877 lines
33 KiB
JavaScript
877 lines
33 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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From the "PDP-10 System Reference Manual", May 1968, p. 1-4:
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1.1 NUMBER SYSTEM
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The program can interpret a data word as a 36-digit, unsigned binary number, or the left and right
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halves of a word can be taken as separate 18-bit numbers. The PDP-10 repertoire includes instructions
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that effectively add or subtract one from both halves of a word, so the right half can be used for
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address modification when the word is addressed as an index register, while the left half is used to
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keep a control count.
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The standard arithmetic instructions in the PDP-10 use twos complement, fixed point conventions to do
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binary arithmetic. In a word used as a number, bit 0 (the leftmost bit) represents the sign, 0 for positive,
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1 for negative. In a positive number the remaining 35 bits are the magnitude in ordinary binary notation.
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The negative of a number is obtained by taking its twos complement. If x is an n-digit binary number, its
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twos complement is 2^n - x, and its ones complement is (2^n - 1) - x, or equivalently (2^n - x) - 1.
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Subtracting a number from 2^n - 1 (ie, from all 1s) is equivalent to performing the logical complement,
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ie changing all 0s to 1s and all 1s to 0s. Therefore, to form the twos complement one takes the logical
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complement (usually referred to merely as the complement) of the entire word including the sign, and adds
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1 to the result. In a negative number the sign bit is 1, and the remaining bits are the twos complement
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of the magnitude.
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Zero is represented by a word containing all 0s. Complementing this number produces all 1s, and adding
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1 to that produces all 0s again. Hence there is only one zero representation and its sign is positive.
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Since the numbers are symmetrical in magnitude about a single zero representation, all even numbers both
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positive and negative end in 0, all odd numbers in 1 (a number all 1s represents -1). But since there are
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the same number of positive and negative numbers and zero is positive, there is one more negative number
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than there are nonzero positive numbers. This is the most negative number and it cannot be produced by
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negating any positive number (its octal representation is 400000 000000 and its magnitude is one greater
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than the largest positive number).
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If ones complements were used for negatives one could read a negative number by attaching significance
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to the as instead of the 1s. In twos complement notation each negative number is one greater than the
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complement of the positive number of the same magnitude, so one can read a negative number by attaching
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significance to the rightmost 1 and attaching significance to the 0s at the left of it (the negative number
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of largest magnitude has a 1 in only the sign position). In a negative integer, 1s may be discarded at the
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left, just as leading 0s may be dropped in a positive integer. In a negative fraction, 0s may be discarded
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at the right. So long as only 0s are discarded, the number remains in twos complement form because it
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still has a 1 that possesses significance; but if a portion including the rightmost 1 is discarded, the
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remaining part of the fraction is now a ones complement.
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The computer does not keep track of a binary point - the programmer must adopt a point convention and shift
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the magnitude of the result to conform to the convention used. Two common conventions are to regard a number
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as an integer (binary point at the right) or as a proper fraction (binary point at the left); in these two
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cases the range of numbers represented by a single word is -2^35 to 2^35 - 1, or -1 to 1 - 2^35. Since
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multiplication and division make use of double length numbers, there are special instructions for performing
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these operations with integral operands.
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SIDEBAR: Multiplication produces a double length product, and the programmer must remember that discarding
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the low order part of a double length negative leaves the high order part in correct twos complement form
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only if the low order part is null.
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...
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2.5 FIXED POINT ARITHMETIC
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For fixed point arithmetic the PDP-10 has instructions for arithmetic shifting (which is essentially
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multiplication by a power of 2) as well as for performing addition, subtraction, multiplication and division
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of numbers in fixed point format [§ 1.1]. In such numbers the position of the binary point is arbitrary
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(the programmer may adopt any point convention). The add and subtract instructions involve only single length
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numbers, whereas multiply supplies a double length product, and divide uses a double length dividend. The high
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and low order words respectively of a double length fixed point number are in accumulators A and A+1 (mod 20),
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where the magnitude is the 70-bit string in bits 1-35 of the two words and the signs of the two are identical.
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There are also integer multiply and divide instructions that involve only single length numbers and are
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especially suited for handling smaller integers, particularly those of eighteen bits or less such as addresses
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(of course they can be used for small fractions as well provided the programmer keeps track of the binary point).
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For convenience in the following, all operands are assumed to be integers (binary point at the right).
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The processor has four flags, Overflow, Carry 0, Carry 1 and No Divide, that indicate when the magnitude of a
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number is or would be larger than can be accommodated. Carry 0 and Carry 1 actually detect carries out of bits
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0 and 1 in certain instructions that employ fixed point arithmetic operations: the add and subtract instructions
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treated here, the move instructions that produce the negative or magnitude of the word moved [§ 2.2], and the
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arithmetic test instructions that increment or decrement the test word [§ 2.7]. In these instructions an
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incorrect result is indicated - and the Overflow flag set - if the carries are different, ie if there is a carry
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into the sign but not out of it, or vice versa. The Overflow flag is also set by No Divide being set, which
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means the processor has failed to perform a division because the magnitude of the dividend is greater than or
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equal to that of the divisor, or in integer divide, simply that the divisor is zero. In other overflow cases
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only Overflow itself is set: these include too large a product in multiplication, and loss of significant bits
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in left arithmetic shifting.
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SIDEBAR: Overflow is determined directly from the carries, not from the carry flags, as their states may reflect
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events in previous instructions.
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*/
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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 should be
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* interpreted as a signed quantity, subtract BIT36 whenever value > MAXPOS.
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*
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* The 'extended' property stores an additional 36 bits of data from a multiplication, and can also
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* provide an additional 36 bits of data to a division. Internally, it should be null whenever the
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* 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 will
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* 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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* NOTE: What we call extended Int36 values DEC refers to as "double length numbers", and they refer
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* to the 'extended' portion as the "low order part" and the 'value' portion as the "high order part",
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* presumably because they number the left-most significant bit 0.
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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.MAXPOS (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 our internal values 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 36-bit arithmetic 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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}
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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 i36Rem = new Int36();
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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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/*
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* Conversion of any 72-bit value should take no more than 3 divisions by 10,000,000,000.
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*/
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var nMaxDivs = 3;
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do {
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i36Tmp.div(i36Div);
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/*
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* In a perfect world, there would be no errors, because all calculations at this point
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* are within known bounds. But let's make sure we don't produce garbage or spin our wheels.
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*/
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if (i36Tmp.error || i36Tmp.remainder >= 10000000000 || !nMaxDivs--) {
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s = "error";
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break;
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}
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var quotient = i36Tmp.value || i36Tmp.extended;
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var nMinDigits = (quotient? 10 : 1);
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i36Rem.set(i36Tmp.remainder);
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do {
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i36Rem.divNum(10);
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if (i36Rem.remainder < 0 || i36Rem.remainder > 9) {
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quotient = 0;
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s = "error";
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break;
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}
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s = String.fromCharCode(0x30 + i36Rem.remainder) + s;
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} while (--nMinDigits > 0 || i36Rem.value);
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} while (quotient);
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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) {
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if (this.error & Int36.ERROR.OVERFLOW) {
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s += " overflow";
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}
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if (this.error & Int36.ERROR.UNDERFLOW) {
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s += " underflow";
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}
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if (this.error & Int36.ERROR.DIVZERO) {
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s += " divide-by-zero";
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}
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}
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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, operand, fSub)
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*
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* The range of valid results (0 - MAXVAL) is divided into two equal sub-ranges: 0 to MAXPOS,
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* where the sign bit is zero (the bottom range), and MAXPOS+1 to MAXVAL (the top range), where
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* the sign bit is one. During a single arithmetic operation, the result can "wrap around" from
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* the bottom range to the top, or from the top range to the bottom, but it's an overflow/underflow
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* error ONLY if the result "wraps across" the midpoint between the two ranges, producing an
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* unnaturally small delta (<= MAXPOS).
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*
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* This can be confirmed independently by examining the sign bits (BIT35) of the original value
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* (V), the operand (O), the result (R), as well as two intermediate calculations, VR = (V ^ R)
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* and OR = (O ^ R), and a final calculation, E = (VR & OR). If E is set, then overflow (V == 0)
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* or underflow (V == 1) occurred.
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*
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* In the case of subtraction (when fSub is true), consult the second table, which replaces OR
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* with OV (O ^ V).
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*
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* V O R VR OR E
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* - - - -- -- -
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* 0 0 0 0 0 0
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* 0 0 1 1 1 1 (adding positive to positive yielded negative: overflow)
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* 0 1 0 0 1 0
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* 0 1 1 1 0 0
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* 1 0 0 1 0 0
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* 1 0 1 0 1 0
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* 1 1 0 1 1 1 (adding negative to negative yielded positive: underflow)
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* 1 1 1 0 0 0
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*
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* V O R VR OV E
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* - - - -- -- -
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* 0 0 0 0 0 0
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* 0 0 1 1 0 0
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* 0 1 0 0 1 0
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* 0 1 1 1 1 1 (subtracting negative from positive yielded negative: overflow)
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* 1 0 0 1 1 1 (subtracting positive from negative yielded positive: underflow)
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* 1 0 1 0 1 0
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* 1 1 0 1 0 0
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* 1 1 1 0 0 0
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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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* @param {number} [operand]
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* @param {boolean} [fSub] (true if operand was subtracted)
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* @return {number}
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*/
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truncate(result, operand, fSub)
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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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/*
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* We don't actually need to know what the operand was to determine overflow or underflow
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* for addition or subtraction, just the original value (this.value) the new value (result).
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*
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* We do, however, need to know the operand if we want to confirm our error calculation using
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* the truth table above, which requires examining the sign bits of all the inputs and outputs.
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*/
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if (operand !== undefined) {
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/*
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* Calculating V, R, O, and E as described above is somewhat tedious, because bits
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* above bit 31 cannot be accessed directly; we shift all the sign bits down to bit 0
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* using division first. We don't need to truncate the results, because the subsequent
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* bit-wise operations perform truncation automatically.
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*/
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var e = 0;
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if (DEBUG) {
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var v = this.value / Int36.BIT35, r = result / Int36.BIT35, o = operand / Int36.BIT35;
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e = ((v ^ r) & (o ^ (fSub? v : r))) & 1;
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}
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if ((result > Int36.MAXPOS) != (this.value > Int36.MAXPOS)) {
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var delta = result - this.value;
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if (Math.abs(delta) <= Int36.MAXPOS) {
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this.error |= (delta > 0 ? Int36.ERROR.OVERFLOW : Int36.ERROR.UNDERFLOW);
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if (DEBUG && (delta > 0) != !(e & v)) e = 0;
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}
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}
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if (DEBUG && (!this.error) != (!e)) console.log("overflow inconsistency");
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}
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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, 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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num = Int36.validate(num);
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this.value = this.truncate(this.value + num, num);
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}
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/**
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* sub(i36)
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|
*
|
|
* @this {Int36}
|
|
* @param {Int36} i36
|
|
*/
|
|
sub(i36)
|
|
{
|
|
this.value = this.truncate(this.value - i36.value, i36.value, true);
|
|
}
|
|
|
|
/**
|
|
* subNum(num)
|
|
*
|
|
* @this {Int36}
|
|
* @param {number} num
|
|
*/
|
|
subNum(num)
|
|
{
|
|
num = Int36.validate(num);
|
|
this.value = this.truncate(this.value - num, num, true);
|
|
}
|
|
|
|
/**
|
|
* mul(i36)
|
|
*
|
|
* @this {Int36}
|
|
* @param {Int36} i36
|
|
*/
|
|
mul(i36)
|
|
{
|
|
this.mulExtended(i36.value);
|
|
}
|
|
|
|
/**
|
|
* mulNum(num)
|
|
*
|
|
* @this {Int36}
|
|
* @param {number} num
|
|
*/
|
|
mulNum(num)
|
|
{
|
|
this.mulExtended(Int36.validate(num));
|
|
}
|
|
|
|
/**
|
|
* mulExtended(value)
|
|
*
|
|
* To support 72-bit results, we perform the multiplication process as you would "by hand",
|
|
* treating the operands to be multiplied as two 2-digit numbers, where each "digit" is an 18-bit
|
|
* number (base 2^18). Each individual multiplication of these 18-bit "digits" will produce
|
|
* a result within 2^36, well within JavaScript integer accuracy.
|
|
*
|
|
* @this {Int36}
|
|
* @param {number} value
|
|
*/
|
|
mulExtended(value)
|
|
{
|
|
var fNeg = false, extended;
|
|
var n1 = this.value, n2 = value;
|
|
|
|
if (n1 > Int36.MAXPOS) {
|
|
n1 = Int36.BIT36 - n1;
|
|
fNeg = !fNeg;
|
|
}
|
|
|
|
if (n2 > Int36.MAXPOS) {
|
|
n2 = Int36.BIT36 - n2;
|
|
fNeg = !fNeg;
|
|
}
|
|
|
|
if (n1 < Int36.BIT18 && n2 < Int36.BIT18) {
|
|
value = n1 * n2;
|
|
extended = 0;
|
|
}
|
|
else {
|
|
var n1d1 = (n1 % Int36.BIT18);
|
|
var n1d2 = Math.trunc(n1 / Int36.BIT18);
|
|
var n2d1 = (n2 % Int36.BIT18);
|
|
var n2d2 = Math.trunc(n2 / Int36.BIT18);
|
|
|
|
var m1d1 = n1d1 * n2d1;
|
|
var m1d2 = (n1d2 * n2d1) + Math.trunc(m1d1 / Int36.BIT18);
|
|
extended = Math.trunc(m1d2 / Int36.BIT18);
|
|
m1d2 = (m1d2 % Int36.BIT18) + (n1d1 * n2d2);
|
|
value = (m1d2 * Int36.BIT18) + (m1d1 % Int36.BIT18);
|
|
extended += Math.trunc(m1d2 / Int36.BIT18) + (n1d2 * n2d2);
|
|
}
|
|
|
|
this.value = this.truncate(value);
|
|
this.extended = this.truncate(extended);
|
|
|
|
if (fNeg) this.negate();
|
|
}
|
|
|
|
/**
|
|
* div(i36)
|
|
*
|
|
* @this {Int36}
|
|
* @param {Int36} i36
|
|
*/
|
|
div(i36)
|
|
{
|
|
this.divExtended(i36.value);
|
|
}
|
|
|
|
/**
|
|
* divNum(num)
|
|
*
|
|
* @this {Int36}
|
|
* @param {number} num
|
|
*/
|
|
divNum(num)
|
|
{
|
|
this.divExtended(Int36.validate(num));
|
|
}
|
|
|
|
/**
|
|
* divExtended(divisor)
|
|
*
|
|
* We disallow a divisor of zero; however, we no longer disallow a divisor smaller than the
|
|
* extended portion of the dividend, even though such a divisor would produce a quotient larger
|
|
* than 36 bits. Instead, we support extended quotients, because some of our internal functions
|
|
* (eg, toDecimal()) require it.
|
|
*
|
|
* For callers that can only handle 36-bit quotients, they can either perform their own preliminary
|
|
* check of the divisor against any extended dividend, or they can simply allow all divisions to
|
|
* proceed, check for an extended quotient afterward, and report the appropriate error.
|
|
*
|
|
* @this {Int36}
|
|
* @param {number} divisor
|
|
*/
|
|
divExtended(divisor)
|
|
{
|
|
if (!divisor) {
|
|
this.error |= Int36.ERROR.DIVZERO;
|
|
return;
|
|
}
|
|
|
|
var fNegQ = false, fNegR = false;
|
|
|
|
if (divisor > Int36.MAXPOS) {
|
|
divisor = Int36.BIT36 - divisor;
|
|
fNegQ = !fNegQ;
|
|
}
|
|
|
|
if (this.isNegative()) {
|
|
this.negate();
|
|
fNegR = true; fNegQ = !fNegQ;
|
|
}
|
|
|
|
this.extend();
|
|
|
|
/*
|
|
* Initialize the four double-length 72-bit "bits" values we need for the division process.
|
|
*
|
|
* The process involves shifting the divisor left 1 bit (ie, doubling it) until it equals
|
|
* or exceeds the dividend, and then repeatedly subtracting the divisor from the dividend and
|
|
* shifting the divisor right 1 bit until the divisor is "exhausted" (no bits left), with an
|
|
* "early out" if the dividend gets "exhausted" first.
|
|
*
|
|
* Note that each element of these "bits" arrays is a 36-bit value, so it's rarely a good idea
|
|
* to use bit-wise operators on them, because those would operate on only the low 32 bits.
|
|
* Stick with the "bits" worker functions I've created, and trust your JavaScript engine to
|
|
* inline/optimize the code.
|
|
*
|
|
* TODO: Profile this code to determine if individual variables (eg, bitsResLo and bitsResHi)
|
|
* instead of 2-element arrays is faster and/or less impactful on garbage collection. I prefer
|
|
* both the simplified syntax of arrays as well as their extensibility if we ever want/need
|
|
* to go beyond 72 bits.
|
|
*/
|
|
var bitsRes = [0, 0];
|
|
var bitsPow = [1, 0];
|
|
var bitsDiv = [divisor, 0];
|
|
var bitsRem = [this.value, this.extended];
|
|
|
|
while (Int36.cmpBits(bitsRem, bitsDiv) > 0) {
|
|
Int36.addBits(bitsDiv, bitsDiv);
|
|
Int36.addBits(bitsPow, bitsPow);
|
|
}
|
|
do {
|
|
if (Int36.cmpBits(bitsRem, bitsDiv) >= 0) {
|
|
Int36.subBits(bitsRem, bitsDiv);
|
|
Int36.addBits(bitsRes, bitsPow);
|
|
if (Int36.zeroBits(bitsRem)) break;
|
|
}
|
|
Int36.shrBits(bitsDiv);
|
|
Int36.shrBits(bitsPow);
|
|
} while (!Int36.zeroBits(bitsPow));
|
|
|
|
/*
|
|
* Since divisors are limited to 36-bit values, something's wrong if we have an extended remainder.
|
|
*/
|
|
if (DEBUG && bitsRem[1]) {
|
|
console.log("divExtended() assertion failure");
|
|
}
|
|
|
|
this.value = bitsRes[0];
|
|
this.extended = bitsRes[1];
|
|
this.remainder = bitsRem[0];
|
|
|
|
if (fNegQ) this.negate();
|
|
|
|
this.reduce();
|
|
|
|
if (fNegR && this.remainder) {
|
|
this.remainder = Int36.BIT36 - this.remainder;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* extend()
|
|
*
|
|
* Sets extended to match the sign of value (if not already set).
|
|
*/
|
|
extend()
|
|
{
|
|
if (this.extended == null) {
|
|
this.extended = (this.value > Int36.MAXPOS? Int36.MAXVAL : 0);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* reduce()
|
|
*
|
|
* Unsets extended if it's superfluous; opposite of extend().
|
|
*
|
|
* It's worth noting DEC's SIDEBAR comment (from above):
|
|
*
|
|
* Multiplication produces a double length product, and the programmer must remember that discarding
|
|
* the low order part ['extended'] of a double length negative leaves the high order part ['value'] in
|
|
* correct twos complement form only if the low order part ['extended'] is null.
|
|
*
|
|
* is not entirely applicable to us. For one thing, when value is MINNEG and extended is ZERO, we interpret
|
|
* that extended value as 34,359,738,368; we cannot simply eliminate the extended portion, otherwise value
|
|
* would be interpreted as -34,359,738,368.
|
|
*
|
|
* DEC can say that because each of the words in a PDP-10 double-length product contains its own sign bit,
|
|
* resulting in only 70 bits of magnitude. However, we don't store our extended (double-length) results that
|
|
* way, so be aware of these mismatches in both terminology and format when converting an Int36 to/from PDP-10
|
|
* registers/memory.
|
|
*/
|
|
reduce()
|
|
{
|
|
if (this.extended == 0 && this.value <= Int36.MAXPOS || this.extended == Int36.MAXVAL && this.value > Int36.MAXPOS) {
|
|
this.extended = null;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* isNegative()
|
|
*
|
|
* @return {boolean}
|
|
*/
|
|
isNegative()
|
|
{
|
|
return (this.extended > Int36.MAXPOS || this.extended == null && this.value > Int36.MAXPOS);
|
|
}
|
|
|
|
/**
|
|
* negate()
|
|
*
|
|
* negate() MUST automatically extend the value, because the two's complement of the most negative
|
|
* number (MINNEG) still has its sign bit set, so we must rely on the sign of the extended value to
|
|
* compensate.
|
|
*
|
|
* This is handled below by setting extended first, based on the opposite of the value's current sign;
|
|
* we could negate extended AFTER negating value, but then we'd need a special test for the MINNEG value.
|
|
*/
|
|
negate()
|
|
{
|
|
if (this.extended == null) {
|
|
/*
|
|
* Set extended to the OPPOSITE of the current value.
|
|
*/
|
|
this.extended = (this.value > Int36.MAXPOS? 0 : Int36.MAXVAL);
|
|
}
|
|
else if (this.value) {
|
|
/*
|
|
* Perform one's complement on the extended value.
|
|
*/
|
|
this.extended = Int36.MAXVAL - this.extended;
|
|
}
|
|
else {
|
|
/*
|
|
* Perform two's complement on the extended value.
|
|
*/
|
|
if (this.extended) this.extended = Int36.BIT36 - this.extended;
|
|
}
|
|
/*
|
|
* Perform two's complement on the value.
|
|
*/
|
|
if (this.value) {
|
|
this.value = Int36.BIT36 - this.value;
|
|
}
|
|
this.error = Int36.ERROR.NONE;
|
|
}
|
|
|
|
/**
|
|
* addBits(bitsDst, bitsSrc)
|
|
*
|
|
* Adds bitsSrc to bitsDst.
|
|
*
|
|
* @param {Array.<number>} bitsDst
|
|
* @param {Array.<number>} bitsSrc
|
|
*/
|
|
static addBits(bitsDst, bitsSrc)
|
|
{
|
|
bitsDst[0] += bitsSrc[0];
|
|
bitsDst[1] += bitsSrc[1];
|
|
if (bitsDst[0] >= Int36.BIT36) {
|
|
bitsDst[0] %= Int36.BIT36;
|
|
bitsDst[1]++;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* cmpBits(bitsDst, bitsSrc)
|
|
*
|
|
* Compares bitsDst to bitsSrc, by computing bitsDst - bitsSrc.
|
|
*
|
|
* @param {Array.<number>} bitsDst
|
|
* @param {Array.<number>} bitsSrc
|
|
* @return {number} > 0 if bitsDst > bitsSrc, == 0 if bitsDst == bitsSrc, < 0 if bitsDst < bitsSrc
|
|
*/
|
|
static cmpBits(bitsDst, bitsSrc)
|
|
{
|
|
var result = bitsDst[1] - bitsSrc[1];
|
|
if (!result) result = bitsDst[0] - bitsSrc[0];
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* 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]--;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* zeroBits(bits)
|
|
*
|
|
* True if bits are all zero, false otherwise.
|
|
*
|
|
* @param {Array.<number>} bits
|
|
*/
|
|
static zeroBits(bits)
|
|
{
|
|
return !bits[0] && !bits[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)
|
|
*
|
|
* This ensures that any incoming (external) 36-bit values conform to our internal requirements.
|
|
*
|
|
* @param {number} num
|
|
* @return {number}
|
|
*/
|
|
static validate(num)
|
|
{
|
|
/*
|
|
* Although it's expected that most callers will supply unsigned 36-bit values, we're nice about
|
|
* converting any signed values to their unsigned (two's complement) counterpart, provided they are
|
|
* within the acceptable range. Any values outside that range will be dealt with afterward.
|
|
*/
|
|
if (num < 0 && num >= Int36.MINNEG) {
|
|
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.BIT35 = Math.pow(2, 35); // 34,359,738,368 (aka the sign bit)
|
|
Int36.BIT36 = Math.pow(2, 36); // 68,719,476,736
|
|
|
|
Int36.MAXPOS = Math.pow(2, 35) - 1; // 34,359,738,367
|
|
Int36.MINNEG = -Math.pow(2, 35); // -34,359,738,368
|
|
|
|
Int36.MAXVAL = Math.pow(2, 36) - 1; // 68,719,476,735
|
|
|
|
if (NODE) module.exports = Int36;
|