Trying a second approach to the Int36 class that sticks to unsigned numbers internally (only downside so far is that the detecting arithmetic overflow/underflow is more work and hasn't been implemented yet)
This commit is contained in:
Jeff Parsons
Jeff Parsons
parent
259dd7d66f
commit
6bc0d8ac49
3 changed files with 713 additions and 97 deletions
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@ -31,8 +31,8 @@
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"use strict";
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var repl = require("repl");
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var Defines = require("../../shared/lib/defines");
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var Int36 = require("../../shared/lib/int36");
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var Defines = require("../lib/defines");
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var Int36 = require("../lib/int36");
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var i36Reg = new Int36();
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@ -1,5 +1,5 @@
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/**
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* @fileoverview Support for 36-bit integers
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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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@ -37,11 +37,8 @@ var DEBUG = true;
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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 a signed integer, meaning if the sign bit
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* (bit 35) is set, we store the corresponding negative (two's complement) value. While there
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* might be some slight benefits to always storing the 36-bit value as an unsigned quantity
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* and negating it "on demand", I like having JavaScript's native representation match the
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* emulated value.
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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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@ -60,15 +57,16 @@ class Int36 {
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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 (signed) 36-bit value, with an optional 36-bit extension
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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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* We guarantee that an Int36 value will be (and will always remain) a signed value within this range:
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* We guarantee that an Int36 value will be (and always remain) an unsigned value within this range:
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*
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* -Math.pow(2, 35) <= i <= Math.pow(2, 35) - 1
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* 0 <= i <= Math.pow(2, 36) - 1
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*
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* Those lower and upper bounds are defined as Int36.MINVAL and Int36.MAXVAL. The sign of an Int36
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* value is determined by (and should always match) its highest bit (bit 35).
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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, call isNegative() to check the sign bit (bit 35) and call negate()
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* as 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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@ -78,7 +76,7 @@ class Int36 {
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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 signed 36-bit range, because
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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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@ -134,17 +132,18 @@ class Int36 {
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}
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/**
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* toDecimal()
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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()
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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 (i36Tmp.isNegative()) {
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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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@ -172,6 +171,10 @@ class Int36 {
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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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@ -187,23 +190,13 @@ class Int36 {
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return s;
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}
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if (radix != 10) {
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fUnsigned = true;
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} else {
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return this.toDecimal();
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}
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if (fUnsigned || extended) {
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if (value < 0) value += Int36.BIT36;
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if (extended != null) {
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if (fUnsigned) extended += Int36.BIT36;
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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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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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@ -227,15 +220,11 @@ class Int36 {
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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 > Int36.MAXVAL) {
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result %= Int36.BIT36;
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if (result > Int36.MAXVAL) result -= Int36.BIT36;
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this.error |= Int36.ERROR.OVERFLOW;
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} else if (result < Int36.MINVAL) {
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result %= Int36.BIT36;
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if (result < Int36.MINVAL) result += Int36.BIT36;
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this.error |= Int36.ERROR.UNDERFLOW;
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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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@ -321,13 +310,13 @@ class Int36 {
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var fNeg = false, extended;
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var n1 = this.value, n2 = value;
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if (n1 < 0) {
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if (n1) n1 = -n1;
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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 < 0) {
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if (n2) n2 = -n2;
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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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@ -352,7 +341,9 @@ class Int36 {
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this.value = this.truncate(value);
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this.extended = this.truncate(extended);
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if (fNeg) this.negate();
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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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@ -398,8 +389,8 @@ class Int36 {
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*/
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var bNegLo = 0, bNegHi = 0;
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if (divisor < 0 && divisor > Int36.MINVAL) {
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divisor = -divisor;
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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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@ -411,10 +402,6 @@ class Int36 {
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var value = this.value;
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var extended = this.extended || 0;
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if (value < 0) {
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value += Int36.BIT36;
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}
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if (!divisor) {
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this.error |= Int36.ERROR.DIVZERO;
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}
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@ -448,11 +435,11 @@ class Int36 {
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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.MINVAL) {
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this.value = -this.value;
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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.MINVAL) {
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this.remainder = -this.remainder;
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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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@ -465,60 +452,37 @@ class Int36 {
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*/
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isNegative()
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{
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return (this.extended < 0 || this.extended == null && this.value < 0);
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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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* negate()
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*
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* Converts the current value to its two's complement. If we were dealing with 8-bit values:
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*
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* Original Two's One's
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* ------- ----- -----
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* -128 -128 127
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* -127 127 126
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* ... ... ...
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* -1 1 0
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* 0 0 -1
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* 1 -1 -2
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* ... ... ...
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* 126 -126 -127
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* 127 -127 -128
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*
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* you can see that, when performing two's complement, MINVAL and ZERO are not modified.
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*
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* However, in our happy little world, since JavaScript numbers CAN represent both positive and negative
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* MINVAL values, we don't need to exclude MINVAL from the conversion.
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*/
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negate()
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{
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this.error = Int36.ERROR.NONE;
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/*
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* Perform two's complement on the value.
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*/
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if (this.value /* && this.value > Int36.MINVAL */) {
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this.value = -this.value;
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}
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if (this.extended == null) {
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/*
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* Set extended to match the sign of the value.
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* Set extended to match the sign of the (negated) value.
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*/
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this.extended = (this.value < 0? -1 : 0);
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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 = -this.extended - 1;
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this.extended = Int36.MAXVAL - this.extended;
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}
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else {
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/*
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* Perform two's complement on the extended value.
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*/
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if (this.extended /* && this.extended > Int36.MINVAL */) {
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this.extended = -this.extended;
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}
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if (this.extended) this.extended = Int36.BIT36 - this.extended;
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}
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/*
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* Perform two's complement on the value.
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*/
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if (this.value) this.value = Int36.BIT36 - this.value;
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this.error = Int36.ERROR.NONE;
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}
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/**
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@ -624,12 +588,10 @@ class Int36 {
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*/
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static validate(num)
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{
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var value = Math.trunc(num) % Int36.BIT36;
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if (value > Int36.MAXVAL) {
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value -= Int36.BIT36;
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} else if (value < Int36.MINVAL) {
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value += Int36.BIT36;
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if (num < 0 && num >= Int36.MINSIGNED) {
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num += Int36.BIT36;
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}
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var value = Math.trunc(Math.abs(num)) % Int36.BIT36;
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if (DEBUG && num !== value) {
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console.log("Int36.validate(" + num + " out of range, truncated to " + value + ")");
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}
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@ -647,7 +609,9 @@ Int36.ERROR = {
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Int36.BIT18 = Math.pow(2, 18); // 262,144
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Int36.BIT36 = Math.pow(2, 36); // 68,719,476,736
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Int36.MAXVAL = Math.pow(2, 35) - 1; // 34,359,738,367
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Int36.MINVAL = -Math.pow(2, 35); // -34,359,738,368
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Int36.MAXSIGNED = Math.pow(2, 35) - 1; // 34,359,738,367
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Int36.MINSIGNED = -Math.pow(2, 35); // -34,359,738,368
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Int36.MAXVAL = Math.pow(2, 36) - 1; // 68,719,476,735
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if (NODE) module.exports = Int36;
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652
modules/shared/lib/int36s.js
Normal file
652
modules/shared/lib/int36s.js
Normal file
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@ -0,0 +1,652 @@
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/**
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* @fileoverview Support for 36-bit integers (using signed 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 a signed integer, meaning if the sign bit
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* (bit 35) is set, we store the corresponding negative (two's complement) value. While there
|
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* might be some slight benefits to always storing the 36-bit value as an unsigned quantity
|
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* and negating it "on demand", I like having JavaScript's native representation match the
|
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* emulated value.
|
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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 (signed) 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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* We guarantee that an Int36 value will be (and will always remain) a signed value within this range:
|
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*
|
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* -Math.pow(2, 35) <= i <= Math.pow(2, 35) - 1
|
||||
*
|
||||
* Those lower and upper bounds are defined as Int36.MINVAL and Int36.MAXVAL. The sign of an Int36
|
||||
* value is determined by (and should always match) its highest bit (bit 35).
|
||||
*
|
||||
* NOTE: We use modern bit numbering, where bit 0 is the right-most (least-significant) bit and
|
||||
* bit 35 is the left-most bit. This is opposite of the PDP-10 convention, which defined bit 0 as the
|
||||
* left-most bit and bit 35 as the right-most bit.
|
||||
*
|
||||
* Although the integer precision of JavaScript floating-point (IEEE 754 double-precision) numbers is:
|
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*
|
||||
* -Math.pow(2, 53) <= i <= Math.pow(2, 53)
|
||||
*
|
||||
* it seems unwise to ever permit the internal value to creep outside the signed 36-bit range, because
|
||||
* floating-point operations will drop least-significant bits in favor of most-significant bits when a
|
||||
* result becomes too large, which is the opposite of what integer operations traditionally do. There
|
||||
* 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;
|
||||
this.extended = obj.extended;
|
||||
this.remainder = obj.remainder;
|
||||
}
|
||||
else {
|
||||
this.value = Int36.validate(obj || 0);
|
||||
this.extended = null;
|
||||
/*
|
||||
* NOTE: Surprisingly, isNaN(null) is false, whereas isNaN(undefined) is true. Go figure.
|
||||
*/
|
||||
if (extended != null && !isNaN(extended)) {
|
||||
this.extended = Int36.validate(extended);
|
||||
}
|
||||
this.remainder = null;
|
||||
}
|
||||
this.error = Int36.ERROR.NONE;
|
||||
}
|
||||
|
||||
/**
|
||||
* toDecimal(fUnsigned)
|
||||
*
|
||||
* @this {Int36}
|
||||
* @param {boolean} fUnsigned
|
||||
* @return {string}
|
||||
*/
|
||||
toDecimal(fUnsigned)
|
||||
{
|
||||
var s = "", fNeg = false;
|
||||
var i36Div = new Int36(10000000000);
|
||||
var i36Tmp = new Int36(this.value, this.extended);
|
||||
if (!fUnsigned && i36Tmp.isNegative()) {
|
||||
i36Tmp.negate();
|
||||
fNeg = true;
|
||||
}
|
||||
do {
|
||||
var quotient = i36Tmp.div(i36Div);
|
||||
var nMinDigits = (quotient? 10 : 1);
|
||||
i36Tmp.value = i36Tmp.remainder;
|
||||
do {
|
||||
i36Tmp.divNum(10);
|
||||
s = String.fromCharCode(0x30 + i36Tmp.remainder) + s;
|
||||
} while (--nMinDigits > 0 || i36Tmp.value);
|
||||
i36Tmp.value = quotient;
|
||||
} while (i36Tmp.value);
|
||||
if (fNeg) s = '-' + s;
|
||||
return s;
|
||||
}
|
||||
|
||||
/**
|
||||
* toString(radix, fUnsigned)
|
||||
*
|
||||
* @this {Int36}
|
||||
* @param {number} [radix] (default is 10)
|
||||
* @param {boolean} [fUnsigned] (default is signed for radix 10, unsigned for any other radix)
|
||||
* @return {string}
|
||||
*/
|
||||
toString(radix = 10, fUnsigned)
|
||||
{
|
||||
if (radix == 10) {
|
||||
return this.toDecimal(fUnsigned);
|
||||
}
|
||||
|
||||
var value = this.value;
|
||||
var extended = this.extended;
|
||||
|
||||
if (radix == 8) {
|
||||
var s = Int36.octal(value);
|
||||
if (extended) {
|
||||
s = Int36.octal(extended) + ',' + s;
|
||||
}
|
||||
if (this.remainder) {
|
||||
s += ':' + Int36.octal(this.remainder);
|
||||
}
|
||||
if (DEBUG && this.error) s += " error 0x" + this.error.toString(16);
|
||||
return s;
|
||||
}
|
||||
|
||||
if (value < 0) {
|
||||
value += Int36.BIT36;
|
||||
}
|
||||
if (extended != null) {
|
||||
if (extended < 0) extended += Int36.BIT36;
|
||||
/*
|
||||
* TODO: Need a radix-independent solution for these extended (up to 72-bit) values,
|
||||
* because after 52 bits, JavaScript will start dropping least-significant bits. Until
|
||||
* then, you're better off sticking with octal (see above).
|
||||
*/
|
||||
value = extended * Int36.BIT36 + value;
|
||||
}
|
||||
return value.toString(radix);
|
||||
}
|
||||
|
||||
/**
|
||||
* truncate(result)
|
||||
*
|
||||
* NOTE: This function's job is to truncate the result of an operation to 36-bit accuracy,
|
||||
* not to remove any fractional portion that might also exist. If an operation could have produced
|
||||
* a non-integer result (eg, div()), it's the caller's responsibility to deal with that first.
|
||||
*
|
||||
* @this {Int36}
|
||||
* @param {number} result
|
||||
* @return {number}
|
||||
*/
|
||||
truncate(result)
|
||||
{
|
||||
if (DEBUG && result !== Math.trunc(result)) {
|
||||
console.log("Int36.truncate(" + result + " is not an integer)");
|
||||
}
|
||||
this.extended = null;
|
||||
this.remainder = null;
|
||||
this.error = Int36.ERROR.NONE;
|
||||
if (result > Int36.MAXVAL) {
|
||||
result %= Int36.BIT36;
|
||||
if (result > Int36.MAXVAL) result -= Int36.BIT36;
|
||||
this.error |= Int36.ERROR.OVERFLOW;
|
||||
} else if (result < Int36.MINVAL) {
|
||||
result %= Int36.BIT36;
|
||||
if (result < Int36.MINVAL) result += Int36.BIT36;
|
||||
this.error |= Int36.ERROR.UNDERFLOW;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/**
|
||||
* add(i36)
|
||||
*
|
||||
* @this {Int36}
|
||||
* @param {Int36} i36
|
||||
*/
|
||||
add(i36)
|
||||
{
|
||||
this.value = this.truncate(this.value + i36.value);
|
||||
}
|
||||
|
||||
/**
|
||||
* addNum(num)
|
||||
*
|
||||
* @this {Int36}
|
||||
* @param {number} num
|
||||
*/
|
||||
addNum(num)
|
||||
{
|
||||
this.value = this.truncate(this.value + Int36.validate(num));
|
||||
}
|
||||
|
||||
/**
|
||||
* sub(i36)
|
||||
*
|
||||
* @this {Int36}
|
||||
* @param {Int36} i36
|
||||
*/
|
||||
sub(i36)
|
||||
{
|
||||
this.value = this.truncate(this.value - i36.value);
|
||||
}
|
||||
|
||||
/**
|
||||
* subNum(num)
|
||||
*
|
||||
* @this {Int36}
|
||||
* @param {number} num
|
||||
*/
|
||||
subNum(num)
|
||||
{
|
||||
this.value = this.truncate(this.value - Int36.validate(num));
|
||||
}
|
||||
|
||||
/**
|
||||
* 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 each of 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 < 0) {
|
||||
if (n1) n1 = -n1;
|
||||
fNeg = !fNeg;
|
||||
}
|
||||
|
||||
if (n2 < 0) {
|
||||
if (n2) n2 = -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
|
||||
* @return {number} (quotient)
|
||||
*/
|
||||
div(i36)
|
||||
{
|
||||
return this.divExtended(i36.value);
|
||||
}
|
||||
|
||||
/**
|
||||
* divNum(num)
|
||||
*
|
||||
* @this {Int36}
|
||||
* @param {number} num
|
||||
* @return {number} (quotient)
|
||||
*/
|
||||
divNum(num)
|
||||
{
|
||||
return this.divExtended(Int36.validate(num));
|
||||
}
|
||||
|
||||
/**
|
||||
* divExtended(divisor)
|
||||
*
|
||||
* @this {Int36}
|
||||
* @param {number} divisor
|
||||
* @return {number} (quotient)
|
||||
*/
|
||||
divExtended(divisor)
|
||||
{
|
||||
/*
|
||||
* dividend divisor quotient remainder
|
||||
* -------- ------- -------- ---------
|
||||
* + + -> + +
|
||||
* + - -> - +
|
||||
* - + -> - -
|
||||
* - - -> + -
|
||||
*/
|
||||
var bNegLo = 0, bNegHi = 0;
|
||||
|
||||
if (divisor < 0 && divisor > Int36.MINVAL) {
|
||||
divisor = -divisor;
|
||||
bNegLo = 1 - bNegLo;
|
||||
}
|
||||
|
||||
if (this.isNegative()) {
|
||||
this.negate();
|
||||
bNegHi = 1; bNegLo = 1 - bNegLo;
|
||||
}
|
||||
|
||||
var value = this.value;
|
||||
var extended = this.extended || 0;
|
||||
|
||||
if (value < 0) {
|
||||
value += Int36.BIT36;
|
||||
}
|
||||
|
||||
if (!divisor) {
|
||||
this.error |= Int36.ERROR.DIVZERO;
|
||||
}
|
||||
else if (divisor <= extended) {
|
||||
this.error |= Int36.ERROR.OVERFLOW;
|
||||
}
|
||||
else {
|
||||
var result = 0, bit = 1;
|
||||
var bitsDiv = Int36.setBits(this.bitsDiv, divisor, 0);
|
||||
var bitsRem = Int36.setBits(this.bitsRem, value, extended);
|
||||
|
||||
while (Int36.cmpBits(bitsRem, bitsDiv) > 0) {
|
||||
Int36.addBits(bitsDiv, bitsDiv);
|
||||
bit += bit;
|
||||
}
|
||||
|
||||
do {
|
||||
if (Int36.cmpBits(bitsRem, bitsDiv) >= 0) {
|
||||
Int36.subBits(bitsRem, bitsDiv);
|
||||
result += bit;
|
||||
}
|
||||
Int36.shrBits(bitsDiv);
|
||||
bit /= 2;
|
||||
} while (bit >= 1);
|
||||
|
||||
if (DEBUG && !(result < Int36.BIT36 && !bitsRem[1])) {
|
||||
console.log("divExtended() assertion failure");
|
||||
}
|
||||
|
||||
this.value = result;
|
||||
this.extended = null;
|
||||
this.remainder = bitsRem[0];
|
||||
|
||||
if (bNegLo && this.value && this.value > Int36.MINVAL) {
|
||||
this.value = -this.value;
|
||||
}
|
||||
if (bNegHi && this.remainder && this.remainder > Int36.MINVAL) {
|
||||
this.remainder = -this.remainder;
|
||||
}
|
||||
}
|
||||
return this.value;
|
||||
}
|
||||
|
||||
/**
|
||||
* isNegative()
|
||||
*
|
||||
* @return {boolean}
|
||||
*/
|
||||
isNegative()
|
||||
{
|
||||
return (this.extended < 0 || this.extended == null && this.value < 0);
|
||||
}
|
||||
|
||||
/**
|
||||
* negate()
|
||||
*
|
||||
* Converts the current value to its two's complement. If we were dealing with 8-bit values:
|
||||
*
|
||||
* Original Two's One's
|
||||
* ------- ----- -----
|
||||
* -128 -128 127
|
||||
* -127 127 126
|
||||
* ... ... ...
|
||||
* -1 1 0
|
||||
* 0 0 -1
|
||||
* 1 -1 -2
|
||||
* ... ... ...
|
||||
* 126 -126 -127
|
||||
* 127 -127 -128
|
||||
*
|
||||
* you can see that, when performing two's complement, MINVAL and ZERO are not modified.
|
||||
*
|
||||
* However, in our happy little world, since JavaScript numbers CAN represent both positive and negative
|
||||
* MINVAL values, we don't need to exclude MINVAL from the conversion.
|
||||
*/
|
||||
negate()
|
||||
{
|
||||
this.error = Int36.ERROR.NONE;
|
||||
/*
|
||||
* Perform two's complement on the value.
|
||||
*/
|
||||
if (this.value /* && this.value > Int36.MINVAL */) {
|
||||
this.value = -this.value;
|
||||
}
|
||||
if (this.extended == null) {
|
||||
/*
|
||||
* Set extended to match the sign of the value.
|
||||
*/
|
||||
this.extended = (this.value < 0? -1 : 0);
|
||||
}
|
||||
else if (this.value) {
|
||||
/*
|
||||
* Perform one's complement on the extended value.
|
||||
*/
|
||||
this.extended = -this.extended - 1;
|
||||
}
|
||||
else {
|
||||
/*
|
||||
* Perform two's complement on the extended value.
|
||||
*/
|
||||
if (this.extended /* && this.extended > Int36.MINVAL */) {
|
||||
this.extended = -this.extended;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* 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;
|
||||
}
|
||||
|
||||
/**
|
||||
* setBits(bits, lo, hi)
|
||||
*
|
||||
* @param {Array.<number>} bits
|
||||
* @param {number} lo
|
||||
* @param {number} hi
|
||||
* @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)
|
||||
{
|
||||
var value = Math.trunc(num) % Int36.BIT36;
|
||||
if (value > Int36.MAXVAL) {
|
||||
value -= Int36.BIT36;
|
||||
} else if (value < Int36.MINVAL) {
|
||||
value += 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.MAXVAL = Math.pow(2, 35) - 1; // 34,359,738,367
|
||||
Int36.MINVAL = -Math.pow(2, 35); // -34,359,738,368
|
||||
|
||||
if (NODE) module.exports = Int36;
|
||||
Loading…
Reference in a new issue