Ethiopian multiplication
You are encouraged to solve this task according to the task description, using any language you may know.
Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
Method:
- Take two numbers to be multiplied and write them down at the top of two columns.
- In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
- In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
- Examine the table produced and discard any row where the value in the left column is even.
- Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
For example: 17 × 34
17 34
Halving the first column:
17 34
8
4
2
1
Doubling the second column:
17 34
8 68
4 136
2 272
1 544
Strike-out rows whose first cell is even:
17 34
8 68
4 136
2 272
1 544
Sum the remaining numbers in the right-hand column:
17 34
8 --
4 ---
2 ---
1 544
====
578
So 17 multiplied by 34, by the Ethiopian method is 578.
- Task
The task is to define three named functions/methods/procedures/subroutines:
- one to halve an integer,
- one to double an integer, and
- one to state if an integer is even.
Use these functions to create a function that does Ethiopian multiplication.
- References
- Ethiopian multiplication explained (Video)
- A Night Of Numbers - Go Forth And Multiply (Video)
- Ethiopian multiplication
- Russian Peasant Multiplication
- Programming Praxis: Russian Peasant Multiplication
11l
<lang 11l>F halve(x)
R x I/ 2
F double_(x)
R x * 2
F even(x)
R !(x % 2)
F ethiopian(=multiplier, =multiplicand)
V result = 0
L multiplier >= 1
I !even(multiplier)
result += multiplicand
multiplier = halve(multiplier)
multiplicand = double_(multiplicand)
R result
print(ethiopian(17, 34))</lang>
- Output:
578
ACL2
<lang Lisp>(include-book "arithmetic-3/top" :dir :system)
(defun halve (x)
(floor x 2))
(defun double (x)
(* x 2))
(defun is-even (x)
(evenp x))
(defun multiply (x y)
(if (zp (1- x))
y
(+ (if (is-even x)
0
y)
(multiply (halve x) (double y)))))</lang>
ActionScript
<lang ActionScript>function Divide(a:Number):Number { return ((a-(a%2))/2); } function Multiply(a:Number):Number { return (a *= 2); } function isEven(a:Number):Boolean { if (a%2 == 0) { return (true); } else { return (false); } } function Ethiopian(left:Number, right:Number) { var r:Number = 0; trace(left+" "+right); while (left != 1) { var State:String = "Keep"; if (isEven(Divide(left))) { State = "Strike"; } trace(Divide(left)+" "+Multiply(right)+" "+State); left = Divide(left); right = Multiply(right); if (State == "Keep") { r += right; } } trace("="+" "+r); }
}</lang>
- Output:
ex. Ethiopian(17,34);
17 34 8 68 Strike 4 136 Strike 2 272 Strike 1 544 Keep
Ada
<lang Ada> with ada.text_io;use ada.text_io;
procedure ethiopian is
function double (n : Natural) return Natural is (2*n); function halve (n : Natural) return Natural is (n/2); function is_even (n : Natural) return Boolean is (n mod 2 = 0); function mul (l, r : Natural) return Natural is (if l = 0 then 0 elsif l = 1 then r elsif is_even (l) then mul (halve (l),double (r)) else r + double (mul (halve (l), r)));
begin
put_line (mul (17,34)'img);
end ethiopian;</lang>
Aime
<lang aime>void halve(integer &x) {
x >>= 1;
}
void double(integer &x) {
x <<= 1;
}
integer iseven(integer x) {
return (x & 1) == 0;
}
integer ethiopian(integer plier, integer plicand, integer tutor) {
integer result;
result = 0;
if (tutor) {
o_form("ethiopian multiplication of ~ by ~\n", plier, plicand);
}
while (plier >= 1) {
if (iseven(plier)) {
if (tutor) {
o_form("/w4/ /w6/ struck\n", plier, plicand);
}
} else {
if (tutor) {
o_form("/w4/ /w6/ kept\n", plier, plicand);
}
result += plicand;
}
halve(plier);
double(plicand);
}
return result;
}
integer main(void) {
o_integer(ethiopian(17, 34, 1));
o_byte('\n');
return 0;
}</lang>
17 34 kept 8 68 struck 4 136 struck 2 272 struck 1 544 kept 578
ALGOL 68
<lang algol68>PROC halve = (REF INT x)VOID: x := ABS(BIN x SHR 1); PROC doublit = (REF INT x)VOID: x := ABS(BIN x SHL 1); PROC iseven = (#CONST# INT x)BOOL: NOT ODD x;
PROC ethiopian = (INT in plier,
INT in plicand, #CONST# BOOL tutor)INT:
(
INT plier := in plier, plicand := in plicand;
INT result:=0;
IF tutor THEN
printf(($"ethiopian multiplication of "g(0)," by "g(0)l$, plier, plicand)) FI;
WHILE plier >= 1 DO
IF iseven(plier) THEN
IF tutor THEN printf(($" "4d," "6d" struck"l$, plier, plicand)) FI
ELSE
IF tutor THEN printf(($" "4d," "6d" kept"l$, plier, plicand)) FI;
result +:= plicand
FI;
halve(plier); doublit(plicand)
OD;
result
);
main: (
printf(($g(0)l$, ethiopian(17, 34, TRUE)))
)</lang>
- Output:
ethiopian multiplication of 17 by 34 0017 000034 kept 0008 000068 struck 0004 000136 struck 0002 000272 struck 0001 000544 kept 578
ALGOL-M
<lang algol> BEGIN
INTEGER FUNCTION HALF(I); INTEGER I; BEGIN
HALF := I / 2;
END;
INTEGER FUNCTION DOUBLE(I); INTEGER I; BEGIN
DOUBLE := I + I;
END;
% RETURN 1 IF EVEN, OTHERWISE 0 % INTEGER FUNCTION EVEN(I); INTEGER I; BEGIN
EVEN := 1 - (I - 2 * (I / 2));
END;
% RETURN I * J AND OPTIONALLY SHOW COMPUTATIONAL STEPS % INTEGER FUNCTION ETHIOPIAN(I, J, SHOW); INTEGER I, J, SHOW; BEGIN
INTEGER P, YES;
YES := 1;
P := 0;
WHILE I >= 1 DO
BEGIN
IF EVEN(I) = YES THEN
BEGIN
IF SHOW = YES THEN WRITE(I," ----", J);
END
ELSE
BEGIN
IF SHOW = YES THEN WRITE(I,J);
P := P + J;
END;
I := HALF(I);
J := DOUBLE(J);
END;
IF SHOW = YES THEN WRITE(" =");
ETHIOPIAN := P;
END;
% EXERCISE THE FUNCTION % INTEGER YES; YES := 1; WRITE(ETHIOPIAN(17,34,YES));
END</lang>
- Output:
17 34
8 ---- 68
4 ---- 136
2 ---- 272
1 544
= 578
ALGOL W
<lang algolw>begin
% returns half of a %
integer procedure halve ( integer value a ) ; a div 2;
% returns a doubled %
integer procedure double ( integer value a ) ; a * 2;
% returns true if a is even, false otherwise %
logical procedure even ( integer value a ) ; not odd( a );
% returns the product of a and b using ethopian multiplication %
% rather than keep a table of the intermediate results, %
% we examine then as they are generated %
integer procedure ethopianMultiplication ( integer value a, b ) ;
begin
integer v, r, accumulator;
v := a;
r := b;
accumulator := 0;
i_w := 4; s_w := 0; % set output formatting %
while begin
write( v );
if even( v ) then writeon( " ---" )
else begin
accumulator := accumulator + r;
writeon( " ", r );
end;
v := halve( v );
r := double( r );
v > 0
end do begin end;
write( " =====" );
accumulator
end ethopianMultiplication ;
% task test case %
begin
integer m;
m := ethopianMultiplication( 17, 34 );
write( " ", m )
end
end.</lang>
- Output:
17 34
8 ---
4 ---
2 ---
1 544
=====
578
AppleScript
Note that this algorithm, already described in the Rhind Papyrus (c. BCE 1650), can be used to multiply strings as well as integers, if we change the identity element from 0 to the empty string, and replace integer addition with string concatenation.
See also: Repeat_a_string#AppleScript
<lang AppleScript>on run
{ethMult(17, 34), ethMult("Rhind", 9)}
--> {578, "RhindRhindRhindRhindRhindRhindRhindRhind"}
end run
-- Int -> Int -> Int
-- or
-- Int -> String -> String
on ethMult(m, n)
script fns
property identity : missing value
property plus : missing value
on half(n) -- 1. half an integer (div 2)
n div 2
end half
on double(n) -- 2. double (add to self)
plus(n, n)
end double
on isEven(n) -- 3. is n even ? (mod 2 > 0)
(n mod 2) > 0
end isEven
on chooseFns(c)
if c is string then
set identity of fns to ""
set plus of fns to plusString of fns
else
set identity of fns to 0
set plus of fns to plusInteger of fns
end if
end chooseFns
on plusInteger(a, b)
a + b
end plusInteger
on plusString(a, b)
a & b
end plusString
end script
chooseFns(class of m) of fns
-- MAIN PROCESS OF CALCULATION
set o to identity of fns
if n < 1 then return o
repeat while (n > 1)
if isEven(n) of fns then -- 3. is n even ? (mod 2 > 0)
set o to plus(o, m) of fns
end if
set n to half(n) of fns -- 1. half an integer (div 2)
set m to double(m) of fns -- 2. double (add to self)
end repeat
return plus(o, m) of fns
end ethMult</lang>
- Output:
{578, "RhindRhindRhindRhindRhindRhindRhindRhindRhind"}
AutoHotkey
<lang AutoHotkey>MsgBox % Ethiopian(17, 34) "`n" Ethiopian2(17, 34)
- func definitions
half( x ) { return x >> 1 }
double( x ) { return x << 1 }
isEven( x ) { return x & 1 == 0 }
Ethiopian( a, b ) { r := 0 While (a >= 1) { if !isEven(a) r += b a := half(a) b := double(b) } return r }
- or a recursive function
Ethiopian2( a, b, r = 0 ) { ;omit r param on initial call return a==1 ? r+b : Ethiopian2( half(a), double(b), !isEven(a) ? r+b : r ) }</lang>
AutoIt
<lang AutoIt> Func Halve($x) Return Int($x/2) EndFunc
Func Double($x) Return ($x*2) EndFunc
Func IsEven($x) Return (Mod($x,2) == 0) EndFunc
- this version also supports negative parameters
Func Ethiopian($nPlier, $nPlicand, $bTutor = True) Local $nResult = 0 If ($nPlier < 0) Then $nPlier =- $nPlier $nPlicand =- $nPlicand ElseIf ($nPlicand > 0) And ($nPlier > $nPlicand) Then $nPlier = $nPlicand $nPlicand = $nPlier EndIf If $bTutor Then _
ConsoleWrite(StringFormat("Ethiopian multiplication of %d by %d...\n", $nPlier, $nPlicand))
While ($nPlier >= 1) If Not IsEven($nPlier) Then $nResult += $nPlicand If $bTutor Then ConsoleWrite(StringFormat("%d\t%d\tKeep\n", $nPlier, $nPlicand)) Else If $bTutor Then ConsoleWrite(StringFormat("%d\t%d\tStrike\n", $nPlier, $nPlicand)) EndIf $nPlier = Halve($nPlier) $nPlicand = Double($nPlicand) WEnd If $bTutor Then ConsoleWrite(StringFormat("Answer = %d\n", $nResult)) Return $nResult EndFunc
MsgBox(0, "Ethiopian multiplication of 17 by 34", Ethiopian(17, 34) ) </lang>
AWK
Implemented without the tutor. <lang awk>function halve(x) {
return int(x/2)
}
function double(x) {
return x*2
}
function iseven(x) {
return x%2 == 0
}
function ethiopian(plier, plicand) {
r = 0
while(plier >= 1) {
if ( !iseven(plier) ) {
r += plicand
}
plier = halve(plier)
plicand = double(plicand)
}
return r
}
BEGIN {
print ethiopian(17, 34)
}</lang>
BASIC
BASIC
Works with QBasic. While building the table, it's easier to simply not print unused values, rather than have to go back and strike them out afterward. (Both that and the actual adding happen in the "IF NOT (isEven(x))" block.)
<lang qbasic>DECLARE FUNCTION half% (a AS INTEGER) DECLARE FUNCTION doub% (a AS INTEGER) DECLARE FUNCTION isEven% (a AS INTEGER)
DIM x AS INTEGER, y AS INTEGER, outP AS INTEGER
x = 17 y = 34
DO
PRINT x,
IF NOT (isEven(x)) THEN
outP = outP + y
PRINT y
ELSE
PRINT
END IF
IF x < 2 THEN EXIT DO
x = half(x)
y = doub(y)
LOOP
PRINT " =", outP
FUNCTION doub% (a AS INTEGER)
doub% = a * 2
END FUNCTION
FUNCTION half% (a AS INTEGER)
half% = a \ 2
END FUNCTION
FUNCTION isEven% (a AS INTEGER)
isEven% = (a MOD 2) - 1
END FUNCTION</lang>
- Output:
17 34 8 4 2 1 544 = 578
BBC BASIC
<lang bbcbasic> x% = 17
y% = 34
REPEAT
IF NOT FNeven(x%) THEN
p% += y%
PRINT x%, y%
ELSE
PRINT x%, " ---"
ENDIF
x% = FNhalve(x%)
y% = FNdouble(y%)
UNTIL x% = 0
PRINT " " , " ==="
PRINT " " , p%
END
DEF FNdouble(A%) = A% * 2
DEF FNhalve(A%) = A% DIV 2
DEF FNeven(A%) = ((A% AND 1) = 0)</lang>
- Output:
17 34
8 ---
4 ---
2 ---
1 544
===
578
FreeBASIC
<lang FreeBASIC>Function double_(y As String) As String
Var answer="0"+y
Var addcarry=0
For n_ As Integer=Len(y)-1 To 0 Step -1
Var addup=y[n_]+y[n_]-96
answer[n_+1]=(addup+addcarry) Mod 10+48
addcarry=(-(10<=(addup+addcarry)))
Next n_
answer[0]=addcarry+48
Return Ltrim(answer,"0")
End Function
Function Accumulate(NUM1 As String,NUM2 As String) As String
Var three="0"+NUM1
Var two=String(len(NUM1)-len(NUM2),"0")+NUM2
Var addcarry=0
For n2 As Integer=len(NUM1)-1 To 0 Step -1
Var addup=two[n2]+NUM1[n2]-96
three[n2+1]=(addup+addcarry) Mod 10+48
addcarry=(-(10<=(addup+addcarry)))
Next n2
three[0]=addcarry+48
three=Ltrim(three,"0")
If three="" Then Return "0"
Return three
End Function
Function Half(Byref x As String) As String
Var carry=0
For z As Integer=0 To Len(x)-1
Var temp=(x[z]-48+carry)
Var main=temp Shr 1
carry=(temp And 1) Shl 3 +(temp And 1) Shl 1
x[z]=main+48
Next z
x= Ltrim(x,"0")
Return x
End Function
Function IsEven(x As String) As Integer
If x[Len(x)-1] And 1 Then Return 0 return -1
End Function
Function EthiopianMultiply(n1 As String,n2 As String) As String
Dim As String x=n1,y=n2
If Len(y)>Len(x) Then Swap y,x
'set the largest one to be halfed
If Len(y)=Len(x) Then
If x<y Then Swap y,x
End If
Dim As String ans
Dim As String temprint,odd
While x<>""
temprint=""
odd=""
If not IsEven(x) Then
temprint=" *"
odd=" <-- odd"
ans=Accumulate(y,ans)
End If
Print x;odd;tab(30);y;temprint
x=Half(x)
y= Double_(y)
Wend
Return ans
End Function '================= Example ==================== Print Dim As String s1="17" Dim As String s2="34" Print "Half";tab(30);"Double * marks those accumulated" print "Biggest";tab(30);"Smallest"
Print
Var ans= EthiopianMultiply(s1,s2)
Print Print Print "Final answer" Print " ";ans print "Float check" Print Val(s1)*Val(s2)
Sleep </lang>note: algorithm uses strings instead of integers
- Output:
Half Double * marks those accumulatedBiggest Smallest
34 17 17 <-- odd 34 * 8 68 4 136 2 272 1 <-- odd 544 *
Final answer
578Float check
578
GW-BASIC
<lang qbasic>10 DEF FNE(A)=(A+1) MOD 2 20 DEF FNH(A)=INT(A/2) 30 DEF FND(A)=2*A 40 X=17:Y=34:TOT=0 50 WHILE X>=1 60 PRINT X, 70 IF FNE(X)=0 THEN TOT=TOT+Y:PRINT Y ELSE PRINT 80 X=FNH(X):Y=FND(Y) 90 WEND 100 PRINT "=", TOT</lang>
Liberty BASIC
<lang lb>x = 17 y = 34 msg$ = str$(x) + " * " + str$(y) + " = " Print str$(x) + " " + str$(y) 'In this routine we will not worry about discarding the right hand value whos left hand partner is even; 'we will just not add it to our product. Do Until x < 2
If Not(isEven(x)) Then
product = (product + y)
End If
x = halveInt(x)
y = doubleInt(y)
Print str$(x) + " " + str$(y)
Loop product = (product + y) If (x < 0) Then product = (product * -1) Print msg$ + str$(product)
Function isEven(num)
isEven = Abs(Not(num Mod 2))
End Function
Function halveInt(num)
halveInt = Int(num/ 2)
End Function
Function doubleInt(num)
doubleInt = Int(num * 2)
End Function</lang>
Microsoft Small Basic
<lang microsoftsmallbasic> x = 17 y = 34 tot = 0 While x >= 1
TextWindow.Write(x)
TextWindow.CursorLeft = 10
If Math.Remainder(x + 1, 2) = 0 Then
tot = tot + y
TextWindow.WriteLine(y)
Else
TextWindow.WriteLine("")
EndIf
x = Math.Floor(x / 2)
y = 2 * y
EndWhile TextWindow.Write("=") TextWindow.CursorLeft = 10 TextWindow.WriteLine(tot) </lang>
PureBasic
<lang PureBasic>Procedure isEven(x)
ProcedureReturn (x & 1) ! 1
EndProcedure
Procedure halveValue(x)
ProcedureReturn x / 2
EndProcedure
Procedure doubleValue(x)
ProcedureReturn x << 1
EndProcedure
Procedure EthiopianMultiply(x, y)
Protected sum
Print("Ethiopian multiplication of " + Str(x) + " and " + Str(y) + " ... ")
Repeat
If Not isEven(x)
sum + y
EndIf
x = halveValue(x)
y = doubleValue(y)
Until x < 1
PrintN(" equals " + Str(sum))
ProcedureReturn sum
EndProcedure
If OpenConsole()
EthiopianMultiply(17,34) Print(#CRLF$ + #CRLF$ + "Press ENTER to exit") Input() CloseConsole()
EndIf</lang>
- Output:
Ethiopian multiplication of 17 and 34 ... equals 578
It became apparent that according to the way the Ethiopian method is described above it can't produce a correct result if the first multiplicand (the one being repeatedly halved) is negative. I've addressed that in this variation. If the first multiplicand is negative then the resulting sum (which may already be positive or negative) is negated. <lang PureBasic>Procedure isEven(x)
ProcedureReturn (x & 1) ! 1
EndProcedure
Procedure halveValue(x)
ProcedureReturn x / 2
EndProcedure
Procedure doubleValue(x)
ProcedureReturn x << 1
EndProcedure
Procedure EthiopianMultiply(x, y)
Protected sum, sign = x
Print("Ethiopian multiplication of " + Str(x) + " and " + Str(y) + " ...")
Repeat
If Not isEven(x)
sum + y
EndIf
x = halveValue(x)
y = doubleValue(y)
Until x = 0
If sign < 0 : sum * -1: EndIf
PrintN(" equals " + Str(sum))
ProcedureReturn sum
EndProcedure
If OpenConsole()
EthiopianMultiply(17,34) EthiopianMultiply(-17,34) EthiopianMultiply(-17,-34) Print(#CRLF$ + #CRLF$ + "Press ENTER to exit") Input() CloseConsole()
EndIf</lang>
- Output:
Ethiopian multiplication of 17 and 34 ... equals 578 Ethiopian multiplication of -17 and 34 ... equals -578 Ethiopian multiplication of -17 and -34 ... equals 578
Sinclair ZX81 BASIC
Requires at least 2k of RAM. The specification is emphatic about wanting named functions: in a language where user-defined functions do not exist, the best we can do is to use subroutines and assign their line numbers to variables. This allows us to GOSUB HALVE instead of having to GOSUB 320. (It would however be more idiomatic to avoid using subroutines at all, for simple operations like these, and to refer to them by line number if they were used.)
<lang basic> 10 LET HALVE=320
20 LET DOUBLE=340 30 LET EVEN=360 40 DIM L(20) 50 DIM R(20) 60 INPUT L(1) 70 INPUT R(1) 80 LET I=1 90 PRINT L(1),R(1)
100 IF L(I)=1 THEN GOTO 200 110 LET I=I+1 120 IF I>20 THEN STOP 130 LET X=L(I-1) 140 GOSUB HALVE 150 LET L(I)=Y 160 LET X=R(I-1) 170 GOSUB DOUBLE 180 LET R(I)=Y 190 GOTO 90 200 FOR K=1 TO I 210 LET X=L(K) 220 GOSUB EVEN 230 IF NOT Y THEN GOTO 260 240 LET R(K)=0 250 PRINT AT K-1,16;" " 260 NEXT K 270 LET A=0 280 FOR K=1 TO I 290 LET A=A+R(K) 300 NEXT K 310 GOTO 380 320 LET Y=INT (X/2) 330 RETURN 340 LET Y=X*2 350 RETURN 360 LET Y=X/2=INT (X/2) 370 RETURN 380 PRINT AT I+1,16;A</lang>
- Input:
17 34
- Output:
17 34
8
4
2
1 544
578
True BASIC
A translation of BBC BASIC. True BASIC does not have Boolean operations built-in. <lang basic> !RosettaCode: Ethiopian Multiplication ! True BASIC v6.007 PROGRAM EthiopianMultiplication DECLARE DEF FNdouble DECLARE DEF FNhalve DECLARE DEF FNeven
LET x = 17 LET y = 34
DO IF FNeven(x) = 0 THEN LET p = p + y PRINT x,y ELSE PRINT x," ---" END IF
LET x = FNhalve(x) LET y = FNdouble(y) LOOP UNTIL x = 0 PRINT " ", " ===" PRINT " ", p GET KEY done
DEF FNdouble(A) = A * 2 DEF FNhalve(A) = INT(A / 2) DEF FNeven(A) = MOD(A+1,2) END
</lang>
XBasic
<lang xbasic> PROGRAM "ethmult" VERSION "0.0000"
DECLARE FUNCTION Entry() INTERNAL FUNCTION Double(@a&&) INTERNAL FUNCTION Halve(@a&&) INTERNAL FUNCTION IsEven(a&&)
FUNCTION Entry()
x&& = 17
y&& = 34
tot&& = 0
DO WHILE x&& >= 1
PRINT FORMAT$("#########", x&&);
PRINT " ";
IFF IsEven(x&&) THEN
tot&& = tot&& + y&&
PRINT FORMAT$("#########", y&&);
END IF
PRINT
Halve(@x&&)
Double(@y&&)
LOOP
PRINT "= ";
PRINT FORMAT$("#########", tot&&);
PRINT
END FUNCTION
FUNCTION Double(a&&)
a&& = 2 * a&&
END FUNCTION
FUNCTION Halve(a&&)
a&& = a&& / 2
END FUNCTION
FUNCTION IsEven(a&&)
RETURN a&& MOD 2 = 0
END FUNCTION END PROGRAM </lang>
- Output:
17 34
8
4
2
1 544
= 578
Batch File
<lang dos> @echo off
- Pick 2 random, non-zero, 2-digit numbers to send to :_main
set /a param1=%random% %% 98 + 1 set /a param2=%random% %% 98 + 1 call:_main %param1% %param2% pause>nul exit /b
- This is the main function that outputs the answer in the form of "%1 * %2 = %answer%"
- _main
setlocal enabledelayedexpansion set l0=%1 set r0=%2 set leftcount=1 set lefttempcount=0 set rightcount=1 set righttempcount=0
- Creates an array ("l[]") with the :_halve function. %l0% is the initial left number parsed
- This section will loop until the most recent member of "l[]" is equal to 0
- left
set /a lefttempcount=%leftcount%-1 if !l%lefttempcount%!==1 goto right call:_halve !l%lefttempcount%! set l%leftcount%=%errorlevel% set /a leftcount+=1 goto left
- Creates an array ("r[]") with the :_double function, %r0% is the initial right number parsed
- This section will loop until it has the same amount of entries as "l[]"
- right
set /a righttempcount=%rightcount%-1 if %rightcount%==%leftcount% goto both call:_double !r%righttempcount%! set r%rightcount%=%errorlevel% set /a rightcount+=1 goto right
- both
- Creates an boolean array ("e[]") corresponding with whether or not the respective "l[]" entry is even
for /l %%i in (0,1,%lefttempcount%) do (
call:_even !l%%i! set e%%i=!errorlevel!
)
- Adds up all entries of "r[]" based on the value of "e[]", respectively
set answer=0 for /l %%i in (0,1,%lefttempcount%) do (
if !e%%i!==1 ( set /a answer+=!r%%i! :: Everything from this----------------------------- set iseven%%i=KEEP ) else ( set iseven%%i=STRIKE ) echo L: !l%%i! R: !r%%i! - !iseven%%i! :: To this, is for cosmetics and is optional--------
) echo %l0% * %r0% = %answer% exit /b
- These are the three functions being used. The output of these functions are expressed in the errorlevel that they return
- _halve
setlocal set /a temp=%1/2 exit /b %temp%
- _double
setlocal set /a temp=%1*2 exit /b %temp%
- _even
setlocal set int=%1 set /a modint=%int% %% 2 exit /b %modint% </lang>
- Output:
L: 17 R: 34 - KEEP L: 8 R: 68 - STRIKE L: 4 R: 136 - STRIKE L: 2 R: 272 - STRIKE L: 1 R: 544 - KEEP 17 * 34 = 578
Bracmat
<lang bracmat>( (halve=.div$(!arg.2)) & (double=.2*!arg) & (isEven=.mod$(!arg.2):0) & ( mul
= a b as bs newbs result
. !arg:(?as.?bs)
& whl
' ( !as:? (%@:~1:?a)
& !as halve$!a:?as
& !bs:? %@?b
& !bs double$!b:?bs
)
& :?newbs
& whl
' ( !as:%@?a ?as
& !bs:%@?b ?bs
& (isEven$!a|!newbs !b:?newbs)
)
& 0:?result
& whl
' (!newbs:%@?b ?newbs&!b+!result:?result)
& !result
)
& out$(mul$(17.34)) );</lang> Output
578
C
<lang c>#include <stdio.h>
- include <stdbool.h>
void halve(int *x) { *x >>= 1; } void doublit(int *x) { *x <<= 1; } bool iseven(const int x) { return (x & 1) == 0; }
int ethiopian(int plier, int plicand, const bool tutor) {
int result=0;
if (tutor)
printf("ethiopian multiplication of %d by %d\n", plier, plicand);
while(plier >= 1) {
if ( iseven(plier) ) {
if (tutor) printf("%4d %6d struck\n", plier, plicand);
} else {
if (tutor) printf("%4d %6d kept\n", plier, plicand);
result += plicand;
}
halve(&plier); doublit(&plicand);
}
return result;
}
int main() {
printf("%d\n", ethiopian(17, 34, true));
return 0;
}</lang>
C#
<lang csharp> using System; using System.Linq;
namespace RosettaCode.Tasks { public static class EthiopianMultiplication_Task { public static void Test ( ) { Console.WriteLine ( "Ethiopian Multiplication" ); int A = 17, B = 34; Console.WriteLine ( "Recursion: {0}*{1}={2}", A, B, EM_Recursion ( A, B ) ); Console.WriteLine ( "Linq: {0}*{1}={2}", A, B, EM_Linq ( A, B ) ); Console.WriteLine ( "Loop: {0}*{1}={2}", A, B, EM_Loop ( A, B ) ); Console.WriteLine ( ); }
public static int Halve ( this int p_Number ) { return p_Number >> 1; } public static int Double ( this int p_Number ) { return p_Number << 1; } public static bool IsEven ( this int p_Number ) { return ( p_Number % 2 ) == 0; }
public static int EM_Recursion ( int p_NumberA, int p_NumberB ) { // Anchor Point, Recurse to find the next row Sum it with the second number according to the rules return p_NumberA == 1 ? p_NumberB : EM_Recursion ( p_NumberA.Halve ( ), p_NumberB.Double ( ) ) + ( p_NumberA.IsEven ( ) ? 0 : p_NumberB ); } public static int EM_Linq ( int p_NumberA, int p_NumberB ) { // Creating a range from 1 to x where x the number of times p_NumberA can be halved. // This will be 2^x where 2^x <= p_NumberA. Basically, ln(p_NumberA)/ln(2). return Enumerable.Range ( 1, Convert.ToInt32 ( Math.Log ( p_NumberA, Math.E ) / Math.Log ( 2, Math.E ) ) + 1 ) // For every item (Y) in that range, create a new list, comprising the pair (p_NumberA,p_NumberB) Y times. .Select ( ( item ) => Enumerable.Repeat ( new { Col1 = p_NumberA, Col2 = p_NumberB }, item ) // The aggregate method iterates over every value in the target list, passing the accumulated value and the current item's value. .Aggregate ( ( agg_pair, orig_pair ) => new { Col1 = agg_pair.Col1.Halve ( ), Col2 = agg_pair.Col2.Double ( ) } ) ) // Remove all even items .Where ( pair => !pair.Col1.IsEven ( ) ) // And sum! .Sum ( pair => pair.Col2 ); } public static int EM_Loop ( int p_NumberA, int p_NumberB ) { int RetVal = 0; while ( p_NumberA >= 1 ) { RetVal += p_NumberA.IsEven ( ) ? 0 : p_NumberB; p_NumberA = p_NumberA.Halve ( ); p_NumberB = p_NumberB.Double ( ); } return RetVal; } } }</lang>
C++
Using C++ templates, these kind of tasks can be implemented as meta-programs. The program runs at compile time, and the result is statically saved into regularly compiled code. Here is such an implementation without tutor, since there is no mechanism in C++ to output messages during program compilation. <lang cpp>template<int N> struct Half {
enum { Result = N >> 1 };
};
template<int N> struct Double {
enum { Result = N << 1 };
};
template<int N> struct IsEven {
static const bool Result = (N & 1) == 0;
};
template<int Multiplier, int Multiplicand> struct EthiopianMultiplication {
template<bool Cond, int Plier, int RunningTotal>
struct AddIfNot
{
enum { Result = Plier + RunningTotal };
};
template<int Plier, int RunningTotal>
struct AddIfNot <true, Plier, RunningTotal>
{
enum { Result = RunningTotal };
};
template<int Plier, int Plicand, int RunningTotal>
struct Loop
{
enum { Result = Loop<Half<Plier>::Result, Double<Plicand>::Result,
AddIfNot<IsEven<Plier>::Result, Plicand, RunningTotal >::Result >::Result };
};
template<int Plicand, int RunningTotal>
struct Loop <0, Plicand, RunningTotal>
{
enum { Result = RunningTotal };
};
enum { Result = Loop<Multiplier, Multiplicand, 0>::Result };
};
- include <iostream>
int main(int, char **) {
std::cout << EthiopianMultiplication<17, 54>::Result << std::endl;
return 0;
}</lang>
Clojure
<lang lisp>(defn halve [n]
(bit-shift-right n 1))
(defn twice [n] ; 'double' is taken
(bit-shift-left n 1))
(defn even [n] ; 'even?' is the standard fn
(zero? (bit-and n 1)))
(defn emult [x y]
(reduce +
(map second
(filter #(not (even (first %))) ; a.k.a. 'odd?'
(take-while #(pos? (first %))
(map vector
(iterate halve x)
(iterate twice y)))))))
(defn emult2 [x y]
(loop [a x, b y, r 0]
(if (= a 1)
(+ r b)
(if (even a)
(recur (halve a) (twice b) r)
(recur (halve a) (twice b) (+ r b))))))</lang>
COBOL
In COBOL, double is a reserved word, so the doubling functions is named twice, instead. <lang COBOL> *>* Ethiopian multiplication
IDENTIFICATION DIVISION.
PROGRAM-ID. ethiopian-multiplication.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01 l PICTURE 9(10) VALUE 17.
01 r PICTURE 9(10) VALUE 34.
01 ethiopian-multiply PICTURE 9(20).
01 product PICTURE 9(20).
PROCEDURE DIVISION.
CALL "ethiopian-multiply" USING
BY CONTENT l, BY CONTENT r,
BY REFERENCE ethiopian-multiply
END-CALL
DISPLAY ethiopian-multiply END-DISPLAY
MULTIPLY l BY r GIVING product END-MULTIPLY
DISPLAY product END-DISPLAY
STOP RUN.
END PROGRAM ethiopian-multiplication.
IDENTIFICATION DIVISION.
PROGRAM-ID. ethiopian-multiply.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01 evenp PICTURE 9.
88 even VALUE 1.
88 odd VALUE 0.
LINKAGE SECTION.
01 l PICTURE 9(10).
01 r PICTURE 9(10).
01 product PICTURE 9(20) VALUE ZERO.
PROCEDURE DIVISION using l, r, product.
MOVE ZEROES TO product
PERFORM UNTIL l EQUAL ZERO
CALL "evenp" USING
BY CONTENT l,
BY REFERENCE evenp
END-CALL
IF odd
ADD r TO product GIVING product END-ADD
END-IF
CALL "halve" USING
BY CONTENT l,
BY REFERENCE l
END-CALL
CALL "twice" USING
BY CONTENT r,
BY REFERENCE r
END-CALL
END-PERFORM
GOBACK.
END PROGRAM ethiopian-multiply.
IDENTIFICATION DIVISION.
PROGRAM-ID. halve.
DATA DIVISION.
LOCAL-STORAGE SECTION.
LINKAGE SECTION.
01 n PICTURE 9(10).
01 m PICTURE 9(10).
PROCEDURE DIVISION USING n, m.
DIVIDE n BY 2 GIVING m END-DIVIDE
GOBACK.
END PROGRAM halve.
IDENTIFICATION DIVISION.
PROGRAM-ID. twice.
DATA DIVISION.
LOCAL-STORAGE SECTION.
LINKAGE SECTION.
01 n PICTURE 9(10).
01 m PICTURE 9(10).
PROCEDURE DIVISION USING n, m.
MULTIPLY n by 2 GIVING m END-MULTIPLY
GOBACK.
END PROGRAM twice.
IDENTIFICATION DIVISION.
PROGRAM-ID. evenp.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01 q PICTURE 9(10).
LINKAGE SECTION.
01 n PICTURE 9(10).
01 m PICTURE 9(1).
88 even VALUE 1.
88 odd VALUE 0.
PROCEDURE DIVISION USING n, m.
DIVIDE n BY 2 GIVING q REMAINDER m END-DIVIDE
SUBTRACT m FROM 1 GIVING m END-SUBTRACT
GOBACK.
END PROGRAM evenp.</lang>
CoffeeScript
<lang coffeescript> halve = (n) -> Math.floor n / 2 double = (n) -> n * 2 is_even = (n) -> n % 2 == 0
multiply = (a, b) ->
prod = 0 while a > 0 prod += b if !is_even a a = halve a b = double b prod
- tests
do ->
for i in [0..100]
for j in [0..100]
throw Error("broken for #{i} * #{j}") if multiply(i,j) != i * j
</lang>
ColdFusion
Version with as a function of functions:
<lang cfm><cffunction name="double">
<cfargument name="number" type="numeric" required="true">
<cfset answer = number * 2>
<cfreturn answer>
</cffunction>
<cffunction name="halve">
<cfargument name="number" type="numeric" required="true">
<cfset answer = int(number / 2)>
<cfreturn answer>
</cffunction>
<cffunction name="even">
<cfargument name="number" type="numeric" required="true">
<cfset answer = number mod 2>
<cfreturn answer>
</cffunction>
<cffunction name="ethiopian">
<cfargument name="Number_A" type="numeric" required="true">
<cfargument name="Number_B" type="numeric" required="true">
<cfset Result = 0>
<cfloop condition = "Number_A GTE 1">
<cfif even(Number_A) EQ 1>
<cfset Result = Result + Number_B>
</cfif>
<cfset Number_A = halve(Number_A)>
<cfset Number_B = double(Number_B)>
</cfloop>
<cfreturn Result>
</cffunction>
<cfoutput>#ethiopian(17,34)#</cfoutput></lang>Version with display pizza:<lang cfm><cfset Number_A = 17>
<cfset Number_B = 34>
<cfset Result = 0>
<cffunction name="double">
<cfargument name="number" type="numeric" required="true">
<cfset answer = number * 2>
<cfreturn answer>
</cffunction>
<cffunction name="halve">
<cfargument name="number" type="numeric" required="true">
<cfset answer = int(number / 2)>
<cfreturn answer>
</cffunction>
<cffunction name="even">
<cfargument name="number" type="numeric" required="true">
<cfset answer = number mod 2>
<cfreturn answer>
</cffunction>
<cfoutput>
Ethiopian multiplication of #Number_A# and #Number_B#...
| #Number_A# | #Number_B# | #Action# |
...equals #Result#
</cfoutput></lang>
Sample output:
Ethiopian multiplication of 17 and 34... 17 34 Keep 8 68 Strike 4 136 Strike 2 272 Strike 1 544 Keep ...equals 578
Common Lisp
Common Lisp already has evenp, but all three of halve, double, and even-p are locally defined within ethiopian-multiply. (Note that the termination condition is (zerop l) because we terminate 'after' the iteration wherein the left column contains 1, and (halve 1) is 0.)<lang lisp>(defun ethiopian-multiply (l r)
(flet ((halve (n) (floor n 2))
(double (n) (* n 2))
(even-p (n) (zerop (mod n 2))))
(do ((product 0 (if (even-p l) product (+ product r)))
(l l (halve l))
(r r (double r)))
((zerop l) product))))</lang>
D
<lang d>int ethiopian(int n1, int n2) pure nothrow @nogc in {
assert(n1 >= 0, "Multiplier can't be negative");
} body {
static enum doubleNum = (in int n) pure nothrow @nogc => n * 2; static enum halveNum = (in int n) pure nothrow @nogc => n / 2; static enum isEven = (in int n) pure nothrow @nogc => !(n & 1);
int result;
while (n1 >= 1) {
if (!isEven(n1))
result += n2;
n1 = halveNum(n1);
n2 = doubleNum(n2);
}
return result;
} unittest {
assert(ethiopian(77, 54) == 77 * 54); assert(ethiopian(8, 923) == 8 * 923); assert(ethiopian(64, -4) == 64 * -4);
}
void main() {
import std.stdio;
writeln("17 ethiopian 34 is ", ethiopian(17, 34));
}</lang>
- Output:
17 ethiopian 34 is 578
dc
<lang dc>0k [ Make sure we're doing integer division ]sx [ 2 / ] sH [ Define "halve" function in register H ]sx [ 2 * ] sD [ Define "double" function in register D ]sx [ 2 % 1 r - ] sE [ Define "even?" function in register E ]sx
[ Entry into the main Ethiopian multiplication function is register M ]sx [ Keeps running value for the product in register p ]sx [ 0 sp lLx lp ] sM
[ The body of the main loop is in register L ]sx
[
sb sa [ First thing we do is cheat and store the parameters in
registers, which is safe because the only recursion is of
the tail variety. This avoids tricky stack
manipulations, which dc doesn't have good support for
(unlike, say, Forth). ]sx
la lEx sr [ r = even?(a) ]sx lr 0 =S [ if r = 0 then call s]sx la lHx d [ a = halve(a)]sx lb lDx [ b = double(b)]sx r 0 !=L [ if a !=0 then recurse ]
] sL
[ Utility macro that just adds the current value of b to the total in p ]sx [ lp lb + sp ]sS
[ Demo by multiplying 17 and 34 ]sx 17 34 lMx p</lang>
- Output:
578
E
<lang e>def halve(&x) { x //= 2 } def double(&x) { x *= 2 } def even(x) { return x %% 2 <=> 0 }
def multiply(var a, var b) {
var ab := 0
while (a > 0) {
if (!even(a)) { ab += b }
halve(&a)
double(&b)
}
return ab
}</lang>
Eiffel
<lang Eiffel> class APPLICATION
create make
feature {NONE}
make do io.put_integer (ethiopian_multiplication (17, 34)) end
ethiopian_multiplication (a, b: INTEGER): INTEGER -- Product of 'a' and 'b'. require a_positive: a > 0 b_positive: b > 0 local x, y: INTEGER do x := a y := b from until x <= 0 loop if not is_even_int (x) then Result := Result + y end x := halve_int (x) y := double_int (y) end ensure Result_correct: Result = a * b end
feature {NONE}
double_int (n: INTEGER): INTEGER
--Two times 'n'.
do Result := n * 2 end
halve_int (n: INTEGER): INTEGER
--'n' divided by two.
do Result := n // 2 end
is_even_int (n: INTEGER): BOOLEAN
--Is 'n' an even integer?
do Result := n \\ 2 = 0 end
end
</lang>
- Output:
578
Ela
Translation of Haskell: <lang ela>open list number
halve x = x `div` 2 double = (2*)
ethiopicmult a b = sum <| map snd <| filter (odd << fst) <| zip
(takeWhile (>=1) <| iterate halve a) (iterate double b)
ethiopicmult 17 34</lang>
- Output:
578
Elixir
<lang elixir>defmodule Ethiopian do
def halve(n), do: div(n, 2)
def double(n), do: n * 2
def even(n), do: rem(n, 2) == 0
def multiply(lhs, rhs) when is_integer(lhs) and lhs > 0 and is_integer(rhs) and rhs > 0 do
multiply(lhs, rhs, 0)
end
def multiply(1, rhs, acc), do: rhs + acc
def multiply(lhs, rhs, acc) do
if even(lhs), do: multiply(halve(lhs), double(rhs), acc),
else: multiply(halve(lhs), double(rhs), acc+rhs)
end
end
IO.inspect Ethiopian.multiply(17, 34)</lang>
- Output:
578
Emacs Lisp
Emacs Lisp has cl-evenp in cl-lib.el (its Common Lisp library), but for the sake of completeness the desired effect is achieved here via mod.
<lang lisp>
(defun even-p (n)
(= (mod n 2) 0))
(defun halve (n)
(floor n 2))
(defun double (n)
(* n 2))
(defun ethiopian-multiplication (l r)
(let ((sum 0))
(while (>= l 1)
(unless (even-p l)
(setq sum (+ r sum)))
(setq l (halve l))
(setq r (double r)))
sum))
</lang>
Erlang
<lang erlang>-module(ethopian). -export([multiply/2]).
halve(N) ->
N div 2.
double(N) ->
N * 2.
even(N) ->
(N rem 2) == 0.
multiply(LHS,RHS) when is_integer(Lhs) and Lhs > 0 and is_integer(Rhs) and Rhs > 0 ->
multiply(LHS,RHS,0).
multiply(1,RHS,Acc) ->
RHS+Acc;
multiply(LHS,RHS,Acc) ->
case even(LHS) of
true ->
multiply(halve(LHS),double(RHS),Acc);
false ->
multiply(halve(LHS),double(RHS),Acc+RHS)
end.</lang>
ERRE
<lang ERRE>PROGRAM ETHIOPIAN_MULT
FUNCTION EVEN(A)
EVEN=(A+1) MOD 2
END FUNCTION
FUNCTION HALF(A)
HALF=INT(A/2)
END FUNCTION
FUNCTION DOUBLE(A)
DOUBLE=2*A
END FUNCTION
BEGIN
X=17 Y=34 TOT=0
WHILE X>=1 DO
PRINT(X,)
IF EVEN(X)=0 THEN TOT=TOT+Y PRINT(Y) ELSE PRINT END IF
X=HALF(X) Y=DOUBLE(Y)
END WHILE
PRINT("=",TOT)
END PROGRAM </lang>
- Output:
17 34 8 4 2 1 544 = 578
Euphoria
<lang euphoria>function emHalf(integer n)
return floor(n/2)
end function
function emDouble(integer n)
return n*2
end function
function emIsEven(integer n)
return (remainder(n,2) = 0)
end function
function emMultiply(integer a, integer b)
integer sum sum = 0 while (a) do if (not emIsEven(a)) then sum += b end if a = emHalf(a) b = emDouble(b) end while return sum
end function
-- runtime
printf(1,"emMultiply(%d,%d) = %d\n",{17,34,emMultiply(17,34)})
printf(1,"\nPress Any Key\n",{}) while (get_key() = -1) do end while</lang>
F#
<lang fsharp>let ethopian n m =
let halve n = n / 2
let double n = n * 2
let even n = n % 2 = 0
let rec loop n m result =
if n <= 1 then result + m
else if even n then loop (halve n) (double m) result
else loop (halve n) (double m) (result + m)
loop n m 0</lang>
Factor
<lang factor>USING: arrays kernel math multiline sequences ; IN: ethiopian-multiplication
/* This function is built-in
- odd? ( n -- ? ) 1 bitand 1 number= ;
- /
- double ( n -- 2*n ) 2 * ;
- halve ( n -- n/2 ) 2 /i ;
- ethiopian-mult ( a b -- a*b )
[ 0 ] 2dip
[ dup 0 > ] [
[ odd? [ + ] [ drop ] if ] 2keep
[ double ] [ halve ] bi*
] while 2drop ;</lang>
FALSE
<lang false>[2/]h: [2*]d: [$2/2*-]o: [0[@$][$o;![@@\$@+@]?h;!@d;!@]#%\%]m: 17 34m;!. {578}</lang>
Forth
Halve and double are standard words, spelled 2/ and 2* respectively. <lang forth>: even? ( n -- ? ) 1 and 0= ;
- e* ( x y -- x*y )
dup 0= if nip exit then over 2* over 2/ recurse swap even? if nip else + then ;</lang>The author of Forth, Chuck Moore, designed a similar primitive into his MISC Forth microprocessors. The +* instruction is a multiply step: it adds S to T if A is odd, then shifts both A and T right one. The idea is that you only need to perform as many of these multiply steps as you have significant bits in the operand.(See his core instruction set for details.)
Fortran
<lang fortran>program EthiopicMult
implicit none
print *, ethiopic(17, 34, .true.)
contains
subroutine halve(v) integer, intent(inout) :: v v = int(v / 2) end subroutine halve
subroutine doublit(v) integer, intent(inout) :: v v = v * 2 end subroutine doublit
function iseven(x) logical :: iseven integer, intent(in) :: x iseven = mod(x, 2) == 0 end function iseven
function ethiopic(multiplier, multiplicand, tutorialized) result(r) integer :: r integer, intent(in) :: multiplier, multiplicand logical, intent(in), optional :: tutorialized
integer :: plier, plicand logical :: tutor
plier = multiplier plicand = multiplicand
if ( .not. present(tutorialized) ) then
tutor = .false.
else
tutor = tutorialized
endif
r = 0
if ( tutor ) write(*, '(A, I0, A, I0)') "ethiopian multiplication of ", plier, " by ", plicand
do while(plier >= 1)
if ( iseven(plier) ) then
if (tutor) write(*, '(I4, " ", I6, A)') plier, plicand, " struck"
else
if (tutor) write(*, '(I4, " ", I6, A)') plier, plicand, " kept"
r = r + plicand
endif
call halve(plier)
call doublit(plicand)
end do
end function ethiopic
end program EthiopicMult</lang>
Go
<lang go>package main
import "fmt"
func halve(i int) int { return i/2 }
func double(i int) int { return i*2 }
func isEven(i int) bool { return i%2 == 0 }
func ethMulti(i, j int) (r int) {
for ; i > 0; i, j = halve(i), double(j) {
if !isEven(i) {
r += j
}
}
return
}
func main() {
fmt.Printf("17 ethiopian 34 = %d\n", ethMulti(17, 34))
}</lang>
Haskell
Using integer (+)
<lang haskell>import Prelude hiding (odd) import Control.Monad (join)
halve :: Int -> Int halve = (`div` 2)
double :: Int -> Int double = join (+)
odd :: Int -> Bool odd = (== 1) . (`mod` 2)
ethiopicmult :: Int -> Int -> Int ethiopicmult a b =
sum $ map snd $ filter (odd . fst) $ zip (takeWhile (>= 1) $ iterate halve a) (iterate double b)
main :: IO () main = print $ ethiopicmult 17 34 == 17 * 34</lang>
- Output:
*Main> ethiopicmult 17 34 578
Or, as an unfold followed by a refold:
<lang haskell>import Data.List (intercalate, unfoldr) import Debug.Trace (trace) import Data.Tuple (swap) import Data.Bool (bool)
-- ETHIOPIAN MULTIPLICATION -------------------------------
ethMult :: Int -> Int -> Int ethMult n m =
let addedWhereOdd (d, x) a
| 0 < d = (+) a x
| otherwise = a
halved h
| 0 < h = Just $ trace (showHalf h) (swap $ quotRem h 2)
| otherwise = Nothing
doubled x = x + x
pairs = zip (unfoldr halved n) (iterate doubled m)
in (let x = foldr addedWhereOdd 0 pairs
in trace (showDoubles pairs ++ " = " ++ show x ++ "\n") x)
-- TRACE DISPLAY -------------------------------------------
showHalf :: Int -> String showHalf x = "halve: " ++ rjust 6 ' ' (show (quotRem x 2))
showDoubles :: [(Int, Int)] -> String showDoubles xs =
"double:\n" ++
unlines
(fmap
(\x ->
bool
(rjust 6 ' ' $ show $ snd x)
("-> " ++ rjust 3 ' ' (show $ snd x))
(0 < fst x))
xs) ++
intercalate " + " (xs >>= (\(r, q) -> bool [] [show q] (0 < r)))
rjust :: Int -> Char -> String -> String rjust n c s = drop (length s) (replicate n c ++ s)
-- TEST --------------------------------------------------- main :: IO () main = do
print $ ethMult 17 34 print $ ethMult 34 17</lang>
- Output:
halve: (8,1)
halve: (4,0)
halve: (2,0)
halve: (1,0)
halve: (0,1)
double:
-> 34
68
136
272
-> 544
34 + 544 = 578
halve: (17,0)
halve: (8,1)
halve: (4,0)
halve: (2,0)
halve: (1,0)
halve: (0,1)
double:
17
-> 34
68
136
272
-> 544
34 + 544 = 578
578
578
Using monoid mappend
Alternatively, we can express Ethiopian multiplication in terms of mappend and mempty, in place of (+) and 0.
This additional generality means that our ethMult function can now replicate a string n times as readily as it multiplies an integer n times, or raises an integer to the nth power.
<lang haskell>import Data.Monoid (mempty, (<>), getSum, getProduct) import Control.Monad (join) import Data.List (unfoldr) import Data.Tuple (swap)
-- ETHIOPIAN MULTIPLICATION ------------------------------- ethMult
:: (Monoid m) => Int -> m -> m
ethMult n m =
let half n
| 0 /= n = Just . swap $ quotRem n 2
| otherwise = Nothing
addedWhereOdd (d, x) a
| 0 /= d = a <> x
| otherwise = a
in foldr addedWhereOdd mempty $ zip (unfoldr half n) (iterate (join (<>)) m)
-- TEST --------------------------------------------------- main :: IO () main = do
mapM_ print $ [ getSum $ ethMult 17 34 -- 34 * 17 , getProduct $ ethMult 3 34 -- 34 ^ 3 ] <> (getProduct <$> ([ethMult 17] <*> [3, 4])) -- [3 ^ 17, 4 ^ 17] print $ ethMult 17 "34" print $ ethMult 17 [3, 4]</lang>
- Output:
578 39304 129140163 17179869184 "3434343434343434343434343434343434" [3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4]
HicEst
<lang hicest> WRITE(Messagebox) ethiopian( 17, 34 ) END ! of "main"
FUNCTION ethiopian(x, y)
ethiopian = 0
left = x
right = y
DO i = x, 1, -1
IF( isEven(left) == 0 ) ethiopian = ethiopian + right
IF( left == 1 ) RETURN
left = halve(left)
right = double(right)
ENDDO
END
FUNCTION halve( x )
halve = INT( x/2 ) END
FUNCTION double( x )
double = 2 * x END
FUNCTION isEven( x )
isEven = MOD(x, 2) == 0 END </lang>
Icon and Unicon
<lang Icon>procedure main(arglist) while ethiopian(integer(get(arglist)),integer(get(arglist))) # multiply successive pairs of command line arguments end
procedure ethiopian(i,j) # recursive Ethiopian multiplication return ( if not even(i) then j # this exploits that icon control expressions return values
else 0 ) +
( if i ~= 0 then ethiopian(halve(i),double(j))
else 0 )
end
procedure double(i) return i * 2 end
procedure halve(i) return i / 2 end
procedure even(i) return ( i % 2 = 0, i ) end</lang>While not it seems a task requirement, most implementations have a tutorial version. This seemed easiest in an iterative version.<lang Icon>procedure ethiopian(i,j) # iterative tutor local p,w w := *j+3 write("Ethiopian Multiplication of ",i," * ",j)
p := 0 until i = 0 do {
writes(right(i,w),right(j,w))
if not even(i) then {
p +:= j
write(" add")
}
else write(" discard")
i := halve(i)
j := double(j)
}
write(right("=",w),right(p,w)) return p end</lang>
J
Solution:<lang j>double =: 2&* halve =: %&2 NB. or the primitive -: odd =: 2&|
ethiop =: +/@(odd@] # (double~ <@#)) (1>.<.@halve)^:a:</lang>
Example:
17 ethiop 34 578
Note that double will repeatedly double its right argument if given a repetition count for its left argument:
(<5) double 17 17 34 68 136 272
Note: this implementation assumes that the number on the right is a positive integer. In contexts where it can be negative, its absolute value should be used and you should multiply the result of ethiop by its sign.<lang j>ethio=: *@] * (ethiop |)</lang>
Alternatively, if multiplying by negative 1 is prohibited, you can use a conditional function which optionally negates its argument.<lang j>ethio=: *@] -@]^:(0 > [) (ethiop |)</lang> Examples:<lang j> 7 ethio 11 77
7 ethio _11
_77
_7 ethio 11
_77
_7 ethio _11
77</lang>
Java
<lang java5>import java.util.HashMap; import java.util.Map; import java.util.Scanner; public class Mult{
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int first = sc.nextInt();
int second = sc.nextInt();
if(first < 0){
first = -first;
second = -second;
}
Map<Integer, Integer> columns = new HashMap<Integer, Integer>();
columns.put(first, second);
int sum = isEven(first)? 0 : second;
do{
first = halveInt(first);
second = doubleInt(second);
columns.put(first, second);
if(!isEven(first)){
sum += second;
}
}while(first > 1);
System.out.println(sum);
}
public static int doubleInt(int doubleMe){
return doubleMe << 1; //shift left
}
public static int halveInt(int halveMe){
return halveMe >>> 1; //shift right
}
public static boolean isEven(int num){
return (num & 1) == 0;
}
}</lang>An optimised variant using the three helper functions from the other example.<lang java5>/**
* This method will use ethiopian styled multiplication. * @param a Any non-negative integer. * @param b Any integer. * @result a multiplied by b */
public static int ethiopianMultiply(int a, int b) {
if(a==0 || b==0) {
return 0;
}
int result = 0;
while(a>=1) {
if(!isEven(a)) {
result+=b;
}
b = doubleInt(b);
a = halveInt(a);
}
return result;
}
/**
* This method is an improved version that will use * ethiopian styled multiplication, and also * supports negative parameters. * @param a Any integer. * @param b Any integer. * @result a multiplied by b */
public static int ethiopianMultiplyWithImprovement(int a, int b) {
if(a==0 || b==0) {
return 0;
}
if(a<0) {
a=-a;
b=-b;
} else if(b>0 && a>b) {
int tmp = a;
a = b;
b = tmp;
}
int result = 0;
while(a>=1) {
if(!isEven(a)) {
result+=b;
}
b = doubleInt(b);
a = halveInt(a);
}
return result;
}</lang>
JavaScript
<lang javascript>var eth = {
halve : function ( n ){ return Math.floor(n/2); }, double: function ( n ){ return 2*n; }, isEven: function ( n ){ return n%2 === 0); },
mult: function ( a , b ){ var sum = 0, a = [a], b = [b];
while ( a[0] !== 1 ){ a.unshift( eth.halve( a[0] ) ); b.unshift( eth.double( b[0] ) ); }
for( var i = a.length - 1; i > 0 ; i -= 1 ){
if( !eth.isEven( a[i] ) ){ sum += b[i]; } } return sum + b[0]; } } // eth.mult(17,34) returns 578</lang>
Or, avoiding the use of a multiplication operator in the version above, we can alternatively:
- Halve an integer, in this sense, with a right-shift (n >>= 1)
- Double an integer by addition to self (m += m)
- Test if an integer is odd by bitwise and (n & 1)
<lang javascript>function ethMult(m, n) {
var o = !isNaN(m) ? 0 : ; // same technique works with strings
if (n < 1) return o;
while (n > 1) {
if (n & 1) o += m; // 3. integer odd/even? (bit-wise and 1)
n >>= 1; // 1. integer halved (by right-shift)
m += m; // 2. integer doubled (addition to self)
}
return o + m;
}
ethMult(17, 34)</lang>
- Output:
578
Note that the same function will also multiply strings with some efficiency, particularly where n is larger. See Repeat_a_string
<lang javascript>ethMult('Ethiopian', 34)</lang>
- Output:
"EthiopianEthiopianEthiopianEthiopianEthiopianEthiopian EthiopianEthiopianEthiopianEthiopianEthiopianEthiopianEthiopian EthiopianEthiopianEthiopianEthiopianEthiopianEthiopianEthiopian EthiopianEthiopianEthiopianEthiopianEthiopianEthiopianEthiopian EthiopianEthiopianEthiopianEthiopianEthiopianEthiopianEthiopian"
jq
The following implementation is intended for jq 1.4 and later.
If your jq has while/2, then the implementation of the inner function, pairs, can be simplified to:<lang jq>def pairs: while( .[0] > 0; [ (.[0] | halve), (.[1] | double) ]);</lang><lang jq>def halve: (./2) | floor;
def double: 2 * .;
def isEven: . % 2 == 0;
def ethiopian_multiply(a;b):
def pairs: recurse( if .[0] > 0
then [ (.[0] | halve), (.[1] | double) ]
else empty
end );
reduce ([a,b] | pairs
| select( .[0] | isEven | not)
| .[1] ) as $i
(0; . + $i) ;</lang>Example:<lang jq>ethiopian_multiply(17;34) # => 578</lang>
Jsish
From Javascript entry. <lang javascript>/* Ethiopian multiplication in Jsish */ var eth = {
halve : function(n) { return Math.floor(n / 2); },
double: function(n) { return n << 1; },
isEven: function(n) { return n % 2 === 0; },
mult: function(a, b){
var sum = 0;
a = [a], b = [b];
while (a[0] !== 1) {
a.unshift(eth.halve(a[0]));
b.unshift(eth.double(b[0]));
}
for (var i = a.length - 1; i > 0; i -= 1) {
if(!eth.isEven(a[i])) sum += b[i];
}
return sum + b[0];
}
};
- eth.mult(17,34);
/*
!EXPECTSTART!
eth.mult(17,34) ==> 578
!EXPECTEND!
- /</lang>
- Output:
prompt$ jsish -u ethiopianMultiplication.jsi [PASS] ethiopianMultiplication.jsi
Julia
Helper functions (type stable): <lang julia>halve(x::Integer) = x >> one(x) double(x::Integer) = Int8(2) * x even(x::Integer) = x & 1 != 1</lang>
Main function: <lang julia>function ethmult(a::Integer, b::Integer)
r = 0
while a > 0
r += b * !even(a)
a = halve(a)
b = double(b)
end
return r
end
@show ethmult(17, 34)</lang>
Array version (more similar algorithm to the one from the task description): <lang julia>function ethmult2(a::Integer, b::Integer)
A = [a]
B = [b]
while A[end] > 1
push!(A, halve(A[end]))
push!(B, double(B[end]))
end
return sum(B[map(!even, A)])
end
@show ethmult2(17, 34)</lang>
- Output:
ethmult(17, 34) = 578 ethmult2(17, 34) = 578
Benchmark test:
julia> @time ethmult(17, 34) 0.000003 seconds (5 allocations: 176 bytes) 578 julia> @time ethmult2(17, 34) 0.000007 seconds (18 allocations: 944 bytes) 578
Kotlin
<lang scala>// version 1.1.2
fun halve(n: Int) = n / 2
fun double(n: Int) = n * 2
fun isEven(n: Int) = n % 2 == 0
fun ethiopianMultiply(x: Int, y: Int): Int {
var xx = x
var yy = y
var sum = 0
while (xx >= 1) {
if (!isEven(xx)) sum += yy
xx = halve(xx)
yy = double(yy)
}
return sum
}
fun main(args: Array<String>) {
println("17 x 34 = ${ethiopianMultiply(17, 34)}")
println("99 x 99 = ${ethiopianMultiply(99, 99)}")
}</lang>
- Output:
17 x 34 = 578 99 x 99 = 9801
Lambdatalk
A translation from the javascript entry.
<lang Scheme> {def halve {lambda {:n} {floor {/ :n 2}}}} -> halve {def double {lambda {:n} {* 2 :n}}} -> double {def isEven {lambda {:n} {= {% :n 2} 0}}} -> isEven
{def mult
{def mult.r
{lambda {:a :b}
{if {= {A.first :a} 1}
then {+ {S.map {{lambda {:a :b :i}
{if {isEven {A.get :i :a}}
then else {A.get :i :b}}} :a :b}
{S.serie {- {A.length :a} 1} 0 -1}}}
else {mult.r {A.addfirst! {halve {A.first :a}} :a}
{A.addfirst! {double {A.first :b}} :b}}}}}
{lambda {:a :b}
{mult.r {A.new :a} {A.new :b}}}}
-> mult
{mult 17 34} -> 578
</lang>
Limbo
<lang Limbo>implement Ethiopian;
include "sys.m"; sys: Sys; print: import sys; include "draw.m"; draw: Draw;
Ethiopian : module { init : fn(ctxt : ref Draw->Context, args : list of string); };
init (ctxt: ref Draw->Context, args: list of string) { sys = load Sys Sys->PATH;
print("\n%d\n", ethiopian(17, 34, 0)); print("\n%d\n", ethiopian(99, 99, 1)); }
halve(n: int): int { return (n /2); }
double(n: int): int { return (n * 2); }
iseven(n: int): int { return ((n%2) == 0); }
ethiopian(a: int, b: int, tutor: int): int { product := 0; if (tutor) print("\nmultiplying %d x %d", a, b); while (a >= 1) { if (!(iseven(a))) { if (tutor) print("\n%3d %d", a, b); product += b; } else if (tutor) print("\n%3d ----", a); a = halve(a); b = double(b); } return product; } </lang>
Locomotive Basic
<lang locobasic>10 DEF FNiseven(a)=(a+1) MOD 2 20 DEF FNhalf(a)=INT(a/2) 30 DEF FNdouble(a)=2*a 40 x=17:y=34:tot=0 50 WHILE x>=1 60 PRINT x, 70 IF FNiseven(x)=0 THEN tot=tot+y:PRINT y ELSE PRINT 80 x=FNhalf(x):y=FNdouble(y) 90 WEND 100 PRINT "=", tot</lang>
Output:
17 34 8 4 2 1 544 = 578
Logo
<lang logo>to double :x
output ashift :x 1
end to halve :x
output ashift :x -1
end to even? :x
output equal? 0 bitand 1 :x
end to eproduct :x :y
if :x = 0 [output 0] ifelse even? :x ~ [output eproduct halve :x double :y] ~ [output :y + eproduct halve :x double :y]
end</lang>
LOLCODE
<lang lolcode>HAI 1.3
HOW IZ I Halve YR Integer
FOUND YR QUOSHUNT OF Integer AN 2
IF U SAY SO
HOW IZ I Dubble YR Integer
FOUND YR PRODUKT OF Integer AN 2
IF U SAY SO
HOW IZ I IzEven YR Integer
FOUND YR BOTH SAEM 0 AN MOD OF Integer AN 2
IF U SAY SO
HOW IZ I EthiopianProdukt YR a AN YR b
I HAS A Result ITZ 0
IM IN YR Loop UPPIN YR x WILE DIFFRINT a AN 0
NOT I IZ IzEven YR a MKAY
O RLY?
YA RLY
Result R SUM OF Result AN b
OIC
a R I IZ Halve YR a MKAY
b R I IZ Dubble YR b MKAY
IM OUTTA YR Loop
FOUND YR Result
IF U SAY SO
VISIBLE I IZ EthiopianProdukt YR 17 AN YR 34 MKAY KTHXBYE</lang>
Output:
578
Lua
<lang lua>function halve(a)
return a/2
end
function double(a)
return a*2
end
function isEven(a)
return a%2 == 0
end
function ethiopian(x, y)
local result = 0
while (x >= 1) do
if not isEven(x) then
result = result + y
end
x = math.floor(halve(x))
y = double(y)
end
return result;
end
print(ethiopian(17, 34))</lang>
Mathematica / Wolfram Language
<lang Mathematica>IntegerHalving[x_]:=Floor[x/2] IntegerDoubling[x_]:=x*2; OddInteger OddQ Ethiopian[x_, y_] := Total[Select[NestWhileList[{IntegerHalving[#1],IntegerDoubling[#2]}&, {x,y}, (#1>1&)], OddQ[#1]&]]2
Ethiopian[17, 34]</lang>
Output:
578
MATLAB
First we define the three subroutines needed for this task. These must be saved in their own individual ".m" files. The file names must be the same as the function name stored in that file. Also, they must be saved in the same directory as the script that performs the Ethiopian Multiplication.
In addition, with the exception of the "isEven" and "doubleInt" functions, the inputs of the functions have to be an integer data type. This means that the input to these functions must be coerced from the default IEEE754 double precision floating point data type that all numbers and variables are represented as, to integer data types. As of MATLAB 2007a, 64-bit integer arithmetic is not supported. So, at best, these will work for 32-bit integer data types.
halveInt.m: <lang MATLAB>function result = halveInt(number)
result = idivide(number,2,'floor');
end</lang>
doubleInt.m: <lang MATLAB>function result = doubleInt(number)
result = times(2,number);
end</lang>
isEven.m: <lang MATLAB>%Returns a logical 1 if the number is even, 0 otherwise. function trueFalse = isEven(number)
trueFalse = logical( mod(number,2)==0 );
end</lang>
ethiopianMultiplication.m: <lang MATLAB>function answer = ethiopianMultiplication(multiplicand,multiplier)
%Generate columns
while multiplicand(end)>1
multiplicand(end+1,1) = halveInt( multiplicand(end) );
multiplier(end+1,1) = doubleInt( multiplier(end) );
end
%Strike out appropriate rows
multiplier( isEven(multiplicand) ) = [];
%Generate answer
answer = sum(multiplier);
end</lang>
Sample input: (with data type coercion) <lang MATLAB>ethiopianMultiplication( int32(17),int32(34) )
ans =
578
</lang>
Metafont
Implemented without the tutor. <lang metafont>vardef halve(expr x) = floor(x/2) enddef; vardef double(expr x) = x*2 enddef; vardef iseven(expr x) = if (x mod 2) = 0: true else: false fi enddef;
primarydef a ethiopicmult b =
begingroup
save r_, plier_, plicand_;
plier_ := a; plicand_ := b;
r_ := 0;
forever: exitif plier_ < 1;
if not iseven(plier_): r_ := r_ + plicand_; fi
plier_ := halve(plier_);
plicand_ := double(plicand_);
endfor
r_
endgroup
enddef;
show( (17 ethiopicmult 34) ); end</lang>
МК-61/52
<lang>П1 П2 <-> П0 ИП0 1 - x#0 29 ИП1 2 * П1 ИП0 2 / [x] П0 2 / {x} x#0 04 ИП2 ИП1 + П2 БП 04 ИП2 С/П</lang>
MMIX
In order to assemble and run this program you'll have to install MMIXware from [1]. This provides you with a simple assembler, a simulator, example programs and full documentation.
<lang mmix>A IS 17 B IS 34
pliar IS $255 % designating main registers pliand GREG acc GREG str IS pliar % reuse reg $255 for printing
LOC Data_Segment GREG @ BUF OCTA #3030303030303030 % reserve a buffer that is big enough to hold OCTA #3030303030303030 % a max (signed) 64 bit integer: OCTA #3030300a00000000 % 2^63 - 1 = 9223372036854775807 % string is terminated with NL, 0
LOC #1000 % locate program at address GREG @ halve SR pliar,pliar,1 GO $127,$127,0
double SL pliand,pliand,1 GO $127,$127,0
odd DIV $77,pliar,2 GET $78,rR GO $127,$127,0
% Main is the entry point of the program Main SET pliar,A % initialize registers for calculation SET pliand,B SET acc,0 1H GO $127,odd BZ $78,2F % if pliar is even skip incr. acc with pliand ADD acc,acc,pliand % 2H GO $127,halve % halve pliar GO $127,double % and double pliand PBNZ pliar,1B % repeat from 1H while pliar > 0 // result: acc = 17 x 34 // next: print result --> stdout // $0 is a temp register LDA str,BUF+19 % points after the end of the string 2H SUB str,str,1 % update buffer pointer DIV acc,acc,10 % do a divide and mod GET $0,rR % get digit from special purpose reg. rR % containing the remainder of the division INCL $0,'0' % convert to ascii STBU $0,str % place digit in buffer PBNZ acc,2B % next % 'str' points to the start of the result TRAP 0,Fputs,StdOut % output answer to stdout TRAP 0,Halt,0 % exit</lang> Assembling:
~/MIX/MMIX/Progs> mmixal ethiopianmult.mms
Running:
~/MIX/MMIX/Progs> mmix ethiopianmult 578
Modula-2
<lang modula2> MODULE EthiopianMultiplication;
FROM SWholeIO IMPORT
WriteCard;
FROM STextIO IMPORT
WriteString, WriteLn;
PROCEDURE Halve(VAR A: CARDINAL); BEGIN
A := A / 2;
END Halve;
PROCEDURE Double(VAR A: CARDINAL); BEGIN
A := 2 * A;
END Double;
PROCEDURE IsEven(A: CARDINAL): BOOLEAN; BEGIN
RETURN A REM 2 = 0;
END IsEven;
VAR
X, Y, Tot: CARDINAL;
BEGIN
X := 17;
Y := 34;
Tot := 0;
WHILE X >= 1 DO
WriteCard(X, 9);
WriteString(" ");
IF NOT(IsEven(X)) THEN
INC(Tot, Y);
WriteCard(Y, 9)
END;
WriteLn;
Halve(X);
Double(Y);
END;
WriteString("= ");
WriteCard(Tot, 9);
WriteLn;
END EthiopianMultiplication. </lang>
- Output:
17 34
8
4
2
1 544
= 578
Modula-3
<lang modula3>MODULE Ethiopian EXPORTS Main;
IMPORT IO, Fmt;
PROCEDURE IsEven(n: INTEGER): BOOLEAN =
BEGIN RETURN n MOD 2 = 0; END IsEven;
PROCEDURE Double(n: INTEGER): INTEGER =
BEGIN RETURN n * 2; END Double;
PROCEDURE Half(n: INTEGER): INTEGER =
BEGIN RETURN n DIV 2; END Half;
PROCEDURE Multiply(a, b: INTEGER): INTEGER =
VAR
temp := 0;
plier := a;
plicand := b;
BEGIN
WHILE plier >= 1 DO
IF NOT IsEven(plier) THEN
temp := temp + plicand;
END;
plier := Half(plier);
plicand := Double(plicand);
END;
RETURN temp;
END Multiply;
BEGIN
IO.Put("17 times 34 = " & Fmt.Int(Multiply(17, 34)) & "\n");
END Ethiopian.</lang>
==MUMPS==<lang MUMPS> HALVE(I)
;I should be an integer QUIT I\2
DOUBLE(I)
;I should be an integer QUIT I*2
ISEVEN(I)
;I should be an integer QUIT '(I#2)
E2(M,N)
New W,A,E,L Set W=$Select($Length(M)>=$Length(N):$Length(M)+2,1:$L(N)+2),A=0,L=0,A(L,1)=M,A(L,2)=N Write "Multiplying two numbers:" For Write !,$Justify(A(L,1),W),?W,$Justify(A(L,2),W) Write:$$ISEVEN(A(L,1)) ?(2*W)," Struck" Set:'$$ISEVEN(A(L,1)) A=A+A(L,2) Set L=L+1,A(L,1)=$$HALVE(A(L-1,1)),A(L,2)=$$DOUBLE(A(L-1,2)) Quit:A(L,1)<1 Write ! For E=W:1:(2*W) Write ?E,"=" Write !,?W,$Justify(A,W),! Kill W,A,E,L
Q</lang>
- Output:
USER>D E2^ROSETTA(1439,7)
Multiplying two numbers:
1439 7
719 14
359 28
179 56
89 112
44 224 Struck
22 448 Struck
11 896
5 1792
2 3584 Struck
1 7168
=======
10073
Nemerle
<lang Nemerle>using System; using System.Console;
module Ethiopian {
Multiply(x : int, y : int) : int
{
def halve(a) {a / 2}
def doble(a) {a * 2}
def isEven(a) {a % 2 == 0}
def multiply(p, q)
{
match(p)
{
|p when (p < 1) => 0
|p when (isEven(p)) => 0 + multiply(halve(p), doble(q))
|_ => q + multiply(halve(p), doble(q))
}
}
multiply(x, y)
}
Main() : void
{
WriteLine("By Ethiopian multiplication, 17 * 34 = {0}", Multiply(17, 34));
}
}</lang>
NetRexx
<lang NetRexx>/* NetRexx */ options replace format comments java crossref savelog symbols nobinary
/*REXX program multiplies 2 integers by Ethiopian/Russian peasant method*/ numeric digits 1000 /*handle extremely large integers. */
/*handles zeroes and negative integers.*/
/*A & B should be checked if integers.*/
parse arg a b . say 'a=' a say 'b=' b say 'product=' emult(a,b) return
method emult(x,y) private static
parse x x 1 ox prod=0 loop while x\==0 if \iseven(x) then prod=prod+y x=halve(x) y=dubble(y) end return prod*ox.sign
method halve(x) private static
return x % 2
method dubble(x) private static
return x + x
method iseven(x) private static
return x//2 == 0</lang>
Nim
<lang nim>proc halve(x): int = x div 2 proc double(x): int = x * 2 proc even(x): bool = x mod 2 == 0
proc ethiopian(x, y): int =
var x = x var y = y
while x >= 1:
if not even x:
result += y
x = halve x
y = double y
echo ethiopian(17, 34)</lang>
Objeck
<lang objeck>
use Collection;
class EthiopianMultiplication {
function : Main(args : String[]) ~ Nil {
first := IO.Console->ReadString()->ToInt();
second := IO.Console->ReadString()->ToInt();
"----"->PrintLine();
Mul(first, second)->PrintLine();
}
function : native : Mul(first : Int, second : Int) ~ Int {
if(first < 0){
first := -1 * first;
second := -1 * second;
};
sum := isEven(first)? 0 : second;
do {
first := halveInt(first);
second := doubleInt(second);
if(isEven(first) = false){
sum += second;
};
}
while(first > 1);
return sum;
}
function : halveInt(num : Int) ~ Bool {
return num >> 1;
}
function : doubleInt(num : Int) ~ Bool {
return num << 1;
}
function : isEven(num : Int) ~ Bool {
return (num and 1) = 0;
}
}</lang>
Object Pascal
multiplication.pas:<lang pascal>unit Multiplication; interface
function Double(Number: Integer): Integer; function Halve(Number: Integer): Integer; function Even(Number: Integer): Boolean; function Ethiopian(NumberA, NumberB: Integer): Integer;
implementation
function Double(Number: Integer): Integer; begin result := Number * 2 end;
function Halve(Number: Integer): Integer; begin result := Number div 2 end;
function Even(Number: Integer): Boolean; begin result := Number mod 2 = 0 end;
function Ethiopian(NumberA, NumberB: Integer): Integer;
begin
result := 0;
while NumberA >= 1 do
begin
if not Even(NumberA) then
result := result + NumberB;
NumberA := Halve(NumberA);
NumberB := Double(NumberB)
end
end;
begin end.</lang>ethiopianmultiplication.pas:<lang pascal>program EthiopianMultiplication;
uses
Multiplication;
begin
WriteLn('17 * 34 = ', Ethiopian(17, 34))
end.</lang>
- Output:
17 * 34 = 578
Objective-C
Using class methods except for the generic useful function iseven. <lang objc>#import <stdio.h>
BOOL iseven(int x) {
return (x&1) == 0;
}
@interface EthiopicMult : NSObject + (int)mult: (int)plier by: (int)plicand; + (int)halve: (int)a; + (int)double: (int)a; @end
@implementation EthiopicMult + (int)mult: (int)plier by: (int)plicand {
int r = 0;
while(plier >= 1) {
if ( !iseven(plier) ) r += plicand;
plier = [EthiopicMult halve: plier];
plicand = [EthiopicMult double: plicand];
}
return r;
}
+ (int)halve: (int)a {
return (a>>1);
}
+ (int)double: (int)a {
return (a<<1);
} @end
int main() {
@autoreleasepool {
printf("%d\n", [EthiopicMult mult: 17 by: 34]);
}
return 0;
}</lang>
OCaml
<lang ocaml>(* We optimize a bit by not keeping the intermediate lists, and summing
the right column on-the-fly, like in the C version. The function takes "halve" and "double" operators and "is_even" predicate as arguments, but also "is_zero", "zero" and "add". This allows for more general uses of the ethiopian multiplication. *)
let ethiopian is_zero is_even halve zero double add b a =
let rec g a b r = if is_zero a then (r) else g (halve a) (double b) (if not (is_even a) then (add b r) else (r)) in g a b zero
let imul =
ethiopian (( = ) 0) (fun x -> x mod 2 = 0) (fun x -> x / 2) 0 (( * ) 2) ( + );;
imul 17 34;; (* - : int = 578 *)
(* Now, we have implemented the same algorithm as "rapid exponentiation",
merely changing operator names *)
let ipow =
ethiopian (( = ) 0) (fun x -> x mod 2 = 0) (fun x -> x / 2) 1 (fun x -> x*x) ( * )
ipow 2 16;; (* - : int = 65536 *)
(* still renaming operators, if "halving" is just subtracting one,
and "doubling", adding one, then we get an addition *)
let iadd a b =
ethiopian (( = ) 0) (fun x -> false) (pred) b (function x -> x) (fun x y -> succ y) 0 a
iadd 421 1000;; (* - : int = 1421 *)
(* One can do much more with "ethiopian multiplication",
since the two "multiplicands" and the result may be of three different types, as shown by the typing system of ocaml *)
ethiopian;; - : ('a -> bool) -> (* is_zero *)
('a -> bool) -> (* is_even *)
('a -> 'a) -> (* halve *)
'b -> (* zero *)
('c -> 'c) -> (* double *)
('c -> 'b -> 'b) -> (* add *)
'c -> (* b *)
'a -> (* a *)
'b (* result *)
= <fun>
(* Here zero is the starting value for the accumulator of the sums
of values in the right column in the original algorithm. But the "add" me do something else, see for example the RosettaCode page on "Exponentiation operator". *)</lang>
Octave
<lang octave>function r = halve(a)
r = floor(a/2);
endfunction
function r = doublit(a)
r = a*2;
endfunction
function r = iseven(a)
r = mod(a,2) == 0;
endfunction
function r = ethiopicmult(plier, plicand, tutor=false)
r = 0;
if (tutor)
printf("ethiopic multiplication of %d and %d\n", plier, plicand);
endif
while(plier >= 1)
if ( iseven(plier) )
if (tutor)
printf("%4d %6d struck\n", plier, plicand);
endif
else
r = r + plicand;
if (tutor)
printf("%4d %6d kept\n", plier, plicand);
endif endif plier = halve(plier); plicand = doublit(plicand); endwhile
endfunction
disp(ethiopicmult(17, 34, true))</lang>
Oforth
Based on Forth version.
isEven is already defined for Integers.
<lang Oforth>: halve 2 / ;
- double 2 * ;
- ethiopian
dup ifZero: [ nip return ] over double over halve ethiopian swap isEven ifTrue: [ nip ] else: [ + ] ;</lang>
- Output:
17 34 ethiopian . 578
Ol
<lang ol> (define (ethiopian-multiplication l r)
(let ((even? (lambda (n)
(eq? (mod n 2) 0))))
(let loop ((sum 0) (l l) (r r))
(print "sum: " sum ", l: " l ", r: " r)
(if (eq? l 0)
sum
(loop
(if (even? l) (+ sum r) sum)
(floor (/ l 2)) (* r 2))))))
(print (ethiopian-multiplication 17 34)) </lang>
- Output:
sum: 0, l: 17, r: 34 sum: 0, l: 8, r: 68 sum: 68, l: 4, r: 136 sum: 204, l: 2, r: 272 sum: 476, l: 1, r: 544 sum: 476, l: 0, r: 1088 476
ooRexx
The Rexx solution shown herein applies equally to ooRexx.
Oz
<lang oz>declare
fun {Halve X} X div 2 end
fun {Double X} X * 2 end
fun {Even X} {Abs X mod 2} == 0 end %% standard function: Int.isEven
fun {EthiopicMult X Y}
X >= 0 = true %% assert: X must not be negative
Rows = for
L in X; L>0; {Halve L} %% C-like iterator: "Init; While; Next"
R in Y; true; {Double R}
collect:Collect
do {Collect L#R} end
OddRows = {Filter Rows LeftIsOdd}
RightColumn = {Map OddRows SelectRight}
in
{Sum RightColumn}
end
%% Helpers
fun {LeftIsOdd L#_} {Not {Even L}} end
fun {SelectRight _#R} R end
fun {Sum Xs} {FoldL Xs Number.'+' 0} end
in
{Show {EthiopicMult 17 34}}</lang>
PARI/GP
<lang parigp>halve(n)=n\2; double(n)=2*n; even(n)=!(n%2); multE(a,b)={ my(d=0);
while(a,
if(!even(a),
d+=b);
a=halve(a);
b=double(b));
d
};</lang>
Pascal
<lang pascal>program EthiopianMultiplication;
function Double(Number: Integer): Integer; begin Double := Number * 2 end;
function Halve(Number: Integer): Integer; begin Halve := Number div 2 end;
function Even(Number: Integer): Boolean; begin Even := Number mod 2 = 0 end;
function Ethiopian(NumberA, NumberB: Integer): Integer; begin Ethiopian := 0; while NumberA >= 1 do
begin if not Even(NumberA) then Ethiopian := Ethiopian + NumberB; NumberA := Halve(NumberA); NumberB := Double(NumberB) end
end;
begin
Write(Ethiopian(17, 34))
end.</lang>
Perl
<lang perl>use strict;
sub halve { int((shift) / 2); } sub double { (shift) * 2; } sub iseven { ((shift) & 1) == 0; }
sub ethiopicmult {
my ($plier, $plicand, $tutor) = @_;
print "ethiopic multiplication of $plier and $plicand\n" if $tutor;
my $r = 0;
while ($plier >= 1)
{
$r += $plicand unless iseven($plier); if ($tutor) { print "$plier, $plicand ", (iseven($plier) ? " struck" : " kept"), "\n"; } $plier = halve($plier); $plicand = double($plicand);
} return $r;
}
print ethiopicmult(17,34, 1), "\n";</lang>
Phix
<lang Phix>function emHalf(integer n)
return floor(n/2)
end function
function emDouble(integer n)
return n*2
end function
function emIsEven(integer n)
return (remainder(n,2)=0)
end function
function emMultiply(integer a, integer b) integer sum = 0
while a!=0 do
if not emIsEven(a) then sum += b end if
a = emHalf(a)
b = emDouble(b)
end while
return sum
end function
printf(1,"emMultiply(%d,%d) = %d\n",{17,34,emMultiply(17,34)})</lang>
PHP
Not object oriented version:<lang php><?php function halve($x) {
return floor($x/2);
}
function double($x) {
return $x*2;
}
function iseven($x) {
return !($x & 0x1);
}
function ethiopicmult($plier, $plicand, $tutor) {
if ($tutor) echo "ethiopic multiplication of $plier and $plicand\n";
$r = 0;
while($plier >= 1) {
if ( !iseven($plier) ) $r += $plicand;
if ($tutor)
echo "$plier, $plicand ", (iseven($plier) ? "struck" : "kept"), "\n";
$plier = halve($plier);
$plicand = double($plicand);
}
return $r;
}
echo ethiopicmult(17, 34, true), "\n";
?></lang>
- Output:
ethiopic multiplication of 17 and 34 17, 34 kept 8, 68 struck 4, 136 struck 2, 272 struck 1, 544 kept 578
Object Oriented version:
<lang php><?php
class ethiopian_multiply {
protected $result = 0;
protected function __construct($x, $y){
while($x >= 1){
$this->sum_result($x, $y);
$x = $this->half_num($x);
$y = $this->double_num($y);
}
}
protected function half_num($x){
return floor($x/2);
}
protected function double_num($y){
return $y*2;
}
protected function not_even($n){
return $n%2 != 0 ? true : false;
}
protected function sum_result($x, $y){
if($this->not_even($x)){
$this->result += $y;
}
}
protected function get_result(){
return $this->result;
}
static public function init($x, $y){
$init = new ethiopian_multiply($x, $y);
return $init->get_result();
}
}
echo ethiopian_multiply::init(17, 34); ?></lang>
PicoLisp
<lang PicoLisp>(de halve (N)
(/ N 2) )
(de double (N)
(* N 2) )
(de even? (N)
(not (bit? 1 N)) )
(de ethiopian (X Y)
(let R 0
(while (>= X 1)
(or (even? X) (inc 'R Y))
(setq
X (halve X)
Y (double Y) ) )
R ) )</lang>
Pike
<lang Pike>int ethopian_multiply(int l, int r) {
int halve(int n) { return n/2; };
int double(int n) { return n*2; };
int(0..1) evenp(int n) { return !(n%2); };
int product = 0;
do
{
write("%5d %5d\n", l, r);
if (!evenp(l))
product += r;
l = halve(l);
r = double(r);
}
while(l);
return product;
}</lang>
PL/I
<lang PL/I>
declare (L(30), R(30)) fixed binary; declare (i, s) fixed binary;
L, R = 0;
put skip list
('Hello, please type two values and I will print their product:');
get list (L(1), R(1));
put edit ('The product of ', trim(L(1)), ' and ', trim(R(1)), ' is ') (a);
do i = 1 by 1 while (L(i) ^= 0);
L(i+1) = halve(L(i));
R(i+1) = double(R(i));
end;
s = 0;
do i = 1 by 1 while (L(i) > 0);
if odd(L(i)) then s = s + R(i);
end;
put edit (trim(s)) (a);
halve: procedure (k) returns (fixed binary);
declare k fixed binary; return (k/2);
end halve; double: procedure (k) returns (fixed binary);
declare k fixed binary; return (2*k);
end; odd: procedure (k) returns (bit (1));
return (iand(k, 1) ^= 0);
end odd;</lang>
PL/SQL
This code was taken from the ADA example above - very minor differences. <lang plsql>create or replace package ethiopian is
function multiply
( left in integer,
right in integer)
return integer;
end ethiopian; /
create or replace package body ethiopian is
function is_even(item in integer) return boolean is begin return item mod 2 = 0; end is_even;
function double(item in integer) return integer is begin return item * 2; end double;
function half(item in integer) return integer is begin return trunc(item / 2); end half;
function multiply
( left in integer,
right in integer)
return Integer
is
temp integer := 0;
plier integer := left;
plicand integer := right;
begin
loop
if not is_even(plier) then
temp := temp + plicand;
end if;
exit when plier <= 1;
plier := half(plier);
plicand := double(plicand);
end loop;
return temp;
end multiply;
end ethiopian; /
/* example call */ begin
dbms_output.put_line(ethiopian.multiply(17, 34));
end; /</lang>
Powerbuilder
<lang powerbuilder>public function boolean wf_iseven (long al_arg);return mod(al_arg, 2 ) = 0 end function
public function long wf_halve (long al_arg);RETURN int(al_arg / 2) end function
public function long wf_double (long al_arg);RETURN al_arg * 2 end function
public function long wf_ethiopianmultiplication (long al_multiplicand, long al_multiplier);// calculate result long ll_product
DO WHILE al_multiplicand >= 1 IF wf_iseven(al_multiplicand) THEN // do nothing ELSE ll_product += al_multiplier END IF al_multiplicand = wf_halve(al_multiplicand) al_multiplier = wf_double(al_multiplier) LOOP
return ll_product end function
// example call long ll_answer ll_answer = wf_ethiopianmultiplication(17,34)</lang>
PowerShell
Traditional
<lang PowerShell>function isEven { param ([int]$value) return [bool]($value % 2 -eq 0) }
function doubleValue { param ([int]$value) return [int]($value * 2) }
function halveValue { param ([int]$value) return [int]($value / 2) }
function multiplyValues { param ( [int]$plier, [int]$plicand, [int]$temp = 0 )
while ($plier -ge 1) { if (!(isEven $plier)) { $temp += $plicand } $plier = halveValue $plier $plicand = doubleValue $plicand }
return $temp }
multiplyValues 17 34</lang>
Pipes with Busywork
This uses several PowerShell specific features, in functions everything is returned automatically, so explicitly stating return is unnecessary. type conversion happens automatically for certain types, [int] into [boolean] maps 0 to false and everything else to true. A hash is used to store the values as they are being written, then a pipeline is used to iterate over the keys of the hash, determine which are odd, and only sum those. The three-valued ForEach-Object is used to set a start expression, an iterative expression, and a return expression. <lang PowerShell>function halveInt( [int] $rhs ) { [math]::floor( $rhs / 2 ) }
function doubleInt( [int] $rhs ) { $rhs*2 }
function isEven( [int] $rhs ) { -not ( $_ % 2 ) }
function Ethiopian( [int] $lhs , [int] $rhs ) { $scratch = @{} 1..[math]::floor( [math]::log( $lhs , 2 ) + 1 ) | ForEach-Object { $scratch[$lhs] = $rhs $lhs $lhs = halveInt( $lhs ) $rhs = doubleInt( $rhs ) } | Where-Object { -not ( isEven $_ ) } | ForEach-Object { $sum = 0 } { $sum += $scratch[$_] } { $sum } }
Ethiopian 17 34</lang>
Prolog
Traditional
<lang prolog>halve(X,Y) :- Y is X // 2. double(X,Y) :- Y is 2*X. is_even(X) :- 0 is X mod 2.
% columns(First,Second,Left,Right) is true if integers First and Second % expand into the columns Left and Right, respectively columns(1,Second,[1],[Second]). columns(First,Second,[First|Left],[Second|Right]) :-
halve(First,Halved), double(Second,Doubled), columns(Halved,Doubled,Left,Right).
% contribution(Left,Right,Amount) is true if integers Left and Right, % from their respective columns contribute Amount to the final sum. contribution(Left,_Right,0) :-
is_even(Left).
contribution(Left,Right,Right) :-
\+ is_even(Left).
ethiopian(First,Second,Product) :-
columns(First,Second,Left,Right), maplist(contribution,Left,Right,Contributions), sumlist(Contributions,Product).</lang>
Functional Style
Using the same definitions as above for "halve/2", "double/2" and "is_even/2" along with an SWI-Prolog pack for function notation, one might write the following solution
<lang prolog>:- use_module(library(func)).
% halve/2, double/2, is_even/2 definitions go here
ethiopian(First,Second,Product) :-
ethiopian(First,Second,0,Product).
ethiopian(1,Second,Sum0,Sum) :-
Sum is Sum0 + Second.
ethiopian(First,Second,Sum0,Sum) :-
Sum1 is Sum0 + Second*(First mod 2), ethiopian(halve $ First, double $ Second, Sum1, Sum).</lang>
Constraint Handling Rules
This is a CHR solution for this problem using Prolog as the host language. Code will work in SWI-Prolog and YAP (and possibly in others with or without some minor tweaking). <lang prolog>:- module(ethiopia, [test/0, mul/3]).
- - use_module(library(chr)).
- - chr_constraint mul/3, halve/2, double/2, even/1, add_odd/4.
mul(1, Y, S) <=> S = Y. mul(X, Y, S) <=> X \= 1 | halve(X, X1),
double(Y, Y1),
mul(X1, Y1, S1),
add_odd(X, Y, S1, S).
halve(X, Y) <=> Y is X // 2.
double(X, Y) <=> Y is X * 2.
even(X) <=> 0 is X mod 2 | true. even(X) <=> 1 is X mod 2 | false.
add_odd(X, _, A, S) <=> even(X) | S is A. add_odd(X, Y, A, S) <=> \+ even(X) | S is A + Y.
test :-
mul(17, 34, Z), !, writeln(Z).</lang>Note that the task statement is what makes the halve and double constraints required. Their use is highly artificial and a more realistic implementation would look like this:
<lang prolog>:- module(ethiopia, [test/0, mul/3]).
- - use_module(library(chr)).
- - chr_constraint mul/3, even/1, add_if_odd/4.
mul(1, Y, S) <=> S = Y. mul(X, Y, S) <=> X \= 1 | X1 is X // 2,
Y1 is Y * 2,
mul(X1, Y1, S1),
add_if_odd(X, Y, S1, S).
even(X) <=> 0 is X mod 2 | true. even(X) <=> 1 is X mod 2 | false.
add_if_odd(X, _, A, S) <=> even(X) | S is A. add_if_odd(X, Y, A, S) <=> \+ even(X) | S is A + Y.
test :-
mul(17, 34, Z), writeln(Z).</lang>Even this is more verbose than what a more native solution would look like.
Python
Python: With tutor
<lang python>tutor = True
def halve(x):
return x // 2
def double(x):
return x * 2
def even(x):
return not x % 2
def ethiopian(multiplier, multiplicand):
if tutor:
print("Ethiopian multiplication of %i and %i" %
(multiplier, multiplicand))
result = 0
while multiplier >= 1:
if even(multiplier):
if tutor:
print("%4i %6i STRUCK" %
(multiplier, multiplicand))
else:
if tutor:
print("%4i %6i KEPT" %
(multiplier, multiplicand))
result += multiplicand
multiplier = halve(multiplier)
multiplicand = double(multiplicand)
if tutor:
print()
return result</lang>
Sample output
Python 3.1 (r31:73574, Jun 26 2009, 20:21:35) [MSC v.1500 32 bit (Intel)] on win32 Type "copyright", "credits" or "license()" for more information. >>> ethiopian(17, 34) Ethiopian multiplication of 17 and 34 17 34 KEPT 8 68 STRUCK 4 136 STRUCK 2 272 STRUCK 1 544 KEPT 578 >>>
Python: Without tutor
Without the tutorial code, and taking advantage of Python's lambda:
<lang python>halve = lambda x: x // 2 double = lambda x: x*2 even = lambda x: not x % 2
def ethiopian(multiplier, multiplicand):
result = 0
while multiplier >= 1:
if not even(multiplier):
result += multiplicand
multiplier = halve(multiplier)
multiplicand = double(multiplicand)
return result</lang>
Python: With tutor. More Functional
Using some features which Python has for use in functional programming. The example also tries to show how to mix different programming styles while keeping close to the task specification, a kind of "executable pseudocode". Note: While column2 could theoretically generate a sequence of infinite length, izip will stop requesting values from it (and so provide the necessary stop condition) when column1 has no more values. When not using the tutor, table will generate the table on the fly in an efficient way, not keeping any intermediate values.<lang python>tutor = True
from itertools import izip, takewhile
def iterate(function, arg):
while 1:
yield arg
arg = function(arg)
def halve(x): return x // 2 def double(x): return x * 2 def even(x): return x % 2 == 0
def show_heading(multiplier, multiplicand):
print "Multiplying %d by %d" % (multiplier, multiplicand), print "using Ethiopian multiplication:" print
TABLE_FORMAT = "%8s %8s %8s %8s %8s"
def show_table(table):
for p, q in table:
print TABLE_FORMAT % (p, q, "->",
p, q if not even(p) else "-" * len(str(q)))
def show_result(result):
print TABLE_FORMAT % (, , , , "=" * (len(str(result)) + 1)) print TABLE_FORMAT % (, , , , result)
def ethiopian(multiplier, multiplicand):
def column1(x): return takewhile(lambda v: v >= 1, iterate(halve, x))
def column2(x): return iterate(double, x)
def rows(x, y): return izip(column1(x), column2(y))
table = rows(multiplier, multiplicand)
if tutor:
table = list(table)
show_heading(multiplier, multiplicand)
show_table(table)
result = sum(q for p, q in table if not even(p))
if tutor:
show_result(result)
return result</lang>
- Example output:
>>> ethiopian(17, 34) Multiplying 17 by 34 using Ethiopian multiplication:
17 34 -> 17 34
8 68 -> 8 --
4 136 -> 4 ---
2 272 -> 2 ---
1 544 -> 1 544
====
578
578
Python: as an unfold followed by a fold
<lang python>Ethiopian multiplication
from functools import reduce
- ethMult :: Int -> Int -> Int
def ethMult(n):
Ethiopian multiplication of n by m.
def doubled(x):
return x + x
def halved(h):
qr = divmod(h, 2)
if 0 < h:
print('halve:', str(qr).rjust(8, ' '))
return Just(qr) if 0 < h else Nothing()
def addedWhereOdd(a, remx):
odd, x = remx
if odd:
print(
str(a).rjust(2, ' '), '+',
str(x).rjust(3, ' '), '->',
str(a + x).rjust(3, ' ')
)
return a + x
else:
print(str(x).rjust(8, ' '))
return a
return lambda m: reduce(
addedWhereOdd,
zip(
unfoldr(halved)(n),
iterate(doubled)(m)
),
0
)
- TEST -------------------------------------------------
def main():
Tests of multiplication.
print(
'\nProduct: ' + str(
ethMult(17)(34)
),
'\n_______________\n'
)
print(
'\nProduct: ' + str(
ethMult(34)(17)
)
)
- GENERIC -------------------------------------------------
- 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}
- iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
An infinite list of repeated
applications of f to x.
def go(x):
v = x
while True:
yield v
v = f(v)
return lambda x: go(x)
- showLog :: a -> IO String
def showLog(*s):
Arguments printed with
intercalated arrows.
print(
' -> '.join(map(str, s))
)
- unfoldr(lambda x: Just((x, x - 1)) if 0 != x else Nothing())(10)
- -> [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]
- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
def unfoldr(f):
Dual to reduce or foldr.
Where catamorphism reduces a list to a summary value,
the anamorphic unfoldr builds a list from a seed value.
As long as f returns Just(a, b), a is prepended 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):
xr = v, v
xs = []
while True:
mb = f(xr[0])
if mb.get('Nothing'):
return xs
else:
xr = mb.get('Just')
xs.append(xr[1])
return xs
return lambda x: go(x)
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
halve: (8, 1)
halve: (4, 0)
halve: (2, 0)
halve: (1, 0)
halve: (0, 1)
0 + 34 -> 34
68
136
272
34 + 544 -> 578
Product: 578
_______________
halve: (17, 0)
halve: (8, 1)
halve: (4, 0)
halve: (2, 0)
halve: (1, 0)
halve: (0, 1)
17
0 + 34 -> 34
68
136
272
34 + 544 -> 578
Product: 578
R
R: With tutor
<lang R>halve <- function(a) floor(a/2) double <- function(a) a*2 iseven <- function(a) (a%%2)==0
ethiopicmult <- function(plier, plicand, tutor=FALSE) {
if (tutor) { cat("ethiopic multiplication of", plier, "and", plicand, "\n") }
result <- 0
while(plier >= 1) {
if (!iseven(plier)) { result <- result + plicand }
if (tutor) {
cat(plier, ", ", plicand, " ", ifelse(iseven(plier), "struck", "kept"), "\n", sep="")
}
plier <- halve(plier)
plicand <- double(plicand)
}
result
}
print(ethiopicmult(17, 34, TRUE))</lang>
R: Without tutor
Simplified version. <lang R> halve <- function(a) floor(a/2) double <- function(a) a*2 iseven <- function(a) (a%%2)==0
ethiopicmult<-function(x,y){ res<-ifelse(iseven(y),0,x) while(!y==1){ x<-double(x) y<-halve(y) if(!iseven(y)) res<-res+x } return(res) }
print(ethiopicmult(17,34)) </lang>
Racket
<lang Racket>#lang racket
(define (halve i) (quotient i 2)) (define (double i) (* i 2))
- `even?' is built-in
(define (ethiopian-multiply x y)
(cond [(zero? x) 0]
[(even? x) (ethiopian-multiply (halve x) (double y))]
[else (+ y (ethiopian-multiply (halve x) (double y)))]))
(ethiopian-multiply 17 34) ; -> 578</lang>
Raku
(formerly Perl 6) <lang perl6>sub halve (Int $n is rw) { $n div= 2 } sub double (Int $n is rw) { $n *= 2 } sub even (Int $n --> Bool) { $n %% 2 }
sub ethiopic-mult (Int $a is copy, Int $b is copy --> Int) {
my Int $r = 0;
while $a {
even $a or $r += $b; halve $a; double $b;
} return $r;
}
say ethiopic-mult(17,34);</lang>
- Output:
578
More succinctly using implicit typing, primed lambdas, and an infinite loop: <lang perl6>sub ethiopic-mult {
my &halve = * div= 2; my &double = * *= 2; my &even = * %% 2;
my ($a,$b) = @_;
my $r;
loop {
even $a or $r += $b;
halve $a or return $r;
double $b;
}
}
say ethiopic-mult(17,34);</lang> More succinctly still, using a pure functional approach (reductions, mappings, lazy infinite sequences): <lang perl6>sub halve { $^n div 2 } sub double { $^n * 2 } sub even { $^n %% 2 }
sub ethiopic-mult ($a, $b) {
[+] ($b, &double ... *)
Z*
($a, &halve ... 0).map: { not even $^n }
}
say ethiopic-mult(17,34);</lang>(same output)
Rascal
<lang Rascal>import IO;
public int halve(int n) = n/2;
public int double(int n) = n*2;
public bool uneven(int n) = (n % 2) != 0);
public int ethiopianMul(int n, int m) { result = 0; while(n >= 1) { if(uneven(n)) result += m; n = halve(n); m = double(m); } return result; } </lang>
REXX
These two REXX versions properly handle negative integers.
sans error checking
<lang rexx>/*REXX program multiplies two integers by the Ethiopian (or Russian peasant) method. */ numeric digits 3000 /*handle some gihugeic integers. */ parse arg a b . /*get two numbers from the command line*/ say 'a=' a /*display a formatted value of A. */ say 'b=' b /* " " " " " B. */ say 'product=' eMult(a, b) /*invoke eMult & multiple two integers.*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ eMult: procedure; parse arg x,y; s=sign(x) /*obtain the two arguments; sign for X.*/
$=0 /*product of the two integers (so far).*/
do while x\==0 /*keep processing while X not zero.*/
if \isEven(x) then $=$+y /*if odd, then add Y to product. */
x= halve(x) /*invoke the HALVE function. */
y=double(y) /* " " DOUBLE " */
end /*while*/ /* [↑] Ethiopian multiplication method*/
return $*s/1 /*maintain the correct sign for product*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ double: return arg(1) * 2 /* * is REXX's multiplication. */ halve: return arg(1) % 2 /* % " " integer division. */ isEven: return arg(1) // 2 == 0 /* // " " division remainder.*/</lang> output when the following input is used: 30 -7
a= 30 b= -7 product= -210
with error checking
This REXX version also aligns the "input" messages and also performs some basic error checking.
Note that the 2nd number needn't be an integer, any valid number will work. <lang rexx>/*REXX program multiplies two integers by the Ethiopian (or Russian peasant) method. */ numeric digits 3000 /*handle some gihugeic integers. */ parse arg a b _ . /*get two numbers from the command line*/ if a== then call error "1st argument wasn't specified." if b== then call error "2nd argument wasn't specified." if _\== then call error "too many arguments were specified: " _ if \datatype(a, 'W') then call error "1st argument isn't an integer: " a if \datatype(b, 'N') then call error "2nd argument isn't a valid number: " b p=eMult(a, b) /*Ethiopian or Russian peasant method. */ w=max(length(a), length(b), length(p)) /*find the maximum width of 3 numbers. */ say ' a=' right(a, w) /*use right justification to display A.*/ say ' b=' right(b, w) /* " " " " " B.*/ say 'product=' right(p, w) /* " " " " " P.*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ eMult: procedure; parse arg x,y; s=sign(x) /*obtain the two arguments; sign for X.*/
$=0 /*product of the two integers (so far).*/
do while x\==0 /*keep processing while X not zero.*/
if \isEven(x) then $=$+y /*if odd, then add Y to product. */
x= halve(x) /*invoke the HALVE function. */
y=double(y) /* " " DOUBLE " */
end /*while*/ /* [↑] Ethiopian multiplication method*/
return $*s/1 /*maintain the correct sign for product*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ double: return arg(1) * 2 /* * is REXX's multiplication. */ halve: return arg(1) % 2 /* % " " integer division. */ isEven: return arg(1) // 2 == 0 /* // " " division remainder.*/ error: say '***error!***' arg(1); exit 13 /*display an error message to terminal.*/</lang> output when the following input is used: 200 0.333
a= 200
b= 0.333
product= 66.6
Ring
<lang ring> x = 17 y = 34 p = 0 while x != 0
if not even(x)
p += y
see "" + x + " " + " " + y + nl
else
see "" + x + " ---" + nl ok
x = halve(x)
y = double(y)
end see " " + " ===" + nl see " " + p
func double n return (n * 2) func halve n return floor(n / 2) func even n return ((n & 1) = 0) </lang> Output:
17 34 8 --- 4 --- 2 --- 1 544 === 578
Ruby
Iterative and recursive implementations here. I've chosen to highlight the example 20*5 which I think is more illustrative. <lang ruby>def halve(x) x/2 end def double(x) x*2 end
- iterative
def ethiopian_multiply(a, b)
product = 0 while a >= 1 p [a, b, a.even? ? "STRIKE" : "KEEP"] if $DEBUG product += b unless a.even? a = halve(a) b = double(b) end product
end
- recursive
def rec_ethiopian_multiply(a, b)
return 0 if a < 1 p [a, b, a.even? ? "STRIKE" : "KEEP"] if $DEBUG (a.even? ? 0 : b) + rec_ethiopian_multiply(halve(a), double(b))
end
$DEBUG = true # $DEBUG also set to true if "-d" option given a, b = 20, 5 puts "#{a} * #{b} = #{ethiopian_multiply(a,b)}"; puts</lang>
- Output:
[20, 5, "STRIKE"] [10, 10, "STRIKE"] [5, 20, "KEEP"] [2, 40, "STRIKE"] [1, 80, "KEEP"] 20 * 5 = 100
A test suite: <lang ruby>require 'test/unit' class EthiopianTests < Test::Unit::TestCase
def test_iter1; assert_equal(578, ethopian_multiply(17,34)); end def test_iter2; assert_equal(100, ethopian_multiply(20,5)); end def test_iter3; assert_equal(5, ethopian_multiply(5,1)); end def test_iter4; assert_equal(5, ethopian_multiply(1,5)); end def test_iter5; assert_equal(0, ethopian_multiply(5,0)); end def test_iter6; assert_equal(0, ethopian_multiply(0,5)); end def test_rec1; assert_equal(578, rec_ethopian_multiply(17,34)); end def test_rec2; assert_equal(100, rec_ethopian_multiply(20,5)); end def test_rec3; assert_equal(5, rec_ethopian_multiply(5,1)); end def test_rec4; assert_equal(5, rec_ethopian_multiply(1,5)); end def test_rec5; assert_equal(0, rec_ethopian_multiply(5,0)); end def test_rec6; assert_equal(0, rec_ethopian_multiply(0,5)); end
end</lang>
Run options: # Running tests: ............ Finished tests in 0.014001s, 857.0816 tests/s, 857.0816 assertions/s. 12 tests, 12 assertions, 0 failures, 0 errors, 0 skips ruby -v: ruby 2.0.0p247 (2013-06-27) [i386-mingw32]
Rust
<lang rust>fn double(a: i32) -> i32 {
2*a
}
fn halve(a: i32) -> i32 {
a/2
}
fn is_even(a: i32) -> bool {
a % 2 == 0
}
fn ethiopian_multiplication(mut x: i32, mut y: i32) -> i32 {
let mut sum = 0;
while x >= 1 {
print!("{} \t {}", x, y);
match is_even(x) {
true => println!("\t Not Kept"),
false => {
println!("\t Kept");
sum += y;
}
}
x = halve(x);
y = double(y);
}
sum
}
fn main() {
let output = ethiopian_multiplication(17, 34);
println!("---------------------------------");
println!("\t {}", output);
}</lang>
- Output:
17 34 Kept
8 68 Not Kept
4 136 Not Kept
2 272 Not Kept
1 544 Kept
---------------------------------
578
S_BASIC
<lang basic> $constant true = 0FFFFH $constant false = 0
function half(i = integer) = integer end = i / 2
function twice(i = integer) = integer end = i + i
rem - return true if even, otherwise false function even(i = integer) = integer var k = integer k = 1 rem - only variables are compared bitwise end = ((i and k) = 0)
rem - return i * j, optionally showing steps function ethiopian(i, j, show = integer) = integer
var p = integer
p = 0
while i >= 1 do
begin
if even(i) then
begin
if show then print i;" ---";j
end
else
begin
if show then print i;j
p = p + j
end
i = half(i)
j = twice(j)
end
if show then print " =";
end = p
rem - exercise the function
print ethiopian(17,34,true)
end</lang>
Scala
The first and second are only slightly different and use functional style. The third uses a for loop to yield the result. The fourth uses recursion.
<lang scala> def ethiopian(i:Int, j:Int):Int=
pairIterator(i,j).filter(x=> !isEven(x._1)).map(x=>x._2).foldLeft(0){(x,y)=>x+y}
def ethiopian2(i:Int, j:Int):Int=
pairIterator(i,j).map(x=>if(isEven(x._1)) 0 else x._2).foldLeft(0){(x,y)=>x+y}
def ethiopian3(i:Int, j:Int):Int= {
var res=0; for((h,d) <- pairIterator(i,j) if !isEven(h)) res+=d; res
}
def ethiopian4(i: Int, j: Int): Int = if (i == 1) j else ethiopian(halve(i), double(j)) + (if (isEven(i)) 0 else j)
def isEven(x:Int)=(x&1)==0 def halve(x:Int)=x>>>1 def double(x:Int)=x<<1
// generates pairs of values (halve,double) def pairIterator(x:Int, y:Int)=new Iterator[(Int, Int)] {
var i=(x, y)
def hasNext=i._1>0
def next={val r=i; i=(halve(i._1), double(i._2)); r}
} </lang>
Scheme
In Scheme, even? is a standard procedure.
<lang scheme>(define (halve num)
(quotient num 2))
(define (double num)
(* num 2))
(define (*mul-eth plier plicand acc)
(cond ((zero? plier) acc)
((even? plier) (*mul-eth (halve plier) (double plicand) acc))
(else (*mul-eth (halve plier) (double plicand) (+ acc plicand)))))
(define (mul-eth plier plicand)
(*mul-eth plier plicand 0))
(display (mul-eth 17 34)) (newline)</lang> Output:
578
Seed7
Ethiopian Multiplication is another name for the peasant multiplication:
<lang seed7>const proc: double (inout integer: a) is func
begin a *:= 2; end func;
const proc: halve (inout integer: a) is func
begin a := a div 2; end func;
const func boolean: even (in integer: a) is
return not odd(a);
const func integer: peasantMult (in var integer: a, in var integer: b) is func
result
var integer: result is 0;
begin
while a <> 0 do
if not even(a) then
result +:= b;
end if;
halve(a);
double(b);
end while;
end func;</lang>
Original source (without separate functions for doubling, halving, and checking if a number is even): [2]
Sidef
<lang ruby>func double (n) { n << 1 } func halve (n) { n >> 1 } func isEven (n) { n&1 == 0 }
func ethiopian_mult(a, b) {
var r = 0
while (a > 0) {
r += b if !isEven(a)
a = halve(a)
b = double(b)
}
return r
}
say ethiopian_mult(17, 34)</lang>
- Output:
578
Smalltalk
<lang smalltalk>Number extend [
double [ ^ self * 2 ]
halve [ ^ self // 2 ]
ethiopianMultiplyBy: aNumber withTutor: tutor [
|result multiplier multiplicand|
multiplier := self.
multiplicand := aNumber.
tutor ifTrue: [ ('ethiopian multiplication of %1 and %2' %
{ multiplier. multiplicand }) displayNl ].
result := 0.
[ multiplier >= 1 ]
whileTrue: [
multiplier even ifFalse: [
result := result + multiplicand.
tutor ifTrue: [
('%1, %2 kept' % { multiplier. multiplicand })
displayNl
]
]
ifTrue: [
tutor ifTrue: [
('%1, %2 struck' % { multiplier. multiplicand })
displayNl
]
].
multiplier := multiplier halve.
multiplicand := multiplicand double.
].
^result
]
ethiopianMultiplyBy: aNumber [ ^ self ethiopianMultiplyBy: aNumber withTutor: false ]
].</lang>
<lang smalltalk>(17 ethiopianMultiplyBy: 34 withTutor: true) displayNl.</lang>
SNOBOL4
<lang snobol4> define('halve(num)') :(halve_end) halve eq(num,1) :s(freturn) halve = num / 2 :(return) halve_end
define('double(num)') :(double_end) double double = num * 2 :(return) double_end
define('odd(num)') :(odd_end) odd eq(num,1) :s(return) eq(num,double(halve(num))) :s(freturn)f(return)
odd_end l = trim(input) r = trim(input) s = 0 next s = odd(l) s + r r = double(r) l = halve(l) :s(next) stop output = s end</lang>
SNUSP
<lang snusp> /==!/==atoi==@@@-@-----#
| | /-\ /recurse\ #/?\ zero
$>,@/>,@/?\<=zero=!\?/<=print==!\@\>?!\@/<@\.!\-/
< @ # | \=/ \=itoa=@@@+@+++++#
/==\ \===?!/===-?\>>+# halve ! /+ !/+ !/+ !/+ \ mod10
- ! @ | #>>\?-<+>/ /<+> -\!?-\!?-\!?-\!?-\!
/-<+>\ > ? />+<<++>-\ \?!\-?!\-?!\-?!\-?!\-?/\ div10 ?down? | \-<<<!\=======?/\ add & # +/! +/! +/! +/! +/ \>+<-/ | \=<<<!/====?\=\ | double ! # | \<++>-/ | | \=======\!@>============/!/</lang>
This is possibly the smallest multiply routine so far discovered for SNUSP.
Soar
<lang soar>##########################################
- multiply takes ^left and ^right numbers
- and a ^return-to
sp {multiply*elaborate*initialize
(state^superstate.operator <o>) (<o> ^name multiply ^left <x> ^right <y> ^return-to <r>)
-->
(^name multiply ^left <x> ^right <y> ^return-to <r>)}
sp {multiply*propose*recurse
(state^name multiply ^left <x> > 0 ^right <y> ^return-to <r> -^multiply-done)
-->
(^operator <o> +) (<o> ^name multiply ^left (div <x> 2) ^right (* <y> 2) ^return-to)}
sp {multiply*elaborate*mod
(state^name multiply ^left <x>)
-->
(^left-mod-2 (mod <x> 2))}
sp {multiply*elaborate*recursion-done-even
(state^name multiply ^left <x> ^right <y> ^multiply-done <temp> ^left-mod-2 0)
-->
(^answer <temp>)}
sp {multiply*elaborate*recursion-done-odd
(state^name multiply ^left <x> ^right <y> ^multiply-done <temp> ^left-mod-2 1)
-->
(^answer (+ <temp> <y>))}
sp {multiply*elaborate*zero
(state^name multiply ^left 0)
-->
(^answer 0)}
sp {multiply*elaborate*done
(state^name multiply ^return-to <r> ^answer <a>)
-->
(<r> ^multiply-done <a>)}</lang>
Swift
<lang swift>import Darwin
func ethiopian(var #int1:Int, var #int2:Int) -> Int {
var lhs = [int1], rhs = [int2]
func isEven(#n:Int) -> Bool {return n % 2 == 0}
func double(#n:Int) -> Int {return n * 2}
func halve(#n:Int) -> Int {return n / 2}
while int1 != 1 {
lhs.append(halve(n: int1))
rhs.append(double(n: int2))
int1 = halve(n: int1)
int2 = double(n: int2)
}
var returnInt = 0
for (a,b) in zip(lhs, rhs) {
if (!isEven(n: a)) {
returnInt += b
}
}
return returnInt
}
println(ethiopian(int1: 17, int2: 34))</lang>
- Output:
578
Tcl
<lang tcl># This is how to declare functions - the mathematical entities - as opposed to procedures proc function {name arguments body} {
uplevel 1 [list proc tcl::mathfunc::$name $arguments [list expr $body]]
}
function double n {$n * 2} function halve n {$n / 2} function even n {($n & 1) == 0} function mult {a b} {
$a < 1 ? 0 : even($a) ? [logmult STRUCK] + mult(halve($a), double($b))
: [logmult KEPT] + mult(halve($a), double($b)) + $b }
- Wrapper to set up the logging
proc ethiopianMultiply {a b {tutor false}} {
if {$tutor} {
set wa [expr {[string length $a]+1}] set wb [expr {$wa+[string length $b]-1}] puts stderr "Ethiopian multiplication of $a and $b" interp alias {} logmult {} apply {{wa wb msg} { upvar 1 a a b b puts stderr [format "%*d %*d %s" $wa $a $wb $b $msg] return 0 }} $wa $wb
} else {
proc logmult args {return 0}
}
return [expr {mult($a,$b)}]
}</lang>Demo code:<lang tcl>puts "17 * 34 = [ethiopianMultiply 17 34 true]"</lang>
- Output:
Ethiopian multiplication of 17 and 34 17 34 KEPT 8 68 STRUCK 4 136 STRUCK 2 272 STRUCK 1 544 KEPT 17 * 34 = 578
TUSCRIPT
<lang tuscript> $$ MODE TUSCRIPT ASK "insert number1", nr1="" ASK "insert number2", nr2=""
SET nrs=APPEND(nr1,nr2),size_nrs=SIZE(nrs) IF (size_nrs!=2) ERROR/STOP "insert two numbers" LOOP n=nrs IF (n!='digits') ERROR/STOP n, " is not a digit" ENDLOOP
PRINT "ethopian multiplication of ",nr1," and ",nr2
SET sum=0 SECTION checkifeven SET even=MOD(nr1,2)
IF (even==0) THEN SET action="struck" ELSE SET action="kept" SET sum=APPEND (sum,nr2) ENDIF
SET nr1=CENTER (nr1,+6),nr2=CENTER (nr2,+6),action=CENTER (action,8) PRINT nr1,nr2,action ENDSECTION
SECTION halve_i SET nr1=nr1/2 ENDSECTION
SECTION double_i nr2=nr2*2 ENDSECTION
DO checkifeven
LOOP DO halve_i DO double_i DO checkifeven IF (nr1==1) EXIT ENDLOOP
SET line=REPEAT ("=",20), sum = sum(sum),sum=CENTER (sum,+12) PRINT line PRINT sum
</lang>
- Output:
ethopian multiplication of 17 and 34
17 34 kept
8 68 struck
4 136 struck
2 272 struck
1 544 kept
====================
578
UNIX Shell
Tried with bash --posix, and also with Heirloom's sh. Beware that bash --posix has more features than sh; this script uses only sh features.
<lang bash>halve() {
expr "$1" / 2
}
double() {
expr "$1" \* 2
}
is_even() {
expr "$1" % 2 = 0 >/dev/null
}
ethiopicmult() {
plier=$1 plicand=$2 r=0 while [ "$plier" -ge 1 ]; do
is_even "$plier" || r=`expr $r + "$plicand"` plier=`halve "$plier"` plicand=`double "$plicand"`
done echo $r
}
ethiopicmult 17 34
- => 578</lang>
While breaking if the --posix flag is passed to bash, the following alternative script avoids the *, /, and % operators. It also uses local variables and built-in arithmetic.
<lang bash>halve() {
(( $1 >>= 1 ))
}
double() {
(( $1 <<= 1 ))
}
is_even() {
(( ($1 & 1) == 0 ))
}
multiply() {
local plier=$1 local plicand=$2 local result=0
while (( plier > 0 )) do is_even plier || (( result += plicand )) halve plier double plicand done echo $result
}
multiply 17 34
- => 578</lang>
C Shell
<lang csh>alias halve '@ \!:1 /= 2' alias double '@ \!:1 *= 2' alias is_even '@ \!:1 = ! ( \!:2 % 2 )'
alias multiply eval \set multiply_args=( \!*:q ) \\ @ multiply_plier = $multiply_args[2] \\ @ multiply_plicand = $multiply_args[3] \\ @ multiply_result = 0 \\ while ( $multiply_plier > 0 ) \\ is_even multiply_is_even $multiply_plier \\ if ( ! $multiply_is_even ) then \\ @ multiply_result += $multiply_plicand \\ endif \\ halve multiply_plier \\ double multiply_plicand \\ end \\ @ $multiply_args[1] = $multiply_result \\ '\'
multiply p 17 34 echo $p
- => 578</lang>
Ursala
This solution makes use of the functions odd, double, and half, which respectively check the parity, double a given natural number, or perform truncating division by two. These functions are normally imported from the nat library but defined here explicitly for the sake of completeness.<lang Ursala>odd = ~&ihB double = ~&iNiCB half = ~&itB</lang>The functions above are defined in terms of bit manipulations exploiting the concrete representations of natural numbers. The remaining code treats natural numbers instead as abstract types by way of the library API, and uses the operators for distribution (*-), triangular iteration (|\), and filtering (*~) among others.<lang Ursala>#import nat
emul = sum:-0@rS+ odd@l*~+ ^|(~&,double)|\+ *-^|\~& @iNC ~&h~=0->tx :^/half@h ~&</lang>test program:<lang Ursala>#cast %n
test = emul(34,17)</lang>
- Output:
578
VBA
Define three named functions :
- one to halve an integer,
- one to double an integer, and
- one to state if an integer is even.
<lang vb>Private Function lngHalve(Nb As Long) As Long
lngHalve = Nb / 2
End Function
Private Function lngDouble(Nb As Long) As Long
lngDouble = Nb * 2
End Function
Private Function IsEven(Nb As Long) As Boolean
IsEven = (Nb Mod 2 = 0)
End Function</lang> Use these functions to create a function that does Ethiopian multiplication. The first function below is a non optimized function : <lang vb>Private Function Ethiopian_Multiplication_Non_Optimized(First As Long, Second As Long) As Long Dim Left_Hand_Column As New Collection, Right_Hand_Column As New Collection, i As Long, temp As Long
'Take two numbers to be multiplied and write them down at the top of two columns.
Left_Hand_Column.Add First, CStr(First) Right_Hand_Column.Add Second, CStr(Second)
'In the left-hand column repeatedly halve the last number, discarding any remainders,
'and write the result below the last in the same column, until you write a value of 1.
Do
First = lngHalve(First)
Left_Hand_Column.Add First, CStr(First)
Loop While First > 1
'In the right-hand column repeatedly double the last number and write the result below.
'stop when you add a result in the same row as where the left hand column shows 1.
For i = 2 To Left_Hand_Column.Count
Second = lngDouble(Second)
Right_Hand_Column.Add Second, CStr(Second)
Next
'Examine the table produced and discard any row where the value in the left column is even.
For i = Left_Hand_Column.Count To 1 Step -1
If IsEven(Left_Hand_Column(i)) Then Right_Hand_Column.Remove CStr(Right_Hand_Column(i))
Next
'Sum the values in the right-hand column that remain to produce the result of multiplying
'the original two numbers together
For i = 1 To Right_Hand_Column.Count
temp = temp + Right_Hand_Column(i)
Next
Ethiopian_Multiplication_Non_Optimized = temp
End Function</lang> This one is better : <lang vb>Private Function Ethiopian_Multiplication(First As Long, Second As Long) As Long
Do
If Not IsEven(First) Then Mult_Eth = Mult_Eth + Second
First = lngHalve(First)
Second = lngDouble(Second)
Loop While First >= 1
Ethiopian_Multiplication = Mult_Eth
End Function</lang> Then you can call one of these functions like this : <lang vb>Sub Main_Ethiopian() Dim result As Long
result = Ethiopian_Multiplication(17, 34) ' or : 'result = Ethiopian_Multiplication_Non_Optimized(17, 34) Debug.Print result
End Sub</lang>
VBScript
Nowhere near as optimal a solution as the Ada. Yes, it could have made as optimal, but the long way seemed more interesting.
Demonstrates a List class. The .recall and .replace methods have bounds checking but the code does not test for the exception that would be raised. List class extends the storage allocated for the list when the occupation of the list goes beyond the original allocation.
option explicit makes sure that all variables are declared.
Implementation<lang vb>option explicit
class List private theList private nOccupiable private nTop
sub class_initialize nTop = 0 nOccupiable = 100 redim theList( nOccupiable ) end sub
public sub store( x ) if nTop >= nOccupiable then nOccupiable = nOccupiable + 100 redim preserve theList( nOccupiable ) end if theList( nTop ) = x nTop = nTop + 1 end sub
public function recall( n ) if n >= 0 and n <= nOccupiable then recall = theList( n ) else err.raise vbObjectError + 1000,,"Recall bounds error" end if end function
public sub replace( n, x ) if n >= 0 and n <= nOccupiable then theList( n ) = x else err.raise vbObjectError + 1001,,"Replace bounds error" end if end sub
public property get listCount listCount = nTop end property
end class
function halve( n ) halve = int( n / 2 ) end function
function twice( n ) twice = int( n * 2 ) end function
function iseven( n ) iseven = ( ( n mod 2 ) = 0 ) end function
function multiply( n1, n2 )
dim LL
set LL = new List
dim RR set RR = new List
LL.store n1 RR.store n2
do while n1 <> 1 n1 = halve( n1 ) LL.store n1 n2 = twice( n2 ) RR.store n2 loop
dim i for i = 0 to LL.listCount if iseven( LL.recall( i ) ) then RR.replace i, 0 end if next
dim total total = 0 for i = 0 to RR.listCount total = total + RR.recall( i ) next
multiply = total end function </lang>Invocation<lang vb> wscript.echo multiply(17,34)
</lang>
- Output:
578
x86 Assembly
, linking with the C standard library and start code.
<lang asm> extern printf global main
section .text
halve shr ebx, 1 ret
double shl ebx, 1 ret
iseven and ebx, 1 cmp ebx, 0 ret ; ret preserves flags
main push 1 ; tutor = true push 34 ; 2nd operand push 17 ; 1st operand call ethiopicmult add esp, 12
push eax ; result of 17*34 push fmt call printf add esp, 8
ret
%define plier 8
%define plicand 12
%define tutor 16
ethiopicmult enter 0, 0 cmp dword [ebp + tutor], 0 je .notut0 push dword [ebp + plicand] push dword [ebp + plier] push preamblefmt call printf add esp, 12 .notut0
xor eax, eax ; eax -> result mov ecx, [ebp + plier] ; ecx -> plier mov edx, [ebp + plicand] ; edx -> plicand
.whileloop cmp ecx, 1 jl .multend cmp dword [ebp + tutor], 0 je .notut1 call tutorme .notut1 mov ebx, ecx call iseven je .iseven add eax, edx ; result += plicand .iseven mov ebx, ecx ; plier >>= 1 call halve mov ecx, ebx
mov ebx, edx ; plicand <<= 1 call double mov edx, ebx
jmp .whileloop .multend leave ret
tutorme
push eax
push strucktxt
mov ebx, ecx
call iseven
je .nostruck
mov dword [esp], kepttxt
.nostruck
push edx
push ecx
push tutorfmt
call printf
add esp, 4
pop ecx
pop edx
add esp, 4
pop eax
ret
section .data
fmt db "%d", 10, 0 preamblefmt db "ethiopic multiplication of %d and %d", 10, 0 tutorfmt db "%4d %6d %s", 10, 0 strucktxt db "struck", 0 kepttxt db "kept", 0</lang>
Smaller version
Using old style 16 bit registers created in debug
The functions to halve double and even are coded inline. To half a value
shr,1
to double a value
shl,1
to test if the value is even
<lang asm>test,01 jz Even Odd: Even:</lang><lang asm>;calling program
1BDC:0100 6A11 PUSH 11 ;17 Put operands on the stack 1BDC:0102 6A22 PUSH 22 ;34 1BDC:0104 E80900 CALL 0110 ; call the mulitplcation routine
- putting some space in, (not needed)
1BDC:0107 90 NOP 1BDC:0108 90 NOP 1BDC:0109 90 NOP 1BDC:010A 90 NOP 1BDC:010B 90 NOP 1BDC:010C 90 NOP 1BDC:010D 90 NOP 1BDC:010E 90 NOP 1BDC:010F 90 NOP
- mulitplication routine starts here
1BDC:0110 89E5 MOV BP,SP ; prepare to get operands off stack 1BDC:0112 8B4E02 MOV CX,[BP+02] ; Get the first operand 1BDC:0115 8B5E04 MOV BX,[BP+04] ; get the second oerand 1BDC:0118 31C0 XOR AX,AX ; zero out the result 1BDC:011A F7C10100 TEST CX,0001 ; are we odd 1BDC:011E 7402 JZ 0122 ; no skip the next instruction 1BDC:0120 01D8 ADD AX,BX ; we are odd so add to the result 1BDC:0122 D1E3 SHL BX,1 ; multiply by 2 1BDC:0124 D1E9 SHR CX,1 ; divide by 2 (if zr flag is set, we are done) 1BDC:0126 75F2 JNZ 011A ; cx not 0, go back and do it again 1BDC:0128 C3 RET ; return with the result in AX
- pretty small, just 24 bytes </lang>
XPL0
<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations
func Halve(N); \Return half of N int N; return N>>1;
func Double(N); \Return N doubled int N; return N<<1;
func IsEven(N); \Return 'true' if N is an even number int N; return (N&1)=0;
func EthiopianMul(A, B); \Multiply A times B using Ethiopian method int A, B; int I, J, S, Left(100), Right(100); [Left(0):= A; Right(0):= B; \1. write numbers to be multiplied I:= 1; \2. repeatedly halve number on left repeat A:= Halve(A);
Left(I):= A; I:= I+1;
until A=1; J:= 1; \3. repeatedly double number on right repeat B:= Double(B);
Right(J):= B; J:= J+1;
until J=I; \stop where left column = 1 for J:= 0 to I-1 do \4. discard right value if left is even
if IsEven(Left(J)) then Right(J):= 0;
S:= 0; \5. sum remaining values on right for J:= 0 to I-1 do
S:= S + Right(J);
for J:= 0 to I-1 do \show this insanity
[IntOut(0, Left(J)); ChOut(0, 9\tab\); IntOut(0, Right(J)); CrLf(0)];
Text(0, " -------- "); return S; \sum = product ];
int Product; [Product:= EthiopianMul(17, 34); ChOut(0, 9); IntOut(0, Product); CrLf(0); CrLf(0); Product:= EthiopianMul(1234, 5678); ChOut(0, 9); IntOut(0, Product); CrLf(0);
]</lang>
- Output:
17 34
8 0
4 0
2 0
1 544
--------
578
1234 0
617 11356
308 0
154 0
77 90848
38 0
19 363392
9 726784
4 0
2 0
1 5814272
--------
7006652zkl
Trying to duplicate the task as stated, using columns. isEven is a integer method. <lang zkl>fcn ethiopianMultiply(l,r){ // l is a non-negative integer
halve :=fcn(n){ n/2 };
double :=fcn(n){ n+n };
lr:=List(T(l,r)); // ( (l,r) .. (1,r*n) )
while(l>1){ lr.write( T(l=halve(l),r=double(r)) ) }
lr.filter(fcn([(l,r)]){ (not l.isEven) }); // strike out even left rows
.reduce(fcn(sum,[(l,r)]){ sum + r },0); // sum right column
}</lang> <lang zkl>foreach l,r in ( T(T(17,34),T(34,1),T(34,2),T(34,0)) ){
println(ethiopianMultiply(l,r)," ",ethiopianMultiply(r,l));
}</lang>
- Output:
578 578 34 34 68 68 0 0
ZX Spectrum Basic
<lang zxbasic>10 DEF FN e(a)=a-INT (a/2)*2-1 20 DEF FN h(a)=INT (a/2) 30 DEF FN d(a)=2*a 40 LET x=17: LET y=34: LET tot=0 50 IF x<1 THEN GO TO 100 60 PRINT x;TAB (4); 70 IF FN e(x)=0 THEN LET tot=tot+y: PRINT y: GO TO 90 80 PRINT "---" 90 LET x=FN h(x): LET y=FN d(y): GO TO 50 100 PRINT TAB (4);"===",TAB (4);tot</lang>
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