#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                 |  ad0721694614fe3546cdace8b3ec27e415539b74
   Dependencies:                     |     Stopgaps:
-------------------------------------+-------------------------------------
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 with method
> `_eval_mpfr` and `_eval_mpfi`.
>
> See also the following discussion for upstream integrations:
>
> - [https://groups.google.com/forum/#!topic/flint-devel/WAw4jvBHPyQ thread
> on flint-devel]

New description:

 We implement functions that allow fast evaluations of integer polynomials
 with real input:
 - `fmpz_poly_evaluation_mpfr(mpfr_t res, const fmpz_poly_t poly, const
 mpfr_t a, mpfr_rnd_t rnd)`
 - `fmpz_poly_evaluation_mpfi(mpfi_t res, const fmpz_poly_t poly, const
 mpfi_t a)`
 - `ZZX_evaluation_mpfr(mpfr_t res, ZZX_c poly, const mpfr_t a, const
 mpfr_rnd_t rnd)`
 - `ZZX_evaluation_mpfi(mpfi_t res, ZZX_c poly, const mpfi_t a)`

 These functions are integrated in the polynomial code with method
 `_eval_mpfr` and `_eval_mpfi`.

 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:9>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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