PPS come to think of it, my last PS explains it all. So in summary: -- ZZ= always arbitrary precision. -- int= a C int when the numbers stay < 2^64, so there is an increase of speed -- but not nearly as much of an increase as I expected, which is why I was confused at first, because I wasn't seeing this for what it was. Also, computations start using "long" when the numbers are big, so you don't see the overflow, and you don't always see the increase in speed. -- numpy.int32 or int.64: like "int" initially, but works mod 2^32 or 2^64, and gives an overflow warning when it happens. No increase in speed, for general reasons which I will just call "overhead" for lack of a better understanding. (Still good for numpy functions, obviously).
2016-12-04 9:11 GMT-05:00 Pierre <pierre.guil...@gmail.com>: > PS actually, i am a little wrong with Python ints being arbitrary precision. > In fact there is no such thing as just a python int, there is "int" and > "long", but computations with ints can give you an answer which is "long"; > presumably this mostly means that everything is as slow as if everything was > always a "long". Well, i don't really know, and I wish I did. > > > On Sunday, December 4, 2016 at 8:47:12 AM UTC-5, Pierre wrote: >> >> Hi all, >> >> Thanks for your answers. There are a few things that I now understand, but >> i'm still confused. One crucial mistake I made was, as I see now thanks to >> Ralf's message, to believe that numpy.int meant "C int": no, it means python >> int ! For C ints, use numpy.int32 (or 64). In fact : >> >> sage: numpy.int(2) ^ numpy.int(32) >> 4294967296 >> >> sage: numpy.int(2) ^ numpy.int(64) >> 18446744073709551616L #notice the L, typical of python ints >> >> sage: numpy.int32(2) ^ numpy.int32(32) >> /Applications/SageMath/src/bin/sage-ipython:1: RuntimeWarning: overflow >> encountered in int_scalars >> #!/usr/bin/env python >> 0 >> >> >> All as expected. And to answer Simon's interrogation, if I'm correct a >> python int is actually arbitrary precision (and it prints with an L when >> above 2^64), but it's slower than ZZ. It's not a C int. >> >> However, i've been playing with Simon's code for testing (nice idea!), and >> i'm still puzzled: >> >> sage: %time testfunc(ZZ(1234123), ZZ(1234123), operator.add) >> CPU times: user 69.3 ms, sys: 787 µs, total: 70.1 ms >> Wall time: 70.8 ms >> >> sage: %time testfunc(int(1234123), int(1234123), operator.add) >> CPU times: user 42.3 ms, sys: 631 µs, total: 42.9 ms >> Wall time: 43.5 ms >> >> sage: %time testfunc(numpy.int(1234123), numpy.int(1234123), operator.add) >> CPU times: user 44 ms, sys: 538 µs, total: 44.5 ms >> Wall time: 45 ms >> >> sage: %time testfunc(numpy.int32(1234123), numpy.int32(1234123), >> operator.add) >> CPU times: user 74.2 ms, sys: 822 µs, total: 75 ms >> Wall time: 77.7 ms >> >> So ZZ is slightly slower than python int = numpy.int, which is already >> weird since the arbitrary precision integers of ZZ are meant to faster than >> those of python. >> >> But even more bizarre is the fact that numpy.int32 gives the slowest >> performance! i'm guessing that the operator.add includes overhead when >> asking numpy to add its ints. >> >> Question: Is there a way of using very fast C integers within Sage, >> without using Cython? (the latter because the answer is meant to be >> understandable by beginners). >> >> If I figure this out, I guess the analogous question with floats will be >> answered, too. >> >> Thanks ! >> >> Pierre >> >> >> >> >> >> >> > > -- > You received this message because you are subscribed to a topic in the > Google Groups "sage-devel" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sage-devel/HNX5rHzuBc8/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. -- Pierre 06 06 40 72 28 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
