At 12:23 PM 2/11/00 -0600, you wrote:
>Okay, I was sitting there the other day thinking about a non-FFT squaring
>algorithm...
>
>Say we have 14, which in binary is 1110...
>
>If we left shift this by the position of the 1, for each 1 in the binary
>representation, and add them together, we should get the square... So to
>square 14, we do this:
>1110 << 3 == 1110000 +
>1110 << 2 == 0111000 +
>1110 << 1 == 0011100 +
> == 11000100 which is 196
>
In other words you are saying
14*14 = 14*(8 + 4 + 2) = 14*8 + 14*4 + 14*2
or in base 10
14*14 = 14*(10 + 4) = 14*10 + 14*4
Your logic appears correct, but it appears to be a computer base 2
implementation of what we do longhand in base 10.
You are just taking advantage of the fact that multiplying by 2 is base 2 is
a position shift, just like it is real easy in base 10 for us to take
1234 * 100 = 123400
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