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;; @file      exp-PolyLegendreRoots.lisp
;; @author    Mitch Richling <https://www.mitchr.me>
;; @brief     Compute the nodes for Gauss-Legendre integration with high accuracy.@EOL
;; @std       clisp
;; @copyright 
;;  @parblock
;;  Copyright (c) 2013,2015, Mitchell Jay Richling <https://www.mitchr.me> All rights reserved.
;;
;;  Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
;;
;;  1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
;;
;;  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation
;;     and/or other materials provided with the distribution.
;;
;;  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software
;;     without specific prior written permission.
;;
;;  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
;;  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
;;  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
;;  OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
;;  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
;;  DAMAGE.
;;  @endparblock
;; @filedetails
;;
;;  This code uses clisp's (http://www.clisp.org/) arbitrary precision, software floating point implementation to compute the nodes for Gauss-Legendre
;;  integration.
;;
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;; We set the precision like this:

(setf (ext:long-float-digits) (* 32 16)) ;; Now (float-digits 1.1L0) will return 512 -- which is 128 or so decimal digits.

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;; We also must tell clisp to convert floating point types the ANSI way like so:

(setf CUSTOM:*FLOATING-POINT-CONTAGION-ANSI* 't)

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;; We are now ready to compute some Gauss-Legendre nodes:

(mapc (lambda (x) (format 't "~100,80f~%" x))
      (sort (mjr_poly_root-solve-search-deflate (mjr_poly_make-legendre 21)
                                                :show-progress nil
                                                :show-warnings 't
                                                :retry-factor  5
                                                :refine-steps  100
                                                :only-refined  't
                                                :float-type    0.0L0
                                                :xepsr         1.0L-90
                                                :yepsr         1.0L-90
                                                :xeps          1.0L-5
                                                :yeps          1.0L-5)
            (lambda (a b) (< (realpart a) (realpart b)))))