Function: math-read-big-rec
math-read-big-rec is an autoloaded and byte-compiled function defined
in calc-lang.el.gz.
Signature
(math-read-big-rec RB-H1 RB-V1 RB-H2 RB-V2 &optional BASELINE PREC SHORT)
Source Code
;; Defined in /usr/src/emacs/lisp/calc/calc-lang.el.gz
(defun math-read-big-rec (rb-h1 rb-v1 rb-h2 rb-v2
&optional baseline prec short)
(or prec (setq prec 0))
(let ((math-rb-h1 rb-h1)
(math-rb-v1 rb-v1)
(math-rb-h2 rb-h2)
(math-rb-v2 rb-v2))
;; Clip whitespace above or below.
(while (and (< math-rb-v1 math-rb-v2)
(math-read-big-emptyp math-rb-h1 math-rb-v1 math-rb-h2 (1+ math-rb-v1)))
(setq math-rb-v1 (1+ math-rb-v1)))
(while (and (< math-rb-v1 math-rb-v2)
(math-read-big-emptyp math-rb-h1 (1- math-rb-v2) math-rb-h2 math-rb-v2))
(setq math-rb-v2 (1- math-rb-v2)))
;; If formula is a single line high, normal parser can handle it.
(if (<= math-rb-v2 (1+ math-rb-v1))
(if (or (<= math-rb-v2 math-rb-v1)
(> math-rb-h1 (length (setq math-rb-v2
(nth math-rb-v1 math-read-big-lines)))))
(math-read-big-error math-rb-h1 math-rb-v1)
(setq math-read-big-baseline math-rb-v1
math-read-big-h2 math-rb-h2
math-rb-v2 (nth math-rb-v1 math-read-big-lines)
math-rb-h2 (math-read-expr
(substring math-rb-v2 math-rb-h1
(min math-rb-h2 (length math-rb-v2)))))
(if (eq (car-safe math-rb-h2) 'error)
(math-read-big-error (+ math-rb-h1 (nth 1 math-rb-h2))
math-rb-v1 (nth 2 math-rb-h2))
math-rb-h2))
;; Clip whitespace at left or right.
(while (and (< math-rb-h1 math-rb-h2)
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) math-rb-v2))
(setq math-rb-h1 (1+ math-rb-h1)))
(while (and (< math-rb-h1 math-rb-h2)
(math-read-big-emptyp (1- math-rb-h2) math-rb-v1 math-rb-h2 math-rb-v2))
(setq math-rb-h2 (1- math-rb-h2)))
;; Scan to find widest left-justified "----" in the region.
(let* ((widest nil)
(widest-h2 0)
(lines-v1 (nthcdr math-rb-v1 math-read-big-lines))
(p lines-v1)
(v math-rb-v1)
(other-v nil)
other-char line len h)
(while (< v math-rb-v2)
(setq line (car p)
len (min math-rb-h2 (length line)))
(and (< math-rb-h1 len)
(/= (aref line math-rb-h1) ?\ )
(if (and (= (aref line math-rb-h1) ?\-)
;; Make sure it's not a minus sign.
(or (and (< (1+ math-rb-h1) len)
(= (aref line (1+ math-rb-h1)) ?\-))
(/= (math-read-big-char math-rb-h1 (1- v)) ?\ )
(/= (math-read-big-char math-rb-h1 (1+ v)) ?\ )))
(progn
(setq h math-rb-h1)
(while (and (< (setq h (1+ h)) len)
(= (aref line h) ?\-)))
(if (> h widest-h2)
(setq widest v
widest-h2 h)))
(or other-v (setq other-v v other-char (aref line math-rb-h1)))))
(setq v (1+ v)
p (cdr p)))
(cond ((not (setq v other-v))
(math-read-big-error math-rb-h1 math-rb-v1)) ; Should never happen!
;; Quotient.
(widest
(setq h widest-h2
v widest)
(let ((num (math-read-big-rec math-rb-h1 math-rb-v1 h v))
(den (math-read-big-rec math-rb-h1 (1+ v) h math-rb-v2)))
(setq p (if (and (math-integerp num) (math-integerp den))
(math-make-frac num den)
(list '/ num den)))))
;; Big radical sign.
((= other-char ?\\)
(or (= (math-read-big-char (1+ math-rb-h1) v) ?\|)
(math-read-big-error (1+ math-rb-h1) v "Malformed root sign"))
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(while (= (math-read-big-char (1+ math-rb-h1) (setq v (1- v))) ?\|))
(or (= (math-read-big-char (setq h (+ math-rb-h1 2)) v) ?\_)
(math-read-big-error h v "Malformed root sign"))
(while (= (math-read-big-char (setq h (1+ h)) v) ?\_))
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(math-read-big-emptyp math-rb-h1 (1+ other-v) h math-rb-v2 nil t)
(setq p (list 'calcFunc-sqrt (math-read-big-rec
(+ math-rb-h1 2) (1+ v)
h (1+ other-v) baseline))
v math-read-big-baseline))
;; Small radical sign.
((and (memq other-char '(?V ?√))
(= (math-read-big-char (1+ math-rb-h1) (1- v)) ?\_))
(setq h (1+ math-rb-h1))
(math-read-big-emptyp math-rb-h1 math-rb-v1 h (1- v) nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) h math-rb-v2 nil t)
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(while (= (math-read-big-char (setq h (1+ h)) (1- v)) ?\_))
(setq p (list 'calcFunc-sqrt (math-read-big-rec
(1+ math-rb-h1) v h (1+ v) t))
v math-read-big-baseline))
;; Binomial coefficient.
((and (= other-char ?\()
(= (math-read-big-char (1+ math-rb-h1) v) ?\ )
(= (string-match "( *)" (nth v math-read-big-lines)
math-rb-h1) math-rb-h1))
(setq h (match-end 0))
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) (1+ math-rb-h1) math-rb-v2 nil t)
(math-read-big-emptyp (1- h) math-rb-v1 h v nil t)
(math-read-big-emptyp (1- h) (1+ v) h math-rb-v2 nil t)
(setq p (list 'calcFunc-choose
(math-read-big-rec (1+ math-rb-h1) math-rb-v1 (1- h) v)
(math-read-big-rec (1+ math-rb-h1) (1+ v)
(1- h) math-rb-v2))))
;; Minus sign.
((= other-char ?\-)
(setq p (list 'neg (math-read-big-rec (1+ math-rb-h1) math-rb-v1
math-rb-h2 math-rb-v2 v 250 t))
v math-read-big-baseline
h math-read-big-h2))
;; Parentheses.
((= other-char ?\()
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) (1+ math-rb-h1) math-rb-v2 nil t)
(setq h (math-read-big-balance (1+ math-rb-h1) v "(" t))
(math-read-big-emptyp (1- h) math-rb-v1 h v nil t)
(math-read-big-emptyp (1- h) (1+ v) h math-rb-v2 nil t)
(let ((sep (math-read-big-char (1- h) v))
hmid)
(if (= sep ?\.)
(setq h (1+ h)))
(if (= sep ?\])
(math-read-big-error (1- h) v "Expected `)'"))
(if (= sep ?\))
(setq p (math-read-big-rec
(1+ math-rb-h1) math-rb-v1 (1- h) math-rb-v2 v))
(setq hmid (math-read-big-balance h v "(")
p (list p
(math-read-big-rec h math-rb-v1 (1- hmid) math-rb-v2 v))
h hmid)
(cond ((= sep ?\.)
(setq p (cons 'intv (cons (if (= (math-read-big-char
(1- h) v)
?\))
0 1)
p))))
((= (math-read-big-char (1- h) v) ?\])
(math-read-big-error (1- h) v "Expected `)'"))
((= sep ?\,)
(or (and (math-realp (car p)) (math-realp (nth 1 p)))
(math-read-big-error
math-rb-h1 v "Complex components must be real"))
(setq p (cons 'cplx p)))
((= sep ?\;)
(or (and (math-realp (car p)) (math-anglep (nth 1 p)))
(math-read-big-error
math-rb-h1 v "Complex components must be real"))
(setq p (cons 'polar p)))))))
;; Matrix.
((and (= other-char ?\[)
(or (= (math-read-big-char (setq h math-rb-h1) (1+ v)) ?\[)
(= (math-read-big-char (setq h (1+ h)) v) ?\[)
(and (= (math-read-big-char h v) ?\ )
(= (math-read-big-char (setq h (1+ h)) v) ?\[)))
(= (math-read-big-char h (1+ v)) ?\[))
(math-read-big-emptyp math-rb-h1 math-rb-v1 h v nil t)
(let ((vtop v)
(hleft h)
(hright nil))
(setq p nil)
(while (progn
(setq h (math-read-big-balance (1+ hleft) v "["))
(if hright
(or (= h hright)
(math-read-big-error hright v "Expected `]'"))
(setq hright h))
(setq p (cons (math-read-big-rec
hleft v h (1+ v)) p))
(and (memq (math-read-big-char h v) '(?\ ?\,))
(= (math-read-big-char hleft (1+ v)) ?\[)))
(setq v (1+ v)))
(or (= hleft math-rb-h1)
(progn
(if (= (math-read-big-char h v) ?\ )
(setq h (1+ h)))
(and (= (math-read-big-char h v) ?\])
(setq h (1+ h))))
(math-read-big-error (1- h) v "Expected `]'"))
(if (= (math-read-big-char h vtop) ?\,)
(setq h (1+ h)))
(math-read-big-emptyp math-rb-h1 (1+ v) (1- h) math-rb-v2 nil t)
(setq v (+ vtop (/ (- v vtop) 2))
p (cons 'vec (nreverse p)))))
;; Square brackets.
((= other-char ?\[)
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) (1+ math-rb-h1) math-rb-v2 nil t)
(setq p nil
h (1+ math-rb-h1))
(while (progn
(setq widest (math-read-big-balance h v "[" t))
(math-read-big-emptyp (1- h) math-rb-v1 h v nil t)
(math-read-big-emptyp (1- h) (1+ v) h math-rb-v2 nil t)
(setq p (cons (math-read-big-rec
h math-rb-v1 (1- widest) math-rb-v2 v) p)
h widest)
(= (math-read-big-char (1- h) v) ?\,)))
(setq widest (math-read-big-char (1- h) v))
(if (or (memq widest '(?\; ?\)))
(and (eq widest ?\.) (cdr p)))
(math-read-big-error (1- h) v "Expected `]'"))
(if (= widest ?\.)
(setq h (1+ h)
widest (math-read-big-balance h v "[")
p (nconc p (list (math-read-big-rec
h math-rb-v1 (1- widest) math-rb-v2 v)))
h widest
p (cons 'intv (cons (if (= (math-read-big-char (1- h) v)
?\])
3 2)
p)))
(setq p (cons 'vec (nreverse p)))))
;; Date form.
((= other-char ?\<)
(setq line (nth v math-read-big-lines))
(string-match ">" line math-rb-h1)
(setq h (match-end 0))
(math-read-big-emptyp math-rb-h1 math-rb-v1 h v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) h math-rb-v2 nil t)
(setq p (math-read-big-rec math-rb-h1 v h (1+ v) v)))
;; Variable name or function call.
((or (and (>= other-char ?a) (<= other-char ?z))
(and (>= other-char ?A) (<= other-char ?Z))
(and (>= other-char ?α) (<= other-char ?ω))
(and (>= other-char ?Α) (<= other-char ?Ω)))
(setq line (nth v math-read-big-lines))
(string-match "\\([a-zA-Zα-ωΑ-Ω'_]+\\) *" line math-rb-h1)
(setq h (match-end 1)
widest (match-end 0)
p (math-match-substring line 1))
(math-read-big-emptyp math-rb-h1 math-rb-v1 h v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) h math-rb-v2 nil t)
(if (= (math-read-big-char widest v) ?\()
(progn
(setq line (if (string-search "-" p)
(intern p)
(intern (concat "calcFunc-" p)))
h (1+ widest)
p nil)
(math-read-big-emptyp widest math-rb-v1 h v nil t)
(math-read-big-emptyp widest (1+ v) h math-rb-v2 nil t)
(while (progn
(setq widest (math-read-big-balance h v "(" t))
(math-read-big-emptyp (1- h) math-rb-v1 h v nil t)
(math-read-big-emptyp (1- h) (1+ v) h math-rb-v2 nil t)
(setq p (cons (math-read-big-rec
h math-rb-v1 (1- widest) math-rb-v2 v) p)
h widest)
(= (math-read-big-char (1- h) v) ?\,)))
(or (= (math-read-big-char (1- h) v) ?\))
(math-read-big-error (1- h) v "Expected `)'"))
(setq p (cons line (nreverse p))))
(setq p (list 'var
(intern (math-remove-dashes p))
(if (string-search "-" p)
(intern p)
(intern (concat "var-" p)))))))
;; Number.
(t
(setq line (nth v math-read-big-lines))
(or (= (string-match "_?\\([0-9]+.?0*@ *\\)?\\([0-9]+.?0*' *\\)?\\([0-9]+\\(#\\|\\^\\^\\)[0-9a-zA-Z:]+\\|[0-9]+:[0-9:]+\\|[0-9.]+\\([eE][-+_]?[0-9]+\\)?\"?\\)?" line math-rb-h1) math-rb-h1)
(math-read-big-error h v "Expected a number"))
(setq h (match-end 0)
p (math-read-number (math-match-substring line 0)))
(math-read-big-emptyp math-rb-h1 math-rb-v1 h v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) h math-rb-v2 nil t)))
;; Now left term is bounded by math-rb-h1, math-rb-v1, h, math-rb-v2;
;; baseline = v.
(if baseline
(or (= v baseline)
(math-read-big-error math-rb-h1 v "Inconsistent baseline in formula"))
(setq baseline v))
;; Look for superscripts or subscripts.
(setq line (nth baseline math-read-big-lines)
len (min math-rb-h2 (length line))
widest h)
(while (and (< widest len)
(= (aref line widest) ?\ ))
(setq widest (1+ widest)))
(and (>= widest len) (setq widest math-rb-h2))
(if (math-read-big-emptyp h v widest math-rb-v2)
(if (math-read-big-emptyp h math-rb-v1 widest v)
(setq h widest)
(setq p (list '^ p (math-read-big-rec h math-rb-v1 widest v))
h widest))
(if (math-read-big-emptyp h math-rb-v1 widest v)
(setq p (list 'calcFunc-subscr p
(math-read-big-rec h v widest math-rb-v2))
h widest)))
;; Look for an operator name and grab additional terms.
(while (and (< h len)
(if (setq widest (and (math-read-big-emptyp
h math-rb-v1 (1+ h) v)
(math-read-big-emptyp
h (1+ v) (1+ h) math-rb-v2)
(string-match "<=\\|>=\\|\\+/-\\|!=\\|&&\\|||\\|:=\\|=>\\|." line h)
(assoc (math-match-substring line 0)
(math-standard-ops))))
(and (>= (nth 2 widest) prec)
(setq h (match-end 0)))
(and (not (eq (string-match ",\\|;\\|\\.\\.\\|)\\|\\]\\|:" line h)
h))
(setq widest '("2x" * 196 195)))))
(cond ((eq (nth 3 widest) -1)
(setq p (list (nth 1 widest) p)))
((equal (car widest) "?")
(let ((y (math-read-big-rec h math-rb-v1 math-rb-h2
math-rb-v2 baseline nil t)))
(or (= (math-read-big-char math-read-big-h2 baseline) ?\:)
(math-read-big-error math-read-big-h2 baseline
"Expected `:'"))
(setq p (list (nth 1 widest) p y
(math-read-big-rec
(1+ math-read-big-h2) math-rb-v1 math-rb-h2 math-rb-v2
baseline (nth 3 widest) t))
h math-read-big-h2)))
(t
(setq p (list (nth 1 widest) p
(math-read-big-rec h math-rb-v1 math-rb-h2 math-rb-v2
baseline (nth 3 widest) t))
h math-read-big-h2))))
;; Return all relevant information to caller.
(setq math-read-big-baseline baseline
math-read-big-h2 h)
(or short (= math-read-big-h2 math-rb-h2)
(math-read-big-error h baseline))
p))))