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postgresql/src/test/regress/sql/float8.sql
Dean Rasheed d5d574146d Add support for the error functions erf() and erfc(). 
Expose the standard error functions as SQL-callable functions. These
are 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, they
should in theory be available on all supported platforms. If that
turns out not to be the case, more work will be needed.

On all platforms tested so far, using extra_float_digits = -1 in the
regression tests is sufficient to allow for variations between
implementations. However, past experience has shown that there are
almost certainly going to be additional unexpected portability issues,
so these tests may well need further adjustments, based on the
buildfarm 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
2023-03-14 09:17:36 +00:00

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--
-- FLOAT8
--
--
-- Build a table for testing
-- (This temporarily hides the table created in test_setup.sql)
--
CREATE TEMP TABLE FLOAT8_TBL(f1 float8);
INSERT INTO FLOAT8_TBL(f1) VALUES (' 0.0 ');
INSERT INTO FLOAT8_TBL(f1) VALUES ('1004.30 ');
INSERT INTO FLOAT8_TBL(f1) VALUES (' -34.84');
INSERT INTO FLOAT8_TBL(f1) VALUES ('1.2345678901234e+200');
INSERT INTO FLOAT8_TBL(f1) VALUES ('1.2345678901234e-200');
-- test for underflow and overflow handling
SELECT '10e400'::float8;
SELECT '-10e400'::float8;
SELECT '10e-400'::float8;
SELECT '-10e-400'::float8;
-- test smallest normalized input
SELECT float8send('2.2250738585072014E-308'::float8);
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
INSERT INTO FLOAT8_TBL(f1) VALUES (' ');
INSERT INTO FLOAT8_TBL(f1) VALUES ('xyz');
INSERT INTO FLOAT8_TBL(f1) VALUES ('5.0.0');
INSERT INTO FLOAT8_TBL(f1) VALUES ('5 . 0');
INSERT INTO FLOAT8_TBL(f1) VALUES ('5. 0');
INSERT INTO FLOAT8_TBL(f1) VALUES (' - 3');
INSERT INTO FLOAT8_TBL(f1) VALUES ('123 5');
-- Also try it with non-error-throwing API
SELECT pg_input_is_valid('34.5', 'float8');
SELECT pg_input_is_valid('xyz', 'float8');
SELECT pg_input_is_valid('1e4000', 'float8');
SELECT * FROM pg_input_error_info('1e4000', 'float8');
-- special inputs
SELECT 'NaN'::float8;
SELECT 'nan'::float8;
SELECT ' NAN '::float8;
SELECT 'infinity'::float8;
SELECT ' -INFINiTY '::float8;
-- bad special inputs
SELECT 'N A N'::float8;
SELECT 'NaN x'::float8;
SELECT ' INFINITY x'::float8;
SELECT 'Infinity'::float8 + 100.0;
SELECT 'Infinity'::float8 / 'Infinity'::float8;
SELECT '42'::float8 / 'Infinity'::float8;
SELECT 'nan'::float8 / 'nan'::float8;
SELECT 'nan'::float8 / '0'::float8;
SELECT 'nan'::numeric::float8;
SELECT * FROM FLOAT8_TBL;
SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 <> '1004.3';
SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 = '1004.3';
SELECT f.* FROM FLOAT8_TBL f WHERE '1004.3' > f.f1;
SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 < '1004.3';
SELECT f.* FROM FLOAT8_TBL f WHERE '1004.3' >= f.f1;
SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 <= '1004.3';
SELECT f.f1, f.f1 * '-10' AS x
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
SELECT f.f1, f.f1 + '-10' AS x
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
SELECT f.f1, f.f1 / '-10' AS x
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
SELECT f.f1, f.f1 - '-10' AS x
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
SELECT f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
-- absolute value
SELECT f.f1, @f.f1 AS abs_f1
FROM FLOAT8_TBL f;
-- truncate
SELECT f.f1, trunc(f.f1) AS trunc_f1
FROM FLOAT8_TBL f;
-- round
SELECT f.f1, round(f.f1) AS round_f1
FROM FLOAT8_TBL f;
-- ceil / ceiling
select ceil(f1) as ceil_f1 from float8_tbl f;
select ceiling(f1) as ceiling_f1 from float8_tbl f;
-- floor
select floor(f1) as floor_f1 from float8_tbl f;
-- sign
select sign(f1) as sign_f1 from float8_tbl f;
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
SELECT |/ float8 '64' AS eight;
SELECT f.f1, |/f.f1 AS sqrt_f1
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
-- power
SELECT power(float8 '144', float8 '0.5');
SELECT power(float8 'NaN', float8 '0.5');
SELECT power(float8 '144', float8 'NaN');
SELECT power(float8 'NaN', float8 'NaN');
SELECT power(float8 '-1', float8 'NaN');
SELECT power(float8 '1', float8 'NaN');
SELECT power(float8 'NaN', float8 '0');
SELECT power(float8 'inf', float8 '0');
SELECT power(float8 '-inf', float8 '0');
SELECT power(float8 '0', float8 'inf');
SELECT power(float8 '0', float8 '-inf');
SELECT power(float8 '1', float8 'inf');
SELECT power(float8 '1', float8 '-inf');
SELECT power(float8 '-1', float8 'inf');
SELECT power(float8 '-1', float8 '-inf');
SELECT power(float8 '0.1', float8 'inf');
SELECT power(float8 '-0.1', float8 'inf');
SELECT power(float8 '1.1', float8 'inf');
SELECT power(float8 '-1.1', float8 'inf');
SELECT power(float8 '0.1', float8 '-inf');
SELECT power(float8 '-0.1', float8 '-inf');
SELECT power(float8 '1.1', float8 '-inf');
SELECT power(float8 '-1.1', float8 '-inf');
SELECT power(float8 'inf', float8 '-2');
SELECT power(float8 'inf', float8 '2');
SELECT power(float8 'inf', float8 'inf');
SELECT power(float8 'inf', float8 '-inf');
-- Intel's icc misoptimizes the code that controls the sign of this result,
-- even with -mp1. Pending a fix for that, only test for "is it zero".
SELECT power(float8 '-inf', float8 '-2') = '0';
SELECT power(float8 '-inf', float8 '-3');
SELECT power(float8 '-inf', float8 '2');
SELECT power(float8 '-inf', float8 '3');
SELECT power(float8 '-inf', float8 '3.5');
SELECT power(float8 '-inf', float8 'inf');
SELECT power(float8 '-inf', float8 '-inf');
-- take exp of ln(f.f1)
SELECT f.f1, exp(ln(f.f1)) AS exp_ln_f1
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
-- check edge cases for exp
SELECT exp('inf'::float8), exp('-inf'::float8), exp('nan'::float8);
-- cube root
SELECT ||/ float8 '27' AS three;
SELECT f.f1, ||/f.f1 AS cbrt_f1 FROM FLOAT8_TBL f;
SELECT * FROM FLOAT8_TBL;
UPDATE FLOAT8_TBL
SET f1 = FLOAT8_TBL.f1 * '-1'
WHERE FLOAT8_TBL.f1 > '0.0';
SELECT f.f1 * '1e200' from FLOAT8_TBL f;
SELECT f.f1 ^ '1e200' from FLOAT8_TBL f;
SELECT 0 ^ 0 + 0 ^ 1 + 0 ^ 0.0 + 0 ^ 0.5;
SELECT ln(f.f1) from FLOAT8_TBL f where f.f1 = '0.0' ;
SELECT ln(f.f1) from FLOAT8_TBL f where f.f1 < '0.0' ;
SELECT exp(f.f1) from FLOAT8_TBL f;
SELECT f.f1 / '0.0' from FLOAT8_TBL f;
SELECT * FROM FLOAT8_TBL;
-- hyperbolic functions
-- we run these with extra_float_digits = 0 too, since different platforms
-- tend to produce results that vary in the last place.
SELECT sinh(float8 '1');
SELECT cosh(float8 '1');
SELECT tanh(float8 '1');
SELECT asinh(float8 '1');
SELECT acosh(float8 '2');
SELECT atanh(float8 '0.5');
-- test Inf/NaN cases for hyperbolic functions
SELECT sinh(float8 'infinity');
SELECT sinh(float8 '-infinity');
SELECT sinh(float8 'nan');
SELECT cosh(float8 'infinity');
SELECT cosh(float8 '-infinity');
SELECT cosh(float8 'nan');
SELECT tanh(float8 'infinity');
SELECT tanh(float8 '-infinity');
SELECT tanh(float8 'nan');
SELECT asinh(float8 'infinity');
SELECT asinh(float8 '-infinity');
SELECT asinh(float8 'nan');
-- acosh(Inf) should be Inf, but some mingw versions produce NaN, so skip test
-- SELECT acosh(float8 'infinity');
SELECT acosh(float8 '-infinity');
SELECT acosh(float8 'nan');
SELECT atanh(float8 'infinity');
SELECT atanh(float8 '-infinity');
SELECT atanh(float8 'nan');
-- error functions
-- we run these with extra_float_digits = -1, to get consistently rounded
-- results on all platforms.
SET extra_float_digits = -1;
SELECT x,
erf(x),
erfc(x)
FROM (VALUES (float8 '-infinity'),
(-28), (-6), (-3.4), (-2.1), (-1.1), (-0.45),
(-1.2e-9), (-2.3e-13), (-1.2e-17), (0),
(1.2e-17), (2.3e-13), (1.2e-9),
(0.45), (1.1), (2.1), (3.4), (6), (28),
(float8 'infinity'), (float8 'nan')) AS t(x);
RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-10e400');
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e-400');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-10e-400');
DROP TABLE FLOAT8_TBL;
-- Check the float8 values exported for use by other tests
SELECT * FROM FLOAT8_TBL;
-- test edge-case coercions to integer
SELECT '32767.4'::float8::int2;
SELECT '32767.6'::float8::int2;
SELECT '-32768.4'::float8::int2;
SELECT '-32768.6'::float8::int2;
SELECT '2147483647.4'::float8::int4;
SELECT '2147483647.6'::float8::int4;
SELECT '-2147483648.4'::float8::int4;
SELECT '-2147483648.6'::float8::int4;
SELECT '9223372036854773760'::float8::int8;
SELECT '9223372036854775807'::float8::int8;
SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
-- test exact cases for trigonometric functions in degrees
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
FROM (VALUES (0), (30), (90), (150), (180),
(210), (270), (330), (360)) AS t(x);
SELECT x,
cosd(x),
cosd(x) IN (-1,-0.5,0,0.5,1) AS cosd_exact
FROM (VALUES (0), (60), (90), (120), (180),
(240), (270), (300), (360)) AS t(x);
SELECT x,
tand(x),
tand(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) AS tand_exact,
cotd(x),
cotd(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) AS cotd_exact
FROM (VALUES (0), (45), (90), (135), (180),
(225), (270), (315), (360)) AS t(x);
SELECT x,
asind(x),
asind(x) IN (-90,-30,0,30,90) AS asind_exact,
acosd(x),
acosd(x) IN (0,60,90,120,180) AS acosd_exact
FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
SELECT x,
atand(x),
atand(x) IN (-90,-45,0,45,90) AS atand_exact
FROM (VALUES ('-Infinity'::float8), (-1), (0), (1),
('Infinity'::float8)) AS t(x);
SELECT x, y,
atan2d(y, x),
atan2d(y, x) IN (-90,0,90,180) AS atan2d_exact
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
--
-- test output (and round-trip safety) of various values.
-- To ensure we're testing what we think we're testing, start with
-- float values specified by bit patterns (as a useful side effect,
-- this means we'll fail on non-IEEE platforms).
create type xfloat8;
create function xfloat8in(cstring) returns xfloat8 immutable strict
language internal as 'int8in';
create function xfloat8out(xfloat8) returns cstring immutable strict
language internal as 'int8out';
create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
create cast (xfloat8 as float8) without function;
create cast (float8 as xfloat8) without function;
create cast (xfloat8 as bigint) without function;
create cast (bigint as xfloat8) without function;
-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
-- we don't care to assume the platform's strtod() handles subnormals
-- correctly; those are "use at your own risk". However we do test
-- subnormal outputs, since those are under our control.
with testdata(bits) as (values
-- small subnormals
(x'0000000000000001'),
(x'0000000000000002'), (x'0000000000000003'),
(x'0000000000001000'), (x'0000000100000000'),
(x'0000010000000000'), (x'0000010100000000'),
(x'0000400000000000'), (x'0000400100000000'),
(x'0000800000000000'), (x'0000800000000001'),
-- these values taken from upstream testsuite
(x'00000000000f4240'),
(x'00000000016e3600'),
(x'0000008cdcdea440'),
-- borderline between subnormal and normal
(x'000ffffffffffff0'), (x'000ffffffffffff1'),
(x'000ffffffffffffe'), (x'000fffffffffffff'))
select float8send(flt) as ibits,
flt
from (select bits::bigint::xfloat8::float8 as flt
from testdata
offset 0) s;
-- round-trip tests
with testdata(bits) as (values
(x'0000000000000000'),
-- smallest normal values
(x'0010000000000000'), (x'0010000000000001'),
(x'0010000000000002'), (x'0018000000000000'),
--
(x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
(x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
(x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
(x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
(x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
(x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
(x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
(x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
(x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
(x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
-- values very close to 1
(x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
(x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
(x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
(x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
(x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
(x'3fefffffffffffff'),
(x'3ff0000000000000'),
(x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
(x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
(x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
--
(x'3ff921fb54442d18'),
(x'4005bf0a8b14576a'),
(x'400921fb54442d18'),
--
(x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
(x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
(x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
(x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
(x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
(x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
(x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
(x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
(x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
(x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
(x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
(x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
(x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
(x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
(x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
(x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
(x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
(x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
(x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
(x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
(x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
(x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
(x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
(x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
(x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
--
(x'7feffffffffffffe'), (x'7fefffffffffffff'),
-- round to even tests (+ve)
(x'4350000000000002'),
(x'4350000000002e06'),
(x'4352000000000003'),
(x'4352000000000004'),
(x'4358000000000003'),
(x'4358000000000004'),
(x'435f000000000020'),
-- round to even tests (-ve)
(x'c350000000000002'),
(x'c350000000002e06'),
(x'c352000000000003'),
(x'c352000000000004'),
(x'c358000000000003'),
(x'c358000000000004'),
(x'c35f000000000020'),
-- exercise fixed-point memmoves
(x'42dc12218377de66'),
(x'42a674e79c5fe51f'),
(x'4271f71fb04cb74c'),
(x'423cbe991a145879'),
(x'4206fee0e1a9e061'),
(x'41d26580b487e6b4'),
(x'419d6f34540ca453'),
(x'41678c29dcd6e9dc'),
(x'4132d687e3df217d'),
(x'40fe240c9fcb68c8'),
(x'40c81cd6e63c53d3'),
(x'40934a4584fd0fdc'),
(x'405edd3c07fb4c93'),
(x'4028b0fcd32f7076'),
(x'3ff3c0ca428c59f8'),
-- these cases come from the upstream's testsuite
-- LotsOfTrailingZeros)
(x'3e60000000000000'),
-- Regression
(x'c352bd2668e077c4'),
(x'434018601510c000'),
(x'43d055dc36f24000'),
(x'43e052961c6f8000'),
(x'3ff3c0ca2a5b1d5d'),
-- LooksLikePow5
(x'4830f0cf064dd592'),
(x'4840f0cf064dd592'),
(x'4850f0cf064dd592'),
-- OutputLength
(x'3ff3333333333333'),
(x'3ff3ae147ae147ae'),
(x'3ff3be76c8b43958'),
(x'3ff3c083126e978d'),
(x'3ff3c0c1fc8f3238'),
(x'3ff3c0c9539b8887'),
(x'3ff3c0ca2a5b1d5d'),
(x'3ff3c0ca4283de1b'),
(x'3ff3c0ca43db770a'),
(x'3ff3c0ca428abd53'),
(x'3ff3c0ca428c1d2b'),
(x'3ff3c0ca428c51f2'),
(x'3ff3c0ca428c58fc'),
(x'3ff3c0ca428c59dd'),
(x'3ff3c0ca428c59f8'),
(x'3ff3c0ca428c59fb'),
-- 32-bit chunking
(x'40112e0be8047a7d'),
(x'40112e0be815a889'),
(x'40112e0be826d695'),
(x'40112e0be83804a1'),
(x'40112e0be84932ad'),
-- MinMaxShift
(x'0040000000000000'),
(x'007fffffffffffff'),
(x'0290000000000000'),
(x'029fffffffffffff'),
(x'4350000000000000'),
(x'435fffffffffffff'),
(x'1330000000000000'),
(x'133fffffffffffff'),
(x'3a6fa7161a4d6e0c')
)
select float8send(flt) as ibits,
flt,
flt::text::float8 as r_flt,
float8send(flt::text::float8) as obits,
float8send(flt::text::float8) = float8send(flt) as correct
from (select bits::bigint::xfloat8::float8 as flt
from testdata
offset 0) s;
-- clean up, lest opr_sanity complain
drop type xfloat8 cascade;
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