Does anyone want to try for two's-complement multiplication? 2n-bit
product from n-bit factors, no use of hc or hcinv except to provide data
and check answers?
On 12/11/2011 10:43 PM, Kip Murray wrote:
> Below I present tcpl "two's-complement plus". It works with the
> transpose of the arrangement below for adding two's-complement numbers:
>
> 1 1 0 0 (value _4)
> 1 1 0 1 (value _3)
> -------
> 1 1 0 0 (carries shifted to the right)
> 1 0 0 1 (answer, value _7)
>
> Working above from right to left, you say 0 plus 1 is 0 1 and write 0 1
> vertically below the line. Next you say 0 plus 0 plus 0 is 0 0 (the
> first 0 is the carry from the preceding step) and write 0 0 vertically
> below the line. Continuing, you say 0 plus 1 plus 1 is 1 0 and 1 plus 1
> plus 1 is 1 1 . The answer 1 0 0 1 is in the bottom line.
>
> hc =: {.@#:@(,: 2 * |) NB. Raul's improved #: (hash colon)
>
> hcinv =: ([: -/ [: #. (,: [: +: 1 {. ]))"1 NB. Henry Rich
>
> Table =: 2 2 2 2 $ 0 0,0 1,0 1,1 0,0 1,1 0,1 0,1 1
>
> (< 1 1 1) { Table NB. sum of three bits
> 1 1
>
> stack =: ,.&.|: NB. stacks x over y
>
> hv =: (0 {::<"1) :: ] NB. returns head vector
>
> op =: ] stack~ (2 {. [) , Table {~ [:< (2 {. [) , 2 { [: hv ]
>
> ba =: 0 ,~ 0 ,.~ 0 ,.~ ,. NB. build argument
>
> 1 1 0 0 ba 1 1 0 1 NB. starting table
> 1 1 0 0
> 1 1 0 0
> 0 0 0 0
> 0 1 0 0
> 0 0 0 0
>
> op/ 1 1 0 0 ba 1 1 0 1
> 1 1 1 1
> 1 1 1 0
> 0 0 0 0
> 0 1 0 1
> 0 0 0 0
>
> NB. above see transpose of arrangement at top, with an added
> NB. row of 0's
>
> tcpl =: [: }: [: {:"1 [: op/ ba NB. two's-complement plus
>
> 1 1 0 0 tcpl 1 1 0 1 NB. _4 plus _3 is _7
> 1 0 0 1
>
> hc _4 _3 _7
> 1 1 0 0
> 1 1 0 1
> 1 0 0 1
>
> On 12/10/2011 6:48 PM, Kip Murray wrote:
>> Cool. I think it is an improvement because it neatly avoids a case
>> statement. Now I wonder if we could implement two's-complement addition
>> and multiplication with overflow, basing these on bitwise operations
>>
>> 0 + 0 is 0, 0 + 1 is 1 + 0 is 1, and 1 + 1 is 1 0
>>
>> 0 * 0 is 0 * 1 is 1 * 0 is 0, and 1*1 is 1
>>
>> That is, I do not want hc and hcinv to be used except to produce data
>> and check answers, and I want n-bit two's-complement answers for n-bit
>> two's-complement data so some of them will be wrong because of overflow.
>
> ADDED LATER -- ACCEPT 2n-bit multiplication answers from n-bit data
>
>>
>> Here for Linda is Henry's hcinv expressed without conjunctions other
>> than " .
>>
>> hcinv =: ([: -/ [: #. (,: [: +: 1 {. ]))"1
>>
>> On 12/10/2011 10:00 AM, Henry Rich wrote:
>>> Same idea, better implementation
>>>
>>> hcinv =. -/@:#.@:(,: +:@(1&{.))"1
>>>
>>> Henry Rich
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
