#19824: Faster comparison code in (real embedded) number fields
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/19824 | c9c7133322fe7d762d7fb5c95f5d105c60788f90
Dependencies: #19822 | Stopgaps:
-------------------------------------+-------------------------------------
Changes (by vdelecroix):
* type: PLEASE CHANGE => enhancement
Old description:
> Using #19822 we provide a faster comparison code for number field
> elements when a real embedding is defined (see #17830). We obtain `x10`
> speed up. The new code is also `x50` faster than comparisons in `QQbar`
> (with a fixed number field element!!).
>
> For the benchmarks, we used the following comparison function
> {{{
> def test(a,n):
> cf = continued_fraction(a)
> cv1 = a.parent()(cf.convergent(2*n+1))
> cv2 = a.parent()(cf.convergent(2*n+2))
> for _ in range(200):
> assert cv1 > a > cv2
> }}}
> Before
> {{{
> sage: x = polygen(ZZ)
> sage: K.<a> = NumberField(x^3 - 2, embedding=1.26)
> sage: %timeit test(a,10)
> 10 loops, best of 3: 51.1 ms per loop
> sage: %timeit test(a,20)
> 10 loops, best of 3: 67 ms per loop
> sage: %timeit test(a,100)
> 10 loops, best of 3: 108 ms per loop
> sage: %timeit test(a,200)
> 1 loops, best of 3: 154 ms per loop
> }}}
> after
> {{{
> sage: x = polygen(ZZ)
> sage: K.<a> = NumberField(x^3 - 2, embedding=1.26)
> sage: %timeit test(a,10)
> 100 loops, best of 3: 5.84 ms per loop
> sage: %timeit test(a,20)
> 100 loops, best of 3: 10.2 ms per loop
> sage: %timeit test(a,100)
> 10 loops, best of 3: 33.5 ms per loop
> sage: %timeit test(a,200)
> 10 loops, best of 3: 64.8 ms per loop
> }}}
> To be compared with
> {{{
> sage: a = AA(2)**(1/3)
> sage: a.exactify()
> sage: %timeit test(a,10)
> 10 loops, best of 3: 97.7 ms per loop
> sage: %timeit test(a,20)
> 10 loops, best of 3: 133 ms per loop
> sage: %timeit test(a,100)
> 1 loops, best of 3: 224 ms per loop
> sage: %timeit test(a,200)
> 1 loops, best of 3: 305 ms per loop
> }}}
New description:
Using #19822 we provide a faster comparison code for number field elements
when a real embedding is defined (see #17830). We obtain `x10` speed up
for small elements and `x2` speed up for larger ones. The new code is also
`x50` faster than comparisons in `QQbar` (with a fixed number field
element!!).
For the benchmarks, we used the following comparison function
{{{
def test(a,n):
cf = continued_fraction(a)
cv1 = a.parent()(cf.convergent(2*n+1))
cv2 = a.parent()(cf.convergent(2*n+2))
for _ in range(200):
assert cv1 > a > cv2
}}}
Before
{{{
sage: x = polygen(ZZ)
sage: K.<a> = NumberField(x^3 - 2, embedding=1.26)
sage: %timeit test(a,10)
10 loops, best of 3: 51.1 ms per loop
sage: %timeit test(a,20)
10 loops, best of 3: 67 ms per loop
sage: %timeit test(a,100)
10 loops, best of 3: 108 ms per loop
sage: %timeit test(a,200)
1 loops, best of 3: 154 ms per loop
}}}
after
{{{
sage: x = polygen(ZZ)
sage: K.<a> = NumberField(x^3 - 2, embedding=1.26)
sage: %timeit test(a,10)
100 loops, best of 3: 5.84 ms per loop
sage: %timeit test(a,20)
100 loops, best of 3: 10.2 ms per loop
sage: %timeit test(a,100)
10 loops, best of 3: 33.5 ms per loop
sage: %timeit test(a,200)
10 loops, best of 3: 64.8 ms per loop
}}}
To be compared with
{{{
sage: a = AA(2)**(1/3)
sage: a.exactify()
sage: %timeit test(a,10)
10 loops, best of 3: 97.7 ms per loop
sage: %timeit test(a,20)
10 loops, best of 3: 133 ms per loop
sage: %timeit test(a,100)
1 loops, best of 3: 224 ms per loop
sage: %timeit test(a,200)
1 loops, best of 3: 305 ms per loop
}}}
--
--
Ticket URL: <http://trac.sagemath.org/ticket/19824#comment:4>
Sage <http://www.sagemath.org>
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