Define AO to massage a potential Decimal128 value to an actual one

spec.emu

@@ -75,7 +75,7 @@ location: https://github.com/tc39/proposal-decimal/
           <li>a mathematical value</li>
         </ul></li>
         <li>_q_ is an integer satisfying -6176 ≤ _q_ ≤ 6111,</li>
-        <li>If _v_ is a mathematical value, then v × 10<sup>-_q_</sup> is an integer _n_ such that 0 < _n_ < 10<sup>34</sup></li>
+        <li>If _v_ is a mathematical value, then v × 10<sup>-_q_</sup> is an integer _n_ such that 0 < abs(_n_) < 10<sup>34</sup></li>
       </ul>
     </ul>
     <p>The <dfn id="dfn-decimal128-mathematical-value">mathematical value</dfn> of a finite Decimal128 value _x_ = « _v_, _q_ »<sub>𝔻</sub> is defined as follows:</p>
@@ -247,6 +247,26 @@ location: https://github.com/tc39/proposal-decimal/
         1. Return _O_.
       </emu-alg>
     </emu-clause>
+
+    <emu-clause id="sec-decimal128-d" type="abstract operation">
+      <h1>
+        EnsureDecimal128Value (
+          _coefficient_ : a mathematical value,
+          _intendedExponent_ : a mathematical value
+        ): either a normal completion containing a Decimal128 value or a throw completion
+      </h1>
+      <dl class="header">
+        <dt>description</dt>
+        <dd>It attempts to convert the pair of arguments, which might be out of range when considered as a Decimal128 value, into a Decimal128 value, throwing an exception if the conversion cannot be done.</dd>
+      </dl>
+      <emu-alg>
+        1. If -6111 ≤ _intendedExponent_ ≤ 6176, then
+          1. If _coefficient_ × 10<sup>_intendedExponent_</sup> is an integer _n_ such that 0 < abs(_n_) < 10<sup>34</sup>, return « _coefficient, _intendedExponent_ ».
+          1. Throw a *RangeError* exception.
+        1. If _intendedExponent_ < 0, return ? EnsureDecimal128Value(_coefficient_ / 10, _intendedExponent_ + 1).
+        1. Return ? EnsureDecimal128Value(_coefficient_ × 10, _intendedExponent_ + 1).
+      </emu-alg>
+    </emu-clause>
   </emu-clause>
 
   <emu-clause id="sec-the-decimal-constructor">
@@ -340,7 +360,7 @@ location: https://github.com/tc39/proposal-decimal/
         1. If _d2_ is *+∞*<sub>𝔻</sub>, return Decimal128ValueToObject(*NaN*<sub>𝔻</sub>).
         1. If _d2_ is *-∞*<sub>𝔻</sub>, return Decimal128ValueToObject(*-∞*<sub>𝔻</sub>).
         1. Return Decimal128ValueToObject(*-∞*<sub>𝔻</sub>).
-      1. Return <mark>Decimal128ValueToObject(« _d1_[0] + _d2_[0], min(_d1_[1], _d2_[1]) »)</mark>.
+      1. Return Decimal128ValueToObject(? EnsureDecimal128Value(_d1_[0] + _d2_[0], min(_d1_[1], _d2_[1]))).
     </emu-alg>
   </emu-clause>
 
@@ -362,7 +382,7 @@ location: https://github.com/tc39/proposal-decimal/
         1. If _d2_ is *+∞*<sub>𝔻</sub>, return Decimal128ValueToObject(*-∞*<sub>𝔻</sub>).
         1. If _d2_ is *-∞*<sub>𝔻</sub>, return Decimal128ValueToObject(*NaN*<sub>𝔻</sub>).
         1. Return Decimal128ValueToObject(*-∞*<sub>𝔻</sub>).
-      1. Return <mark>Decimal128ValueToObject(« d1[0] - d2[0], min(d1[1], d2[1]) »)</mark>.
+      1. Return Decimal128ValueToObject(? EnsureDecimal128Value(d1[0] - d2[0], min(d1[1], d2[1]))).
     </emu-alg>
   </emu-clause>
 
@@ -387,7 +407,7 @@ location: https://github.com/tc39/proposal-decimal/
         1. If _d2_ is a zero Decimal128 value, return Decimal128ValueToObject(*NaN*<sub>𝔻</sub>).
         1. If _d2_[0] < 0, return Decimal128ValueToObject(*+∞*<sub>𝔻</sub>).
         1. Return Decimal128ValueToObject(*-∞*<sub>𝔻</sub>).
-      1. Return <mark>Decimal128ValueToObject(« _d1_[0] × _d2_[0], min(_d1_[1], _d2_[1]) »)</mark>.
+      1. Return Decimal128ValueToObject(? EnsureDecimal128Value (_d1_[0] × _d2_[0], _d1_[1] + _d2_[1])).
     </emu-alg>
   </emu-clause>
 
@@ -403,7 +423,7 @@ location: https://github.com/tc39/proposal-decimal/
       1. If _d1_ or _d2_ is *NaN*<sub>𝔻</sub>, return Decimal128ValueToObject(*NaN*<sub>𝔻</sub>).
       1. If _d1_ is *+∞*<sub>𝔻</sub> or *-∞*<sub>𝔻</sub>, return Decimal128ValueToObject(*NaN*<sub>𝔻</sub>).
       1. If _d2_ is *-∞*<sub>𝔻</sub> or *-∞*<sub>𝔻</sub>, return Decimal128ValueToObject(*NaN*<sub>𝔻</sub>).
-      1. Return <mark>Decimal128ValueToObject(« _d1_[0] / _d2_[0], min(_d1_[1], _d2_[1]) »)</mark>.
+      1. Return Decimal128ValueToObject(? EnsureDecimal128Value(_d1_[0] / _d2_[0], min(_d1_[1], _d2_[1]))).</mark>.
     </emu-alg>
   </emu-clause>
 
@@ -419,7 +439,7 @@ location: https://github.com/tc39/proposal-decimal/
       1. If _d1_ or _d2_ is *NaN*<sub>𝔻</sub>, return Decimal128ValueToObject(*NaN*<sub>𝔻</sub>).
       1. If _d1_ is *+∞*<sub>𝔻</sub> or *-∞*<sub>𝔻</sub>, return Decimal128ValueToObject(*NaN*<sub>𝔻</sub>).
       1. If _d1_ is *-∞*<sub>𝔻</sub> or *-∞*<sub>𝔻</sub>, return Decimal128ValueToObject(*NaN*<sub>𝔻</sub>).
-      1. Return <mark>Decimal128ValueToObject(« _d1_[0] % _d2_[0], min(_d1_[1], _d2_[1]) »)</mark>.
+      1. Return Decimal128ValueToObject(? EnsureDecimal128Value(_d1_[0] % _d2_[0], _d1_[1] + _d2_[1])).
     </emu-alg>
     <emu-note>
       <p>The remainder operation specified here deviates from the IEEE 754 remainder operation. We follow the <emu-xref href="#sec-numeric-types-number-remainder">the remainder operation for Number</emu-xref> rather than IEEE 754, which specifies that, for example, the remainder 46 and 10 is -4 rather than 6.</p>