(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.

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  <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.
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))))