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emacs/lisp/calc/calc-bin.el
Jay Belanger 58ba2f8f07 Update copyright information.
2005-07-14 20:05:30 +00:00

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;;; calc-bin.el --- binary functions for Calc
;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
;; 2005 Free Software Foundation, Inc.
;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainer: Jay Belanger <belanger@truman.edu>
;; 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.
;;; Commentary:
;;; Code:
;; This file is autoloaded from calc-ext.el.
(require 'calc-ext)
(require 'calc-macs)
;;; 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-number 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))))))
(defalias 'calcFunc-clip '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"])
(defsubst math-format-radix-digit (a) ; [X D]
(aref math-radix-digits a))
(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)
pos)
(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)))
(when 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))
(when calc-group-digits
(setq str (math-group-float str)))
(if explo
(let ((estr (let ((calc-number-radix 10)
(calc-group-digits nil))
(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))
(defvar math-radix-digits-cache nil)
(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))))))))
(defvar math-radix-float-cache-tag nil)
(defvar math-radix-float-cache)
(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))))))))
(provide 'calc-bin)
;;; arch-tag: f6dba7bc-53b2-41ae-919c-c266ab0ca8b3
;;; calc-bin.el ends here
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