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Added implementation of "Compute parity in parallel" #1

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20 changes: 19 additions & 1 deletion README.md
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Expand Up @@ -235,7 +235,25 @@ Note that 0 is incorrectly considered a power of 2 here. To remedy this, use:
### Compute parity by lookup table
### Compute parity of a byte using 64-bit multiply and modulus division
### Compute parity of word with a multiply

### Compute parity in parallel

```python
>>> v ^= v >> 16
>>> v ^= v >> 8
>>> v ^= v >> 4
>>> v &= 0xf
>>> even_parity = (0x6996 >> v) & 1
```

The method above takes around 9 operations, and works for 32-bit words. It may be optimized to work just on bytes in 5 operations by removing the first two lines.

The method first shifts and XORs the eight nibbles of the 32-bit value together, leaving the result in the lowest nibble of v. Next, the binary number `0110 1001 1001 0110` (`0x6996` in hex) is shifted to the right by the value represented in the lowest nibble of v. This number is like a miniature 16-bit parity-table indexed by the low four bits in v. The result has the parity of `v` in bit 1, which is masked and returned.

Thanks to Mathew Hendry for pointing out the shift-lookup idea at the end on Dec. 15, 2002. That optimization shaves two operations off using only shifting and XORing to find the parity.

> If you want "odd parity", you can change the last line to `odd_parity = 1 - (0x6996 >> v) & 1`

## Swapping Values
### Swapping values with subtraction and addition
### Swapping values with XOR
Expand Down Expand Up @@ -288,4 +306,4 @@ Please take a minute to go over the [Contribution Guidelines](CONTRIBUTING.md).

Contributions are welcome!
* [Issue reports](https://github.com/ianbrayoni/bithacks/issues)
* [Pull Requests](https://github.com/ianbrayoni/bithacks/pulls)
* [Pull Requests](https://github.com/ianbrayoni/bithacks/pulls)