#19822: Fast polynomial evaluation fmpz_poly/ZZX with mpfr/mpfi input
-------------------------------------+-------------------------------------
Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/19822 | 683cd0de16503dc913750fd7c417129409b010c6
Dependencies: | Stopgaps:
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Description changed by vdelecroix:
Old description:
> 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
> }}}
New description:
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
}}}
See also the following discussion for upstream integrations:
- [https://groups.google.com/forum/#!topic/flint-devel/WAw4jvBHPyQ thread
on flint-devel]
--
--
Ticket URL: <http://trac.sagemath.org/ticket/19822#comment:2>
Sage <http://www.sagemath.org>
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and MATLAB
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