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<!doctype html>
<html>
<head>
<meta charset="utf-8">
<title>Fast explicit tail calls in JavaScript</title>
<link rel="stylesheet" type="text/css" href="web/prettify.css">
<style type="text/css">
body {
padding: 0 1em 0 1em;
font-family: helvetica;
font-family: Verdana,Arial,'Lucida Grande',Sans-Serif;
}
.title { margin-bottom: 1em; }
.right { float: right; }
.clear { clear: both; }
.text-center { text-align: center; }
.intro { margin: auto; text-align: justify;
margin-top: 1.5em;
}
.intro code { line-height: normal; }
.top-img { text-align: center; }
.section_anchor { display: none; margin-left: 0.5em; }
h3:hover .section_anchor { display: initial; }
.hidden { display: none; }
.small_img { max-width: 6em; margin: 0.5em; }
.code_cont {
float: left;
position: relative;
width: calc( 100% - 2em );
padding: 1em;
}
@media screen and (max-width: 999px) {
.right, pre, button, .code_cont_header { font-size: 1.8em; }
pre button { font-size: 1.2em; }
#speedtest_output { font-size: 0.85em; }
h3 { margin-top: 3em; }
}
@media screen and (min-width: 1200px) {
.intro { max-width: 600px;
line-height: 1.5em;
}
.code_cont {
width: calc( 50% - 2em );
}
}
.code_cont_header {
margin-top: 2em;
background-color: lightgrey;
border: solid 1px black;
padding: 1em;
}
.code_o { width: 100%; margin: 0; max-height: 100%; }
.code_o.fext_unittest_js { height: 65em; }
.code_o.fext_js { height: 435em; }
.success { color: darkgreen; }
.failure { color: darkred; font-weight: bold;}
.speedtest_patience { display: none; }
.speedtest_running .speedtest_patience { display: inherit; }
.speedtest_running button { display: none; }
</style>
</head>
<body>
<a href="https://github.com/glathoud/fext">
<img style="position: fixed; top: 0; right: 0; border: 0; margin: 0; padding: 0;"
src="web/forkme_right_green_007200.png"
alt="Fork me on GitHub">
</a>
<div class="intro">
<div class="top-img"><img class="small_img" src="web/serpent-mord-queue-2.jpg"/></div>
<h2 class="title">Fast explicit tail calls in JavaScript</h2>
<div class="right">by <a href="../">G. Lathoud</a>, June 2018.</div>
<div class="clear" style="margin-bottom: 3em"></div>
<p>If you don't know what this is about, please have a look at an excellent <a href="http://2ality.com/2015/06/tail-call-optimization.html">background article</a> on tail calls in JavaScript. Also my own <a href="http://glat.info/pub/tailopt-js/">early work</a> on this might be helpful.</p>
<p>In LISP and other languages, tail calls are automatically optimized. In Clojure, there is an explicit keyword <code>recur</code>. Generally, programmers may well not know which "return" statements are optimized by the engine, and which not. This would lead to practical issues when debugging and optimizing [<a href="http://neopythonic.blogspot.de/2009/04/final-words-on-tail-calls.html">2009</a>].</p>
<p>What about JavaScript?</p>
<p>As of 2018, progress is "slow" and the Chrome team has already <em>removed</em> the automatic self-recursion tail call optimization from its JavaScript engine.</p>
<p>Another possibility is to <strong>explicitly mark the tail calls that will be optimized</strong>. JavaScript extensions were proposed that add new keywords to the language [<a href="http://glat.info/js.metaret/">2013</a>] [<a href="https://github.com/tc39/proposal-ptc-syntax">2016</a>].</p>
<p>It turns out that we can do this explicit approach using today's JavaScript, without extending the language.
<code>fext.js</code> demonstrates this.</p>
<p>Mutual recursion is supported. API doc and source on <a href="https://github.com/glathoud/fext">GitHub</a>. Node.js <a href="https://www.npmjs.com/package/fext">package</a>.</p>
<p><strong>Update 2019-03-12:</strong> fext is now available <a href="https://github.com/glathoud/d_glat/blob/master/core_fext.d">in the D language as well</a>.</p>
<section id="section_quick_example">
<h3>Quick example</h3>
<pre class="prettyprint lang-js"><code><script type="text/javascript" src="fext.js"></script>
<script type="text/javascript">
var gcd = mfun(
(a, b) => a > b ? mret( mself, a-b, b )
: a < b ? mret( mself, b-a, a )
: a
);
console.log( gcd( 2*3*5*17, 3*5*19 ) ); // 15 (3*5)
</script></code></pre>
<section id="section_mutual_recursion_example">
<h3>Mutual recursion example</h3>
<pre class="prettyprint lang-js"><code><script type="text/javascript" src="fext.js"></script>
<script type="text/javascript">
var isOdd = mfun( function isOdd( n ) {
return n > 0 ? mret( isEven, n-1 )
: n < 0 ? mret( mself, -n )
: false
;
})
, isEven = mfun( isOdd, function isEven( n ) {
return n > 0 ? mret( isOdd, n-1 )
: n < 0 ? mret( mself, -n )
: true
;
})
console.log( isOdd( 8951531 ) ); // true ; no call stack issue
</script>
</code></pre>
</section>
<section id="section_namespace">
<h3>Namespace alternative</h3>
<p>In some situations the
globals <code>mfun</code>, <code>meth</code>, <code>mfunD</code>,
etc. may feel annoying. Solution: use the <code>fext.*</code> namespace. Below, an example in the Node.js context:</p>
<pre class="prettyprint lang-js"><code>var fx = require( '../fext' ).fext;
var isOdd = fx.mfun( function isOdd( n ) {
return n > 0 ? fx.mret( isEven, n-1 )
: n < 0 ? fx.mret( fx.mself, -n )
: false
;
})
, isEven = fx.mfun( isOdd, function isEven( n ) {
return n > 0 ? fx.mret( isOdd, n-1 )
: n < 0 ? fx.mret( fx.mself, -n )
: true
;
})
console.log( isOdd( 8951531 ) ); // true ; no call stack issue
</code></pre>
</section>
<section id="section_api_doc">
<h3>API Documentation and debugging tools</h3>
<p>On <a href="https://github.com/glathoud/fext#api">GitHub</a> (formatted), or directly <a href="README.md">here</a> (unformatted).</p> <p>Debugging: instead of <code>mfun</code> & <code>meth</code>, simply use <code>mfunD</code> & <code>methD</code> to deactivate the optimizations. You can then set breakpoints as usual.</p>
</section>
<section id="section_speedtest">
<h3>Speed test</h3>
<p>These results present the average relative speed (higher is better):</p>
<ul>
<li><code>100.0</code> is the max of each row,</li>
<li>standard deviation in brackets e.g. <code>(2.9)</code>,</li>
<li>absolute speed in square brackets,
e.g. <code>[5.78e+8]</code> (iterations per second).</li>
</ul>
<p>The <code>isOdd_mfun</code> and <code>isOdd_mret</code>
results show that the proposed approach runs:</p>
<ul>
<li>similar to, or faster than <code>isOdd_metaret</code>,
another approach that extends the JavaScript language with
new keywords
(<a href="http://glat.info/js.metaret/">2013</a>),</li>
<li>much faster than <code>tailtramp</code>, the fastest
trampoline implementation I could find (feel free to
ping me with a faster one).</li>
</ul>
<p><strong>So the proposed approach (1) runs very fast and (2) <em>does not need to extend JavaScript with new keywords</em>.</strong></p>
<pre><code id="speedtest_output">| Browser | isOdd_mfun | isOdd_meth | isOdd_metaret | isOdd_tailtramp |
| :--- | ---: | ---: | ---: | ---: |
| Firefox 60 | 95.5 (2.6) | 100.0 (1.4) | 81.2 (0.2) | 0.1 (<0.1) |
| | [9.34e+8] | [9.78e+8] | [7.93e+8] | [1.25e+6] |
| ---- | ---- | ---- | ---- | ---- |
| Chromium 66 | 98.5 (0.3) | 100.0 (4.9) | 52.0 (0.1) | 0.7 (<0.1) |
| | [8.87e+8] | [9.00e+8] | [4.68e+8] | [6.12e+6] |
| ---- | ---- | ---- | ---- | ---- |
| Chrome 67 | 99.8 (0.8) | 100.0 (0.3) | 62.2 (0.2) | 0.8 (<0.1) |
| | [7.49e+8] | [7.51e+8] | [4.67e+8] | [6.18e+6] |</code></pre>
<p>
<button onclick="fext_speedtest(section_speedtest,speedtest_output)">Run</button>
<span class="speedtest_patience">Running (please be patient...)</span>
</p>
</section>
<section id="section_unit_tests">
<h3>Unit tests</h3>
<pre><code id="unittest_output">Running...</code></pre>
</section>
<section id="section_longer_example">
<h3>Longer example</h3>
<p>Search the first & last indices of a given value in a
sorted array that has duplicates:</p>
<ul>
<li>Code: <a href="#lib_sorted_search_js">lib/sorted_search.js</a>
<ul><li>Unittest: <a href="#lib_sorted_search_js__unit_tests">lib/sorted_search.js: unit tests</a></li></ul>
</li>
<li>Code: <a href="#lib_sorted_search_closure_js">lib/sorted_search_closure.js</a>
<ul><li>Unittest: <a href="#lib_sorted_search_closure_js__unit_tests">lib/sorted_search_closure.js: unit tests</a></li></ul>
</li>
</ul>
</section>
<section id="section_setup_details_speed_test">
<h3>Annex A: Setup details of the speed test</h3>
<p>The <code>isOdd/isEven</code> mutual recursion use case
measures well the overhead due to each approach, since both
<code>isOdd</code> & <code>isEven</code> do little inside
their function bodies.</p>
<p>We measure 10 times the duration of <code class="prettyprint lang-js">isOdd( niter )</code> where <code class="prettyprint lang-js">niter</code> is adjusted to have a duration > 1.0 second.</p>
<p>
<code>isOdd_mfun</code> & <code>isOdd_meth</code> are the
proposed approach, using only standard JavaScript, e.g.:
<pre class="prettyprint lang-js"><code>var isOdd = mfun( function isOdd( n ) {
return n > 0 ? mret( isEven, n-1 )
: n < 0 ? mret( mself, -n )
: false
;
})
, isEven = mfun( isOdd, function isEven( n ) {
return n > 0 ? mret( isOdd, n-1 )
: n < 0 ? mret( mself, -n )
: true
;
})</code></pre>
<p><code>isOdd_metaret</code> is another approach that extends the
JavaScript language with new keywords, including <code>metafun</code> and <code>metaret</code>
(<a href="http://glat.info/js.metaret/">2013</a>):</p>
<pre class="prettyprint lang-js"><code>metafun isEven( self, n )
{
if (n > 0)
metaret isOdd, n - 1; // mutual recursion
if (n < 0)
metaret self, -n;
return true;
}
metafun isOdd( self, n )
{
if (n > 0)
metaret isEven, n - 1;
if (n < 0)
metaret self, -n;
return false;
}</code></pre>
<p>and <code>isOdd_tailtramp</code> is the fastest trampoline implementation that I could find:</p>
<pre class="prettyprint lang-js"><code>var isOdd = tailtramp( function( n ) {
return n > 0 ? isEven( n-1 )
: n < 0 ? isOdd( -n )
: false
;
})
, isEven = tailtramp( function( n ) {
return n > 0 ? isOdd( n-1 )
: n < 0 ? isEven( -n )
: true
;
})
function tailtramp(g)
{
var tailtramp_n = 0;
return tailtramp_impl;
function tailtramp_impl()
{
var arr = [g, this, arguments]
, ret;
// Jump off a small Empire State Building
if (tailtramp_n>5)
return new TailCall(arr);
while (true)
{
tailtramp_n++;
ret = arr[0].apply(arr[1], arr[2]);
tailtramp_n--;
if (!(ret instanceof TailCall))
{
tailtramp_n = 0;
return ret;
}
// Hit 33rd Street and bounce again
arr = ret.arr;
}
}
}
function TailCall(arr)
{
this.arr = arr;
}</code></pre>
</section>
<section id="section_annex_speedup_recursive_expansion">
<h3>Annex B: Speedup through recursive expansion</h3>
<p>To reduce the number of CPU jumps, several levels
of recursion are automatically expanded and inlined.
For an example, have a look at the code generated
for <code>gcd</code>:
</p>
<pre class="prettyprint lang-js"><code>var gcd = mfun(
(a, b) => a > b ? mret( mself, a-b, b )
: a < b ? mret( mself, b-a, a )
: a
);
console.log(gcd._tf_get_bodycode());</code></pre>
<p>Result:</p>
<pre class="prettyprint lang-js" style="max-height: 20em; overflow: scroll;"><code>"use strict";
var that = this, __fext_case_i__ = 0, __fext_ret__, __fext_arg_a__, __fext_arg_b__
;
__fext_main_loop__: for (;;)
{
switch( __fext_case_i__)
{
case 0: __fext_inline_loop_1__: for(;;) {
/*return a > b ? mret( mself, a-b, b )
: a < b ? mret( mself, b-a, a )
: a;*/
{if (a > b)
{
{
(__fext_arg_a__ = a-b, __fext_arg_b__ = b, a = __fext_arg_a__, b = __fext_arg_b__) ;
}
break __fext_inline_loop_1__;
}
if (a < b)
{
{
(__fext_arg_a__ = b-a, __fext_arg_b__ = a, a = __fext_arg_a__, b = __fext_arg_b__) ;
}
break __fext_inline_loop_1__;
}
{
{
return a ;
}
break __fext_inline_loop_1__;
}
}
}
if (__fext_case_i__ === -1) return __fext_ret__;
__fext_inline_loop_2__: for(;;) {
/*return a > b ? mret( mself, a-b, b )
: a < b ? mret( mself, b-a, a )
: a;*/
{if (a > b)
{
{
(__fext_arg_a__ = a-b, __fext_arg_b__ = b, a = __fext_arg_a__, b = __fext_arg_b__) ;
}
break __fext_inline_loop_2__;
}
if (a < b)
{
{
(__fext_arg_a__ = b-a, __fext_arg_b__ = a, a = __fext_arg_a__, b = __fext_arg_b__) ;
}
break __fext_inline_loop_2__;
}
{
{
return a ;
}
break __fext_inline_loop_2__;
}
}
}
if (__fext_case_i__ === -1) return __fext_ret__;
__fext_inline_loop_3__: for(;;) {
/*return a > b ? mret( mself, a-b, b )
: a < b ? mret( mself, b-a, a )
: a;*/
{if (a > b)
{
{
(__fext_arg_a__ = a-b, __fext_arg_b__ = b, a = __fext_arg_a__, b = __fext_arg_b__) ;
}
break __fext_inline_loop_3__;
}
if (a < b)
{
{
(__fext_arg_a__ = b-a, __fext_arg_b__ = a, a = __fext_arg_a__, b = __fext_arg_b__) ;
}
break __fext_inline_loop_3__;
}
{
{
return a ;
}
break __fext_inline_loop_3__;
}
}
}
if (__fext_case_i__ === -1) return __fext_ret__;
__fext_inline_loop_4__: for(;;) {
/*return a > b ? mret( mself, a-b, b )
: a < b ? mret( mself, b-a, a )
: a;*/
{if (a > b)
{
{
(__fext_arg_a__ = a-b, __fext_arg_b__ = b, a = __fext_arg_a__, b = __fext_arg_b__) ;
}
break __fext_inline_loop_4__;
}
if (a < b)
{
{
(__fext_arg_a__ = b-a, __fext_arg_b__ = a, a = __fext_arg_a__, b = __fext_arg_b__) ;
}
break __fext_inline_loop_4__;
}
{
{
return a ;
}
break __fext_inline_loop_4__;
}
}
}
if (__fext_case_i__ === -1) return __fext_ret__;
/*return a > b ? mret( mself, a-b, b )
: a < b ? mret( mself, b-a, a )
: a;*/
{if (a > b)
{
{
(__fext_arg_a__ = a-b, __fext_arg_b__ = b, a = __fext_arg_a__, b = __fext_arg_b__) ;
}
continue __fext_main_loop__;
}
if (a < b)
{
{
(__fext_arg_a__ = b-a, __fext_arg_b__ = a, a = __fext_arg_a__, b = __fext_arg_b__) ;
}
continue __fext_main_loop__;
}
{
{
return a ;
}
continue __fext_main_loop__;
}
} continue __fext_main_loop__;
default: return __fext_ret__;
}
}</code></pre>
<p>Looks overcomplicated? In practice, debugging is not a problem
since one can anytime reverse to the non-optimized implementation
using <code>mfunD</code> and <code>methD</code>:
</p>
<pre class="prettyprint lang-js"><code>var gcd = mfunD(
(a, b) => a > b ? mret( mself, a-b, b )
: a < b ? mret( mself, b-a, a )
: a
);
console.log(gcd._tf_get_dbg_f_code());</code></pre>
<p>Result:</p>
<pre class="prettyprint lang-js"><code>(a, b) => a > b ? mret( mself, a-b, b )
: a < b ? mret( mself, b-a, a )
: a</code></pre>
<p>...indeed, the unmodified source code, which will run as it is.</p>
</section>
<section id="section_annex_more_code">
<h3>Annex C: More code</h3>
<p>On <a href="https://github.com/glathoud/fext/">GitHub</a> and here below.</p>
<p id="toccont">
<ul id="toc"></ul>
</p>
</section>
</div>
<div id="source_code_0" class="code_cont"></div>
<div id="source_code_1" class="code_cont"></div>
<script type="text/html" id="source_code_tmpl">
<p class="code_cont_header" id="$domid">$filename:</p>
<pre><code class="prettyprint lang-js">$sourcecode</code></pre>
</script>
<script type="text/html" id="toctmpl">
<li><a href="#$domid">$filename</a></li>
</script>
<script type="text/javascript" src="fext.js"></script>
<script type="text/javascript" src="lib/sorted_search.js"></script>
<script type="text/javascript" src="lib/sorted_search_closure.js"></script>
<script type="text/javascript" src="lib/sorted_search_unittest.js"></script>
<script type="text/javascript" src="lib/sorted_search_closure_unittest.js"></script>
<script type="text/javascript" src="test/fext_unittest.js"></script>
<script type="text/javascript" src="test/fext_unittest_es6.js"></script>
<script type="text/javascript" src="web/prettify.js"></script>
<script type="text/javascript">
//'
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setup_section_anchors();
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write_source_code( source_code_0, "lib/sorted_search.js" )
write_source_code( source_code_0, "lib/sorted_search_closure.js" )
write_source_code( source_code_1, get_test_arr_sorted_search, "lib/sorted_search.js: unit tests" );
write_source_code( source_code_1, get_test_arr_sorted_search_closure, "lib/sorted_search_closure.js: unit tests" );
}
else
{
do_the_unittests();
}
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, c_arr = x().map( unindent )
;
setTimeout( function () {
receive_source_code(
{
target : {
responseText : c_arr.join( '\n\n\n' )
}
}
);
}, 100 );
}
else
{
var filename = x
, xhr = new XMLHttpRequest()
;
try {
xhr.addEventListener( "load", receive_source_code );
xhr.open( "GET", filename, /*async:*/true );
xhr.send();
} catch( e ) {
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return;
}
}
if (window.toc && window.toctmpl)
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toctmpl.innerHTML, filename
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, first = /\n\s+/.exec( s )
;
return first
? s.replace( new RegExp( first[ 0 ], 'g' )
, '\n'
)
: s;
}
function receive_source_code( a )
{
var et = a && a.target
, etr = et && (et.response || et.responseText)
, domid = filename.replace(/\W/g,'_')
;
to_write[ i_write ] = function () {
contnode.innerHTML += format(
cstmpl.innerHTML, filename, etr
);
};
if (--write_source_code.n < 1)
{
to_write.forEach( function( f ) { f(); } );
prettyPrint();
window.toccont && (toccont.style.display = '');
setTimeout( do_the_unittests, 2000 );
}
}
}
function format( tmpl, filename, sourcecode )
{
var domid = filename.replace(/\W/g,'_')
, ret = tmpl
.replace( /\$filename\b/g, filename)
.replace( /\$domid\b/g, domid )
;
if (sourcecode)
{
ret = ret.replace( /\$sourcecode\b/g
, sourcecode
.replace( /</g, '<' )
.replace( />/g, '>' )
);
}
return ret;
}
function do_the_unittests()
{
fext_unittest(
function ( result )
{
unittest_output.innerHTML = result.text.replace( /^\s+/, '' );
}
);
}
function setup_section_anchors()
{
document.querySelectorAll('[id^="section_"]')
.forEach( setup_one_section_anchor )
;
}
function setup_one_section_anchor( cont )
{
var h3 = cont.querySelector('h3')
, a = document.createElement('a')
;
a.setAttribute( 'href','#' + cont.id );
a.textContent='#';
a.setAttribute( 'class','section_anchor' );
h3.append( a );
}
})();
</script>
<script type="text/javascript" src="test/fext_speedtest.js"></script>
</body>
</html>