mpn_sqrtrem{1,2}

[Torbjörn Granlund]

"Marco Bodrato" <bodrato at mail.dm.unipi.it> writes:

  But it can be useful on some platform. Say mpn/x86_64 ? or
  mpn/x86_64/fast{sse,avx} ?
  
When it's know to be supported and for CPUs where it is kmown to run
well, sure.

We should never use the old x86 FPU stack with 80-bit FP registers.

  > is not predicatble enough.  Even if we do it just for IEEE 754, we can
  > not control the rounding mode.  That means that e.g., sqrt(2)^2 will be
  > greater that 2 sometimes, less than 2 sometimes.
  
  All the algorithms I see implemented in GMP for sqrt give the wrong result
  sometimes... that's why they all have a final check with possible
  correction by 1. I'm sure that also this "sometimes" can be correctly
  handled :-)
  
Testing needs to involve manipulating the rounding mode if the used
instructions change their behaviour according to such a mode.

It might be worth noticing that some recent CPUs have fast integer
division, using up to 4-bit SRT and early-out, meaning that a 64-bit
division takes from about 4 to about 20 cycles.  There, one might be
able to write basecase code using plain old integer divide.

-- 
Torbjörn
Please encrypt, key id 0xC8601622