diff options
Diffstat (limited to 'lisp')
| -rw-r--r-- | lisp/calc/calc-comb.el | 42 |
1 files changed, 29 insertions, 13 deletions
diff --git a/lisp/calc/calc-comb.el b/lisp/calc/calc-comb.el index 2efeb7f0f22..f7e29c6e52c 100644 --- a/lisp/calc/calc-comb.el +++ b/lisp/calc/calc-comb.el @@ -439,12 +439,25 @@ (math-div (calcFunc-fact (math-float n)) (math-mul (calcFunc-fact m) (calcFunc-fact (math-sub n m)))))) - ((math-negp m) 0) - ((math-negp n) - (let ((val (calcFunc-choose (math-add (math-add n m) -1) m))) + ;; For the extension to negative integer arguments we follow + ;; M. J. Kronenburg, The Binomial Coefficient for Negative Arguments, + ;; arXiv:1105.3689v2 + ((and (math-negp n) (not (math-negp m))) + ;; n<0≤m: (n choose m) = (-1)^m (-n+m-1 choose m) + (let ((val (calcFunc-choose (math-add (math-sub m n) -1) m))) (if (math-evenp (math-trunc m)) val (math-neg val)))) + ((and (math-negp n) (math-num-integerp n)) + (if (math-lessp n m) + 0 + ;; m≤n<0: (n choose m) = (-1)^(n-m) (-m-1 choose n-m) + (let ((val (calcFunc-choose (math-sub (math-neg m) 1) + (math-sub n m)))) + (if (math-evenp (math-sub n m)) + val + (math-neg val))))) + ((math-negp m) 0) ((and (math-num-integerp n) (Math-lessp n m)) 0) @@ -461,20 +474,23 @@ (math-choose-float-iter tm n 1 1))))))) (defun math-choose-iter (m n i c) - (if (and (= (% i 5) 1) (> i 5)) + (while (<= i m) + (when (and (= (% i 5) 1) (> i 5)) (math-working (format "choose(%d)" (1- i)) c)) - (if (<= i m) - (math-choose-iter m (1- n) (1+ i) - (math-quotient (math-mul c n) i)) - c)) + (setq c (math-quotient (math-mul c n) i)) + (setq n (1- n)) + (setq i (1+ i))) + c) (defun math-choose-float-iter (count n i c) - (if (= (% i 5) 1) + (while (> count 0) + (when (= (% i 5) 1) (math-working (format "choose(%d)" (1- i)) c)) - (if (> count 0) - (math-choose-float-iter (1- count) (math-sub n 1) (1+ i) - (math-div (math-mul c n) i)) - c)) + (setq c (math-div (math-mul c n) i)) + (setq n (math-sub n 1)) + (setq i (1+ i)) + (setq count (1- count))) + c) ;;; Stirling numbers. |