-
Notifications
You must be signed in to change notification settings - Fork 3
/
exp-PolyLegendreRoots.lisp
61 lines (55 loc) · 4.04 KB
/
exp-PolyLegendreRoots.lisp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
;; -*- Mode:Lisp; Syntax:ANSI-Common-LISP; Coding:us-ascii-unix; fill-column:158 -*-
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;
;; @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.
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; 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.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; We also must tell clisp to convert floating point types the ANSI way like so:
(setf CUSTOM:*FLOATING-POINT-CONTAGION-ANSI* 't)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; 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)))))