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Russian Peasant Multiplication
25 Commits 1 Branch 0 Tags 69 KiB
Assembly 69.6%
JavaScript 22.8%
BASIC 6.1%
Shell 1.1%
C 0.4%
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michaelangel007 b28f22aa7a Point out why standard multiplication is inefficient for a computer
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README.MD

Russian Peasant Multiplication

From Assembly to Basic to Javascript!

Here are my implementations of Russian Peasant Multiplication implemented in various languages:

  • 6502 Assembly Language (Both ca65 and merlin32 sources)
  • Applesoft BASIC
  • JavaScript (Procedural version)
  • JavaScript (OOP version)

A .dsk image has been provided as an convenience.

To see how much faster the Assembly version is then the BASIC version:

RUN  RPM.BAS
BRUN RPM.BIN

And enter in 123456789 * 987654321 respectively for A and B ...

Version Time
Applesoft 33 s
Assembly ~1 s

So what the heck is it?

An alternative algorithm to implement multiplication using only:

  • bit-shifts (left and right), and
  • addition.

Example of "traditional" multiplication:

In base 10:

             86
           x 57
           ----
            602
           430
           ====
           4902

In base 2:

        01010110  (86)
        00111001  (57)
        --------
        01010110  (86 * 2^0 =   86)
       00000000   (86 * 2^1 =  172) <- wasted work, partial sum = 0
      00000000    (86 * 2^2 =  344) <- wasted work, partial sum = 0
     01010110     (86 * 2^3 =  688)
    01010110      (86 * 2^4 = 1376)
   01010110       (86 * 2^5 = 2752)
  ==============
  01001100100110  (4902 = 86*2^0 + 86*2^3 + 86*2^4 + 86*2^5)

Example of Russian Peasant multiplication:

In Base 10:

               A          B   Sum =    0
              86         57   + A =   86 (b is odd)
      x 2 =  172   / 2 = 28       =   86
      x 2 =  344   / 2 = 14       =   86
      x 2 =  688   / 2 =  7   + A =  774 (b is odd)
      x 2 = 1376   / 2 =  3   + A = 2150 (b is odd)
      x 2 = 2752   / 2 =  1   + A = 4902 (b is odd)

In Base 2:

               A          B   Sum = 0
        01010110   00111001   + A = 00000001010110 (b is odd)
       010101100   00011100       = 00000001010110
      0101011000   00001110       = 00000001010110
     01010110000   00000111   + A = 00001100000110 (b is odd)
    010101100000   00000011   + A = 00100001100110 (b is odd)
   0101011000000   00000001   + A = 01001100100110 (b is odd)