From 94d06c45af9cfcd5e8d5b73116c4eb22061cd115 Mon Sep 17 00:00:00 2001
From: Jesse Alama <jessealama@users.noreply.github.com>
Date: Mon, 15 Apr 2024 16:32:45 +0200
Subject: [PATCH] Remove rounding mode option in remainder (#123)

* Remove rounding mode option in remainder

The precision of the result comes from the precision of the
arguments. We do integer division until we get a clean
result; any residue is the remainder.
---
 index.html | 66 +++++++++++++++++++++++++++---------------------------
 spec.emu   |  4 ++--
 2 files changed, 35 insertions(+), 35 deletions(-)

diff --git a/index.html b/index.html
index ddeb086d..aae98600 100644
--- a/index.html
+++ b/index.html
@@ -1557,7 +1557,7 @@
 });
 
 let sdoMap = JSON.parse(`{}`);
-let biblio = JSON.parse(`{"refsByClause":{"sec-decimal-intro":["_ref_0","_ref_1","_ref_2","_ref_3","_ref_4","_ref_50","_ref_51","_ref_52","_ref_53","_ref_54","_ref_55","_ref_56","_ref_57","_ref_58","_ref_59","_ref_60","_ref_61","_ref_62","_ref_63","_ref_64","_ref_65","_ref_66"],"sec-decimal.prototype.abs":["_ref_5","_ref_6","_ref_7","_ref_73"],"sec-decimal.prototype.neg":["_ref_8"],"sec-decimal.prototype.add":["_ref_9","_ref_10","_ref_11","_ref_12","_ref_13","_ref_14","_ref_15","_ref_16","_ref_74","_ref_75","_ref_76","_ref_77"],"sec-decimal.prototype.subtract":["_ref_17","_ref_18","_ref_19","_ref_20","_ref_21","_ref_22","_ref_23","_ref_24","_ref_78","_ref_79","_ref_80","_ref_81"],"sec-decimal.prototype.multiply":["_ref_25","_ref_26","_ref_27","_ref_28","_ref_29","_ref_30","_ref_31","_ref_82","_ref_83","_ref_84","_ref_85"],"sec-decimal.prototype.divide":["_ref_32","_ref_33","_ref_34","_ref_35","_ref_36","_ref_37","_ref_38","_ref_86","_ref_87","_ref_88","_ref_89"],"sec-decimal.prototype.remainder":["_ref_39","_ref_40","_ref_41","_ref_42","_ref_43","_ref_90","_ref_91","_ref_92"],"sec-decimal.prototype.equals":["_ref_44"],"sec-decimal.prototype.lessthan":["_ref_45"],"sec-decimal-method-round":["_ref_46","_ref_93"],"sec-decimal.prototype.tostring":["_ref_47","_ref_48","_ref_49"],"sec-decimal.prototype.isnan":["_ref_67","_ref_68"],"sec-decimal.prototype.isfinite":["_ref_69","_ref_70"],"sec-decimal.prototype.significand":["_ref_71"],"sec-decimal.prototype.exponent":["_ref_72"],"sec-copyright-and-software-license":["_ref_94"]},"entries":[{"type":"clause","id":"sec-scope","titleHTML":"Scope","number":"1"},{"type":"clause","id":"ref-ieee-754-2019","titleHTML":"IEEE 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string","id":"dfn-signed-exponential-string","referencingIds":["_ref_49"]},{"type":"term","term":"mathematical value","id":"dfn-mathematical-value","referencingIds":["_ref_44","_ref_45","_ref_60"]},{"type":"term","term":"normal","id":"dfn-normal","referencingIds":["_ref_64","_ref_65","_ref_66"]},{"type":"clause","id":"sec-decimal-intro","titleHTML":"Introduction","number":""},{"type":"clause","id":"sec-the-decimal-constructor","titleHTML":"The Decimal128 Constructor","number":"3.1"},{"type":"clause","id":"sec-the-decimal-object","titleHTML":"The Decimal128 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)","number":"4.7"},{"type":"clause","id":"sec-decimal.prototype.subtract","title":"Decimal128.prototype.subtract ( x [ , options ] )","titleHTML":"Decimal128.prototype.subtract ( <var>x</var> [ , <var>options</var> ] )","number":"4.8"},{"type":"clause","id":"sec-decimal.prototype.multiply","title":"Decimal128.prototype.multiply ( x [ , options ] )","titleHTML":"Decimal128.prototype.multiply ( <var>x</var> [ , <var>options</var> ] )","number":"4.9"},{"type":"clause","id":"sec-decimal.prototype.divide","title":"Decimal128.prototype.divide ( x [ , options ] )","titleHTML":"Decimal128.prototype.divide ( <var>x</var> [ , <var>options</var> ] )","number":"4.10"},{"type":"clause","id":"sec-decimal.prototype.remainder","title":"Decimal128.prototype.remainder ( x [ , options ] )","titleHTML":"Decimal128.prototype.remainder ( <var>x</var> [ , <var>options</var> ] )","number":"4.11"},{"type":"clause","id":"sec-decimal.prototype.equals","title":"Decimal128.prototype.equals ( x )","titleHTML":"Decimal128.prototype.equals ( <var>x</var> )","number":"4.12"},{"type":"clause","id":"sec-decimal.prototype.lessthan","title":"Decimal128.prototype.lessThan ( x )","titleHTML":"Decimal128.prototype.lessThan ( <var>x</var> )","number":"4.13"},{"type":"clause","id":"sec-decimal-method-round","title":"Decimal128.prototype.round ( numFractionalDigits [ , mode ] )","titleHTML":"Decimal128.prototype.round ( <var>numFractionalDigits</var> [ , <var>mode</var> ] )","number":"4.14"},{"type":"clause","id":"sec-decimal.prototype.tostring","title":"Decimal128.prototype.toString ( [ options ] )","titleHTML":"Decimal128.prototype.toString ( [ <var>options</var> ] )","number":"4.15"},{"type":"clause","id":"sec-decimal.prototype.valueof","title":"Decimal128.prototype.valueOf ( x )","titleHTML":"Decimal128.prototype.valueOf ( <var>x</var> )","number":"4.16"},{"type":"clause","id":"sec-decimal-prototype-properties","titleHTML":"Properties of the Decimal128 Prototype","number":"4"},{"type":"clause","id":"sec-copyright-and-software-license","title":"Copyright & Software License","titleHTML":"Copyright &amp; Software License","number":"A"}]}`);
+let biblio = JSON.parse(`{"refsByClause":{"sec-decimal-intro":["_ref_0","_ref_1","_ref_2","_ref_3","_ref_4","_ref_48","_ref_49","_ref_50","_ref_51","_ref_52","_ref_53","_ref_54","_ref_55","_ref_56","_ref_57","_ref_58","_ref_59","_ref_60","_ref_61","_ref_62","_ref_63","_ref_64"],"sec-decimal.prototype.abs":["_ref_5","_ref_6","_ref_7","_ref_71"],"sec-decimal.prototype.neg":["_ref_8"],"sec-decimal.prototype.add":["_ref_9","_ref_10","_ref_11","_ref_12","_ref_13","_ref_14","_ref_15","_ref_16","_ref_72","_ref_73","_ref_74","_ref_75"],"sec-decimal.prototype.subtract":["_ref_17","_ref_18","_ref_19","_ref_20","_ref_21","_ref_22","_ref_23","_ref_24","_ref_76","_ref_77","_ref_78","_ref_79"],"sec-decimal.prototype.multiply":["_ref_25","_ref_26","_ref_27","_ref_28","_ref_29","_ref_30","_ref_31","_ref_80","_ref_81","_ref_82","_ref_83"],"sec-decimal.prototype.divide":["_ref_32","_ref_33","_ref_34","_ref_35","_ref_36","_ref_37","_ref_38","_ref_84","_ref_85","_ref_86","_ref_87"],"sec-decimal.prototype.remainder":["_ref_39","_ref_40","_ref_41"],"sec-decimal.prototype.equals":["_ref_42"],"sec-decimal.prototype.lessthan":["_ref_43"],"sec-decimal-method-round":["_ref_44","_ref_88"],"sec-decimal.prototype.tostring":["_ref_45","_ref_46","_ref_47"],"sec-decimal.prototype.isnan":["_ref_65","_ref_66"],"sec-decimal.prototype.isfinite":["_ref_67","_ref_68"],"sec-decimal.prototype.significand":["_ref_69"],"sec-decimal.prototype.exponent":["_ref_70"],"sec-copyright-and-software-license":["_ref_89"]},"entries":[{"type":"clause","id":"sec-scope","titleHTML":"Scope","number":"1"},{"type":"clause","id":"ref-ieee-754-2019","titleHTML":"IEEE 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 ;let usesMultipage = false</script><style>/* IBM Plex fonts (Latin subset) have been downloaded from Google Fonts and modified to add support back in for the `zero` substitution (slashed zeroes) */
 
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@@ -2983,7 +2983,7 @@
 </ul></div><div id="menu-toggle"><svg xmlns="http://www.w3.org/2000/svg" style="width:100%; height:100%; stroke:currentColor" viewBox="0 0 120 120">
       <title>Menu</title>
       <path stroke-width="10" stroke-linecap="round" d="M30,60 h60  M30,30 m0,5 h60  M30,90 m0,-5 h60"></path>
-    </svg></div><div id="menu-spacer" class="menu-spacer"></div><div id="menu"><div id="menu-search"><input type="text" id="menu-search-box" placeholder="Search..."><div id="menu-search-results" class="inactive"></div></div><div id="menu-pins"><div class="menu-pane-header">Pins<button class="unpin-all">clear</button></div><ul id="menu-pins-list"></ul></div><div class="menu-pane-header">Table of Contents</div><div id="menu-toc"><ol class="toc"><li><span class="item-toggle-none"></span><a href="#sec-scope" title="Scope"><span class="secnum">1</span> Scope</a></li><li><span class="item-toggle">+</span><a href="#sec-normative-references" title="Normative References"><span class="secnum">2</span> Normative References</a><ol class="toc"><li><span class="item-toggle-none"></span><a href="#ref-ieee-754-2019" title="IEEE 754-2019"><span class="secnum">2.1</span> IEEE 754-2019</a></li></ol></li><li><span class="item-toggle">+</span><a href="#sec-the-decimal-object" title="The Decimal128 Object"><span class="secnum">3</span> The Decimal128 Object</a><ol class="toc"><li><span class="item-toggle-none"></span><a href="#sec-decimal-intro" title="Introduction">Introduction</a></li><li><span class="item-toggle-none"></span><a href="#sec-the-decimal-constructor" title="The Decimal128 Constructor"><span class="secnum">3.1</span> The Decimal128 Constructor</a></li></ol></li><li><span class="item-toggle">+</span><a href="#sec-decimal-prototype-properties" title="Properties of the Decimal128 Prototype"><span class="secnum">4</span> Properties of the Decimal128 Prototype</a><ol class="toc"><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.isnan" title="Decimal128.prototype.isNaN"><span class="secnum">4.1</span> Decimal128.prototype.isNaN</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.isfinite" title="Decimale128.prototype.isFinite"><span class="secnum">4.2</span> Decimale128.prototype.isFinite</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.significand" title="Decimale128.prototype.significand"><span class="secnum">4.3</span> Decimale128.prototype.significand</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.exponent" title="Decimale128.prototype.exponent"><span class="secnum">4.4</span> Decimale128.prototype.exponent</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.abs" title="Decimal128.prototype.abs ( )"><span class="secnum">4.5</span> Decimal128.prototype.abs ( )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.neg" title="Decimal128.prototype.neg ( )"><span class="secnum">4.6</span> Decimal128.prototype.neg ( )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.add" title="Decimal128.prototype.add ( x [ , options ] )"><span class="secnum">4.7</span> Decimal128.prototype.add ( <var>x</var> [ , <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.subtract" title="Decimal128.prototype.subtract ( x [ , options ] )"><span class="secnum">4.8</span> Decimal128.prototype.subtract ( <var>x</var> [ , <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.multiply" title="Decimal128.prototype.multiply ( x [ , options ] )"><span class="secnum">4.9</span> Decimal128.prototype.multiply ( <var>x</var> [ , <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.divide" title="Decimal128.prototype.divide ( x [ , options ] )"><span class="secnum">4.10</span> Decimal128.prototype.divide ( <var>x</var> [ , <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.remainder" title="Decimal128.prototype.remainder ( x [ , options ] )"><span class="secnum">4.11</span> Decimal128.prototype.remainder ( <var>x</var> [ , <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.equals" title="Decimal128.prototype.equals ( x )"><span class="secnum">4.12</span> Decimal128.prototype.equals ( <var>x</var> )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.lessthan" title="Decimal128.prototype.lessThan ( x )"><span class="secnum">4.13</span> Decimal128.prototype.lessThan ( <var>x</var> )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal-method-round" title="Decimal128.prototype.round ( numFractionalDigits [ , mode ] )"><span class="secnum">4.14</span> Decimal128.prototype.round ( <var>numFractionalDigits</var> [ , <var>mode</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.tostring" title="Decimal128.prototype.toString ( [ options ] )"><span class="secnum">4.15</span> Decimal128.prototype.toString ( [ <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.valueof" title="Decimal128.prototype.valueOf ( x )"><span class="secnum">4.16</span> Decimal128.prototype.valueOf ( <var>x</var> )</a></li></ol></li><li><span class="item-toggle-none"></span><a href="#sec-copyright-and-software-license" title="Copyright &amp; Software License"><span class="secnum">A</span> Copyright &amp; Software License</a></li></ol></div></div><div id="spec-container"><h1 class="version">Stage 1 Draft / April 12, 2024</h1><h1 class="title">Decimal</h1>
+    </svg></div><div id="menu-spacer" class="menu-spacer"></div><div id="menu"><div id="menu-search"><input type="text" id="menu-search-box" placeholder="Search..."><div id="menu-search-results" class="inactive"></div></div><div id="menu-pins"><div class="menu-pane-header">Pins<button class="unpin-all">clear</button></div><ul id="menu-pins-list"></ul></div><div class="menu-pane-header">Table of Contents</div><div id="menu-toc"><ol class="toc"><li><span class="item-toggle-none"></span><a href="#sec-scope" title="Scope"><span class="secnum">1</span> Scope</a></li><li><span class="item-toggle">+</span><a href="#sec-normative-references" title="Normative References"><span class="secnum">2</span> Normative References</a><ol class="toc"><li><span class="item-toggle-none"></span><a href="#ref-ieee-754-2019" title="IEEE 754-2019"><span class="secnum">2.1</span> IEEE 754-2019</a></li></ol></li><li><span class="item-toggle">+</span><a href="#sec-the-decimal-object" title="The Decimal128 Object"><span class="secnum">3</span> The Decimal128 Object</a><ol class="toc"><li><span class="item-toggle-none"></span><a href="#sec-decimal-intro" title="Introduction">Introduction</a></li><li><span class="item-toggle-none"></span><a href="#sec-the-decimal-constructor" title="The Decimal128 Constructor"><span class="secnum">3.1</span> The Decimal128 Constructor</a></li></ol></li><li><span class="item-toggle">+</span><a href="#sec-decimal-prototype-properties" title="Properties of the Decimal128 Prototype"><span class="secnum">4</span> Properties of the Decimal128 Prototype</a><ol class="toc"><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.isnan" title="Decimal128.prototype.isNaN"><span class="secnum">4.1</span> Decimal128.prototype.isNaN</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.isfinite" title="Decimale128.prototype.isFinite"><span class="secnum">4.2</span> Decimale128.prototype.isFinite</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.significand" title="Decimale128.prototype.significand"><span class="secnum">4.3</span> Decimale128.prototype.significand</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.exponent" title="Decimale128.prototype.exponent"><span class="secnum">4.4</span> Decimale128.prototype.exponent</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.abs" title="Decimal128.prototype.abs ( )"><span class="secnum">4.5</span> Decimal128.prototype.abs ( )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.neg" title="Decimal128.prototype.neg ( )"><span class="secnum">4.6</span> Decimal128.prototype.neg ( )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.add" title="Decimal128.prototype.add ( x [ , options ] )"><span class="secnum">4.7</span> Decimal128.prototype.add ( <var>x</var> [ , <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.subtract" title="Decimal128.prototype.subtract ( x [ , options ] )"><span class="secnum">4.8</span> Decimal128.prototype.subtract ( <var>x</var> [ , <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.multiply" title="Decimal128.prototype.multiply ( x [ , options ] )"><span class="secnum">4.9</span> Decimal128.prototype.multiply ( <var>x</var> [ , <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.divide" title="Decimal128.prototype.divide ( x [ , options ] )"><span class="secnum">4.10</span> Decimal128.prototype.divide ( <var>x</var> [ , <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.remainder" title="Decimal128.prototype.remainder ( x )"><span class="secnum">4.11</span> Decimal128.prototype.remainder ( <var>x</var> )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.equals" title="Decimal128.prototype.equals ( x )"><span class="secnum">4.12</span> Decimal128.prototype.equals ( <var>x</var> )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.lessthan" title="Decimal128.prototype.lessThan ( x )"><span class="secnum">4.13</span> Decimal128.prototype.lessThan ( <var>x</var> )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal-method-round" title="Decimal128.prototype.round ( numFractionalDigits [ , mode ] )"><span class="secnum">4.14</span> Decimal128.prototype.round ( <var>numFractionalDigits</var> [ , <var>mode</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.tostring" title="Decimal128.prototype.toString ( [ options ] )"><span class="secnum">4.15</span> Decimal128.prototype.toString ( [ <var>options</var> ] )</a></li><li><span class="item-toggle-none"></span><a href="#sec-decimal.prototype.valueof" title="Decimal128.prototype.valueOf ( x )"><span class="secnum">4.16</span> Decimal128.prototype.valueOf ( <var>x</var> )</a></li></ol></li><li><span class="item-toggle-none"></span><a href="#sec-copyright-and-software-license" title="Copyright &amp; Software License"><span class="secnum">A</span> Copyright &amp; Software License</a></li></ol></div></div><div id="spec-container"><h1 class="version">Stage 1 Draft / April 15, 2024</h1><h1 class="title">Decimal</h1>
 
 <emu-clause id="sec-scope">
   <h1><span class="secnum">1</span> Scope</h1>
@@ -3004,20 +3004,20 @@ <h1><span class="secnum">2.1</span> IEEE 754-2019</h1>
   <h1><span class="secnum">3</span> The Decimal128 Object</h1>
   <emu-intro id="sec-decimal-intro">
     <h1>Introduction</h1>
-    <p>Decimal128 values, as specified here, are intended represent base-10 (decimal) numbers. ECMAScript, and many other languages, default to representing numbers in base-2 (binary). The conversion of a decimal <emu-xref href="#dfn-digit" id="_ref_50"><a href="#dfn-digit">digit</a></emu-xref> string to a Number is usually inexact; the Number representing the initial decimal <emu-xref href="#dfn-digit" id="_ref_51"><a href="#dfn-digit">digit</a></emu-xref> string is only approximately correct.</p>
+    <p>Decimal128 values, as specified here, are intended represent base-10 (decimal) numbers. ECMAScript, and many other languages, default to representing numbers in base-2 (binary). The conversion of a decimal <emu-xref href="#dfn-digit" id="_ref_48"><a href="#dfn-digit">digit</a></emu-xref> string to a Number is usually inexact; the Number representing the initial decimal <emu-xref href="#dfn-digit" id="_ref_49"><a href="#dfn-digit">digit</a></emu-xref> string is only approximately correct.</p>
     <p>An <dfn id="dfn-ieee-754-decimal128-value" tabindex="-1">IEEE 754 Decimal128 value</dfn> is an element of the universe of values specified by <emu-xref href="#ref-ieee-754-2019" id="_ref_0"><a href="#ref-ieee-754-2019">IEEE 754</a></emu-xref> standard.</p>
     <p>Decimal128 values defined in this section are ECMAScript analogues of <emu-xref href="#ref-ieee-754-2019" id="_ref_1"><a href="#ref-ieee-754-2019">IEEE-754 Decimal128 values</a></emu-xref>. The full spectrum of values defined by Decimal128 are available here, including NaN and positive and negative infinity. (NB: The values NaN and both infinities, available here, are distinct from the built-in <emu-val>NaN</emu-val>, <emu-val>Infinity</emu-val> and <emu-val>-Infinity</emu-val> values that arise from the 64-bit binarry IEEE arithmetic used outside of the Decimal128 universe.) Decimal128 is a floating-point format whose range of values allows up to 34 significant digits and an exponent ranging from -6143 to 6144.</p>
     <p>Essentially all of the entities defined by the IEEE 754 Decimal128 standard exist as Decimal128 objects, with one class of exceptions: NaN. Decimal128 supports NaN. All Decimal128-NaN values in IEEE 754 Decimal128 are mapped to a NaN Decimal128 value. There may be distinct NaN Decimal128 values in the sense of object identity, but they are all supposed to behave identically. Thus, when we refer to a <dfn id="dfn-decimal128-nan" tabindex="-1">Decimal128 NaN</dfn>, we mean any Decimal128 object whose <emu-xref href="#sec-decimal.prototype.isnan" id="_ref_2"><a href="#sec-decimal.prototype.isnan"><emu-val>isNaN</emu-val></a></emu-xref> property is <emu-val>true</emu-val>. There is no Decimal128 analogue of IEEE 754 signalling NaNs. Any arithmetic operation defined here that takes a Decimal128-NaN argument will return a Decimal128-NaN. Depending on the the operation and its arguments, a Decimal128-NaN may be returned.</p>
-    <p>Thus, we grant ourselves a mapping <dfn id="dfn-map-from-ieee-754-decimal128" tabindex="-1">A</dfn> from the set of <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_3"><a href="#dfn-ieee-754-decimal128-value">IEEE Decimal128 values</a></emu-xref> to Decimal128 objects. Moreover, we grant ourselves a map <dfn id="dfn-map-to-ieee-754-decimal128" tabindex="-1">B</dfn> from Decimal128 objects to IEEE 754 Decimal128 values. We choose a canonical quiet NaN as the IEEE 754 Decimal128 representative for all Decimal128-NaN objects, and similarly for infinities. Apart from NaNs and infinities, the mappings <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_52"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> and <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_53"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> are one-to-one.</p>
-    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_54"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> <dfn id="dfn-rounding-mode" tabindex="-1">rounding mode</dfn> is one of the values <emu-val>"ceil"</emu-val>, <emu-val>"floor"</emu-val>, <emu-val>"expand"</emu-val>, <emu-val>"trunc"</emu-val>, <emu-val>"halfEven"</emu-val>, <emu-val>"halfExpand"</emu-val>, <emu-val>"halfCeil"</emu-val>, <emu-val>"halfFloor"</emu-val>, and <emu-val>"halfTrunc"</emu-val>.</p>
+    <p>Thus, we grant ourselves a mapping <dfn id="dfn-map-from-ieee-754-decimal128" tabindex="-1">A</dfn> from the set of <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_3"><a href="#dfn-ieee-754-decimal128-value">IEEE Decimal128 values</a></emu-xref> to Decimal128 objects. Moreover, we grant ourselves a map <dfn id="dfn-map-to-ieee-754-decimal128" tabindex="-1">B</dfn> from Decimal128 objects to IEEE 754 Decimal128 values. We choose a canonical quiet NaN as the IEEE 754 Decimal128 representative for all Decimal128-NaN objects, and similarly for infinities. Apart from NaNs and infinities, the mappings <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_50"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> and <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_51"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> are one-to-one.</p>
+    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_52"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> <dfn id="dfn-rounding-mode" tabindex="-1">rounding mode</dfn> is one of the values <emu-val>"ceil"</emu-val>, <emu-val>"floor"</emu-val>, <emu-val>"expand"</emu-val>, <emu-val>"trunc"</emu-val>, <emu-val>"halfEven"</emu-val>, <emu-val>"halfExpand"</emu-val>, <emu-val>"halfCeil"</emu-val>, <emu-val>"halfFloor"</emu-val>, and <emu-val>"halfTrunc"</emu-val>.</p>
     <p>The <dfn id="dfn-default-rounding-mode" tabindex="-1">default rounding mode</dfn> is the String value <emu-val>halfEven</emu-val>.</p>
-    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_55"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> <dfn id="dfn-digit" tabindex="-1">digit</dfn> is one of the values <emu-val>"0"</emu-val>, <emu-val>"1"</emu-val>, <emu-val>"2"</emu-val>, <emu-val>"3"</emu-val>, <emu-val>"4"</emu-val>, <emu-val>"5"</emu-val>, <emu-val>"6"</emu-val>, <emu-val>"7"</emu-val>, <emu-val>"8"</emu-val>, and <emu-val>"9"</emu-val></p>
-    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_56"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> <dfn id="dfn-decimal-string" tabindex="-1">decimal string</dfn> is a string whose syntax is that of a sequence of digits followed by, optionally, a <emu-val>"."</emu-val> and a sequence of digits.</p>
-    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_57"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> <dfn id="dfn-signed-decimal-string" tabindex="-1">signed decimal string</dfn> is a <emu-xref href="#dfn-decimal-string" id="_ref_58"><a href="#dfn-decimal-string">decimal string</a></emu-xref> optionally preceded by a <emu-val>"-"</emu-val> (dash).</p>
-    <p>An <dfn id="dfn-exponential-string" tabindex="-1">exponential string</dfn> is a string whose syntax is a <emu-xref href="#dfn-decimal-string" id="_ref_59"><a href="#dfn-decimal-string">decimal string</a></emu-xref> whose <emu-xref href="#dfn-mathematical-value" id="_ref_60"><a href="#dfn-mathematical-value">mathematical value</a></emu-xref> is at least 0 but less than 9, followed by an <emu-val>"E"</emu-val>, optionally a "-" (minus), and a sequence of digits.</p>
-    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_61"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> <dfn id="dfn-signed-exponential-string" tabindex="-1">signed exponential string</dfn> is an <emu-xref href="#dfn-exponential-string" id="_ref_62"><a href="#dfn-exponential-string">exponential string</a></emu-xref> optionally precided by a <emu-val>"-"</emu-val> (dash).</p>
+    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_53"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> <dfn id="dfn-digit" tabindex="-1">digit</dfn> is one of the values <emu-val>"0"</emu-val>, <emu-val>"1"</emu-val>, <emu-val>"2"</emu-val>, <emu-val>"3"</emu-val>, <emu-val>"4"</emu-val>, <emu-val>"5"</emu-val>, <emu-val>"6"</emu-val>, <emu-val>"7"</emu-val>, <emu-val>"8"</emu-val>, and <emu-val>"9"</emu-val></p>
+    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_54"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> <dfn id="dfn-decimal-string" tabindex="-1">decimal string</dfn> is a string whose syntax is that of a sequence of digits followed by, optionally, a <emu-val>"."</emu-val> and a sequence of digits.</p>
+    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_55"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> <dfn id="dfn-signed-decimal-string" tabindex="-1">signed decimal string</dfn> is a <emu-xref href="#dfn-decimal-string" id="_ref_56"><a href="#dfn-decimal-string">decimal string</a></emu-xref> optionally preceded by a <emu-val>"-"</emu-val> (dash).</p>
+    <p>An <dfn id="dfn-exponential-string" tabindex="-1">exponential string</dfn> is a string whose syntax is a <emu-xref href="#dfn-decimal-string" id="_ref_57"><a href="#dfn-decimal-string">decimal string</a></emu-xref> whose <emu-xref href="#dfn-mathematical-value" id="_ref_58"><a href="#dfn-mathematical-value">mathematical value</a></emu-xref> is at least 0 but less than 9, followed by an <emu-val>"E"</emu-val>, optionally a "-" (minus), and a sequence of digits.</p>
+    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_59"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> <dfn id="dfn-signed-exponential-string" tabindex="-1">signed exponential string</dfn> is an <emu-xref href="#dfn-exponential-string" id="_ref_60"><a href="#dfn-exponential-string">exponential string</a></emu-xref> optionally precided by a <emu-val>"-"</emu-val> (dash).</p>
     <p>The <dfn id="dfn-mathematical-value" tabindex="-1">mathematical value</dfn> of a Decimal128 object <emu-val>d</emu-val>, provided <emu-val>d</emu-val> is <emu-xref href="#finite"><a href="https://tc39.es/ecma262/#finite">finite</a></emu-xref> and not NaN, is the rational number <emu-val>coefficient</emu-val> of <emu-val>d</emu-val> multiplied by 10 raised to the power of the <emu-val>exponent</emu-val> of <emu-val>d</emu-val>. If <emu-val>d</emu-val> is infinite, the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>d</emu-val> is -∞ is <emu-val>d</emu-val> is negative and ∞ otherwise. If <emu-val>d</emu-val> is NaN, the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>d</emu-val> is undefined.</p>
-    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_63"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> Decimal128 value is said to be <dfn id="dfn-normal" tabindex="-1">normal</dfn> if its coefficient either (zero and has an exponent of zero) or has an exponent that is not divisible by ten. Example: 1.2 is <emu-xref href="#dfn-normal" id="_ref_64"><a href="#dfn-normal">normal</a></emu-xref>, but 1.20 is not <emu-xref href="#dfn-normal" id="_ref_65"><a href="#dfn-normal">normal</a></emu-xref>. In terms of <emu-xref href="#dfn-decimal-string" id="_ref_4"><a href="#dfn-decimal-string">decimal strings</a></emu-xref>, a <emu-xref href="#dfn-normal" id="_ref_66"><a href="#dfn-normal">normal</a></emu-xref> value corresponds precisely to strings whose decimal part terminates with a sequence of zeros.</p>
+    <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_61"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> Decimal128 value is said to be <dfn id="dfn-normal" tabindex="-1">normal</dfn> if its coefficient either (zero and has an exponent of zero) or has an exponent that is not divisible by ten. Example: 1.2 is <emu-xref href="#dfn-normal" id="_ref_62"><a href="#dfn-normal">normal</a></emu-xref>, but 1.20 is not <emu-xref href="#dfn-normal" id="_ref_63"><a href="#dfn-normal">normal</a></emu-xref>. In terms of <emu-xref href="#dfn-decimal-string" id="_ref_4"><a href="#dfn-decimal-string">decimal strings</a></emu-xref>, a <emu-xref href="#dfn-normal" id="_ref_64"><a href="#dfn-normal">normal</a></emu-xref> value corresponds precisely to strings whose decimal part terminates with a sequence of zeros.</p>
   </emu-intro>
   <emu-clause id="sec-the-decimal-constructor">
     <h1><span class="secnum">3.1</span> The Decimal128 Constructor</h1>
@@ -3035,23 +3035,23 @@ <h1><span class="secnum">3.1</span> The Decimal128 Constructor</h1>
     <h1><span class="secnum">4</span> Properties of the Decimal128 Prototype</h1>
     <emu-clause id="sec-decimal.prototype.isnan">
       <h1><span class="secnum">4.1</span> Decimal128.prototype.isNaN</h1>
-      <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_67"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> property indicating whether <emu-val>this</emu-val> value represents a <emu-xref href="#dfn-decimal128-nan" id="_ref_68"><a href="#dfn-decimal128-nan">Decimal128 NaN</a></emu-xref> value. The possible values are <emu-val>true</emu-val> and <emu-val>false</emu-val>.</p>
+      <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_65"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> property indicating whether <emu-val>this</emu-val> value represents a <emu-xref href="#dfn-decimal128-nan" id="_ref_66"><a href="#dfn-decimal128-nan">Decimal128 NaN</a></emu-xref> value. The possible values are <emu-val>true</emu-val> and <emu-val>false</emu-val>.</p>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.isfinite">
       <h1><span class="secnum">4.2</span> Decimale128.prototype.isFinite</h1>
-      <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_69"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> property indicating whether <emu-val>this</emu-val> value represents a <emu-xref href="#finite"><a href="https://tc39.es/ecma262/#finite">finite</a></emu-xref> value. The possible values are <emu-val>true</emu-val> and <emu-val>false</emu-val>. <emu-xref href="#dfn-decimal128-nan" id="_ref_70"><a href="#dfn-decimal128-nan">Decimal128 NaN</a></emu-xref> values are considered <emu-xref href="#finite"><a href="https://tc39.es/ecma262/#finite">finite</a></emu-xref>.</p>
+      <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_67"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> property indicating whether <emu-val>this</emu-val> value represents a <emu-xref href="#finite"><a href="https://tc39.es/ecma262/#finite">finite</a></emu-xref> value. The possible values are <emu-val>true</emu-val> and <emu-val>false</emu-val>. <emu-xref href="#dfn-decimal128-nan" id="_ref_68"><a href="#dfn-decimal128-nan">Decimal128 NaN</a></emu-xref> values are considered <emu-xref href="#finite"><a href="https://tc39.es/ecma262/#finite">finite</a></emu-xref>.</p>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.significand">
       <h1><span class="secnum">4.3</span> Decimale128.prototype.significand</h1>
-      <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_71"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> property that stores the significand of <emu-val>this</emu-val> value. Its type is BigInt. This property should be a BigInt even if <emu-val>this</emu-val> value is NaN or infinite.</p>
+      <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_69"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> property that stores the significand of <emu-val>this</emu-val> value. Its type is BigInt. This property should be a BigInt even if <emu-val>this</emu-val> value is NaN or infinite.</p>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.exponent">
       <h1><span class="secnum">4.4</span> Decimale128.prototype.exponent</h1>
-      <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_72"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> property that stores the exponent of <emu-val>this</emu-val> value. Its type is Number. It should always be an <emu-xref href="#integer"><a href="https://tc39.es/ecma262/#integer">integer</a></emu-xref>. This property should be a Number even if <emu-val>this</emu-val> value is NaN or infinite.</p>
+      <p><emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_70"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> property that stores the exponent of <emu-val>this</emu-val> value. Its type is Number. It should always be an <emu-xref href="#integer"><a href="https://tc39.es/ecma262/#integer">integer</a></emu-xref>. This property should be a Number even if <emu-val>this</emu-val> value is NaN or infinite.</p>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.abs">
       <h1><span class="secnum">4.5</span> Decimal128.prototype.abs ( )</h1>
-      <p>Computes the absolute value of <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_5"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>this</emu-val> value according to the rules specified in <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_6"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128</a></emu-xref> and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_7"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_73"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>. Returns a fresh result, regardless of the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>this</emu-val> value. <emu-val>this</emu-val> value is not modified.</p>
+      <p>Computes the absolute value of <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_5"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>this</emu-val> value according to the rules specified in <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_6"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128</a></emu-xref> and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_7"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_71"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>. Returns a fresh result, regardless of the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>this</emu-val> value. <emu-val>this</emu-val> value is not modified.</p>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.neg">
       <h1><span class="secnum">4.6</span> Decimal128.prototype.neg ( )</h1>
@@ -3059,63 +3059,63 @@ <h1><span class="secnum">4.6</span> Decimal128.prototype.neg ( )</h1>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.add">
       <h1><span class="secnum">4.7</span> Decimal128.prototype.add ( <var>x</var> [ , <var>options</var> ] )</h1>
-      <p>Adds <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_9"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>this</emu-val> value and <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_10"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>_x_</emu-val> according to the rules specified in <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_11"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128</a></emu-xref> and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_12"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting Decimal128 value. Returns a fresh result, regardless of the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>this</emu-val> value or <emu-val>_x_</emu-val>. Neither <emu-val>this</emu-val> value nor <emu-val>_x_</emu-val> is modified. If, in the computation, more significant are generated than can be stored in an <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_74"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>, consult <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> to determine the final significant <emu-xref href="#dfn-digit" id="_ref_75"><a href="#dfn-digit">digit</a></emu-xref>. If <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_13"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, compute the final significant <emu-xref href="#dfn-digit" id="_ref_76"><a href="#dfn-digit">digit</a></emu-xref> according to <emu-xref href="#dfn-default-rounding-mode" id="_ref_14"><a href="#dfn-default-rounding-mode">the default rounding mode</a></emu-xref>.</p>
+      <p>Adds <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_9"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>this</emu-val> value and <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_10"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>_x_</emu-val> according to the rules specified in <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_11"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128</a></emu-xref> and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_12"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting Decimal128 value. Returns a fresh result, regardless of the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>this</emu-val> value or <emu-val>_x_</emu-val>. Neither <emu-val>this</emu-val> value nor <emu-val>_x_</emu-val> is modified. If, in the computation, more significant are generated than can be stored in an <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_72"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>, consult <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> to determine the final significant <emu-xref href="#dfn-digit" id="_ref_73"><a href="#dfn-digit">digit</a></emu-xref>. If <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_13"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, compute the final significant <emu-xref href="#dfn-digit" id="_ref_74"><a href="#dfn-digit">digit</a></emu-xref> according to <emu-xref href="#dfn-default-rounding-mode" id="_ref_14"><a href="#dfn-default-rounding-mode">the default rounding mode</a></emu-xref>.</p>
       <emu-note><span class="note">Note</span><div class="note-contents">
 	<p>If <var>x</var> is not an instance of the Decimal128 object, then a <emu-val>TypeError</emu-val> will be thrown.</p>
 	<p>Returns the result of adding the current Decimal128 value to <var>x</var>.</p>
-	<p>If <var>options</var> is specified and <var>roundingMode</var> is a property of <var>options</var>, then <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) must be a <emu-xref href="#dfn-rounding-mode" id="_ref_15"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>. If <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) is not a <emu-xref href="#dfn-rounding-mode" id="_ref_16"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, a <emu-val>RangeError</emu-val> will be thrown. The addition will be carried out according to the specified <emu-xref href="#dfn-rounding-mode" id="_ref_77"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>.</p>
+	<p>If <var>options</var> is specified and <var>roundingMode</var> is a property of <var>options</var>, then <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) must be a <emu-xref href="#dfn-rounding-mode" id="_ref_15"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>. If <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) is not a <emu-xref href="#dfn-rounding-mode" id="_ref_16"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, a <emu-val>RangeError</emu-val> will be thrown. The addition will be carried out according to the specified <emu-xref href="#dfn-rounding-mode" id="_ref_75"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>.</p>
       </div></emu-note>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.subtract">
       <h1><span class="secnum">4.8</span> Decimal128.prototype.subtract ( <var>x</var> [ , <var>options</var> ] )</h1>
-      <p>Subtracts <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_17"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>_x_</emu-val> from <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_18"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>this</emu-val> value according to the rules for subtraction in the <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_19"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128</a></emu-xref> specification and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_20"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting IEEE Decimal128 value. Returns a fresh result, regardless of the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>_x_</emu-val>. Neither <emu-val>this</emu-val> value nor <emu-val>_x_</emu-val> is modified. If, in the computation, more significant are generated than can be stored in an <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_78"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>, consult <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> to determine the final significant <emu-xref href="#dfn-digit" id="_ref_79"><a href="#dfn-digit">digit</a></emu-xref>. If <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_21"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, compute the final significant <emu-xref href="#dfn-digit" id="_ref_80"><a href="#dfn-digit">digit</a></emu-xref> according to <emu-xref href="#dfn-default-rounding-mode" id="_ref_22"><a href="#dfn-default-rounding-mode">the default rounding mode</a></emu-xref>.</p>
+      <p>Subtracts <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_17"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>_x_</emu-val> from <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_18"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>this</emu-val> value according to the rules for subtraction in the <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_19"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128</a></emu-xref> specification and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_20"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting IEEE Decimal128 value. Returns a fresh result, regardless of the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>_x_</emu-val>. Neither <emu-val>this</emu-val> value nor <emu-val>_x_</emu-val> is modified. If, in the computation, more significant are generated than can be stored in an <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_76"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>, consult <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> to determine the final significant <emu-xref href="#dfn-digit" id="_ref_77"><a href="#dfn-digit">digit</a></emu-xref>. If <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_21"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, compute the final significant <emu-xref href="#dfn-digit" id="_ref_78"><a href="#dfn-digit">digit</a></emu-xref> according to <emu-xref href="#dfn-default-rounding-mode" id="_ref_22"><a href="#dfn-default-rounding-mode">the default rounding mode</a></emu-xref>.</p>
       <emu-note><span class="note">Note</span><div class="note-contents">
 	<p>Returns the result of subtracting <var>x</var> from the current Decimal128 value, which must be a Decimal128 object.</p>
-	<p>If <var>options</var> is specified and <var>roundingMode</var> is a property of <var>options</var>, then <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) must be a <emu-xref href="#dfn-rounding-mode" id="_ref_23"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>. If <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) is not a <emu-xref href="#dfn-rounding-mode" id="_ref_24"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, throw a <emu-val>RangeError</emu-val> exception. The subtraction will be carried out according to the specified <emu-xref href="#dfn-rounding-mode" id="_ref_81"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>.</p>
+	<p>If <var>options</var> is specified and <var>roundingMode</var> is a property of <var>options</var>, then <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) must be a <emu-xref href="#dfn-rounding-mode" id="_ref_23"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>. If <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) is not a <emu-xref href="#dfn-rounding-mode" id="_ref_24"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, throw a <emu-val>RangeError</emu-val> exception. The subtraction will be carried out according to the specified <emu-xref href="#dfn-rounding-mode" id="_ref_79"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>.</p>
       </div></emu-note>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.multiply">
       <h1><span class="secnum">4.9</span> Decimal128.prototype.multiply ( <var>x</var> [ , <var>options</var> ] )</h1>
-      <p>Multiplies <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_25"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>this</emu-val> value by <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_26"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>_x_</emu-val> according to the rules of the IEEE 754 Decimal128 specification and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_27"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting Decimal128 value. Returns a fresh result, regardless of the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>this</emu-val> value or that of <emu-val>_x_</emu-val>. Neither argument is modified. If, in the computation, more significant are generated than can be stored in an <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_82"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>, consult <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> to determine the final significant <emu-xref href="#dfn-digit" id="_ref_83"><a href="#dfn-digit">digit</a></emu-xref>. If <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_28"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, compute the final significant <emu-xref href="#dfn-digit" id="_ref_84"><a href="#dfn-digit">digit</a></emu-xref> according to <emu-xref href="#dfn-default-rounding-mode" id="_ref_29"><a href="#dfn-default-rounding-mode">the default rounding mode</a></emu-xref>.</p>
+      <p>Multiplies <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_25"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>this</emu-val> value by <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_26"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>_x_</emu-val> according to the rules of the IEEE 754 Decimal128 specification and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_27"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting Decimal128 value. Returns a fresh result, regardless of the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>this</emu-val> value or that of <emu-val>_x_</emu-val>. Neither argument is modified. If, in the computation, more significant are generated than can be stored in an <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_80"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>, consult <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> to determine the final significant <emu-xref href="#dfn-digit" id="_ref_81"><a href="#dfn-digit">digit</a></emu-xref>. If <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_28"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, compute the final significant <emu-xref href="#dfn-digit" id="_ref_82"><a href="#dfn-digit">digit</a></emu-xref> according to <emu-xref href="#dfn-default-rounding-mode" id="_ref_29"><a href="#dfn-default-rounding-mode">the default rounding mode</a></emu-xref>.</p>
       <emu-note><span class="note">Note</span><div class="note-contents">
 	<p>Returns the result of multiplying <emu-val>this</emu-val> value with <var>x</var>, which must be a Decimal128 object.</p>
-	<p>If <var>options</var> is specified and <var>roundingMode</var> is a property of <var>options</var>, then <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) must be a <emu-xref href="#dfn-rounding-mode" id="_ref_30"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>. If <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) is not a <emu-xref href="#dfn-rounding-mode" id="_ref_31"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, a <emu-val>RangeError</emu-val> will be thrown. The multiplication will be carried out according to the specified <emu-xref href="#dfn-rounding-mode" id="_ref_85"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>.</p>
+	<p>If <var>options</var> is specified and <var>roundingMode</var> is a property of <var>options</var>, then <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) must be a <emu-xref href="#dfn-rounding-mode" id="_ref_30"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>. If <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) is not a <emu-xref href="#dfn-rounding-mode" id="_ref_31"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, a <emu-val>RangeError</emu-val> will be thrown. The multiplication will be carried out according to the specified <emu-xref href="#dfn-rounding-mode" id="_ref_83"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>.</p>
       </div></emu-note>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.divide">
       <h1><span class="secnum">4.10</span> Decimal128.prototype.divide ( <var>x</var> [ , <var>options</var> ] )</h1>
-      <p>Divides <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_32"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>this</emu-val> value by <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_33"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>_y_</emu-val> according to the rules of the IEEE 754 Decimal128 specification and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_34"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting Decimal128 value. Returns a fresh result. Neither <emu-val>this</emu-val> value nor <emu-val>_x_</emu-val> is modified. If, in the computation, more significant are generated than can be stored in an <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_86"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>, consult <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> to determine the final significant <emu-xref href="#dfn-digit" id="_ref_87"><a href="#dfn-digit">digit</a></emu-xref>. If <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_35"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, compute the final significant <emu-xref href="#dfn-digit" id="_ref_88"><a href="#dfn-digit">digit</a></emu-xref> according to <emu-xref href="#dfn-default-rounding-mode" id="_ref_36"><a href="#dfn-default-rounding-mode">the default rounding mode</a></emu-xref>.</p>
+      <p>Divides <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_32"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>this</emu-val> value by <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_33"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>_y_</emu-val> according to the rules of the IEEE 754 Decimal128 specification and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_34"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting Decimal128 value. Returns a fresh result. Neither <emu-val>this</emu-val> value nor <emu-val>_x_</emu-val> is modified. If, in the computation, more significant are generated than can be stored in an <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_84"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>, consult <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> to determine the final significant <emu-xref href="#dfn-digit" id="_ref_85"><a href="#dfn-digit">digit</a></emu-xref>. If <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_35"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, compute the final significant <emu-xref href="#dfn-digit" id="_ref_86"><a href="#dfn-digit">digit</a></emu-xref> according to <emu-xref href="#dfn-default-rounding-mode" id="_ref_36"><a href="#dfn-default-rounding-mode">the default rounding mode</a></emu-xref>.</p>
       <emu-note><span class="note">Note</span><div class="note-contents">
 	<p>Returns the result of multiplying <var>x</var> from the current Decimal128 value, which must be a Decimal128 object.</p>
-	<p>If <var>options</var> is specified and <var>roundingMode</var> is a property of <var>options</var>, then <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) must be a <emu-xref href="#dfn-rounding-mode" id="_ref_37"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>. If <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) is not a <emu-xref href="#dfn-rounding-mode" id="_ref_38"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, a <emu-val>RangeError</emu-val> will be thrown. The multiplication will be carried out according to the specified <emu-xref href="#dfn-rounding-mode" id="_ref_89"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>.</p>
+	<p>If <var>options</var> is specified and <var>roundingMode</var> is a property of <var>options</var>, then <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) must be a <emu-xref href="#dfn-rounding-mode" id="_ref_37"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>. If <emu-xref aoid="Get"><a href="https://tc39.es/ecma262/#sec-get-o-p">Get</a></emu-xref>(<var>options</var>, <emu-val>roundingMode</emu-val>) is not a <emu-xref href="#dfn-rounding-mode" id="_ref_38"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, a <emu-val>RangeError</emu-val> will be thrown. The multiplication will be carried out according to the specified <emu-xref href="#dfn-rounding-mode" id="_ref_87"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>.</p>
       </div></emu-note>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.remainder">
-      <h1><span class="secnum">4.11</span> Decimal128.prototype.remainder ( <var>x</var> [ , <var>options</var> ] )</h1>
-      <p>Computes the remainder of dividing <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_39"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of *this_ value by <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_40"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>_x_</emu-val> according to the rules of the IEEE 754 Decimal128 specification and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_41"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting Decimal128 value. The sign of the result is the sign of <emu-val>this</emu-val> value. Returns a fresh result. If, in the computation, more significant are generated than can be stored in an <emu-xref href="#dfn-ieee-754-decimal128-value" id="_ref_90"><a href="#dfn-ieee-754-decimal128-value">IEEE 754 Decimal128 value</a></emu-xref>, consult <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> to determine the final significant <emu-xref href="#dfn-digit" id="_ref_91"><a href="#dfn-digit">digit</a></emu-xref>. If <var class="field">[[_options_]]</var><var class="field">[[roundingMode]]</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_42"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, compute the final significant <emu-xref href="#dfn-digit" id="_ref_92"><a href="#dfn-digit">digit</a></emu-xref> according to <emu-xref href="#dfn-default-rounding-mode" id="_ref_43"><a href="#dfn-default-rounding-mode">the default rounding mode</a></emu-xref>.</p>
+      <h1><span class="secnum">4.11</span> Decimal128.prototype.remainder ( <var>x</var> )</h1>
+      <p>Computes the remainder of dividing <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_39"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of *this_ value by <emu-xref href="#dfn-map-to-ieee-754-decimal128" id="_ref_40"><a href="#dfn-map-to-ieee-754-decimal128">B</a></emu-xref> of <emu-val>_x_</emu-val> according to the rules of the IEEE 754 Decimal128 specification and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_41"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> of the resulting Decimal128 value. The sign of the result is the sign of <emu-val>this</emu-val> value. Returns a fresh result.</p>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.equals">
       <h1><span class="secnum">4.12</span> Decimal128.prototype.equals ( <var>x</var> )</h1>
-      <p>Compares the <emu-xref href="#dfn-mathematical-value" id="_ref_44"><a href="#dfn-mathematical-value">mathematical value</a></emu-xref> of <emu-val>this</emu-val> value with the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>_x_</emu-val>, which is supposed to be a Decimal128 object. If <emu-val>_x_</emu-val> is not a Decimal128 object, throws a <emu-val>TypeError</emu-val>. Returns <emu-val>true</emu-val> or <emu-val>false</emu-val>.</p>
+      <p>Compares the <emu-xref href="#dfn-mathematical-value" id="_ref_42"><a href="#dfn-mathematical-value">mathematical value</a></emu-xref> of <emu-val>this</emu-val> value with the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>_x_</emu-val>, which is supposed to be a Decimal128 object. If <emu-val>_x_</emu-val> is not a Decimal128 object, throws a <emu-val>TypeError</emu-val>. Returns <emu-val>true</emu-val> or <emu-val>false</emu-val>.</p>
       <emu-alg><ol><li>If <var>x</var> is not a Decimal128 object, then<ol><li>throw a <emu-val>TypeError</emu-val> exception.</li></ol></li><li>If [<emu-val>this</emu-val>]<var class="field">[[isNaN]]</var>, then<ol><li>If [<emu-val>_x_</emu-val>]<var class="field">[[isNaN]]</var> is <emu-val>true</emu-val>, return <emu-val>true</emu-val>.</li><li>Return <emu-val>false</emu-val>.</li></ol></li><li>If [<emu-val>_x_</emu-val>]<var class="field">[[isNaN]]</var> is <emu-val>true</emu-val>, return <emu-val>false</emu-val>.</li><li>Let <emu-val>_c_</emu-val> be the result of calling the IEEE 754 Decimal128 compare_total procedure on <emu-val>this</emu-val> value and <emu-val>_x_</emu-val>.</li><li>If <emu-val>_c_</emu-val> is 0, return <emu-val>true</emu-val>, else return <emu-val>false</emu-val>.</li></ol></emu-alg>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.lessthan">
       <h1><span class="secnum">4.13</span> Decimal128.prototype.lessThan ( <var>x</var> )</h1>
-      <p>Compares the <emu-xref href="#dfn-mathematical-value" id="_ref_45"><a href="#dfn-mathematical-value">mathematical value</a></emu-xref> of <emu-val>this</emu-val> value with the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>_x_</emu-val>, which is supposed to be a Decimal128 object. If <emu-val>_x_</emu-val> is not a Decimal128 object, throws a <emu-val>TypeError</emu-val>. Returns <emu-val>true</emu-val> or <emu-val>false</emu-val> according as the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>this</emu-val> value is strictly less than the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>_x_</emu-val>.</p>
+      <p>Compares the <emu-xref href="#dfn-mathematical-value" id="_ref_43"><a href="#dfn-mathematical-value">mathematical value</a></emu-xref> of <emu-val>this</emu-val> value with the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>_x_</emu-val>, which is supposed to be a Decimal128 object. If <emu-val>_x_</emu-val> is not a Decimal128 object, throws a <emu-val>TypeError</emu-val>. Returns <emu-val>true</emu-val> or <emu-val>false</emu-val> according as the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>this</emu-val> value is strictly less than the <emu-xref href="#mathematical-value-of"><a href="https://tc39.es/ecma262/#mathematical-value-of">mathematical value of</a></emu-xref> <emu-val>_x_</emu-val>.</p>
       <emu-alg><ol><li>If <var>x</var> is not a Decimal128 object, then<ol><li>throw a <emu-val>TypeError</emu-val> exception.</li></ol></li><li>If [<emu-val>this</emu-val>]<var class="field">[[isNaN]]</var>, then<ol><li>If [<emu-val>_x_</emu-val>]<var class="field">[[isNaN]]</var> is <emu-val>true</emu-val>, return <emu-val>true</emu-val>.</li><li>Return <emu-val>false</emu-val>.</li></ol></li><li>If [<emu-val>_x_</emu-val>]<var class="field">[[isNaN]]</var> is <emu-val>true</emu-val>, return <emu-val>true</emu-val>.</li><li>Let <emu-val>_c_</emu-val> be the result of calling the IEEE 754 Decimal128 compare_total procedure on <emu-val>this</emu-val> value and <emu-val>_x_</emu-val>.</li><li>If <emu-val>_c_</emu-val> is -1, return <emu-val>true</emu-val>, else return <emu-val>false</emu-val>.</li></ol></emu-alg>
     </emu-clause>
     <emu-clause id="sec-decimal-method-round">
       <h1><span class="secnum">4.14</span> Decimal128.prototype.round ( <var>numFractionalDigits</var> [ , <var>mode</var> ] )</h1>
-      <p>Rounds <emu-val>this</emu-val> value according to the specified <emu-xref href="#dfn-rounding-mode" id="_ref_93"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, returning a fresh result. The result will have at most <var>numFractionalDigits</var> after the decimal point.</p>
+      <p>Rounds <emu-val>this</emu-val> value according to the specified <emu-xref href="#dfn-rounding-mode" id="_ref_88"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, returning a fresh result. The result will have at most <var>numFractionalDigits</var> after the decimal point.</p>
       <emu-note><span class="note">Note</span><div class="note-contents">
 	<p>If <var>mode</var> is neither <emu-val>undefined</emu-val> nor a String, throw a <emu-val>TypeError</emu-val> exception.</p>
-	<p>If <var>mode</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_46"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, throw a <emu-val>RangeError</emu-val> exception.</p>
+	<p>If <var>mode</var> is not a <emu-xref href="#dfn-rounding-mode" id="_ref_44"><a href="#dfn-rounding-mode">rounding mode</a></emu-xref>, throw a <emu-val>RangeError</emu-val> exception.</p>
       </div></emu-note>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.tostring">
       <h1><span class="secnum">4.15</span> Decimal128.prototype.toString ( [ <var>options</var> ] )</h1>
-      <p>Renders <emu-val>this</emu-val> value as a <emu-xref href="#dfn-signed-decimal-string" id="_ref_47"><a href="#dfn-signed-decimal-string">signed decimal string</a></emu-xref>. <var>options</var>, is defined, is supposed to be a plain object. If <var>options</var> has the property <emu-val>numDecimal128Digits</emu-val> and the value of that property is a non-negative Number, the return value will be a string that has exactly that many digits after the decimal point, possibly with the addition of trailing zeros.</p>
-      <emu-alg><ol><li>Let <var>roundingMode</var> be <var class="field">[[_options_]]</var>[roundingMode]].</li><li>If <var>roundingMode</var> is not one of <emu-val>"ceil"</emu-val>, <emu-val>"floor"</emu-val>, <emu-val>"expand"</emu-val>, <emu-val>"trunc"</emu-val>, <emu-val>"halfEven"</emu-val>, <emu-val>"halfExpand"</emu-val>, <emu-val>"halfCeil"</emu-val>, <emu-val>"halfFloor"</emu-val>, or <emu-val>"halfTrunc"</emu-val>, then<ol><li>set <var>roundingMode</var> to <emu-val>"halfEven"</emu-val>.</li></ol></li><li>Let <var>format</var> be <var class="field">[[_options_]]</var>[format]].</li><li>If <var>format</var> is not one of <emu-val>"decimal"</emu-val> or <emu-val>"exponential"</emu-val>, then<ol><li>set <var>format</var> to <emu-val>"decimal"</emu-val>.</li></ol></li><li>If <var>format</var> is <emu-val>"decimal</emu-val>", then<ol><li>return the result of calling IEEE 754's convertToDecimalCharacter with a second argument ensuring that a <emu-xref href="#dfn-signed-decimal-string" id="_ref_48"><a href="#dfn-signed-decimal-string">signed decimal string</a></emu-xref> is generated. TODO convertToDecimalCharacter is unspecified, so we need to do that work here.</li></ol></li><li>Return the result of calling IEEE 754's convertToDecimalCharacter with a second argument ensuring that a <emu-xref href="#dfn-signed-exponential-string" id="_ref_49"><a href="#dfn-signed-exponential-string">signed exponential string</a></emu-xref> is generated. TODO convertToDecimalCharacter is unspecified, so we need to do that work here.</li></ol></emu-alg>
+      <p>Renders <emu-val>this</emu-val> value as a <emu-xref href="#dfn-signed-decimal-string" id="_ref_45"><a href="#dfn-signed-decimal-string">signed decimal string</a></emu-xref>. <var>options</var>, is defined, is supposed to be a plain object. If <var>options</var> has the property <emu-val>numDecimal128Digits</emu-val> and the value of that property is a non-negative Number, the return value will be a string that has exactly that many digits after the decimal point, possibly with the addition of trailing zeros.</p>
+      <emu-alg><ol><li>Let <var>roundingMode</var> be <var class="field">[[_options_]]</var>[roundingMode]].</li><li>If <var>roundingMode</var> is not one of <emu-val>"ceil"</emu-val>, <emu-val>"floor"</emu-val>, <emu-val>"expand"</emu-val>, <emu-val>"trunc"</emu-val>, <emu-val>"halfEven"</emu-val>, <emu-val>"halfExpand"</emu-val>, <emu-val>"halfCeil"</emu-val>, <emu-val>"halfFloor"</emu-val>, or <emu-val>"halfTrunc"</emu-val>, then<ol><li>set <var>roundingMode</var> to <emu-val>"halfEven"</emu-val>.</li></ol></li><li>Let <var>format</var> be <var class="field">[[_options_]]</var>[format]].</li><li>If <var>format</var> is not one of <emu-val>"decimal"</emu-val> or <emu-val>"exponential"</emu-val>, then<ol><li>set <var>format</var> to <emu-val>"decimal"</emu-val>.</li></ol></li><li>If <var>format</var> is <emu-val>"decimal</emu-val>", then<ol><li>return the result of calling IEEE 754's convertToDecimalCharacter with a second argument ensuring that a <emu-xref href="#dfn-signed-decimal-string" id="_ref_46"><a href="#dfn-signed-decimal-string">signed decimal string</a></emu-xref> is generated. TODO convertToDecimalCharacter is unspecified, so we need to do that work here.</li></ol></li><li>Return the result of calling IEEE 754's convertToDecimalCharacter with a second argument ensuring that a <emu-xref href="#dfn-signed-exponential-string" id="_ref_47"><a href="#dfn-signed-exponential-string">signed exponential string</a></emu-xref> is generated. TODO convertToDecimalCharacter is unspecified, so we need to do that work here.</li></ol></emu-alg>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.valueof">
       <h1><span class="secnum">4.16</span> Decimal128.prototype.valueOf ( <var>x</var> )</h1>
@@ -3138,7 +3138,7 @@ <h2>Software License</h2>
   <li>Neither the name of the authors nor Ecma International may be used to endorse or promote products derived from this software without specific prior written permission.</li>
 </ol>
 
-<p>THIS SOFTWARE IS PROVIDED BY THE ECMA INTERNATIONAL "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_94"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL ECMA INTERNATIONAL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</p>
+<p>THIS SOFTWARE IS PROVIDED BY THE ECMA INTERNATIONAL "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR <emu-xref href="#dfn-map-from-ieee-754-decimal128" id="_ref_89"><a href="#dfn-map-from-ieee-754-decimal128">A</a></emu-xref> PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL ECMA INTERNATIONAL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</p>
 
     </emu-annex>
 
diff --git a/spec.emu b/spec.emu
index d6f6b3c5..e21de491 100644
--- a/spec.emu
+++ b/spec.emu
@@ -149,8 +149,8 @@ location: https://github.com/tc39/proposal-decimal/
       </emu-note>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.remainder">
-      <h1>Decimal128.prototype.remainder ( _x_ [ , _options_ ] )</h1>
-      <p>Computes the remainder of dividing <emu-xref href="#dfn-map-to-ieee-754-decimal128">B</emu-xref> of *this_ value by <emu-xref href="#dfn-map-to-ieee-754-decimal128">B</emu-xref> of *_x_* according to the rules of the IEEE 754 Decimal128 specification and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128">A</emu-xref> of the resulting Decimal128 value. The sign of the result is the sign of *this* value. Returns a fresh result. If, in the computation, more significant are generated than can be stored in an IEEE 754 Decimal128 value, consult [[_options_]][[roundingMode]] to determine the final significant digit. If [[_options_]][[roundingMode]] is not a <emu-xref href="#dfn-rounding-mode">rounding mode</emu-xref>, compute the final significant digit according to <emu-xref href="#dfn-default-rounding-mode">the default rounding mode</emu-xref>.</p>
+      <h1>Decimal128.prototype.remainder ( _x_ )</h1>
+      <p>Computes the remainder of dividing <emu-xref href="#dfn-map-to-ieee-754-decimal128">B</emu-xref> of *this_ value by <emu-xref href="#dfn-map-to-ieee-754-decimal128">B</emu-xref> of *_x_* according to the rules of the IEEE 754 Decimal128 specification and returns <emu-xref href="#dfn-map-from-ieee-754-decimal128">A</emu-xref> of the resulting Decimal128 value. The sign of the result is the sign of *this* value. Returns a fresh result.</p>
     </emu-clause>
     <emu-clause id="sec-decimal.prototype.equals">
       <h1>Decimal128.prototype.equals ( _x_ )</h1>