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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Created by GNU Texinfo 6.1, http://www.gnu.org/software/texinfo/ -->
<!-- Created by GNU Texinfo 6.5, http://www.gnu.org/software/texinfo/ -->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>Javascript Bignum Extensions</title>
<meta name="description" content="Javascript Bignum Extensions">
@@ -9,7 +10,6 @@
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="#SEC_Contents" rel="contents" title="Table of Contents">
<style type="text/css">
<!--
@@ -52,61 +52,33 @@ ul.no-bullet {list-style: none}
<div class="contents">
<ul class="no-bullet">
<li><a name="toc-Introduction" href="#Introduction">1 Introduction</a></li>
<li><a name="toc-Operator-overloading" href="#Operator-overloading">2 Operator overloading</a>
<li><a name="toc-Operator-overloading" href="#Operator-overloading">2 Operator overloading</a></li>
<li><a name="toc-BigInt-extensions" href="#BigInt-extensions">3 BigInt extensions</a></li>
<li><a name="toc-BigFloat" href="#BigFloat">4 BigFloat</a>
<ul class="no-bullet">
<li><a name="toc-Introduction-1" href="#Introduction-1">2.1 Introduction</a></li>
<li><a name="toc-Builtin-Object-changes" href="#Builtin-Object-changes">2.2 Builtin Object changes</a>
<ul class="no-bullet">
<li><a name="toc-Symbol-constructor" href="#Symbol-constructor">2.2.1 <code>Symbol</code> constructor</a></li>
</ul></li>
</ul></li>
<li><a name="toc-The-BigInt-Mode" href="#The-BigInt-Mode">3 The BigInt Mode</a>
<ul class="no-bullet">
<li><a name="toc-Introduction-2" href="#Introduction-2">3.1 Introduction</a></li>
<li><a name="toc-Changes-that-introduce-incompatibilities-with-Javascript" href="#Changes-that-introduce-incompatibilities-with-Javascript">3.2 Changes that introduce incompatibilities with Javascript</a>
<ul class="no-bullet">
<li><a name="toc-Standard-mode" href="#Standard-mode">3.2.1 Standard mode</a></li>
<li><a name="toc-Bigint-mode" href="#Bigint-mode">3.2.2 Bigint mode</a></li>
</ul></li>
<li><a name="toc-Operators" href="#Operators">3.3 Operators</a>
<ul class="no-bullet">
<li><a name="toc-Arithmetic-operators" href="#Arithmetic-operators">3.3.1 Arithmetic operators</a></li>
<li><a name="toc-Logical-operators" href="#Logical-operators">3.3.2 Logical operators</a></li>
<li><a name="toc-Relational-operators" href="#Relational-operators">3.3.3 Relational operators</a></li>
</ul></li>
<li><a name="toc-Number-literals" href="#Number-literals">3.4 Number literals</a></li>
<li><a name="toc-Builtin-Object-changes-1" href="#Builtin-Object-changes-1">3.5 Builtin Object changes</a>
<ul class="no-bullet">
<li><a name="toc-BigInt-function" href="#BigInt-function">3.5.1 <code>BigInt</code> function</a></li>
<li><a name="toc-BigInt_002eprototype" href="#BigInt_002eprototype">3.5.2 <code>BigInt.prototype</code></a></li>
<li><a name="toc-Number-constructor" href="#Number-constructor">3.5.3 <code>Number</code> constructor</a></li>
<li><a name="toc-Number_002eprototype" href="#Number_002eprototype">3.5.4 <code>Number.prototype</code></a></li>
<li><a name="toc-Math-object" href="#Math-object">3.5.5 <code>Math</code> object</a></li>
</ul></li>
</ul></li>
<li><a name="toc-Arbitrarily-large-floating-point-numbers" href="#Arbitrarily-large-floating-point-numbers">4 Arbitrarily large floating point numbers</a>
<ul class="no-bullet">
<li><a name="toc-Introduction-3" href="#Introduction-3">4.1 Introduction</a></li>
<li><a name="toc-Introduction-1" href="#Introduction-1">4.1 Introduction</a></li>
<li><a name="toc-Floating-point-rounding" href="#Floating-point-rounding">4.2 Floating point rounding</a></li>
<li><a name="toc-Operators-1" href="#Operators-1">4.3 Operators</a></li>
<li><a name="toc-Operators" href="#Operators">4.3 Operators</a></li>
<li><a name="toc-BigFloat-literals" href="#BigFloat-literals">4.4 BigFloat literals</a></li>
<li><a name="toc-Builtin-Object-changes-2" href="#Builtin-Object-changes-2">4.5 Builtin Object changes</a>
<li><a name="toc-Builtin-Object-changes" href="#Builtin-Object-changes">4.5 Builtin Object changes</a>
<ul class="no-bullet">
<li><a name="toc-BigFloat-function" href="#BigFloat-function">4.5.1 <code>BigFloat</code> function</a></li>
<li><a name="toc-BigFloat_002eprototype" href="#BigFloat_002eprototype">4.5.2 <code>BigFloat.prototype</code></a></li>
<li><a name="toc-BigFloatEnv-constructor" href="#BigFloatEnv-constructor">4.5.3 <code>BigFloatEnv</code> constructor</a></li>
<li><a name="toc-Math-object-1" href="#Math-object-1">4.5.4 <code>Math</code> object</a></li>
</ul></li>
</ul></li>
<li><a name="toc-Math-mode" href="#Math-mode">5 Math mode</a>
<li><a name="toc-BigDecimal" href="#BigDecimal">5 BigDecimal</a>
<ul class="no-bullet">
<li><a name="toc-Introduction-4" href="#Introduction-4">5.1 Introduction</a></li>
<li><a name="toc-Builtin-Object-changes-3" href="#Builtin-Object-changes-3">5.2 Builtin Object changes</a>
<li><a name="toc-Operators-1" href="#Operators-1">5.1 Operators</a></li>
<li><a name="toc-BigDecimal-literals" href="#BigDecimal-literals">5.2 BigDecimal literals</a></li>
<li><a name="toc-Builtin-Object-changes-1" href="#Builtin-Object-changes-1">5.3 Builtin Object changes</a>
<ul class="no-bullet">
<li><a name="toc-Symbol-constructor-1" href="#Symbol-constructor-1">5.2.1 <code>Symbol</code> constructor</a></li>
<li><a name="toc-The-BigDecimal-function_002e" href="#The-BigDecimal-function_002e">5.3.1 The <code>BigDecimal</code> function.</a></li>
<li><a name="toc-Properties-of-the-BigDecimal-object" href="#Properties-of-the-BigDecimal-object">5.3.2 Properties of the <code>BigDecimal</code> object</a></li>
<li><a name="toc-Properties-of-the-BigDecimal_002eprototype-object" href="#Properties-of-the-BigDecimal_002eprototype-object">5.3.3 Properties of the <code>BigDecimal.prototype</code> object</a></li>
</ul></li>
<li><a name="toc-Remaining-issues" href="#Remaining-issues">5.3 Remaining issues</a></li>
</ul></li>
<li><a name="toc-Math-mode" href="#Math-mode">6 Math mode</a></li>
</ul>
</div>
@@ -119,379 +91,52 @@ ul.no-bullet {list-style: none}
language while being 100% backward compatible:
</p>
<ul>
<li> Overloading of the standard operators
to support new types such as complex numbers, fractions or matrices.
</li><li> Bigint mode where arbitrarily large integers are available by default (no <code>n</code> suffix is necessary as in the TC39 BigInt proposal<a name="DOCF1" href="#FOOT1"><sup>1</sup></a>).
<li> Operator overloading with a dispatch logic inspired from the proposal available at <a href="https://github.com/tc39/proposal-operator-overloading/">https://github.com/tc39/proposal-operator-overloading/</a>.
</li><li> Arbitrarily large floating point numbers (<code>BigFloat</code>) in base 2 using the IEEE 754 semantics.
</li><li> Optional <code>math</code> mode which modifies the semantics of the division, modulo and power operator. The division and power operator return a fraction with integer operands and the modulo operator is defined as the Euclidian remainder.
</li><li> Arbitrarily large floating point numbers (<code>BigDecimal</code>) in base 10 based on the proposal available at
<a href="https://github.com/littledan/proposal-bigdecimal">https://github.com/littledan/proposal-bigdecimal</a>.
</li><li> <code>math</code> mode: arbitrarily large integers and floating point numbers are available by default. The integer division and power can be overloaded for example to return a fraction. The modulo operator (<code>%</code>) is defined as the Euclidian
remainder. <code>^</code> is an alias to the power operator
(<code>**</code>). <code>^^</code> is used as the exclusive or operator.
</li></ul>
<p>The extensions are independent from each other except the <code>math</code>
mode which relies on the bigint mode and the operator overloading.
mode which relies on BigFloat and operator overloading.
</p>
<a name="Operator-overloading"></a>
<h2 class="chapter">2 Operator overloading</h2>
<a name="Introduction-1"></a>
<h3 class="section">2.1 Introduction</h3>
<p>If the operands of an operator have at least one object type, a custom
operator method is searched before doing the legacy Javascript
<code>ToNumber</code> conversion.
<p>Operator overloading is inspired from the proposal available at
<a href="https://github.com/tc39/proposal-operator-overloading/">https://github.com/tc39/proposal-operator-overloading/</a>. It
implements the same dispatch logic but finds the operator sets by
looking at the <code>Symbol.operatorSet</code> property in the objects. The
changes were done in order to simplify the implementation.
</p>
<p>For unary operators, the custom function is looked up in the object
and has the following name:
</p>
<dl compact="compact">
<dt><code>unary +</code></dt>
<dd><p><code>Symbol.operatorPlus</code>
</p>
</dd>
<dt><code>unary -</code></dt>
<dd><p><code>Symbol.operatorNeg</code>
</p>
</dd>
<dt><code>++</code></dt>
<dd><p><code>Symbol.operatorInc</code>
</p>
</dd>
<dt><code>--</code></dt>
<dd><p><code>Symbol.operatorDec</code>
</p>
</dd>
<dt><code>~</code></dt>
<dd><p><code>Symbol.operatorNot</code>
</p>
</dd>
</dl>
<p>For binary operators:
<p>More precisely, the following modifications were made:
</p>
<ul>
<li> If both operands have the same constructor function, then the operator
is looked up in the constructor.
<li> <code>with operators from</code> is not supported. Operator overloading is always enabled.
</li><li> Otherwise, the property <code>Symbol.operatorOrder</code> is looked up in both
constructors and converted to <code>Int32</code>. The operator is then
looked in the constructor with the larger <code>Symbol.operatorOrder</code>
value. A <code>TypeError</code> is raised if both constructors have the same
<code>Symbol.operatorOrder</code> value.
</li><li> The dispatch is not based on a static <code>[[OperatorSet]]</code> field in all instances. Instead, a dynamic lookup the of the <code>Symbol.operatorSet</code> property is done. This property is typically added in the prototype of each object.
</li><li> <code>Operators.create(...dictionaries)</code> is used to create a new OperatorSet object. The <code>Operators</code> function is supported as an helper to be closer to the TC39 proposal.
</li><li> <code>[]</code> cannot be overloaded.
</li><li> In math mode, the BigInt division and power operators can be overloaded with <code>Operators.updateBigIntOperators(dictionary)</code>.
</li></ul>
<p>The operator is looked up with the following name:
<a name="BigInt-extensions"></a>
<h2 class="chapter">3 BigInt extensions</h2>
<p>A few properties are added to the BigInt object:
</p>
<dl compact="compact">
<dt><code>+</code></dt>
<dd><p><code>Symbol.operatorAdd</code>
</p>
</dd>
<dt><code>-</code></dt>
<dd><p><code>Symbol.operatorSub</code>
</p>
</dd>
<dt><code>*</code></dt>
<dd><p><code>Symbol.operatorMul</code>
</p>
</dd>
<dt><code>/</code></dt>
<dd><p><code>Symbol.operatorDiv</code>
</p>
</dd>
<dt><code>%</code></dt>
<dd><p><code>Symbol.operatorMod</code>
</p>
</dd>
<dt><code>% (math mode)</code></dt>
<dd><p><code>Symbol.operatorMathMod</code>
</p>
</dd>
<dt><code>**</code></dt>
<dd><p><code>Symbol.operatorPow</code>
</p>
</dd>
<dt><code>|</code></dt>
<dd><p><code>Symbol.operatorOr</code>
</p>
</dd>
<dt><code>^</code></dt>
<dd><p><code>Symbol.operatorXor</code>
</p>
</dd>
<dt><code>&amp;</code></dt>
<dd><p><code>Symbol.operatorAnd</code>
</p>
</dd>
<dt><code>&lt;&lt;</code></dt>
<dd><p><code>Symbol.operatorShl</code>
</p>
</dd>
<dt><code>&gt;&gt;</code></dt>
<dd><p><code>Symbol.operatorShr</code>
</p>
</dd>
<dt><code>&lt;</code></dt>
<dd><p><code>Symbol.operatorCmpLT</code>
</p>
</dd>
<dt><code>&gt;</code></dt>
<dd><p><code>Symbol.operatorCmpLT</code>, operands swapped
</p>
</dd>
<dt><code>&lt;=</code></dt>
<dd><p><code>Symbol.operatorCmpLE</code>
</p>
</dd>
<dt><code>&gt;=</code></dt>
<dd><p><code>Symbol.operatorCmpLE</code>, operands swapped
</p>
</dd>
<dt><code>==, !=</code></dt>
<dd><p><code>Symbol.operatorCmpEQ</code>
</p>
</dd>
</dl>
<p>The return value of <code>Symbol.operatorCmpLT</code>, <code>Symbol.operatorCmpLE</code> and
<code>Symbol.operatorCmpEQ</code> is converted to <code>Boolean</code>.
</p>
<a name="Builtin-Object-changes"></a>
<h3 class="section">2.2 Builtin Object changes</h3>
<a name="Symbol-constructor"></a>
<h4 class="subsection">2.2.1 <code>Symbol</code> constructor</h4>
<p>The following global symbols are added for the operator overloading:
</p><dl compact="compact">
<dt><code>operatorOrder</code></dt>
<dt><code>operatorAdd</code></dt>
<dt><code>operatorSub</code></dt>
<dt><code>operatorMul</code></dt>
<dt><code>operatorDiv</code></dt>
<dt><code>operatorMod</code></dt>
<dt><code>operatorPow</code></dt>
<dt><code>operatorShl</code></dt>
<dt><code>operatorShr</code></dt>
<dt><code>operatorAnd</code></dt>
<dt><code>operatorOr</code></dt>
<dt><code>operatorXor</code></dt>
<dt><code>operatorCmpLT</code></dt>
<dt><code>operatorCmpLE</code></dt>
<dt><code>operatorCmpEQ</code></dt>
<dt><code>operatorPlus</code></dt>
<dt><code>operatorNeg</code></dt>
<dt><code>operatorNot</code></dt>
<dt><code>operatorInc</code></dt>
<dt><code>operatorDec</code></dt>
</dl>
<a name="The-BigInt-Mode"></a>
<h2 class="chapter">3 The BigInt Mode</h2>
<a name="Introduction-2"></a>
<h3 class="section">3.1 Introduction</h3>
<p>The bigint mode is enabled with the <code>&quot;use bigint&quot;</code> directive. It
propagates the same way as the strict mode. In bigint mode, all
integers are considered as <code>bigint</code> (arbitrarily large integer,
similar to the TC39 BigInt
proposal<a name="DOCF2" href="#FOOT2"><sup>2</sup></a>)
instead of <code>number</code> (floating point number). In order to be able
to exchange data between standard and bigint modes, numbers are
internally represented as 3 different types:
</p>
<ul>
<li> Small integer (SmallInt): 32 bit integer<a name="DOCF3" href="#FOOT3"><sup>3</sup></a>.
</li><li> Big integer (BigInt): arbitrarily large integer.
</li><li> Floating point number (Float).
</li></ul>
<p>In standard mode, the semantics of each operation is modified so that
when it returns a <code>number</code>, it is either of SmallInt or
Float. But the difference between SmallInt and Float is not observable
in standard mode.
</p>
<p>In bigint mode, each operation behaves differently whether its
operands are integer or float. The difference between SmallInt and
BigInt is not observable (i.e. they are both integers).
</p>
<p>The following table summarizes the observable types:
</p>
<table>
<thead><tr><th width="30%">Internal type</th><th width="30%">Observable type<br> (standard mode)</th><th width="30%">Observable type<br> (bigint mode)</th></tr></thead>
<tr><td width="30%">SmallInt</td><td width="30%">number</td><td width="30%">bigint</td></tr>
<tr><td width="30%">BigInt</td><td width="30%">bigint</td><td width="30%">bigint</td></tr>
<tr><td width="30%">Float</td><td width="30%">number</td><td width="30%">number</td></tr>
</table>
<a name="Changes-that-introduce-incompatibilities-with-Javascript"></a>
<h3 class="section">3.2 Changes that introduce incompatibilities with Javascript</h3>
<a name="Standard-mode"></a>
<h4 class="subsection">3.2.1 Standard mode</h4>
<p>There is no incompatibility with Javascript.
</p>
<a name="Bigint-mode"></a>
<h4 class="subsection">3.2.2 Bigint mode</h4>
<p>The following changes are visible:
</p>
<ul>
<li> Integer and Float are different types. Constants are typed. For example: <code>typeof 1.0 === &quot;number&quot;</code> and <code>typeof 1 === &quot;bigint&quot;</code>. Another consequence is that <code>1.0 === 1</code> is false.
</li><li> The range of integers is unlimited. In standard mode: <code>2**53 + 1 === 2**53</code>. This is no longer true with the bignum extensions.
</li><li> Binary bitwise operators do not truncate to 32 bits i.e. <code>0x800000000 | 1 === 0x800000001</code> while it gives <code>1</code> in standard mode.
</li><li> Bitwise shift operators do not truncate to 32 bits and do not mask the shift count with <code>0x1f</code> i.e. <code>1 &lt;&lt; 32 === 4294967296</code> while it gives <code>1</code> in standard mode. However, the <code>&gt;&gt;&gt;</code> operator (unsigned right shift) which is useless with bignums keeps its standard mode behavior<a name="DOCF4" href="#FOOT4"><sup>4</sup></a>.
</li><li> Operators with integer operands never return the minus zero floating point value as result. Hence <code>Object.is(0, -0) === true</code>. Use <code>-0.0</code> to create a minus zero floating point value.
</li><li> The <code>ToPrimitive</code> abstract operation is called with the <code>&quot;integer&quot;</code> preferred type when an integer is required (e.g. for bitwise binary or shift operations).
</li><li> The prototype of integers is no longer <code>Number.prototype</code>. Instead<br> <code>Object.getPrototypeOf(1) === BigInt.prototype</code>. The prototype of floats remains Number.prototype.
</li><li> If the TC39 BigInt proposal is supported, there is no observable difference between integers and <code>bigint</code>s.
</li></ul>
<a name="Operators"></a>
<h3 class="section">3.3 Operators</h3>
<a name="Arithmetic-operators"></a>
<h4 class="subsection">3.3.1 Arithmetic operators</h4>
<p>The operands are converted to number values as in normal
Javascript. Then the general case is that an Integer is returned if
both operands are Integer. Otherwise, a float is returned.
</p>
<p>The <code>+</code> operator also accepts strings as input and behaves like
standard Javascript in this case.
</p>
<p>The binary operator <code>%</code> returns the truncated remainder of the
division. When the result is an Integer type, a dividend of zero yields a
RangeError exception.
</p>
<p>The binary operator <code>%</code> in math mode returns the Euclidian
remainder of the division i.e. it is always positive.
</p>
<p>The binary operator <code>/</code> returns a float.
</p>
<p>The binary operator <code>/</code> in math mode returns a float if one of
the operands is float. Otherwise, <code>BigInt[Symbol.operatorDiv]</code> is
invoked.
</p>
<p>The returned type of <code>a ** b</code> is Float if <em>a</em> or <em>b</em>
are Float. If <em>a</em> and <em>b</em> are integers:
</p><ul>
<li> <em>b &lt; 0</em> returns a Float in bigint mode. In math mode, <code>BigInt[Symbol.operatorPow]</code> is invoked.
</li><li> <em>b &gt;= 0</em> returns an integer.
</li></ul>
<p>The unary <code>-</code> and unary <code>+</code> return the same type as their
operand. They performs no floating point rounding when the result is a
float.
</p>
<p>The unary operators <code>++</code> and <code>--</code> return the same type as
their operand.
</p>
<p>In standard mode:
</p>
<p>If the operator returns an Integer and that the result fits a
SmallInt, it is converted to SmallInt. Otherwise, the Integer is
converted to a Float.
</p>
<p>In bigint mode:
</p>
<p>If the operator returns an Integer and that the result fits a
SmallInt, it is converted to SmallInt. Otherwise it is a BigInt.
</p>
<a name="Logical-operators"></a>
<h4 class="subsection">3.3.2 Logical operators</h4>
<p>In standard mode:
</p>
<p>The operands have their standard behavior. If the result fits a
SmallInt it is converted to a SmallInt. Otherwise it is a Float.
</p>
<p>In bigint mode:
</p>
<p>The operands are converted to integer values. The floating point
values are converted to integer by rounding them to zero.
</p>
<p>The logical operators are defined assuming the integers are
represented in two complement notation.
</p>
<p>For <code>&lt;&lt;</code> and <code>&lt;&lt;</code>, the shift can be positive or negative. So
<code>a &lt;&lt; b</code> is defined as <em>\lfloor a/2^{-b} \rfloor</em> and
<code>a &gt;&gt; b</code> is defined as <em>\lfloor a/2^{b} \rfloor</em>.
</p>
<p>The operator <code>&gt;&gt;&gt;</code> is supported for backward compatibility and
behaves the same way as Javascript i.e. implicit conversion to <code>Uint32</code>.
</p>
<p>If the result fits a SmallInt it is converted to a SmallInt. Otherwise
it is a BigInt.
</p>
<a name="Relational-operators"></a>
<h4 class="subsection">3.3.3 Relational operators</h4>
<p>The relational operators &lt;, &lt;=, &gt;, &gt;=, ==, != work as expected with
integers and floating point numbers (e.g. <code>1.0 == 1</code> is true).
</p>
<p>The strict equality operators === and !== have the usual Javascript
semantics. In particular, different types never equal, so <code>1.0
=== 1</code> is false.
</p>
<a name="Number-literals"></a>
<h3 class="section">3.4 Number literals</h3>
<p>Number literals in bigint mode have a slightly different behavior than
in standard Javascript:
</p>
<ol>
<li> A number literal without a decimal point or an exponent is considered
as an Integer. Otherwise it is a Float.
</li><li> Hexadecimal, octal or binary floating point literals are accepted with
a decimal point or an exponent. The exponent is specified with the
<code>p</code> letter assuming a base 2. The same convention is used by
C99. Example: <code>0x1p3</code> is the same as <code>8.0</code>.
</li></ol>
<a name="Builtin-Object-changes-1"></a>
<h3 class="section">3.5 Builtin Object changes</h3>
<a name="BigInt-function"></a>
<h4 class="subsection">3.5.1 <code>BigInt</code> function</h4>
<p>The <code>BigInt</code> function cannot be invoked as a constructor. When
invoked as a function, it converts its first parameter to an
integer. When a floating point number is given as parameter, it is
truncated to an integer with infinite precision.
</p>
<p><code>BigInt</code> properties:
</p>
<dl compact="compact">
<dt><code>asIntN(bits, a)</code></dt>
<dd><p>Set <em>b=a \pmod{2^{bits}}</em>. Return <em>b</em> if <em>b &lt; 2^{bits-1}</em>
otherwise <em>b-2^{bits}</em>.
</p>
</dd>
<dt><code>asUintN(bits, a)</code></dt>
<dd><p>Return <em>a \pmod{2^{bits}}</em>.
</p>
</dd>
<dt><code>tdiv(a, b)</code></dt>
<dd><p>Return <em>trunc(a/b)</em>. <code>b = 0</code> raises a RangeError
exception.
@@ -542,70 +187,10 @@ raised if <em>a &lt; 0</em>.
</dd>
</dl>
<a name="BigInt_002eprototype"></a>
<h4 class="subsection">3.5.2 <code>BigInt.prototype</code></h4>
<a name="BigFloat"></a>
<h2 class="chapter">4 BigFloat</h2>
<p>It is a normal object.
</p>
<a name="Number-constructor"></a>
<h4 class="subsection">3.5.3 <code>Number</code> constructor</h4>
<p>The number constructor returns its argument rounded to a Float using
the global floating point environment. In bigint mode, the Number
constructor returns a Float. In standard mode, it returns a SmallInt
if the value fits it, otherwise a Float.
</p>
<a name="Number_002eprototype"></a>
<h4 class="subsection">3.5.4 <code>Number.prototype</code></h4>
<p>The following properties are modified:
</p>
<dl compact="compact">
<dt><code>toString(radix)</code></dt>
<dd>
<p>In bigint mode, integers are converted to the specified radix with
infinite precision.
</p>
</dd>
<dt><code>toPrecision(p)</code></dt>
<dt><code>toFixed(p)</code></dt>
<dt><code>toExponential(p)</code></dt>
<dd>
<p>In bigint mode, integers are accepted and converted to string with
infinite precision.
</p>
</dd>
<dt><code>parseInt(string, radix)</code></dt>
<dd>
<p>In bigint mode, an integer is returned and the conversion is done with
infinite precision.
</p>
</dd>
</dl>
<a name="Math-object"></a>
<h4 class="subsection">3.5.5 <code>Math</code> object</h4>
<p>The following properties are modified:
</p>
<dl compact="compact">
<dt><code>abs(x)</code></dt>
<dd><p>Absolute value. Return an integer if <code>x</code> is an Integer. Otherwise
return a Float. No rounding is performed.
</p>
</dd>
<dt><code>min(a, b)</code></dt>
<dt><code>max(a, b)</code></dt>
<dd><p>No rounding is performed. The returned type is the same one as the
minimum (resp. maximum) value.
</p>
</dd>
</dl>
<a name="Arbitrarily-large-floating-point-numbers"></a>
<h2 class="chapter">4 Arbitrarily large floating point numbers</h2>
<a name="Introduction-3"></a>
<a name="Introduction-1"></a>
<h3 class="section">4.1 Introduction</h3>
<p>This extension adds the <code>BigFloat</code> primitive type. The
@@ -628,8 +213,8 @@ environment are also set according to the result of the operation.
point environment is used.
</p>
<p>The rounding mode of the global floating point environment is always
<code>RNDN</code> (&ldquo;round to nearest with ties to even&rdquo;)<a name="DOCF5" href="#FOOT5"><sup>5</sup></a>. The status flags of the global environment cannot be
read<a name="DOCF6" href="#FOOT6"><sup>6</sup></a>. The precision of the global environment is
<code>RNDN</code> (&ldquo;round to nearest with ties to even&rdquo;)<a name="DOCF1" href="#FOOT1"><sup>1</sup></a>. The status flags of the global environment cannot be
read<a name="DOCF2" href="#FOOT2"><sup>2</sup></a>. The precision of the global environment is
<code>BigFloatEnv.prec</code>. The number of exponent bits of the global
environment is <code>BigFloatEnv.expBits</code>. If <code>BigFloatEnv.expBits</code> is
strictly smaller than the maximum allowed number of exponent bits
@@ -646,7 +231,7 @@ when calling a function (see <code>BigFloatEnv.setPrec</code>). Hence a
function can change the global floating point environment for its
callees but not for its caller.
</p>
<a name="Operators-1"></a>
<a name="Operators"></a>
<h3 class="section">4.3 Operators</h3>
<p>The builtin operators are extended so that a BigFloat is returned if
@@ -669,9 +254,9 @@ equal when using the strict comparison operators (e.g. <code>0.0 ===
<p>BigFloat literals are floating point numbers with a trailing <code>l</code>
suffix. BigFloat literals have an infinite precision. They are rounded
according to the global floating point environment when they are
evaluated.<a name="DOCF7" href="#FOOT7"><sup>7</sup></a>
evaluated.<a name="DOCF3" href="#FOOT3"><sup>3</sup></a>
</p>
<a name="Builtin-Object-changes-2"></a>
<a name="Builtin-Object-changes"></a>
<h3 class="section">4.5 Builtin Object changes</h3>
<a name="BigFloat-function"></a>
@@ -739,6 +324,10 @@ point number <code>a</code> according to the floating point environment
<dd><p>Round to an integer. No additional rounding is performed.
</p>
</dd>
<dt><code>abs(x)</code></dt>
<dd><p>Return the absolute value of x. No additional rounding is performed.
</p>
</dd>
<dt><code>fmod(x, y[, e])</code></dt>
<dt><code>remainder(x, y[, e])</code></dt>
<dd><p>Floating point remainder. The quotient is truncated to zero (fmod) or
@@ -773,6 +362,10 @@ number. <code>e</code> is an optional floating point environment.
<p>The following properties are modified:
</p>
<dl compact="compact">
<dt><code>valueOf()</code></dt>
<dd><p>Return the bigfloat primitive value corresponding to <code>this</code>.
</p>
</dd>
<dt><code>toString(radix)</code></dt>
<dd>
<p>For floating point numbers:
@@ -787,14 +380,17 @@ the global precision and round to nearest gives the same number.
</li></ul>
<p>The exponent letter is <code>e</code> for base 10, <code>p</code> for bases 2, 8,
16 with a binary exponent and <code>@</code> for the other bases.
</p>
</dd>
<dt><code>toPrecision(p[, rnd_mode])</code></dt>
<dt><code>toFixed(p[, rnd_mode])</code></dt>
<dt><code>toExponential(p[, rnd_mode])</code></dt>
<dt><code>toPrecision(p, rnd_mode = BigFloatEnv.RNDNA, radix = 10)</code></dt>
<dt><code>toFixed(p, rnd_mode = BigFloatEnv.RNDNA, radix = 10)</code></dt>
<dt><code>toExponential(p, rnd_mode = BigFloatEnv.RNDNA, radix = 10)</code></dt>
<dd><p>Same semantics as the corresponding <code>Number</code> functions with
BigFloats. There is no limit on the accepted precision <code>p</code>. The
rounding mode can be optionally specified. It is set by default to
<code>BigFloatEnv.RNDNA</code>.
rounding mode and radix can be optionally specified. The radix must be
between 2 and 36.
</p>
</dd>
</dl>
@@ -832,14 +428,14 @@ subnormal flags is set to <code>false</code>. If <code>rndMode</code> is
<dl compact="compact">
<dt><code>prec</code></dt>
<dd><p>Getter. Return the precision in bits of the global floating point
environment. The initial value is <code>53</code>.
environment. The initial value is <code>113</code>.
</p>
</dd>
<dt><code>expBits</code></dt>
<dd><p>Getter. Return the exponent size in bits of the global floating point
environment assuming an IEEE 754 representation. If <code>expBits &lt;
expBitsMax</code>, then subnormal numbers are supported. The initial value
is <code>11</code>.
is <code>15</code>.
</p>
</dd>
<dt><code>setPrec(f, p[, e])</code></dt>
@@ -848,9 +444,7 @@ and the exponent size to <code>e</code> then call the function
<code>f</code>. Then the Float precision and exponent size are reset to
their precious value and the return value of <code>f</code> is returned (or
an exception is raised if <code>f</code> raised an exception). If <code>e</code>
is <code>undefined</code> it is set to <code>BigFloatEnv.expBitsMax</code>. <code>p</code>
must be &gt;= 53 and <code>e</code> must be &gt;= 11 so that the global precision
is at least equivalent to the IEEE 754 64 bit doubles.
is <code>undefined</code> it is set to <code>BigFloatEnv.expBitsMax</code>.
</p>
</dd>
<dt><code>precMin</code></dt>
@@ -858,7 +452,7 @@ is at least equivalent to the IEEE 754 64 bit doubles.
</p>
</dd>
<dt><code>precMax</code></dt>
<dd><p>Read-only integer. Return the maximum allowed precision. Must be at least 53.
<dd><p>Read-only integer. Return the maximum allowed precision. Must be at least 113.
</p>
</dd>
<dt><code>expBitsMin</code></dt>
@@ -868,7 +462,7 @@ bits. Must be at least 3.
</dd>
<dt><code>expBitsMax</code></dt>
<dd><p>Read-only integer. Return the maximum allowed exponent size in
bits. Must be at least 11.
bits. Must be at least 15.
</p>
</dd>
<dt><code>RNDN</code></dt>
@@ -891,11 +485,11 @@ bits. Must be at least 11.
<dd><p>Read-only integer. Round to nearest, with ties away from zero rounding mode.
</p>
</dd>
<dt><code>RNDNU</code></dt>
<dd><p>Read-only integer. Round to nearest, with ties to +Infinity rounding mode.
<dt><code>RNDA</code></dt>
<dd><p>Read-only integer. Round away from zero rounding mode.
</p>
</dd>
<dt><code>RNDF<a name="DOCF8" href="#FOOT8"><sup>8</sup></a></code></dt>
<dt><code>RNDF<a name="DOCF4" href="#FOOT4"><sup>4</sup></a></code></dt>
<dd><p>Read-only integer. Faithful rounding mode. The result is
non-deterministically rounded to -Infinity or +Infinity. This rounding
mode usually gives a faster and deterministic running time for the
@@ -939,102 +533,200 @@ assuming an IEEE 754 representation.
</dd>
</dl>
<a name="Math-object-1"></a>
<h4 class="subsection">4.5.4 <code>Math</code> object</h4>
<a name="BigDecimal"></a>
<h2 class="chapter">5 BigDecimal</h2>
<p>The following properties are modified:
<p>This extension adds the <code>BigDecimal</code> primitive type. The
<code>BigDecimal</code> type represents floating point numbers in base
10. It is inspired from the proposal available at
<a href="https://github.com/littledan/proposal-bigdecimal">https://github.com/littledan/proposal-bigdecimal</a>.
</p>
<p>The <code>BigDecimal</code> floating point numbers are always normalized and
finite. There is no concept of <code>-0</code>, <code>Infinity</code> or
<code>NaN</code>. By default, all the computations are done with infinite
precision.
</p>
<a name="Operators-1"></a>
<h3 class="section">5.1 Operators</h3>
<p>The following builtin operators support BigDecimal:
</p>
<dl compact="compact">
<dt><code>abs(x)</code></dt>
<dd><p>Absolute value. If <code>x</code> is a BigFloat, its absolute value is
returned as a BigFloat. No rounding is performed.
<dt><code>+</code></dt>
<dt><code>-</code></dt>
<dt><code>*</code></dt>
<dd><p>Both operands must be BigDecimal. The result is computed with infinite
precision.
</p></dd>
<dt><code>%</code></dt>
<dd><p>Both operands must be BigDecimal. The result is computed with infinite
precision. A range error is throws in case of division by zero.
</p>
</dd>
<dt><code>min(a, b)</code></dt>
<dt><code>max(a, b)</code></dt>
<dd><p>The returned type is the same one as the minimum (resp. maximum)
value, so <code>BigFloat</code> values are accepted. When a <code>BigFloat</code>
is returned, no rounding is performed.
<dt><code>/</code></dt>
<dd><p>Both operands must be BigDecimal. A range error is throws in case of
division by zero or if the result cannot be represented with infinite
precision (use <code>BigDecimal.div</code> to specify the rounding).
</p>
</dd>
<dt><code>**</code></dt>
<dd><p>Both operands must be BigDecimal. The exponent must be a positive
integer. The result is computed with infinite precision.
</p>
</dd>
<dt><code>===</code></dt>
<dd><p>When one of the operand is a BigDecimal, return true if both operands
are a BigDecimal and if they are equal.
</p>
</dd>
<dt><code>==</code></dt>
<dt><code>!=</code></dt>
<dt><code>&lt;=</code></dt>
<dt><code>&gt;=</code></dt>
<dt><code>&lt;</code></dt>
<dt><code>&gt;</code></dt>
<dd>
<p>Numerical comparison. When one of the operand is not a BigDecimal, it is
converted to BigDecimal by using ToString(). Hence comparisons between
Number and BigDecimal do not use the exact mathematical value of the
Number value.
</p>
</dd>
</dl>
<a name="BigDecimal-literals"></a>
<h3 class="section">5.2 BigDecimal literals</h3>
<p>BigDecimal literals are decimal floating point numbers with a trailing
<code>m</code> suffix.
</p>
<a name="Builtin-Object-changes-1"></a>
<h3 class="section">5.3 Builtin Object changes</h3>
<a name="The-BigDecimal-function_002e"></a>
<h4 class="subsection">5.3.1 The <code>BigDecimal</code> function.</h4>
<p>It returns <code>0m</code> if no parameter is provided. Otherwise the first
parameter is converted to a bigdecimal by using ToString(). Hence
Number value are not converted to their exact numerical value as
BigDecimal.
</p>
<a name="Properties-of-the-BigDecimal-object"></a>
<h4 class="subsection">5.3.2 Properties of the <code>BigDecimal</code> object</h4>
<dl compact="compact">
<dt><code>add(a, b[, e])</code></dt>
<dt><code>sub(a, b[, e])</code></dt>
<dt><code>mul(a, b[, e])</code></dt>
<dt><code>div(a, b[, e])</code></dt>
<dt><code>mod(a, b[, e])</code></dt>
<dt><code>sqrt(a, e)</code></dt>
<dt><code>round(a, e)</code></dt>
<dd><p>Perform the specified floating point operation and round the floating
point result according to the rounding object <code>e</code>. If the
rounding object is not present, the operation is executed with
infinite precision.
</p>
<p>For <code>div</code>, a <code>RangeError</code> exception is thrown in case of
division by zero or if the result cannot be represented with infinite
precision if no rounding object is present.
</p>
<p>For <code>sqrt</code>, a range error is thrown if <code>a</code> is less than
zero.
</p>
<p>The rounding object must contain the following properties:
<code>roundingMode</code> is a string specifying the rounding mode
(<code>&quot;floor&quot;</code>, <code>&quot;ceiling&quot;</code>, <code>&quot;down&quot;</code>, <code>&quot;up&quot;</code>,
<code>&quot;half-even&quot;</code>, <code>&quot;half-up&quot;</code>). Either
<code>maximumSignificantDigits</code> or <code>maximumFractionDigits</code> must
be present to specify respectively the number of significant digits
(must be &gt;= 1) or the number of digits after the decimal point (must
be &gt;= 0).
</p>
</dd>
</dl>
<a name="Properties-of-the-BigDecimal_002eprototype-object"></a>
<h4 class="subsection">5.3.3 Properties of the <code>BigDecimal.prototype</code> object</h4>
<dl compact="compact">
<dt><code>valueOf()</code></dt>
<dd><p>Return the bigdecimal primitive value corresponding to <code>this</code>.
</p>
</dd>
<dt><code>toString()</code></dt>
<dd><p>Convert <code>this</code> to a string with infinite precision in base 10.
</p>
</dd>
<dt><code>toPrecision(p, rnd_mode = &quot;half-up&quot;)</code></dt>
<dt><code>toFixed(p, rnd_mode = &quot;half-up&quot;)</code></dt>
<dt><code>toExponential(p, rnd_mode = &quot;half-up&quot;)</code></dt>
<dd><p>Convert the BigDecimal <code>this</code> to string with the specified
precision <code>p</code>. There is no limit on the accepted precision
<code>p</code>. The rounding mode can be optionally
specified. <code>toPrecision</code> outputs either in decimal fixed notation
or in decimal exponential notation with a <code>p</code> digits of
precision. <code>toExponential</code> outputs in decimal exponential
notation with <code>p</code> digits after the decimal point. <code>toFixed</code>
outputs in decimal notation with <code>p</code> digits after the decimal
point.
</p>
</dd>
</dl>
<a name="Math-mode"></a>
<h2 class="chapter">5 Math mode</h2>
<a name="Introduction-4"></a>
<h3 class="section">5.1 Introduction</h3>
<h2 class="chapter">6 Math mode</h2>
<p>A new <em>math mode</em> is enabled with the <code>&quot;use math&quot;</code>
directive. <code>&quot;use bigint&quot;</code> is implied in math mode. With this
mode, writing mathematical expressions is more intuitive, exact
results (e.g. fractions) can be computed for all operators and floating
point literals have the <code>BigFloat</code> type by default.
directive. It propagates the same way as the <em>strict mode</em>. It is
designed so that arbitrarily large integers and floating point numbers
are available by default. In order to minimize the number of changes
in the Javascript semantics, integers are represented either as Number
or BigInt depending on their magnitude. Floating point numbers are
always represented as BigFloat.
</p>
<p>It propagates the same way as the <em>strict mode</em>. In
this mode:
<p>The following changes are made to the Javascript semantics:
</p>
<ul>
<li> The <code>^</code> operator is a similar to the power operator (<code>**</code>).
<li> Floating point literals (i.e. number with a decimal point or an exponent) are <code>BigFloat</code> by default (i.e. a <code>l</code> suffix is implied). Hence <code>typeof 1.0 === &quot;bigfloat&quot;</code>.
</li><li> Integer literals (i.e. numbers without a decimal point or an exponent) with or without the <code>n</code> suffix are <code>BigInt</code> if their value cannot be represented as a safe integer. A safe integer is defined as a integer whose absolute value is smaller or equal to <code>2**53-1</code>. Hence <code>typeof 1 === &quot;number &quot;</code>, <code>typeof 1n === &quot;number&quot;</code> but <code>typeof 9007199254740992 === &quot;bigint&quot; </code>.
</li><li> All the bigint builtin operators and functions are modified so that their result is returned as a Number if it is a safe integer. Otherwise the result stays a BigInt.
</li><li> The builtin operators are modified so that they return an exact result (which can be a BigInt) if their operands are safe integers. Operands between Number and BigInt are accepted provided the Number operand is a safe integer. The integer power with a negative exponent returns a BigFloat as result. The integer division returns a BigFloat as result.
</li><li> The <code>^</code> operator is an alias to the power operator (<code>**</code>).
</li><li> The power operator (both <code>^</code> and <code>**</code>) grammar is modified so that <code>-2^2</code> is allowed and yields <code>-4</code>.
</li><li> The logical xor operator is still available with the <code>^^</code> operator.
</li><li> The division operator invokes <code>BigInt[Symbol.operatorDiv]</code> in case both operands are integers.
</li><li> The integer division operator can be overloaded by modifying the corresponding operator in <code>BigInt.prototype.[[OperatorSet]]</code>.
</li><li> The power operator invokes <code>BigInt[Symbol.operatorPow]</code> in case both operands are integers and the exponent is strictly negative.
</li><li> The integer power operator with a non zero negative exponent can be overloaded by modifying the corresponding operator in <code>BigInt.prototype.[[OperatorSet]]</code>.
</li><li> The modulo operator returns the Euclidian remainder (always positive) instead of the truncated remainder.
</li><li> Floating point literals are <code>BigFloat</code> by default (i.e. a <code>l</code> suffix is implied).
</li><li> The modulo operator (<code>%</code>) returns the Euclidian remainder (always positive) instead of the truncated remainder.
</li></ul>
<a name="Builtin-Object-changes-3"></a>
<h3 class="section">5.2 Builtin Object changes</h3>
<a name="Symbol-constructor-1"></a>
<h4 class="subsection">5.2.1 <code>Symbol</code> constructor</h4>
<p>The following global symbol is added for the operator overloading:
</p><dl compact="compact">
<dt><code>operatorMathMod</code></dt>
</dl>
<a name="Remaining-issues"></a>
<h3 class="section">5.3 Remaining issues</h3>
<ol>
<li> A new floating point literal suffix could be added for <code>Number</code> literals.
</li></ol>
<div class="footnote">
<hr>
<h4 class="footnotes-heading">Footnotes</h4>
<h3><a name="FOOT1" href="#DOCF1">(1)</a></h3>
<p><a href="https://tc39.github.io/proposal-bigint/">https://tc39.github.io/proposal-bigint/</a></p>
<h3><a name="FOOT2" href="#DOCF2">(2)</a></h3>
<p><a href="https://tc39.github.io/proposal-bigint/">https://tc39.github.io/proposal-bigint/</a></p>
<h3><a name="FOOT3" href="#DOCF3">(3)</a></h3>
<p>Could be extended to 53 bits without changing the principle.</p>
<h3><a name="FOOT4" href="#DOCF4">(4)</a></h3>
<p>The unsigned right right operator could be removed in bigint mode.</p>
<h3><a name="FOOT5" href="#DOCF5">(5)</a></h3>
<p>The
rationale is that the rounding mode changes must always be
explicit.</p>
<h3><a name="FOOT6" href="#DOCF6">(6)</a></h3>
<h3><a name="FOOT2" href="#DOCF2">(2)</a></h3>
<p>The rationale is to avoid side effects for the built-in
operators.</p>
<h3><a name="FOOT7" href="#DOCF7">(7)</a></h3>
<h3><a name="FOOT3" href="#DOCF3">(3)</a></h3>
<p>Base 10 floating point literals cannot usually be
exactly represented as base 2 floating point number. In order to
ensure that the literal is represented accurately with the current
precision, it must be evaluated at runtime.</p>
<h3><a name="FOOT8" href="#DOCF8">(8)</a></h3>
<h3><a name="FOOT4" href="#DOCF4">(4)</a></h3>
<p>Could be removed in case a deterministic behavior for floating point operations is required.</p>
</div>
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@@ -10,12 +10,12 @@
@sp 7
@center @titlefont{Javascript Bignum Extensions}
@sp 3
@center Version 2018-06-16
@center Version 2020-01-11
@sp 3
@center Author: Fabrice Bellard
@end titlepage
@setfilename spec.info
@setfilename jsbignum.info
@settitle Javascript Bignum Extensions
@contents
@@ -27,347 +27,51 @@ language while being 100% backward compatible:
@itemize
@item Overloading of the standard operators
to support new types such as complex numbers, fractions or matrices.
@item Bigint mode where arbitrarily large integers are available by default (no @code{n} suffix is necessary as in the TC39 BigInt proposal@footnote{@url{https://tc39.github.io/proposal-bigint/}}).
@item Operator overloading with a dispatch logic inspired from the proposal available at @url{https://github.com/tc39/proposal-operator-overloading/}.
@item Arbitrarily large floating point numbers (@code{BigFloat}) in base 2 using the IEEE 754 semantics.
@item Optional @code{math} mode which modifies the semantics of the division, modulo and power operator. The division and power operator return a fraction with integer operands and the modulo operator is defined as the Euclidian remainder.
@item Arbitrarily large floating point numbers (@code{BigDecimal}) in base 10 based on the proposal available at
@url{https://github.com/littledan/proposal-bigdecimal}.
@item @code{math} mode: arbitrarily large integers and floating point numbers are available by default. The integer division and power can be overloaded for example to return a fraction. The modulo operator (@code{%}) is defined as the Euclidian
remainder. @code{^} is an alias to the power operator
(@code{**}). @code{^^} is used as the exclusive or operator.
@end itemize
The extensions are independent from each other except the @code{math}
mode which relies on the bigint mode and the operator overloading.
mode which relies on BigFloat and operator overloading.
@chapter Operator overloading
@section Introduction
Operator overloading is inspired from the proposal available at
@url{https://github.com/tc39/proposal-operator-overloading/}. It
implements the same dispatch logic but finds the operator sets by
looking at the @code{Symbol.operatorSet} property in the objects. The
changes were done in order to simplify the implementation.
If the operands of an operator have at least one object type, a custom
operator method is searched before doing the legacy Javascript
@code{ToNumber} conversion.
For unary operators, the custom function is looked up in the object
and has the following name:
@table @code
@item unary +
@code{Symbol.operatorPlus}
@item unary -
@code{Symbol.operatorNeg}
@item ++
@code{Symbol.operatorInc}
@item --
@code{Symbol.operatorDec}
@item ~
@code{Symbol.operatorNot}
@end table
For binary operators:
More precisely, the following modifications were made:
@itemize
@item
If both operands have the same constructor function, then the operator
is looked up in the constructor.
@item @code{with operators from} is not supported. Operator overloading is always enabled.
@item
Otherwise, the property @code{Symbol.operatorOrder} is looked up in both
constructors and converted to @code{Int32}. The operator is then
looked in the constructor with the larger @code{Symbol.operatorOrder}
value. A @code{TypeError} is raised if both constructors have the same
@code{Symbol.operatorOrder} value.
@item The dispatch is not based on a static @code{[[OperatorSet]]} field in all instances. Instead, a dynamic lookup the of the @code{Symbol.operatorSet} property is done. This property is typically added in the prototype of each object.
@item @code{Operators.create(...dictionaries)} is used to create a new OperatorSet object. The @code{Operators} function is supported as an helper to be closer to the TC39 proposal.
@item @code{[]} cannot be overloaded.
@item In math mode, the BigInt division and power operators can be overloaded with @code{Operators.updateBigIntOperators(dictionary)}.
@end itemize
The operator is looked up with the following name:
@chapter BigInt extensions
A few properties are added to the BigInt object:
@table @code
@item +
@code{Symbol.operatorAdd}
@item -
@code{Symbol.operatorSub}
@item *
@code{Symbol.operatorMul}
@item /
@code{Symbol.operatorDiv}
@item %
@code{Symbol.operatorMod}
@item % (math mode)
@code{Symbol.operatorMathMod}
@item **
@code{Symbol.operatorPow}
@item |
@code{Symbol.operatorOr}
@item ^
@code{Symbol.operatorXor}
@item &
@code{Symbol.operatorAnd}
@item <<
@code{Symbol.operatorShl}
@item >>
@code{Symbol.operatorShr}
@item <
@code{Symbol.operatorCmpLT}
@item >
@code{Symbol.operatorCmpLT}, operands swapped
@item <=
@code{Symbol.operatorCmpLE}
@item >=
@code{Symbol.operatorCmpLE}, operands swapped
@item ==, !=
@code{Symbol.operatorCmpEQ}
@end table
The return value of @code{Symbol.operatorCmpLT}, @code{Symbol.operatorCmpLE} and
@code{Symbol.operatorCmpEQ} is converted to @code{Boolean}.
@section Builtin Object changes
@subsection @code{Symbol} constructor
The following global symbols are added for the operator overloading:
@table @code
@item operatorOrder
@item operatorAdd
@item operatorSub
@item operatorMul
@item operatorDiv
@item operatorMod
@item operatorPow
@item operatorShl
@item operatorShr
@item operatorAnd
@item operatorOr
@item operatorXor
@item operatorCmpLT
@item operatorCmpLE
@item operatorCmpEQ
@item operatorPlus
@item operatorNeg
@item operatorNot
@item operatorInc
@item operatorDec
@end table
@chapter The BigInt Mode
@section Introduction
The bigint mode is enabled with the @code{"use bigint"} directive. It
propagates the same way as the strict mode. In bigint mode, all
integers are considered as @code{bigint} (arbitrarily large integer,
similar to the TC39 BigInt
proposal@footnote{@url{https://tc39.github.io/proposal-bigint/}})
instead of @code{number} (floating point number). In order to be able
to exchange data between standard and bigint modes, numbers are
internally represented as 3 different types:
@itemize
@item Small integer (SmallInt): 32 bit integer@footnote{Could be extended to 53 bits without changing the principle.}.
@item Big integer (BigInt): arbitrarily large integer.
@item Floating point number (Float).
@end itemize
In standard mode, the semantics of each operation is modified so that
when it returns a @code{number}, it is either of SmallInt or
Float. But the difference between SmallInt and Float is not observable
in standard mode.
In bigint mode, each operation behaves differently whether its
operands are integer or float. The difference between SmallInt and
BigInt is not observable (i.e. they are both integers).
The following table summarizes the observable types:
@multitable @columnfractions .3 .3 .3
@headitem Internal type @tab Observable type@* (standard mode) @tab Observable type@* (bigint mode)
@item SmallInt @tab number @tab bigint
@item BigInt @tab bigint @tab bigint
@item Float @tab number @tab number
@end multitable
@section Changes that introduce incompatibilities with Javascript
@subsection Standard mode
There is no incompatibility with Javascript.
@subsection Bigint mode
The following changes are visible:
@itemize
@item Integer and Float are different types. Constants are typed. For example: @code{typeof 1.0 === "number"} and @code{typeof 1 === "bigint"}. Another consequence is that @code{1.0 === 1} is false.
@item The range of integers is unlimited. In standard mode: @code{2**53 + 1 === 2**53}. This is no longer true with the bignum extensions.
@item Binary bitwise operators do not truncate to 32 bits i.e. @code{0x800000000 | 1 === 0x800000001} while it gives @code{1} in standard mode.
@item Bitwise shift operators do not truncate to 32 bits and do not mask the shift count with @code{0x1f} i.e. @code{1 << 32 === 4294967296} while it gives @code{1} in standard mode. However, the @code{>>>} operator (unsigned right shift) which is useless with bignums keeps its standard mode behavior@footnote{The unsigned right right operator could be removed in bigint mode.}.
@item Operators with integer operands never return the minus zero floating point value as result. Hence @code{Object.is(0, -0) === true}. Use @code{-0.0} to create a minus zero floating point value.
@item The @code{ToPrimitive} abstract operation is called with the @code{"integer"} preferred type when an integer is required (e.g. for bitwise binary or shift operations).
@item The prototype of integers is no longer @code{Number.prototype}. Instead@* @code{Object.getPrototypeOf(1) === BigInt.prototype}. The prototype of floats remains Number.prototype.
@item If the TC39 BigInt proposal is supported, there is no observable difference between integers and @code{bigint}s.
@end itemize
@section Operators
@subsection Arithmetic operators
The operands are converted to number values as in normal
Javascript. Then the general case is that an Integer is returned if
both operands are Integer. Otherwise, a float is returned.
The @code{+} operator also accepts strings as input and behaves like
standard Javascript in this case.
The binary operator @code{%} returns the truncated remainder of the
division. When the result is an Integer type, a dividend of zero yields a
RangeError exception.
The binary operator @code{%} in math mode returns the Euclidian
remainder of the division i.e. it is always positive.
The binary operator @code{/} returns a float.
The binary operator @code{/} in math mode returns a float if one of
the operands is float. Otherwise, @code{BigInt[Symbol.operatorDiv]} is
invoked.
The returned type of @code{a ** b} is Float if @math{a} or @math{b}
are Float. If @math{a} and @math{b} are integers:
@itemize
@item @math{b < 0} returns a Float in bigint mode. In math mode, @code{BigInt[Symbol.operatorPow]} is invoked.
@item @math{b >= 0} returns an integer.
@end itemize
The unary @code{-} and unary @code{+} return the same type as their
operand. They performs no floating point rounding when the result is a
float.
The unary operators @code{++} and @code{--} return the same type as
their operand.
In standard mode:
If the operator returns an Integer and that the result fits a
SmallInt, it is converted to SmallInt. Otherwise, the Integer is
converted to a Float.
In bigint mode:
If the operator returns an Integer and that the result fits a
SmallInt, it is converted to SmallInt. Otherwise it is a BigInt.
@subsection Logical operators
In standard mode:
The operands have their standard behavior. If the result fits a
SmallInt it is converted to a SmallInt. Otherwise it is a Float.
In bigint mode:
The operands are converted to integer values. The floating point
values are converted to integer by rounding them to zero.
The logical operators are defined assuming the integers are
represented in two complement notation.
For @code{<<} and @code{<<}, the shift can be positive or negative. So
@code{a << b} is defined as @math{\lfloor a/2^{-b} \rfloor} and
@code{a >> b} is defined as @math{\lfloor a/2^{b} \rfloor}.
The operator @code{>>>} is supported for backward compatibility and
behaves the same way as Javascript i.e. implicit conversion to @code{Uint32}.
If the result fits a SmallInt it is converted to a SmallInt. Otherwise
it is a BigInt.
@subsection Relational operators
The relational operators <, <=, >, >=, ==, != work as expected with
integers and floating point numbers (e.g. @code{1.0 == 1} is true).
The strict equality operators === and !== have the usual Javascript
semantics. In particular, different types never equal, so @code{1.0
=== 1} is false.
@section Number literals
Number literals in bigint mode have a slightly different behavior than
in standard Javascript:
@enumerate
@item
A number literal without a decimal point or an exponent is considered
as an Integer. Otherwise it is a Float.
@item
Hexadecimal, octal or binary floating point literals are accepted with
a decimal point or an exponent. The exponent is specified with the
@code{p} letter assuming a base 2. The same convention is used by
C99. Example: @code{0x1p3} is the same as @code{8.0}.
@end enumerate
@section Builtin Object changes
@subsection @code{BigInt} function
The @code{BigInt} function cannot be invoked as a constructor. When
invoked as a function, it converts its first parameter to an
integer. When a floating point number is given as parameter, it is
truncated to an integer with infinite precision.
@code{BigInt} properties:
@table @code
@item asIntN(bits, a)
Set @math{b=a \pmod{2^{bits}}}. Return @math{b} if @math{b < 2^{bits-1}}
otherwise @math{b-2^{bits}}.
@item asUintN(bits, a)
Return @math{a \pmod{2^{bits}}}.
@item tdiv(a, b)
Return @math{trunc(a/b)}. @code{b = 0} raises a RangeError
@@ -410,58 +114,7 @@ Return the number of trailing zeros in the two's complement binary representatio
@end table
@subsection @code{BigInt.prototype}
It is a normal object.
@subsection @code{Number} constructor
The number constructor returns its argument rounded to a Float using
the global floating point environment. In bigint mode, the Number
constructor returns a Float. In standard mode, it returns a SmallInt
if the value fits it, otherwise a Float.
@subsection @code{Number.prototype}
The following properties are modified:
@table @code
@item toString(radix)
In bigint mode, integers are converted to the specified radix with
infinite precision.
@item toPrecision(p)
@item toFixed(p)
@item toExponential(p)
In bigint mode, integers are accepted and converted to string with
infinite precision.
@item parseInt(string, radix)
In bigint mode, an integer is returned and the conversion is done with
infinite precision.
@end table
@subsection @code{Math} object
The following properties are modified:
@table @code
@item abs(x)
Absolute value. Return an integer if @code{x} is an Integer. Otherwise
return a Float. No rounding is performed.
@item min(a, b)
@item max(a, b)
No rounding is performed. The returned type is the same one as the
minimum (resp. maximum) value.
@end table
@chapter Arbitrarily large floating point numbers
@chapter BigFloat
@section Introduction
@@ -590,6 +243,9 @@ point number @code{a} according to the floating point environment
@item trunc(x)
Round to an integer. No additional rounding is performed.
@item abs(x)
Return the absolute value of x. No additional rounding is performed.
@item fmod(x, y[, e])
@item remainder(x, y[, e])
Floating point remainder. The quotient is truncated to zero (fmod) or
@@ -620,6 +276,9 @@ number. @code{e} is an optional floating point environment.
The following properties are modified:
@table @code
@item valueOf()
Return the bigfloat primitive value corresponding to @code{this}.
@item toString(radix)
For floating point numbers:
@@ -636,13 +295,16 @@ the global precision and round to nearest gives the same number.
@end itemize
@item toPrecision(p[, rnd_mode])
@item toFixed(p[, rnd_mode])
@item toExponential(p[, rnd_mode])
The exponent letter is @code{e} for base 10, @code{p} for bases 2, 8,
16 with a binary exponent and @code{@@} for the other bases.
@item toPrecision(p, rnd_mode = BigFloatEnv.RNDNA, radix = 10)
@item toFixed(p, rnd_mode = BigFloatEnv.RNDNA, radix = 10)
@item toExponential(p, rnd_mode = BigFloatEnv.RNDNA, radix = 10)
Same semantics as the corresponding @code{Number} functions with
BigFloats. There is no limit on the accepted precision @code{p}. The
rounding mode can be optionally specified. It is set by default to
@code{BigFloatEnv.RNDNA}.
rounding mode and radix can be optionally specified. The radix must be
between 2 and 36.
@end table
@@ -679,13 +341,13 @@ subnormal flags is set to @code{false}. If @code{rndMode} is
@item prec
Getter. Return the precision in bits of the global floating point
environment. The initial value is @code{53}.
environment. The initial value is @code{113}.
@item expBits
Getter. Return the exponent size in bits of the global floating point
environment assuming an IEEE 754 representation. If @code{expBits <
expBitsMax}, then subnormal numbers are supported. The initial value
is @code{11}.
is @code{15}.
@item setPrec(f, p[, e])
Set the precision of the global floating point environment to @code{p}
@@ -693,15 +355,13 @@ and the exponent size to @code{e} then call the function
@code{f}. Then the Float precision and exponent size are reset to
their precious value and the return value of @code{f} is returned (or
an exception is raised if @code{f} raised an exception). If @code{e}
is @code{undefined} it is set to @code{BigFloatEnv.expBitsMax}. @code{p}
must be >= 53 and @code{e} must be >= 11 so that the global precision
is at least equivalent to the IEEE 754 64 bit doubles.
is @code{undefined} it is set to @code{BigFloatEnv.expBitsMax}.
@item precMin
Read-only integer. Return the minimum allowed precision. Must be at least 2.
@item precMax
Read-only integer. Return the maximum allowed precision. Must be at least 53.
Read-only integer. Return the maximum allowed precision. Must be at least 113.
@item expBitsMin
Read-only integer. Return the minimum allowed exponent size in
@@ -709,7 +369,7 @@ bits. Must be at least 3.
@item expBitsMax
Read-only integer. Return the maximum allowed exponent size in
bits. Must be at least 11.
bits. Must be at least 15.
@item RNDN
Read-only integer. Round to nearest, with ties to even rounding mode.
@@ -726,8 +386,8 @@ Read-only integer. Round to +Infinity rounding mode.
@item RNDNA
Read-only integer. Round to nearest, with ties away from zero rounding mode.
@item RNDNU
Read-only integer. Round to nearest, with ties to +Infinity rounding mode.
@item RNDA
Read-only integer. Round away from zero rounding mode.
@item RNDF@footnote{Could be removed in case a deterministic behavior for floating point operations is required.}
Read-only integer. Faithful rounding mode. The result is
@@ -767,69 +427,166 @@ Getter and setter (Boolean). Status flags.
@end table
@subsection @code{Math} object
@chapter BigDecimal
The following properties are modified:
This extension adds the @code{BigDecimal} primitive type. The
@code{BigDecimal} type represents floating point numbers in base
10. It is inspired from the proposal available at
@url{https://github.com/littledan/proposal-bigdecimal}.
The @code{BigDecimal} floating point numbers are always normalized and
finite. There is no concept of @code{-0}, @code{Infinity} or
@code{NaN}. By default, all the computations are done with infinite
precision.
@section Operators
The following builtin operators support BigDecimal:
@table @code
@item abs(x)
Absolute value. If @code{x} is a BigFloat, its absolute value is
returned as a BigFloat. No rounding is performed.
@item min(a, b)
@item max(a, b)
The returned type is the same one as the minimum (resp. maximum)
value, so @code{BigFloat} values are accepted. When a @code{BigFloat}
is returned, no rounding is performed.
@item +
@item -
@item *
Both operands must be BigDecimal. The result is computed with infinite
precision.
@item %
Both operands must be BigDecimal. The result is computed with infinite
precision. A range error is throws in case of division by zero.
@item /
Both operands must be BigDecimal. A range error is throws in case of
division by zero or if the result cannot be represented with infinite
precision (use @code{BigDecimal.div} to specify the rounding).
@item **
Both operands must be BigDecimal. The exponent must be a positive
integer. The result is computed with infinite precision.
@item ===
When one of the operand is a BigDecimal, return true if both operands
are a BigDecimal and if they are equal.
@item ==
@item !=
@item <=
@item >=
@item <
@item >
Numerical comparison. When one of the operand is not a BigDecimal, it is
converted to BigDecimal by using ToString(). Hence comparisons between
Number and BigDecimal do not use the exact mathematical value of the
Number value.
@end table
@section BigDecimal literals
BigDecimal literals are decimal floating point numbers with a trailing
@code{m} suffix.
@section Builtin Object changes
@subsection The @code{BigDecimal} function.
It returns @code{0m} if no parameter is provided. Otherwise the first
parameter is converted to a bigdecimal by using ToString(). Hence
Number value are not converted to their exact numerical value as
BigDecimal.
@subsection Properties of the @code{BigDecimal} object
@table @code
@item add(a, b[, e])
@item sub(a, b[, e])
@item mul(a, b[, e])
@item div(a, b[, e])
@item mod(a, b[, e])
@item sqrt(a, e)
@item round(a, e)
Perform the specified floating point operation and round the floating
point result according to the rounding object @code{e}. If the
rounding object is not present, the operation is executed with
infinite precision.
For @code{div}, a @code{RangeError} exception is thrown in case of
division by zero or if the result cannot be represented with infinite
precision if no rounding object is present.
For @code{sqrt}, a range error is thrown if @code{a} is less than
zero.
The rounding object must contain the following properties:
@code{roundingMode} is a string specifying the rounding mode
(@code{"floor"}, @code{"ceiling"}, @code{"down"}, @code{"up"},
@code{"half-even"}, @code{"half-up"}). Either
@code{maximumSignificantDigits} or @code{maximumFractionDigits} must
be present to specify respectively the number of significant digits
(must be >= 1) or the number of digits after the decimal point (must
be >= 0).
@end table
@subsection Properties of the @code{BigDecimal.prototype} object
@table @code
@item valueOf()
Return the bigdecimal primitive value corresponding to @code{this}.
@item toString()
Convert @code{this} to a string with infinite precision in base 10.
@item toPrecision(p, rnd_mode = "half-up")
@item toFixed(p, rnd_mode = "half-up")
@item toExponential(p, rnd_mode = "half-up")
Convert the BigDecimal @code{this} to string with the specified
precision @code{p}. There is no limit on the accepted precision
@code{p}. The rounding mode can be optionally
specified. @code{toPrecision} outputs either in decimal fixed notation
or in decimal exponential notation with a @code{p} digits of
precision. @code{toExponential} outputs in decimal exponential
notation with @code{p} digits after the decimal point. @code{toFixed}
outputs in decimal notation with @code{p} digits after the decimal
point.
@end table
@chapter Math mode
@section Introduction
A new @emph{math mode} is enabled with the @code{"use math"}
directive. @code{"use bigint"} is implied in math mode. With this
mode, writing mathematical expressions is more intuitive, exact
results (e.g. fractions) can be computed for all operators and floating
point literals have the @code{BigFloat} type by default.
directive. It propagates the same way as the @emph{strict mode}. It is
designed so that arbitrarily large integers and floating point numbers
are available by default. In order to minimize the number of changes
in the Javascript semantics, integers are represented either as Number
or BigInt depending on their magnitude. Floating point numbers are
always represented as BigFloat.
It propagates the same way as the @emph{strict mode}. In
this mode:
The following changes are made to the Javascript semantics:
@itemize
@item The @code{^} operator is a similar to the power operator (@code{**}).
@item Floating point literals (i.e. number with a decimal point or an exponent) are @code{BigFloat} by default (i.e. a @code{l} suffix is implied). Hence @code{typeof 1.0 === "bigfloat"}.
@item Integer literals (i.e. numbers without a decimal point or an exponent) with or without the @code{n} suffix are @code{BigInt} if their value cannot be represented as a safe integer. A safe integer is defined as a integer whose absolute value is smaller or equal to @code{2**53-1}. Hence @code{typeof 1 === "number "}, @code{typeof 1n === "number"} but @code{typeof 9007199254740992 === "bigint" }.
@item All the bigint builtin operators and functions are modified so that their result is returned as a Number if it is a safe integer. Otherwise the result stays a BigInt.
@item The builtin operators are modified so that they return an exact result (which can be a BigInt) if their operands are safe integers. Operands between Number and BigInt are accepted provided the Number operand is a safe integer. The integer power with a negative exponent returns a BigFloat as result. The integer division returns a BigFloat as result.
@item The @code{^} operator is an alias to the power operator (@code{**}).
@item The power operator (both @code{^} and @code{**}) grammar is modified so that @code{-2^2} is allowed and yields @code{-4}.
@item The logical xor operator is still available with the @code{^^} operator.
@item The division operator invokes @code{BigInt[Symbol.operatorDiv]} in case both operands are integers.
@item The integer division operator can be overloaded by modifying the corresponding operator in @code{BigInt.prototype.[[OperatorSet]]}.
@item The power operator invokes @code{BigInt[Symbol.operatorPow]} in case both operands are integers and the exponent is strictly negative.
@item The integer power operator with a non zero negative exponent can be overloaded by modifying the corresponding operator in @code{BigInt.prototype.[[OperatorSet]]}.
@item The modulo operator returns the Euclidian remainder (always positive) instead of the truncated remainder.
@item Floating point literals are @code{BigFloat} by default (i.e. a @code{l} suffix is implied).
@item The modulo operator (@code{%}) returns the Euclidian remainder (always positive) instead of the truncated remainder.
@end itemize
@section Builtin Object changes
@subsection @code{Symbol} constructor
The following global symbol is added for the operator overloading:
@table @code
@item operatorMathMod
@end table
@section Remaining issues
@enumerate
@item A new floating point literal suffix could be added for @code{Number} literals.
@end enumerate
@bye

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@@ -1,7 +1,8 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Created by GNU Texinfo 6.1, http://www.gnu.org/software/texinfo/ -->
<!-- Created by GNU Texinfo 6.5, http://www.gnu.org/software/texinfo/ -->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>QuickJS Javascript Engine</title>
<meta name="description" content="QuickJS Javascript Engine">
@@ -9,7 +10,6 @@
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="#SEC_Contents" rel="contents" title="Table of Contents">
<style type="text/css">
<!--
@@ -206,7 +206,7 @@ Javascript files and/or expressions as arguments to execute them:
<a name="qjs-interpreter"></a>
<h4 class="subsection">2.3.1 <code>qjs</code> interpreter</h4>
<pre class="verbatim">usage: qjs [options] [files]
<pre class="verbatim">usage: qjs [options] [file [args]]
</pre>
<p>Options are:
</p><dl compact="compact">
@@ -241,6 +241,11 @@ source is <code>import</code>.
the <code>&quot;use bigint&quot;</code> and <code>&quot;use math&quot;</code> directives.
</p>
</dd>
<dt><code>-I file</code></dt>
<dt><code>--include file</code></dt>
<dd><p>Include an additional file.
</p>
</dd>
</dl>
<p>Advanced options are:
@@ -767,6 +772,10 @@ pathname of <code>path</code> and <code>err</code> the error code.
and <code>err</code> the error code.
</p>
</dd>
<dt><code>chdir(path)</code></dt>
<dd><p>Change the current directory. Return the error code.
</p>
</dd>
<dt><code>mkdir(path, mode = 0o777)</code></dt>
<dd><p>Create a directory at <code>path</code>. Return the error code.
</p>

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@@ -92,7 +92,7 @@ generates a @code{hello} executable with no external dependency.
@subsection @code{qjs} interpreter
@verbatim
usage: qjs [options] [files]
usage: qjs [options] [file [args]]
@end verbatim
Options are:
@@ -122,6 +122,10 @@ Load as ES6 script (default=autodetect).
Enable the bignum extensions: BigDecimal object, BigFloat object and
the @code{"use bigint"} and @code{"use math"} directives.
@item -I file
@item --include file
Include an additional file.
@end table
Advanced options are:
@@ -576,6 +580,9 @@ pathname of @code{path} and @code{err} the error code.
Return @code{[str, err]} where @code{str} is the current working directory
and @code{err} the error code.
@item chdir(path)
Change the current directory. Return the error code.
@item mkdir(path, mode = 0o777)
Create a directory at @code{path}. Return the error code.