spec: explicitly define notion of "representability" (clarification)

Throughout the spec we use the notion of a constant x being
representable by a value of type T. While intuitively clear,
at least for floating-point and complex constants types, the
concept was not well-defined. In the section on Conversions
there was an extra rule for floating-point types only and it
missed the case of floating-point values overflowing to an
infinity after rounding.

Since the concept is important to Go, and a compiler most
certainly will have a function to test "representability",
it seems warranted to define the term explicitly in the spec.

This change introduces a new entry "Representability" under
the section on "Properties of types and values", and defines
the term explicitly, together with examples.

The phrase used is "representable by" rather than "representable as"
because the former use is prevalent in the spec.

Additionally, it clarifies that a floating-point constant
that overflows to an infinity after rounding is never
representable by a value of a floating-point type, even though
infinities are valid values of IEEE floating point types.
This is required because there are not infinite value constants
in the language (like there is also no -0.0) and representability
also matters for constant conversions. This is not a language
change, and type-checkers have been following this rule before.

The change also introduces links throughout the spec to the new
section as appropriate and removes duplicate text and examples
elsewhere (Constants and Conversions sections), leading to
simplifications in the relevant paragraphs.

Fixes #15389.

Change-Id: I8be0e071552df0f18998ef4c5ef521f64ffe8c44
Reviewed-on: https://go-review.googlesource.com/57530
Reviewed-by: Rob Pike <r@golang.org>
Reviewed-by: Ian Lance Taylor <iant@golang.org>
Reviewed-by: Matthew Dempsky <mdempsky@google.com>

doc/go_spec.html

@@ -577,11 +577,7 @@ <h2 id="Constants">Constants</h2>
 <a href="#Assignments">assignment</a> or as an
 operand in an <a href="#Expressions">expression</a>.
 It is an error if the constant value
-cannot be represented as a value of the respective type.
-For instance, <code>3.0</code> can be given any integer or any
-floating-point type, while <code>2147483648.0</code> (equal to <code>1&lt;&lt;31</code>)
-can be given the types <code>float32</code>, <code>float64</code>, or <code>uint32</code> but
-not <code>int32</code> or <code>string</code>.
+cannot be <a href="#Representability">represented</a> as a value of the respective type.
 </p>
 
 <p>
@@ -861,7 +857,8 @@ <h3 id="Array_types">Array types</h3>
 
 <p>
 The length is part of the array's type; it must evaluate to a
-non-negative <a href="#Constants">constant</a> representable by a value
+non-negative <a href="#Constants">constant</a>
+<a href="#Representability">representable</a> by a value
 of type <code>int</code>.
 The length of array <code>a</code> can be discovered
 using the built-in function <a href="#Length_and_capacity"><code>len</code></a>.
@@ -1514,7 +1511,7 @@ <h3 id="Assignability">Assignability</h3>
 
 <p>
 A value <code>x</code> is <i>assignable</i> to a <a href="#Variables">variable</a> of type <code>T</code>
-("<code>x</code> is assignable to <code>T</code>") in any of these cases:
+("<code>x</code> is assignable to <code>T</code>") if one of the following conditions applies:
 </p>
 
 <ul>
@@ -1540,12 +1537,68 @@ <h3 id="Assignability">Assignability</h3>
 is a pointer, function, slice, map, channel, or interface type.
 </li>
 <li>
-<code>x</code> is an untyped <a href="#Constants">constant</a> representable
+<code>x</code> is an untyped <a href="#Constants">constant</a>
+<a href="#Representability">representable</a>
 by a value of type <code>T</code>.
 </li>
 </ul>
 
 
+<h3 id="Representability">Representability</h3>
+
+<p>
+A <a href="#Constants">constant</a> <code>x</code> is <i>representable</i>
+by a value of type <code>T</code> if one of the following conditions applies:
+</p>
+
+<ul>
+<li>
+<code>x</code> is in the set of values <a href="#Types">determined</a> by <code>T</code>.
+</li>
+
+<li>
+<code>T</code> is a floating-point type and <code>x</code> can be rounded to <code>T</code>'s
+precision without overflow. Rounding uses IEEE 754 round-to-even rules but with an IEEE
+negative zero further simplified to an unsigned zero. Note that constant values never result
+in an IEEE negative zero, NaN, or infinity.
+</li>
+
+<li>
+<code>T</code> is a complex type, and <code>x</code>'s
+<a href="#Complex_numbers">components</a> <code>real(x)</code> and <code>imag(x)</code>
+are representable by values of <code>T</code>'s component type (<code>float32</code> or
+<code>float64</code>).
+</li>
+</ul>
+
+<pre>
+x                   T           x is representable by a value of T because
+
+'a'                 byte        97 is in the set of byte values
+97                  rune        rune is an alias for int32, and 97 is in the set of 32-bit integers
+"foo"               string      "foo" is in the set of string values
+1024                int16       1024 is in the set of 16-bit integers
+42.0                byte        42 is in the set of unsigned 8-bit integers
+1e10                uint64      10000000000 is in the set of unsigned 64-bit integers
+2.718281828459045   float32     2.718281828459045 rounds to 2.7182817 which is in the set of float32 values
+-1e-1000            float64     -1e-1000 rounds to IEEE -0.0 which is further simplified to 0.0
+0i                  int         0 is an integer value
+(42 + 0i)           float32     42.0 (with zero imaginary part) is in the set of float32 values
+</pre>
+
+<pre>
+x                   T           x is not representable by a value of T because
+
+0                   bool        0 is not in the set of boolean values
+'a'                 string      'a' is a rune, it is not in the set of string values
+1024                byte        1024 is not in the set of unsigned 8-bit integers
+-1                  uint16      -1 is not in the set of unsigned 16-bit integers
+1.1                 int         1.1 is not an integer value
+42i                 float32     (0 + 42i) is not in the set of float32 values
+1e1000              float64     1e1000 overflows to IEEE +Inf after rounding
+</pre>
+
+
 <h2 id="Blocks">Blocks</h2>
 
 <p>
@@ -2348,7 +2401,8 @@ <h3 id="Composite_literals">Composite literals</h3>
 	    its position in the array.
 	</li>
 	<li>An element with a key uses the key as its index. The
-	    key must be a non-negative constant representable by
+	    key must be a non-negative constant
+	    <a href="#Representability">representable</a> by
 	    a value of type <code>int</code>; and if it is typed
 	    it must be of integer type.
 	</li>
@@ -2925,7 +2979,8 @@ <h3 id="Index_expressions">Index expressions</h3>
 	    it is <i>in range</i> if <code>0 &lt;= x &lt; len(a)</code>,
 	    otherwise it is <i>out of range</i></li>
 	<li>a <a href="#Constants">constant</a> index must be non-negative
-	    and representable by a value of type <code>int</code>
+	    and <a href="#Representability">representable</a> by a value
+	    of type <code>int</code></li>
 </ul>
 
 <p>
@@ -3075,7 +3130,8 @@ <h4>Simple slice expressions</h4>
 <code>0</code> &lt;= <code>low</code> &lt;= <code>high</code> &lt;= <code>len(a)</code>,
 otherwise they are <i>out of range</i>.
 For slices, the upper index bound is the slice capacity <code>cap(a)</code> rather than the length.
-A <a href="#Constants">constant</a> index must be non-negative and representable by a value of type
+A <a href="#Constants">constant</a> index must be non-negative and
+<a href="#Representability">representable</a> by a value of type
 <code>int</code>; for arrays or constant strings, constant indices must also be in range.
 If both indices are constant, they must satisfy <code>low &lt;= high</code>.
 If the indices are out of range at run time, a <a href="#Run_time_panics">run-time panic</a> occurs.
@@ -3135,7 +3191,8 @@ <h4>Full slice expressions</h4>
 <p>
 The indices are <i>in range</i> if <code>0 &lt;= low &lt;= high &lt;= max &lt;= cap(a)</code>,
 otherwise they are <i>out of range</i>.
-A <a href="#Constants">constant</a> index must be non-negative and representable by a value of type
+A <a href="#Constants">constant</a> index must be non-negative and
+<a href="#Representability">representable</a> by a value of type
 <code>int</code>; for arrays, constant indices must also be in range.
 If multiple indices are constant, the constants that are present must be in range relative to each
 other.
@@ -3384,7 +3441,8 @@ <h3 id="Operators">Operators</h3>
 
 <p>
 The right operand in a shift expression must have unsigned integer type
-or be an untyped constant representable by a value of type <code>uint</code>.
+or be an untyped constant <a href="#Representability">representable</a> by a
+value of type <code>uint</code>.
 If the left operand of a non-constant shift expression is an untyped constant,
 it is first converted to the type it would assume if the shift expression were
 replaced by its left operand alone.
@@ -3877,30 +3935,14 @@ <h3 id="Conversions">Conversions</h3>
 
 <p>
 A <a href="#Constants">constant</a> value <code>x</code> can be converted to
-type <code>T</code> in any of these cases:
+type <code>T</code> if <code>x</code> is <a href="#Representability">representable</a>
+by a value of <code>T</code>.
+As a special case, an integer constant <code>x</code> can be converted to a
+<a href="#String_types">string type</a> using the
+<a href="#Conversions_to_and_from_a_string_type">same rule</a>
+as for non-constant <code>x</code>.
 </p>
 
-<ul>
-	<li>
-	<code>x</code> is representable by a value of type <code>T</code>.
-	</li>
-	<li>
-	<code>x</code> is a floating-point constant,
-	<code>T</code> is a floating-point type,
-	and <code>x</code> is representable by a value
-	of type <code>T</code> after rounding using
-	IEEE 754 round-to-even rules, but with an IEEE <code>-0.0</code>
-	further rounded to an unsigned <code>0.0</code>.
-	The constant <code>T(x)</code> is the rounded value.
-	</li>
-	<li>
-	<code>x</code> is an integer constant and <code>T</code> is a
-	<a href="#String_types">string type</a>.
-	The <a href="#Conversions_to_and_from_a_string_type">same rule</a>
-	as for non-constant <code>x</code> applies in this case.
-	</li>
-</ul>
-
 <p>
 Converting a constant yields a typed constant as result.
 </p>
@@ -4187,7 +4229,8 @@ <h3 id="Constant_expressions">Constant expressions</h3>
 </pre>
 
 <p>
-The values of <i>typed</i> constants must always be accurately representable as values
+The values of <i>typed</i> constants must always be accurately
+<a href="#Representability">representable</a> by values
 of the constant type. The following constant expressions are illegal:
 </p>
 
@@ -5683,7 +5726,7 @@ <h3 id="Making_slices_maps_and_channels">Making slices, maps and channels</h3>
 <p>
 The size arguments <code>n</code> and <code>m</code> must be of integer type or untyped.
 A <a href="#Constants">constant</a> size argument must be non-negative and
-representable by a value of type <code>int</code>.
+<a href="#Representability">representable</a> by a value of type <code>int</code>.
 If both <code>n</code> and <code>m</code> are provided and are constant, then
 <code>n</code> must be no larger than <code>m</code>.
 If <code>n</code> is negative or larger than <code>m</code> at run time,