#11628: GF() arithmetic slower than IntegerModRing()
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Reporter: zimmerma | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.2
Component: basic arithmetic | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Consider the following code:
{{{
# tries to find x^2+(y/2^delta)^2 + small = (2z+1)^2
# (2^delta*x)^2 + y^2 + err = (2^delta*(2z+1))^2
def table1_mod2(p,delta,err):
l = [[0,0]]
P = 1 # values in l are mod P
q = 1
twop = 2^p
twodelta = 2^delta
while P<twop:
q = next_prime(q)
R = IntegerModRing(P*q)
newl = []
for t in l:
for hx in range(q):
x = t[0]+hx*P
if x>=twop:
break
u = R((twodelta*x)^2+err)
for hz in range(q):
z = t[1]+hz*P
if z>=twop:
break
y2 = R((twodelta*(2*z+1))^2)-u
if y2.is_square():
newl.append([x,z])
l = newl
P = P * q
return l, P
}}}
With Sage 4.7 I get:
{{{
sage: time l=table1_mod2(10,0,1)
Time: CPU 2.61 s, Wall: 2.63 s
sage: len(l[0])
76940
}}}
If I change {{{R = IntegerModRing(P*q)}}} by {{{R=GF(q)}}}, which
does not change the algorithm (we are lifting modulo 2*3*5*...),
then strangely the program is slower:
{{{
sage: time l=table1_mod2(10,0,1)
Time: CPU 19.28 s, Wall: 19.33 s
sage: len(l[0])
76940
}}}
Is that normal?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11628>
Sage <http://www.sagemath.org>
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