Update copyright year to 2014 by running admin/update-copyright.

[emacs.git] / lisp / calc / calccomp.el

;;; calccomp.el --- composition functions for Calc

;; Copyright (C) 1990-1993, 2001-2014 Free Software Foundation, Inc.

;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>

;; This file is part of GNU Emacs.

;; GNU Emacs is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or
;; (at your option) any later version.

;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
;; GNU General Public License for more details.

;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs.  If not, see <http://www.gnu.org/licenses/>.

;;; Commentary:

;;; Code:

;; This file is autoloaded from calc-ext.el.

(require 'calc-ext)
(require 'calc-macs)

;;; A "composition" has one of the following forms:
;;;
;;;    "string"              A literal string
;;;
;;;    (horiz C1 C2 ...)     Horizontally abutted sub-compositions
;;;
;;;    (set LEVEL OFF)       Set left margin + offset for line-break level
;;;    (break LEVEL)         A potential line-break point
;;;
;;;    (vleft N C1 C2 ...)   Vertically stacked, left-justified sub-comps
;;;    (vcent N C1 C2 ...)   Vertically stacked, centered sub-comps
;;;    (vright N C1 C2 ...)  Vertically stacked, right-justified sub-comps
;;;                          N specifies baseline of the stack, 0=top line.
;;;
;;;    (supscr C1 C2)        Composition C1 with superscript C2
;;;    (subscr C1 C2)        Composition C1 with subscript C2
;;;    (rule X)              Horizontal line of X, full width of enclosing comp
;;;
;;;    (tag X C)             Composition C corresponds to sub-expression X

;; math-comp-just and math-comp-comma-spc are local to
;; math-compose-expr, but are used by math-compose-matrix, which is
;; called by math-compose-expr
(defvar math-comp-just)
(defvar math-comp-comma-spc)

;; math-comp-vector-prec is local to math-compose-expr, but is used by
;; math-compose-matrix and math-compose-rows, which are called by
;; math-compose-expr.
(defvar math-comp-vector-prec)

;; math-comp-left-bracket, math-comp-right-bracket and math-comp-comma are
;; local to math-compose-expr, but are used by math-compose-rows, which is
;; called by math-compose-expr.
(defvar math-comp-left-bracket)
(defvar math-comp-right-bracket)
(defvar math-comp-comma)

(defun math-compose-var (a)
  (let (v sn)
    (if (and math-compose-hash-args
             (let ((p calc-arg-values))
               (setq v 1)
               (while (and p (not (equal (car p) a)))
                 (setq p (and (eq math-compose-hash-args t) (cdr p))
                       v (1+ v)))
               p))
        (if (eq math-compose-hash-args 1)
            "#"
          (format "#%d" v))
      (setq sn (symbol-name (nth 1 a)))
      (if (memq calc-language calc-lang-allow-percentsigns)
          (setq sn (math-to-percentsigns sn)))
      (if (memq calc-language calc-lang-allow-underscores)
          (setq sn (math-to-underscores sn)))
      sn)))

;;; Give multiplication precedence when composing to avoid
;;; writing a*(b c) instead of a b c
(defun math-compose-expr (a prec &optional div)
  (let ((calc-multiplication-has-precedence t)
        (math-compose-level (1+ math-compose-level))
        (math-expr-opers (math-expr-ops))
        spfn)
    (cond
     ((or (and (eq a math-comp-selected) a)
          (and math-comp-tagged
               (not (eq math-comp-tagged a))))
      (let ((math-comp-selected nil))
        (and math-comp-tagged (setq math-comp-tagged a))
        (list 'tag a (math-compose-expr a prec))))
     ((and (not (consp a)) (not (integerp a)))
      (concat "'" (prin1-to-string a)))
     ((setq spfn (assq (car-safe a)
                       (get calc-language 'math-special-function-table)))
      (setq spfn (cdr spfn))
      (if (consp spfn)
          (funcall (car spfn) a spfn)
        (funcall spfn a)))
     ((math-scalarp a)
      (if (or (eq (car-safe a) 'frac)
              (and (nth 1 calc-frac-format) (Math-integerp a)))
          (if (and
               calc-language
               (not (memq calc-language
                          '(flat big unform))))
              (let ((aa (math-adjust-fraction a))
                    (calc-frac-format nil))
                (math-compose-expr (list '/
                                         (if (memq calc-language
                                                   calc-lang-slash-idiv)
                                             (math-float (nth 1 aa))
                                           (nth 1 aa))
                                         (nth 2 aa)) prec))
            (if (and (eq calc-language 'big)
                     (= (length (car calc-frac-format)) 1))
                (let* ((aa (math-adjust-fraction a))
                       (calc-frac-format nil)
                       (math-radix-explicit-format nil)
                       (c (list 'horiz
                                (if (math-negp (nth 1 aa))
                                    "- " "")
                                (list 'vcent 1
                                      (math-format-number
                                       (math-abs (nth 1 aa)))
                                      '(rule ?-)
                                      (math-format-number (nth 2 aa))))))
                  (if (= calc-number-radix 10)
                      c
                    (list 'horiz "(" c
                          (list 'subscr ")"
                                (int-to-string calc-number-radix)))))
              (math-format-number a)))
        (if (not (eq calc-language 'big))
            (math-format-number a prec)
          (if (memq (car-safe a) '(cplx polar))
              (if (math-zerop (nth 2 a))
                  (math-compose-expr (nth 1 a) prec)
                (list 'horiz "("
                      (math-compose-expr (nth 1 a) 0)
                      (if (eq (car a) 'cplx) ", " "; ")
                      (math-compose-expr (nth 2 a) 0) ")"))
            (if (or (= calc-number-radix 10)
                    (not (Math-realp a))
                    (and calc-group-digits
                         (not (assoc calc-group-char '((",") (" "))))))
                (math-format-number a prec)
              (let ((s (math-format-number a prec))
                    (c nil))
                (while (string-match (if (> calc-number-radix 14)
                                         "\\([0-9]+\\)#\\([0-9a-zA-Z., ]+\\)"
                                       "\\([0-9]+\\)#\\([0-9a-dA-D., ]+\\)")
                                     s)
                  (setq c (nconc c (list (substring s 0 (match-beginning 0))
                                         (list 'subscr
                                               (math-match-substring s 2)
                                               (math-match-substring s 1))))
                        s (substring s (match-end 0))))
                (if (string-match
                     "\\*\\([0-9.]+\\)\\^\\(-?[0-9]+\\)\\()?\\)\\'" s)
                    (setq s (list 'horiz
                                  (substring s 0 (match-beginning 0)) " "
                                  (list 'supscr
                                        (math-match-substring s 1)
                                        (math-match-substring s 2))
                                  (math-match-substring s 3))))
                (if c (cons 'horiz (nconc c (list s))) s)))))))
     ((and (get (car a) 'math-compose-forms)
           (not (eq calc-language 'unform))
           (let ((comps (get (car a) 'math-compose-forms))
                 temp temp2)
             (or (and (setq temp (assq calc-language comps))
                      (or (and (setq temp2 (assq (1- (length a)) (cdr temp)))
                               (setq temp (apply (cdr temp2) (cdr a)))
                               (math-compose-expr temp prec))
                          (and (setq temp2 (assq nil (cdr temp)))
                               (funcall (cdr temp2) a))))
                 (and (setq temp (assq nil comps))
                      (or (and (setq temp2 (assq (1- (length a)) (cdr temp)))
                               (setq temp (apply (cdr temp2) (cdr a)))
                               (math-compose-expr temp prec))
                          (and (setq temp2 (assq nil (cdr temp)))
                               (funcall (cdr temp2) a))))))))
     ((eq (car a) 'vec)
      (let* ((math-comp-left-bracket (if calc-vector-brackets
                               (substring calc-vector-brackets 0 1) ""))
             (math-comp-right-bracket (if calc-vector-brackets
                                (substring calc-vector-brackets 1 2) ""))
             (inner-brackets (memq 'R calc-matrix-brackets))
             (outer-brackets (memq 'O calc-matrix-brackets))
             (row-commas (memq 'C calc-matrix-brackets))
             (math-comp-comma-spc (or calc-vector-commas " "))
             (math-comp-comma (or calc-vector-commas ""))
             (math-comp-vector-prec (if (or (and calc-vector-commas
                                       (math-vector-no-parens a))
                                  (memq 'P calc-matrix-brackets)) 0 1000))
             (math-comp-just (cond ((eq calc-matrix-just 'right) 'vright)
                                      ((eq calc-matrix-just 'center) 'vcent)
                                      (t 'vleft)))
             (break calc-break-vectors))
        (if (and (memq calc-language '(nil big))
                 (not calc-break-vectors)
                 (math-matrixp a) (not (math-matrixp (nth 1 a)))
                 (or calc-full-vectors
                     (and (< (length a) 7) (< (length (nth 1 a)) 7))
                     (progn (setq break t) nil)))
            (if (progn
                  (setq math-comp-vector-prec (if (or (and calc-vector-commas
                                                           (math-vector-no-parens
                                                            (nth 1 a)))
                                                      (memq 'P calc-matrix-brackets))
                                                  0 1000))
                  (= (length a) 2))
                (list 'horiz
                      (concat math-comp-left-bracket math-comp-left-bracket " ")
                      (math-compose-vector (cdr (nth 1 a)) (concat math-comp-comma " ")
                                           math-comp-vector-prec)
                      (concat " " math-comp-right-bracket math-comp-right-bracket))
              (let* ((rows (1- (length a)))
                     (cols (1- (length (nth 1 a))))
                     (base (/ (1- rows) 2))
                     (calc-language 'flat))
                (append '(horiz)
                        (list (append '(vleft)
                                      (list base)
                                      (list (concat (and outer-brackets
                                                         (concat math-comp-left-bracket
                                                                 " "))
                                                    (and inner-brackets
                                                         (concat math-comp-left-bracket
                                                                 " "))))
                                      (make-list (1- rows)
                                                 (concat (and outer-brackets
                                                              "  ")
                                                         (and inner-brackets
                                                              (concat
                                                               math-comp-left-bracket
                                                               " "))))))
                        (math-compose-matrix (cdr a) 1 cols base)
                        (list (append '(vleft)
                                      (list base)
                                      (make-list (1- rows)
                                                 (if inner-brackets
                                                     (concat " "
                                                             math-comp-right-bracket
                                                             (and row-commas
                                                                  math-comp-comma))
                                                   (if (and outer-brackets
                                                            row-commas)
                                                       ";" "")))
                                      (list (concat
                                             (and inner-brackets
                                                  (concat " "
                                                          math-comp-right-bracket))
                                             (and outer-brackets
                                                  (concat
                                                   " "
                                                   math-comp-right-bracket)))))))))
          (if (and calc-display-strings
                   (cdr a)
                   (math-vector-is-string a))
              (math-vector-to-string a t)
            (if (and break (cdr a)
                     (not (eq calc-language 'flat)))
                (let* ((full (or calc-full-vectors (< (length a) 7)))
                       (rows (if full (1- (length a)) 5))
                       (base (/ (1- rows) 2))
                       (calc-break-vectors nil))
                  (list 'horiz
                        (cons 'vleft (cons base
                                           (math-compose-rows
                                            (cdr a)
                                            (if full rows 3) t)))))
              (if (or calc-full-vectors (< (length a) 7))
                  (if (and
                       (setq spfn (get calc-language 'math-matrix-formatter))
                       (math-matrixp a))
                      (funcall spfn a)
                    (list 'horiz
                          math-comp-left-bracket
                          (math-compose-vector (cdr a)
                                               (concat math-comp-comma " ")
                                               math-comp-vector-prec)
                          math-comp-right-bracket))
                (list 'horiz
                      math-comp-left-bracket
                      (math-compose-vector (list (nth 1 a) (nth 2 a) (nth 3 a))
                                           (concat math-comp-comma " ")
                                           math-comp-vector-prec)
                      math-comp-comma
                      (if (setq spfn (get calc-language 'math-dots))
                          (concat " " spfn)
                        " ...")
                      math-comp-comma " "
                      (list 'break math-compose-level)
                      (math-compose-expr (nth (1- (length a)) a)
                                         (if (equal math-comp-comma "") 1000 0))
                      math-comp-right-bracket)))))))
     ((eq (car a) 'incomplete)
      (if (cdr (cdr a))
          (cond ((eq (nth 1 a) 'vec)
                 (list 'horiz "["
                       (math-compose-vector (cdr (cdr a)) ", " 0)
                       " ..."))
                ((eq (nth 1 a) 'cplx)
                 (list 'horiz "("
                       (math-compose-vector (cdr (cdr a)) ", " 0)
                       ", ..."))
                ((eq (nth 1 a) 'polar)
                 (list 'horiz "("
                       (math-compose-vector (cdr (cdr a)) "; " 0)
                       "; ..."))
                ((eq (nth 1 a) 'intv)
                 (list 'horiz
                       (if (memq (nth 2 a) '(0 1)) "(" "[")
                       (math-compose-vector (cdr (cdr (cdr a))) " .. " 0)
                       " .. ..."))
                (t (format "%s" a)))
        (cond ((eq (nth 1 a) 'vec) "[ ...")
              ((eq (nth 1 a) 'intv)
               (if (memq (nth 2 a) '(0 1)) "( ..." "[ ..."))
              (t "( ..."))))
     ((eq (car a) 'var)
      (let ((v (rassq (nth 2 a) math-expr-variable-mapping)))
        (if v
            (symbol-name (car v))
          (if (setq spfn (get calc-language 'math-var-formatter))
              (funcall spfn a prec)
            (math-compose-var a)))))
     ((eq (car a) 'intv)
      (list 'horiz
            (if (memq (nth 1 a) '(0 1)) "(" "[")
            (math-compose-expr (nth 2 a) 0)
            " .. "
            (math-compose-expr (nth 3 a) 0)
            (if (memq (nth 1 a) '(0 2)) ")" "]")))
     ((eq (car a) 'date)
      (if (eq (car calc-date-format) 'X)
          (math-format-date a)
        (concat "<" (math-format-date a) ">")))
     ((and (eq (car a) 'calcFunc-subscr)
           (setq spfn (get calc-language 'math-compose-subscr)))
      (funcall spfn a))
     ((and (eq (car a) 'calcFunc-subscr) (= (length a) 3)
           (eq calc-language 'big))
      (let* ((a1 (math-compose-expr (nth 1 a) 1000))
             (calc-language 'flat)
             (a2 (math-compose-expr (nth 2 a) 0)))
        (if (or (eq (car-safe a1) 'subscr)
                (and (eq (car-safe a1) 'tag)
                     (eq (car-safe (nth 2 a1)) 'subscr)
                     (setq a1 (nth 2 a1))))
            (list 'subscr
                  (nth 1 a1)
                  (list 'horiz
                        (nth 2 a1)
                        ", "
                        a2))
          (list 'subscr a1 a2))))
     ((and (eq (car a) '^)
           (eq calc-language 'big))
      (list 'supscr
            (if (or (math-looks-negp (nth 1 a))
                    (memq (car-safe (nth 1 a)) '(^ / frac calcFunc-sqrt))
                    (and (eq (car-safe (nth 1 a)) 'cplx)
                         (math-negp (nth 1 (nth 1 a)))
                         (eq (nth 2 (nth 1 a)) 0)))
                (list 'horiz "(" (math-compose-expr (nth 1 a) 0) ")")
              (math-compose-expr (nth 1 a) 201))
            (let ((calc-language 'flat)
                  (calc-number-radix 10)
                  (calc-twos-complement-mode nil))
              (math-compose-expr (nth 2 a) 0))))
     ((and (eq (car a) '/)
           (eq calc-language 'big))
      (let ((a1 (let ((calc-language (if (memq (car-safe (nth 1 a)) '(/ frac))
                                         'flat 'big)))
                  (math-compose-expr (nth 1 a) 0)))
            (a2 (let ((calc-language (if (memq (car-safe (nth 2 a)) '(/ frac))
                                         'flat 'big)))
                  (math-compose-expr (nth 2 a) 0))))
        (list 'vcent
              (math-comp-height a1)
              a1 '(rule ?-) a2)))
     ((and (eq (car a) 'calcFunc-lambda)
           (> (length a) 2)
           (memq calc-language '(nil flat big)))
      (let ((p (cdr a))
            (ap calc-arg-values)
            (math-compose-hash-args (if (= (length a) 3) 1 t)))
        (while (and (cdr p) (equal (car p) (car ap)))
          (setq p (cdr p) ap (cdr ap)))
        (append '(horiz "<")
                (if (cdr p)
                    (list (math-compose-vector
                           (nreverse (cdr (reverse (cdr a)))) ", " 0)
                          " : ")
                  nil)
                (list (math-compose-expr (nth (1- (length a)) a) 0)
                      ">"))))
     ((and (eq (car a) 'calcFunc-string)
           (= (length a) 2)
           (math-vectorp (nth 1 a))
           (math-vector-is-string (nth 1 a)))
      (if (eq calc-language 'unform)
          (concat "string(" (math-vector-to-string (nth 1 a) t) ")")
        (math-vector-to-string (nth 1 a) nil)))
     ((and (eq (car a) 'calcFunc-bstring)
           (= (length a) 2)
           (math-vectorp (nth 1 a))
           (math-vector-is-string (nth 1 a)))
      (if (eq calc-language 'unform)
          (concat "bstring(" (math-vector-to-string (nth 1 a) t) ")")
        (let ((c nil)
              (s (math-vector-to-string (nth 1 a) nil))
              p)
          (while (string-match "[^ ] +[^ ]" s)
            (setq p (1- (match-end 0))
                  c (cons (list 'break math-compose-level)
                          (cons (substring s 0 p)
                                c))
                  s (substring s p)))
          (setq c (nreverse (cons s c)))
          (or (= prec -123)
              (setq c (cons (list 'set math-compose-level 2) c)))
          (cons 'horiz c))))
     ((and (eq (car a) 'calcFunc-cprec)
           (not (eq calc-language 'unform))
           (= (length a) 3)
           (integerp (nth 2 a)))
      (let ((c (math-compose-expr (nth 1 a) -1)))
        (if (> prec (nth 2 a))
            (if (setq spfn (get calc-language 'math-big-parens))
                (list 'horiz (car spfn) c (cdr spfn))
              (list 'horiz "(" c ")"))
          c)))
     ((and (eq (car a) 'calcFunc-choriz)
           (not (eq calc-language 'unform))
           (memq (length a) '(2 3 4))
           (math-vectorp (nth 1 a))
           (if (integerp (nth 2 a))
               (or (null (nth 3 a))
                   (and (math-vectorp (nth 3 a))
                        (math-vector-is-string (nth 3 a))))
             (or (null (nth 2 a))
                 (and (math-vectorp (nth 2 a))
                      (math-vector-is-string (nth 2 a))))))
      (let* ((cprec (and (integerp (nth 2 a)) (nth 2 a)))
             (sep (nth (if cprec 3 2) a))
             (bprec nil))
        (if sep
            (math-compose-vector (cdr (nth 1 a))
                                 (math-vector-to-string sep nil)
                                 (or cprec prec))
          (cons 'horiz (mapcar (function
                                (lambda (x)
                                  (if (eq (car-safe x) 'calcFunc-bstring)
                                      (prog1
                                          (math-compose-expr
                                           x (or bprec cprec prec))
                                        (setq bprec -123))
                                    (math-compose-expr x (or cprec prec)))))
                               (cdr (nth 1 a)))))))
     ((and (memq (car a) '(calcFunc-cvert calcFunc-clvert calcFunc-crvert))
           (not (eq calc-language 'unform))
           (memq (length a) '(2 3))
           (math-vectorp (nth 1 a))
           (or (null (nth 2 a))
               (integerp (nth 2 a))))
      (let* ((base 0)
             (v 0)
             (prec (or (nth 2 a) prec))
             (c (mapcar (function
                         (lambda (x)
                           (let ((b nil) (cc nil) a d)
                             (if (and (memq (car-safe x) '(calcFunc-cbase
                                                           calcFunc-ctbase
                                                           calcFunc-cbbase))
                                      (memq (length x) '(1 2)))
                                 (setq b (car x)
                                       x (nth 1 x)))
                             (if (and (eq (car-safe x) 'calcFunc-crule)
                                      (memq (length x) '(1 2))
                                      (or (null (nth 1 x))
                                          (and (math-vectorp (nth 1 x))
                                               (= (length (nth 1 x)) 2)
                                               (math-vector-is-string
                                                (nth 1 x)))
                                          (and (natnump (nth 1 x))
                                               (<= (nth 1 x) 255))))
                                 (setq cc (list
                                           'rule
                                           (if (math-vectorp (nth 1 x))
                                               (aref (math-vector-to-string
                                                      (nth 1 x) nil) 0)
                                             (or (nth 1 x) ?-))))
                               (or (and (memq (car-safe x) '(calcFunc-cvspace
                                                             calcFunc-ctspace
                                                             calcFunc-cbspace))
                                        (memq (length x) '(2 3))
                                        (eq (nth 1 x) 0))
                                   (null x)
                                   (setq cc (math-compose-expr x prec))))
                             (setq a (if cc (math-comp-ascent cc) 0)
                                   d (if cc (math-comp-descent cc) 0))
                             (if (eq b 'calcFunc-cbase)
                                 (setq base (+ v a -1))
                               (if (eq b 'calcFunc-ctbase)
                                   (setq base v)
                                 (if (eq b 'calcFunc-cbbase)
                                     (setq base (+ v a d -1)))))
                             (setq v (+ v a d))
                             cc)))
                        (cdr (nth 1 a)))))
        (setq c (delq nil c))
        (if c
            (cons (if (eq (car a) 'calcFunc-cvert) 'vcent
                    (if (eq (car a) 'calcFunc-clvert) 'vleft 'vright))
                  (cons base c))
          " ")))
     ((and (memq (car a) '(calcFunc-csup calcFunc-csub))
           (not (eq calc-language 'unform))
           (memq (length a) '(3 4))
           (or (null (nth 3 a))
               (integerp (nth 3 a))))
      (list (if (eq (car a) 'calcFunc-csup) 'supscr 'subscr)
            (math-compose-expr (nth 1 a) (or (nth 3 a) 0))
            (math-compose-expr (nth 2 a) 0)))
     ((and (eq (car a) 'calcFunc-cflat)
           (not (eq calc-language 'unform))
           (memq (length a) '(2 3))
           (or (null (nth 2 a))
               (integerp (nth 2 a))))
      (let ((calc-language (if (memq calc-language '(nil big))
                               'flat calc-language)))
        (math-compose-expr (nth 1 a) (or (nth 2 a) 0))))
     ((and (eq (car a) 'calcFunc-cspace)
           (memq (length a) '(2 3))
           (natnump (nth 1 a)))
      (if (nth 2 a)
          (cons 'horiz (make-list (nth 1 a)
                                  (if (and (math-vectorp (nth 2 a))
                                           (math-vector-is-string (nth 2 a)))
                                      (math-vector-to-string (nth 2 a) nil)
                                    (math-compose-expr (nth 2 a) 0))))
        (make-string (nth 1 a) ?\ )))
     ((and (memq (car a) '(calcFunc-cvspace calcFunc-ctspace calcFunc-cbspace))
           (memq (length a) '(2 3))
           (natnump (nth 1 a)))
      (if (= (nth 1 a) 0)
          ""
        (let* ((c (if (nth 2 a)
                      (if (and (math-vectorp (nth 2 a))
                               (math-vector-is-string (nth 2 a)))
                          (math-vector-to-string (nth 2 a) nil)
                        (math-compose-expr (nth 2 a) 0))
                    " "))
               (ca (math-comp-ascent c))
               (cd (math-comp-descent c)))
          (cons 'vleft
                (cons (if (eq (car a) 'calcFunc-ctspace)
                          (1- ca)
                        (if (eq (car a) 'calcFunc-cbspace)
                            (+ (* (1- (nth 1 a)) (+ ca cd)) (1- ca))
                          (/ (1- (* (nth 1 a) (+ ca cd))) 2)))
                      (make-list (nth 1 a) c))))))
     ((and (eq (car a) 'calcFunc-evalto)
           (setq calc-any-evaltos t)
           (setq spfn (get calc-language 'math-evalto))
           (= math-compose-level (if math-comp-tagged 2 1))
           (= (length a) 3))
      (list 'horiz
            (car spfn)
            (math-compose-expr (nth 1 a) 0)
            (cdr spfn)
            (math-compose-expr (nth 2 a) 0)))
     (t
      (let ((op (and (not (eq calc-language 'unform))
                     (if (and (eq (car a) 'calcFunc-if) (= (length a) 4))
                         (assoc "?" math-expr-opers)
                       (math-assq2 (car a) math-expr-opers)))))
        (cond ((and op
                    (or (= (length a) 3) (eq (car a) 'calcFunc-if))
                    (/= (nth 3 op) -1))
               (cond
                ((or
                  (> prec (or (nth 4 op) (min (nth 2 op) (nth 3 op))))
                  (and div (eq (car a) '*)))
                 (if (and (memq calc-language '(tex latex))
                          (not (math-tex-expr-is-flat a)))
                     (if (eq (car-safe a) '/)
                         (list 'horiz "{" (math-compose-expr a -1) "}")
                       (list 'horiz "\\left( "
                             (math-compose-expr a -1)
                             " \\right)"))
                   (if (eq calc-language 'eqn)
                       (if (or (eq (car-safe a) '/)
                               (= (/ prec 100) 9))
                           (list 'horiz "{" (math-compose-expr a -1) "}")
                         (if (math-tex-expr-is-flat a)
                             (list 'horiz "( " (math-compose-expr a -1) " )")
                           (list 'horiz "{left ( "
                                 (math-compose-expr a -1)
                                 " right )}")))
                     (list 'horiz "(" (math-compose-expr a 0) ")"))))
                ((and (memq calc-language '(tex latex))
                      (memq (car a) '(/ calcFunc-choose calcFunc-evalto))
                      (>= prec 0))
                 (list 'horiz "{" (math-compose-expr a -1) "}"))
                ((eq (car a) 'calcFunc-if)
                 (list 'horiz
                       (math-compose-expr (nth 1 a) (nth 2 op))
                       " ? "
                       (math-compose-expr (nth 2 a) 0)
                       " : "
                       (math-compose-expr (nth 3 a) (nth 3 op))))
                (t
                 (let* ((math-comp-tagged (and math-comp-tagged
                                               (not (math-primp a))
                                               math-comp-tagged))
                        (setlev (if (= prec (min (nth 2 op) (nth 3 op)))
                                    (progn
                                      (setq math-compose-level
                                            (1- math-compose-level))
                                      nil)
                                  math-compose-level))
                        (lhs (math-compose-expr (nth 1 a) (nth 2 op)))
                        (rhs (math-compose-expr (nth 2 a) (nth 3 op) (eq (nth 1 op) '/))))
                   (and (equal (car op) "^")
                        (eq (math-comp-first-char lhs) ?-)
                        (setq lhs (list 'horiz "(" lhs ")")))
                   (and (memq calc-language '(tex latex))
                        (or (equal (car op) "^") (equal (car op) "_"))
                        (not (and (stringp rhs) (= (length rhs) 1)))
                        (setq rhs (list 'horiz "{" rhs "}")))
                   (or (and (eq (car a) '*)
                            (or (null calc-language)
                                (assoc "2x" math-expr-opers))
                            (let* ((prevt (math-prod-last-term (nth 1 a)))
                                   (nextt (math-prod-first-term (nth 2 a)))
                                   (prevc (or (math-comp-last-char lhs)
                                              (and (memq (car-safe prevt)
                                                         '(^ calcFunc-subscr
                                                             calcFunc-sqrt
                                                             frac))
                                                   (eq calc-language 'big)
                                                   ?0)))
                                   (nextc (or (math-comp-first-char rhs)
                                              (and (memq (car-safe nextt)
                                                         '(calcFunc-sqrt
                                                           calcFunc-sum
                                                           calcFunc-prod
                                                           calcFunc-integ))
                                                   (eq calc-language 'big)
                                                   ?0))))
                              (and prevc nextc
                                   (or (and (>= nextc ?a) (<= nextc ?z))
                                       (and (>= nextc ?A) (<= nextc ?Z))
                                       (and (>= nextc ?α) (<= nextc ?ω))
                                       (and (>= nextc ?Α) (<= nextc ?Ω))
                                       (and (>= nextc ?0) (<= nextc ?9))
                                       (memq nextc '(?. ?_ ?#
                                                        ?\( ?\[ ?\{))
                                       (and (eq nextc ?\\)
                                            (not (string-match
                                                  "\\`\\\\left("
                                                  (math-comp-first-string
                                                   rhs)))))
                                   (not (and (eq (car-safe prevt) 'var)
                                             (eq nextc ?\()))
                                   (list 'horiz
                                         (list 'set setlev 1)
                                         lhs
                                         (list 'break math-compose-level)
                                         " "
                                         rhs))))
                       (list 'horiz
                             (list 'set setlev 1)
                             lhs
                             (list 'break math-compose-level)
                             (if (or (equal (car op) "^")
                                     (equal (car op) "_")
                                     (equal (car op) "**")
                                     (and (equal (car op) "*")
                                          (math-comp-last-char lhs)
                                          (math-comp-first-char rhs))
                                     (and (equal (car op) "/")
                                          (math-num-integerp (nth 1 a))
                                          (math-integerp (nth 2 a))))
                                 (car op)
                               (if (and (eq calc-language 'big)
                                        (equal (car op) "=>"))
                                   "  =>  "
                                 (concat " " (car op) " ")))
                             rhs))))))
              ((and op (= (length a) 2) (= (nth 3 op) -1))
               (cond
                ((or (> prec (or (nth 4 op) (nth 2 op)))
                     (and (not (eq (assoc (car op) math-expr-opers) op))
                          (> prec 0)))   ; don't write x% + y
                 (if (and (memq calc-language '(tex latex))
                          (not (math-tex-expr-is-flat a)))
                     (list 'horiz "\\left( "
                           (math-compose-expr a -1)
                           " \\right)")
                   (if (eq calc-language 'eqn)
                       (if (= (/ prec 100) 9)
                           (list 'horiz "{" (math-compose-expr a -1) "}")
                         (if (math-tex-expr-is-flat a)
                             (list 'horiz "{( " (math-compose-expr a -1) " )}")
                           (list 'horiz "{left ( "
                                 (math-compose-expr a -1)
                                 " right )}")))
                     (list 'horiz "(" (math-compose-expr a 0) ")"))))
                (t
                 (let ((lhs (math-compose-expr (nth 1 a) (nth 2 op))))
                 (list 'horiz
                       lhs
                       (if (or (> (length (car op)) 1)
                               (not (math-comp-is-flat lhs)))
                           (concat " " (car op))
                         (car op)))))))
              ((and op (= (length a) 2) (= (nth 2 op) -1))
               (cond
                ((eq (nth 3 op) 0)
                 (let ((lr (and (memq calc-language '(tex latex))
                                (not (math-tex-expr-is-flat (nth 1 a))))))
                   (list 'horiz
                         (if lr "\\left" "")
                         (if (string-match "\\`u\\([^a-zA-Zα-ωΑ-Ω]\\)\\'" (car op))
                             (substring (car op) 1)
                           (car op))
                         (if (or lr (> (length (car op)) 2)) " " "")
                         (math-compose-expr (nth 1 a) -1)
                         (if (or lr (> (length (car op)) 2)) " " "")
                         (if lr "\\right" "")
                         (car (nth 1 (memq op math-expr-opers))))))
                ((> prec (or (nth 4 op) (nth 3 op)))
                 (if (and (memq calc-language '(tex latex))
                          (not (math-tex-expr-is-flat a)))
                     (list 'horiz "\\left( "
                           (math-compose-expr a -1)
                           " \\right)")
                   (if (eq calc-language 'eqn)
                       (if (= (/ prec 100) 9)
                           (list 'horiz "{" (math-compose-expr a -1) "}")
                         (if (math-tex-expr-is-flat a)
                             (list 'horiz "{( " (math-compose-expr a -1) " )}")
                           (list 'horiz "{left ( "
                                 (math-compose-expr a -1)
                                 " right )}")))
                     (list 'horiz "(" (math-compose-expr a 0) ")"))))
                (t
                 (let ((rhs (math-compose-expr (nth 1 a) (nth 3 op))))
                   (list 'horiz
                         (let ((ops (if (string-match "\\`u\\([^a-zA-Zα-ωΑ-Ω]\\)\\'"
                                                      (car op))
                                        (substring (car op) 1)
                                      (car op))))
                           (if (or (> (length ops) 1)
                                   (not (math-comp-is-flat rhs)))
                               (concat ops " ")
                             ops))
                         rhs)))))
              ((and (eq calc-language 'big)
                    (setq op (get (car a) 'math-compose-big))
                    (funcall op a prec)))
              ((and (setq op (assq calc-language
                                   '( ( nil . math-compose-normal )
                                      ( flat . math-compose-normal )
                                      ( big . math-compose-normal )
                                      ( c . math-compose-c )
                                      ( pascal . math-compose-pascal )
                                      ( fortran . math-compose-fortran )
                                      ( tex . math-compose-tex )
                                      ( latex . math-compose-latex )
                                      ( eqn . math-compose-eqn )
                                      ( yacas . math-compose-yacas )
                                      ( maxima . math-compose-maxima )
                                      ( giac . math-compose-giac )
                                      ( math . math-compose-math )
                                      ( maple . math-compose-maple ))))
                    (setq op (get (car a) (cdr op)))
                    (funcall op a prec)))
              (t
               (let* ((func (car a))
                      (func2 (assq func '(( mod . calcFunc-makemod )
                                          ( sdev . calcFunc-sdev )
                                          ( + . calcFunc-add )
                                          ( - . calcFunc-sub )
                                          ( * . calcFunc-mul )
                                          ( / . calcFunc-div )
                                          ( % . calcFunc-mod )
                                          ( ^ . calcFunc-pow )
                                          ( neg . calcFunc-neg )
                                          ( | . calcFunc-vconcat ))))
                      left right args)
                 (if func2
                     (setq func (cdr func2)))
                 (if (setq func2 (rassq func math-expr-function-mapping))
                     (setq func (car func2)))
                 (setq func (math-remove-dashes
                             (if (string-match
                                  "\\`calcFunc-\\([a-zA-Zα-ωΑ-Ω0-9']+\\)\\'"
                                  (symbol-name func))
                                 (math-match-substring (symbol-name func) 1)
                               (symbol-name func))))
                 (if (memq calc-language calc-lang-allow-percentsigns)
                     (setq func (math-to-percentsigns func)))
                 (if (memq calc-language calc-lang-allow-underscores)
                     (setq func (math-to-underscores func)))
                 (if (setq spfn (get calc-language 'math-func-formatter))
                     (funcall spfn func a)

                   (list 'horiz func calc-function-open
                       (math-compose-vector (cdr a) ", " 0)
                       calc-function-close))))))))))


(defun math-prod-first-term (x)
  (while (eq (car-safe x) '*)
    (setq x (nth 1 x)))
  x)

(defun math-prod-last-term (x)
  (while (eq (car-safe x) '*)
    (setq x (nth 2 x)))
  x)

(defun math-compose-vector (a sep prec)
  (if a
      (cons 'horiz
            (cons (list 'set math-compose-level)
                  (let ((c (list (math-compose-expr (car a) prec))))
                    (while (setq a (cdr a))
                      (setq c (cons (if (eq (car-safe (car a))
                                            'calcFunc-bstring)
                                        (let ((math-compose-level
                                               (1- math-compose-level)))
                                          (math-compose-expr (car a) -123))
                                      (math-compose-expr (car a) prec))
                                    (cons (list 'break math-compose-level)
                                          (cons sep c)))))
                    (nreverse c))))
    ""))

(defun math-vector-no-parens (a)
  (or (cdr (cdr a))
      (not (eq (car-safe (nth 1 a)) '*))))

(defun math-compose-matrix (a col cols base)
  (let ((col 0)
        (res nil))
    (while (<= (setq col (1+ col)) cols)
      (setq res (cons (cons math-comp-just
                            (cons base
                                  (mapcar (function
                                           (lambda (r)
                                             (list 'horiz
                                                   (math-compose-expr
                                                    (nth col r)
                                                    math-comp-vector-prec)
                                                   (if (= col cols)
                                                       ""
                                                     (concat
                                                      math-comp-comma-spc " ")))))
                                          a)))
                      res)))
    (nreverse res)))

(defun math-compose-rows (a count first)
  (if (cdr a)
      (if (<= count 0)
          (if (< count 0)
              (math-compose-rows (cdr a) -1 nil)
            (cons (concat
                   (let ((mdots (get calc-language 'math-dots)))
                     (if mdots
                         (concat " " mdots)
                       "  ..."))
                   math-comp-comma)
                  (math-compose-rows (cdr a) -1 nil)))
        (cons (list 'horiz
                    (if first (concat math-comp-left-bracket " ") "  ")
                    (math-compose-expr (car a) math-comp-vector-prec)
                    math-comp-comma)
              (math-compose-rows (cdr a) (1- count) nil)))
    (list (list 'horiz
                (if first (concat math-comp-left-bracket " ") "  ")
                (math-compose-expr (car a) math-comp-vector-prec)
                (concat " " math-comp-right-bracket)))))

(defun math-vector-is-string (a)
  (while (and (setq a (cdr a))
              (or (and (natnump (car a))
                       (<= (car a) 255))
                  (and (eq (car-safe (car a)) 'cplx)
                       (natnump (nth 1 (car a)))
                       (eq (nth 2 (car a)) 0)
                       (<= (nth 1 (car a)) 255)))))
  (null a))

(defconst math-vector-to-string-chars '( ( ?\" . "\\\"" )
                                         ( ?\\ . "\\\\" )
                                         ( ?\a . "\\a" )
                                         ( ?\b . "\\b" )
                                         ( ?\e . "\\e" )
                                         ( ?\f . "\\f" )
                                         ( ?\n . "\\n" )
                                         ( ?\r . "\\r" )
                                         ( ?\t . "\\t" )
                                         ( ?\^? . "\\^?" )))

(defun math-vector-to-string (a &optional quoted)
  (setq a (concat (mapcar (function (lambda (x) (if (consp x) (nth 1 x) x)))
                          (cdr a))))
  (if (string-match "[\000-\037\177\\\"]" a)
      (let ((p 0)
            (pat (if quoted "[\000-\037\177\\\"]" "[\000-\037\177]"))
            (codes (if quoted math-vector-to-string-chars '((?\^? . "^?"))))
            (fmt (if quoted "\\^%c" "^%c"))
            new)
        (while (setq p (string-match pat a p))
          (if (setq new (assq (aref a p) codes))
              (setq a (concat (substring a 0 p)
                              (cdr new)
                              (substring a (1+ p)))
                    p (+ p (length (cdr new))))
            (setq a (concat (substring a 0 p)
                            (format fmt (+ (aref a p) 64))
                            (substring a (1+ p)))
                  p (+ p 2))))))
  (if quoted
      (concat "\"" a "\"")
    a))


(defun math-to-underscores (x)
  (if (string-match "\\`\\(.*\\)#\\(.*\\)\\'" x)
      (math-to-underscores
       (concat (math-match-substring x 1) "_" (math-match-substring x 2)))
    x))

(defun math-to-percentsigns (x)
  (if (string-match "\\`\\(.*\\)o'o\\(.*\\)\\'" x)
      (math-to-underscores
       (concat (math-match-substring x 1) "%" (math-match-substring x 2)))
    x))

(defun math-tex-expr-is-flat (a)
  (or (Math-integerp a)
      (memq (car a) '(float var))
      (and (memq (car a) '(+ - * neg))
           (progn
             (while (and (setq a (cdr a))
                         (math-tex-expr-is-flat (car a))))
             (null a)))
      (and (memq (car a) '(^ calcFunc-subscr))
           (math-tex-expr-is-flat (nth 1 a)))))

(put 'calcFunc-log 'math-compose-big 'math-compose-log)
(defun math-compose-log (a prec)
  (and (= (length a) 3)
       (list 'horiz
             (list 'subscr "log"
                   (let ((calc-language 'flat))
                     (math-compose-expr (nth 2 a) 1000)))
             "("
             (math-compose-expr (nth 1 a) 1000)
             ")")))

(put 'calcFunc-log10 'math-compose-big 'math-compose-log10)
(defun math-compose-log10 (a prec)
  (and (= (length a) 2)
       (list 'horiz
             (list 'subscr "log" "10")
             "("
             (math-compose-expr (nth 1 a) 1000)
             ")")))

(put 'calcFunc-deriv 'math-compose-big 'math-compose-deriv)
(put 'calcFunc-tderiv 'math-compose-big 'math-compose-deriv)
(defun math-compose-deriv (a prec)
  (when (= (length a) 3)
    (math-compose-expr (list '/
                             (list 'calcFunc-choriz
                                   (list 'vec
                                         '(calcFunc-string (vec ?d))
                                         (nth 1 a)))
                             (list 'calcFunc-choriz
                                   (list 'vec
                                         '(calcFunc-string (vec ?d))
                                         (nth 2 a))))
                       prec)))

(put 'calcFunc-sqrt 'math-compose-big 'math-compose-sqrt)
(defun math-compose-sqrt (a prec)
  (when (= (length a) 2)
    (let* ((c (math-compose-expr (nth 1 a) 0))
           (a (math-comp-ascent c))
           (d (math-comp-descent c))
           (h (+ a d))
           (w (math-comp-width c)))
      (list 'vleft
            a
            (concat (if (= h 1) " " "  ")
                    (make-string (+ w 2) ?\_))
            (list 'horiz
                  (if (= h 1)
                      "V"
                    (append (list 'vleft (1- a))
                            (make-list (1- h) " |")
                            '("\\|")))
                  " "
                  c)))))

(put 'calcFunc-choose 'math-compose-big 'math-compose-choose)
(defun math-compose-choose (a prec)
  (let ((a1 (math-compose-expr (nth 1 a) 0))
        (a2 (math-compose-expr (nth 2 a) 0)))
    (list 'horiz
          "("
          (list 'vcent
                (math-comp-height a1)
                a1 " " a2)
          ")")))

(put 'calcFunc-integ 'math-compose-big 'math-compose-integ)
(defun math-compose-integ (a prec)
  (and (memq (length a) '(3 5))
       (eq (car-safe (nth 2 a)) 'var)
       (let* ((parens (and (>= prec 196) (/= prec 1000)))
              (var (math-compose-expr (nth 2 a) 0))
              (over (and (eq (car-safe (nth 2 a)) 'var)
                         (or (and (eq (car-safe (nth 1 a)) '/)
                                  (math-numberp (nth 1 (nth 1 a))))
                             (and (eq (car-safe (nth 1 a)) '^)
                                  (math-looks-negp (nth 2 (nth 1 a)))))))
              (expr (math-compose-expr (if over
                                           (math-mul (nth 1 a)
                                                     (math-build-var-name
                                                      (format
                                                       "d%s"
                                                       (nth 1 (nth 2 a)))))
                                         (nth 1 a)) 185))
              (calc-language 'flat)
              (low (and (nth 3 a) (math-compose-expr (nth 3 a) 0)))
              (high (and (nth 4 a) (math-compose-expr (nth 4 a) 0))))
         (list 'horiz
               (if parens "(" "")
               (append (list 'vcent (if high 3 2))
                       (and high (list (list 'horiz "  " high)))
                       '("  /"
                         " | "
                         " | "
                         " | "
                         "/  ")
                       (and low (list (list 'horiz low "  "))))
               expr
               (if over
                   ""
                 (list 'horiz " d" var))
               (if parens ")" "")))))

(put 'calcFunc-sum 'math-compose-big 'math-compose-sum)
(defun math-compose-sum (a prec)
  (and (memq (length a) '(3 5 6))
       (let* ((expr (math-compose-expr (nth 1 a) 185))
              (calc-language 'flat)
              (var (math-compose-expr (nth 2 a) 0))
              (low (and (nth 3 a) (math-compose-expr (nth 3 a) 0)))
              (high (and (nth 4 a) (math-compose-vector (nthcdr 4 a) ", " 0))))
         (list 'horiz
               (if (memq prec '(180 201)) "(" "")
               (append (list 'vcent (if high 3 2))
                       (and high (list high))
                       '("---- "
                         "\\    "
                         " >   "
                         "/    "
                         "---- ")
                       (if low
                           (list (list 'horiz var " = " low))
                         (list var)))
               (if (memq (car-safe (nth 1 a)) '(calcFunc-sum calcFunc-prod))
                   " " "")
               expr
               (if (memq prec '(180 201)) ")" "")))))

(put 'calcFunc-prod 'math-compose-big 'math-compose-prod)
(defun math-compose-prod (a prec)
  (and (memq (length a) '(3 5 6))
       (let* ((expr (math-compose-expr (nth 1 a) 198))
              (calc-language 'flat)
              (var (math-compose-expr (nth 2 a) 0))
              (low (and (nth 3 a) (math-compose-expr (nth 3 a) 0)))
              (high (and (nth 4 a) (math-compose-vector (nthcdr 4 a) ", " 0))))
         (list 'horiz
               (if (memq prec '(196 201)) "(" "")
               (append (list 'vcent (if high 3 2))
                       (and high (list high))
                       '("----- "
                         " | |  "
                         " | |  "
                         " | |  ")
                       (if low
                           (list (list 'horiz var " = " low))
                         (list var)))
               (if (memq (car-safe (nth 1 a)) '(calcFunc-sum calcFunc-prod))
                   " " "")
               expr
               (if (memq prec '(196 201)) ")" "")))))

;; The variables math-svo-c, math-svo-wid and math-svo-off are local
;; to math-stack-value-offset in calc.el, but are used by
;; math-stack-value-offset-fancy, which is called by math-stack-value-offset..
(defvar math-svo-c)
(defvar math-svo-wid)
(defvar math-svo-off)

(defun math-stack-value-offset-fancy ()
  (let ((cwid (+ (math-comp-width math-svo-c))))
    (cond ((eq calc-display-just 'right)
           (if calc-display-origin
               (setq math-svo-wid (max calc-display-origin 5))
             (if (integerp calc-line-breaking)
                 (setq math-svo-wid calc-line-breaking)))
           (setq math-svo-off (- math-svo-wid cwid
                        (max (- (length calc-right-label)
                                (if (and (integerp calc-line-breaking)
                                         calc-display-origin)
                                    (max (- calc-line-breaking
                                            calc-display-origin)
                                         0)
                                  0))
                             0))))
          (t
           (if calc-display-origin
               (progn
                 (setq math-svo-off (- calc-display-origin (/ cwid 2)))
                 (if (integerp calc-line-breaking)
                     (setq math-svo-off (min math-svo-off (- calc-line-breaking cwid
                                           (length calc-right-label)))))
                 (if (>= math-svo-off 0)
                     (setq math-svo-wid (max math-svo-wid (+ math-svo-off cwid)))))
             (if (integerp calc-line-breaking)
                 (setq math-svo-wid calc-line-breaking))
             (setq math-svo-off (/ (- math-svo-wid cwid) 2)))))
    (and (integerp calc-line-breaking)
         (or (< math-svo-off 0)
             (and calc-display-origin
                  (> calc-line-breaking calc-display-origin)))
         (setq math-svo-wid calc-line-breaking))))


;;; Convert a composition to string form, with embedded \n's if necessary.

(defun math-composition-to-string (c &optional width)
  (or width (setq width (calc-window-width)))
  (if calc-display-raw
      (math-comp-to-string-raw c 0)
    (if (math-comp-is-flat c)
        (math-comp-to-string-flat c width)
      (math-vert-comp-to-string
       (math-comp-simplify c width)))))

(defvar math-comp-buf-string (make-vector 10 ""))
(defvar math-comp-buf-margin (make-vector 10 0))
(defvar math-comp-buf-level (make-vector 10 0))
(defun math-comp-is-flat (c)     ; check if c's height is 1.
  (cond ((not (consp c)) t)
        ((memq (car c) '(set break)) t)
        ((eq (car c) 'horiz)
         (while (and (setq c (cdr c))
                     (math-comp-is-flat (car c))))
         (null c))
        ((memq (car c) '(vleft vcent vright))
         (and (= (length c) 3)
              (= (nth 1 c) 0)
              (math-comp-is-flat (nth 2 c))))
        ((eq (car c) 'tag)
         (math-comp-is-flat (nth 2 c)))
        (t nil)))


;;; Convert a one-line composition to a string.  Break into multiple
;;; lines if necessary, choosing break points according to the structure
;;; of the formula.

;; The variables math-comp-full-width, math-comp-highlight, math-comp-word,
;; math-comp-level, math-comp-margin and math-comp-buf are local to
;; math-comp-to-string-flat, but are used by math-comp-to-string-flat-term,
;; which is called by math-comp-to-string-flat.
;; math-comp-highlight and math-comp-buf are also local to
;; math-comp-simplify-term and math-comp-simplify respectively, but are used
;; by math-comp-add-string.
(defvar math-comp-full-width)
(defvar math-comp-highlight)
(defvar math-comp-word)
(defvar math-comp-level)
(defvar math-comp-margin)
(defvar math-comp-buf)
;; The variable math-comp-pos is local to math-comp-to-string-flat, but
;; is used by math-comp-to-string-flat-term and math-comp-sel-first-term,
;; which are called by math-comp-to-string-flat.
(defvar math-comp-pos)

(defun math-comp-to-string-flat (c math-comp-full-width)
  (if math-comp-sel-hpos
      (let ((math-comp-pos 0))
        (math-comp-sel-flat-term c))
    (let ((math-comp-buf "")
          (math-comp-word "")
          (math-comp-pos 0)
          (math-comp-margin 0)
          (math-comp-highlight (and math-comp-selected calc-show-selections))
          (math-comp-level -1))
      (math-comp-to-string-flat-term '(set -1 0))
      (math-comp-to-string-flat-term c)
      (math-comp-to-string-flat-term '(break -1))
      (let ((str (aref math-comp-buf-string 0))
            (prefix ""))
        (and (> (length str) 0) (= (aref str 0) ? )
             (> (length math-comp-buf) 0)
             (let ((k (length math-comp-buf)))
               (while (not (= (aref math-comp-buf (setq k (1- k))) ?\n)))
               (aset math-comp-buf k ? )
               (if (and (< (1+ k) (length math-comp-buf))
                        (= (aref math-comp-buf (1+ k)) ? ))
                   (progn
                     (aset math-comp-buf (1+ k) ?\n)
                     (setq prefix " "))
                 (setq prefix "\n"))))
        (concat math-comp-buf prefix str)))))

(defun math-comp-to-string-flat-term (c)
  (cond ((not (consp c))
         (if math-comp-highlight
             (setq c (math-comp-highlight-string c)))
         (setq math-comp-word (if (= (length math-comp-word) 0) c
                                (concat math-comp-word c))
               math-comp-pos (+ math-comp-pos (length c))))

        ((eq (car c) 'horiz)
         (while (setq c (cdr c))
           (math-comp-to-string-flat-term (car c))))

        ((eq (car c) 'set)
         (if (nth 1 c)
             (progn
               (setq math-comp-level (1+ math-comp-level))
               (if (>= math-comp-level (length math-comp-buf-string))
                   (setq math-comp-buf-string (vconcat math-comp-buf-string
                                                       math-comp-buf-string)
                         math-comp-buf-margin (vconcat math-comp-buf-margin
                                                       math-comp-buf-margin)
                         math-comp-buf-level (vconcat math-comp-buf-level
                                                      math-comp-buf-level)))
               (aset math-comp-buf-string math-comp-level "")
               (aset math-comp-buf-margin math-comp-level (+ math-comp-pos
                                                        (or (nth 2 c) 0)))
               (aset math-comp-buf-level math-comp-level (nth 1 c)))))

        ((eq (car c) 'break)
         (if (not calc-line-breaking)
             (setq math-comp-buf (concat math-comp-buf math-comp-word)
                   math-comp-word "")
           (let ((i 0) str)
             (if (and (> math-comp-pos math-comp-full-width)
                      (progn
                        (while (progn
                                 (setq str (aref math-comp-buf-string i))
                                 (and (= (length str) 0) (< i math-comp-level)))
                          (setq i (1+ i)))
                        (or (> (length str) 0) (> (length math-comp-buf) 0))))
                 (let ((prefix "") mrg wid)
                   (setq mrg (aref math-comp-buf-margin i))
                   (if (> mrg 12)  ; indenting too far, go back to far left
                       (setq mrg (if calc-line-numbering 5 1)))
                   (setq wid (+ (length str) math-comp-margin))
                   (and (> (length str) 0) (= (aref str 0) ? )
                        (> (length math-comp-buf) 0)
                        (let ((k (length math-comp-buf)))
                          (while (not (= (aref math-comp-buf (setq k (1- k))) ?\n)))
                          (aset math-comp-buf k ? )
                          (if (and (< (1+ k) (length math-comp-buf))
                                   (= (aref math-comp-buf (1+ k)) ? ))
                              (progn
                                (aset math-comp-buf (1+ k) ?\n)
                                (setq prefix " "))
                            (setq prefix "\n"))))
                   (setq math-comp-buf (concat math-comp-buf prefix str "\n"
                                          (make-string mrg ? ))
                         math-comp-pos (+ math-comp-pos (- mrg wid))
                         math-comp-margin mrg)
                   (aset math-comp-buf-string i "")
                   (while (<= (setq i (1+ i)) math-comp-level)
                     (if (> (aref math-comp-buf-margin i) wid)
                         (aset math-comp-buf-margin i
                               (+ (aref math-comp-buf-margin i)
                                  (- mrg wid))))))))
           (if (and (= (nth 1 c) (aref math-comp-buf-level math-comp-level))
                    (< math-comp-pos (+ (aref math-comp-buf-margin math-comp-level) 2)))
               ()  ; avoid stupid breaks, e.g., "1 +\n really_long_expr"
             (let ((str (aref math-comp-buf-string math-comp-level)))
               (setq str (if (= (length str) 0)
                             math-comp-word
                           (concat str math-comp-word))
                     math-comp-word "")
               (while (< (nth 1 c) (aref math-comp-buf-level math-comp-level))
                 (setq math-comp-level (1- math-comp-level))
                 (or (= (length (aref math-comp-buf-string math-comp-level)) 0)
                     (setq str (concat (aref math-comp-buf-string math-comp-level)
                                       str))))
               (aset math-comp-buf-string math-comp-level str)))))

        ((eq (car c) 'tag)
         (cond ((eq (nth 1 c) math-comp-selected)
                (let ((math-comp-highlight (not calc-show-selections)))
                  (math-comp-to-string-flat-term (nth 2 c))))
               ((eq (nth 1 c) t)
                (let ((math-comp-highlight nil))
                  (math-comp-to-string-flat-term (nth 2 c))))
               (t (math-comp-to-string-flat-term (nth 2 c)))))

        (t (math-comp-to-string-flat-term (nth 2 c)))))

(defun math-comp-highlight-string (s)
  (setq s (copy-sequence s))
  (if calc-highlight-selections-with-faces
      (if (not calc-show-selections)
          (propertize s 'face 'calc-selected-face)
        (propertize s 'face 'calc-nonselected-face))
    (let ((i (length s)))
      (while (>= (setq i (1- i)) 0)
        (or (memq (aref s i) '(32 ?\n))
            (aset s i (if calc-show-selections ?\. ?\#)))))
    s))

;; The variable math-comp-sel-tag is local to calc-find-selected-part
;; in calc-sel.el, but is used by math-comp-sel-flat-term and
;; math-comp-add-string-sel, which are called (indirectly) by
;; calc-find-selected-part.
(defvar math-comp-sel-tag)

(defun math-comp-sel-flat-term (c)
  (cond ((not (consp c))
         (setq math-comp-pos (+ math-comp-pos (length c))))
        ((memq (car c) '(set break)))
        ((eq (car c) 'horiz)
         (while (and (setq c (cdr c)) (< math-comp-sel-cpos 1000000))
           (math-comp-sel-flat-term (car c))))
        ((eq (car c) 'tag)
         (if (<= math-comp-pos math-comp-sel-cpos)
             (progn
               (math-comp-sel-flat-term (nth 2 c))
               (if (> math-comp-pos math-comp-sel-cpos)
                   (setq math-comp-sel-tag c
                         math-comp-sel-cpos 1000000)))
           (math-comp-sel-flat-term (nth 2 c))))
        (t (math-comp-sel-flat-term (nth 2 c)))))


;;; Simplify a composition to a canonical form consisting of
;;;   (vleft n "string" "string" "string" ...)
;;; where 0 <= n < number-of-strings.

;; The variables math-comp-base, math-comp-hgt, math-comp-tag,
;; math-comp-hpos and math-comp-vpos are local to math-comp-simplify,
;; but are used by math-comp-add-string (math-comp-base, math-comp-hgt),
;; math-comp-add-string-sel (math-comp-tag) and math-comp-simplify-term
;; (math-comp-tag, math-comp-vpos, math-comp-hpos), which are called by
;; math-comp-simplify.
(defvar math-comp-base)
(defvar math-comp-hgt)
(defvar math-comp-tag)
(defvar math-comp-hpos)
(defvar math-comp-vpos)

(defun math-comp-simplify (c full-width)
  (let ((math-comp-buf (list ""))
        (math-comp-base 0)
        (math-comp-hgt 1)
        (math-comp-hpos 0)
        (math-comp-vpos 0)
        (math-comp-highlight (and math-comp-selected calc-show-selections))
        (math-comp-tag nil))
    (math-comp-simplify-term c)
    (cons 'vleft (cons math-comp-base math-comp-buf))))

(defun math-comp-add-string (s h v)
  (and (> (length s) 0)
       (let ((vv (+ v math-comp-base)))
         (if math-comp-sel-hpos
             (math-comp-add-string-sel h vv (length s) 1)
           (if (< vv 0)
               (setq math-comp-buf (nconc (make-list (- vv) "") math-comp-buf)
                     math-comp-base (- v)
                     math-comp-hgt (- math-comp-hgt vv)
                     vv 0)
             (if (>= vv math-comp-hgt)
                 (setq math-comp-buf (nconc math-comp-buf
                                       (make-list (1+ (- vv math-comp-hgt)) ""))
                       math-comp-hgt (1+ vv))))
           (let ((str (nthcdr vv math-comp-buf)))
             (setcar str (concat (car str)
                                 (make-string (- h (length (car str))) 32)
                                 (if math-comp-highlight
                                     (math-comp-highlight-string s)
                                   s))))))))

(defun math-comp-add-string-sel (x y w h)
  (if (and (<= y math-comp-sel-vpos)
           (> (+ y h) math-comp-sel-vpos)
           (<= x math-comp-sel-hpos)
           (> (+ x w) math-comp-sel-hpos))
      (setq math-comp-sel-tag math-comp-tag
            math-comp-sel-vpos 10000)))

(defun math-comp-simplify-term (c)
  (cond ((stringp c)
         (math-comp-add-string c math-comp-hpos math-comp-vpos)
         (setq math-comp-hpos (+ math-comp-hpos (length c))))
        ((memq (car c) '(set break))
         nil)
        ((eq (car c) 'horiz)
         (while (setq c (cdr c))
           (math-comp-simplify-term (car c))))
        ((memq (car c) '(vleft vcent vright))
         (let* ((math-comp-vpos (+ (- math-comp-vpos (nth 1 c))
                              (1- (math-comp-ascent (nth 2 c)))))
                (widths (mapcar 'math-comp-width (cdr (cdr c))))
                (maxwid (apply 'max widths))
                (bias (cond ((eq (car c) 'vleft) 0)
                            ((eq (car c) 'vcent) 1)
                            (t 2))))
           (setq c (cdr c))
           (while (setq c (cdr c))
             (if (eq (car-safe (car c)) 'rule)
                 (math-comp-add-string (make-string maxwid (nth 1 (car c)))
                                       math-comp-hpos math-comp-vpos)
               (let ((math-comp-hpos (+ math-comp-hpos (/ (* bias (- maxwid
                                                           (car widths)))
                                                2))))
                 (math-comp-simplify-term (car c))))
             (and (cdr c)
                  (setq math-comp-vpos (+ math-comp-vpos
                                     (+ (math-comp-descent (car c))
                                        (math-comp-ascent (nth 1 c))))
                        widths (cdr widths))))
           (setq math-comp-hpos (+ math-comp-hpos maxwid))))
        ((eq (car c) 'supscr)
         (let* ((asc (or 1 (math-comp-ascent (nth 1 c))))
                (desc (math-comp-descent (nth 2 c)))
                (oldh (prog1
                          math-comp-hpos
                        (math-comp-simplify-term (nth 1 c))))
                (math-comp-vpos (- math-comp-vpos (+ asc desc))))
           (math-comp-simplify-term (nth 2 c))
           (if math-comp-sel-hpos
               (math-comp-add-string-sel oldh
                                         (- math-comp-vpos
                                            -1
                                            (math-comp-ascent (nth 2 c)))
                                         (- math-comp-hpos oldh)
                                         (math-comp-height c)))))
        ((eq (car c) 'subscr)
         (let* ((asc (math-comp-ascent (nth 2 c)))
                (desc (math-comp-descent (nth 1 c)))
                (oldv math-comp-vpos)
                (oldh (prog1
                          math-comp-hpos
                        (math-comp-simplify-term (nth 1 c))))
                (math-comp-vpos (+ math-comp-vpos (+ asc desc))))
           (math-comp-simplify-term (nth 2 c))
           (if math-comp-sel-hpos
               (math-comp-add-string-sel oldh oldv
                                         (- math-comp-hpos oldh)
                                         (math-comp-height c)))))
        ((eq (car c) 'tag)
         (cond ((eq (nth 1 c) math-comp-selected)
                (let ((math-comp-highlight (not calc-show-selections)))
                  (math-comp-simplify-term (nth 2 c))))
               ((eq (nth 1 c) t)
                (let ((math-comp-highlight nil))
                  (math-comp-simplify-term (nth 2 c))))
               (t (let ((math-comp-tag c))
                    (math-comp-simplify-term (nth 2 c))))))))


;;; Measuring a composition.

(defun math-comp-first-char (c)
  (cond ((stringp c)
         (and (> (length c) 0)
              (elt c 0)))
        ((memq (car c) '(horiz subscr supscr))
         (while (and (setq c (cdr c))
                     (math-comp-is-null (car c))))
         (and c (math-comp-first-char (car c))))
        ((eq (car c) 'tag)
         (math-comp-first-char (nth 2 c)))))

(defun math-comp-first-string (c)
  (cond ((stringp c)
         (and (> (length c) 0)
              c))
        ((eq (car c) 'horiz)
         (while (and (setq c (cdr c))
                     (math-comp-is-null (car c))))
         (and c (math-comp-first-string (car c))))
        ((eq (car c) 'tag)
         (math-comp-first-string (nth 2 c)))))

(defun math-comp-last-char (c)
  (cond ((stringp c)
         (and (> (length c) 0)
              (elt c (1- (length c)))))
        ((eq (car c) 'horiz)
         (let ((c (reverse (cdr c))))
           (while (and c (math-comp-is-null (car c)))
             (setq c (cdr c)))
           (and c (math-comp-last-char (car c)))))
        ((eq (car c) 'tag)
         (math-comp-last-char (nth 2 c)))))

(defun math-comp-is-null (c)
  (cond ((stringp c) (= (length c) 0))
        ((memq (car c) '(horiz subscr supscr))
         (while (and (setq c (cdr c))
                     (math-comp-is-null (car c))))
         (null c))
        ((eq (car c) 'tag)
         (math-comp-is-null (nth 2 c)))
        ((memq (car c) '(set break)) t)))

(defun math-comp-width (c)
  (cond ((not (consp c)) (length c))
        ((memq (car c) '(horiz subscr supscr))
         (let ((accum 0))
           (while (setq c (cdr c))
             (setq accum (+ accum (math-comp-width (car c)))))
           accum))
        ((memq (car c) '(vcent vleft vright))
         (setq c (cdr c))
         (let ((accum 0))
           (while (setq c (cdr c))
             (setq accum (max accum (math-comp-width (car c)))))
           accum))
        ((eq (car c) 'tag)
         (math-comp-width (nth 2 c)))
        (t 0)))

(defun math-comp-height (c)
  (if (stringp c)
      1
    (+ (math-comp-ascent c) (math-comp-descent c))))

(defun math-comp-ascent (c)
  (cond ((not (consp c)) 1)
        ((eq (car c) 'horiz)
         (let ((accum 0))
           (while (setq c (cdr c))
             (setq accum (max accum (math-comp-ascent (car c)))))
           accum))
        ((memq (car c) '(vcent vleft vright))
         (if (> (nth 1 c) 0) (1+ (nth 1 c)) 1))
        ((eq (car c) 'supscr)
         (max (math-comp-ascent (nth 1 c)) (1+ (math-comp-height (nth 2 c)))))
        ((eq (car c) 'subscr)
         (math-comp-ascent (nth 1 c)))
        ((eq (car c) 'tag)
         (math-comp-ascent (nth 2 c)))
        (t 1)))

(defun math-comp-descent (c)
  (cond ((not (consp c)) 0)
        ((eq (car c) 'horiz)
         (let ((accum 0))
           (while (setq c (cdr c))
             (setq accum (max accum (math-comp-descent (car c)))))
           accum))
        ((memq (car c) '(vcent vleft vright))
         (let ((accum (- (nth 1 c))))
           (setq c (cdr c))
           (while (setq c (cdr c))
             (setq accum (+ accum (math-comp-height (car c)))))
           (max (1- accum) 0)))
        ((eq (car c) 'supscr)
         (math-comp-descent (nth 1 c)))
        ((eq (car c) 'subscr)
         (+ (math-comp-descent (nth 1 c)) (math-comp-height (nth 2 c))))
        ((eq (car c) 'tag)
         (math-comp-descent (nth 2 c)))
        (t 0)))

(defun calcFunc-cwidth (a &optional prec)
  (if (and prec (not (integerp prec))) (math-reject-arg prec 'fixnump))
  (math-comp-width (math-compose-expr a (or prec 0))))

(defun calcFunc-cheight (a &optional prec)
  (if (and prec (not (integerp prec))) (math-reject-arg prec 'fixnump))
  (if (and (memq (car a) '(calcFunc-cvspace calcFunc-ctspace calcFunc-cbspace))
           (memq (length a) '(2 3))
           (eq (nth 1 a) 0))
      0
    (math-comp-height (math-compose-expr a (or prec 0)))))

(defun calcFunc-cascent (a &optional prec)
  (if (and prec (not (integerp prec))) (math-reject-arg prec 'fixnump))
  (if (and (memq (car a) '(calcFunc-cvspace calcFunc-ctspace calcFunc-cbspace))
           (memq (length a) '(2 3))
           (eq (nth 1 a) 0))
      0
    (math-comp-ascent (math-compose-expr a (or prec 0)))))

(defun calcFunc-cdescent (a &optional prec)
  (if (and prec (not (integerp prec))) (math-reject-arg prec 'fixnump))
  (math-comp-descent (math-compose-expr a (or prec 0))))


;;; Convert a simplified composition into string form.

(defun math-vert-comp-to-string (c)
  (if (stringp c)
      c
    (math-vert-comp-to-string-step (cdr (cdr c)))))

(defun math-vert-comp-to-string-step (c)
  (if (cdr c)
      (concat (car c) "\n" (math-vert-comp-to-string-step (cdr c)))
    (car c)))


;;; Convert a composition to a string in "raw" form (for debugging).

(defun math-comp-to-string-raw (c indent)
  (cond ((or (not (consp c)) (eq (car c) 'set))
         (prin1-to-string c))
        ((null (cdr c))
         (concat "(" (symbol-name (car c)) ")"))
        (t
         (let ((next-indent (+ indent 2 (length (symbol-name (car c))))))
           (concat "("
                   (symbol-name (car c))
                   " "
                   (math-comp-to-string-raw (nth 1 c) next-indent)
                   (math-comp-to-string-raw-step (cdr (cdr c))
                                                 next-indent)
                   ")")))))

(defun math-comp-to-string-raw-step (cl indent)
  (if cl
      (concat "\n"
              (make-string indent 32)
              (math-comp-to-string-raw (car cl) indent)
              (math-comp-to-string-raw-step (cdr cl) indent))
    ""))

(provide 'calccomp)

;; Local variables:
;; coding: utf-8
;; End:

;;; calccomp.el ends here