Here's some timings for exact_log:
In Sage:
def random(n):
a = ZZ.random_element(n)
return a
def z_exact_log_test(m, n, k):
for i in range(0, m) :
a = random(n) + 2
b = random(k)
c = a^b
d = c.exact_log(a)
if b != d:
print "Error", b, "!=", d
time z_exact_log_test(100000, 64, 1000)
4.72s
In Magma:
t:=Cputime();
for i := 0 to 100000 do
a := Random(64) + 2;
b := Random(1000);
c := a^b;
d := Ilog(a,c);
if d ne b then
print "Error";
end if;
end for;
Cputime(t);
0.72s
Bill.
On 8 Apr, 07:17, Bill Hart <goodwillh...@googlemail.com> wrote:
> I've been looking through the methods for ZZ with a view to doing a
> Magma/Sage comparison for marketing purposes. I've been noticing a few
> issues as I go. There's going to be lots of these, so I think I should
> give my list in small blocks. I can file trac tickets for them once
> someone verifies that these are really not just me not knowing enough
> python, or whatever.
>
> ZZ
> ====
>
> Speed Issues:
>
> * n.bits takes much longer than n.binary(), but the latter needs to
> compute the former first!!!
> * n.coprime_integers uses a hopelessly slow algorithm (we should at
> least use a sieve)
> * n.factor is bizarrely slow for small integers (e.g. n < 1,000,000)
> by a HUGE factor
> * n.exact_log can be done faster for small bases by making careful use
> of the identity log_m(n) = log_2(n)/log_2(m) (I wrote a crappy broken
> python implementation and timed this - I don't know how to write it
> properly as I don't know enough about Sage yet)
>
> Missing doc strings:
>
> * n.base_extend
> * n.additive_order
> * n.category
> * n.db (doesn't give an example)
> * n.degree
>
> Missing methods:
>
> * n.euler_phi
> * n.random (random integer less than n - I will believe you if you
> tell me this is not the python way)
>
> Weird names:
>
> * n.divide_knowing_divisible_by (perhaps div_exact, exact_quotient,
> divide_exact would be better)
>
> Documentation issues:
>
> * n.dump says "Same as self.save(filename, compress)", but compress is
> not discussed in save docstring
>
> Bill.
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