Just for everybody edification:
d0=: >:@<....@^. NB. Length to represent y in base x
time =. 6!:2 NB. time in seconds
pow=: 4 : '*/ *~^:(I.|.#:y) x' NB. same as x^y
powGB =: (**:)/@(|....@#:@]{1x,[) NB. same as x^y
time '<: 2x ^ 216091'
7.57745
time '<: 2x pow 216091'
3.86865
time '<: 2x & powGB"0 ] 216091'
3.216
So. for extended numbers, powGB is a little faster than pow
which is about 2 times faster than *
d0 <: 2x ^ 216091
149783
d0 <: 2x pow 216091
149783
d0 <: 2x & powGB"0 ] 216091
149783
All answers have 149783 decimal digits.
aexp =: <: 2x ^ 216091
apow =: <: 2x pow 216091
apowGB =: 2x & powGB"0 ] 216091
aexp = apow
1
apow = apowGB
1
So all the results are the same.
Thanks to everybody for their help.
:-)
----- Original Message Follows -----
From: "Dan Bron" <[email protected]>
To: "'Programming forum'" <[email protected]>
Subject: Re: [Jprogramming] Mersenne Prime initialization.
Date: Fri, 10 Apr 2009 20:26:23 -0400
>Butch Lakeshore wrote:
>> Cut/past what was in your email
>>
>> powGB =: (* *:)/@(|.@|....@#:@] { 1x , [)
>
>You still have two |.s in there. Did you cut/paste the
>first definition (the quoted one) or the second (Bill's)?
>The two |.s look like you took the copied the first, but
>the spacing looks like you copied the second.
>
>Maybe your system, for some reason, duplicates |.@ when
>it's in your copy buffer? I can see no other reason for
>|.@ to be duplicated (assuming you're not doing it by
>hand).
>
>Try taking the definition above, and deleting the leftmost
>|.@ so that you only have one instance of that train, and
>your definition looks byte for byte like this:
>
> powGB =: (* *:)/@(|....@#:@] { 1x , [)
>
>If you put the above in quotes and enter the following
>sentences, you should get identical results:
>
> # ;: 'powGB =: (* *:)/@(|....@#:@] { 1x , [)'
> 19
>
> '|.@' +/@E.&;: 'powGB =: (* *:)/@(|....@#:@] { 1x , [)'
> 1
>
>And, yes, testing reveals this definition is correct:
>
> 2 powGB 11
> 2048
>
> 2 powGB 13
> 8192
>
> 2 (powGB"0 -: ^) i. 100x
> 1
>
>I will be very surprised if it doesn't produce the same
>results on your system, once you have the proper
>definition.
>
>-Dan
>
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