[Pixman] [RFC] mmx: add and use expand_4xpacked565

[Bill Spitzak]

Also this original one:

  R8 = ( R5 * 527 + 23 ) >> 6;

produces the same results as the floor(i*255/31.0+.5) result.

I believe almost *all* graphics software will do the bit-shifting math 
and thus the (i*33)>>2 result is the one to use.

Bill Spitzak wrote:
> 
> 
> Søren Sandmann wrote:
>> Søren Sandmann <sandmann at cs.au.dk> writes:
>>
>>>> Given a pixel with only the red component of these values, the results
>>>> are off-by-one.
>>>>
>>>> 0x03 -> 0x19 (0x18)
>>>> 0x07 -> 0x3A (0x39)
>>>> 0x18 -> 0xC5 (0xC6)
>>>> 0x1C -> 0xE6 (0xE7)
>>>>
>>>> (Same for blue, and green has many more cases)
>>>>
>>>> It uses
>>>> R8 = ( R5 * 527 + 23 ) >> 6;
>>>> G8 = ( G6 * 259 + 33 ) >> 6;
>>>> B8 = ( B5 * 527 + 23 ) >> 6;
>>>>
>>>> I don't guess there's a way to tweak this to produce the same results
>>>> we get from expand565, is there?
>>> Maybe I'm missing something, but this certainly produces the correct
>>> result:
>>>
>>>     r8 = (r5 * 8 + r5 / 4) = r5 * (8 + 0.25) = r5 * (32 + 1) / 4 
>>>        = (r5 * 33) >> 2
>>
>> I should maybe expand a bit more on this: Pixman uses bit replication
>> when it goes from lower bit depths to higher ones. That is, a five bit
>> value:
>>
>>         abcdef
>>
>> is expanded to
>>         abcdefabc
>>
>> which corresponds to a left-shifting r5 by 3 and adding r5 right-shifted
>> by 2. This is the computation that is turned into a multiplication and a
>> shift in the formula above.
>>
>> A more correct way to expand would be
>>
>>         floor ((r5 / 31.0) * 255.0 + 0.5)
>>
>> but this is fairly expensive (although it can be done with integer
>> arithmetic and without divisions, and may actually be equivalent to your
>> formula -- I haven't checked).
> 
> for i in range(0,32):
>   print i,int((i*33)/4),int(i*255/31.0+.5)
> 
> 0 0 0
> 1 8 8
> 2 16 16
> 3 24 25 *
> 4 33 33
> 5 41 41
> 6 49 49
> 7 57 58 *
> 8 66 66
> 9 74 74
> 10 82 82
> 11 90 90
> 12 99 99
> 13 107 107
> 14 115 115
> 15 123 123
> 16 132 132
> 17 140 140
> 18 148 148
> 19 156 156
> 20 165 165
> 21 173 173
> 22 181 181
> 23 189 189
> 24 198 197 *
> 25 206 206
> 26 214 214
> 27 222 222
> 28 231 230 *
> 29 239 239
> 30 247 247
> 31 255 255
> 
> Asterix marks the examples where these are unequal.