Doc: improve explanation of type interval, especially extract().

The explanation of interval's behavior in datatype.sgml wasn't wrong
exactly, but it was unclear, partly because it buried the lede about
there being three internal fields.  Rearrange and wordsmith for more
clarity.

The discussion of extract() claimed that input of type date was
handled by casting, but actually there's been a separate SQL function
taking date for a very long time.  Also, it was mostly silent about
how interval inputs are handled, but there are several field types
for which it seems useful to be specific.

Improve discussion of justify_days()/justify_hours() too.

In passing, remove vertical space in some groups of examples,
as there was little consistency about whether to have such space
or not.  (I only did this within the datetime functions section;
there are some related inconsistencies elsewhere.)

Per discussion of bug #18348 from Michael Bondarenko.  There
may be some code changes coming out of that discussion too,
but we likely won't back-patch them.  This docs-only patch
seems useful to back-patch, though I only carried it back to
v13 because it didn't apply easily in v12.

Discussion: https://postgr.es/m/18348-b097a3587dfde8a4@postgresql.org

doc/src/sgml/datatype.sgml

@@ -2869,10 +2869,31 @@ P <optional> <replaceable>years</replaceable>-<replaceable>months</replaceable>-
     </para>
 
     <para>
-     Field values can have fractional parts:  for example, <literal>'1.5
+     Internally, <type>interval</type> values are stored as three integral
+     fields: months, days, and microseconds.  These fields are kept
+     separate because the number of days in a month varies, while a day
+     can have 23 or 25 hours if a daylight savings time transition is
+     involved.  An interval input string that uses other units is
+     normalized into this format, and then reconstructed in a standardized
+     way for output, for example:
+
+<programlisting>
+SELECT '2 years 15 months 100 weeks 99 hours 123456789 milliseconds'::interval;
+               interval
+---------------------------------------
+ 3 years 3 mons 700 days 133:17:36.789
+</programlisting>
+
+     Here weeks, which are understood as <quote>7 days</quote>, have been
+     kept separate, while the smaller and larger time units were
+     combined and normalized.
+    </para>
+
+    <para>
+     Input field values can have fractional parts, for example <literal>'1.5
      weeks'</literal> or <literal>'01:02:03.45'</literal>.  However,
-     because interval internally stores only three integer units (months,
+     because <type>interval</type> internally stores only integral fields,
-     days, microseconds), fractional units must be spilled to smaller
+     fractional values must be converted into smaller
      units.  Fractional parts of units greater than months are rounded to
      be an integer number of months, e.g. <literal>'1.5 years'</literal>
      becomes <literal>'1 year 6 mons'</literal>.  Fractional parts of
@@ -2922,33 +2943,6 @@ P <optional> <replaceable>years</replaceable>-<replaceable>months</replaceable>-
       </tgroup>
      </table>
 
-    <para>
-     Internally <type>interval</type> values are stored as months, days,
-     and microseconds. This is done because the number of days in a month
-     varies, and a day can have 23 or 25 hours if a daylight savings
-     time adjustment is involved.  The months and days fields are integers
-     while the microseconds field can store fractional seconds.  Because intervals are
-     usually created from constant strings or <type>timestamp</type> subtraction,
-     this storage method works well in most cases, but can cause unexpected
-     results:
-
-<programlisting>
-SELECT EXTRACT(hours from '80 minutes'::interval);
- date_part
------------
-         1
-
-SELECT EXTRACT(days from '80 hours'::interval);
- date_part
------------
-         0
-</programlisting>
-
-     Functions <function>justify_days</function> and
-     <function>justify_hours</function> are available for adjusting days
-     and hours that overflow their normal ranges.
-    </para>
-
    </sect2>
 
    <sect2 id="datatype-interval-output">
@@ -2960,6 +2954,23 @@ SELECT EXTRACT(days from '80 hours'::interval);
      <seealso>formatting</seealso>
     </indexterm>
 
+    <para>
+     As previously explained, <productname>PostgreSQL</productname>
+     stores <type>interval</type> values as months, days, and
+     microseconds.  For output, the months field is converted to years and
+     months by dividing by 12.  The days field is shown as-is.  The
+     microseconds field is converted to hours, minutes, seconds, and
+     fractional seconds.  Thus months, minutes, and seconds will never be
+     shown as exceeding the ranges 0&ndash;11, 0&ndash;59, and 0&ndash;59
+     respectively, while the displayed years, days, and hours fields can
+     be quite large.  (The <link
+     linkend="function-justify-days"><function>justify_days</function></link>
+     and <link
+     linkend="function-justify-hours"><function>justify_hours</function></link>
+     functions can be used if it is desirable to transpose large days or
+     hours values into the next higher field.)
+    </para>
+
     <para>
      The output format of the interval type can be set to one of the
      four styles <literal>sql_standard</literal>, <literal>postgres</literal>,

doc/src/sgml/func.sgml

@@ -9166,7 +9166,8 @@ SELECT regexp_match('abc01234xyz', '(?:(.*?)(\d+)(.*)){1,1}');
         </para>
         <para>
          Subtract timestamps (converting 24-hour intervals into days,
-         similarly to <function>justify_hours()</function>)
+         similarly to <link
+         linkend="function-justify-hours"><function>justify_hours()</function></link>)
         </para>
         <para>
          <literal>timestamp '2001-09-29 03:00' - timestamp '2001-07-27 12:00'</literal>
@@ -9579,35 +9580,35 @@ SELECT regexp_match('abc01234xyz', '(?:(.*?)(\d+)(.*)){1,1}');
 
        <row>
         <entry role="func_table_entry"><para role="func_signature">
-         <indexterm>
+         <indexterm id="function-justify-days">
           <primary>justify_days</primary>
          </indexterm>
          <function>justify_days</function> ( <type>interval</type> )
          <returnvalue>interval</returnvalue>
         </para>
         <para>
-         Adjust interval so 30-day time periods are represented as months
+         Adjust interval, converting 30-day time periods to months
         </para>
         <para>
-         <literal>justify_days(interval '35 days')</literal>
+         <literal>justify_days(interval '1 year 65 days')</literal>
-         <returnvalue>1 mon 5 days</returnvalue>
+         <returnvalue>1 year 2 mons 5 days</returnvalue>
         </para></entry>
        </row>
 
        <row>
         <entry role="func_table_entry"><para role="func_signature">
-         <indexterm>
+         <indexterm id="function-justify-hours">
           <primary>justify_hours</primary>
          </indexterm>
          <function>justify_hours</function> ( <type>interval</type> )
          <returnvalue>interval</returnvalue>
         </para>
         <para>
-         Adjust interval so 24-hour time periods are represented as days
+         Adjust interval, converting 24-hour time periods to days
         </para>
         <para>
-         <literal>justify_hours(interval '27 hours')</literal>
+         <literal>justify_hours(interval '50 hours 10 minutes')</literal>
-         <returnvalue>1 day 03:00:00</returnvalue>
+         <returnvalue>2 days 02:10:00</returnvalue>
         </para></entry>
        </row>
 
@@ -10040,13 +10041,19 @@ EXTRACT(<replaceable>field</replaceable> FROM <replaceable>source</replaceable>)
     The <function>extract</function> function retrieves subfields
     such as year or hour from date/time values.
     <replaceable>source</replaceable> must be a value expression of
-    type <type>timestamp</type>, <type>time</type>, or <type>interval</type>.
+    type <type>timestamp</type>, <type>date</type>, <type>time</type>,
-    (Expressions of type <type>date</type> are
+    or <type>interval</type>.  (Timestamps and times can be with or
-    cast to <type>timestamp</type> and can therefore be used as
+    without time zone.)
-    well.)  <replaceable>field</replaceable> is an identifier or
+    <replaceable>field</replaceable> is an identifier or
     string that selects what field to extract from the source value.
+    Not all fields are valid for every input data type; for example, fields
+    smaller than a day cannot be extracted from a <type>date</type>, while
+    fields of a day or more cannot be extracted from a <type>time</type>.
     The <function>extract</function> function returns values of type
     <type>numeric</type>.
+   </para>
+
+   <para>
     The following are valid field names:
 
     <!-- alphabetical -->
@@ -10055,7 +10062,8 @@ EXTRACT(<replaceable>field</replaceable> FROM <replaceable>source</replaceable>)
       <term><literal>century</literal></term>
       <listitem>
        <para>
-        The century
+        The century; for <type>interval</type> values, the year field
+        divided by 100
        </para>
 
 <screen>
@@ -10063,17 +10071,13 @@ SELECT EXTRACT(CENTURY FROM TIMESTAMP '2000-12-16 12:21:13');
 <lineannotation>Result: </lineannotation><computeroutput>20</computeroutput>
 SELECT EXTRACT(CENTURY FROM TIMESTAMP '2001-02-16 20:38:40');
 <lineannotation>Result: </lineannotation><computeroutput>21</computeroutput>
+SELECT EXTRACT(CENTURY FROM DATE '0001-01-01 AD');
+<lineannotation>Result: </lineannotation><computeroutput>1</computeroutput>
+SELECT EXTRACT(CENTURY FROM DATE '0001-12-31 BC');
+<lineannotation>Result: </lineannotation><computeroutput>-1</computeroutput>
+SELECT EXTRACT(CENTURY FROM INTERVAL '2001 years');
+<lineannotation>Result: </lineannotation><computeroutput>20</computeroutput>
 </screen>
-
-       <para>
-        The first century starts at 0001-01-01 00:00:00 AD, although
-        they did not know it at the time. This definition applies to all
-        Gregorian calendar countries. There is no century number 0,
-        you go from -1 century to 1 century.
-
-        If you disagree with this, please write your complaint to:
-        Pope, Cathedral Saint-Peter of Roma, Vatican.
-       </para>
       </listitem>
      </varlistentry>
 
@@ -10081,14 +10085,13 @@ SELECT EXTRACT(CENTURY FROM TIMESTAMP '2001-02-16 20:38:40');
       <term><literal>day</literal></term>
       <listitem>
        <para>
-        For <type>timestamp</type> values, the day (of the month) field
+        The day of the month (1&ndash;31); for <type>interval</type>
-        (1&ndash;31) ; for <type>interval</type> values, the number of days
+        values, the number of days
        </para>
 
 <screen>
 SELECT EXTRACT(DAY FROM TIMESTAMP '2001-02-16 20:38:40');
 <lineannotation>Result: </lineannotation><computeroutput>16</computeroutput>
-
 SELECT EXTRACT(DAY FROM INTERVAL '40 days 1 minute');
 <lineannotation>Result: </lineannotation><computeroutput>40</computeroutput>
 </screen>
@@ -10162,10 +10165,8 @@ SELECT EXTRACT(DOY FROM TIMESTAMP '2001-02-16 20:38:40');
 <screen>
 SELECT EXTRACT(EPOCH FROM TIMESTAMP WITH TIME ZONE '2001-02-16 20:38:40.12-08');
 <lineannotation>Result: </lineannotation><computeroutput>982384720.120000</computeroutput>
-
 SELECT EXTRACT(EPOCH FROM TIMESTAMP '2001-02-16 20:38:40.12');
 <lineannotation>Result: </lineannotation><computeroutput>982355920.120000</computeroutput>
-
 SELECT EXTRACT(EPOCH FROM INTERVAL '5 days 3 hours');
 <lineannotation>Result: </lineannotation><computeroutput>442800.000000</computeroutput>
 </screen>
@@ -10193,7 +10194,8 @@ SELECT to_timestamp(982384720.12);
       <term><literal>hour</literal></term>
       <listitem>
        <para>
-        The hour field (0&ndash;23)
+        The hour field (0&ndash;23 in timestamps, unrestricted in
+        intervals)
        </para>
 
 <screen>
@@ -10228,7 +10230,7 @@ SELECT EXTRACT(ISODOW FROM TIMESTAMP '2001-02-18 20:38:40');
       <listitem>
        <para>
         The <acronym>ISO</acronym> 8601 week-numbering year that the date
-        falls in (not applicable to intervals)
+        falls in
        </para>
 
 <screen>
@@ -10245,9 +10247,6 @@ SELECT EXTRACT(ISOYEAR FROM DATE '2006-01-02');
         different from the Gregorian year.  See the <literal>week</literal>
         field for more information.
        </para>
-       <para>
-        This field is not available in PostgreSQL releases prior to 8.3.
-       </para>
       </listitem>
      </varlistentry>
 
@@ -10256,7 +10255,7 @@ SELECT EXTRACT(ISOYEAR FROM DATE '2006-01-02');
       <listitem>
        <para>
         The <firstterm>Julian Date</firstterm> corresponding to the
-        date or timestamp (not applicable to intervals).  Timestamps
+        date or timestamp.  Timestamps
         that are not local midnight result in a fractional value.  See
         <xref linkend="datetime-julian-dates"/> for more information.
        </para>
@@ -10289,12 +10288,15 @@ SELECT EXTRACT(MICROSECONDS FROM TIME '17:12:28.5');
       <term><literal>millennium</literal></term>
       <listitem>
        <para>
-        The millennium
+        The millennium; for <type>interval</type> values, the year field
+        divided by 1000
        </para>
 
 <screen>
 SELECT EXTRACT(MILLENNIUM FROM TIMESTAMP '2001-02-16 20:38:40');
 <lineannotation>Result: </lineannotation><computeroutput>3</computeroutput>
+SELECT EXTRACT(MILLENNIUM FROM INTERVAL '2001 years');
+<lineannotation>Result: </lineannotation><computeroutput>2</computeroutput>
 </screen>
 
        <para>
@@ -10337,18 +10339,16 @@ SELECT EXTRACT(MINUTE FROM TIMESTAMP '2001-02-16 20:38:40');
       <term><literal>month</literal></term>
       <listitem>
        <para>
-        For <type>timestamp</type> values, the number of the month
+        The number of the month within the year (1&ndash;12);
-        within the year (1&ndash;12) ; for <type>interval</type> values,
+        for <type>interval</type> values, the number of months modulo 12
-        the number of months, modulo 12 (0&ndash;11)
+        (0&ndash;11)
        </para>
 
 <screen>
 SELECT EXTRACT(MONTH FROM TIMESTAMP '2001-02-16 20:38:40');
 <lineannotation>Result: </lineannotation><computeroutput>2</computeroutput>
-
 SELECT EXTRACT(MONTH FROM INTERVAL '2 years 3 months');
 <lineannotation>Result: </lineannotation><computeroutput>3</computeroutput>
-
 SELECT EXTRACT(MONTH FROM INTERVAL '2 years 13 months');
 <lineannotation>Result: </lineannotation><computeroutput>1</computeroutput>
 </screen>
@@ -10379,7 +10379,6 @@ SELECT EXTRACT(QUARTER FROM TIMESTAMP '2001-02-16 20:38:40');
 <screen>
 SELECT EXTRACT(SECOND FROM TIMESTAMP '2001-02-16 20:38:40');
 <lineannotation>Result: </lineannotation><computeroutput>40.000000</computeroutput>
-
 SELECT EXTRACT(SECOND FROM TIME '17:12:28.5');
 <lineannotation>Result: </lineannotation><computeroutput>28.500000</computeroutput>
 </screen>
@@ -10461,6 +10460,20 @@ SELECT EXTRACT(YEAR FROM TIMESTAMP '2001-02-16 20:38:40');
     </variablelist>
    </para>
 
+   <para>
+    When processing an <type>interval</type> value,
+    the <function>extract</function> function produces field values that
+    match the interpretation used by the interval output function.  This
+    can produce surprising results if one starts with a non-normalized
+    interval representation, for example:
+<screen>
+SELECT INTERVAL '80 minutes';
+<lineannotation>Result: </lineannotation><computeroutput>01:20:00</computeroutput>
+SELECT EXTRACT(MINUTES FROM INTERVAL '80 minutes');
+<lineannotation>Result: </lineannotation><computeroutput>20</computeroutput>
+</screen>
+   </para>
+
    <note>
     <para>
      When the input value is +/-Infinity, <function>extract</function> returns
@@ -10502,7 +10515,6 @@ date_part('<replaceable>field</replaceable>', <replaceable>source</replaceable>)
 <screen>
 SELECT date_part('day', TIMESTAMP '2001-02-16 20:38:40');
 <lineannotation>Result: </lineannotation><computeroutput>16</computeroutput>
-
 SELECT date_part('hour', INTERVAL '4 hours 3 minutes');
 <lineannotation>Result: </lineannotation><computeroutput>4</computeroutput>
 </screen>
@@ -10580,16 +10592,12 @@ date_trunc(<replaceable>field</replaceable>, <replaceable>source</replaceable> [
 <screen>
 SELECT date_trunc('hour', TIMESTAMP '2001-02-16 20:38:40');
 <lineannotation>Result: </lineannotation><computeroutput>2001-02-16 20:00:00</computeroutput>
-
 SELECT date_trunc('year', TIMESTAMP '2001-02-16 20:38:40');
 <lineannotation>Result: </lineannotation><computeroutput>2001-01-01 00:00:00</computeroutput>
-
 SELECT date_trunc('day', TIMESTAMP WITH TIME ZONE '2001-02-16 20:38:40+00');
 <lineannotation>Result: </lineannotation><computeroutput>2001-02-16 00:00:00-05</computeroutput>
-
 SELECT date_trunc('day', TIMESTAMP WITH TIME ZONE '2001-02-16 20:38:40+00', 'Australia/Sydney');
 <lineannotation>Result: </lineannotation><computeroutput>2001-02-16 08:00:00-05</computeroutput>
-
 SELECT date_trunc('hour', INTERVAL '3 days 02:47:33');
 <lineannotation>Result: </lineannotation><computeroutput>3 days 02:00:00</computeroutput>
 </screen>
@@ -10628,7 +10636,6 @@ date_bin(<replaceable>stride</replaceable>, <replaceable>source</replaceable>, <
 <screen>
 SELECT date_bin('15 minutes', TIMESTAMP '2020-02-11 15:44:17', TIMESTAMP '2001-01-01');
 <lineannotation>Result: </lineannotation><computeroutput>2020-02-11 15:30:00</computeroutput>
-
 SELECT date_bin('15 minutes', TIMESTAMP '2020-02-11 15:44:17', TIMESTAMP '2001-01-01 00:02:30');
 <lineannotation>Result: </lineannotation><computeroutput>2020-02-11 15:32:30</computeroutput>
 </screen>
@@ -10814,16 +10821,12 @@ SELECT date_bin('15 minutes', TIMESTAMP '2020-02-11 15:44:17', TIMESTAMP '2001-0
 <screen>
 SELECT TIMESTAMP '2001-02-16 20:38:40' AT TIME ZONE 'America/Denver';
 <lineannotation>Result: </lineannotation><computeroutput>2001-02-16 19:38:40-08</computeroutput>
-
 SELECT TIMESTAMP WITH TIME ZONE '2001-02-16 20:38:40-05' AT TIME ZONE 'America/Denver';
 <lineannotation>Result: </lineannotation><computeroutput>2001-02-16 18:38:40</computeroutput>
-
 SELECT TIMESTAMP '2001-02-16 20:38:40' AT TIME ZONE 'Asia/Tokyo' AT TIME ZONE 'America/Chicago';
 <lineannotation>Result: </lineannotation><computeroutput>2001-02-16 05:38:40</computeroutput>
-
 SELECT TIMESTAMP WITH TIME ZONE '2001-02-16 20:38:40-05' AT LOCAL;
 <lineannotation>Result: </lineannotation><computeroutput>2001-02-16 17:38:40</computeroutput>
-
 SELECT TIME WITH TIME ZONE '20:38:40-05' AT LOCAL;
 <lineannotation>Result: </lineannotation><computeroutput>17:38:40</computeroutput>
 </screen>
@@ -10928,16 +10931,12 @@ LOCALTIMESTAMP(<replaceable>precision</replaceable>)
 <screen>
 SELECT CURRENT_TIME;
 <lineannotation>Result: </lineannotation><computeroutput>14:39:53.662522-05</computeroutput>
-
 SELECT CURRENT_DATE;
 <lineannotation>Result: </lineannotation><computeroutput>2019-12-23</computeroutput>
-
 SELECT CURRENT_TIMESTAMP;
 <lineannotation>Result: </lineannotation><computeroutput>2019-12-23 14:39:53.662522-05</computeroutput>
-
 SELECT CURRENT_TIMESTAMP(2);
 <lineannotation>Result: </lineannotation><computeroutput>2019-12-23 14:39:53.66-05</computeroutput>
-
 SELECT LOCALTIMESTAMP;
 <lineannotation>Result: </lineannotation><computeroutput>2019-12-23 14:39:53.662522</computeroutput>
 </screen>