Re: [PATCHv2 1/3] lib: vsprintf: optimised put_dec_trunc() and put_dec_full()

[Michal Nazarewicz]

Denys Vlasenko <vda.linux@xxxxxxxxxxxxxx> writes:

> 2010/8/10 MichaÅ Nazarewicz <m.nazarewicz@xxxxxxxxxxx>:
>>> On Sunday 08 August 2010 21:29, Michal Nazarewicz wrote:
>>>>
>>>> + Â Â Â /*
>>>> + Â Â Â Â* '(x * 0xcccd) >> 19' is an approximation of 'x / 10' that
>>>> + Â Â Â Â* gives correct results for all x < 81920. ÂHowever, because
>>>> + Â Â Â Â* intermediate result can be at most 32-bit we limit x to be
>>>> + Â Â Â Â* 16-bit.
>>>> + Â Â Â Â*
>>>> + Â Â Â Â* Because of those, we check if we are dealing with a "big"
>>>> + Â Â Â Â* number and if so, we make it smaller remembering to add to
>>>> + Â Â Â Â* the most significant digit.
>>>> + Â Â Â Â*/
>>>> + Â Â Â if (q >= 50000) {
>>>> + Â Â Â Â Â Â Â a Â= '5';
>>>> + Â Â Â Â Â Â Â q -= 50000;
>>>
>>> ...
>>>>
>>>> + Â Â Â /*
>>>> + Â Â Â Â* We need to check if q is < 65536 so we might as well check
>>
>> On Tue, 10 Aug 2010 05:17:48 +0200, Denys Vlasenko
>> <vda.linux@xxxxxxxxxxxxxx> wrote:
>>>
>>> You meant "need to check if q is < 81920"?
>>
>> No. Â81920 is a 17 bit number and when we multiply it by 0xcccd we lose
>> the most significant bit.
>>  Therefore we cannot use the '(x * 0xcccd) >>
>> 19' approximation for numbers which are higher then 65535.
>
> No. All x up to (exclusive) 81920 can be multiplied by 0xcccd
> and result still fits into 32 bits. Proof:
>
> # printf "%x\n" $((81919 * 0xcccd))
> ffff7333

Turns out something else was a problem ((x * 13) >> 7 works for x <
69).  I'll update comments in the next version.

-- 
Best regards,                                         _     _
 .o. | Liege of Serenly Enlightened Majesty of      o' \,=./ `o
 ..o | Computer Science,  Michal "mina86" Nazarewicz   (o o)
 ooo +--<mina86-tlen.pl>--<jid:mina86-jabber.org>--ooO--(_)--Ooo--
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