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Re: n00b confusion regarding the implementation vs. specification of *

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On 3/20/2017 4:53 AM, Andrew Haley wrote:
> rickman <gnuarm@gmail.com> wrote:
>> On 3/19/2017 2:58 PM, Andrew Haley wrote:
>>>
>>> In two's complement representation, for every pair of arguments,
>>> signed or unsigned, the resulting bit pattern is correct when
>>> interpreted as either signed or unsigned.  This follows because signed
>>> and unsigned addition don't need special handling, and multiplication
>>> is no more than repeated addition.
>>
>> Try it sometime.  A multiplication routine doing shift and add of the
>> multiplicand using the bits in the multiplier as enable flags does not
>> work for a negative multiplier.  If your statement were correct, it
>> should work regardless.  Instead the multiplier has to be negated along
>> with the result.
>
> Please provide an example of a pair of numbers which demonstrates
> this.

Any non-trivial negative number for a multiplier.  Try it, you'll see. 
I wracked my brain trying to figure out a way to adjust the result to 
make it work.  After all, negative numbers just have the sign bit 
different, right?  Good luck!

Albert, indicated that multiply works the same for unsigned and signed 
numbers as long as the unsigned numbers don't overflow.  However if you 
do a signed multiply using an unsigned number with the msb set, that 
screws it up.  This is true even if the result is double precision.  So 
you can't do an unsigned multiply on signed numbers in the general case.

   0101  (5)  multiplicand
x 1010  (-6) multiplier

Here is each step
Multiplier  Product
1010        0000 0000
    ^--- zero, so don't add multiplicand and shift

0101        0010 1000
    ^--- one, so add multiplicand and shift

0010        0001 0100
    ^--- zero, so don't add multiplicand and shift

0001        0011 0010
    ^--- one, so add multiplicand and shift

Result is 0x32 or 50.


Negate first...

Multiplier  Product
0110        0000 0000
    ^--- zero, so don't add multiplicand and shift

0011        0010 1000
    ^--- one, so add multiplicand and shift

0001        0011 1100
    ^--- one, so add multiplicand and shift

0000        0001 1110
    ^--- zero, so don't add multiplicand and shift

Negate product
0001 1110   -->  1110 0010

Result is 0xE2 or -30.


Using the same binary numbers, but treating them as all unsigned gets 
the opposite results.  The -6 is now a 10.  The unsigned multiply gives 
the right result, 50 and the signed multiply gives 226, a wrong result.

I've read that Booth's algorithm works for both signed and unsigned 
numbers, but I don't know if they have to be handled differently.

-- 

Rick C

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n00b confusion regarding the implementation vs. specification of * Michael Barry <barrym95838@yahoo.com> - 2017-03-19 10:41 -0700
  Re: n00b confusion regarding the implementation vs. specification of * Andrew Haley <andrew29@littlepinkcloud.invalid> - 2017-03-19 13:58 -0500
    Re: n00b confusion regarding the implementation vs. specification of * rickman <gnuarm@gmail.com> - 2017-03-19 19:06 -0400
      Re: n00b confusion regarding the implementation vs. specification of * Andrew Haley <andrew29@littlepinkcloud.invalid> - 2017-03-20 03:53 -0500
        Re: n00b confusion regarding the implementation vs. specification of * rickman <gnuarm@gmail.com> - 2017-03-20 06:56 -0400
          Re: n00b confusion regarding the implementation vs. specification of * Andrew Haley <andrew29@littlepinkcloud.invalid> - 2017-03-20 07:53 -0500
            Re: n00b confusion regarding the implementation vs. specification of * rickman <gnuarm@gmail.com> - 2017-03-20 18:15 -0400
              Re: n00b confusion regarding the implementation vs. specification of * Coos Haak <htrofhc@gmail.com> - 2017-03-20 23:30 +0100
              Re: n00b confusion regarding the implementation vs. specification of * julian.fondren@endurance.com - 2017-03-20 15:34 -0700
              Re: n00b confusion regarding the implementation vs. specification of * "Elizabeth D. Rather" <erather@forth.com> - 2017-03-20 14:40 -1000
                Re: n00b confusion regarding the implementation vs. specification of * hughaguilar96@gmail.com - 2017-03-20 19:41 -0700
                Re: n00b confusion regarding the implementation vs. specification of * anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2017-03-21 17:18 +0000
          Re: n00b confusion regarding the implementation vs. specification of * anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2017-03-20 15:07 +0000
  Re: n00b confusion regarding the implementation vs. specification of * hughaguilar96@gmail.com - 2017-03-19 12:32 -0700
    Re: n00b confusion regarding the implementation vs. specification of * hughaguilar96@gmail.com - 2017-03-19 13:54 -0700
  Re: n00b confusion regarding the implementation vs. specification of * albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-03-19 21:21 +0100
    Re: n00b confusion regarding the implementation vs. specification of * Michael Barry <barrym95838@yahoo.com> - 2017-03-19 16:41 -0700
      Re: n00b confusion regarding the implementation vs. specification of * anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2017-03-21 17:56 +0000
  Re: n00b confusion regarding the implementation vs. specification of * anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2017-03-20 08:57 +0000

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