Is there a way to get the size of an integer (really fast, like a macro getting the number of words)? One could perhaps override _strassen_default_cutoff (though I don't know how much overhead this would be for matrices with smallish entries).
One can always enforce it by doing M._multiply_strassen(N) For huge Z, I wonder if it's still trying to do multi-modular? That would probably be bad. I'm also not sure how much of the dispatching is done in Linbox vs. Sage. - Robert On Oct 23, 2007, at 6:17 PM, David Harvey wrote: > > Hi, > > I'm interested in multiplying smallish matrices over Z with huge > entries. > > On my machine, sage can multiply 3000000-bit integers in about 0.14s, > and adding integers of that size takes about 1/1000 of the time: > > sage: x = ZZ.random_element(2^3000000) > sage: y = ZZ.random_element(2^3000000) > sage: timeit z = x * y > 10 loops, best of 3: 141 ms per loop > sage: timeit z = x + y > 10000 loops, best of 3: 152 µs per loop > > So clearly for matrix multiply, we want to Strassen all the way to > the bottom. > > But look at this: > > sage: M1 = matrix(8, 8, [ZZ.random_element(2^3000000) for i in range > (64)]) > sage: M2 = matrix(8, 8, [ZZ.random_element(2^3000000) for i in range > (64)]) > sage: time M3 = M1 * M2 > CPU times: user 69.43 s, sys: 2.29 s, total: 71.72 s > Wall time: 71.76 > > By my reckoning, it should only have to do 7*7*7 multiplies, which > should take < 50s. It looks like it's really doing 8*8*8 multiplies. > > david > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
