Add trigonometric functions that work in degrees.

The implementations go to some lengths to deliver exact results for values
where an exact result can be expected, such as sind(30) = 0.5 exactly.

Dean Rasheed, reviewed by Michael Paquier

doc/src/sgml/func.sgml

@@ -1006,20 +1006,19 @@
    Finally, <xref linkend="functions-math-trig-table"> shows the
    available trigonometric functions.  All trigonometric functions
    take arguments and return values of type <type>double
-   precision</type>. Trigonometric functions arguments are expressed
-   in radians. Inverse functions return values are expressed in
-   radians.  See unit transformation functions
-   <literal><function>radians()</function></literal> and
-   <literal><function>degrees()</function></literal> above.
+   precision</type>.  Each of the trigonometric functions comes in
+   two variants, one that measures angles in radians and one that
+   measures angles in degrees.
   </para>
 
    <table id="functions-math-trig-table">
     <title>Trigonometric Functions</title>
 
-    <tgroup cols="2">
+    <tgroup cols="3">
      <thead>
       <row>
-       <entry>Function</entry>
+       <entry>Function (radians)</entry>
+       <entry>Function (degrees)</entry>
        <entry>Description</entry>
       </row>
      </thead>
@@ -1031,6 +1030,11 @@
          <primary>acos</primary>
         </indexterm><literal><function>acos(<replaceable>x</replaceable>)</function></literal>
        </entry>
+       <entry>
+        <indexterm>
+         <primary>acosd</primary>
+        </indexterm><literal><function>acosd(<replaceable>x</replaceable>)</function></literal>
+       </entry>
        <entry>inverse cosine</entry>
       </row>
 
@@ -1041,6 +1045,12 @@
         </indexterm>
         <literal><function>asin(<replaceable>x</replaceable>)</function></literal>
        </entry>
+       <entry>
+        <indexterm>
+         <primary>asind</primary>
+        </indexterm>
+        <literal><function>asind(<replaceable>x</replaceable>)</function></literal>
+       </entry>
        <entry>inverse sine</entry>
       </row>
 
@@ -1051,6 +1061,12 @@
         </indexterm>
         <literal><function>atan(<replaceable>x</replaceable>)</function></literal>
        </entry>
+       <entry>
+        <indexterm>
+         <primary>atand</primary>
+        </indexterm>
+        <literal><function>atand(<replaceable>x</replaceable>)</function></literal>
+       </entry>
        <entry>inverse tangent</entry>
       </row>
 
@@ -1062,6 +1078,13 @@
         <literal><function>atan2(<replaceable>y</replaceable>,
         <replaceable>x</replaceable>)</function></literal>
        </entry>
+       <entry>
+        <indexterm>
+         <primary>atan2d</primary>
+        </indexterm>
+        <literal><function>atan2d(<replaceable>y</replaceable>,
+        <replaceable>x</replaceable>)</function></literal>
+       </entry>
        <entry>inverse tangent of
         <literal><replaceable>y</replaceable>/<replaceable>x</replaceable></literal></entry>
       </row>
@@ -1073,6 +1096,12 @@
         </indexterm>
         <literal><function>cos(<replaceable>x</replaceable>)</function></literal>
        </entry>
+       <entry>
+        <indexterm>
+         <primary>cosd</primary>
+        </indexterm>
+        <literal><function>cosd(<replaceable>x</replaceable>)</function></literal>
+       </entry>
        <entry>cosine</entry>
       </row>
 
@@ -1083,6 +1112,12 @@
         </indexterm>
         <literal><function>cot(<replaceable>x</replaceable>)</function></literal>
        </entry>
+       <entry>
+        <indexterm>
+         <primary>cotd</primary>
+        </indexterm>
+        <literal><function>cotd(<replaceable>x</replaceable>)</function></literal>
+       </entry>
        <entry>cotangent</entry>
       </row>
 
@@ -1093,6 +1128,12 @@
         </indexterm>
         <literal><function>sin(<replaceable>x</replaceable>)</function></literal>
        </entry>
+       <entry>
+        <indexterm>
+         <primary>sind</primary>
+        </indexterm>
+        <literal><function>sind(<replaceable>x</replaceable>)</function></literal>
+       </entry>
        <entry>sine</entry>
       </row>
 
@@ -1103,12 +1144,29 @@
         </indexterm>
         <literal><function>tan(<replaceable>x</replaceable>)</function></literal>
        </entry>
+       <entry>
+        <indexterm>
+         <primary>tand</primary>
+        </indexterm>
+        <literal><function>tand(<replaceable>x</replaceable>)</function></literal>
+       </entry>
        <entry>tangent</entry>
       </row>
      </tbody>
     </tgroup>
    </table>
 
+  <note>
+   <para>
+    Another way to work with angles measured in degrees is to use the unit
+    transformation functions <literal><function>radians()</function></literal>
+    and <literal><function>degrees()</function></literal> shown earlier.
+    However, using the degree-based trigonometric functions is preferred,
+    as that way avoids roundoff error for special cases such
+    as <literal>sind(30)</>.
+   </para>
+  </note>
+
   </sect1>
 
 

src/include/catalog/catversion.h

@@ -53,6 +53,6 @@
  */
 
 /*							yyyymmddN */
-#define CATALOG_VERSION_NO	201601201
+#define CATALOG_VERSION_NO	201601221
 
 #endif

src/include/catalog/pg_proc.h

@@ -1793,6 +1793,24 @@ DATA(insert OID = 1606 (  tan				PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701
 DESCR("tangent");
 DATA(insert OID = 1607 (  cot				PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_ dcot _null_ _null_ _null_ ));
 DESCR("cotangent");
+
+DATA(insert OID = 2731 (  asind				PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_ dasind _null_ _null_ _null_ ));
+DESCR("arcsine, degrees");
+DATA(insert OID = 2732 (  acosd				PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_ dacosd _null_ _null_ _null_ ));
+DESCR("arccosine, degrees");
+DATA(insert OID = 2733 (  atand				PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_ datand _null_ _null_ _null_ ));
+DESCR("arctangent, degrees");
+DATA(insert OID = 2734 (  atan2d			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 2 0 701 "701 701" _null_ _null_ _null_ _null_ _null_ datan2d _null_ _null_ _null_ ));
+DESCR("arctangent, two arguments, degrees");
+DATA(insert OID = 2735 (  sind				PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_ dsind _null_ _null_ _null_ ));
+DESCR("sine, degrees");
+DATA(insert OID = 2736 (  cosd				PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_ dcosd _null_ _null_ _null_ ));
+DESCR("cosine, degrees");
+DATA(insert OID = 2737 (  tand				PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_ dtand _null_ _null_ _null_ ));
+DESCR("tangent, degrees");
+DATA(insert OID = 2738 (  cotd				PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_ dcotd _null_ _null_ _null_ ));
+DESCR("cotangent, degrees");
+
 DATA(insert OID = 1608 (  degrees			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_ degrees _null_ _null_ _null_ ));
 DESCR("radians to degrees");
 DATA(insert OID = 1609 (  radians			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_ radians _null_ _null_ _null_ ));

src/include/utils/builtins.h

@@ -407,6 +407,14 @@ extern Datum dcos(PG_FUNCTION_ARGS);
 extern Datum dcot(PG_FUNCTION_ARGS);
 extern Datum dsin(PG_FUNCTION_ARGS);
 extern Datum dtan(PG_FUNCTION_ARGS);
+extern Datum dacosd(PG_FUNCTION_ARGS);
+extern Datum dasind(PG_FUNCTION_ARGS);
+extern Datum datand(PG_FUNCTION_ARGS);
+extern Datum datan2d(PG_FUNCTION_ARGS);
+extern Datum dcosd(PG_FUNCTION_ARGS);
+extern Datum dcotd(PG_FUNCTION_ARGS);
+extern Datum dsind(PG_FUNCTION_ARGS);
+extern Datum dtand(PG_FUNCTION_ARGS);
 extern Datum degrees(PG_FUNCTION_ARGS);
 extern Datum dpi(PG_FUNCTION_ARGS);
 extern Datum radians(PG_FUNCTION_ARGS);

src/test/regress/expected/float8-exp-three-digits-win32.out

@@ -444,3 +444,80 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
       | -1.2345678901234e-200
 (5 rows)
 
+-- test exact cases for trigonometric functions in degrees
+SELECT x,
+       CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
+       CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
+       CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
+                             1,'Infinity'::float8) THEN tand(x) END AS tand,
+       CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
+                             1,'Infinity'::float8) THEN cotd(x) END AS cotd
+FROM generate_series(0, 360, 15) AS t(x);
+  x  | sind | cosd |   tand    |   cotd    
+-----+------+------+-----------+-----------
+   0 |    0 |    1 |         0 |  Infinity
+  15 |      |      |           |          
+  30 |  0.5 |      |           |          
+  45 |      |      |         1 |         1
+  60 |      |  0.5 |           |          
+  75 |      |      |           |          
+  90 |    1 |    0 |  Infinity |         0
+ 105 |      |      |           |          
+ 120 |      | -0.5 |           |          
+ 135 |      |      |        -1 |        -1
+ 150 |  0.5 |      |           |          
+ 165 |      |      |           |          
+ 180 |    0 |   -1 |        -0 | -Infinity
+ 195 |      |      |           |          
+ 210 | -0.5 |      |           |          
+ 225 |      |      |         1 |         1
+ 240 |      | -0.5 |           |          
+ 255 |      |      |           |          
+ 270 |   -1 |    0 | -Infinity |        -0
+ 285 |      |      |           |          
+ 300 |      |  0.5 |           |          
+ 315 |      |      |        -1 |        -1
+ 330 | -0.5 |      |           |          
+ 345 |      |      |           |          
+ 360 |    0 |    1 |         0 |  Infinity
+(25 rows)
+
+SELECT x,
+       CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
+       CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
+       CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
+FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
+  x   | asind | acosd | atand 
+------+-------+-------+-------
+   -1 |   -90 |   180 |   -45
+ -0.5 |   -30 |   120 |      
+    0 |     0 |    90 |     0
+  0.5 |    30 |    60 |      
+    1 |    90 |     0 |    45
+(5 rows)
+
+SELECT atand('-Infinity'::float8) = -90;
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT atand('Infinity'::float8) = 90;
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT x, y,
+       CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
+FROM (SELECT 10*cosd(a), 10*sind(a)
+      FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
+  x  |  y  | atan2d 
+-----+-----+--------
+  10 |   0 |      0
+   0 |  10 |     90
+ -10 |   0 |    180
+   0 | -10 |    -90
+  10 |   0 |      0
+(5 rows)
+

src/test/regress/expected/float8-small-is-zero.out

@@ -442,3 +442,80 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
       | -1.2345678901234e-200
 (5 rows)
 
+-- test exact cases for trigonometric functions in degrees
+SELECT x,
+       CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
+       CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
+       CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
+                             1,'Infinity'::float8) THEN tand(x) END AS tand,
+       CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
+                             1,'Infinity'::float8) THEN cotd(x) END AS cotd
+FROM generate_series(0, 360, 15) AS t(x);
+  x  | sind | cosd |   tand    |   cotd    
+-----+------+------+-----------+-----------
+   0 |    0 |    1 |         0 |  Infinity
+  15 |      |      |           |          
+  30 |  0.5 |      |           |          
+  45 |      |      |         1 |         1
+  60 |      |  0.5 |           |          
+  75 |      |      |           |          
+  90 |    1 |    0 |  Infinity |         0
+ 105 |      |      |           |          
+ 120 |      | -0.5 |           |          
+ 135 |      |      |        -1 |        -1
+ 150 |  0.5 |      |           |          
+ 165 |      |      |           |          
+ 180 |    0 |   -1 |        -0 | -Infinity
+ 195 |      |      |           |          
+ 210 | -0.5 |      |           |          
+ 225 |      |      |         1 |         1
+ 240 |      | -0.5 |           |          
+ 255 |      |      |           |          
+ 270 |   -1 |    0 | -Infinity |        -0
+ 285 |      |      |           |          
+ 300 |      |  0.5 |           |          
+ 315 |      |      |        -1 |        -1
+ 330 | -0.5 |      |           |          
+ 345 |      |      |           |          
+ 360 |    0 |    1 |         0 |  Infinity
+(25 rows)
+
+SELECT x,
+       CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
+       CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
+       CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
+FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
+  x   | asind | acosd | atand 
+------+-------+-------+-------
+   -1 |   -90 |   180 |   -45
+ -0.5 |   -30 |   120 |      
+    0 |     0 |    90 |     0
+  0.5 |    30 |    60 |      
+    1 |    90 |     0 |    45
+(5 rows)
+
+SELECT atand('-Infinity'::float8) = -90;
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT atand('Infinity'::float8) = 90;
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT x, y,
+       CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
+FROM (SELECT 10*cosd(a), 10*sind(a)
+      FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
+  x  |  y  | atan2d 
+-----+-----+--------
+  10 |   0 |      0
+   0 |  10 |     90
+ -10 |   0 |    180
+   0 | -10 |    -90
+  10 |   0 |      0
+(5 rows)
+

src/test/regress/expected/float8-small-is-zero_1.out

@@ -442,3 +442,80 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
       | -1.2345678901234e-200
 (5 rows)
 
+-- test exact cases for trigonometric functions in degrees
+SELECT x,
+       CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
+       CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
+       CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
+                             1,'Infinity'::float8) THEN tand(x) END AS tand,
+       CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
+                             1,'Infinity'::float8) THEN cotd(x) END AS cotd
+FROM generate_series(0, 360, 15) AS t(x);
+  x  | sind | cosd |   tand    |   cotd    
+-----+------+------+-----------+-----------
+   0 |    0 |    1 |         0 |  Infinity
+  15 |      |      |           |          
+  30 |  0.5 |      |           |          
+  45 |      |      |         1 |         1
+  60 |      |  0.5 |           |          
+  75 |      |      |           |          
+  90 |    1 |    0 |  Infinity |         0
+ 105 |      |      |           |          
+ 120 |      | -0.5 |           |          
+ 135 |      |      |        -1 |        -1
+ 150 |  0.5 |      |           |          
+ 165 |      |      |           |          
+ 180 |    0 |   -1 |        -0 | -Infinity
+ 195 |      |      |           |          
+ 210 | -0.5 |      |           |          
+ 225 |      |      |         1 |         1
+ 240 |      | -0.5 |           |          
+ 255 |      |      |           |          
+ 270 |   -1 |    0 | -Infinity |        -0
+ 285 |      |      |           |          
+ 300 |      |  0.5 |           |          
+ 315 |      |      |        -1 |        -1
+ 330 | -0.5 |      |           |          
+ 345 |      |      |           |          
+ 360 |    0 |    1 |         0 |  Infinity
+(25 rows)
+
+SELECT x,
+       CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
+       CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
+       CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
+FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
+  x   | asind | acosd | atand 
+------+-------+-------+-------
+   -1 |   -90 |   180 |   -45
+ -0.5 |   -30 |   120 |      
+    0 |     0 |    90 |     0
+  0.5 |    30 |    60 |      
+    1 |    90 |     0 |    45
+(5 rows)
+
+SELECT atand('-Infinity'::float8) = -90;
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT atand('Infinity'::float8) = 90;
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT x, y,
+       CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
+FROM (SELECT 10*cosd(a), 10*sind(a)
+      FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
+  x  |  y  | atan2d 
+-----+-----+--------
+  10 |   0 |      0
+   0 |  10 |     90
+ -10 |   0 |    180
+   0 | -10 |    -90
+  10 |   0 |      0
+(5 rows)
+

src/test/regress/expected/float8.out

@@ -444,3 +444,80 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
       | -1.2345678901234e-200
 (5 rows)
 
+-- test exact cases for trigonometric functions in degrees
+SELECT x,
+       CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
+       CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
+       CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
+                             1,'Infinity'::float8) THEN tand(x) END AS tand,
+       CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
+                             1,'Infinity'::float8) THEN cotd(x) END AS cotd
+FROM generate_series(0, 360, 15) AS t(x);
+  x  | sind | cosd |   tand    |   cotd    
+-----+------+------+-----------+-----------
+   0 |    0 |    1 |         0 |  Infinity
+  15 |      |      |           |          
+  30 |  0.5 |      |           |          
+  45 |      |      |         1 |         1
+  60 |      |  0.5 |           |          
+  75 |      |      |           |          
+  90 |    1 |    0 |  Infinity |         0
+ 105 |      |      |           |          
+ 120 |      | -0.5 |           |          
+ 135 |      |      |        -1 |        -1
+ 150 |  0.5 |      |           |          
+ 165 |      |      |           |          
+ 180 |    0 |   -1 |        -0 | -Infinity
+ 195 |      |      |           |          
+ 210 | -0.5 |      |           |          
+ 225 |      |      |         1 |         1
+ 240 |      | -0.5 |           |          
+ 255 |      |      |           |          
+ 270 |   -1 |    0 | -Infinity |        -0
+ 285 |      |      |           |          
+ 300 |      |  0.5 |           |          
+ 315 |      |      |        -1 |        -1
+ 330 | -0.5 |      |           |          
+ 345 |      |      |           |          
+ 360 |    0 |    1 |         0 |  Infinity
+(25 rows)
+
+SELECT x,
+       CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
+       CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
+       CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
+FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
+  x   | asind | acosd | atand 
+------+-------+-------+-------
+   -1 |   -90 |   180 |   -45
+ -0.5 |   -30 |   120 |      
+    0 |     0 |    90 |     0
+  0.5 |    30 |    60 |      
+    1 |    90 |     0 |    45
+(5 rows)
+
+SELECT atand('-Infinity'::float8) = -90;
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT atand('Infinity'::float8) = 90;
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT x, y,
+       CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
+FROM (SELECT 10*cosd(a), 10*sind(a)
+      FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
+  x  |  y  | atan2d 
+-----+-----+--------
+  10 |   0 |      0
+   0 |  10 |     90
+ -10 |   0 |    180
+   0 | -10 |    -90
+  10 |   0 |      0
+(5 rows)
+

src/test/regress/sql/float8.sql

@@ -167,3 +167,27 @@ INSERT INTO FLOAT8_TBL(f1) VALUES ('-1.2345678901234e+200');
 INSERT INTO FLOAT8_TBL(f1) VALUES ('-1.2345678901234e-200');
 
 SELECT '' AS five, * FROM FLOAT8_TBL;
+
+-- test exact cases for trigonometric functions in degrees
+SELECT x,
+       CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
+       CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
+       CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
+                             1,'Infinity'::float8) THEN tand(x) END AS tand,
+       CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
+                             1,'Infinity'::float8) THEN cotd(x) END AS cotd
+FROM generate_series(0, 360, 15) AS t(x);
+
+SELECT x,
+       CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
+       CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
+       CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
+FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
+
+SELECT atand('-Infinity'::float8) = -90;
+SELECT atand('Infinity'::float8) = 90;
+
+SELECT x, y,
+       CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
+FROM (SELECT 10*cosd(a), 10*sind(a)
+      FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);