bellard
2 years ago
23 changed files with 1870 additions and 4294 deletions
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<head> |
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<title>Javascript Bignum Extensions</title> |
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<meta name="description" content="Javascript Bignum Extensions"> |
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<meta name="keywords" content="Javascript Bignum Extensions"> |
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<link href="#SEC_Contents" rel="contents" title="Table of Contents"> |
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</head> |
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<body lang="en"> |
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<h1 class="settitle" align="center">Javascript Bignum Extensions</h1> |
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<a name="SEC_Contents"></a> |
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<h2 class="contents-heading">Table of Contents</h2> |
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|
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<div class="contents"> |
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<ul class="no-bullet"> |
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<li><a name="toc-Introduction" href="#Introduction">1 Introduction</a></li> |
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<li><a name="toc-Operator-overloading" href="#Operator-overloading">2 Operator overloading</a></li> |
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<li><a name="toc-BigInt-extensions" href="#BigInt-extensions">3 BigInt extensions</a></li> |
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<li><a name="toc-BigFloat" href="#BigFloat">4 BigFloat</a> |
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<ul class="no-bullet"> |
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<li><a name="toc-Introduction-1" href="#Introduction-1">4.1 Introduction</a></li> |
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<li><a name="toc-Floating-point-rounding" href="#Floating-point-rounding">4.2 Floating point rounding</a></li> |
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<li><a name="toc-Operators" href="#Operators">4.3 Operators</a></li> |
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<li><a name="toc-BigFloat-literals" href="#BigFloat-literals">4.4 BigFloat literals</a></li> |
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<li><a name="toc-Builtin-Object-changes" href="#Builtin-Object-changes">4.5 Builtin Object changes</a> |
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<ul class="no-bullet"> |
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<li><a name="toc-BigFloat-function" href="#BigFloat-function">4.5.1 <code>BigFloat</code> function</a></li> |
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<li><a name="toc-BigFloat_002eprototype" href="#BigFloat_002eprototype">4.5.2 <code>BigFloat.prototype</code></a></li> |
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<li><a name="toc-BigFloatEnv-constructor" href="#BigFloatEnv-constructor">4.5.3 <code>BigFloatEnv</code> constructor</a></li> |
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</ul></li> |
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</ul></li> |
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<li><a name="toc-BigDecimal" href="#BigDecimal">5 BigDecimal</a> |
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<ul class="no-bullet"> |
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<li><a name="toc-Operators-1" href="#Operators-1">5.1 Operators</a></li> |
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<li><a name="toc-BigDecimal-literals" href="#BigDecimal-literals">5.2 BigDecimal literals</a></li> |
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<li><a name="toc-Builtin-Object-changes-1" href="#Builtin-Object-changes-1">5.3 Builtin Object changes</a> |
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<ul class="no-bullet"> |
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<li><a name="toc-The-BigDecimal-function_002e" href="#The-BigDecimal-function_002e">5.3.1 The <code>BigDecimal</code> function.</a></li> |
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<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> |
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<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> |
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</ul></li> |
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</ul></li> |
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<li><a name="toc-Math-mode" href="#Math-mode">6 Math mode</a></li> |
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|
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</ul> |
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</div> |
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|
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|
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<a name="Introduction"></a> |
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<h2 class="chapter">1 Introduction</h2> |
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|
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<p>The Bignum extensions add the following features to the Javascript |
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language while being 100% backward compatible: |
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</p> |
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<ul> |
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<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>. |
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|
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</li><li> Arbitrarily large floating point numbers (<code>BigFloat</code>) in base 2 using the IEEE 754 semantics. |
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|
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</li><li> Arbitrarily large floating point numbers (<code>BigDecimal</code>) in base 10 based on the proposal available at |
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<a href="https://github.com/littledan/proposal-bigdecimal">https://github.com/littledan/proposal-bigdecimal</a>. |
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|
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</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 |
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remainder. <code>^</code> is an alias to the power operator |
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(<code>**</code>). <code>^^</code> is used as the exclusive or operator. |
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|
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</li></ul> |
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|
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<p>The extensions are independent from each other except the <code>math</code> |
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mode which relies on BigFloat and operator overloading. |
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</p> |
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<a name="Operator-overloading"></a> |
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<h2 class="chapter">2 Operator overloading</h2> |
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|
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<p>Operator overloading is inspired from the proposal available at |
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<a href="https://github.com/tc39/proposal-operator-overloading/">https://github.com/tc39/proposal-operator-overloading/</a>. It |
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implements the same dispatch logic but finds the operator sets by |
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looking at the <code>Symbol.operatorSet</code> property in the objects. The |
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changes were done in order to simplify the implementation. |
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</p> |
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<p>More precisely, the following modifications were made: |
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</p> |
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<ul> |
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<li> <code>with operators from</code> is not supported. Operator overloading is always enabled. |
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|
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</li><li> The dispatch is not based on a static <code>[[OperatorSet]]</code> field in all instances. Instead, a dynamic lookup of the <code>Symbol.operatorSet</code> property is done. This property is typically added in the prototype of each object. |
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|
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</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. |
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|
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</li><li> <code>[]</code> cannot be overloaded. |
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</li><li> In math mode, the BigInt division and power operators can be overloaded with <code>Operators.updateBigIntOperators(dictionary)</code>. |
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</li></ul> |
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|
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<a name="BigInt-extensions"></a> |
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<h2 class="chapter">3 BigInt extensions</h2> |
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|
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<p>A few properties are added to the BigInt object: |
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</p> |
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<dl compact="compact"> |
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<dt><code>tdiv(a, b)</code></dt> |
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<dd><p>Return <em>trunc(a/b)</em>. <code>b = 0</code> raises a RangeError |
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exception. |
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</p> |
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</dd> |
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<dt><code>fdiv(a, b)</code></dt> |
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<dd><p>Return <em>\lfloor a/b \rfloor</em>. <code>b = 0</code> raises a RangeError |
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exception. |
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</p> |
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</dd> |
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<dt><code>cdiv(a, b)</code></dt> |
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<dd><p>Return <em>\lceil a/b \rceil</em>. <code>b = 0</code> raises a RangeError |
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exception. |
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</p> |
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</dd> |
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<dt><code>ediv(a, b)</code></dt> |
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<dd><p>Return <em>sgn(b) \lfloor a/{|b|} \rfloor</em> (Euclidian |
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division). <code>b = 0</code> raises a RangeError exception. |
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</p> |
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</dd> |
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<dt><code>tdivrem(a, b)</code></dt> |
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<dt><code>fdivrem(a, b)</code></dt> |
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<dt><code>cdivrem(a, b)</code></dt> |
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<dt><code>edivrem(a, b)</code></dt> |
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<dd><p>Return an array of two elements. The first element is the quotient, |
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the second is the remainder. The same rounding is done as the |
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corresponding division operation. |
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</p> |
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</dd> |
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<dt><code>sqrt(a)</code></dt> |
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<dd><p>Return <em>\lfloor \sqrt(a) \rfloor</em>. A RangeError exception is |
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raised if <em>a < 0</em>. |
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</p> |
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</dd> |
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<dt><code>sqrtrem(a)</code></dt> |
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<dd><p>Return an array of two elements. The first element is <em>\lfloor |
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\sqrt{a} \rfloor</em>. The second element is <em>a-\lfloor \sqrt{a} |
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\rfloor^2</em>. A RangeError exception is raised if <em>a < 0</em>. |
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</p> |
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</dd> |
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<dt><code>floorLog2(a)</code></dt> |
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<dd><p>Return -1 if <em>a \leq 0</em> otherwise return <em>\lfloor \log2(a) \rfloor</em>. |
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</p> |
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</dd> |
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<dt><code>ctz(a)</code></dt> |
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<dd><p>Return the number of trailing zeros in the two’s complement binary representation of a. Return -1 if <em>a=0</em>. |
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</p> |
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</dd> |
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</dl> |
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|
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<a name="BigFloat"></a> |
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<h2 class="chapter">4 BigFloat</h2> |
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|
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<a name="Introduction-1"></a> |
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<h3 class="section">4.1 Introduction</h3> |
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|
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<p>This extension adds the <code>BigFloat</code> primitive type. The |
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<code>BigFloat</code> type represents floating point numbers in base 2 |
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with the IEEE 754 semantics. A floating |
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point number is represented as a sign, mantissa and exponent. The |
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special values <code>NaN</code>, <code>+/-Infinity</code>, <code>+0</code> and <code>-0</code> |
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are supported. The mantissa and exponent can have any bit length with |
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an implementation specific minimum and maximum. |
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</p> |
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<a name="Floating-point-rounding"></a> |
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<h3 class="section">4.2 Floating point rounding</h3> |
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|
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<p>Each floating point operation operates with infinite precision and |
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then rounds the result according to the specified floating point |
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environment (<code>BigFloatEnv</code> object). The status flags of the |
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environment are also set according to the result of the operation. |
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</p> |
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<p>If no floating point environment is provided, the global floating |
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point environment is used. |
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</p> |
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<p>The rounding mode of the global floating point environment is always |
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<code>RNDN</code> (“round to nearest with ties to even”)<a name="DOCF1" href="#FOOT1"><sup>1</sup></a>. The status flags of the global environment cannot be |
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read<a name="DOCF2" href="#FOOT2"><sup>2</sup></a>. The precision of the global environment is |
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<code>BigFloatEnv.prec</code>. The number of exponent bits of the global |
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environment is <code>BigFloatEnv.expBits</code>. The global environment |
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subnormal flag is set to <code>true</code>. |
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</p> |
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<p>For example, <code>prec = 53</code> and <code> expBits = 11</code> exactly give |
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the same precision as the IEEE 754 64 bit floating point format. The |
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default precision is <code>prec = 113</code> and <code> expBits = 15</code> (IEEE |
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754 128 bit floating point format). |
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</p> |
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<p>The global floating point environment can only be modified temporarily |
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when calling a function (see <code>BigFloatEnv.setPrec</code>). Hence a |
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function can change the global floating point environment for its |
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callees but not for its caller. |
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</p> |
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<a name="Operators"></a> |
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<h3 class="section">4.3 Operators</h3> |
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|
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<p>The builtin operators are extended so that a BigFloat is returned if |
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at least one operand is a BigFloat. The computations are always done |
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with infinite precision and rounded according to the global floating |
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point environment. |
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</p> |
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<p><code>typeof</code> applied on a <code>BigFloat</code> returns <code>bigfloat</code>. |
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</p> |
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<p>BigFloat can be compared with all the other numeric types and the |
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result follows the expected mathematical relations. |
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</p> |
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<p>However, since BigFloat and Number are different types they are never |
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equal when using the strict comparison operators (e.g. <code>0.0 === |
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0.0l</code> is false). |
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</p> |
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<a name="BigFloat-literals"></a> |
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<h3 class="section">4.4 BigFloat literals</h3> |
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|
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<p>BigFloat literals are floating point numbers with a trailing <code>l</code> |
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suffix. BigFloat literals have an infinite precision. They are rounded |
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according to the global floating point environment when they are |
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evaluated.<a name="DOCF3" href="#FOOT3"><sup>3</sup></a> |
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</p> |
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<a name="Builtin-Object-changes"></a> |
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<h3 class="section">4.5 Builtin Object changes</h3> |
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|
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<a name="BigFloat-function"></a> |
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<h4 class="subsection">4.5.1 <code>BigFloat</code> function</h4> |
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|
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<p>The <code>BigFloat</code> function cannot be invoked as a constructor. When |
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invoked as a function: the parameter is converted to a primitive |
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type. If the result is a numeric type, it is converted to BigFloat |
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without rounding. If the result is a string, it is converted to |
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BigFloat using the precision of the global floating point environment. |
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</p> |
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<p><code>BigFloat</code> properties: |
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</p> |
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<dl compact="compact"> |
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<dt><code>LN2</code></dt> |
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<dt><code>PI</code></dt> |
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<dd><p>Getter. Return the value of the corresponding mathematical constant |
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rounded to nearest, ties to even with the current global |
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precision. The constant values are cached for small precisions. |
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</p> |
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</dd> |
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<dt><code>MIN_VALUE</code></dt> |
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<dt><code>MAX_VALUE</code></dt> |
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<dt><code>EPSILON</code></dt> |
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<dd><p>Getter. Return the minimum, maximum and epsilon <code>BigFloat</code> values |
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(same definition as the corresponding <code>Number</code> constants). |
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</p> |
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</dd> |
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<dt><code>fpRound(a[, e])</code></dt> |
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<dd><p>Round the floating point number <code>a</code> according to the floating |
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point environment <code>e</code> or the global environment if <code>e</code> is |
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undefined. |
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</p> |
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</dd> |
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<dt><code>parseFloat(a[, radix[, e]])</code></dt> |
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<dd><p>Parse the string <code>a</code> as a floating point number in radix |
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<code>radix</code>. The radix is 0 (default) or from 2 to 36. The radix 0 |
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means radix 10 unless there is a hexadecimal or binary prefix. The |
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result is rounded according to the floating point environment <code>e</code> |
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or the global environment if <code>e</code> is undefined. |
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</p> |
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</dd> |
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<dt><code>isFinite(a)</code></dt> |
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<dd><p>Return true if <code>a</code> is a finite bigfloat. |
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</p> |
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</dd> |
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<dt><code>isNaN(a)</code></dt> |
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<dd><p>Return true if <code>a</code> is a NaN bigfloat. |
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</p> |
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</dd> |
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<dt><code>add(a, b[, e])</code></dt> |
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<dt><code>sub(a, b[, e])</code></dt> |
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<dt><code>mul(a, b[, e])</code></dt> |
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<dt><code>div(a, b[, e])</code></dt> |
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<dd><p>Perform the specified floating point operation and round the floating |
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point number <code>a</code> according to the floating point environment |
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<code>e</code> or the global environment if <code>e</code> is undefined. If |
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<code>e</code> is specified, the floating point status flags are updated. |
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</p> |
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</dd> |
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<dt><code>floor(x)</code></dt> |
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<dt><code>ceil(x)</code></dt> |
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<dt><code>round(x)</code></dt> |
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<dt><code>trunc(x)</code></dt> |
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<dd><p>Round to an integer. No additional rounding is performed. |
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</p> |
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</dd> |
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<dt><code>abs(x)</code></dt> |
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<dd><p>Return the absolute value of x. No additional rounding is performed. |
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</p> |
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</dd> |
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<dt><code>fmod(x, y[, e])</code></dt> |
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<dt><code>remainder(x, y[, e])</code></dt> |
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<dd><p>Floating point remainder. The quotient is truncated to zero (fmod) or |
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to the nearest integer with ties to even (remainder). <code>e</code> is an |
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optional floating point environment. |
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</p> |
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</dd> |
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<dt><code>sqrt(x[, e])</code></dt> |
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<dd><p>Square root. Return a rounded floating point number. <code>e</code> is an |
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optional floating point environment. |
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</p> |
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</dd> |
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<dt><code>sin(x[, e])</code></dt> |
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<dt><code>cos(x[, e])</code></dt> |
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<dt><code>tan(x[, e])</code></dt> |
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<dt><code>asin(x[, e])</code></dt> |
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<dt><code>acos(x[, e])</code></dt> |
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<dt><code>atan(x[, e])</code></dt> |
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<dt><code>atan2(x, y[, e])</code></dt> |
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<dt><code>exp(x[, e])</code></dt> |
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<dt><code>log(x[, e])</code></dt> |
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<dt><code>pow(x, y[, e])</code></dt> |
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<dd><p>Transcendental operations. Return a rounded floating point |
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number. <code>e</code> is an optional floating point environment. |
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</p> |
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</dd> |
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</dl> |
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|
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<a name="BigFloat_002eprototype"></a> |
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<h4 class="subsection">4.5.2 <code>BigFloat.prototype</code></h4> |
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|
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<p>The following properties are modified: |
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</p> |
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<dl compact="compact"> |
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<dt><code>valueOf()</code></dt> |
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<dd><p>Return the bigfloat primitive value corresponding to <code>this</code>. |
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</p> |
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</dd> |
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<dt><code>toString(radix)</code></dt> |
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<dd> |
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<p>For floating point numbers: |
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</p> |
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<ul> |
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<li> If the radix is a power of two, the conversion is done with infinite |
||||
precision. |
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</li><li> Otherwise, the number is rounded to nearest with ties to even using |
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the global precision. It is then converted to string using the minimum |
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number of digits so that its conversion back to a floating point using |
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the global precision and round to nearest gives the same number. |
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|
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</li></ul> |
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|
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<p>The exponent letter is <code>e</code> for base 10, <code>p</code> for bases 2, 8, |
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16 with a binary exponent and <code>@</code> for the other bases. |
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</p> |
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</dd> |
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<dt><code>toPrecision(p, rnd_mode = BigFloatEnv.RNDNA, radix = 10)</code></dt> |
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<dt><code>toFixed(p, rnd_mode = BigFloatEnv.RNDNA, radix = 10)</code></dt> |
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<dt><code>toExponential(p, rnd_mode = BigFloatEnv.RNDNA, radix = 10)</code></dt> |
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<dd><p>Same semantics as the corresponding <code>Number</code> functions with |
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BigFloats. There is no limit on the accepted precision <code>p</code>. The |
||||
rounding mode and radix can be optionally specified. The radix must be |
||||
between 2 and 36. |
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</p> |
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</dd> |
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</dl> |
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|
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<a name="BigFloatEnv-constructor"></a> |
||||
<h4 class="subsection">4.5.3 <code>BigFloatEnv</code> constructor</h4> |
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|
||||
<p>The <code>BigFloatEnv([p, [,rndMode]]</code> constructor cannot be invoked as a |
||||
function. The floating point environment contains: |
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</p> |
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<ul> |
||||
<li> the mantissa precision in bits |
||||
|
||||
</li><li> the exponent size in bits assuming an IEEE 754 representation; |
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|
||||
</li><li> the subnormal flag (if true, subnormal floating point numbers can |
||||
be generated by the floating point operations). |
||||
|
||||
</li><li> the rounding mode |
||||
|
||||
</li><li> the floating point status. The status flags can only be set by the floating point operations. They can be reset with <code>BigFloatEnv.prototype.clearStatus()</code> or with the various status flag setters. |
||||
|
||||
</li></ul> |
||||
|
||||
<p><code>new BigFloatEnv([p, [,rndMode]]</code> creates a new floating point |
||||
environment. The status flags are reset. If no parameter is given the |
||||
precision, exponent bits and subnormal flags are copied from the |
||||
global floating point environment. Otherwise, the precision is set to |
||||
<code>p</code>, the number of exponent bits is set to <code>expBitsMax</code> and the |
||||
subnormal flags is set to <code>false</code>. If <code>rndMode</code> is |
||||
<code>undefined</code>, the rounding mode is set to <code>RNDN</code>. |
||||
</p> |
||||
<p><code>BigFloatEnv</code> properties: |
||||
</p> |
||||
<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>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. The initial value is |
||||
<code>15</code>. |
||||
</p> |
||||
</dd> |
||||
<dt><code>setPrec(f, p[, e])</code></dt> |
||||
<dd><p>Set the precision of the global floating point environment to <code>p</code> |
||||
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>. |
||||
</p> |
||||
</dd> |
||||
<dt><code>precMin</code></dt> |
||||
<dd><p>Read-only integer. Return the minimum allowed precision. Must be at least 2. |
||||
</p> |
||||
</dd> |
||||
<dt><code>precMax</code></dt> |
||||
<dd><p>Read-only integer. Return the maximum allowed precision. Must be at least 113. |
||||
</p> |
||||
</dd> |
||||
<dt><code>expBitsMin</code></dt> |
||||
<dd><p>Read-only integer. Return the minimum allowed exponent size in |
||||
bits. Must be at least 3. |
||||
</p> |
||||
</dd> |
||||
<dt><code>expBitsMax</code></dt> |
||||
<dd><p>Read-only integer. Return the maximum allowed exponent size in |
||||
bits. Must be at least 15. |
||||
</p> |
||||
</dd> |
||||
<dt><code>RNDN</code></dt> |
||||
<dd><p>Read-only integer. Round to nearest, with ties to even rounding mode. |
||||
</p> |
||||
</dd> |
||||
<dt><code>RNDZ</code></dt> |
||||
<dd><p>Read-only integer. Round to zero rounding mode. |
||||
</p> |
||||
</dd> |
||||
<dt><code>RNDD</code></dt> |
||||
<dd><p>Read-only integer. Round to -Infinity rounding mode. |
||||
</p> |
||||
</dd> |
||||
<dt><code>RNDU</code></dt> |
||||
<dd><p>Read-only integer. Round to +Infinity rounding mode. |
||||
</p> |
||||
</dd> |
||||
<dt><code>RNDNA</code></dt> |
||||
<dd><p>Read-only integer. Round to nearest, with ties away from zero rounding mode. |
||||
</p> |
||||
</dd> |
||||
<dt><code>RNDA</code></dt> |
||||
<dd><p>Read-only integer. Round away from zero rounding mode. |
||||
</p> |
||||
</dd> |
||||
<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 |
||||
floating point operations. |
||||
</p> |
||||
</dd> |
||||
</dl> |
||||
|
||||
<p><code>BigFloatEnv.prototype</code> properties: |
||||
</p> |
||||
<dl compact="compact"> |
||||
<dt><code>prec</code></dt> |
||||
<dd><p>Getter and setter (Integer). Return or set the precision in bits. |
||||
</p> |
||||
</dd> |
||||
<dt><code>expBits</code></dt> |
||||
<dd><p>Getter and setter (Integer). Return or set the exponent size in bits |
||||
assuming an IEEE 754 representation. |
||||
</p> |
||||
</dd> |
||||
<dt><code>rndMode</code></dt> |
||||
<dd><p>Getter and setter (Integer). Return or set the rounding mode. |
||||
</p> |
||||
</dd> |
||||
<dt><code>subnormal</code></dt> |
||||
<dd><p>Getter and setter (Boolean). subnormal flag. It is false when |
||||
<code>expBits = expBitsMax</code>. |
||||
</p> |
||||
</dd> |
||||
<dt><code>clearStatus()</code></dt> |
||||
<dd><p>Clear the status flags. |
||||
</p> |
||||
</dd> |
||||
<dt><code>invalidOperation</code></dt> |
||||
<dt><code>divideByZero</code></dt> |
||||
<dt><code>overflow</code></dt> |
||||
<dt><code>underflow</code></dt> |
||||
<dt><code>inexact</code></dt> |
||||
<dd><p>Getter and setter (Boolean). Status flags. |
||||
</p> |
||||
</dd> |
||||
</dl> |
||||
|
||||
<a name="BigDecimal"></a> |
||||
<h2 class="chapter">5 BigDecimal</h2> |
||||
|
||||
<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>+</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>/</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><=</code></dt> |
||||
<dt><code>>=</code></dt> |
||||
<dt><code><</code></dt> |
||||
<dt><code>></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 values 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>"floor"</code>, <code>"ceiling"</code>, <code>"down"</code>, <code>"up"</code>, |
||||
<code>"half-even"</code>, <code>"half-up"</code>). Either |
||||
<code>maximumSignificantDigits</code> or <code>maximumFractionDigits</code> 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). |
||||
</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 = "half-up")</code></dt> |
||||
<dt><code>toFixed(p, rnd_mode = "half-up")</code></dt> |
||||
<dt><code>toExponential(p, rnd_mode = "half-up")</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">6 Math mode</h2> |
||||
|
||||
<p>A new <em>math mode</em> is enabled with the <code>"use math"</code> |
||||
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>The following changes are made to the Javascript semantics: |
||||
</p> |
||||
<ul> |
||||
<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 === "bigfloat"</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 === "number "</code>, <code>typeof 1n === "number"</code> but <code>typeof 9007199254740992 === "bigint" </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 modulo operator (<code>%</code>) returns the Euclidian remainder (always positive) instead of the truncated remainder. |
||||
|
||||
</li><li> The integer division operator can be overloaded with <code>Operators.updateBigIntOperators(dictionary)</code>. |
||||
|
||||
</li><li> The integer power operator with a non zero negative exponent can be overloaded with <code>Operators.updateBigIntOperators(dictionary)</code>. |
||||
|
||||
</li></ul> |
||||
|
||||
<div class="footnote"> |
||||
<hr> |
||||
<h4 class="footnotes-heading">Footnotes</h4> |
||||
|
||||
<h3><a name="FOOT1" href="#DOCF1">(1)</a></h3> |
||||
<p>The |
||||
rationale is that the rounding mode changes must always be |
||||
explicit.</p> |
||||
<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="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="FOOT4" href="#DOCF4">(4)</a></h3> |
||||
<p>Could be removed in case a deterministic behavior for floating point operations is required.</p> |
||||
</div> |
||||
<hr> |
||||
|
||||
|
||||
|
||||
</body> |
||||
</html> |
||||
Binary file not shown.
Binary file not shown.
@ -1,918 +0,0 @@
|
||||
/*
|
||||
* Javascript Compressor |
||||
*
|
||||
* Copyright (c) 2008-2018 Fabrice Bellard |
||||
* Copyright (c) 2017-2018 Charlie Gordon |
||||
* |
||||
* Permission is hereby granted, free of charge, to any person obtaining a copy |
||||
* of this software and associated documentation files (the "Software"), to deal |
||||
* in the Software without restriction, including without limitation the rights |
||||
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
||||
* copies of the Software, and to permit persons to whom the Software is |
||||
* furnished to do so, subject to the following conditions: |
||||
* |
||||
* The above copyright notice and this permission notice shall be included in |
||||
* all copies or substantial portions of the Software. |
||||
* |
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
||||
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
||||
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL |
||||
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
||||
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
||||
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
||||
* THE SOFTWARE. |
||||
*/ |
||||
#include <stdlib.h> |
||||
#include <stdio.h> |
||||
#include <getopt.h> |
||||
#include <stdarg.h> |
||||
#include <string.h> |
||||
#include <inttypes.h> |
||||
#include <unistd.h> |
||||
|
||||
#include "cutils.h" |
||||
|
||||
typedef struct JSToken { |
||||
int tok; |
||||
char buf[20]; |
||||
char *str; |
||||
int len; |
||||
int size; |
||||
int line_num; /* line number for start of token */ |
||||
int lines; /* number of embedded linefeeds in token */ |
||||
} JSToken; |
||||
|
||||
enum { |
||||
TOK_EOF = 256, |
||||
TOK_IDENT, |
||||
TOK_STR1, |
||||
TOK_STR2, |
||||
TOK_STR3, |
||||
TOK_NUM, |
||||
TOK_COM, |
||||
TOK_LCOM, |
||||
}; |
||||
|
||||
void tok_reset(JSToken *tt) |
||||
{ |
||||
if (tt->str != tt->buf) { |
||||
free(tt->str); |
||||
tt->str = tt->buf; |
||||
tt->size = sizeof(tt->buf); |
||||
} |
||||
tt->len = 0; |
||||
} |
||||
|
||||
void tok_add_ch(JSToken *tt, int c) |
||||
{ |
||||
if (tt->len + 1 > tt->size) { |
||||
tt->size *= 2; |
||||
if (tt->str == tt->buf) { |
||||
tt->str = malloc(tt->size); |
||||
memcpy(tt->str, tt->buf, tt->len); |
||||
} else { |
||||
tt->str = realloc(tt->str, tt->size); |
||||
} |
||||
} |
||||
tt->str[tt->len++] = c; |
||||
} |
||||
|
||||
FILE *infile; |
||||
const char *filename; |
||||
int output_line_num; |
||||
int line_num; |
||||
int ch; |
||||
JSToken tokc; |
||||
|
||||
int skip_mask; |
||||
#define DEFINE_MAX 20 |
||||
char *define_tab[DEFINE_MAX]; |
||||
int define_len; |
||||
|
||||
void error(const char *fmt, ...) |
||||
{ |
||||
va_list ap; |
||||
va_start(ap, fmt); |
||||
if (filename) { |
||||
fprintf(stderr, "%s:%d: ", filename, line_num); |
||||
} else { |
||||
fprintf(stderr, "jscompress: "); |
||||
} |
||||
vfprintf(stderr, fmt, ap); |
||||
fprintf(stderr, "\n"); |
||||
va_end(ap); |
||||
exit(1); |
||||
} |
||||
|
||||
void define_symbol(const char *def) |
||||
{ |
||||
int i; |
||||
for (i = 0; i < define_len; i++) { |
||||
if (!strcmp(tokc.str, define_tab[i])) |
||||
return; |
||||
} |
||||
if (define_len >= DEFINE_MAX) |
||||
error("too many defines"); |
||||
define_tab[define_len++] = strdup(def); |
||||
} |
||||
|
||||
void undefine_symbol(const char *def) |
||||
{ |
||||
int i, j; |
||||
for (i = j = 0; i < define_len; i++) { |
||||
if (!strcmp(tokc.str, define_tab[i])) { |
||||
free(define_tab[i]); |
||||
} else { |
||||
define_tab[j++] = define_tab[i]; |
||||
} |
||||
} |
||||
define_len = j; |
||||
} |
||||
|
||||
const char *find_symbol(const char *def) |
||||
{ |
||||
int i; |
||||
for (i = 0; i < define_len; i++) { |
||||
if (!strcmp(tokc.str, define_tab[i])) |
||||
return "1"; |
||||
} |
||||
return NULL; |
||||
} |
||||
|
||||
void next(void); |
||||
|
||||
void nextch(void) |
||||
{ |
||||
ch = fgetc(infile); |
||||
if (ch == '\n') |
||||
line_num++; |
||||
} |
||||
|
||||
int skip_blanks(void) |
||||
{ |
||||
for (;;) { |
||||
next(); |
||||
if (tokc.tok != ' ' && tokc.tok != '\t' && |
||||
tokc.tok != TOK_COM && tokc.tok != TOK_LCOM) |
||||
return tokc.tok; |
||||
} |
||||
} |
||||
|
||||
void parse_directive(void) |
||||
{ |
||||
int ifdef, mask = skip_mask; |
||||
/* simplistic preprocessor:
|
||||
#define / #undef / #ifdef / #ifndef / #else / #endif |
||||
no symbol substitution. |
||||
*/ |
||||
skip_mask = 0; /* disable skipping to parse preprocessor line */ |
||||
nextch(); |
||||
if (skip_blanks() != TOK_IDENT) |
||||
error("expected preprocessing directive after #"); |
||||
|
||||
if (!strcmp(tokc.str, "define")) { |
||||
if (skip_blanks() != TOK_IDENT) |
||||
error("expected identifier after #define"); |
||||
define_symbol(tokc.str); |
||||
} else if (!strcmp(tokc.str, "undef")) { |
||||
if (skip_blanks() != TOK_IDENT) |
||||
error("expected identifier after #undef"); |
||||
undefine_symbol(tokc.str); |
||||
} else if ((ifdef = 1, !strcmp(tokc.str, "ifdef")) || |
||||
(ifdef = 0, !strcmp(tokc.str, "ifndef"))) { |
||||
if (skip_blanks() != TOK_IDENT) |
||||
error("expected identifier after #ifdef/#ifndef"); |
||||
mask = (mask << 2) | 2 | ifdef; |
||||
if (find_symbol(tokc.str)) |
||||
mask ^= 1; |
||||
} else if (!strcmp(tokc.str, "else")) { |
||||
if (!(mask & 2)) |
||||
error("#else without a #if"); |
||||
mask ^= 1; |
||||
} else if (!strcmp(tokc.str, "endif")) { |
||||
if (!(mask & 2)) |
||||
error("#endif without a #if"); |
||||
mask >>= 2; |
||||
} else { |
||||
error("unsupported preprocessing directive"); |
||||
} |
||||
if (skip_blanks() != '\n') |
||||
error("extra characters on preprocessing line"); |
||||
skip_mask = mask; |
||||
} |
||||
|
||||
/* return -1 if invalid char */ |
||||
static int hex_to_num(int ch) |
||||
{ |
||||
if (ch >= 'a' && ch <= 'f') |
||||
return ch - 'a' + 10; |
||||
else if (ch >= 'A' && ch <= 'F') |
||||
return ch - 'A' + 10; |
||||
else if (ch >= '0' && ch <= '9') |
||||
return ch - '0'; |
||||
else |
||||
return -1; |
||||
} |
||||
|
||||
void next(void) |
||||
{ |
||||
again:
|
||||
tok_reset(&tokc); |
||||
tokc.line_num = line_num; |
||||
tokc.lines = 0; |
||||
switch(ch) { |
||||
case EOF: |
||||
tokc.tok = TOK_EOF; |
||||
if (skip_mask) |
||||
error("missing #endif"); |
||||
break; |
||||
case 'a' ... 'z': |
||||
case 'A' ... 'Z': |
||||
case '_': |
||||
case '$': |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
while ((ch >= 'a' && ch <= 'z') || |
||||
(ch >= 'A' && ch <= 'Z') || |
||||
(ch >= '0' && ch <= '9') || |
||||
(ch == '_' || ch == '$')) { |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
} |
||||
tok_add_ch(&tokc, '\0'); |
||||
tokc.tok = TOK_IDENT; |
||||
break; |
||||
case '.': |
||||
nextch(); |
||||
if (ch >= '0' && ch <= '9') { |
||||
tok_add_ch(&tokc, '.'); |
||||
goto has_dot; |
||||
} |
||||
tokc.tok = '.'; |
||||
break; |
||||
case '0': |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
if (ch == 'x' || ch == 'X') { |
||||
/* hexa */ |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
while ((ch >= 'a' && ch <= 'f') || |
||||
(ch >= 'A' && ch <= 'F') || |
||||
(ch >= '0' && ch <= '9')) { |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
} |
||||
tok_add_ch(&tokc, '\0'); |
||||
tokc.tok = TOK_NUM; |
||||
break; |
||||
} |
||||
goto has_digit; |
||||
|
||||
case '1' ... '9': |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
has_digit: |
||||
/* decimal */ |
||||
while (ch >= '0' && ch <= '9') { |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
} |
||||
if (ch == '.') { |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
has_dot: |
||||
while (ch >= '0' && ch <= '9') { |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
} |
||||
} |
||||
if (ch == 'e' || ch == 'E') { |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
if (ch == '+' || ch == '-') { |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
} |
||||
while (ch >= '0' && ch <= '9') { |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
} |
||||
} |
||||
tok_add_ch(&tokc, '\0'); |
||||
tokc.tok = TOK_NUM; |
||||
break; |
||||
case '`': |
||||
{ |
||||
nextch(); |
||||
while (ch != '`' && ch != EOF) { |
||||
if (ch == '\\') { |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
if (ch == EOF) { |
||||
error("unexpected char after '\\'"); |
||||
} |
||||
tok_add_ch(&tokc, ch); |
||||
} else { |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
} |
||||
} |
||||
nextch(); |
||||
tok_add_ch(&tokc, 0); |
||||
tokc.tok = TOK_STR3; |
||||
} |
||||
break; |
||||
case '\"': |
||||
case '\'': |
||||
{ |
||||
int n, i, c, hex_digit_count; |
||||
int quote_ch; |
||||
quote_ch = ch; |
||||
nextch(); |
||||
while (ch != quote_ch && ch != EOF) { |
||||
if (ch == '\\') { |
||||
nextch(); |
||||
switch(ch) { |
||||
case 'n': |
||||
tok_add_ch(&tokc, '\n'); |
||||
nextch(); |
||||
break; |
||||
case 'r': |
||||
tok_add_ch(&tokc, '\r'); |
||||
nextch(); |
||||
break; |
||||
case 't': |
||||
tok_add_ch(&tokc, '\t'); |
||||
nextch(); |
||||
break; |
||||
case 'v': |
||||
tok_add_ch(&tokc, '\v'); |
||||
nextch(); |
||||
break; |
||||
case '\"': |
||||
case '\'': |
||||
case '\\': |
||||
tok_add_ch(&tokc, ch); |
||||
nextch(); |
||||
break; |
||||
case '0' ... '7': |
||||
n = | ||||