Re: [boost] [complex] Feedback and Potential Review Manager

Subject: Re: [boost] [complex] Feedback and Potential Review Manager
From: Christopher Kormanyos (e_float_at_[hidden])
Date: 2012-05-02 14:20:10

>> You are doing binary splitting of the exponent.

>> But it looks like you still have a redundant multiplication step
>> that could be removed with a recursive call. In particular, I believe
>> your routine would need 14 multiplications to compute
>> x^255, whereas only 7 would be needed with a recursive call.

> I don't see how it's possible to compute
> x^255 in 7 multiplies.  The best
> I can come up with is 10:
> x^2 = x * x
> x^4 = x^2 * x^2
> x^8 = x^4 * x^4
> x^16 = x^8 * x^8
> x^17 = x^16 * x
> x^34 = x^17 * x^17
> x^51 = x^34 * x^17
> x^102 = x^51 * x^51
> x^204 = x^102 * x^102
> x^255 = x^204 * x^51
> In Christ,
> Steven Watanabe

Thanks. It looks like I was wrong again. I was mostly interested in
the author's potential redundant multiplication---which we did
successfully identify.

I'll try to do better in the future.

Best regards, Chris.