Ethiopian multiplication: Difference between revisions
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print ethiopian(17, 34) |
print ethiopian(17, 34) |
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}</lang> |
}</lang> |
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=={{header|Bash}}== |
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<lang bash>halve() { |
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local n=$1 |
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echo -n $(( n >> 1 )) |
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} |
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double() { |
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local n=$1 |
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echo -n $(( n << 1 )) |
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} |
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is_even() { |
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local n=$1 |
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[ $(( n & 1 )) -eq 0 ] |
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} |
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multiply() { |
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local plier=$1 |
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local plicand=$2 |
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local result=0 |
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while [ $plier -gt 0 ] |
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do |
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! is_even $plier && (( result += plicand )) |
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plier=$( halve $plier ) |
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plicand=$( double $plicand ) |
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done |
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echo -n $result |
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} |
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echo $( multiply 17 34 )</lang> |
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=={{header|BASIC}}== |
=={{header|BASIC}}== |
||
Revision as of 17:02, 9 June 2010
You are encouraged to solve this task according to the task description, using any language you may know.
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.
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
- A Night Of Numbers - Go Forth And Multiply (Video)
- Ethiopian multiplication
- Russian Peasant Multiplication
- Programming Praxis: Russian Peasant Multiplication
Ada
<lang Ada>package Ethiopian is
function Multiply(Left, Right : Integer) return Integer;
end Ethiopian;</lang> <lang Ada>package body Ethiopian is
function Is_Even(Item : Integer) return Boolean is
begin
return Item mod 2 = 0;
end Is_Even;
function Double(Item : Integer) return Integer is
begin
return Item * 2;
end Double;
function Half(Item : Integer) return Integer is
begin
return Item / 2;
end Half;
function Multiply(Left, Right : Integer) return Integer is
Temp : Integer := 0;
Plier : Integer := Left;
Plicand : Integer := Right;
begin
while Plier >= 1 loop
if not Is_Even(Plier) then
Temp := Temp + Plicand;
end if;
Plier := Half(Plier);
Plicand := Double(Plicand);
end loop;
return Temp;
end Multiply;
end Ethiopian;</lang>
<lang Ada>with Ethiopian; use Ethiopian; with Ada.Text_Io; use Ada.Text_Io;
procedure Ethiopian_Test is
First : Integer := 17; Second : Integer := 34;
begin
Put_Line(Integer'Image(First) & " times " &
Integer'Image(Second) & " = " &
Integer'Image(Multiply(First, Second)));
end Ethiopian_Test;</lang>
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$, ethiopian(17, 34, TRUE)))
)</lang> Output:
ethiopian multiplication of 17 by 34 0017 000034 kept 0008 000068 struck 0004 000136 struck 0002 000272 struck 0001 000544 kept 578
AutoIt
<lang AutoIt> Func Halve($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>
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>
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
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
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++
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>
C#
<lang csharp>static void Main(string[] args) {
EthiopianMultiplication(17, 34); Console.ReadKey();
}
static int Half(int value) {
return value >> 1;
}
static int Double(int value) {
return value << 1;
}
static bool Even(int value) {
return (value % 2) == 0;
}
static void EthopianMultiplication(int lhs, int rhs) {
int total = 0; int col1 = lhs; int col2 = rhs;
while (col1 > 0)
{
Console.WriteLine("{0,4} | {1,4}", col1, col2);
if (!Even(col1))
{
total = total + col2;
}
col1 = Half(col1);
col2 = Double(col2);
}
Console.WriteLine("Total = {0}", total);
}</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
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>
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) {
static int doubleNum(int n) { return n * 2; }
static int halveNum(int n) { return n / 2; }
static bool isEven(int n) { return !(n % 2); }
int result;
while (n1 >= 1) {
if (!isEven(n1))
result += n2;
n1 = halveNum(n1);
n2 = doubleNum(n2);
}
return result;
}
void main() {
printf("17 ethiopian 34 is %d\n", ethiopian(17, 34));
}</lang>
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>
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: [1&]o: [0[@$][$o;![@@\$@+@]?h;!@d;!@]#%\%]m: 17 34m;!. {578}</lang>
Forth
<lang forth>: e* ( x y -- x*y )
dup 0= if nip exit then over 2* over 2/ recurse swap 1 and if + else nip 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
<lang haskell>import Prelude hiding (odd)
halve, double :: Integral a => a -> a halve = (`div` 2) double = (2 *)
odd :: Integral a => a -> Bool odd = (== 1) . (`mod` 2)
ethiopicmult :: Integral a => a -> a -> a ethiopicmult a b = sum $ map snd $ filter (odd . fst) $ zip
(takeWhile (>= 1) $ iterate halve a) (iterate double b)
main = print $ ethiopicmult 17 34 == 17 * 34</lang>
Usage example from the interpreter
*Main> ethiopicmult 17 34 578
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
Icon
<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>
Unicon
This Icon solution works in Unicon.
J
Solution: <lang j>double =: 2&* halve =: %&2 NB. or the primitive -: odd =: 2&|
ethiop =: +/@(odd@] # (double~ <@#)) (1>.<.@halve)^:a:</lang>
Example: <lang j> 17 ethiop 34 578</lang>
Note that double will repeatedly double its right argument if given a repetition count for its left argument:
<lang J> (<5) double 17 17 34 68 136 272</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();
Map <Integer, Integer> columns = new HashMap <Integer, Integer>();
columns.put(first, second);
do{
first = doubleInt(first);
second = halveInt(second);
columns.put(first, second);
}while(first != 1);
int sum = 0;
for(Map.Entry <Integer, Integer> entry : columns.entrySet()){
if(!isEven(entry.getKey())){
sum += entry.getValue();
}
}
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, but can fully * support 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]; } else { break; } }
return sum + b[0];
} }
// eth.mult(17,34) returns 578</lang>
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>
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>
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>
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>
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's 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-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>
Objective-C
Using class methods except for the generic useful function iseven. <lang objc>#import <stdio.h>
- import <objc/Object.h>
BOOL iseven(int x) {
return (x&1) == 0;
}
@interface EthiopicMult : Object + (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() {
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>
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>
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>
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 ethiopicmult (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 $r;
}</lang>
PHP
<lang php><?php function halve($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
PHP - OOP
<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>
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;
plier := half(plier);
plicand := double(plicand);
exit when plier <= 1;
end loop;
temp := temp + plicand;
return temp;
end multiply;
end ethiopian; /
/* example call */ begin
dbms_output.put_line(ethiopian.multiply(17, 34));
end; /</lang>
PowerShell
<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 $temp }
multiplyValues 17 34</lang>
PureBasic
<lang PureBasic>Procedure isEven(x)
ProcedureReturn (x & 1) ! 1
EndProcedure
Procedure halveValue(x)
ProcedureReturn x / 2
EndProcedure
Procedure doubleValue(x)
ProcedureReturn x << 1
EndProcedure
Procedure EthiopianMultiply(x, y)
Protected sum
Print("Ethiopian multiplication of " + Str(x) + " and " + Str(y) + " ... ")
Repeat
If Not isEven(x)
sum + y
EndIf
x = halveValue(x)
y = doubleValue(y)
Until x < 1
PrintN(" equals " + Str(sum))
ProcedureReturn sum
EndProcedure
If OpenConsole()
EthiopianMultiply(17,34) Print(#CRLF$ + #CRLF$ + "Press ENTER to exit") Input() CloseConsole()
EndIf</lang> Sample 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> Sample 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
Python
<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 >>>
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>
R
<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>
Ruby
Iterative and recursive implementations here. I've chosen to highlight the example 20*5 which I think is more illustrative. <lang ruby>def even(x); x.even?; end def halve(x); x/2; end def double(x); x*2; end
- iterative
def ethopian_multiply(a, b)
product = 0 while a >= 1 p [a, b, even(a) ? "STRIKE" : "KEEP"] if $DEBUG product += b if not even(a) a = halve(a) b = double(b) end product
end
- recursive
def rec_ethopian_multiply(a, b)
return 0 if a < 1 p [a, b, even(a) ? "STRIKE" : "KEEP"] if $DEBUG (even(a) ? 0 : b) + rec_ethopian_multiply(halve(a), double(b))
end
$DEBUG = true # $DEBUG also set to true if "-d" option given a, b = 20, 5 puts "#{a} * #{b} = #{ethopian_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>
Loaded suite ethopian Started ............ Finished in 0.001 seconds. 12 tests, 12 assertions, 0 failures, 0 errors
Scala
The first and second are only slightly different and use functional style. The third uses a for loop to yield the result.
<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 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]
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
$>,@/>,@/?\<=zero=!\?/<=print==!\@\>?!\@/<@\.!\-/
< @ # | \=/ \=itoa=@@@+@+++++#
/==\ \===?!/===-?\>>+# halve ! /+ !/+ !/+ !/+ \ mod10
- ! @ | #>>\?-<+>/ /<+> -\!?-\!?-\!?-\!?-\!
/-<+>\ > ? />+<<++>-\ \?!\-?!\-?!\-?!\-?!\-?/\ div10 ?down? | \-<<<!\=======?/\ add & # +/! +/! +/! +/! +/ \>+<-/ | \=<<<!/====?\=\ | double ! # | \<++>-/ | | \=======\!@>============/!/</lang>
This is possibly the smallest multiply routine so far discovered for SNUSP.
Tcl
<lang tcl># This is how to declare functions - the mathematical entities - as opposed to procedures proc function {name arguments body} {
uplevel 1 [list proc tcl::mathfunc::$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
UNIX Shell
(Tried with bash --posix, so it should run in sh too) <lang bash>halve() {
echo $(( $1 / 2 ))
}
double() {
echo $(( $1 * 2 ))
}
iseven() {
echo $(( $1 % 2 == 0 ))
}
ethiopicmult() {
plier=$1 plicand=$2 r=0 while [ $plier -ge 1 ]; do
if [ $(iseven $plier) -eq 0 ]; then r=$(( r + plicand)) fi plier=$(halve $plier) plicand=$(double $plicand)
done echo $r
}
echo $(ethiopicmult 17 34)</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
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
<lang vb> 578 </lang>
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>
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