Commit a6d107f1 authored by Jay Belanger's avatar Jay Belanger
Browse files

(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.
parent d621bc0a
2007-06-22 Jay Belanger <jay.p.belanger@gmail.com>
* 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 <dann@ics.uci.edu>
* vc-hg.el (vc-hg-log-view-mode): Fix last change.
......
......@@ -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 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 @@ 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))))
......
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