(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.
This commit is contained in:
Jay Belanger
parent
d621bc0ad7
commit
a6d107f171
2 changed files with 125 additions and 76 deletions
|
|
@ -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))))
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue