Apple-2-SW/apple2_russian_peasant_multiplication
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@ -25,3 +25,64 @@ And enter in `123456789` * `987654321` respectively for A and B ...
| 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
* 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
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
```