Ethiopian multiplication

Ethiopian multiplication
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 x 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    -- 
        4   --- 
        2   --- 
        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 functions/methods/procedures/subroutines: to half an integer; 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

C

<lang c>#include <stdio.h>

1. include <stdbool.h>

void halve(int *x) { *x >>= 1; } void doublit(int *x) { *x <<= 1; } bool iseven(const int x) { return (x%2) == 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>

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
>>> 

Smalltalk

Works with: GNU 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>

Tcl

<lang tcl>proc tcl::mathfunc::double n {expr {$n * 2}} proc tcl::mathfunc::halve n {expr {$n / 2}} proc tcl::mathfunc::even n {expr {($n & 1) == 0}} proc tcl::mathfunc::mult {a b} {expr {

   $a < 1 ? 0 :
   even($a) ? [logmult STRUCK] + mult(halve($a), double($b))

 : [logmult KEPT] + mult(halve($a), double($b)) + $b }}

1. Wrapper to set up the logging

proc ethiopianMultiply {a b {noisy false}} {

   if {$noisy} {

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