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809 lines
24 KiB
EmacsLisp
809 lines
24 KiB
EmacsLisp
;;; calc-bin.el --- binary functions for Calc
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;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
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;; 2005, 2006, 2007 Free Software Foundation, Inc.
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;; Author: David Gillespie <daveg@synaptics.com>
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;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
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;; This file is part of GNU Emacs.
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;; GNU Emacs is free software; you can redistribute it and/or modify
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;; it under the terms of the GNU General Public License as published by
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;; the Free Software Foundation; either version 2, or (at your option)
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;; any later version.
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;; GNU Emacs is distributed in the hope that it will be useful,
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;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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;; GNU General Public License for more details.
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;; You should have received a copy of the GNU General Public License
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;; along with GNU Emacs; see the file COPYING. If not, write to the
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;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
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;; Boston, MA 02110-1301, USA.
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;;; Commentary:
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;;; Code:
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;; This file is autoloaded from calc-ext.el.
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(require 'calc-ext)
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(require 'calc-macs)
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;;; b-prefix binary commands.
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(defun calc-and (n)
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(interactive "P")
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(calc-slow-wrapper
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(calc-enter-result 2 "and"
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(append '(calcFunc-and)
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(calc-top-list-n 2)
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(and n (list (prefix-numeric-value n)))))))
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(defun calc-or (n)
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(interactive "P")
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(calc-slow-wrapper
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(calc-enter-result 2 "or"
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(append '(calcFunc-or)
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(calc-top-list-n 2)
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(and n (list (prefix-numeric-value n)))))))
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(defun calc-xor (n)
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(interactive "P")
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(calc-slow-wrapper
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(calc-enter-result 2 "xor"
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(append '(calcFunc-xor)
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(calc-top-list-n 2)
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(and n (list (prefix-numeric-value n)))))))
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(defun calc-diff (n)
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(interactive "P")
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(calc-slow-wrapper
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(calc-enter-result 2 "diff"
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(append '(calcFunc-diff)
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(calc-top-list-n 2)
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(and n (list (prefix-numeric-value n)))))))
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(defun calc-not (n)
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(interactive "P")
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(calc-slow-wrapper
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(calc-enter-result 1 "not"
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(append '(calcFunc-not)
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(calc-top-list-n 1)
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(and n (list (prefix-numeric-value n)))))))
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(defun calc-lshift-binary (n)
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(interactive "P")
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(calc-slow-wrapper
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(let ((hyp (if (calc-is-hyperbolic) 2 1)))
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(calc-enter-result hyp "lsh"
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(append '(calcFunc-lsh)
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(calc-top-list-n hyp)
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(and n (list (prefix-numeric-value n))))))))
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(defun calc-rshift-binary (n)
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(interactive "P")
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(calc-slow-wrapper
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(let ((hyp (if (calc-is-hyperbolic) 2 1)))
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(calc-enter-result hyp "rsh"
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(append '(calcFunc-rsh)
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(calc-top-list-n hyp)
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(and n (list (prefix-numeric-value n))))))))
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(defun calc-lshift-arith (n)
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(interactive "P")
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(calc-slow-wrapper
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(let ((hyp (if (calc-is-hyperbolic) 2 1)))
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(calc-enter-result hyp "ash"
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(append '(calcFunc-ash)
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(calc-top-list-n hyp)
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(and n (list (prefix-numeric-value n))))))))
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(defun calc-rshift-arith (n)
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(interactive "P")
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(calc-slow-wrapper
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(let ((hyp (if (calc-is-hyperbolic) 2 1)))
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(calc-enter-result hyp "rash"
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(append '(calcFunc-rash)
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(calc-top-list-n hyp)
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(and n (list (prefix-numeric-value n))))))))
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(defun calc-rotate-binary (n)
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(interactive "P")
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(calc-slow-wrapper
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(let ((hyp (if (calc-is-hyperbolic) 2 1)))
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(calc-enter-result hyp "rot"
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(append '(calcFunc-rot)
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(calc-top-list-n hyp)
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(and n (list (prefix-numeric-value n))))))))
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(defun calc-clip (n)
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(interactive "P")
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(calc-slow-wrapper
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(calc-enter-result 1 "clip"
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(append '(calcFunc-clip)
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(calc-top-list-n 1)
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(and n (list (prefix-numeric-value n)))))))
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(defun calc-word-size (n)
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(interactive "P")
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(calc-wrapper
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(or n (setq n (read-string (format "Binary word size: (default %d) "
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calc-word-size))))
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(setq n (if (stringp n)
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(if (equal n "")
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calc-word-size
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(if (string-match "\\`[-+]?[0-9]+\\'" n)
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(string-to-number n)
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(error "Expected an integer")))
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(prefix-numeric-value n)))
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(or (= n calc-word-size)
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(if (> (math-abs n) 100)
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(calc-change-mode 'calc-word-size n calc-leading-zeros)
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(calc-change-mode '(calc-word-size calc-previous-modulo)
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(list n (math-power-of-2 (math-abs n)))
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calc-leading-zeros)))
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(if (< n 0)
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(message "Binary word size is %d bits (2's complement)" (- n))
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(message "Binary word size is %d bits" n))))
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;;; d-prefix mode commands.
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(defun calc-radix (n)
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(interactive "NDisplay radix (2-36): ")
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(calc-wrapper
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(if (and (>= n 2) (<= n 36))
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(progn
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(calc-change-mode 'calc-number-radix n t)
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;; also change global value so minibuffer sees it
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(setq-default calc-number-radix calc-number-radix))
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(setq n calc-number-radix))
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(message "Number radix is %d" n)))
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(defun calc-decimal-radix ()
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(interactive)
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(calc-radix 10))
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(defun calc-binary-radix ()
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(interactive)
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(calc-radix 2))
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(defun calc-octal-radix ()
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(interactive)
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(calc-radix 8))
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(defun calc-hex-radix ()
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(interactive)
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(calc-radix 16))
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(defun calc-leading-zeros (n)
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(interactive "P")
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(calc-wrapper
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(if (calc-change-mode 'calc-leading-zeros n t t)
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(message "Zero-padding integers to %d digits (assuming radix %d)"
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(let* ((calc-internal-prec 6))
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(math-compute-max-digits (math-abs calc-word-size)
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calc-number-radix))
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calc-number-radix)
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(message "Omitting leading zeros on integers"))))
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(defvar math-power-of-2-cache (list 1 2 4 8 16 32 64 128 256 512 1024))
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(defvar math-big-power-of-2-cache nil)
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(defun math-power-of-2 (n) ; [I I] [Public]
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(if (and (natnump n) (<= n 100))
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(or (nth n math-power-of-2-cache)
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(let* ((i (length math-power-of-2-cache))
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(val (nth (1- i) math-power-of-2-cache)))
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(while (<= i n)
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(setq val (math-mul val 2)
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math-power-of-2-cache (nconc math-power-of-2-cache
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(list val))
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i (1+ i)))
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val))
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(let ((found (assq n math-big-power-of-2-cache)))
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(if found
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(cdr found)
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(let ((po2 (math-ipow 2 n)))
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(setq math-big-power-of-2-cache
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(cons (cons n po2) math-big-power-of-2-cache))
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po2)))))
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(defun math-integer-log2 (n) ; [I I] [Public]
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(let ((i 0)
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(p math-power-of-2-cache)
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val)
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(while (and p (Math-natnum-lessp (setq val (car p)) n))
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(setq p (cdr p)
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i (1+ i)))
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(if p
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(and (equal val n)
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i)
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(while (Math-natnum-lessp
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(prog1
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(setq val (math-mul val 2))
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(setq math-power-of-2-cache (nconc math-power-of-2-cache
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(list val))))
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n)
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(setq i (1+ i)))
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(and (equal val n)
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i))))
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;;; Bitwise operations.
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(defun calcFunc-and (a b &optional w) ; [I I I] [Public]
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(cond ((Math-messy-integerp w)
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(calcFunc-and a b (math-trunc w)))
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((and w (not (integerp w)))
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(math-reject-arg w 'fixnump))
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((and (integerp a) (integerp b))
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(math-clip (logand a b) w))
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((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod))
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(math-binary-modulo-args 'calcFunc-and a b w))
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((not (Math-num-integerp a))
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(math-reject-arg a 'integerp))
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((not (Math-num-integerp b))
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(math-reject-arg b 'integerp))
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(t (math-clip (cons 'bigpos
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(math-and-bignum (math-binary-arg a w)
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(math-binary-arg b w)))
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w))))
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(defun math-binary-arg (a w)
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(if (not (Math-integerp a))
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(setq a (math-trunc a)))
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(if (Math-integer-negp a)
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(math-not-bignum (cdr (math-bignum-test (math-sub -1 a)))
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(math-abs (if w (math-trunc w) calc-word-size)))
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(cdr (Math-bignum-test a))))
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(defun math-binary-modulo-args (f a b w)
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(let (mod)
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(if (eq (car-safe a) 'mod)
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(progn
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(setq mod (nth 2 a)
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a (nth 1 a))
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(if (eq (car-safe b) 'mod)
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(if (equal mod (nth 2 b))
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(setq b (nth 1 b))
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(math-reject-arg b "*Inconsistent modulos"))))
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(setq mod (nth 2 b)
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b (nth 1 b)))
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(if (Math-messy-integerp mod)
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(setq mod (math-trunc mod))
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(or (Math-integerp mod)
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(math-reject-arg mod 'integerp)))
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(let ((bits (math-integer-log2 mod)))
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(if bits
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(if w
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(if (/= w bits)
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(calc-record-why
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"*Warning: Modulo inconsistent with word size"))
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(setq w bits))
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(calc-record-why "*Warning: Modulo is not a power of 2"))
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(math-make-mod (if b
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(funcall f a b w)
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(funcall f a w))
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mod))))
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(defun math-and-bignum (a b) ; [l l l]
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(and a b
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(let ((qa (math-div-bignum-digit a 512))
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(qb (math-div-bignum-digit b 512)))
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(math-mul-bignum-digit (math-and-bignum (math-norm-bignum (car qa))
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(math-norm-bignum (car qb)))
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512
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(logand (cdr qa) (cdr qb))))))
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(defun calcFunc-or (a b &optional w) ; [I I I] [Public]
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(cond ((Math-messy-integerp w)
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(calcFunc-or a b (math-trunc w)))
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((and w (not (integerp w)))
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(math-reject-arg w 'fixnump))
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((and (integerp a) (integerp b))
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(math-clip (logior a b) w))
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((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod))
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(math-binary-modulo-args 'calcFunc-or a b w))
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((not (Math-num-integerp a))
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(math-reject-arg a 'integerp))
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((not (Math-num-integerp b))
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(math-reject-arg b 'integerp))
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(t (math-clip (cons 'bigpos
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(math-or-bignum (math-binary-arg a w)
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(math-binary-arg b w)))
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w))))
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(defun math-or-bignum (a b) ; [l l l]
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(and (or a b)
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(let ((qa (math-div-bignum-digit a 512))
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(qb (math-div-bignum-digit b 512)))
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(math-mul-bignum-digit (math-or-bignum (math-norm-bignum (car qa))
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(math-norm-bignum (car qb)))
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512
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(logior (cdr qa) (cdr qb))))))
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(defun calcFunc-xor (a b &optional w) ; [I I I] [Public]
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(cond ((Math-messy-integerp w)
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(calcFunc-xor a b (math-trunc w)))
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((and w (not (integerp w)))
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(math-reject-arg w 'fixnump))
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((and (integerp a) (integerp b))
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(math-clip (logxor a b) w))
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((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod))
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(math-binary-modulo-args 'calcFunc-xor a b w))
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((not (Math-num-integerp a))
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(math-reject-arg a 'integerp))
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((not (Math-num-integerp b))
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(math-reject-arg b 'integerp))
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(t (math-clip (cons 'bigpos
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(math-xor-bignum (math-binary-arg a w)
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(math-binary-arg b w)))
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w))))
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(defun math-xor-bignum (a b) ; [l l l]
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(and (or a b)
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(let ((qa (math-div-bignum-digit a 512))
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(qb (math-div-bignum-digit b 512)))
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(math-mul-bignum-digit (math-xor-bignum (math-norm-bignum (car qa))
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(math-norm-bignum (car qb)))
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512
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(logxor (cdr qa) (cdr qb))))))
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(defun calcFunc-diff (a b &optional w) ; [I I I] [Public]
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(cond ((Math-messy-integerp w)
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(calcFunc-diff a b (math-trunc w)))
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((and w (not (integerp w)))
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(math-reject-arg w 'fixnump))
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((and (integerp a) (integerp b))
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(math-clip (logand a (lognot b)) w))
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((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod))
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(math-binary-modulo-args 'calcFunc-diff a b w))
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((not (Math-num-integerp a))
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(math-reject-arg a 'integerp))
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((not (Math-num-integerp b))
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(math-reject-arg b 'integerp))
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(t (math-clip (cons 'bigpos
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(math-diff-bignum (math-binary-arg a w)
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(math-binary-arg b w)))
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w))))
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(defun math-diff-bignum (a b) ; [l l l]
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(and a
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(let ((qa (math-div-bignum-digit a 512))
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(qb (math-div-bignum-digit b 512)))
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(math-mul-bignum-digit (math-diff-bignum (math-norm-bignum (car qa))
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(math-norm-bignum (car qb)))
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512
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(logand (cdr qa) (lognot (cdr qb)))))))
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(defun calcFunc-not (a &optional w) ; [I I] [Public]
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(cond ((Math-messy-integerp w)
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(calcFunc-not a (math-trunc w)))
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((eq (car-safe a) 'mod)
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(math-binary-modulo-args 'calcFunc-not a nil w))
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((and w (not (integerp w)))
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(math-reject-arg w 'fixnump))
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((not (Math-num-integerp a))
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(math-reject-arg a 'integerp))
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((< (or w (setq w calc-word-size)) 0)
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(math-clip (calcFunc-not a (- w)) w))
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(t (math-normalize
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(cons 'bigpos
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(math-not-bignum (math-binary-arg a w)
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w))))))
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(defun math-not-bignum (a w) ; [l l]
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(let ((q (math-div-bignum-digit a 512)))
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(if (<= w 9)
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(list (logand (lognot (cdr q))
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(1- (lsh 1 w))))
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(math-mul-bignum-digit (math-not-bignum (math-norm-bignum (car q))
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(- w 9))
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512
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(logxor (cdr q) 511)))))
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(defun calcFunc-lsh (a &optional n w) ; [I I] [Public]
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(setq a (math-trunc a)
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n (if n (math-trunc n) 1))
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(if (eq (car-safe a) 'mod)
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(math-binary-modulo-args 'calcFunc-lsh a n w)
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(setq w (if w (math-trunc w) calc-word-size))
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(or (integerp w)
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(math-reject-arg w 'fixnump))
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(or (Math-integerp a)
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(math-reject-arg a 'integerp))
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(or (Math-integerp n)
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(math-reject-arg n 'integerp))
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(if (< w 0)
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(math-clip (calcFunc-lsh a n (- w)) w)
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(if (Math-integer-negp a)
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(setq a (math-clip a w)))
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(cond ((or (Math-lessp n (- w))
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(Math-lessp w n))
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0)
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((< n 0)
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(math-quotient (math-clip a w) (math-power-of-2 (- n))))
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(t
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(math-clip (math-mul a (math-power-of-2 n)) w))))))
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(defun calcFunc-rsh (a &optional n w) ; [I I] [Public]
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(calcFunc-lsh a (math-neg (or n 1)) w))
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(defun calcFunc-ash (a &optional n w) ; [I I] [Public]
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(if (or (null n)
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(not (Math-negp n)))
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(calcFunc-lsh a n w)
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(setq a (math-trunc a)
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n (if n (math-trunc n) 1))
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(if (eq (car-safe a) 'mod)
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(math-binary-modulo-args 'calcFunc-ash a n w)
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(setq w (if w (math-trunc w) calc-word-size))
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(or (integerp w)
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(math-reject-arg w 'fixnump))
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(or (Math-integerp a)
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(math-reject-arg a 'integerp))
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(or (Math-integerp n)
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|
(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
|