#5130: [with patch; positive review] create a prime_pi function that doesn't 
just
compute len(prime_range(n))
---------------------------+------------------------------------------------
 Reporter:  was            |       Owner:  was     
     Type:  defect         |      Status:  new     
 Priority:  major          |   Milestone:  sage-4.0
Component:  number theory  |    Keywords:          
---------------------------+------------------------------------------------

Comment(by mabshoff):

 Well, I am not too happy that there are special long long sqrt() work
 around function in this file. Since the code is by Bill I think they
 should be somewhat reliable and they seems to detect numerical precision
 issues, but I still do not trust them to work reliably, i.e. Sparc.

 Anyway, I would like them to be moved to its own file and I would like to
 see a test that compares and verifies their output for a wide range of
 inputs against MPFR for example. Even nicer would be the ability to switch
 away from this function and use MPFR functionality in its place. This is
 not something that will prevent this code from going in unless the current
 doctests will get broken on something like Sparc/Solaris where I have
 detected problems with the number_of_partitions() test that also relies on
 some sqrtl() function.

 Cheers,

 Michael

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5130#comment:18>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of 
Reinventing the Wheel

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