# Re: [HACKERS] Proposal: Trigonometric functions in degrees

```On 27 October 2015 at 08:24, Dean Rasheed <dean.a.rash...@gmail.com> wrote:
> I think it's still feasible to have sind(30) = 0.5 exactly and keep
> monotonicity....
>```
```
Here's a patch along those lines. It turned out to be fairly
straightforward. It's still basically a thin wrapper on top of the
math library trig functions, with a bit of careful scaling to ensure
that curves join together to form continuous functions that are
monotonic in the expected regions and return exact values in all the
special cases 0,30,45,60,90,...

I also modified some of the CHECKFLOATVAL() checks which didn't look
right to me, unless there's some odd platform-specific behaviour that
I'm not aware of, functions like sin and asin should never return
infinity.

Regards,
Dean
```
```diff --git a/doc/src/sgml/func.sgml b/doc/src/sgml/func.sgml
new file mode 100644
index 2946122..434fb88
--- a/doc/src/sgml/func.sgml
+++ b/doc/src/sgml/func.sgml
@@ -993,9 +993,9 @@
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
+   precision</type>.  Each of the trigonometric functions comes in
+   two varieties, one which works in radians and one which works in
+   degrees.  See unit transformation functions
<literal><function>degrees()</function></literal> above.
</para>
@@ -1003,10 +1003,11 @@
<table id="functions-math-trig-table">
<title>Trigonometric Functions</title>

-    <tgroup cols="2">
+    <tgroup cols="3">
<row>
-       <entry>Function</entry>
+       <entry>Function (degrees)</entry>
<entry>Description</entry>
</row>
@@ -1018,6 +1019,11 @@
<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>

@@ -1028,6 +1034,12 @@
</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>

@@ -1038,6 +1050,12 @@
</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>

@@ -1049,6 +1067,13 @@
<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>
@@ -1060,6 +1085,12 @@
</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>

@@ -1070,6 +1101,12 @@
</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>

@@ -1080,6 +1117,12 @@
</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>

@@ -1090,6 +1133,12 @@
</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>
new file mode 100644
index 4e927d8..d2318f7
@@ -1535,7 +1535,7 @@ dacos(PG_FUNCTION_ARGS)
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("input is out of range")));

-	CHECKFLOATVAL(result, isinf(arg1), true);
+	CHECKFLOATVAL(result, false, true);
PG_RETURN_FLOAT8(result);
}

@@ -1556,7 +1556,7 @@ dasin(PG_FUNCTION_ARGS)
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("input is out of range")));

-	CHECKFLOATVAL(result, isinf(arg1), true);
+	CHECKFLOATVAL(result, false, true);
PG_RETURN_FLOAT8(result);
}

@@ -1577,7 +1577,7 @@ datan(PG_FUNCTION_ARGS)
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("input is out of range")));

-	CHECKFLOATVAL(result, isinf(arg1), true);
+	CHECKFLOATVAL(result, false, true);
PG_RETURN_FLOAT8(result);
}

@@ -1599,7 +1599,7 @@ datan2(PG_FUNCTION_ARGS)
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("input is out of range")));

-	CHECKFLOATVAL(result, isinf(arg1) || isinf(arg2), true);
+	CHECKFLOATVAL(result, false, true);
PG_RETURN_FLOAT8(result);
}

@@ -1620,7 +1620,7 @@ dcos(PG_FUNCTION_ARGS)
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("input is out of range")));

-	CHECKFLOATVAL(result, isinf(arg1), true);
+	CHECKFLOATVAL(result, false, true);
PG_RETURN_FLOAT8(result);
}

@@ -1642,7 +1642,7 @@ dcot(PG_FUNCTION_ARGS)
errmsg("input is out of range")));

result = 1.0 / result;
-	CHECKFLOATVAL(result, true /* cotan(pi/2) == inf */ , true);
+	CHECKFLOATVAL(result, true /* cot(0) == Inf */ , true);
PG_RETURN_FLOAT8(result);
}

@@ -1663,7 +1663,7 @@ dsin(PG_FUNCTION_ARGS)
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("input is out of range")));

-	CHECKFLOATVAL(result, isinf(arg1), true);
+	CHECKFLOATVAL(result, false, true);
PG_RETURN_FLOAT8(result);
}

@@ -1688,6 +1688,368 @@ dtan(PG_FUNCTION_ARGS)
PG_RETURN_FLOAT8(result);
}

+
+/*
+ *		asind_q1		- returns the inverse sine of x in degrees, where x is
+ *						  assumed to be in the range [0, 1] and the result is
+ *						  an angle in the first quadrant (0 to 90 degrees).
+ *
+ * In this quadrant there are 3 special case inputs (0, 0.5 and 1) for which
+ * this function will return exact values (0, 30 and 90 respectively).
+ */
+static double
+asind_q1(double x)
+{
+	/*
+	 * Stitch together inverse sine and cosine functions for the ranges
+	 * [0, 0.5] and [0.5, 1].  Each expression below is guaranteed to return
+	 * exactly 30 for x=0.5, so the result is a continuous monotonic function
+	 * over the full range.
+	 */
+	if (x <= 0.5)
+		return (asin(x) / asin(0.5)) * 30;
+	else
+		return 90 - (acos(x) / acos(0.5)) * 60;
+}
+
+
+/*
+ *		acosd_q1		- returns the inverse cosine of x in degrees, where x
+ *						  is assumed to be in the range [0, 1] and the result
+ *						  is an angle in the first quadrant (0 to 90 degrees).
+ *
+ * In this quadrant there are 3 special case inputs (0, 0.5 and 1) for which
+ * this function will return exact values (0, 60 and 90 respectively).
+ */
+static double
+acosd_q1(double x)
+{
+	/*
+	 * Stitch together inverse sine and cosine functions for the ranges
+	 * [0, 0.5] and [0.5, 1].  Each expression below is guaranteed to return
+	 * exactly 60 for x=0.5, so the result is a continuous monotonic function
+	 * over the full range.
+	 */
+	if (x <= 0.5)
+		return 90 - (asin(x) / asin(0.5)) * 30;
+	else
+		return (acos(x) / acos(0.5)) * 60;
+}
+
+
+/*
+ *		dacosd			- returns the arccos of arg1 (degrees)
+ */
+Datum
+dacosd(PG_FUNCTION_ARGS)
+{
+	float8		arg1 = PG_GETARG_FLOAT8(0);
+	float8		result;
+
+	if (isinf(arg1) || arg1 < -1 || arg1 > 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+				 errmsg("input is out of range")));
+
+	if (isnan(arg1))
+		result = arg1;
+	else if (arg1 >= 0)
+		result = acosd_q1(arg1);
+	else
+		result = 90 + asind_q1(-arg1);
+
+	CHECKFLOATVAL(result, false, true);
+	PG_RETURN_FLOAT8(result);
+}
+
+
+/*
+ *		dasind			- returns the arcsin of arg1 (degrees)
+ */
+Datum
+dasind(PG_FUNCTION_ARGS)
+{
+	float8		arg1 = PG_GETARG_FLOAT8(0);
+	float8		result;
+
+	if (isinf(arg1) || arg1 < -1 || arg1 > 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+				 errmsg("input is out of range")));
+
+	if (isnan(arg1))
+		result = arg1;
+	else if (arg1 >= 0)
+		result = asind_q1(arg1);
+	else
+		result = -asind_q1(-arg1);
+
+	CHECKFLOATVAL(result, false, true);
+	PG_RETURN_FLOAT8(result);
+}
+
+
+/*
+ *		datand			- returns the arctan of arg1 (degrees)
+ */
+Datum
+datand(PG_FUNCTION_ARGS)
+{
+	float8		arg1 = PG_GETARG_FLOAT8(0);
+	float8		result;
+
+	errno = 0;
+	result = atan(arg1);
+	if (errno != 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+				 errmsg("input is out of range")));
+
+	result = (result / atan(1.0)) * 45;
+	CHECKFLOATVAL(result, false, true);
+	PG_RETURN_FLOAT8(result);
+}
+
+
+/*
+ *		atan2d			- returns the arctan2 of arg1 (degrees)
+ */
+Datum
+datan2d(PG_FUNCTION_ARGS)
+{
+	float8		arg1 = PG_GETARG_FLOAT8(0);
+	float8		arg2 = PG_GETARG_FLOAT8(1);
+	float8		result;
+
+	errno = 0;
+	result = atan2(arg1, arg2);
+	if (errno != 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+				 errmsg("input is out of range")));
+
+	result = (result / atan(1.0)) * 45;
+	CHECKFLOATVAL(result, false, true);
+	PG_RETURN_FLOAT8(result);
+}
+
+
+/*
+ *		sind_0_to_30	- returns the sine of an angle that lies between 0 and
+ *						  30 degrees.  This will return exactly 0 when x is 0,
+ *						  and exactly 0.5 when x is 30 degrees.
+ */
+static double
+sind_0_to_30(double x)
+{
+	return ( sin(x * (M_PI/180)) / sin(30 * (M_PI/180)) ) / 2;
+}
+
+
+/*
+ *		cosd_0_to_60	- returns the cosine of an angle that lies between 0
+ *						  and 60 degrees.  This will return exactly 1 when x
+ *						  is 0 and exactly 0.5 when x is 60 degrees.
+ */
+static double
+cosd_0_to_60(double x)
+{
+	return ( 2 - (1 - cos(x * (M_PI/180))) / (1 - cos(60 * (M_PI/180))) ) / 2;
+}
+
+
+/*
+ *		sind_q1			- returns the sine of an angle in the first quadrant
+ *						  (0 to 90 degrees).
+ */
+static double
+sind_q1(double x)
+{
+	/*
+	 * Stitch together the sine and cosine functions for the ranges [0, 30]
+	 * and [30, 90].  These guarantee to return exact answers at their
+	 * endpoints, so the overall result is a continuous monotonic function
+	 * that gives exact results when x = 0, 30 and 90 degrees.
+	 */
+	return x <= 30 ? sind_0_to_30(x) : cosd_0_to_60(90-x);
+}
+
+
+/*
+ *		cosd_q1			- returns the cosine of an angle in the first quadrant
+ *						  (0 to 90 degrees).
+ */
+static double
+cosd_q1(double x)
+{
+	/*
+	 * Stitch together the sine and cosine functions for the ranges [0, 60]
+	 * and [60, 90].  These guarantee to return exact answers at their
+	 * endpoints, so the overall result is a continuous monotonic function
+	 * that gives exact results when x = 0, 60 and 90 degrees.
+	 */
+	return x <= 60 ? cosd_0_to_60(x) : sind_0_to_30(90-x);
+}
+
+
+/*
+ *		dcosd			- returns the cosine of arg1 (degrees)
+ */
+Datum
+dcosd(PG_FUNCTION_ARGS)
+{
+	float8		arg1 = PG_GETARG_FLOAT8(0);
+	int			sign = 1;
+	float8		result;
+
+	/* Reduce the range of the input to [0,90] degrees */
+	arg1 = fmod(arg1, 360.0);
+	if (isnan(arg1))
+		PG_RETURN_FLOAT8(arg1);
+
+	if (arg1 < 0)
+		/* cosd(-x) = cosd(x) */
+		arg1 = -arg1;
+
+	if (arg1 > 180)
+		/* cosd(360-x) = cosd(x) */
+		arg1 = 360 - arg1;
+
+	if (arg1 > 90)
+	{
+		/* cosd(180-x) = -cosd(x) */
+		arg1 = 180 - arg1;
+		sign = -sign;
+	}
+
+	result = sign * cosd_q1(arg1);
+	CHECKFLOATVAL(result, false, true);
+	PG_RETURN_FLOAT8(result);
+}
+
+
+/*
+ *		dcotd			- returns the cotangent of arg1 (degrees)
+ */
+Datum
+dcotd(PG_FUNCTION_ARGS)
+{
+	float8		arg1 = PG_GETARG_FLOAT8(0);
+	int			sign = 1;
+	float8		result;
+
+	/* Reduce the range of the input to [0,90] degrees */
+	arg1 = fmod(arg1, 360.0);
+	if (isnan(arg1))
+		PG_RETURN_FLOAT8(arg1);
+
+	if (arg1 < 0)
+	{
+		/* cotd(-x) = -cotd(x) */
+		arg1 = -arg1;
+		sign = -sign;
+	}
+
+	if (arg1 > 180)
+	{
+		/* cotd(360-x) = -cotd(x) */
+		arg1 = 360 - arg1;
+		sign = -sign;
+	}
+
+	if (arg1 > 90)
+	{
+		/* cotd(180-x) = -cotd(x) */
+		arg1 = 180 - arg1;
+		sign = -sign;
+	}
+
+	result = sign * cosd_q1(arg1) / sind_q1(arg1);
+	CHECKFLOATVAL(result, true /* cotd(0) == Inf */ , true);
+	PG_RETURN_FLOAT8(result);
+}
+
+
+/*
+ *		dsind			- returns the sine of arg1 (degrees)
+ */
+Datum
+dsind(PG_FUNCTION_ARGS)
+{
+	float8		arg1 = PG_GETARG_FLOAT8(0);
+	int			sign = 1;
+	float8		result;
+
+	/* Reduce the range of the input to [0,90] degrees */
+	arg1 = fmod(arg1, 360.0);
+	if (isnan(arg1))
+		PG_RETURN_FLOAT8(arg1);
+
+	if (arg1 < 0)
+	{
+		/* sind(-x) = -sind(x) */
+		arg1 = -arg1;
+		sign = -sign;
+	}
+
+	if (arg1 > 180)
+	{
+		/* sind(360-x) = -sind(x) */
+		arg1 = 360 - arg1;
+		sign = -sign;
+	}
+
+	if (arg1 > 90)
+		/* sind(180-x) = sind(x) */
+		arg1 = 180 - arg1;
+
+	result = sign * sind_q1(arg1);
+	CHECKFLOATVAL(result, false, true);
+	PG_RETURN_FLOAT8(result);
+}
+
+
+/*
+ *		dtand			- returns the tangent of arg1 (degrees)
+ */
+Datum
+dtand(PG_FUNCTION_ARGS)
+{
+	float8		arg1 = PG_GETARG_FLOAT8(0);
+	int			sign = 1;
+	float8		result;
+
+	/* Reduce the range of the input to [0,90] degrees */
+	arg1 = fmod(arg1, 360.0);
+	if (isnan(arg1))
+		PG_RETURN_FLOAT8(arg1);
+
+	if (arg1 < 0)
+	{
+		/* tand(-x) = -tand(x) */
+		arg1 = -arg1;
+		sign = -sign;
+	}
+
+	if (arg1 > 180)
+	{
+		/* tand(360-x) = -tand(x) */
+        arg1 = 360 - arg1;
+		sign = -sign;
+	}
+
+	if (arg1 > 90)
+	{
+		/* tand(180-x) = -tand(x) */
+		arg1 = 180 - arg1;
+		sign = -sign;
+	}
+
+	result = sign * sind_q1(arg1) / cosd_q1(arg1);
+	CHECKFLOATVAL(result, true /* tand(90) == Inf */ , true);
+	PG_RETURN_FLOAT8(result);
+}
+

/*
*		degrees		- returns degrees converted from radians
diff --git a/src/include/catalog/pg_proc.h b/src/include/catalog/pg_proc.h
new file mode 100644
index f688454..18a9e1d
--- a/src/include/catalog/pg_proc.h
+++ b/src/include/catalog/pg_proc.h
@@ -1892,6 +1892,24 @@ DATA(insert OID = 1606 (  tan				PGNSP P
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 = 3300 (  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 = 3308 (  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 = 3309 (  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 = 3315 (  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 = 3316 (  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 = 3317 (  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 = 3318 (  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 = 3319 (  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_ ));
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_ ));
diff --git a/src/include/utils/builtins.h b/src/include/utils/builtins.h
new file mode 100644
index fc1679e..62751ec
--- a/src/include/utils/builtins.h
+++ b/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);
diff --git a/src/test/regress/expected/float8.out b/src/test/regress/expected/float8.out
new file mode 100644
index 6221538..a6261d2
--- a/src/test/regress/expected/float8.out
+++ b/src/test/regress/expected/float8.out
@@ -444,3 +444,330 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)

+-- Test the trigonometric functions.
+-- Use a lower precision to eliminate variations between platforms.
+SET extra_float_digits TO -5;
+-- sine and cosine
+SELECT x,
+FROM generate_series(-360, 360, 10) AS t(x)
+WHERE x = 0 OR x % 90 != 0; -- skip tests that are very platform-dependent
+  x   |  sin_radians  |     sind      |  cos_radians  |     cosd
+------+---------------+---------------+---------------+---------------
+ -350 |  0.1736481777 |  0.1736481777 |   0.984807753 |   0.984807753
+ -340 |  0.3420201433 |  0.3420201433 |  0.9396926208 |  0.9396926208
+ -330 |           0.5 |           0.5 |  0.8660254038 |  0.8660254038
+ -320 |  0.6427876097 |  0.6427876097 |  0.7660444431 |  0.7660444431
+ -310 |  0.7660444431 |  0.7660444431 |  0.6427876097 |  0.6427876097
+ -300 |  0.8660254038 |  0.8660254038 |           0.5 |           0.5
+ -290 |  0.9396926208 |  0.9396926208 |  0.3420201433 |  0.3420201433
+ -280 |   0.984807753 |   0.984807753 |  0.1736481777 |  0.1736481777
+ -260 |   0.984807753 |   0.984807753 | -0.1736481777 | -0.1736481777
+ -250 |  0.9396926208 |  0.9396926208 | -0.3420201433 | -0.3420201433
+ -240 |  0.8660254038 |  0.8660254038 |          -0.5 |          -0.5
+ -230 |  0.7660444431 |  0.7660444431 | -0.6427876097 | -0.6427876097
+ -220 |  0.6427876097 |  0.6427876097 | -0.7660444431 | -0.7660444431
+ -210 |           0.5 |           0.5 | -0.8660254038 | -0.8660254038
+ -200 |  0.3420201433 |  0.3420201433 | -0.9396926208 | -0.9396926208
+ -190 |  0.1736481777 |  0.1736481777 |  -0.984807753 |  -0.984807753
+ -170 | -0.1736481777 | -0.1736481777 |  -0.984807753 |  -0.984807753
+ -160 | -0.3420201433 | -0.3420201433 | -0.9396926208 | -0.9396926208
+ -150 |          -0.5 |          -0.5 | -0.8660254038 | -0.8660254038
+ -140 | -0.6427876097 | -0.6427876097 | -0.7660444431 | -0.7660444431
+ -130 | -0.7660444431 | -0.7660444431 | -0.6427876097 | -0.6427876097
+ -120 | -0.8660254038 | -0.8660254038 |          -0.5 |          -0.5
+ -110 | -0.9396926208 | -0.9396926208 | -0.3420201433 | -0.3420201433
+ -100 |  -0.984807753 |  -0.984807753 | -0.1736481777 | -0.1736481777
+  -80 |  -0.984807753 |  -0.984807753 |  0.1736481777 |  0.1736481777
+  -70 | -0.9396926208 | -0.9396926208 |  0.3420201433 |  0.3420201433
+  -60 | -0.8660254038 | -0.8660254038 |           0.5 |           0.5
+  -50 | -0.7660444431 | -0.7660444431 |  0.6427876097 |  0.6427876097
+  -40 | -0.6427876097 | -0.6427876097 |  0.7660444431 |  0.7660444431
+  -30 |          -0.5 |          -0.5 |  0.8660254038 |  0.8660254038
+  -20 | -0.3420201433 | -0.3420201433 |  0.9396926208 |  0.9396926208
+  -10 | -0.1736481777 | -0.1736481777 |   0.984807753 |   0.984807753
+    0 |             0 |             0 |             1 |             1
+   10 |  0.1736481777 |  0.1736481777 |   0.984807753 |   0.984807753
+   20 |  0.3420201433 |  0.3420201433 |  0.9396926208 |  0.9396926208
+   30 |           0.5 |           0.5 |  0.8660254038 |  0.8660254038
+   40 |  0.6427876097 |  0.6427876097 |  0.7660444431 |  0.7660444431
+   50 |  0.7660444431 |  0.7660444431 |  0.6427876097 |  0.6427876097
+   60 |  0.8660254038 |  0.8660254038 |           0.5 |           0.5
+   70 |  0.9396926208 |  0.9396926208 |  0.3420201433 |  0.3420201433
+   80 |   0.984807753 |   0.984807753 |  0.1736481777 |  0.1736481777
+  100 |   0.984807753 |   0.984807753 | -0.1736481777 | -0.1736481777
+  110 |  0.9396926208 |  0.9396926208 | -0.3420201433 | -0.3420201433
+  120 |  0.8660254038 |  0.8660254038 |          -0.5 |          -0.5
+  130 |  0.7660444431 |  0.7660444431 | -0.6427876097 | -0.6427876097
+  140 |  0.6427876097 |  0.6427876097 | -0.7660444431 | -0.7660444431
+  150 |           0.5 |           0.5 | -0.8660254038 | -0.8660254038
+  160 |  0.3420201433 |  0.3420201433 | -0.9396926208 | -0.9396926208
+  170 |  0.1736481777 |  0.1736481777 |  -0.984807753 |  -0.984807753
+  190 | -0.1736481777 | -0.1736481777 |  -0.984807753 |  -0.984807753
+  200 | -0.3420201433 | -0.3420201433 | -0.9396926208 | -0.9396926208
+  210 |          -0.5 |          -0.5 | -0.8660254038 | -0.8660254038
+  220 | -0.6427876097 | -0.6427876097 | -0.7660444431 | -0.7660444431
+  230 | -0.7660444431 | -0.7660444431 | -0.6427876097 | -0.6427876097
+  240 | -0.8660254038 | -0.8660254038 |          -0.5 |          -0.5
+  250 | -0.9396926208 | -0.9396926208 | -0.3420201433 | -0.3420201433
+  260 |  -0.984807753 |  -0.984807753 | -0.1736481777 | -0.1736481777
+  280 |  -0.984807753 |  -0.984807753 |  0.1736481777 |  0.1736481777
+  290 | -0.9396926208 | -0.9396926208 |  0.3420201433 |  0.3420201433
+  300 | -0.8660254038 | -0.8660254038 |           0.5 |           0.5
+  310 | -0.7660444431 | -0.7660444431 |  0.6427876097 |  0.6427876097
+  320 | -0.6427876097 | -0.6427876097 |  0.7660444431 |  0.7660444431
+  330 |          -0.5 |          -0.5 |  0.8660254038 |  0.8660254038
+  340 | -0.3420201433 | -0.3420201433 |  0.9396926208 |  0.9396926208
+  350 | -0.1736481777 | -0.1736481777 |   0.984807753 |   0.984807753
+(65 rows)
+
+-- test exactness
+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
+FROM generate_series(0, 360, 30) AS t(x);
+  x  | sind | cosd
+-----+------+------
+   0 |    0 |    1
+  30 |  0.5 |
+  60 |      |  0.5
+  90 |    1 |    0
+ 120 |      | -0.5
+ 150 |  0.5 |
+ 180 |    0 |   -1
+ 210 | -0.5 |
+ 240 |      | -0.5
+ 270 |   -1 |    0
+ 300 |      |  0.5
+ 330 | -0.5 |
+ 360 |    0 |    1
+(13 rows)
+
+-- tangent and cotangent
+SELECT x,
+FROM generate_series(-360, 360, 10) AS t(x)
+WHERE x = 0 OR x % 90 != 0; -- skip tests that are very platform-dependent
+  x   |  tan_radians  |     tand      |  cot_radians  |     cotd
+------+---------------+---------------+---------------+---------------
+ -350 |  0.1763269807 |  0.1763269807 |    5.67128182 |    5.67128182
+ -340 |  0.3639702343 |  0.3639702343 |   2.747477419 |   2.747477419
+ -330 |  0.5773502692 |  0.5773502692 |   1.732050808 |   1.732050808
+ -320 |  0.8390996312 |  0.8390996312 |   1.191753593 |   1.191753593
+ -310 |   1.191753593 |   1.191753593 |  0.8390996312 |  0.8390996312
+ -300 |   1.732050808 |   1.732050808 |  0.5773502692 |  0.5773502692
+ -290 |   2.747477419 |   2.747477419 |  0.3639702343 |  0.3639702343
+ -280 |    5.67128182 |    5.67128182 |  0.1763269807 |  0.1763269807
+ -260 |   -5.67128182 |   -5.67128182 | -0.1763269807 | -0.1763269807
+ -250 |  -2.747477419 |  -2.747477419 | -0.3639702343 | -0.3639702343
+ -240 |  -1.732050808 |  -1.732050808 | -0.5773502692 | -0.5773502692
+ -230 |  -1.191753593 |  -1.191753593 | -0.8390996312 | -0.8390996312
+ -220 | -0.8390996312 | -0.8390996312 |  -1.191753593 |  -1.191753593
+ -210 | -0.5773502692 | -0.5773502692 |  -1.732050808 |  -1.732050808
+ -200 | -0.3639702343 | -0.3639702343 |  -2.747477419 |  -2.747477419
+ -190 | -0.1763269807 | -0.1763269807 |   -5.67128182 |   -5.67128182
+ -170 |  0.1763269807 |  0.1763269807 |    5.67128182 |    5.67128182
+ -160 |  0.3639702343 |  0.3639702343 |   2.747477419 |   2.747477419
+ -150 |  0.5773502692 |  0.5773502692 |   1.732050808 |   1.732050808
+ -140 |  0.8390996312 |  0.8390996312 |   1.191753593 |   1.191753593
+ -130 |   1.191753593 |   1.191753593 |  0.8390996312 |  0.8390996312
+ -120 |   1.732050808 |   1.732050808 |  0.5773502692 |  0.5773502692
+ -110 |   2.747477419 |   2.747477419 |  0.3639702343 |  0.3639702343
+ -100 |    5.67128182 |    5.67128182 |  0.1763269807 |  0.1763269807
+  -80 |   -5.67128182 |   -5.67128182 | -0.1763269807 | -0.1763269807
+  -70 |  -2.747477419 |  -2.747477419 | -0.3639702343 | -0.3639702343
+  -60 |  -1.732050808 |  -1.732050808 | -0.5773502692 | -0.5773502692
+  -50 |  -1.191753593 |  -1.191753593 | -0.8390996312 | -0.8390996312
+  -40 | -0.8390996312 | -0.8390996312 |  -1.191753593 |  -1.191753593
+  -30 | -0.5773502692 | -0.5773502692 |  -1.732050808 |  -1.732050808
+  -20 | -0.3639702343 | -0.3639702343 |  -2.747477419 |  -2.747477419
+  -10 | -0.1763269807 | -0.1763269807 |   -5.67128182 |   -5.67128182
+    0 |             0 |             0 |      Infinity |      Infinity
+   10 |  0.1763269807 |  0.1763269807 |    5.67128182 |    5.67128182
+   20 |  0.3639702343 |  0.3639702343 |   2.747477419 |   2.747477419
+   30 |  0.5773502692 |  0.5773502692 |   1.732050808 |   1.732050808
+   40 |  0.8390996312 |  0.8390996312 |   1.191753593 |   1.191753593
+   50 |   1.191753593 |   1.191753593 |  0.8390996312 |  0.8390996312
+   60 |   1.732050808 |   1.732050808 |  0.5773502692 |  0.5773502692
+   70 |   2.747477419 |   2.747477419 |  0.3639702343 |  0.3639702343
+   80 |    5.67128182 |    5.67128182 |  0.1763269807 |  0.1763269807
+  100 |   -5.67128182 |   -5.67128182 | -0.1763269807 | -0.1763269807
+  110 |  -2.747477419 |  -2.747477419 | -0.3639702343 | -0.3639702343
+  120 |  -1.732050808 |  -1.732050808 | -0.5773502692 | -0.5773502692
+  130 |  -1.191753593 |  -1.191753593 | -0.8390996312 | -0.8390996312
+  140 | -0.8390996312 | -0.8390996312 |  -1.191753593 |  -1.191753593
+  150 | -0.5773502692 | -0.5773502692 |  -1.732050808 |  -1.732050808
+  160 | -0.3639702343 | -0.3639702343 |  -2.747477419 |  -2.747477419
+  170 | -0.1763269807 | -0.1763269807 |   -5.67128182 |   -5.67128182
+  190 |  0.1763269807 |  0.1763269807 |    5.67128182 |    5.67128182
+  200 |  0.3639702343 |  0.3639702343 |   2.747477419 |   2.747477419
+  210 |  0.5773502692 |  0.5773502692 |   1.732050808 |   1.732050808
+  220 |  0.8390996312 |  0.8390996312 |   1.191753593 |   1.191753593
+  230 |   1.191753593 |   1.191753593 |  0.8390996312 |  0.8390996312
+  240 |   1.732050808 |   1.732050808 |  0.5773502692 |  0.5773502692
+  250 |   2.747477419 |   2.747477419 |  0.3639702343 |  0.3639702343
+  260 |    5.67128182 |    5.67128182 |  0.1763269807 |  0.1763269807
+  280 |   -5.67128182 |   -5.67128182 | -0.1763269807 | -0.1763269807
+  290 |  -2.747477419 |  -2.747477419 | -0.3639702343 | -0.3639702343
+  300 |  -1.732050808 |  -1.732050808 | -0.5773502692 | -0.5773502692
+  310 |  -1.191753593 |  -1.191753593 | -0.8390996312 | -0.8390996312
+  320 | -0.8390996312 | -0.8390996312 |  -1.191753593 |  -1.191753593
+  330 | -0.5773502692 | -0.5773502692 |  -1.732050808 |  -1.732050808
+  340 | -0.3639702343 | -0.3639702343 |  -2.747477419 |  -2.747477419
+  350 | -0.1763269807 | -0.1763269807 |   -5.67128182 |   -5.67128182
+(65 rows)
+
+-- test exactness
+SELECT x,
+       CASE WHEN tand(x) IN (-1,0,1) THEN tand(x) END AS tand,
+       CASE WHEN cotd(x) IN (-1,0,1) THEN cotd(x) END AS cotd
+FROM generate_series(0, 360, 45) AS t(x);
+  x  | tand | cotd
+-----+------+------
+   0 |    0 |
+  45 |    1 |    1
+  90 |      |    0
+ 135 |   -1 |   -1
+ 180 |   -0 |
+ 225 |    1 |    1
+ 270 |      |   -0
+ 315 |   -1 |   -1
+ 360 |    0 |
+(9 rows)
+
+-- arcsine and arccosine
+SELECT x,
+       degrees(asin(x)) AS degrees_asin, asind(x),
+       degrees(acos(x)) AS degrees_acos, acosd(x)
+FROM generate_series(-1.0, 1.0, 0.1) AS t(x);
+  x   | degrees_asin |    asind     | degrees_acos |    acosd
+------+--------------+--------------+--------------+-------------
+ -1.0 |          -90 |          -90 |          180 |         180
+ -0.9 | -64.15806724 | -64.15806724 |  154.1580672 | 154.1580672
+ -0.8 | -53.13010235 | -53.13010235 |  143.1301024 | 143.1301024
+ -0.7 |   -44.427004 |   -44.427004 |   134.427004 |  134.427004
+ -0.6 | -36.86989765 | -36.86989765 |  126.8698976 | 126.8698976
+ -0.5 |          -30 |          -30 |          120 |         120
+ -0.4 | -23.57817848 | -23.57817848 |  113.5781785 | 113.5781785
+ -0.3 | -17.45760312 | -17.45760312 |  107.4576031 | 107.4576031
+ -0.2 | -11.53695903 | -11.53695903 |   101.536959 |  101.536959
+ -0.1 | -5.739170477 | -5.739170477 |  95.73917048 | 95.73917048
+  0.0 |            0 |            0 |           90 |          90
+  0.1 |  5.739170477 |  5.739170477 |  84.26082952 | 84.26082952
+  0.2 |  11.53695903 |  11.53695903 |  78.46304097 | 78.46304097
+  0.3 |  17.45760312 |  17.45760312 |  72.54239688 | 72.54239688
+  0.4 |  23.57817848 |  23.57817848 |  66.42182152 | 66.42182152
+  0.5 |           30 |           30 |           60 |          60
+  0.6 |  36.86989765 |  36.86989765 |  53.13010235 | 53.13010235
+  0.7 |    44.427004 |    44.427004 |    45.572996 |   45.572996
+  0.8 |  53.13010235 |  53.13010235 |  36.86989765 | 36.86989765
+  0.9 |  64.15806724 |  64.15806724 |  25.84193276 | 25.84193276
+  1.0 |           90 |           90 |            0 |           0
+(21 rows)
+
+-- arctangent
+SELECT x, degrees(atan(x)) AS degrees_atan, atand(x)
+FROM (SELECT '-Infinity'::float8
+      UNION ALL
+      SELECT generate_series(-10, -2)
+      UNION ALL
+      SELECT generate_series(-1.0, 1.0, 0.1)
+      UNION ALL
+      SELECT generate_series(2, 10)
+      UNION ALL
+      SELECT 'Infinity'::float8
+      UNION ALL
+      SELECT 'NaN'::float8) AS t(x);
+     x     | degrees_atan |    atand
+-----------+--------------+--------------
+ -Infinity |          -90 |          -90
+       -10 | -84.28940686 | -84.28940686
+        -9 | -83.65980825 | -83.65980825
+        -8 | -82.87498365 | -82.87498365
+        -7 | -81.86989765 | -81.86989765
+        -6 | -80.53767779 | -80.53767779
+        -5 | -78.69006753 | -78.69006753
+        -4 | -75.96375653 | -75.96375653
+        -3 | -71.56505118 | -71.56505118
+        -2 | -63.43494882 | -63.43494882
+        -1 |          -45 |          -45
+      -0.9 |  -41.9872125 |  -41.9872125
+      -0.8 | -38.65980825 | -38.65980825
+      -0.7 |  -34.9920202 |  -34.9920202
+      -0.6 | -30.96375653 | -30.96375653
+      -0.5 | -26.56505118 | -26.56505118
+      -0.4 | -21.80140949 | -21.80140949
+      -0.3 | -16.69924423 | -16.69924423
+      -0.2 | -11.30993247 | -11.30993247
+      -0.1 | -5.710593137 | -5.710593137
+         0 |            0 |            0
+       0.1 |  5.710593137 |  5.710593137
+       0.2 |  11.30993247 |  11.30993247
+       0.3 |  16.69924423 |  16.69924423
+       0.4 |  21.80140949 |  21.80140949
+       0.5 |  26.56505118 |  26.56505118
+       0.6 |  30.96375653 |  30.96375653
+       0.7 |   34.9920202 |   34.9920202
+       0.8 |  38.65980825 |  38.65980825
+       0.9 |   41.9872125 |   41.9872125
+         1 |           45 |           45
+         2 |  63.43494882 |  63.43494882
+         3 |  71.56505118 |  71.56505118
+         4 |  75.96375653 |  75.96375653
+         5 |  78.69006753 |  78.69006753
+         6 |  80.53767779 |  80.53767779
+         7 |  81.86989765 |  81.86989765
+         8 |  82.87498365 |  82.87498365
+         9 |  83.65980825 |  83.65980825
+        10 |  84.28940686 |  84.28940686
+  Infinity |           90 |           90
+       NaN |          NaN |          NaN
+(42 rows)
+
+-- 4 quadrant arctangent
+SELECT x, y, degrees(atan2(y, x)) AS degrees_atan2, atan2d(y, x)
+FROM (SELECT 10*cosd(a), 10*sind(a)
+      FROM generate_series(0, 360, 10) AS t(a)) AS t(x,y);
+      x       |      y       | degrees_atan2 | atan2d
+--------------+--------------+---------------+--------
+           10 |            0 |             0 |      0
+   9.84807753 |  1.736481777 |            10 |     10
+  9.396926208 |  3.420201433 |            20 |     20
+  8.660254038 |            5 |            30 |     30
+  7.660444431 |  6.427876097 |            40 |     40
+  6.427876097 |  7.660444431 |            50 |     50
+            5 |  8.660254038 |            60 |     60
+  3.420201433 |  9.396926208 |            70 |     70
+  1.736481777 |   9.84807753 |            80 |     80
+            0 |           10 |            90 |     90
+ -1.736481777 |   9.84807753 |           100 |    100
+ -3.420201433 |  9.396926208 |           110 |    110
+           -5 |  8.660254038 |           120 |    120
+ -6.427876097 |  7.660444431 |           130 |    130
+ -7.660444431 |  6.427876097 |           140 |    140
+ -8.660254038 |            5 |           150 |    150
+ -9.396926208 |  3.420201433 |           160 |    160
+  -9.84807753 |  1.736481777 |           170 |    170
+          -10 |            0 |           180 |    180
+  -9.84807753 | -1.736481777 |          -170 |   -170
+ -9.396926208 | -3.420201433 |          -160 |   -160
+ -8.660254038 |           -5 |          -150 |   -150
+ -7.660444431 | -6.427876097 |          -140 |   -140
+ -6.427876097 | -7.660444431 |          -130 |   -130
+           -5 | -8.660254038 |          -120 |   -120
+ -3.420201433 | -9.396926208 |          -110 |   -110
+ -1.736481777 |  -9.84807753 |          -100 |   -100
+            0 |          -10 |           -90 |    -90
+  1.736481777 |  -9.84807753 |           -80 |    -80
+  3.420201433 | -9.396926208 |           -70 |    -70
+            5 | -8.660254038 |           -60 |    -60
+  6.427876097 | -7.660444431 |           -50 |    -50
+  7.660444431 | -6.427876097 |           -40 |    -40
+  8.660254038 |           -5 |           -30 |    -30
+  9.396926208 | -3.420201433 |           -20 |    -20
+   9.84807753 | -1.736481777 |           -10 |    -10
+           10 |            0 |             0 |      0
+(37 rows)
+
diff --git a/src/test/regress/sql/float8.sql b/src/test/regress/sql/float8.sql
new file mode 100644
index 92a574a..49363d0
--- a/src/test/regress/sql/float8.sql
+++ b/src/test/regress/sql/float8.sql
@@ -167,3 +167,58 @@ INSERT INTO FLOAT8_TBL(f1) VALUES ('-1.2
INSERT INTO FLOAT8_TBL(f1) VALUES ('-1.2345678901234e-200');

SELECT '' AS five, * FROM FLOAT8_TBL;
+
+-- Test the trigonometric functions.
+-- Use a lower precision to eliminate variations between platforms.
+SET extra_float_digits TO -5;
+
+-- sine and cosine
+SELECT x,
+FROM generate_series(-360, 360, 10) AS t(x)
+WHERE x = 0 OR x % 90 != 0; -- skip tests that are very platform-dependent
+
+-- test exactness
+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
+FROM generate_series(0, 360, 30) AS t(x);
+
+-- tangent and cotangent
+SELECT x,
+FROM generate_series(-360, 360, 10) AS t(x)
+WHERE x = 0 OR x % 90 != 0; -- skip tests that are very platform-dependent
+
+-- test exactness
+SELECT x,
+       CASE WHEN tand(x) IN (-1,0,1) THEN tand(x) END AS tand,
+       CASE WHEN cotd(x) IN (-1,0,1) THEN cotd(x) END AS cotd
+FROM generate_series(0, 360, 45) AS t(x);
+
+-- arcsine and arccosine
+SELECT x,
+       degrees(asin(x)) AS degrees_asin, asind(x),
+       degrees(acos(x)) AS degrees_acos, acosd(x)
+FROM generate_series(-1.0, 1.0, 0.1) AS t(x);
+
+-- arctangent
+SELECT x, degrees(atan(x)) AS degrees_atan, atand(x)
+FROM (SELECT '-Infinity'::float8
+      UNION ALL
+      SELECT generate_series(-10, -2)
+      UNION ALL
+      SELECT generate_series(-1.0, 1.0, 0.1)
+      UNION ALL
+      SELECT generate_series(2, 10)
+      UNION ALL
+      SELECT 'Infinity'::float8
+      UNION ALL
+      SELECT 'NaN'::float8) AS t(x);
+
+-- 4 quadrant arctangent
+SELECT x, y, degrees(atan2(y, x)) AS degrees_atan2, atan2d(y, x)
+FROM (SELECT 10*cosd(a), 10*sind(a)
+      FROM generate_series(0, 360, 10) AS t(a)) AS t(x,y);
```
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