Michaelangel007 7a7167ab95
2016-08-19 07:20:29 -07:00

# Russian Peasant Multiplication

From Assembly to Basic to Javascript.

Here are muy 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 algorith to implement multiplication using only:

• bit-shift (left and right), and

Example of "normal" 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)
00000000    (86 * 2^2 =  344)
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
86  57    86
172  28    86
344  14    86
688   7   774
1376   3  2150
2752   1  4902

``````

In Base 2:

``````               A  B         Sum            Sum  = 0
01010110  00111001  00000001010110 Sum += A
010101100  00011100  00000001010110 --
0101011000  00001110  00000001010110 --
01010110000  00000111  00001100000110 Sum += A
010101100000  00000011  00100001100110 Sum += A
0101011000000  00000001  01001100100110 Sum += A
``````