diff options
Diffstat (limited to 'lisp/calc/calc-comb.el')
| -rw-r--r-- | lisp/calc/calc-comb.el | 75 |
1 files changed, 42 insertions, 33 deletions
diff --git a/lisp/calc/calc-comb.el b/lisp/calc/calc-comb.el index cbc81ce8b6c..90a0a20f5d6 100644 --- a/lisp/calc/calc-comb.el +++ b/lisp/calc/calc-comb.el @@ -294,6 +294,19 @@ ;;; Factorial and related functions. +(defconst math-small-factorial-table + (eval-when-compile + (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) @@ -302,14 +315,7 @@ (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)) @@ -551,9 +557,9 @@ 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) @@ -601,7 +607,8 @@ ;;; 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)) @@ -621,17 +628,17 @@ ;;; 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 () @@ -802,7 +809,7 @@ (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 @@ -815,15 +822,17 @@ ((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))) + (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)) |