Allow numeric scale to be negative or greater than precision.

Formerly, when specifying NUMERIC(precision, scale), the scale had to
be in the range [0, precision], which was per SQL spec. This commit
extends the range of allowed scales to [-1000, 1000], independent of
the precision (whose valid range remains [1, 1000]).

A negative scale implies rounding before the decimal point. For
example, a column might be declared with a scale of -3 to round values
to the nearest thousand. Note that the display scale remains
non-negative, so in this case the display scale will be zero, and all
digits before the decimal point will be displayed.

A scale greater than the precision supports fractional values with
zeros immediately after the decimal point.

Take the opportunity to tidy up the code that packs, unpacks and
validates the contents of a typmod integer, encapsulating it in a
small set of new inline functions.

Bump the catversion because the allowed contents of atttypmod have
changed for numeric columns. This isn't a change that requires a
re-initdb, but negative scale values in the typmod would confuse old
backends.

Dean Rasheed, with additional improvements by Tom Lane. Reviewed by
Tom Lane.

Discussion: https://postgr.es/m/CAEZATCWdNLgpKihmURF8nfofP0RFtAKJ7ktY6GcZOPnMfUoRqA@mail.gmail.com

doc/src/sgml/datatype.sgml

@@ -545,8 +545,8 @@
 <programlisting>
 NUMERIC(<replaceable>precision</replaceable>, <replaceable>scale</replaceable>)
 </programlisting>
-     The precision must be positive, the scale zero or positive.
-     Alternatively:
+     The precision must be positive, while the scale may be positive or
+     negative (see below).  Alternatively:
 <programlisting>
 NUMERIC(<replaceable>precision</replaceable>)
 </programlisting>
@@ -569,8 +569,8 @@ NUMERIC
     <note>
      <para>
       The maximum precision that can be explicitly specified in
-      a <type>NUMERIC</type> type declaration is 1000.  An
-      unconstrained <type>NUMERIC</type> column is subject to the limits
+      a <type>numeric</type> type declaration is 1000.  An
+      unconstrained <type>numeric</type> column is subject to the limits
       described in <xref linkend="datatype-numeric-table"/>.
      </para>
     </note>
@@ -581,8 +581,48 @@ NUMERIC
      number of fractional digits.  Then, if the number of digits to the
      left of the decimal point exceeds the declared precision minus the
      declared scale, an error is raised.
+     For example, a column declared as
+<programlisting>
+NUMERIC(3, 1)
+</programlisting>
+     will round values to 1 decimal place and can store values between
+     -99.9 and 99.9, inclusive.
     </para>
 
+    <para>
+     Beginning in <productname>PostgreSQL</productname> 15, it is allowed
+     to declare a <type>numeric</type> column with a negative scale.  Then
+     values will be rounded to the left of the decimal point.  The
+     precision still represents the maximum number of non-rounded digits.
+     Thus, a column declared as
+<programlisting>
+NUMERIC(2, -3)
+</programlisting>
+     will round values to the nearest thousand and can store values
+     between -99000 and 99000, inclusive.
+     It is also allowed to declare a scale larger than the declared
+     precision.  Such a column can only hold fractional values, and it
+     requires the number of zero digits just to the right of the decimal
+     point to be at least the declared scale minus the declared precision.
+     For example, a column declared as
+<programlisting>
+NUMERIC(3, 5)
+</programlisting>
+     will round values to 5 decimal places and can store values between
+     -0.00999 and 0.00999, inclusive.
+    </para>
+
+    <note>
+     <para>
+      <productname>PostgreSQL</productname> permits the scale in a
+      <type>numeric</type> type declaration to be any value in the range
+      -1000 to 1000.  However, the <acronym>SQL</acronym> standard requires
+      the scale to be in the range 0 to <replaceable>precision</replaceable>.
+      Using scales outside that range may not be portable to other database
+      systems.
+     </para>
+    </note>
+
     <para>
      Numeric values are physically stored without any extra leading or
      trailing zeroes.  Thus, the declared precision and scale of a column