Editorial: change dfn for "mathematical value" and add "mathematical …

…value of" (#2822)

spec.html

@@ -1002,8 +1002,8 @@ <h1>Static Semantics</h1>
       <h1>Mathematical Operations</h1>
       <p>This specification makes reference to these kinds of numeric values:</p>
       <ul>
-        <li><em>Mathematical values</em>: Arbitrary real numbers, used as the default numeric type.</li>
-        <li><em>Extended mathematical values</em>: Mathematical values together with +&infin; and -&infin;.</li>
+        <li><dfn id="mathematical-value" variants="mathematical value,mathematical values">Mathematical values</dfn>: Arbitrary real numbers, used as the default numeric type.</li>
+        <li><dfn id="extended-mathematical-value" variants="extended mathematical value,extended mathematical values">Extended mathematical values</dfn>: Mathematical values together with +&infin; and -&infin;.</li>
         <li><em>Numbers</em>: IEEE 754-2019 double-precision floating point values.</li>
         <li><em>BigInts</em>: ECMAScript language values representing arbitrary integers in a one-to-one correspondence.</li>
       </ul>
@@ -1014,7 +1014,7 @@ <h1>Mathematical Operations</h1>
       <p>Numeric operators applied to mixed-type operands (such as a Number and a mathematical value) are not defined and should be considered an editorial error in this specification.</p>
       <p>This specification denotes most numeric values in base 10; it also uses numeric values of the form 0x followed by digits 0-9 or A-F as base-16 values.</p>
       <p>When the term <dfn id="integer" oldids="mathematical integer" variants="integers">integer</dfn> is used in this specification, it refers to a mathematical value which is in the set of integers, unless otherwise stated. When the term <dfn id="integral-number" variants="integral Numbers">integral Number</dfn> is used in this specification, it refers to a Number value whose mathematical value is in the set of integers.</p>
-      <p>Conversions between mathematical values and Numbers or BigInts are always explicit in this document. A conversion from a mathematical value or extended mathematical value _x_ to a Number is denoted as "the Number value for _x_" or <emu-eqn id="𝔽" aoid="𝔽">𝔽(_x_)</emu-eqn>, and is defined in <emu-xref href="#sec-ecmascript-language-types-number-type"></emu-xref>. A conversion from an integer _x_ to a BigInt is denoted as "the BigInt value for _x_" or <emu-eqn id="ℤ" aoid="ℤ">ℤ(_x_)</emu-eqn>. A conversion from a Number or BigInt _x_ to a mathematical value is denoted as "the <dfn id="mathematical-value">mathematical value</dfn> of _x_", or <emu-eqn id="ℝ" aoid="ℝ">ℝ(_x_)</emu-eqn>. The mathematical value of *+0*<sub>𝔽</sub> and *-0*<sub>𝔽</sub> is the mathematical value 0. The mathematical value of non-finite values is not defined. The <dfn id="extended-mathematical-value">extended mathematical value</dfn> of _x_ is the mathematical value of _x_ for finite values, and is +&infin; and -&infin; for *+&infin;*<sub>𝔽</sub> and *-&infin;*<sub>𝔽</sub> respectively; it is not defined for *NaN*.</p>
+      <p>Conversions between mathematical values and Numbers or BigInts are always explicit in this document. A conversion from a mathematical value or extended mathematical value _x_ to a Number is denoted as "the Number value for _x_" or <emu-eqn id="𝔽" aoid="𝔽">𝔽(_x_)</emu-eqn>, and is defined in <emu-xref href="#sec-ecmascript-language-types-number-type"></emu-xref>. A conversion from an integer _x_ to a BigInt is denoted as "the <dfn id="bigint-value-for">BigInt value for</dfn> _x_" or <emu-eqn id="ℤ" aoid="ℤ">ℤ(_x_)</emu-eqn>. A conversion from a Number or BigInt _x_ to a mathematical value is denoted as "the <dfn id="mathematical-value-of">mathematical value of</dfn> _x_", or <emu-eqn id="ℝ" aoid="ℝ">ℝ(_x_)</emu-eqn>. The mathematical value of *+0*<sub>𝔽</sub> and *-0*<sub>𝔽</sub> is the mathematical value 0. The mathematical value of non-finite values is not defined. The <dfn id="extended-mathematical-value-of">extended mathematical value of</dfn> _x_ is the mathematical value of _x_ for finite values, and is +&infin; and -&infin; for *+&infin;*<sub>𝔽</sub> and *-&infin;*<sub>𝔽</sub> respectively; it is not defined for *NaN*.</p>
       <p>The mathematical function <emu-eqn id="eqn-abs" aoid="abs">abs(_x_)</emu-eqn> produces the absolute value of _x_, which is <emu-eqn>-_x_</emu-eqn> if _x_ &lt; 0 and otherwise is _x_ itself.</p>
       <p>The mathematical function <emu-eqn id="eqn-min" aoid="min">min(_x1_, _x2_, &hellip; , _xN_)</emu-eqn> produces the mathematically smallest of <emu-eqn>_x1_</emu-eqn> through <emu-eqn>_xN_</emu-eqn>. The mathematical function <emu-eqn id="eqn-max" aoid="max">max(_x1_, _x2_, ..., _xN_)</emu-eqn> produces the mathematically largest of <emu-eqn>_x1_</emu-eqn> through <emu-eqn>_xN_</emu-eqn>. The domain and range of these mathematical functions are the extended mathematical values.</p>
       <p>The notation &ldquo;<emu-eqn id="eqn-modulo" aoid="modulo">_x_ modulo _y_</emu-eqn>&rdquo; (_y_ must be finite and non-zero) computes a value _k_ of the same sign as _y_ (or zero) such that <emu-eqn>abs(_k_) &lt; abs(_y_) and _x_ - _k_ = _q_ &times; _y_</emu-eqn> for some integer _q_.</p>
@@ -1768,7 +1768,7 @@ <h1>The Number Type</h1>
         <p>where _s_ is 1 or -1, _m_ is an integer such that 0 &lt; _m_ &lt; 2<sup>52</sup>, and _e_ is -1074.</p>
         <p>Note that all the positive and negative integers whose magnitude is no greater than 2<sup>53</sup> are representable in the Number type. The integer 0 has two representations in the Number type: *+0*<sub>𝔽</sub> and *-0*<sub>𝔽</sub>.</p>
         <p>A finite number has an <em>odd significand</em> if it is non-zero and the integer _m_ used to express it (in one of the two forms shown above) is odd. Otherwise, it has an <em>even significand</em>.</p>
-        <p>In this specification, the phrase &ldquo;the <dfn id="number-value">Number value</dfn> for _x_&rdquo; where _x_ represents an exact real mathematical quantity (which might even be an irrational number such as &pi;) means a Number value chosen in the following manner. Consider the set of all finite values of the Number type, with *-0*<sub>𝔽</sub> removed and with two additional values added to it that are not representable in the Number type, namely 2<sup>1024</sup> (which is <emu-eqn>+1 &times; 2<sup>53</sup> &times; 2<sup>971</sup></emu-eqn>) and <emu-eqn>-2<sup>1024</sup></emu-eqn> (which is <emu-eqn>-1 &times; 2<sup>53</sup> &times; 2<sup>971</sup></emu-eqn>). Choose the member of this set that is closest in value to _x_. If two values of the set are equally close, then the one with an even significand is chosen; for this purpose, the two extra values 2<sup>1024</sup> and <emu-eqn>-2<sup>1024</sup></emu-eqn> are considered to have even significands. Finally, if 2<sup>1024</sup> was chosen, replace it with *+&infin;*<sub>𝔽</sub>; if <emu-eqn>-2<sup>1024</sup></emu-eqn> was chosen, replace it with *-&infin;*<sub>𝔽</sub>; if *+0*<sub>𝔽</sub> was chosen, replace it with *-0*<sub>𝔽</sub> if and only if _x_ &lt; 0; any other chosen value is used unchanged. The result is the Number value for _x_. (This procedure corresponds exactly to the behaviour of the IEEE 754-2019 roundTiesToEven mode.)</p>
+        <p>In this specification, the phrase &ldquo;the <dfn id="number-value-for" oldids="number-value">Number value for</dfn> _x_&rdquo; where _x_ represents an exact real mathematical quantity (which might even be an irrational number such as &pi;) means a Number value chosen in the following manner. Consider the set of all finite values of the Number type, with *-0*<sub>𝔽</sub> removed and with two additional values added to it that are not representable in the Number type, namely 2<sup>1024</sup> (which is <emu-eqn>+1 &times; 2<sup>53</sup> &times; 2<sup>971</sup></emu-eqn>) and <emu-eqn>-2<sup>1024</sup></emu-eqn> (which is <emu-eqn>-1 &times; 2<sup>53</sup> &times; 2<sup>971</sup></emu-eqn>). Choose the member of this set that is closest in value to _x_. If two values of the set are equally close, then the one with an even significand is chosen; for this purpose, the two extra values 2<sup>1024</sup> and <emu-eqn>-2<sup>1024</sup></emu-eqn> are considered to have even significands. Finally, if 2<sup>1024</sup> was chosen, replace it with *+&infin;*<sub>𝔽</sub>; if <emu-eqn>-2<sup>1024</sup></emu-eqn> was chosen, replace it with *-&infin;*<sub>𝔽</sub>; if *+0*<sub>𝔽</sub> was chosen, replace it with *-0*<sub>𝔽</sub> if and only if _x_ &lt; 0; any other chosen value is used unchanged. The result is the Number value for _x_. (This procedure corresponds exactly to the behaviour of the IEEE 754-2019 roundTiesToEven mode.)</p>
         <p>The Number value for +&infin; is *+&infin;*<sub>𝔽</sub>, and the Number value for -&infin; is *-&infin;*<sub>𝔽</sub>.</p>
         <p>Some ECMAScript operators deal only with integers in specific ranges such as <emu-eqn>-2<sup>31</sup></emu-eqn> through <emu-eqn>2<sup>31</sup> - 1</emu-eqn>, inclusive, or in the range 0 through <emu-eqn>2<sup>16</sup> - 1</emu-eqn>, inclusive. These operators accept any value of the Number type but first convert each such value to an integer value in the expected range. See the descriptions of the numeric conversion operations in <emu-xref href="#sec-type-conversion"></emu-xref>.</p>