Attached is a patch adding support for the gamma and log-gamma
functions. See, for example:
https://en.wikipedia.org/wiki/Gamma_function
I think these are very useful general-purpose mathematical functions.
They're part of C99, and they're commonly included in other
mathematical libraries, such as the python math module, so I think
it's useful to make them available from SQL.
The error-handling for these functions seems to be a little trickier
than most, so that might need further discussion.
Regards,
Dean
diff --git a/doc/src/sgml/func.sgml b/doc/src/sgml/func.sgml
new file mode 100644
index 5a16910..6464a8b
--- a/doc/src/sgml/func.sgml
+++ b/doc/src/sgml/func.sgml
@@ -1399,6 +1399,27 @@ SELECT NOT(ROW(table.*) IS NOT NULL) FRO
<row>
<entry role="func_table_entry"><para role="func_signature">
<indexterm>
+ <primary>gamma</primary>
+ </indexterm>
+ <function>gamma</function> ( <type>double precision</type> )
+ <returnvalue>double precision</returnvalue>
+ </para>
+ <para>
+ Gamma function
+ </para>
+ <para>
+ <literal>gamma(0.5)</literal>
+ <returnvalue>1.772453850905516</returnvalue>
+ </para>
+ <para>
+ <literal>gamma(6)</literal>
+ <returnvalue>120</returnvalue>
+ </para></entry>
+ </row>
+
+ <row>
+ <entry role="func_table_entry"><para role="func_signature">
+ <indexterm>
<primary>gcd</primary>
</indexterm>
<function>gcd</function> ( <replaceable>numeric_type</replaceable>, <replaceable>numeric_type</replaceable> )
@@ -1436,6 +1457,23 @@ SELECT NOT(ROW(table.*) IS NOT NULL) FRO
</para></entry>
</row>
+ <row>
+ <entry role="func_table_entry"><para role="func_signature">
+ <indexterm>
+ <primary>lgamma</primary>
+ </indexterm>
+ <function>lgamma</function> ( <type>double precision</type> )
+ <returnvalue>double precision</returnvalue>
+ </para>
+ <para>
+ Natural logarithm of the absolute value of the gamma function
+ </para>
+ <para>
+ <literal>lgamma(1000)</literal>
+ <returnvalue>5905.220423209181</returnvalue>
+ </para></entry>
+ </row>
+
<row>
<entry role="func_table_entry"><para role="func_signature">
<indexterm>
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
new file mode 100644
index cbbb8ae..e43aa42
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -2779,6 +2779,91 @@ derfc(PG_FUNCTION_ARGS)
}
+/* ========== GAMMA FUNCTIONS ========== */
+
+
+/*
+ * dgamma - returns the gamma function of arg1
+ */
+Datum
+dgamma(PG_FUNCTION_ARGS)
+{
+ float8 arg1 = PG_GETARG_FLOAT8(0);
+ float8 result;
+
+ /*
+ * Per the POSIX spec, return NaN if the input is NaN, +/-infinity if the
+ * input is +/-0, NaN if the input is -infinity, and infinity if the input
+ * is infinity.
+ */
+ if (isnan(arg1))
+ PG_RETURN_FLOAT8(get_float8_nan());
+ if (arg1 == 0)
+ {
+ if (signbit(arg1))
+ PG_RETURN_FLOAT8(-get_float8_infinity());
+ else
+ PG_RETURN_FLOAT8(get_float8_infinity());
+ }
+ if (isinf(arg1))
+ {
+ if (arg1 < 0)
+ PG_RETURN_FLOAT8(get_float8_nan());
+ else
+ PG_RETURN_FLOAT8(get_float8_infinity());
+ }
+
+ /*
+ * Note that the POSIX/C99 gamma function is called "tgamma", not "gamma".
+ *
+ * For negative integer inputs, it may raise a domain error or a pole
+ * error, or return NaN or +/-infinity (the POSIX spec indicates that this
+ * may change in future implementations). Since we can't reliably detect
+ * integer inputs above a certain size, and we can't distinguish this from
+ * any other overflow error, just treat them all the same.
+ */
+ errno = 0;
+ result = tgamma(arg1);
+ if (errno != 0 || isinf(result) || isnan(result))
+ float_overflow_error();
+
+ PG_RETURN_FLOAT8(result);
+}
+
+
+/*
+ * dlgamma - natural logarithm of absolute value of gamma of arg1
+ */
+Datum
+dlgamma(PG_FUNCTION_ARGS)
+{
+ float8 arg1 = PG_GETARG_FLOAT8(0);
+ float8 result;
+
+ /* Per the POSIX spec, return NaN if the input is NaN */
+ if (isnan(arg1))
+ PG_RETURN_FLOAT8(get_float8_nan());
+
+ errno = 0;
+ result = lgamma(arg1);
+
+ /*
+ * If an ERANGE error occurs, it means there is an overflow. This can
+ * happen if the input is 0, a negative integer, -infinity, or infinity.
+ * In each of those cases, the correct result is infinity. However, it
+ * can also happen in other cases where the correct result is finite, but
+ * too large to be represented (e.g., if the input is larger than around
+ * 2.5e305). There seems to be no way to distinguish those cases, so we
+ * just return infinity for them too. That's not ideal, but in practice,
+ * lgamma() is much less likely to overflow than tgamma(), so it seems OK.
+ */
+ if (unlikely(errno == ERANGE))
+ result = get_float8_infinity();
+
+ PG_RETURN_FLOAT8(result);
+}
+
+
/*
* =========================
diff --git a/src/include/catalog/pg_proc.dat b/src/include/catalog/pg_proc.dat
new file mode 100644
index 6a5476d..acaf4fb
--- a/src/include/catalog/pg_proc.dat
+++ b/src/include/catalog/pg_proc.dat
@@ -3484,6 +3484,13 @@
proname => 'erfc', prorettype => 'float8', proargtypes => 'float8',
prosrc => 'derfc' },
+{ oid => '8702', descr => 'gamma function',
+ proname => 'gamma', prorettype => 'float8', proargtypes => 'float8',
+ prosrc => 'dgamma' },
+{ oid => '8703', descr => 'natural logarithm of absolute value of gamma function',
+ proname => 'lgamma', prorettype => 'float8', proargtypes => 'float8',
+ prosrc => 'dlgamma' },
+
{ oid => '1618',
proname => 'interval_mul', prorettype => 'interval',
proargtypes => 'interval float8', prosrc => 'interval_mul' },
diff --git a/src/test/regress/expected/float8.out b/src/test/regress/expected/float8.out
new file mode 100644
index 344d6b7..f16d670
--- a/src/test/regress/expected/float8.out
+++ b/src/test/regress/expected/float8.out
@@ -830,6 +830,50 @@ FROM (VALUES (float8 '-infinity'),
(22 rows)
RESET extra_float_digits;
+-- gamma functions
+-- we run these with extra_float_digits = -1, to get consistently rounded
+-- results on all platforms.
+SET extra_float_digits = -1;
+SELECT x,
+ gamma(x),
+ lgamma(x)
+FROM (VALUES (float8 '-infinity'),
+ ('-0'), (0), (0.5), (1), (2), (3), (4), (5),
+ (float8 'infinity'), (float8 'nan')) AS t(x);
+ x | gamma | lgamma
+-----------+-----------------+------------------
+ -Infinity | NaN | Infinity
+ -0 | -Infinity | Infinity
+ 0 | Infinity | Infinity
+ 0.5 | 1.7724538509055 | 0.5723649429247
+ 1 | 1 | 0
+ 2 | 1 | 0
+ 3 | 2 | 0.69314718055995
+ 4 | 6 | 1.7917594692281
+ 5 | 24 | 3.1780538303479
+ Infinity | Infinity | Infinity
+ NaN | NaN | NaN
+(11 rows)
+
+-- invalid inputs for gamma()
+SELECT gamma(-1);
+ERROR: value out of range: overflow
+SELECT gamma(1000000);
+ERROR: value out of range: overflow
+-- valid for lgamma()
+SELECT lgamma(-1);
+ lgamma
+----------
+ Infinity
+(1 row)
+
+SELECT lgamma(1000000);
+ lgamma
+-----------------
+ 12815504.569148
+(1 row)
+
+RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
diff --git a/src/test/regress/sql/float8.sql b/src/test/regress/sql/float8.sql
new file mode 100644
index 98e9926..68c68f0
--- a/src/test/regress/sql/float8.sql
+++ b/src/test/regress/sql/float8.sql
@@ -245,6 +245,25 @@ FROM (VALUES (float8 '-infinity'),
RESET extra_float_digits;
+-- gamma functions
+-- we run these with extra_float_digits = -1, to get consistently rounded
+-- results on all platforms.
+SET extra_float_digits = -1;
+SELECT x,
+ gamma(x),
+ lgamma(x)
+FROM (VALUES (float8 '-infinity'),
+ ('-0'), (0), (0.5), (1), (2), (3), (4), (5),
+ (float8 'infinity'), (float8 'nan')) AS t(x);
+-- invalid inputs for gamma()
+SELECT gamma(-1);
+SELECT gamma(1000000);
+-- valid for lgamma()
+SELECT lgamma(-1);
+SELECT lgamma(1000000);
+
+RESET extra_float_digits;
+
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
