You seem to think that an extended integer is stored as a big binary
number. This is not so.
3!:3 ] 9999x
e1000000
40000000
01000000
00000000
14000000
e1000000
04000000
01000000
01000000
01000000
0f270000 NB. Here is where the value starts
3!:3 ] 10000x
e1000000
40000000
01000000
00000000
14000000
e1000000
04000000
02000000
01000000
02000000
00000000 NB. Here is where the value starts
01000000
3!:3 ] 10001x
e1000000
40000000
01000000
00000000
14000000
e1000000
04000000
02000000
01000000
02000000
01000000 NB. Here is where the value starts
01000000
As you can see, long integers are stored in base-10000 representation.
I don't know why, but I'd guess it makes multiplication faster.
You can create the representation of your data in an array like this and
use 3!:2 to make that a long integer, if you want to build your values
by hand.
Henry Rich
[email protected] wrote:
> initializing a hunk of memory with binary 1s should be very
> fast in machine language.
>
> Anybody have pointers to where I might find a discussion of
> linking in a custom
> made assembler program into J?
>
> Given N equals the number of binary 1's
>
> Vec =: myMersenneInitialization N
>
>
> produces the same thing as:
>
> Vec =: <: 2x^N
>
> thanks
>
>
>
>
> ----- Original Message Follows -----
> From: Aai <[email protected]>
> To: Programming forum <[email protected]>
> Subject: Re: [Jprogramming] Mersenne Prime initialization.
> Date: Wed, 08 Apr 2009 13:55:10 +0200
>
>> Also, it's possible that:
>>
>> #. 110503$1x
>> |out of memory
>> | #.110503$1
>>
>> You can use a folding instead:
>>
>> ([++:@])/ 110503$1x
>> 5219283133417550597608921138394131714748003987...
>>
>> or ignoring the 1s:
>>
>> >:@+:@]/ 110503$1x
>>
>> or with power ^:
>>
>> >:@+:^: (<: 110503) 1x
>> 5219283133417550597608921138394131714748003987...
>>
>>
>> but it's also very slow..
>>
>> ts '([++:@])/ 110503$1x'
>> 16.633282 788352
>>
>> ts '>:@+:^: (110502) 1x'
>> 16.738218 329344
>>
>>
>> Using a specialized exponentiation provides some speed up:
>>
>> powGB=: (**:)/@(|....@#:@]{1x,[) NB. don't know who's
>> brainchild, sorry
>>
>> .. and showing the last 31 digits:
>>
>> ts 'it=:_31{.": <: 2x powGB 110503'
>> 0.633862 296960
>> it
>> 9131999107769951621083465515007
>>
>> Compared to:
>>
>> ts 'it=:_31{.": <: 2x ^ 110503'
>> 1.414242 430912
>> it
>> 9131999107769951621083465515007
>>
>> I didn't try MP39 though (well, just for a while). :-)
>>
>> To obtain MP39 I used Haskell's interpreter GHCi (using the
>> equivalence of ext. prec.: arbitrary prec. integers)
>> showing the last 46 digits from a total of 4053946 digits (
>>> .13466917*10^.2) :
>> *Main> (take 9 &&& (take 9 .drop 4053937)).show . pred $
>> 2^13466917 ("924947738","256259071")
>> (19.89 secs, 155769356 bytes)
>>
>> Check with: http://en.wikipedia.org/wiki/Mersenne_prime
>>
>>
>>
>> Hallo Matthew Brand, je schreef op 08-04-09 09:09:
>>> You can do it like this:
>>> #. N # 1x
>>>
>>> ... but it is *much* slower than doing <: 2x^N
>>>
>>> On Tue, Apr 7, 2009 at 7:39 PM,
>>> <[email protected]> wrote:
>>>> The following are Mersenne Primes 2, 3, 15, 29 and 39
>>>>
>>>> MP2 =: <:2x^3
>>>> MP3 =: <: 2x^5
>>>> MP5 =: <: 2x^13
>>>> MP15 =: <: 2x^1279
>>>> MP29 =: <: 2x^110503
>>>> MP39 =: <: 2x^13466917
>>>>
>>>> As an example <: 2x^3 in binary is 1000 - 1 which is
>>>> binary 111
>>>>
>>>> Any mersenne prime of the form <: 2x^N is "N binary
>>>> 1s"
>>>> It takes a very long time to calculate MP39.
>>>>
>>>> How could I accomplish the same thing by noting that in
>>>> the case of MP39, I need to create an
>>>> extended value that is "13466917 binary 1s"
>>>>
>>>> thanks
>>>>
>>>>
>>>>
>>>>
>>>>
>> -----------------------------------------------------------
>>>> ----------- For information about J forums see
>>>> http://www.jsoftware.com/forums.htm
>>>>
>>>
>>>
>>>
>> --
>> =@@i
>>
>> -----------------------------------------------------------
>> ----------- For information about J forums see
>> http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
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