Correct URL parsing of base elements

Fixes #1060.

source

@@ -12073,9 +12073,10 @@ gave me some of the songs they wrote. I love sharing my music.</p>
   data-x="attr-base-target">target</code> attributes, all but the first are ignored.</p>
 
   <p>A <code>base</code> element that is the first <code>base</code> element with an <code
-  data-x="attr-base-href">href</code> content attribute in a particular <code>Document</code> has a
-  <dfn>frozen base URL</dfn>. The <span>frozen base URL</span> must be <span>immediately</span> <span data-x="set the frozen
-  base URL">set</span> for an element whenever any of the following situations occur:</p>
+  data-x="attr-base-href">href</code> content attribute <span>in a <code>Document</code></span> has
+  a <dfn>frozen base URL</dfn>. The <span>frozen base URL</span> must be <span>immediately</span>
+  <span data-x="set the frozen base URL">set</span> for an element whenever any of the following
+  situations occur:</p>
 
   <ul class="brief">
 
@@ -12095,47 +12096,46 @@ gave me some of the songs they wrote. I love sharing my music.&lt;/p>
   <ol>
    <li><p>Let <var>document</var> be <var>element</var>'s <span>node document</span>.
 
-   <li><p><span data-x="parse a URL">Parse</span> the value of <var>element</var>'s <code
-   data-x="attr-base-href">href</code> content attribute relative to <var>document</var>.</p></li>
-
-   <li>
-    <p>If that algorithm fails or if running <span>Is base allowed for Document?</span> on the
-    <span>resulting URL record</span> and <var>document</var> returns "<code
-    data-x="">Blocked</code>", then set <var>element</var>'s <span>frozen base URL</span> to the
-    <span>fallback base URL</span>.</p>
+   <li><p>Let <var>urlRecord</var> be the result of <span data-x="URL parser">parsing</span> the
+   value of <var>element</var>'s <code data-x="attr-base-href">href</code> content attribute with
+   <var>document</var>'s <span>fallback base URL</span>, and <var>document</var>'s <span
+   data-x="document's character encoding">character encoding</span>. (Thus, the <code>base</code>
+   element isn't affected by itself.)</p></li>
+   <!-- This uses the URL parser rather than parse a URL since otherwise we'd have to unnessarily
+        complicate the latter for two callsites. -->
 
-    <p>Otherwise, set <var>element</var>'s <span>frozen base URL</span> to the <var>resulting URL
-    record</var>.</p>
-   </li>
+   <li><p>Set <var>element</var>'s <span>frozen base URL</span> to <var>document</var>'s
+   <span>fallback base URL</span>, if <var>urlRecord</var> is failure or running <span>Is base
+   allowed for Document?</span> on the <span>resulting URL record</span> and <var>document</var>
+   returns "<code data-x="">Blocked</code>", and to <var>urlRecord</var> otherwise.</p></li>
   </ol>
 
   <p>The <dfn><code data-x="dom-base-href">href</code></dfn> IDL attribute, on getting, must return
   the result of running the following algorithm:
+  <!-- http://software.hixie.ch/utilities/js/live-dom-viewer/saved/1715
+       https://github.com/whatwg/html/issues/1060#issuecomment-211221664 -->
 
-  <ol> <!-- http://software.hixie.ch/utilities/js/live-dom-viewer/saved/1715 -->
-
-   <li><p>If the <code>base</code> element has no <code data-x="attr-base-href">href</code> content
-   attribute, then return the <span>document base URL</span> and abort these steps.</p></li>
+  <ol>
+   <li><p>If this element has a <span>frozen base URL</span>, return it, <span
+   data-x="concept-url-serialiser">serialised</span>.</p></li>
 
-   <li><p>Let <var>fallback base url</var> be the <code>Document</code>'s <span>fallback
-   base URL</span>.</p></li>
+   <li><p>Let <var>document</var> be <var>element</var>'s <span>node document</span>.
 
    <li><p>Let <var>url</var> be the value of the <code data-x="attr-base-href">href</code>
-   attribute of the <code>base</code> element.</p></li>
+   attribute of this element, if it has one, and the empty string otherwise.</p></li>
 
    <li><p>Let <var>urlRecord</var> be the result of <span data-x="URL parser">parsing</span>
-   <var>url</var> with <var>fallback base url</var>, and the <code>Document</code>'s <span
-   data-x="document's character encoding">character encoding</span>. (Thus, the <code>base</code>'s
-   <code data-x="attr-base-href">href</code> attribute isn't affected by other <code>base</code>
-   elements).</p></li>
+   <var>url</var> with <var>document</var>'s <span>fallback base URL</span>, and
+   <var>document</var>'s <span data-x="document's character encoding">character encoding</span>.
+   (Thus, the <code>base</code> element isn't affected by other <code>base</code> elements or
+   itself.)</p></li>
    <!-- This uses the URL parser rather than parse a URL since otherwise we'd have to unnessarily
-        complicate the latter for this single callsite. -->
+        complicate the latter for two callsites. -->
 
    <li><p>If <var>urlRecord</var> is failure, return the empty string.</p></li>
 
    <li><p>Return the <span data-x="concept-url-serialiser">serialisation</span> of
    <var>urlRecord</var>.</p></li>
-
   </ol>
 
   <p>The <code data-x="dom-base-href">href</code> IDL attribute, on setting, must set the <code