[Top][All Lists]
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
[Emacs-diffs] Changes to emacs/lisp/calc/calc.el,v
|
From: |
Jay Belanger |
|
Subject: |
[Emacs-diffs] Changes to emacs/lisp/calc/calc.el,v |
|
Date: |
Sat, 23 Jun 2007 04:05:29 +0000 |
CVSROOT: /cvsroot/emacs
Module name: emacs
Changes by: Jay Belanger <jpb> 07/06/23 04:05:29
Index: calc.el
===================================================================
RCS file: /cvsroot/emacs/emacs/lisp/calc/calc.el,v
retrieving revision 1.80
retrieving revision 1.81
diff -u -b -r1.80 -r1.81
--- calc.el 22 Jun 2007 01:03:24 -0000 1.80
+++ calc.el 23 Jun 2007 04:05:29 -0000 1.81
@@ -2283,7 +2283,18 @@
+(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 @@
;;; 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 @@
(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 @@
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 @@
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 @@
(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 @@
(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 @@
(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 @@
(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 @@
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 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)
- (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)))))))
+ (* 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 @@
(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 @@
((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 @@
(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 @@
(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 @@
(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 @@
(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 @@
(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 @@
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 @@
(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 @@
(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 @@
(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 @@
(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 @@
(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 @@
(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 @@
(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 @@
(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 @@
""))
(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))))