From a6d107f1713c2fd9686bef09e8cee009d0119fc8 Mon Sep 17 00:00:00 2001 From: Jay Belanger Date: Sat, 23 Jun 2007 04:08:18 +0000 Subject: [PATCH] (math-bignum-digit-length,math-bignum-digit-size,math-small-integer-size): New constants. (math-normalize,math-bignum-big,math-make-float,math-div10-bignum) (math-scale-left,math-scale-left-bignum,math-scale-right) (math-scale-right-bignum,math-scale-rounding,math-add,math-add-bignum) (math-sub-bignum,math-sub,math-mul,math-mul-bignum,math-mul-bignum-digit) (math-idivmod,math-quotient,math-div-bignum,math-div-bignum-digit) (math-div-bignum-part,math-format-bignum-decimal,math-read-bignum): Use math-bignum-digit-length, math-bignum-digit-size and math-small-integer-size. --- lisp/ChangeLog | 15 ++++ lisp/calc/calc.el | 186 +++++++++++++++++++++++++++------------------- 2 files changed, 125 insertions(+), 76 deletions(-) diff --git a/lisp/ChangeLog b/lisp/ChangeLog index 5865c2ff0c1..5e573024c87 100644 --- a/lisp/ChangeLog +++ b/lisp/ChangeLog @@ -1,3 +1,18 @@ +2007-06-22 Jay Belanger + + * calc/calc.el (math-bignum-digit-length) + (math-bignum-digit-size,math-small-integer-size): + New constants. + (math-normalize,math-bignum-big,math-make-float) + (math-div10-bignum,math-scale-left,math-scale-left-bignum) + (math-scale-right,math-scale-right-bignum,math-scale-rounding) + (math-add,math-add-bignum,math-sub-bignum,math-sub,math-mul) + (math-mul-bignum,math-mul-bignum-digit,math-idivmod) + (math-quotient,math-div-bignum,math-div-bignum-digit) + (math-div-bignum-part,math-format-bignum-decimal) + (math-read-bignum): Use math-bignum-digit-length, + math-bignum-digit-size and math-small-integer-size. + 2007-06-23 Dan Nicolaescu * vc-hg.el (vc-hg-log-view-mode): Fix last change. diff --git a/lisp/calc/calc.el b/lisp/calc/calc.el index 96f93e0467b..78d6231cb15 100644 --- a/lisp/calc/calc.el +++ b/lisp/calc/calc.el @@ -2283,7 +2283,18 @@ See calc-keypad for details." +(defconst math-bignum-digit-length 3 + "The length of a \"digit\" in Calc bignums. +If a big integer is of the form (bigpos N0 N1 ...), this is the +length of the allowable Emacs integers N0, N1,... +The value of 2*10^(2*MATH-BIGNUM-DIGIT-LENGTH) must be less than the +largest Emacs integer.") +(defconst math-bignum-digit-size (expt 10 math-bignum-digit-length) + "An upper bound for the size of the \"digit\"s in Calc bignums.") + +(defconst math-small-integer-size (expt 10 (* 2 math-bignum-digit-length)) + "An upper bound for the size of \"small integer\"s in Calc.") ;;;; Arithmetic routines. @@ -2292,11 +2303,17 @@ See calc-keypad for details." ;;; following forms: ;;; ;;; integer An integer. For normalized numbers, this format -;;; is used only for -999999 ... 999999. +;;; is used only for +;;; negative math-small-integer-size + 1 to +;;; math-small-integer-size - 1 ;;; -;;; (bigpos N0 N1 N2 ...) A big positive integer, N0 + N1*1000 + N2*10^6 ... -;;; (bigneg N0 N1 N2 ...) A big negative integer, - N0 - N1*1000 ... -;;; Each digit N is in the range 0 ... 999. +;;; (bigpos N0 N1 N2 ...) A big positive integer, +;;; N0 + N1*math-bignum-digit-size +;;; + N2*(math-bignum-digit-size)^2 ... +;;; (bigneg N0 N1 N2 ...) A big negative integer, +;;; - N0 - N1*math-bignum-digit-size ... +;;; Each digit N is in the range +;;; 0 ... math-bignum-digit-size -1. ;;; Normalized, always at least three N present, ;;; and the most significant N is nonzero. ;;; @@ -2386,7 +2403,8 @@ See calc-keypad for details." (cond ((not (consp math-normalize-a)) (if (integerp math-normalize-a) - (if (or (>= math-normalize-a 1000000) (<= math-normalize-a -1000000)) + (if (or (>= math-normalize-a math-small-integer-size) + (<= math-normalize-a (- math-small-integer-size))) (math-bignum math-normalize-a) math-normalize-a) math-normalize-a)) @@ -2401,7 +2419,8 @@ See calc-keypad for details." math-normalize-a (cond ((cdr (cdr math-normalize-a)) (+ (nth 1 math-normalize-a) - (* (nth 2 math-normalize-a) 1000))) + (* (nth 2 math-normalize-a) + math-bignum-digit-size))) ((cdr math-normalize-a) (nth 1 math-normalize-a)) (t 0)))) ((eq (car math-normalize-a) 'bigneg) @@ -2415,7 +2434,8 @@ See calc-keypad for details." math-normalize-a (cond ((cdr (cdr math-normalize-a)) (- (+ (nth 1 math-normalize-a) - (* (nth 2 math-normalize-a) 1000)))) + (* (nth 2 math-normalize-a) + math-bignum-digit-size)))) ((cdr math-normalize-a) (- (nth 1 math-normalize-a))) (t 0)))) ((eq (car math-normalize-a) 'float) @@ -2535,7 +2555,8 @@ See calc-keypad for details." (defun math-bignum-big (a) ; [L s] (if (= a 0) nil - (cons (% a 1000) (math-bignum-big (/ a 1000))))) + (cons (% a math-bignum-digit-size) + (math-bignum-big (/ a math-bignum-digit-size))))) ;;; Build a normalized floating-point number. [F I S] @@ -2552,7 +2573,7 @@ See calc-keypad for details." (progn (while (= (car digs) 0) (setq digs (cdr digs) - exp (+ exp 3))) + exp (+ exp math-bignum-digit-length))) (while (= (% (car digs) 10) 0) (setq digs (math-div10-bignum digs) exp (1+ exp))) @@ -2570,7 +2591,8 @@ See calc-keypad for details." (defun math-div10-bignum (a) ; [l l] (if (cdr a) - (cons (+ (/ (car a) 10) (* (% (nth 1 a) 10) 100)) + (cons (+ (/ (car a) 10) (* (% (nth 1 a) 10) + (expt 10 (1- math-bignum-digit-length)))) (math-div10-bignum (cdr a))) (list (/ (car a) 10)))) @@ -2601,7 +2623,7 @@ See calc-keypad for details." (if (cdr a) (let* ((len (1- (length a))) (top (nth len a))) - (+ (* len 3) (cond ((>= top 100) 0) ((>= top 10) -1) (t -2)))) + (+ (* (1- len) math-bignum-digit-length) (math-numdigs top))) 0) (cond ((>= a 100) (+ (math-numdigs (/ a 1000)) 3)) ((>= a 10) 2) @@ -2622,24 +2644,24 @@ See calc-keypad for details." a (if (consp a) (cons (car a) (math-scale-left-bignum (cdr a) n)) - (if (>= n 3) - (if (or (>= a 1000) (<= a -1000)) + (if (>= n math-bignum-digit-length) + (if (or (>= a math-bignum-digit-size) + (<= a (- math-bignum-digit-size))) (math-scale-left (math-bignum a) n) - (math-scale-left (* a 1000) (- n 3))) - (if (= n 2) - (if (or (>= a 10000) (<= a -10000)) - (math-scale-left (math-bignum a) 2) - (* a 100)) - (if (or (>= a 100000) (<= a -100000)) - (math-scale-left (math-bignum a) 1) - (* a 10))))))) + (math-scale-left (* a math-bignum-digit-size) + (- n math-bignum-digit-length))) + (let ((sz (expt 10 (- (* 2 math-bignum-digit-length) n)))) + (if (or (>= a sz) (<= a (- sz))) + (math-scale-left (math-bignum a) n) + (* a (expt 10 n)))))))) (defun math-scale-left-bignum (a n) - (if (>= n 3) + (if (>= n math-bignum-digit-length) (while (>= (setq a (cons 0 a) - n (- n 3)) 3))) + n (- n math-bignum-digit-length)) + math-bignum-digit-length))) (if (> n 0) - (math-mul-bignum-digit a (if (= n 2) 100 10) 0) + (math-mul-bignum-digit a (expt 10 n) 0) a)) (defun math-scale-right (a n) ; [i i S] @@ -2651,21 +2673,20 @@ See calc-keypad for details." (if (= a 0) 0 (- (math-scale-right (- a) n))) - (if (>= n 3) - (while (and (> (setq a (/ a 1000)) 0) - (>= (setq n (- n 3)) 3)))) - (if (= n 2) - (/ a 100) - (if (= n 1) - (/ a 10) - a)))))) + (if (>= n math-bignum-digit-length) + (while (and (> (setq a (/ a math-bignum-digit-size)) 0) + (>= (setq n (- n math-bignum-digit-length)) + math-bignum-digit-length)))) + (if (> n 0) + (/ a (expt 10 n)) + a))))) (defun math-scale-right-bignum (a n) ; [L L S; l l S] - (if (>= n 3) - (setq a (nthcdr (/ n 3) a) - n (% n 3))) + (if (>= n math-bignum-digit-length) + (setq a (nthcdr (/ n math-bignum-digit-length) a) + n (% n math-bignum-digit-length))) (if (> n 0) - (cdr (math-mul-bignum-digit a (if (= n 2) 10 100) 0)) + (cdr (math-mul-bignum-digit a (expt 10 (- math-bignum-digit-length n)) 0)) a)) ;;; Multiply (with rounding) the integer A by 10^N. [I i S] @@ -2675,16 +2696,18 @@ See calc-keypad for details." ((consp a) (math-normalize (cons (car a) - (let ((val (if (< n -3) - (math-scale-right-bignum (cdr a) (- -3 n)) - (if (= n -2) - (math-mul-bignum-digit (cdr a) 10 0) - (if (= n -1) - (math-mul-bignum-digit (cdr a) 100 0) - (cdr a)))))) ; n = -3 - (if (and val (>= (car val) 500)) + (let ((val (if (< n (- math-bignum-digit-length)) + (math-scale-right-bignum + (cdr a) + (- (- math-bignum-digit-length) n)) + (if (< n 0) + (math-mul-bignum-digit + (cdr a) + (expt 10 (+ math-bignum-digit-length n)) 0) + (cdr a))))) ; n = -math-bignum-digit-length + (if (and val (>= (car val) (/ math-bignum-digit-size 2))) (if (cdr val) - (if (eq (car (cdr val)) 999) + (if (eq (car (cdr val)) (1- math-bignum-digit-size)) (math-add-bignum (cdr val) '(1)) (cons (1+ (car (cdr val))) (cdr (cdr val)))) '(1)) @@ -2703,7 +2726,7 @@ See calc-keypad for details." (and (not (or (consp a) (consp b))) (progn (setq a (+ a b)) - (if (or (<= a -1000000) (>= a 1000000)) + (if (or (<= a (- math-small-integer-size)) (>= a math-small-integer-size)) (math-bignum a) a))) (and (Math-zerop a) (not (eq (car-safe a) 'mod)) @@ -2752,14 +2775,15 @@ See calc-keypad for details." (let* ((a (copy-sequence a)) (aa a) (carry nil) sum) (while (and aa b) (if carry - (if (< (setq sum (+ (car aa) (car b))) 999) + (if (< (setq sum (+ (car aa) (car b))) + (1- math-bignum-digit-size)) (progn (setcar aa (1+ sum)) (setq carry nil)) (setcar aa (+ sum -999))) - (if (< (setq sum (+ (car aa) (car b))) 1000) + (if (< (setq sum (+ (car aa) (car b))) math-bignum-digit-size) (setcar aa sum) - (setcar aa (+ sum -1000)) + (setcar aa (- sum math-bignum-digit-size)) (setq carry t))) (setq aa (cdr aa) b (cdr b))) @@ -2790,17 +2814,17 @@ See calc-keypad for details." (progn (setcar aa (1- diff)) (setq borrow nil)) - (setcar aa (+ diff 999))) + (setcar aa (+ diff (1- math-bignum-digit-size)))) (if (>= (setq diff (- (car aa) (car b))) 0) (setcar aa diff) - (setcar aa (+ diff 1000)) + (setcar aa (+ diff math-bignum-digit-size)) (setq borrow t))) (setq aa (cdr aa) b (cdr b))) (if borrow (progn (while (eq (car aa) 0) - (setcar aa 999) + (setcar aa (1- math-bignum-digit-size)) (setq aa (cdr aa))) (if aa (progn @@ -2840,7 +2864,7 @@ See calc-keypad for details." (if (or (consp a) (consp b)) (math-add a (math-neg b)) (setq a (- a b)) - (if (or (<= a -1000000) (>= a 1000000)) + (if (or (<= a (- math-small-integer-size)) (>= a math-small-integer-size)) (math-bignum a) a))) @@ -2867,7 +2891,8 @@ See calc-keypad for details." (defun math-mul (a b) (or (and (not (consp a)) (not (consp b)) - (< a 1000) (> a -1000) (< b 1000) (> b -1000) + (< a math-bignum-digit-size) (> a (- math-bignum-digit-size)) + (< b math-bignum-digit-size) (> b (- math-bignum-digit-size)) (* a b)) (and (Math-zerop a) (not (eq (car-safe b) 'mod)) (if (Math-scalarp b) @@ -2936,14 +2961,14 @@ See calc-keypad for details." aa a) (while (progn (setcar ss (% (setq prod (+ (+ (car ss) (* (car aa) d)) - c)) 1000)) + c)) math-bignum-digit-size)) (setq aa (cdr aa))) - (setq c (/ prod 1000) + (setq c (/ prod math-bignum-digit-size) ss (or (cdr ss) (setcdr ss (list 0))))) - (if (>= prod 1000) + (if (>= prod math-bignum-digit-size) (if (cdr ss) - (setcar (cdr ss) (+ (/ prod 1000) (car (cdr ss)))) - (setcdr ss (list (/ prod 1000)))))) + (setcar (cdr ss) (+ (/ prod math-bignum-digit-size) (car (cdr ss)))) + (setcdr ss (list (/ prod math-bignum-digit-size)))))) sum))) ;;; Multiply digit list A by digit D. [L L D D; l l D D] @@ -2953,12 +2978,14 @@ See calc-keypad for details." (and (= d 1) a) (let* ((a (copy-sequence a)) (aa a) prod) (while (progn - (setcar aa (% (setq prod (+ (* (car aa) d) c)) 1000)) + (setcar aa + (% (setq prod (+ (* (car aa) d) c)) + math-bignum-digit-size)) (cdr aa)) (setq aa (cdr aa) - c (/ prod 1000))) - (if (>= prod 1000) - (setcdr aa (list (/ prod 1000)))) + c (/ prod math-bignum-digit-size))) + (if (>= prod math-bignum-digit-size) + (setcdr aa (list (/ prod math-bignum-digit-size)))) a)) (and (> c 0) (list c)))) @@ -2971,7 +2998,7 @@ See calc-keypad for details." (if (eq b 0) (math-reject-arg a "*Division by zero")) (if (or (consp a) (consp b)) - (if (and (natnump b) (< b 1000)) + (if (and (natnump b) (< b math-bignum-digit-size)) (let ((res (math-div-bignum-digit (cdr a) b))) (cons (math-normalize (cons (car a) (car res))) @@ -2990,7 +3017,7 @@ See calc-keypad for details." (if (= b 0) (math-reject-arg a "*Division by zero") (/ a b)) - (if (and (natnump b) (< b 1000)) + (if (and (natnump b) (< b math-bignum-digit-size)) (if (= b 0) (math-reject-arg a "*Division by zero") (math-normalize (cons (car a) @@ -2999,7 +3026,7 @@ See calc-keypad for details." (or (consp b) (setq b (math-bignum b))) (let* ((alen (1- (length a))) (blen (1- (length b))) - (d (/ 1000 (1+ (nth (1- blen) (cdr b))))) + (d (/ math-bignum-digit-size (1+ (nth (1- blen) (cdr b))))) (res (math-div-bignum-big (math-mul-bignum-digit (cdr a) d 0) (math-mul-bignum-digit (cdr b) d 0) alen blen))) @@ -3013,7 +3040,7 @@ See calc-keypad for details." (if (cdr b) (let* ((alen (length a)) (blen (length b)) - (d (/ 1000 (1+ (nth (1- blen) b)))) + (d (/ math-bignum-digit-size (1+ (nth (1- blen) b)))) (res (math-div-bignum-big (math-mul-bignum-digit a d 0) (math-mul-bignum-digit b d 0) alen blen))) @@ -3028,7 +3055,7 @@ See calc-keypad for details." (defun math-div-bignum-digit (a b) (if a (let* ((res (math-div-bignum-digit (cdr a) b)) - (num (+ (* (cdr res) 1000) (car a)))) + (num (+ (* (cdr res) math-bignum-digit-size) (car a)))) (cons (cons (/ num b) (car res)) (% num b))) @@ -3044,10 +3071,11 @@ See calc-keypad for details." (cons (car res2) (car res)) (cdr res2))))) -(defun math-div-bignum-part (a b blen) ; a < b*1000 [D.l l L] - (let* ((num (+ (* (or (nth blen a) 0) 1000) (or (nth (1- blen) a) 0))) +(defun math-div-bignum-part (a b blen) ; a < b*math-bignum-digit-size [D.l l L] + (let* ((num (+ (* (or (nth blen a) 0) math-bignum-digit-size) + (or (nth (1- blen) a) 0))) (den (nth (1- blen) b)) - (guess (min (/ num den) 999))) + (guess (min (/ num den) (1- math-bignum-digit-size)))) (math-div-bignum-try a b (math-mul-bignum-digit b guess 0) guess))) (defun math-div-bignum-try (a b c guess) ; [D.l l l D] @@ -3358,9 +3386,15 @@ See calc-keypad for details." (if a (let ((s "")) (while (cdr (cdr a)) - (setq s (concat (format "%06d" (+ (* (nth 1 a) 1000) (car a))) s) + (setq s (concat + (format + (concat "%0" + (number-to-string (* 2 math-bignum-digit-length)) + "d") + (+ (* (nth 1 a) math-bignum-digit-size) (car a))) s) a (cdr (cdr a)))) - (concat (int-to-string (+ (* (or (nth 1 a) 0) 1000) (car a))) s)) + (concat (int-to-string + (+ (* (or (nth 1 a) 0) math-bignum-digit-size) (car a))) s)) "0")) @@ -3447,9 +3481,9 @@ See calc-keypad for details." "")) (defun math-read-bignum (s) ; [l X] - (if (> (length s) 3) - (cons (string-to-number (substring s -3)) - (math-read-bignum (substring s 0 -3))) + (if (> (length s) math-bignum-digit-length) + (cons (string-to-number (substring s (- math-bignum-digit-length))) + (math-read-bignum (substring s 0 (- math-bignum-digit-length)))) (list (string-to-number s)))) -- 2.39.2