619 lines
18 KiB
JavaScript
619 lines
18 KiB
JavaScript
/**
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* @fileoverview Support for 36-bit integers (using unsigned JavaScript numbers)
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* @author <a href="mailto:Jeff@pcjs.org">Jeff Parsons</a> (@jeffpar)
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* @copyright © Jeff Parsons 2012-2017
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*
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* This file is part of PCjs, a computer emulation software project at <http://pcjs.org/>.
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*
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* PCjs is free software: you can redistribute it and/or modify it under the terms of the
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* GNU General Public License as published by the Free Software Foundation, either version 3
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* of the License, or (at your option) any later version.
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*
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* PCjs is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without
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* even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along with PCjs. If not,
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* see <http://www.gnu.org/licenses/gpl.html>.
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*
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* You are required to include the above copyright notice in every modified copy of this work
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* and to display that copyright notice when the software starts running; see COPYRIGHT in
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* <http://pcjs.org/modules/shared/lib/defines.js>.
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*
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* Some PCjs files also attempt to load external resource files, such as character-image files,
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* ROM files, and disk image files. Those external resource files are not considered part of PCjs
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* for purposes of the GNU General Public License, and the author does not claim any copyright
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* as to their contents.
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*/
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"use strict";
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var DEBUG = true;
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/**
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* @class Int36
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* @property {number} value
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* @property {number|null} extended
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* @property {number|null} remainder
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* @property {number} error
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*
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* The 'value' property stores the 36-bit value as an unsigned integer. When the value
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* should be interpreted as a signed quantity, subtract BIT36 whenever value > MAXSIGNED.
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*
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* The 'extended' property stores an additional 36 bits of data from a multiplication;
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* it must also be set prior to a division. Internally, it will be set to null whenever the
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* current value is not extended.
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*
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* The 'remainder' property stores the remainder from the last division. You should assume it
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* will be set to null by any other operation.
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*
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* The 'error' property records any error(s) from the last operation.
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*/
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class Int36 {
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/**
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* Int36(obj, extended)
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*
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* The constructor, which simply calls set(), creates an Int36 from either:
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*
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* 1) another Int36
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* 2) a single 36-bit value, with an optional 36-bit extension
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* 3) nothing (initial value will be zero)
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*
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* All internal Int36 values (ie, the value and any extension) are unsigned values in the range:
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*
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* 0 <= i <= Math.pow(2, 36) - 1
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*
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* The lower bound is ZERO and the upper bound is Int36.MAXVAL. Whenever an Int36 value should be
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* interpreted as a signed value, values above Int36.MAXSIGNED (ie, values with bit 35 set) should be
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* converted to their signed counterpart by subtracting the value from Int36.BIT36 (aka MAXVAL + 1);
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* the easiest way to do that is call isNegative() to check the sign bit and then call negate() as
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* appropriate.
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*
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* NOTE: We use modern bit numbering, where bit 0 is the right-most (least-significant) bit and
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* bit 35 is the left-most bit. This is opposite of the PDP-10 convention, which defined bit 0 as the
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* left-most bit and bit 35 as the right-most bit.
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*
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* Although the integer precision of JavaScript floating-point (IEEE 754 double-precision) numbers is:
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*
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* -Math.pow(2, 53) <= i <= Math.pow(2, 53)
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*
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* it seems unwise to ever permit the internal value to creep outside the 36-bit range, because
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* floating-point operations will drop least-significant bits in favor of most-significant bits when a
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* result becomes too large, which is the opposite of what integer operations traditionally do. There
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* might be some optimization benefits to performing our internal 36-bit truncation "lazily", but at
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* least initially, I prefer to truncate the results of all operations immediately.
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*
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* Most of the Int36 operations come in two flavors: those that accept numbers, and those that accept
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* another Int36. The latter are more efficient, because (as just explained) an Int36's internal value
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* should always be in range, whereas external numbers could be out of range OR have a fractional value
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* OR be something else entirely (NaN, Infinity, -Infinity, undefined, etc), so numeric inputs are
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* always passed through the static validate() function.
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*
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* We could eliminate the two flavors and check each parameter's type, like we do in the constructor,
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* but constructor calls are infrequent (if they're not, you're doing something wrong), whereas Int36-only
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* operations should be as fast and unchecked as possible.
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*
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* @this {Int36}
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* @param {Int36|number} [obj] (if omitted, the default is zero)
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* @param {number|null} [extended]
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*/
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constructor(obj, extended)
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{
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this.set(obj, extended);
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this.bitsDiv = [0, 0];
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this.bitsRem = [0, 0];
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}
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/**
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* set(obj, extended)
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*
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* @this {Int36}
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* @param {Int36|number} [obj] (if omitted, the default is zero)
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* @param {number|null} [extended]
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*/
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set(obj = 0, extended)
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{
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if (obj instanceof Int36) {
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this.value = obj.value;
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this.extended = obj.extended;
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this.remainder = obj.remainder;
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}
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else {
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this.value = Int36.validate(obj || 0);
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this.extended = null;
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/*
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* NOTE: Surprisingly, isNaN(null) is false, whereas isNaN(undefined) is true. Go figure.
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*/
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if (extended != null && !isNaN(extended)) {
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this.extended = Int36.validate(extended);
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}
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this.remainder = null;
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}
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this.error = Int36.ERROR.NONE;
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}
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/**
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* toDecimal(fUnsigned)
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*
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* @this {Int36}
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* @param {boolean} fUnsigned
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* @return {string}
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*/
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toDecimal(fUnsigned)
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{
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var s = "", fNeg = false;
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var i36Div = new Int36(10000000000);
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var i36Tmp = new Int36(this.value, this.extended);
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if (!fUnsigned && i36Tmp.isNegative()) {
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i36Tmp.negate();
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fNeg = true;
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}
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do {
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var quotient = i36Tmp.div(i36Div);
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var nMinDigits = (quotient? 10 : 1);
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i36Tmp.value = i36Tmp.remainder;
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do {
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i36Tmp.divNum(10);
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s = String.fromCharCode(0x30 + i36Tmp.remainder) + s;
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} while (--nMinDigits > 0 || i36Tmp.value);
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i36Tmp.value = quotient;
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} while (i36Tmp.value);
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if (fNeg) s = '-' + s;
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return s;
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}
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/**
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* toString(radix, fUnsigned)
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*
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* @this {Int36}
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* @param {number} [radix] (default is 10)
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* @param {boolean} [fUnsigned] (default is signed for radix 10, unsigned for any other radix)
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* @return {string}
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*/
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toString(radix = 10, fUnsigned)
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{
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if (radix == 10) {
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return this.toDecimal(fUnsigned);
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}
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var value = this.value;
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var extended = this.extended;
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if (radix == 8) {
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var s = Int36.octal(value);
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if (extended) {
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s = Int36.octal(extended) + ',' + s;
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}
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if (this.remainder) {
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s += ':' + Int36.octal(this.remainder);
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}
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if (DEBUG && this.error) s += " error 0x" + this.error.toString(16);
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return s;
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}
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if (extended != null) {
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/*
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* TODO: Need a radix-independent solution for these extended (up to 72-bit) values,
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* because after 52 bits, JavaScript will start dropping least-significant bits. Until
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* then, you're better off sticking with octal (see above).
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*/
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value = extended * Int36.BIT36 + value;
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}
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return value.toString(radix);
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}
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/**
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* truncate(result)
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*
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* NOTE: This function's job is to truncate the result of an operation to 36-bit accuracy,
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* not to remove any fractional portion that might also exist. If an operation could have produced
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* a non-integer result (eg, div()), it's the caller's responsibility to deal with that first.
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*
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* @this {Int36}
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* @param {number} result
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* @return {number}
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*/
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truncate(result)
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{
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if (DEBUG && result !== Math.trunc(result)) {
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console.log("Int36.truncate(" + result + " is not an integer)");
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}
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this.extended = null;
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this.remainder = null;
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this.error = Int36.ERROR.NONE;
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if (result < 0) {
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result += Int36.BIT36;
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}
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result %= Int36.BIT36;
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return result;
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}
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/**
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* add(i36)
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*
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* @this {Int36}
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* @param {Int36} i36
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*/
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add(i36)
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{
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this.value = this.truncate(this.value + i36.value);
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}
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/**
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* addNum(num)
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*
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* @this {Int36}
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* @param {number} num
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*/
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addNum(num)
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{
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this.value = this.truncate(this.value + Int36.validate(num));
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}
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/**
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* sub(i36)
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*
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* @this {Int36}
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* @param {Int36} i36
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*/
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sub(i36)
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{
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this.value = this.truncate(this.value - i36.value);
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}
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/**
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* subNum(num)
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*
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* @this {Int36}
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* @param {number} num
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*/
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subNum(num)
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{
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this.value = this.truncate(this.value - Int36.validate(num));
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}
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/**
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* mul(i36)
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*
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* @this {Int36}
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* @param {Int36} i36
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*/
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mul(i36)
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{
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this.mulExtended(i36.value);
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}
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/**
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* mulNum(num)
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*
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* @this {Int36}
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* @param {number} num
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*/
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mulNum(num)
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{
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this.mulExtended(Int36.validate(num));
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}
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/**
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* mulExtended(value)
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*
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* To support 72-bit results, we perform the multiplication process as you would "by hand",
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* treating each of the operands to be multiplied as two 2-digit numbers, where each digit is
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* an 18-bit number (base 2^18). Each individual multiplication of these 18-bit "digits"
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* will produce a result within 2^36, well within JavaScript integer accuracy.
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*
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* @this {Int36}
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* @param {number} value
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*/
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mulExtended(value)
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{
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var fNeg = false, extended;
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var n1 = this.value, n2 = value;
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if (n1 > Int36.MAXSIGNED) {
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n1 = Int36.BIT36 - n1;
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fNeg = !fNeg;
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}
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if (n2 > Int36.MAXSIGNED) {
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n2 = Int36.BIT36 - n2;
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fNeg = !fNeg;
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}
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if (n1 < Int36.BIT18 && n2 < Int36.BIT18) {
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value = n1 * n2;
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extended = 0;
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}
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else {
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var n1d1 = (n1 % Int36.BIT18);
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var n1d2 = Math.trunc(n1 / Int36.BIT18);
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var n2d1 = (n2 % Int36.BIT18);
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var n2d2 = Math.trunc(n2 / Int36.BIT18);
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var m1d1 = n1d1 * n2d1;
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var m1d2 = (n1d2 * n2d1) + Math.trunc(m1d1 / Int36.BIT18);
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extended = Math.trunc(m1d2 / Int36.BIT18);
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m1d2 = (m1d2 % Int36.BIT18) + (n1d1 * n2d2);
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value = (m1d2 * Int36.BIT18) + (m1d1 % Int36.BIT18);
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extended += Math.trunc(m1d2 / Int36.BIT18) + (n1d2 * n2d2);
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}
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this.value = this.truncate(value);
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this.extended = this.truncate(extended);
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if (fNeg) {
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this.negate();
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}
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}
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/**
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* div(i36)
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*
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* @this {Int36}
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* @param {Int36} i36
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* @return {number} (quotient)
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*/
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div(i36)
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{
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return this.divExtended(i36.value);
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}
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/**
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* divNum(num)
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*
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* @this {Int36}
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* @param {number} num
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* @return {number} (quotient)
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*/
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divNum(num)
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{
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return this.divExtended(Int36.validate(num));
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}
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/**
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* divExtended(divisor)
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*
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* @this {Int36}
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* @param {number} divisor
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* @return {number} (quotient)
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*/
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divExtended(divisor)
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{
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/*
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* dividend divisor quotient remainder
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* -------- ------- -------- ---------
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* + + -> + +
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* + - -> - +
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* - + -> - -
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* - - -> + -
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*/
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var bNegLo = 0, bNegHi = 0;
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if (divisor > Int36.MAXSIGNED) {
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divisor = Int36.BIT36 - divisor;
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bNegLo = 1 - bNegLo;
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}
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if (this.isNegative()) {
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this.negate();
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bNegHi = 1; bNegLo = 1 - bNegLo;
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}
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var value = this.value;
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var extended = this.extended || 0;
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if (!divisor) {
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this.error |= Int36.ERROR.DIVZERO;
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}
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else if (divisor <= extended) {
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this.error |= Int36.ERROR.OVERFLOW;
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}
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else {
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var result = 0, bit = 1;
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var bitsDiv = Int36.setBits(this.bitsDiv, divisor, 0);
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var bitsRem = Int36.setBits(this.bitsRem, value, extended);
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while (Int36.cmpBits(bitsRem, bitsDiv) > 0) {
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Int36.addBits(bitsDiv, bitsDiv);
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bit += bit;
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}
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do {
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if (Int36.cmpBits(bitsRem, bitsDiv) >= 0) {
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Int36.subBits(bitsRem, bitsDiv);
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result += bit;
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}
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Int36.shrBits(bitsDiv);
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bit /= 2;
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} while (bit >= 1);
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if (DEBUG && !(result < Int36.BIT36 && !bitsRem[1])) {
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console.log("divExtended() assertion failure");
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}
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this.value = result;
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this.extended = null;
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this.remainder = bitsRem[0];
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if (bNegLo && this.value && this.value > Int36.MINSIGNED) {
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this.value = Int36.BIT36 - this.value;
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}
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if (bNegHi && this.remainder && this.remainder > Int36.MINSIGNED) {
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this.remainder = Int36.BIT36 - this.remainder;
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}
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}
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return this.value;
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}
|
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|
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/**
|
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* isNegative()
|
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*
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* @return {boolean}
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*/
|
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isNegative()
|
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{
|
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return (this.extended > Int36.MAXSIGNED || this.extended == null && this.value > Int36.MAXSIGNED);
|
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}
|
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|
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/**
|
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* negate()
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*/
|
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negate()
|
|
{
|
|
if (this.extended == null) {
|
|
/*
|
|
* Set extended to match the sign of the (negated) value.
|
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*/
|
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this.extended = (this.value > Int36.MAXSIGNED? 0 : Int36.MAXVAL);
|
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}
|
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else if (this.value) {
|
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/*
|
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* Perform one's complement on the extended value.
|
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*/
|
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this.extended = Int36.MAXVAL - this.extended;
|
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}
|
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else {
|
|
/*
|
|
* Perform two's complement on the extended value.
|
|
*/
|
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if (this.extended) this.extended = Int36.BIT36 - this.extended;
|
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}
|
|
/*
|
|
* Perform two's complement on the value.
|
|
*/
|
|
if (this.value) this.value = Int36.BIT36 - this.value;
|
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this.error = Int36.ERROR.NONE;
|
|
}
|
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|
|
/**
|
|
* addBits(bitsDst, bitsSrc)
|
|
*
|
|
* Adds bitsSrc to bitsDst.
|
|
*
|
|
* @param {Array.<number>} bitsDst
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|
* @param {Array.<number>} bitsSrc
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*/
|
|
static addBits(bitsDst, bitsSrc)
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|
{
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bitsDst[0] += bitsSrc[0];
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bitsDst[1] += bitsSrc[1];
|
|
if (bitsDst[0] >= Int36.BIT36) {
|
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bitsDst[0] %= Int36.BIT36;
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bitsDst[1]++;
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}
|
|
}
|
|
|
|
/**
|
|
* cmpBits(bitsDst, bitsSrc)
|
|
*
|
|
* Compares bitsDst to bitsSrc, by computing bitsDst - bitsSrc.
|
|
*
|
|
* @param {Array.<number>} bitsDst
|
|
* @param {Array.<number>} bitsSrc
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|
* @return {number} > 0 if bitsDst > bitsSrc, == 0 if bitsDst == bitsSrc, < 0 if bitsDst < bitsSrc
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*/
|
|
static cmpBits(bitsDst, bitsSrc)
|
|
{
|
|
var result = bitsDst[1] - bitsSrc[1];
|
|
if (!result) result = bitsDst[0] - bitsSrc[0];
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* setBits(bits, lo, hi)
|
|
*
|
|
* @param {Array.<number>} bits
|
|
* @param {number} lo
|
|
* @param {number} hi
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|
* @return {Array.<number>}
|
|
*/
|
|
static setBits(bits, lo, hi)
|
|
{
|
|
bits[0] = lo;
|
|
bits[1] = hi;
|
|
return bits;
|
|
}
|
|
|
|
/**
|
|
* shrBits(bitsDst)
|
|
*
|
|
* Shifts bitsDst right one bit.
|
|
*
|
|
* @param {Array.<number>} bitsDst
|
|
*/
|
|
static shrBits(bitsDst)
|
|
{
|
|
if (bitsDst[1] % 2) {
|
|
bitsDst[0] += Int36.BIT36;
|
|
}
|
|
bitsDst[0] = Math.trunc(bitsDst[0] / 2);
|
|
bitsDst[1] = Math.trunc(bitsDst[1] / 2);
|
|
}
|
|
|
|
/**
|
|
* subBits(bitsDst, bitsSrc)
|
|
*
|
|
* Subtracts bitsSrc from bitsDst.
|
|
*
|
|
* @param {Array.<number>} bitsDst
|
|
* @param {Array.<number>} bitsSrc
|
|
*/
|
|
static subBits(bitsDst, bitsSrc)
|
|
{
|
|
bitsDst[0] -= bitsSrc[0];
|
|
bitsDst[1] -= bitsSrc[1];
|
|
if (bitsDst[0] < 0) {
|
|
bitsDst[0] += Int36.BIT36;
|
|
bitsDst[1]--;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* octal(value)
|
|
*
|
|
* @param {number} value
|
|
* @return {string}
|
|
*/
|
|
static octal(value)
|
|
{
|
|
if (value < 0) value += Int36.BIT36;
|
|
return ("00000000000" + value.toString(8)).slice(-12);
|
|
}
|
|
|
|
/**
|
|
* validate(num)
|
|
*
|
|
* @param {number} num
|
|
* @return {number}
|
|
*/
|
|
static validate(num)
|
|
{
|
|
if (num < 0 && num >= Int36.MINSIGNED) {
|
|
num += Int36.BIT36;
|
|
}
|
|
var value = Math.trunc(Math.abs(num)) % Int36.BIT36;
|
|
if (DEBUG && num !== value) {
|
|
console.log("Int36.validate(" + num + " out of range, truncated to " + value + ")");
|
|
}
|
|
return value;
|
|
}
|
|
}
|
|
|
|
Int36.ERROR = {
|
|
NONE: 0x0,
|
|
OVERFLOW: 0x1,
|
|
UNDERFLOW: 0x2,
|
|
DIVZERO: 0x4
|
|
};
|
|
|
|
Int36.BIT18 = Math.pow(2, 18); // 262,144
|
|
Int36.BIT36 = Math.pow(2, 36); // 68,719,476,736
|
|
|
|
Int36.MAXSIGNED = Math.pow(2, 35) - 1; // 34,359,738,367
|
|
Int36.MINSIGNED = -Math.pow(2, 35); // -34,359,738,368
|
|
|
|
Int36.MAXVAL = Math.pow(2, 36) - 1; // 68,719,476,735
|
|
|
|
if (NODE) module.exports = Int36;
|