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Commitd5d5741

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Add support for the error functions erf() and erfc().
Expose the standard error functions as SQL-callable functions. Theseare expected to be useful to people working with normal distributions,and we use them here to test the distribution from random_normal().Since these functions are defined in the POSIX and C99 standards, theyshould in theory be available on all supported platforms. If thatturns out not to be the case, more work will be needed.On all platforms tested so far, using extra_float_digits = -1 in theregression tests is sufficient to allow for variations betweenimplementations. However, past experience has shown that there arealmost certainly going to be additional unexpected portability issues,so these tests may well need further adjustments, based on thebuildfarm results.Dean Rasheed, reviewed by Nathan Bossart and Thomas Munro.Discussion:https://postgr.es/m/CAEZATCXv5fi7+Vu-POiyai+ucF95+YMcCMafxV+eZuN1B-=MkQ@mail.gmail.com
1 parent3a465cc commitd5d5741

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8 files changed

+205
-1
lines changed

8 files changed

+205
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lines changed

‎doc/src/sgml/func.sgml

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@@ -1286,6 +1286,41 @@ repeat('Pg', 4) <returnvalue>PgPgPgPg</returnvalue>
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</para></entry>
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</row>
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<row>
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<entry role="func_table_entry"><para role="func_signature">
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<indexterm>
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<primary>erf</primary>
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</indexterm>
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<function>erf</function> ( <type>double precision</type> )
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<returnvalue>double precision</returnvalue>
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</para>
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<para>
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Error function
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</para>
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<para>
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<literal>erf(1.0)</literal>
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<returnvalue>0.8427007929497149</returnvalue>
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</para></entry>
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</row>
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<row>
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<entry role="func_table_entry"><para role="func_signature">
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<indexterm>
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<primary>erfc</primary>
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</indexterm>
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<function>erfc</function> ( <type>double precision</type> )
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<returnvalue>double precision</returnvalue>
1313+
</para>
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<para>
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Complementary error function (<literal>1 - erf(x)</literal>, without
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loss of precision for large inputs)
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</para>
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<para>
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<literal>erfc(1.0)</literal>
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<returnvalue>0.15729920705028513</returnvalue>
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</para></entry>
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</row>
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<row>
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<entry role="func_table_entry"><para role="func_signature">
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<indexterm>

‎src/backend/utils/adt/float.c

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Original file line numberDiff line numberDiff line change
@@ -2742,6 +2742,53 @@ datanh(PG_FUNCTION_ARGS)
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}
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/* ========== ERROR FUNCTIONS ========== */
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/*
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*derf- returns the error function: erf(arg1)
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*/
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Datum
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derf(PG_FUNCTION_ARGS)
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{
2754+
float8arg1=PG_GETARG_FLOAT8(0);
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float8result;
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2757+
/*
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* For erf, we don't need an errno check because it never overflows.
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*/
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result=erf(arg1);
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if (unlikely(isinf(result)))
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float_overflow_error();
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PG_RETURN_FLOAT8(result);
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}
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/*
2769+
*derfc- returns the complementary error function: 1 - erf(arg1)
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*/
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Datum
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derfc(PG_FUNCTION_ARGS)
2773+
{
2774+
float8arg1=PG_GETARG_FLOAT8(0);
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float8result;
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/*
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* For erfc, we don't need an errno check because it never overflows.
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*/
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result=erfc(arg1);
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if (unlikely(isinf(result)))
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float_overflow_error();
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PG_RETURN_FLOAT8(result);
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}
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/* ========== RANDOM FUNCTIONS ========== */
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/*
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* initialize_drandom_seed - initialize drandom_seed if not yet done
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*/

‎src/include/catalog/catversion.h

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -57,6 +57,6 @@
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*/
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/*yyyymmddN */
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#defineCATALOG_VERSION_NO202303131
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#defineCATALOG_VERSION_NO202303141
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#endif

‎src/include/catalog/pg_proc.dat

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@@ -3465,6 +3465,13 @@
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proname => 'atanh', prorettype => 'float8', proargtypes => 'float8',
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prosrc => 'datanh' },
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{ oid => '8788', descr => 'error function',
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proname => 'erf', prorettype => 'float8', proargtypes => 'float8',
3470+
prosrc => 'derf' },
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{ oid => '8789', descr => 'complementary error function',
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proname => 'erfc', prorettype => 'float8', proargtypes => 'float8',
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prosrc => 'derfc' },
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34683475
{ oid => '1618',
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proname => 'interval_mul', prorettype => 'interval',
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proargtypes => 'interval float8', prosrc => 'interval_mul' },

‎src/test/regress/expected/float8.out

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Original file line numberDiff line numberDiff line change
@@ -790,6 +790,45 @@ SELECT atanh(float8 'nan');
790790
NaN
791791
(1 row)
792792

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-- error functions
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-- we run these with extra_float_digits = -1, to get consistently rounded
795+
-- results on all platforms.
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SET extra_float_digits = -1;
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SELECT x,
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erf(x),
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erfc(x)
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FROM (VALUES (float8 '-infinity'),
801+
(-28), (-6), (-3.4), (-2.1), (-1.1), (-0.45),
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(-1.2e-9), (-2.3e-13), (-1.2e-17), (0),
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(1.2e-17), (2.3e-13), (1.2e-9),
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(0.45), (1.1), (2.1), (3.4), (6), (28),
805+
(float8 'infinity'), (float8 'nan')) AS t(x);
806+
x | erf | erfc
807+
-----------+----------------------+---------------------
808+
-Infinity | -1 | 2
809+
-28 | -1 | 2
810+
-6 | -1 | 2
811+
-3.4 | -0.99999847800664 | 1.9999984780066
812+
-2.1 | -0.99702053334367 | 1.9970205333437
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-1.1 | -0.88020506957408 | 1.8802050695741
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-0.45 | -0.47548171978692 | 1.4754817197869
815+
-1.2e-09 | -1.3540550005146e-09 | 1.0000000013541
816+
-2.3e-13 | -2.5952720843197e-13 | 1.0000000000003
817+
-1.2e-17 | -1.3540550005146e-17 | 1
818+
0 | 0 | 1
819+
1.2e-17 | 1.3540550005146e-17 | 1
820+
2.3e-13 | 2.5952720843197e-13 | 0.99999999999974
821+
1.2e-09 | 1.3540550005146e-09 | 0.99999999864595
822+
0.45 | 0.47548171978692 | 0.52451828021308
823+
1.1 | 0.88020506957408 | 0.11979493042592
824+
2.1 | 0.99702053334367 | 0.002979466656333
825+
3.4 | 0.99999847800664 | 1.5219933628623e-06
826+
6 | 1 | 2.1519736712499e-17
827+
28 | 1 | 0
828+
Infinity | 1 | 0
829+
NaN | NaN | NaN
830+
(22 rows)
831+
793832
RESET extra_float_digits;
794833
-- test for over- and underflow
795834
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');

‎src/test/regress/expected/random.out

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Original file line numberDiff line numberDiff line change
@@ -88,6 +88,38 @@ GROUP BY r;
8888
-10 | 100
8989
(1 row)
9090

91+
-- Check standard normal distribution using the Kolmogorov-Smirnov test.
92+
CREATE FUNCTION ks_test_normal_random()
93+
RETURNS boolean AS
94+
$$
95+
DECLARE
96+
n int := 1000; -- Number of samples
97+
c float8 := 1.94947; -- Critical value for 99.9% confidence
98+
ok boolean;
99+
BEGIN
100+
ok := (
101+
WITH samples AS (
102+
SELECT random_normal() r FROM generate_series(1, n) ORDER BY 1
103+
), indexed_samples AS (
104+
SELECT (row_number() OVER())-1.0 i, r FROM samples
105+
)
106+
SELECT max(abs((1+erf(r/sqrt(2)))/2 - i/n)) < c / sqrt(n)
107+
FROM indexed_samples
108+
);
109+
RETURN ok;
110+
END
111+
$$
112+
LANGUAGE plpgsql;
113+
-- As above, ks_test_normal_random() returns true about 99.9%
114+
-- of the time, so try it 3 times and accept if any test passes.
115+
SELECT ks_test_normal_random() OR
116+
ks_test_normal_random() OR
117+
ks_test_normal_random() AS standard_normal;
118+
standard_normal
119+
-----------------
120+
t
121+
(1 row)
122+
91123
-- setseed() should produce a reproducible series of random() values.
92124
SELECT setseed(0.5);
93125
setseed

‎src/test/regress/sql/float8.sql

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Original file line numberDiff line numberDiff line change
@@ -229,6 +229,20 @@ SELECT atanh(float8 'infinity');
229229
SELECT atanh(float8'-infinity');
230230
SELECT atanh(float8'nan');
231231

232+
-- error functions
233+
-- we run these with extra_float_digits = -1, to get consistently rounded
234+
-- results on all platforms.
235+
SET extra_float_digits=-1;
236+
SELECT x,
237+
erf(x),
238+
erfc(x)
239+
FROM (VALUES (float8'-infinity'),
240+
(-28), (-6), (-3.4), (-2.1), (-1.1), (-0.45),
241+
(-1.2e-9), (-2.3e-13), (-1.2e-17), (0),
242+
(1.2e-17), (2.3e-13), (1.2e-9),
243+
(0.45), (1.1), (2.1), (3.4), (6), (28),
244+
(float8'infinity'), (float8'nan'))AS t(x);
245+
232246
RESET extra_float_digits;
233247

234248
-- test for over- and underflow

‎src/test/regress/sql/random.sql

Lines changed: 30 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -70,6 +70,36 @@ SELECT r, count(*)
7070
FROM (SELECT random_normal(-10,0) rFROM generate_series(1,100)) ss
7171
GROUP BY r;
7272

73+
-- Check standard normal distribution using the Kolmogorov-Smirnov test.
74+
75+
CREATEFUNCTIONks_test_normal_random()
76+
RETURNSbooleanAS
77+
$$
78+
DECLARE
79+
nint :=1000;-- Number of samples
80+
c float8 :=1.94947;-- Critical value for 99.9% confidence
81+
okboolean;
82+
BEGIN
83+
ok := (
84+
WITH samplesAS (
85+
SELECT random_normal() rFROM generate_series(1, n)ORDER BY1
86+
), indexed_samplesAS (
87+
SELECT (row_number() OVER())-1.0 i, rFROM samples
88+
)
89+
SELECTmax(abs((1+erf(r/sqrt(2)))/2- i/n))< c/ sqrt(n)
90+
FROM indexed_samples
91+
);
92+
RETURN ok;
93+
END
94+
$$
95+
LANGUAGE plpgsql;
96+
97+
-- As above, ks_test_normal_random() returns true about 99.9%
98+
-- of the time, so try it 3 times and accept if any test passes.
99+
SELECT ks_test_normal_random()OR
100+
ks_test_normal_random()OR
101+
ks_test_normal_random()AS standard_normal;
102+
73103
-- setseed() should produce a reproducible series of random() values.
74104

75105
SELECT setseed(0.5);

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