Russian Peasant Multiplication
michaelangel007 b8902a61ab
2020-02-05 08:48:04 -08:00
2016-08-18 18:21:06 -07:00
2016-08-18 17:43:21 -07:00
2016-08-18 17:42:31 -07:00
2020-02-05 08:48:04 -08:00
2016-08-18 17:42:31 -07:00
2016-08-18 17:42:48 -07:00
2016-08-18 18:20:12 -07:00
2016-08-18 18:20:12 -07:00
2016-08-18 18:21:06 -07:00
2016-08-29 20:19:53 -06:00
2016-08-29 20:19:53 -06:00

# 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

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   B Odd?   Sum =    0
86         57   Yes      + A =   86
x 2 =  172   / 2 = 28   No           =   86
x 2 =  344   / 2 = 14   No           =   86
x 2 =  688   / 2 =  7   Yes      + A =  774
x 2 = 1376   / 2 =  3   Yes      + A = 2150
x 2 = 2752   / 2 =  1   Yes      + A = 4902
``````

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)
``````

In Base 8:

``````                A          B   B Odd?   Sum =     0
126         71   Yes      + A =   126
x 2 =  254   / 2 = 34   No           =   126
x 2 =  530   / 2 = 16   No           =   126
x 2 = 1260   / 2 =  7   Yes      + A =  1406
x 2 = 2540   / 2 =  3   Yes      + A =  4146
x 2 = 5300   / 2 =  1   Yes      + A = 11446
``````

In Base 16:

``````               A          B   B Odd?   Sum =    0
56         39   Yes      + A =   56
x 2 =  AC   / 2 = 1C   No           =   56
x 2 = 158   / 2 =  E   No           =   56
x 2 = 2B0   / 2 =  7   Yes      + A =  306
x 2 = 560   / 2 =  3   Yes      + A =  866
x 2 = AC0   / 2 =  1   Yes      + A = 1326
``````