Subject: Re: [PATCH RFC] reciprocal_divide: correction/update of the algorithm

From: Austin S Hemmelgarn <[email-masked]>
Date: Tue, 14 Jan 2014 14:22:23 -0500

On 2014-01-14 13:07, Eric Dumazet wrote:
> On Mon, 2014-01-13 at 22:42 +0100, Hannes Frederic Sowa wrote:
>> This patch is a RFC and part of a series Daniel Borkmann and me want to
>> do when introducing prandom_u32_range{,_ro} and prandom_u32_max{,_ro}
>> helpers later this week.
> 
>> -static inline u32 reciprocal_divide(u32 A, u32 R)
>> +struct reciprocal_value reciprocal_value(u32 d);
>> +
>> +static inline u32 reciprocal_divide(u32 a, struct reciprocal_value R)
>>  {
>> -	return (u32)(((u64)A * R) >> 32);
>> +	u32 t = (u32)(((u64)a * R.m) >> 32);
>> +	return (t + ((a - t) >> R.sh1)) >> R.sh2;
>>  }
> 
> I would rather introduce new helpers and convert users that really need
> them.
> 
> For instance, just use a divide in BPF, because doing this on JIT might
> be too complex for the gains. Strangely, libpcap doesn't seem to
> optimize any divide, like divides by a power of two...
> 
> Reciprocal were added 7 years ago, for very specific uses, but current
> cpus have reasonably fast dividers.

I disagree with the statement that current CPU's have reasonably fast
dividers.  A lot of embedded processors and many low-end x86 CPU's do
not in-fact have any hardware divider, and usually provide it using
microcode based emulation if they provide it at all.  The AMD Jaguar
micro-architecture in particular comes to mind, it uses an iterative
division algorithm provided by the microcode that only produces 2 bits
of quotient per cycle, even in the best case (2 8-bit integers and an
integral 8-bit quotient) this still takes 4 cycles, which is twice as
slow as any other math operation on the same processor.