -> \(
when <{doubling: <..\$dividend>}> do
\$ !
{ powerOf2: \$.powerOf2 * 2, doubling: \$.doubling * 2 } -> #
\)];
@: { answer: 0"1", accumulator: 0"1" };
\$table(last..1:-1)... -> #
\$@ !

when <{doubling: <..\$dividend-\$@.accumulator>}> do
end egyptianDivision

[580"1", 34"1"] -> egyptianDivision -> 'Quotient: \$.answer; Remainder: \$: 580"1" - \$.accumulator;' -> !OUT::write```
Output:
`Quotient: 17"1" Remainder: 2"1"`

## VBA

```Option Explicit

Private Type MyTable
powers_of_2 As Long
doublings As Long
End Type

Private Type Assemble
accumulator As Long
End Type

Private Type Division
Quotient As Long
Remainder As Long
End Type

Private Type DivEgyp
Dividend As Long
Divisor As Long
End Type

Private Deg As DivEgyp

Sub Main()
Dim d As Division
Deg.Dividend = 580
Deg.Divisor = 34
d = Divise(CreateTable)
Debug.Print "Quotient = " & d.Quotient & " Remainder = " & d.Remainder
End Sub

Private Function CreateTable() As MyTable()
Dim t() As MyTable, i As Long
Do
i = i + 1
ReDim Preserve t(i)
t(i).powers_of_2 = 2 ^ (i - 1)
t(i).doublings = Deg.Divisor * t(i).powers_of_2
Loop While 2 * t(i).doublings <= Deg.Dividend
CreateTable = t
End Function

Private Function Divise(t() As MyTable) As Division
Dim a As Assemble, i As Long
a.accumulator = 0
For i = UBound(t) To LBound(t) Step -1
If a.accumulator + t(i).doublings <= Deg.Dividend Then
a.accumulator = a.accumulator + t(i).doublings
End If
Next
Divise.Remainder = Deg.Dividend - a.accumulator
End Function```
Output:
`Quotient = 17 Remainder = 2`

## V (Vlang)

Translation of: Go
```fn egyptian_divide(dividend int, divisor int) ?(int, int) {

if dividend < 0 || divisor <= 0 {
panic("Invalid argument(s)")
}
if dividend < divisor {
return 0, dividend
}
mut powers_of_two := [1]
mut doublings := [divisor]
mut doubling := divisor
for {
doubling *= 2
if doubling > dividend {
break
}
l := powers_of_two.len
powers_of_two << powers_of_two[l-1]*2
doublings << doubling
}
mut accumulator := 0
for i := doublings.len - 1; i >= 0; i-- {
if accumulator+doublings[i] <= dividend {
accumulator += doublings[i]
if accumulator == dividend {
break
}
}
}
}

fn main() {
dividend := 580
divisor := 34
quotient, remainder := egyptian_divide(dividend, divisor)?
println("\$dividend divided by \$divisor is \$quotient with remainder \$remainder")
}```
Output:
```580 divided by 34 is 17 with remainder 2
```

## Wren

Translation of: Go
```var egyptianDivide = Fn.new { |dividend, divisor|
if (dividend < 0 || divisor <= 0) Fiber.abort("Invalid argument(s).")
if (dividend < divisor) return [0, dividend]
var powersOfTwo = [1]
var doublings = [divisor]
var doubling = divisor
while (true) {
doubling = 2 * doubling
if (doubling > dividend) break
}
var accumulator = 0
for (i in doublings.count-1..0) {
if (accumulator + doublings[i] <= dividend) {
accumulator = accumulator + doublings[i]
if (accumulator == dividend) break
}
}
}

var dividend = 580
var divisor = 34
var res = egyptianDivide.call(dividend, divisor)
System.print("%(dividend) ÷ %(divisor) = %(res[0]) with remainder %(res[1]).")
```
Output:
```580 ÷ 34 = 17 with remainder 2.
```

## XPL0

Translation of: Wren
```include xpllib; \for Print

int  PowersOfTwo(100), Doublings(100), Doubling, Accumulator, I;
[if Dividend < Divisor then
PowersOfTwo(0):= 1;  Doublings(0):= Divisor;  Doubling:= Divisor;  I:= 1;
loop    [Doubling:= Doubling*2;
if Doubling > Dividend then quit;
PowersOfTwo(I):= PowersOfTwo(I-1)*2;
Doublings(I):= Doubling;
I:= I+1;
];
for I:= I-1 downto 0 do
[if Accumulator + Doublings(I) <= Dividend then
[Accumulator:= Accumulator + Doublings(I);
if Accumulator = Dividend then I:= 0;
];
];
];

int  Dividend, Divisor, Quotient, Remainder;
[Dividend:= 580;  Divisor:= 34;
EgyptianDivide(Dividend, Divisor, @Quotient, @Remainder);
Print("%d / %d = %d with remainder %d.\n", Dividend, Divisor, Quotient, Remainder);
]```
Output:
```580 / 34 = 17 with remainder 2.
```

## Zig

Translation of: C
```const std = @import("std");

pub fn egyptianDivision(dividend: u64, divisor: u64) [2]u64 {
const SIZE = 64;
var powers = [_]u64{0} ** SIZE;
var doublings = [_]u64{0} ** SIZE;

var i: u64 = 0;

while (i < SIZE) {
powers[i] = std.math.shl(u64, 1, i);
doublings[i] = std.math.shl(u64, divisor, i);
if (doublings[i] > dividend) {
break;
}
i += 1;
}

var accumulator: u64 = 0;
i -= 1;
while (i >= 0) {
if (accumulator + doublings[i] <= dividend) {
accumulator += doublings[i];
}
if (i > 0) {
i -= 1;
} else {
break;
}
}
var remainder = dividend - accumulator;
}

test "Expect 10, 0 from egyptianDivision(20, 2)" {
var output = egyptianDivision(20, 2);
try std.testing.expect(output[0] == 10);
try std.testing.expect(output[1] == 0);
}

test "Expect 580 divided by 34 is 17 and the remainder is 2" {
var output = egyptianDivision(580, 34);
try std.testing.expect(output[0] == 17);
try std.testing.expect(output[1] == 2);
}

pub fn main() !void {
var result = egyptianDivision(20, 2);
std.debug.print("20 divided by 2 is {} with remainder {}\n", .{ result[0], result[1] });
}
```
Output:
`20 divided by 2 is 10 with remainder 0`

## zkl

```fcn egyptianDivmod(dividend,divisor){
table:=[0..].pump(List, 'wrap(n){	// (2^n,divisor*2^n)
r:=T( p:=(2).pow(n), s:=divisor*p); (s<=dividend) and r or Void.Stop });
accumulator:=0;
foreach p2,d in (table.reverse()){
if(dividend>=d){ accumulator+=p2; dividend-=d; }
}
return(accumulator,dividend);
}```
```foreach dividend,divisor in (T(T(580,34), T(580,17), T(578,34), T(7532795332300578,235117))){
println("%d %% %d = %s".fmt(dividend,divisor,egyptianDivmod(dividend,divisor)));
}```
Output:
```580 % 34 = L(17,2)
580 % 17 = L(34,2)
578 % 34 = L(17,0)
7532795332300578 % 235117 = L(32038497141,81)
```