#19822: Fast polynomial evaluation fmpz_poly/ZZX with mpfr/mpfi input
---------------------------+-------------------------------------
Reporter: vdelecroix | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.0
Component: algebra | Keywords:
Merged in: | Authors: Vincent Delecroix
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
---------------------------+-------------------------------------
We implement functions that allow fast evaluations of integer polynomials
with real input:
- `fmpz_poly_eval_mpfr(mpfr_t res, const fmpz_poly_t poly, const mpfr_t a,
mpfr_rnd_t rnd)`
- `fmpz_poly_eval_mpfi(mpfi_t res, const fmpz_poly_t poly, const mpfi_t
a)`
- `ZZX_eval_mpfr(mpfr_t res, ZZX_c poly, const mpfr_t a, const mpfr_rnd_t
rnd)`
- `ZZX_eval_mpfi(mpfi_t res, ZZX_c poly, const mpfi_t a)`
These functions are integrated in the polynomial code and number field
element comparisons (when real embedding is defined, see #17830). For the
latter we win a great `x10` speed up. The new code is also is `x50` faster
than comparisons in `QQbar`. 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: sage: %timeit test(a,10)
10 loops, best of 3: 51.1 ms per loop
sage: sage: %timeit test(a,20)
10 loops, best of 3: 67 ms per loop
sage: sage: %timeit test(a,100)
10 loops, best of 3: 108 ms per loop
sage: 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: sage: sage: %timeit test(a,10)
100 loops, best of 3: 5.84 ms per loop
sage: sage: sage: %timeit test(a,20)
100 loops, best of 3: 10.2 ms per loop
sage: sage: sage: %timeit test(a,100)
10 loops, best of 3: 33.5 ms per loop
sage: sage: 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: sage: %timeit test(a,10)
10 loops, best of 3: 97.7 ms per loop
sage: sage: %timeit test(a,20)
10 loops, best of 3: 133 ms per loop
sage: sage: %timeit test(a,100)
1 loops, best of 3: 224 ms per loop
sage: sage: %timeit test(a,200)
1 loops, best of 3: 305 ms per loop
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/19822>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
