Language/OS - Multiplatform Resource Library/LANGUAGE OS.iso/gnu/calc202a.lha/calc-2.02a/calc-bin.el

Lisp/Scheme | 1993-06-01 | 25KB | 848 lines

;; Calculator for GNU Emacs, part II [calc-bin.el]
;; Copyright (C) 1990, 1991, 1992, 1993 Free Software Foundation, Inc.
;; Written by Dave Gillespie, [e-mail].

;; This file is part of GNU Emacs.

;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY.  No author or distributor
;; accepts responsibility to anyone for the consequences of using it
;; or for whether it serves any particular purpose or works at all,
;; unless he says so in writing.  Refer to the GNU Emacs General Public
;; License for full details.

;; Everyone is granted permission to copy, modify and redistribute
;; GNU Emacs, but only under the conditions described in the
;; GNU Emacs General Public License.   A copy of this license is
;; supposed to have been given to you along with GNU Emacs so you
;; can know your rights and responsibilities.  It should be in a
;; file named COPYING.  Among other things, the copyright notice
;; and this notice must be preserved on all copies.



;; This file is autoloaded from calc-ext.el.
(require 'calc-ext)

(require 'calc-macs)

(defun calc-Need-calc-bin () nil)


;;; b-prefix binary commands.

(defun calc-and (n)
  (interactive "P")
  (calc-slow-wrapper
   (calc-enter-result 2 "and"
              (append '(calcFunc-and)
                  (calc-top-list-n 2)
                  (and n (list (prefix-numeric-value n))))))
)

(defun calc-or (n)
  (interactive "P")
  (calc-slow-wrapper
   (calc-enter-result 2 "or"
              (append '(calcFunc-or)
                  (calc-top-list-n 2)
                  (and n (list (prefix-numeric-value n))))))
)

(defun calc-xor (n)
  (interactive "P")
  (calc-slow-wrapper
   (calc-enter-result 2 "xor"
              (append '(calcFunc-xor)
                  (calc-top-list-n 2)
                  (and n (list (prefix-numeric-value n))))))
)

(defun calc-diff (n)
  (interactive "P")
  (calc-slow-wrapper
   (calc-enter-result 2 "diff"
              (append '(calcFunc-diff)
                  (calc-top-list-n 2)
                  (and n (list (prefix-numeric-value n))))))
)

(defun calc-not (n)
  (interactive "P")
  (calc-slow-wrapper
   (calc-enter-result 1 "not"
              (append '(calcFunc-not)
                  (calc-top-list-n 1)
                  (and n (list (prefix-numeric-value n))))))
)

(defun calc-lshift-binary (n)
  (interactive "P")
  (calc-slow-wrapper
   (let ((hyp (if (calc-is-hyperbolic) 2 1)))
     (calc-enter-result hyp "lsh"
            (append '(calcFunc-lsh)
                (calc-top-list-n hyp)
                (and n (list (prefix-numeric-value n)))))))
)

(defun calc-rshift-binary (n)
  (interactive "P")
  (calc-slow-wrapper
   (let ((hyp (if (calc-is-hyperbolic) 2 1)))
     (calc-enter-result hyp "rsh"
            (append '(calcFunc-rsh)
                (calc-top-list-n hyp)
                (and n (list (prefix-numeric-value n)))))))
)

(defun calc-lshift-arith (n)
  (interactive "P")
  (calc-slow-wrapper
   (let ((hyp (if (calc-is-hyperbolic) 2 1)))
     (calc-enter-result hyp "ash"
            (append '(calcFunc-ash)
                (calc-top-list-n hyp)
                (and n (list (prefix-numeric-value n)))))))
)

(defun calc-rshift-arith (n)
  (interactive "P")
  (calc-slow-wrapper
   (let ((hyp (if (calc-is-hyperbolic) 2 1)))
     (calc-enter-result hyp "rash"
            (append '(calcFunc-rash)
                (calc-top-list-n hyp)
                (and n (list (prefix-numeric-value n)))))))
)

(defun calc-rotate-binary (n)
  (interactive "P")
  (calc-slow-wrapper
   (let ((hyp (if (calc-is-hyperbolic) 2 1)))
     (calc-enter-result hyp "rot"
            (append '(calcFunc-rot)
                (calc-top-list-n hyp)
                (and n (list (prefix-numeric-value n)))))))
)

(defun calc-clip (n)
  (interactive "P")
  (calc-slow-wrapper
   (calc-enter-result 1 "clip"
              (append '(calcFunc-clip)
                  (calc-top-list-n 1)
                  (and n (list (prefix-numeric-value n))))))
)

(defun calc-word-size (n)
  (interactive "P")
  (calc-wrapper
   (or n (setq n (read-string (format "Binary word size: (default %d) "
                      calc-word-size))))
   (setq n (if (stringp n)
           (if (equal n "")
           calc-word-size
         (if (string-match "\\`[-+]?[0-9]+\\'" n)
             (string-to-int n)
           (error "Expected an integer")))
         (prefix-numeric-value n)))
   (or (= n calc-word-size)
       (if (> (math-abs n) 100)
       (calc-change-mode 'calc-word-size n calc-leading-zeros)
     (calc-change-mode '(calc-word-size calc-previous-modulo)
               (list n (math-power-of-2 (math-abs n)))
               calc-leading-zeros)))
   (if (< n 0)
       (message "Binary word size is %d bits (2's complement)." (- n))
     (message "Binary word size is %d bits." n)))
)





;;; d-prefix mode commands.

(defun calc-radix (n)
  (interactive "NDisplay radix (2-36): ")
  (calc-wrapper
   (if (and (>= n 2) (<= n 36))
       (progn
     (calc-change-mode 'calc-number-radix n t)
     ;; also change global value so minibuffer sees it
     (setq-default calc-number-radix calc-number-radix))
     (setq n calc-number-radix))
   (message "Number radix is %d." n))
)

(defun calc-decimal-radix ()
  (interactive)
  (calc-radix 10)
)

(defun calc-binary-radix ()
  (interactive)
  (calc-radix 2)
)

(defun calc-octal-radix ()
  (interactive)
  (calc-radix 8)
)

(defun calc-hex-radix ()
  (interactive)
  (calc-radix 16)
)

(defun calc-leading-zeros (n)
  (interactive "P")
  (calc-wrapper
   (if (calc-change-mode 'calc-leading-zeros n t t)
       (message "Zero-padding integers to %d digits (assuming radix %d)."
        (let* ((calc-internal-prec 6))
          (math-compute-max-digits (math-abs calc-word-size)
                       calc-number-radix))
        calc-number-radix)
     (message "Omitting leading zeros on integers.")))
)


(defvar math-power-of-2-cache (list 1 2 4 8 16 32 64 128 256 512 1024))
(defvar math-big-power-of-2-cache nil)
(defun math-power-of-2 (n)    ;  [I I] [Public]
  (if (and (natnump n) (<= n 100))
      (or (nth n math-power-of-2-cache)
      (let* ((i (length math-power-of-2-cache))
         (val (nth (1- i) math-power-of-2-cache)))
        (while (<= i n)
          (setq val (math-mul val 2)
            math-power-of-2-cache (nconc math-power-of-2-cache
                         (list val))
            i (1+ i)))
        val))
    (let ((found (assq n math-big-power-of-2-cache)))
      (if found
      (cdr found)
    (let ((po2 (math-ipow 2 n)))
      (setq math-big-power-of-2-cache
        (cons (cons n po2) math-big-power-of-2-cache))
      po2))))
)

(defun math-integer-log2 (n)    ; [I I] [Public]
  (let ((i 0)
    (p math-power-of-2-cache)
    val)
    (while (and p (Math-natnum-lessp (setq val (car p)) n))
      (setq p (cdr p)
        i (1+ i)))
    (if p
    (and (equal val n)
         i)
      (while (Math-natnum-lessp
          (prog1
          (setq val (math-mul val 2))
        (setq math-power-of-2-cache (nconc math-power-of-2-cache
                           (list val))))
          n)
    (setq i (1+ i)))
      (and (equal val n)
       i)))
)




;;; Bitwise operations.

(defun calcFunc-and (a b &optional w)   ; [I I I] [Public]
  (cond ((Math-messy-integerp w)
     (calcFunc-and a b (math-trunc w)))
    ((and w (not (integerp w)))
     (math-reject-arg w 'fixnump))
    ((and (integerp a) (integerp b))
     (math-clip (logand a b) w))
    ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod))
     (math-binary-modulo-args 'calcFunc-and a b w))
    ((not (Math-num-integerp a))
     (math-reject-arg a 'integerp))
    ((not (Math-num-integerp b))
     (math-reject-arg b 'integerp))
    (t (math-clip (cons 'bigpos
                (math-and-bignum (math-binary-arg a w)
                         (math-binary-arg b w)))
              w)))
)

(defun math-binary-arg (a w)
  (if (not (Math-integerp a))
      (setq a (math-trunc a)))
  (if (Math-integer-negp a)
      (math-not-bignum (cdr (math-bignum-test (math-sub -1 a)))
               (math-abs (if w (math-trunc w) calc-word-size)))
    (cdr (Math-bignum-test a)))
)

(defun math-binary-modulo-args (f a b w)
  (let (mod)
    (if (eq (car-safe a) 'mod)
    (progn
      (setq mod (nth 2 a)
        a (nth 1 a))
      (if (eq (car-safe b) 'mod)
          (if (equal mod (nth 2 b))
          (setq b (nth 1 b))
        (math-reject-arg b "*Inconsistent modulos"))))
      (setq mod (nth 2 b)
        b (nth 1 b)))
    (if (Math-messy-integerp mod)
    (setq mod (math-trunc mod))
      (or (Math-integerp mod)
      (math-reject-arg mod 'integerp)))
    (let ((bits (math-integer-log2 mod)))
      (if bits
      (if w
          (if (/= w bits)
          (calc-record-why
           "*Warning: Modulo inconsistent with word size"))
        (setq w bits))
    (calc-record-why "*Warning: Modulo is not a power of 2"))
      (math-make-mod (if b
             (funcall f a b w)
               (funcall f a w))
             mod)))
)

(defun math-and-bignum (a b)   ; [l l l]
  (and a b
       (let ((qa (math-div-bignum-digit a 512))
         (qb (math-div-bignum-digit b 512)))
     (math-mul-bignum-digit (math-and-bignum (math-norm-bignum (car qa))
                          (math-norm-bignum (car qb)))
                 512
                 (logand (cdr qa) (cdr qb)))))
)

(defun calcFunc-or (a b &optional w)   ; [I I I] [Public]
  (cond ((Math-messy-integerp w)
     (calcFunc-or a b (math-trunc w)))
    ((and w (not (integerp w)))
     (math-reject-arg w 'fixnump))
    ((and (integerp a) (integerp b))
     (math-clip (logior a b) w))
    ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod))
     (math-binary-modulo-args 'calcFunc-or a b w))
    ((not (Math-num-integerp a))
     (math-reject-arg a 'integerp))
    ((not (Math-num-integerp b))
     (math-reject-arg b 'integerp))
    (t (math-clip (cons 'bigpos
                (math-or-bignum (math-binary-arg a w)
                        (math-binary-arg b w)))
              w)))
)

(defun math-or-bignum (a b)   ; [l l l]
  (and (or a b)
       (let ((qa (math-div-bignum-digit a 512))
         (qb (math-div-bignum-digit b 512)))
     (math-mul-bignum-digit (math-or-bignum (math-norm-bignum (car qa))
                         (math-norm-bignum (car qb)))
                 512
                 (logior (cdr qa) (cdr qb)))))
)

(defun calcFunc-xor (a b &optional w)   ; [I I I] [Public]
  (cond ((Math-messy-integerp w)
     (calcFunc-xor a b (math-trunc w)))
    ((and w (not (integerp w)))
     (math-reject-arg w 'fixnump))
    ((and (integerp a) (integerp b))
     (math-clip (logxor a b) w))
    ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod))
     (math-binary-modulo-args 'calcFunc-xor a b w))
    ((not (Math-num-integerp a))
     (math-reject-arg a 'integerp))
    ((not (Math-num-integerp b))
     (math-reject-arg b 'integerp))
    (t (math-clip (cons 'bigpos
                (math-xor-bignum (math-binary-arg a w)
                         (math-binary-arg b w)))
              w)))
)

(defun math-xor-bignum (a b)   ; [l l l]
  (and (or a b)
       (let ((qa (math-div-bignum-digit a 512))
         (qb (math-div-bignum-digit b 512)))
     (math-mul-bignum-digit (math-xor-bignum (math-norm-bignum (car qa))
                          (math-norm-bignum (car qb)))
                 512
                 (logxor (cdr qa) (cdr qb)))))
)

(defun calcFunc-diff (a b &optional w)   ; [I I I] [Public]
  (cond ((Math-messy-integerp w)
     (calcFunc-diff a b (math-trunc w)))
    ((and w (not (integerp w)))
     (math-reject-arg w 'fixnump))
    ((and (integerp a) (integerp b))
     (math-clip (logand a (lognot b)) w))
    ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod))
     (math-binary-modulo-args 'calcFunc-diff a b w))
    ((not (Math-num-integerp a))
     (math-reject-arg a 'integerp))
    ((not (Math-num-integerp b))
     (math-reject-arg b 'integerp))
    (t (math-clip (cons 'bigpos
                (math-diff-bignum (math-binary-arg a w)
                          (math-binary-arg b w)))
              w)))
)

(defun math-diff-bignum (a b)   ; [l l l]
  (and a
       (let ((qa (math-div-bignum-digit a 512))
         (qb (math-div-bignum-digit b 512)))
     (math-mul-bignum-digit (math-diff-bignum (math-norm-bignum (car qa))
                           (math-norm-bignum (car qb)))
                 512
                 (logand (cdr qa) (lognot (cdr qb))))))
)

(defun calcFunc-not (a &optional w)   ; [I I] [Public]
  (cond ((Math-messy-integerp w)
     (calcFunc-not a (math-trunc w)))
    ((eq (car-safe a) 'mod)
     (math-binary-modulo-args 'calcFunc-not a nil w))
    ((and w (not (integerp w)))
     (math-reject-arg w 'fixnump))
    ((not (Math-num-integerp a))
     (math-reject-arg a 'integerp))
    ((< (or w (setq w calc-word-size)) 0)
     (math-clip (calcFunc-not a (- w)) w))
    (t (math-normalize
        (cons 'bigpos
          (math-not-bignum (math-binary-arg a w)
                   w)))))
)

(defun math-not-bignum (a w)   ; [l l]
  (let ((q (math-div-bignum-digit a 512)))
    (if (<= w 9)
    (list (logand (lognot (cdr q))
              (1- (lsh 1 w))))
      (math-mul-bignum-digit (math-not-bignum (math-norm-bignum (car q))
                           (- w 9))
                  512
                  (logxor (cdr q) 511))))
)

(defun calcFunc-lsh (a &optional n w)   ; [I I] [Public]
  (setq a (math-trunc a)
    n (if n (math-trunc n) 1))
  (if (eq (car-safe a) 'mod)
      (math-binary-modulo-args 'calcFunc-lsh a n w)
    (setq w (if w (math-trunc w) calc-word-size))
    (or (integerp w)
    (math-reject-arg w 'fixnump))
    (or (Math-integerp a)
    (math-reject-arg a 'integerp))
    (or (Math-integerp n)
    (math-reject-arg n 'integerp))
    (if (< w 0)
    (math-clip (calcFunc-lsh a n (- w)) w)
      (if (Math-integer-negp a)
      (setq a (math-clip a w)))
      (cond ((or (Math-lessp n (- w))
         (Math-lessp w n))
         0)
        ((< n 0)
         (math-quotient (math-clip a w) (math-power-of-2 (- n))))
        (t
         (math-clip (math-mul a (math-power-of-2 n)) w)))))
)

(defun calcFunc-rsh (a &optional n w)   ; [I I] [Public]
  (calcFunc-lsh a (math-neg (or n 1)) w)
)

(defun calcFunc-ash (a &optional n w)   ; [I I] [Public]
  (if (or (null n)
      (not (Math-negp n)))
      (calcFunc-lsh a n w)
    (setq a (math-trunc a)
      n (if n (math-trunc n) 1))
    (if (eq (car-safe a) 'mod)
    (math-binary-modulo-args 'calcFunc-ash a n w)
      (setq w (if w (math-trunc w) calc-word-size))
      (or (integerp w)
      (math-reject-arg w 'fixnump))
      (or (Math-integerp a)
      (math-reject-arg a 'integerp))
      (or (Math-integerp n)
      (math-reject-arg n 'integerp))
      (if (< w 0)
      (math-clip (calcFunc-ash a n (- w)) w)
    (if (Math-integer-negp a)
        (setq a (math-clip a w)))
    (let ((two-to-sizem1 (math-power-of-2 (1- w)))
          (sh (calcFunc-lsh a n w)))
      (cond ((Math-natnum-lessp a two-to-sizem1)
         sh)
        ((Math-lessp n (- 1 w))
         (math-add (math-mul two-to-sizem1 2) -1))
        (t (let ((two-to-n (math-power-of-2 (- n))))
             (math-add (calcFunc-lsh (math-add two-to-n -1)
                         (+ w n) w)
                   sh))))))))
)

(defun calcFunc-rash (a &optional n w)   ; [I I] [Public]
  (calcFunc-ash a (math-neg (or n 1)) w)
)

(defun calcFunc-rot (a &optional n w)   ; [I I] [Public]
  (setq a (math-trunc a)
    n (if n (math-trunc n) 1))
  (if (eq (car-safe a) 'mod)
      (math-binary-modulo-args 'calcFunc-rot a n w)
    (setq w (if w (math-trunc w) calc-word-size))
    (or (integerp w)
    (math-reject-arg w 'fixnump))
    (or (Math-integerp a)
    (math-reject-arg a 'integerp))
    (or (Math-integerp n)
    (math-reject-arg n 'integerp))
    (if (< w 0)
    (math-clip (calcFunc-rot a n (- w)) w)
      (if (Math-integer-negp a)
      (setq a (math-clip a w)))
      (cond ((or (Math-integer-negp n)
         (not (Math-natnum-lessp n w)))
         (calcFunc-rot a (math-mod n w) w))
        (t
         (math-add (calcFunc-lsh a (- n w) w)
               (calcFunc-lsh a n w))))))
)

(defun math-clip (a &optional w)   ; [I I] [Public]
  (cond ((Math-messy-integerp w)
     (math-clip a (math-trunc w)))
    ((eq (car-safe a) 'mod)
     (math-binary-modulo-args 'math-clip a nil w))
    ((and w (not (integerp w)))
     (math-reject-arg w 'fixnump))
    ((not (Math-num-integerp a))
     (math-reject-arg a 'integerp))
    ((< (or w (setq w calc-word-size)) 0)
     (setq a (math-clip a (- w)))
     (if (Math-natnum-lessp a (math-power-of-2 (- -1 w)))
         a
       (math-sub a (math-power-of-2 (- w)))))
    ((Math-negp a)
     (math-normalize (cons 'bigpos (math-binary-arg a w))))
    ((and (integerp a) (< a 1000000))
     (if (>= w 20)
         a
       (logand a (1- (lsh 1 w)))))
    (t
     (math-normalize
      (cons 'bigpos
        (math-clip-bignum (cdr (math-bignum-test (math-trunc a)))
                  w)))))
)
(fset 'calcFunc-clip (symbol-function 'math-clip))

(defun math-clip-bignum (a w)   ; [l l]
  (let ((q (math-div-bignum-digit a 512)))
    (if (<= w 9)
    (list (logand (cdr q)
              (1- (lsh 1 w))))
      (math-mul-bignum-digit (math-clip-bignum (math-norm-bignum (car q))
                        (- w 9))
                  512
                  (cdr q))))
)




(defvar math-max-digits-cache nil)
(defun math-compute-max-digits (w r)
  (let* ((pair (+ (* r 100000) w))
     (res (assq pair math-max-digits-cache)))
    (if res
    (cdr res)
      (let* ((calc-command-flags nil)
         (digs (math-ceiling (math-div w (math-real-log2 r)))))
    (setq math-max-digits-cache (cons (cons pair digs)
                      math-max-digits-cache))
    digs)))
)

(defvar math-log2-cache (list '(2 . 1)
                  '(4 . 2)
                  '(8 . 3)
                  '(10 . (float 332193 -5))
                  '(16 . 4)
                  '(32 . 5)))
(defun math-real-log2 (x)   ;;; calc-internal-prec must be 6
  (let ((res (assq x math-log2-cache)))
    (if res
    (cdr res)
      (let* ((calc-symbolic-mode nil)
         (calc-display-working-message nil)
         (log (calcFunc-log x 2)))
    (setq math-log2-cache (cons (cons x log) math-log2-cache))
    log)))
)

(defconst math-radix-digits ["0" "1" "2" "3" "4" "5" "6" "7" "8" "9"
                 "A" "B" "C" "D" "E" "F" "G" "H" "I" "J"
                 "K" "L" "M" "N" "O" "P" "Q" "R" "S" "T"
                 "U" "V" "W" "X" "Y" "Z"])

(defun math-format-radix (a)   ; [X S]
  (if (< a calc-number-radix)
      (if (< a 0)
      (concat "-" (math-format-radix (- a)))
    (math-format-radix-digit a))
    (let ((s ""))
      (while (> a 0)
    (setq s (concat (math-format-radix-digit (% a calc-number-radix)) s)
          a (/ a calc-number-radix)))
      s))
)

(defconst math-binary-digits ["000" "001" "010" "011"
                  "100" "101" "110" "111"])
(defun math-format-binary (a)   ; [X S]
  (if (< a 8)
      (if (< a 0)
      (concat "-" (math-format-binary (- a)))
    (math-format-radix a))
    (let ((s ""))
      (while (> a 7)
    (setq s (concat (aref math-binary-digits (% a 8)) s)
          a (/ a 8)))
      (concat (math-format-radix a) s)))
)

(defun math-format-bignum-radix (a)   ; [X L]
  (cond ((null a) "0")
    ((and (null (cdr a))
          (< (car a) calc-number-radix))
     (math-format-radix-digit (car a)))
    (t
     (let ((q (math-div-bignum-digit a calc-number-radix)))
       (concat (math-format-bignum-radix (math-norm-bignum (car q)))
           (math-format-radix-digit (cdr q))))))
)

(defun math-format-bignum-binary (a)   ; [X L]
  (cond ((null a) "0")
    ((null (cdr a))
     (math-format-binary (car a)))
    (t
     (let ((q (math-div-bignum-digit a 512)))
       (concat (math-format-bignum-binary (math-norm-bignum (car q)))
           (aref math-binary-digits (/ (cdr q) 64))
           (aref math-binary-digits (% (/ (cdr q) 8) 8))
           (aref math-binary-digits (% (cdr q) 8))))))
)

(defun math-format-bignum-octal (a)   ; [X L]
  (cond ((null a) "0")
    ((null (cdr a))
     (math-format-radix (car a)))
    (t
     (let ((q (math-div-bignum-digit a 512)))
       (concat (math-format-bignum-octal (math-norm-bignum (car q)))
           (math-format-radix-digit (/ (cdr q) 64))
           (math-format-radix-digit (% (/ (cdr q) 8) 8))
           (math-format-radix-digit (% (cdr q) 8))))))
)

(defun math-format-bignum-hex (a)   ; [X L]
  (cond ((null a) "0")
    ((null (cdr a))
     (math-format-radix (car a)))
    (t
     (let ((q (math-div-bignum-digit a 256)))
       (concat (math-format-bignum-hex (math-norm-bignum (car q)))
           (math-format-radix-digit (/ (cdr q) 16))
           (math-format-radix-digit (% (cdr q) 16))))))
)

;;; Decompose into integer and fractional parts, without depending
;;; on calc-internal-prec.
(defun math-float-parts (a need-frac)    ; returns ( int frac fracdigs )
  (if (>= (nth 2 a) 0)
      (list (math-scale-rounding (nth 1 a) (nth 2 a)) '(float 0 0) 0)
    (let* ((d (math-numdigs (nth 1 a)))
       (n (- (nth 2 a))))
      (if need-frac
      (if (>= n d)
          (list 0 a n)
        (let ((qr (math-idivmod (nth 1 a) (math-scale-int 1 n))))
          (list (car qr) (math-make-float (cdr qr) (- n)) n)))
    (list (math-scale-rounding (nth 1 a) (nth 2 a))
          '(float 0 0) 0))))
)

(defun math-format-radix-float (a prec)
  (let ((fmt (car calc-float-format))
    (figs (nth 1 calc-float-format))
    (point calc-point-char)
    (str nil))
    (if (eq fmt 'fix)
    (let* ((afigs (math-abs figs))
           (fp (math-float-parts a (> afigs 0)))
           (calc-internal-prec (+ 3 (max (nth 2 fp)
                         (math-convert-radix-digits
                          afigs t))))
           (int (car fp))
           (frac (math-round (math-mul (math-normalize (nth 1 fp))
                       (math-radix-float-power afigs)))))
      (if (not (and (math-zerop frac) (math-zerop int) (< figs 0)))
          (let ((math-radix-explicit-format nil))
        (let ((calc-group-digits nil))
          (setq str (if (> afigs 0) (math-format-number frac) ""))
          (if (< (length str) afigs)
              (setq str (concat (make-string (- afigs (length str)) ?0)
                    str))
            (if (> (length str) afigs)
            (setq str (substring str 1)
                  int (math-add int 1))))
          (setq str (concat (math-format-number int) point str)))
        (if calc-group-digits
            (setq str (math-group-float str))))
        (setq figs 0))))
    (or str
    (let* ((prec calc-internal-prec)
           (afigs (if (> figs 0)
              figs
            (max 1 (+ figs
                  (1- (math-convert-radix-digits
                       (max prec
                        (math-numdigs (nth 1 a)))))))))
           (calc-internal-prec (+ 3 (math-convert-radix-digits afigs t)))
           (explo -1) (vlo (math-radix-float-power explo))
           (exphi 1) (vhi (math-radix-float-power exphi))
           expmid vmid eadj)
      (setq a (math-normalize a))
      (if (Math-zerop a)
          (setq explo 0)
        (if (math-lessp-float '(float 1 0) a)
        (while (not (math-lessp-float a vhi))
          (setq explo exphi vlo vhi
            exphi (math-mul exphi 2)
            vhi (math-radix-float-power exphi)))
          (while (math-lessp-float a vlo)
        (setq exphi explo vhi vlo
              explo (math-mul explo 2)
              vlo (math-radix-float-power explo))))
        (while (not (eq (math-sub exphi explo) 1))
          (setq expmid (math-div2 (math-add explo exphi))
            vmid (math-radix-float-power expmid))
          (if (math-lessp-float a vmid)
          (setq exphi expmid vhi vmid)
        (setq explo expmid vlo vmid)))
        (setq a (math-div-float a vlo)))
      (let* ((sc (math-round (math-mul a (math-radix-float-power
                          (1- afigs)))))
         (math-radix-explicit-format nil))
        (let ((calc-group-digits nil))
          (setq str (math-format-number sc))))
      (if (> (length str) afigs)
          (setq str (substring str 0 -1)
            explo (1+ explo)))
      (if (and (eq fmt 'float)
           (math-lessp explo (+ (if (= figs 0)
                        (1- (math-convert-radix-digits
                         prec))
                      afigs)
                    calc-display-sci-high 1))
           (math-lessp calc-display-sci-low explo))
          (let ((dpos (1+ explo)))
        (cond ((<= dpos 0)
               (setq str (concat "0" point (make-string (- dpos) ?0)
                     str)))
              ((> dpos (length str))
               (setq str (concat str (make-string (- dpos (length str))
                              ?0) point)))
              (t
               (setq str (concat (substring str 0 dpos) point
                     (substring str dpos)))))
        (setq explo nil))
        (setq eadj (if (eq fmt 'eng)
               (min (math-mod explo 3) (length str))
             0)
          str (concat (substring str 0 (1+ eadj)) point
                  (substring str (1+ eadj)))))
      (setq pos (length str))
      (while (eq (aref str (1- pos)) ?0) (setq pos (1- pos)))
      (and explo (eq (aref str (1- pos)) ?.) (setq pos (1- pos)))
      (setq str (substring str 0 pos))
      (if calc-group-digits
          (setq str (math-group-float str)))
      (if explo
          (let ((estr (let ((calc-number-radix 10)
                (calc-group-digits nil))
                (setq estr (math-format-number
                    (math-sub explo eadj))))))
        (setq str (if (or (memq calc-language '(math maple))
                  (> calc-number-radix 14))
                  (format "%s*%d.^%s" str calc-number-radix estr)
                (format "%se%s" str estr)))))))
    str)
)

(defun math-convert-radix-digits (n &optional to-dec)
  (let ((key (cons n (cons to-dec calc-number-radix))))
    (or (cdr (assoc key math-radix-digits-cache))
    (let* ((calc-internal-prec 6)
           (log (math-div (math-real-log2 calc-number-radix)
                  '(float 332193 -5))))
      (cdr (car (setq math-radix-digits-cache
              (cons (cons key (math-ceiling (if to-dec
                                (math-mul n log)
                              (math-div n log))))
                math-radix-digits-cache)))))))
)
(setq math-radix-digits-cache nil)

(defun math-radix-float-power (n)
  (if (eq n 0)
      '(float 1 0)
    (or (and (eq calc-number-radix (car math-radix-float-cache-tag))
         (<= calc-internal-prec (cdr math-radix-float-cache-tag)))
    (setq math-radix-float-cache-tag (cons calc-number-radix
                           calc-internal-prec)
          math-radix-float-cache nil))
    (math-normalize
     (or (cdr (assoc n math-radix-float-cache))
     (cdr (car (setq math-radix-float-cache
             (cons (cons
                n
                (let ((calc-internal-prec
                       (cdr math-radix-float-cache-tag)))
                  (if (math-negp n)
                      (math-div-float '(float 1 0)
                              (math-radix-float-power
                               (math-neg n)))
                    (math-mul-float (math-sqr-float
                             (math-radix-float-power
                              (math-div2 n)))
                            (if (math-evenp n)
                            '(float 1 0)
                              (math-float
                               calc-number-radix))))))
                   math-radix-float-cache)))))))
)
(setq math-radix-float-cache-tag nil)