;;; calc-comb.el --- combinatoric functions for Calc
-;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
-;; 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
+;; Copyright (C) 1990-1993, 2001-2015 Free Software Foundation, Inc.
;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
;; This file is part of GNU Emacs.
-;; GNU Emacs is free software; you can redistribute it and/or modify
+;; GNU Emacs is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
-;; the Free Software Foundation; either version 3, or (at your option)
-;; any later version.
+;; the Free Software Foundation, either version 3 of the License, or
+;; (at your option) any later version.
;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; GNU General Public License for more details.
;; You should have received a copy of the GNU General Public License
-;; along with GNU Emacs; see the file COPYING. If not, write to the
-;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
-;; Boston, MA 02110-1301, USA.
+;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
;;; Commentary:
4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973
4987 4993 4999 5003])
-;; The variable math-prime-factors-finished is set by calcFunc-prfac to
+;; The variable math-prime-factors-finished is set by calcFunc-prfac to
;; indicate whether factoring is complete, and used by calcFunc-factors,
;; calcFunc-totient and calcFunc-moebius.
(defvar math-prime-factors-finished)
;;; Factorial and related functions.
+(defconst math-small-factorial-table
+ (vector 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800
+ (math-read-number-simple "479001600")
+ (math-read-number-simple "6227020800")
+ (math-read-number-simple "87178291200")
+ (math-read-number-simple "1307674368000")
+ (math-read-number-simple "20922789888000")
+ (math-read-number-simple "355687428096000")
+ (math-read-number-simple "6402373705728000")
+ (math-read-number-simple "121645100408832000")
+ (math-read-number-simple "2432902008176640000")))
+
(defun calcFunc-fact (n) ; [I I] [F F] [Public]
(let (temp)
(cond ((Math-integer-negp n)
(math-reject-arg n 'range)))
((integerp n)
(if (<= n 20)
- (aref '[1 1 2 6 24 120 720 5040 40320 362880
- (bigpos 800 628 3) (bigpos 800 916 39)
- (bigpos 600 1 479) (bigpos 800 20 227 6)
- (bigpos 200 291 178 87) (bigpos 0 368 674 307 1)
- (bigpos 0 888 789 922 20) (bigpos 0 96 428 687 355)
- (bigpos 0 728 705 373 402 6)
- (bigpos 0 832 408 100 645 121)
- (bigpos 0 640 176 8 902 432 2)] n)
+ (aref math-small-factorial-table n)
(math-factorial-iter (1- n) 2 1)))
((and (math-messy-integerp n)
(Math-lessp n 100))
(while (<= (length math-stirling-local-cache) n)
(let ((i (1- (length math-stirling-local-cache)))
row)
- (setq math-stirling-local-cache
- (vconcat math-stirling-local-cache
+ (setq math-stirling-local-cache
+ (vconcat math-stirling-local-cache
(make-vector (length math-stirling-local-cache) nil)))
(aset math-stirling-cache k math-stirling-local-cache)
(while (< (setq i (1+ i)) (length math-stirling-local-cache))
nil
(if (Math-integerp var-RandSeed)
(let* ((seed (math-sub 161803 var-RandSeed))
- (mj (1+ (math-mod seed '(bigpos 0 0 1))))
- (mk (1+ (math-mod (math-quotient seed '(bigpos 0 0 1))
- '(bigpos 0 0 1))))
+ (mj (1+ (math-mod seed 1000000)))
+ (mk (1+ (math-mod (math-quotient seed 1000000)
+ 1000000)))
(i 0))
(setq math-random-table (cons 'vec (make-list 55 mj)))
(while (<= (setq i (1+ i)) 54)
(let ((i 200))
(while (> (setq i (1- i)) 0)
(math-random-base))))
- (random t)
(setq var-RandSeed nil
math-random-cache nil
math-random-shift -4) ; assume RAND_MAX >= 16383
;;; Avoid various pitfalls that may lurk in the built-in (random) function!
;;; Shuffling algorithm from Numerical Recipes, section 7.1.
(defvar math-random-last)
-(defun math-random-digit ()
+(defun math-random-three-digit-number ()
+ "Return a random three digit number."
(let (i)
(or (and (boundp 'var-RandSeed) (eq var-RandSeed math-last-RandSeed))
(math-init-random-base))
;;; Produce an N-digit random integer.
(defun math-random-digits (n)
- (cond ((<= n 6)
- (math-scale-right (+ (* (math-random-digit) 1000) (math-random-digit))
- (- 6 n)))
- (t (let* ((slop (% (- 900003 n) 3))
- (i (/ (+ n slop) 3))
- (digs nil))
- (while (> i 0)
- (setq digs (cons (math-random-digit) digs)
- i (1- i)))
- (math-normalize (math-scale-right (cons 'bigpos digs)
- slop))))))
+ "Produce a random N digit integer."
+ (let* ((slop (% (- 3 (% n 3)) 3))
+ (i (/ (+ n slop) 3))
+ (rnum 0))
+ (while (> i 0)
+ (setq rnum
+ (math-add
+ (math-random-three-digit-number)
+ (math-mul rnum 1000)))
+ (setq i (1- i)))
+ (math-normalize (math-scale-right rnum slop))))
;;; Produce a uniformly-distributed random float 0 <= N < 1.
(defun math-random-float ()
(error "Argument must be an integer"))
((Math-integer-negp n)
'(nil))
- ((Math-natnum-lessp n '(bigpos 0 0 8))
+ ((Math-natnum-lessp n 8000000)
(setq n (math-fixnum n))
(let ((i -1) v)
(while (and (> (% n (setq v (aref math-primes-table
(list nil v)
'(t))))
((not (equal n (car math-prime-test-cache)))
- (cond ((= (% (nth 1 n) 2) 0) '(nil 2))
- ((= (% (nth 1 n) 5) 0) '(nil 5))
- (t (let ((dig (cdr n)) (sum 0))
- (while dig
- (if (cdr dig)
- (setq sum (% (+ (+ sum (car dig))
- (* (nth 1 dig) 1000))
- 111111)
- dig (cdr (cdr dig)))
- (setq sum (% (+ sum (car dig)) 111111)
- dig nil)))
+ (cond ((if (consp n)
+ (= (% (nth 1 n) 2) 0)
+ (= (% n 2) 0))
+ '(nil 2))
+ ((if (consp n)
+ (= (% (nth 1 n) 5) 0)
+ (= (% n 5) 0))
+ '(nil 5))
+ (t (let ((q n) (sum 0))
+ (while (not (eq q 0))
+ (setq sum (%
+ (+
+ sum
+ (calcFunc-mod
+ q 1000000))
+ 111111))
+ (setq q
+ (math-quotient
+ q 1000000)))
(cond ((= (% sum 3) 0) '(nil 3))
((= (% sum 7) 0) '(nil 7))
((= (% sum 11) 0) '(nil 11))
(provide 'calc-comb)
-;;; arch-tag: 1d75ee9b-0815-42bd-a321-bb3dc001cc02
;;; calc-comb.el ends here