;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
;; Author: David Gillespie <daveg@synaptics.com>
-;; Maintainer: Colin Walters <walters@debian.org>
+;; Maintainers: D. Goel <deego@gnufans.org>
+;; Colin Walters <walters@debian.org>
;; This file is part of GNU Emacs.
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
+;; indicate whether factoring is complete, and used by calcFunc-factors,
+;; calcFunc-totient and calcFunc-moebius.
+(defvar math-prime-factors-finished)
+
;;; Combinatorics
(defun calc-gcd (arg)
(res (math-prime-test n iters)))
(calc-report-prime-test res))))
+(defvar calc-verbose-nextprime nil)
+
(defun calc-next-prime (iters)
(interactive "p")
(calc-slow-wrapper
(math-div
(math-pow -2 (- tn))
(math-double-factorial-iter (* -2 tn) 3 1 2))
- (math-div
+ (math-div
(math-double-factorial-iter (* 2 tn) 3 1 2)
(math-pow 2 tn)))))
(math-mul q (if calc-symbolic-mode
(if (math-evenp temp)
even
(math-div (calcFunc-fact n) even))))
- (list 'calcFunc-dfact max))))
+ (list 'calcFunc-dfact n))))
((equal n '(var inf var-inf)) n)
(t (calc-record-why 'natnump n)
(list 'calcFunc-dfact n))))
(math-stirling-number n m 0))
(defvar math-stirling-cache (vector [[1]] [[1]]))
+
+;; The variable math-stirling-local-cache is local to
+;; math-stirling-number, but is used by math-stirling-1
+;; and math-stirling-2, which are called by math-stirling-number.
+(defvar math-stirling-local-cache)
+
(defun math-stirling-number (n m k)
(or (math-num-natnump n) (math-reject-arg n 'natnump))
(or (math-num-natnump m) (math-reject-arg m 'natnump))
(or (integerp m) (math-reject-arg m 'fixnump))
(if (< n m)
0
- (let ((cache (aref math-stirling-cache k)))
- (while (<= (length cache) n)
- (let ((i (1- (length cache)))
+ (let ((math-stirling-local-cache (aref math-stirling-cache k)))
+ (while (<= (length math-stirling-local-cache) n)
+ (let ((i (1- (length math-stirling-local-cache)))
row)
- (setq cache (vconcat cache (make-vector (length cache) nil)))
- (aset math-stirling-cache k cache)
- (while (< (setq i (1+ i)) (length cache))
- (aset cache i (setq row (make-vector (1+ i) nil)))
+ (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))
+ (aset math-stirling-local-cache i (setq row (make-vector (1+ i) nil)))
(aset row 0 0)
(aset row i 1))))
(if (= k 1)
(math-stirling-2 n m)))))
(defun math-stirling-1 (n m)
- (or (aref (aref cache n) m)
- (aset (aref cache n) m
+ (or (aref (aref math-stirling-local-cache n) m)
+ (aset (aref math-stirling-local-cache n) m
(math-add (math-stirling-1 (1- n) (1- m))
(math-mul (- 1 n) (math-stirling-1 (1- n) m))))))
(defun math-stirling-2 (n m)
- (or (aref (aref cache n) m)
- (aset (aref cache n) m
+ (or (aref (aref math-stirling-local-cache n) m)
+ (aset (aref math-stirling-local-cache n) m
(math-add (math-stirling-2 (1- n) (1- m))
(math-mul m (math-stirling-2 (1- n) m))))))
;;; Produce a random 10-bit integer, with (random) if no seed provided,
;;; or else with Numerical Recipes algorithm ran3 / Knuth 3.2.2-A.
+
+(defvar var-RandSeed nil)
+(defvar math-random-cache nil)
+(defvar math-gaussian-cache nil)
+
(defun math-init-random-base ()
- (if (and (boundp 'var-RandSeed) var-RandSeed)
+ (if var-RandSeed
(if (eq (car-safe var-RandSeed) 'vec)
nil
(if (Math-integerp var-RandSeed)
(random t)
(setq var-RandSeed nil
math-random-cache nil
- i 0
math-random-shift -4) ; assume RAND_MAX >= 16383
;; This exercises the random number generator and also helps
;; deduce a better value for RAND_MAX.
- (while (< (setq i (1+ i)) 30)
- (if (> (lsh (math-abs (random)) math-random-shift) 4095)
- (setq math-random-shift (1- math-random-shift)))))
+ (let ((i 0))
+ (while (< (setq i (1+ i)) 30)
+ (if (> (lsh (math-abs (random)) math-random-shift) 4095)
+ (setq math-random-shift (1- math-random-shift))))))
(setq math-last-RandSeed var-RandSeed
math-gaussian-cache nil))
;;; Avoid various pitfalls that may lurk in the built-in (random) function!
;;; Shuffling algorithm from Numerical Recipes, section 7.1.
(defun math-random-digit ()
- (let (i)
- (or (and (boundp 'var-RandSeed) (eq var-RandSeed math-last-RandSeed))
+ (let (i math-random-last)
+ (or (eq var-RandSeed math-last-RandSeed)
(math-init-random-base))
(or math-random-cache
(progn
(aset math-random-cache i (math-random-base))
(>= math-random-last 1000)))
math-random-last))
-(setq math-random-cache nil)
;;; Produce an N-digit random integer.
(defun math-random-digits (n)
(setq math-gaussian-cache (cons calc-internal-prec
(math-mul v1 fac)))
(math-mul v2 fac))))))
-(setq math-gaussian-cache nil)
;;; Produce a random integer or real 0 <= N < MAX.
(defun calcFunc-random (max)
;;; (nil unknown) if non-prime with no known factors,
;;; (t) if prime,
;;; (maybe N P) if probably prime (after N iters with probability P%)
+(defvar math-prime-test-cache '(-1))
+
+(defvar math-prime-test-cache-k)
+(defvar math-prime-test-cache-q)
+(defvar math-prime-test-cache-nm1)
+
(defun math-prime-test (n iters)
(if (and (Math-vectorp n) (cdr n))
(setq n (nth (1- (length n)) n)))
(1- iters)
0)))
res))
-(defvar math-prime-test-cache '(-1))
(defun calcFunc-prime (n &optional iters)
(or (math-num-integerp n) (math-reject-arg n 'integerp))
(if (Math-realp n)
(calcFunc-nextprime (math-trunc n) iters)
(math-reject-arg n 'integerp))))
-(setq calc-verbose-nextprime nil)
(defun calcFunc-prevprime (n &optional iters)
(if (Math-integerp n)
+;;; arch-tag: 1d75ee9b-0815-42bd-a321-bb3dc001cc02
;;; calc-comb.el ends here