summaryrefslogtreecommitdiff
path: root/lisp/calc/calc-bin.el
diff options
context:
space:
mode:
Diffstat (limited to 'lisp/calc/calc-bin.el')
-rw-r--r--lisp/calc/calc-bin.el847
1 files changed, 847 insertions, 0 deletions
diff --git a/lisp/calc/calc-bin.el b/lisp/calc/calc-bin.el
new file mode 100644
index 00000000000..23c682a0da1
--- /dev/null
+++ b/lisp/calc/calc-bin.el
@@ -0,0 +1,847 @@
+;; Calculator for GNU Emacs, part II [calc-bin.el]
+;; Copyright (C) 1990, 1991, 1992, 1993 Free Software Foundation, Inc.
+;; Written by Dave Gillespie, daveg@synaptics.com.
+
+;; 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)
+
generated by cgit v1.2.3 (git 2.39.1) at 2025-04-18 22:17:30 +0000