2.1 KiB
2.1 KiB
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 algorithm to implement multiplication using only:
- bit-shift (left and right), and
- addition.
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 = 0
86 57 0 + A = 86 (b is odd)
x 2 = 172 / 2 = 28 86 = 86
x 2 = 344 / 2 = 14 86 = 86
x 2 = 688 / 2 = 7 86 + A = 774 (b is odd)
x 2 = 1376 / 2 = 3 774 + A = 2150 (b is odd)
x 2 = 2752 / 2 = 1 2150 + 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)