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float4.sql
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float4.sql
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--
-- FLOAT4
--
CREATE TABLE FLOAT4_TBL (f1 float4);
INSERT INTO FLOAT4_TBL(f1) VALUES (' 0.0');
INSERT INTO FLOAT4_TBL(f1) VALUES ('1004.30 ');
INSERT INTO FLOAT4_TBL(f1) VALUES (' -34.84 ');
INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e+20');
INSERT INTO FLOAT4_TBL(f1) VALUES ('1.2345678901234e-20');
-- test for over and under flow
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
INSERT INTO FLOAT4_TBL(f1) VALUES (' ');
INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
INSERT INTO FLOAT4_TBL(f1) VALUES ('5. 0');
INSERT INTO FLOAT4_TBL(f1) VALUES (' - 3.0');
INSERT INTO FLOAT4_TBL(f1) VALUES ('123 5');
-- special inputs
SELECT 'NaN'::float4;
SELECT 'nan'::float4;
SELECT ' NAN '::float4;
SELECT 'infinity'::float4;
SELECT ' -INFINiTY '::float4;
-- bad special inputs
SELECT 'N A N'::float4;
SELECT 'NaN x'::float4;
SELECT ' INFINITY x'::float4;
SELECT 'Infinity'::float4 + 100.0;
SELECT 'Infinity'::float4 / 'Infinity'::float4;
SELECT 'nan'::float4 / 'nan'::float4;
SELECT 'nan'::numeric::float4;
SELECT '' AS five, * FROM FLOAT4_TBL;
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
-- test divide by zero
SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
SELECT '' AS five, * FROM FLOAT4_TBL;
-- test the unary float4abs operator
SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
UPDATE FLOAT4_TBL
SET f1 = FLOAT4_TBL.f1 * '-1'
WHERE FLOAT4_TBL.f1 > '0.0';
SELECT '' AS five, * FROM FLOAT4_TBL;
-- test edge-case coercions to integer
SELECT '32767.4'::float4::int2;
SELECT '32767.6'::float4::int2;
SELECT '-32768.4'::float4::int2;
SELECT '-32768.6'::float4::int2;
SELECT '2147483520'::float4::int4;
SELECT '2147483647'::float4::int4;
SELECT '-2147483648.5'::float4::int4;
SELECT '-2147483900'::float4::int4;
SELECT '9223369837831520256'::float4::int8;
SELECT '9223372036854775807'::float4::int8;
SELECT '-9223372036854775808.5'::float4::int8;
SELECT '-9223380000000000000'::float4::int8;
-- Test for correct input rounding in edge cases.
-- These lists are from Paxson 1991, excluding subnormals and
-- inputs of over 9 sig. digits.
SELECT float4send('5e-20'::float4);
SELECT float4send('67e14'::float4);
SELECT float4send('985e15'::float4);
SELECT float4send('55895e-16'::float4);
SELECT float4send('7038531e-32'::float4);
SELECT float4send('702990899e-20'::float4);
SELECT float4send('3e-23'::float4);
SELECT float4send('57e18'::float4);
SELECT float4send('789e-35'::float4);
SELECT float4send('2539e-18'::float4);
SELECT float4send('76173e28'::float4);
SELECT float4send('887745e-11'::float4);
SELECT float4send('5382571e-37'::float4);
SELECT float4send('82381273e-35'::float4);
SELECT float4send('750486563e-38'::float4);
-- Test that the smallest possible normalized input value inputs
-- correctly, either in 9-significant-digit or shortest-decimal
-- format.
--
-- exact val is 1.1754943508...
-- shortest val is 1.1754944000
-- midpoint to next val is 1.1754944208...
SELECT float4send('1.17549435e-38'::float4);
SELECT float4send('1.1754944e-38'::float4);
-- 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 xfloat4;
create function xfloat4in(cstring) returns xfloat4 immutable strict
language internal as 'int4in';
create function xfloat4out(xfloat4) returns cstring immutable strict
language internal as 'int4out';
create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
create cast (xfloat4 as float4) without function;
create cast (float4 as xfloat4) without function;
create cast (xfloat4 as integer) without function;
create cast (integer as xfloat4) without function;
-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
-- 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'00000001'),
(x'00000002'), (x'00000003'),
(x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
(x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
-- stress values
(x'0053c4f4'), -- 7693e-42
(x'006c85c4'), -- 996622e-44
(x'0041ca76'), -- 60419369e-46
(x'004b7678'), -- 6930161142e-48
-- taken from upstream testsuite
(x'00000007'),
(x'00424fe2'),
-- borderline between subnormal and normal
(x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
select float4send(flt) as ibits,
flt
from (select bits::integer::xfloat4::float4 as flt
from testdata
offset 0) s;
with testdata(bits) as (values
(x'00000000'),
-- smallest normal values
(x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
(x'00800006'),
-- small normal values chosen for short vs. long output
(x'008002f1'), (x'008002f2'), (x'008002f3'),
(x'00800e17'), (x'00800e18'), (x'00800e19'),
-- assorted values (random mantissae)
(x'01000001'), (x'01102843'), (x'01a52c98'),
(x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
(x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
(x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
(x'1f850283'), (x'2874a9d6'),
-- values around 5e-08
(x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
-- around 1e-07
(x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
-- around 3e-07 .. 1e-04
(x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
(x'350637bc'), (x'350637bd'), (x'350637be'),
(x'35719786'), (x'35719787'), (x'35719788'),
(x'358637bc'), (x'358637bd'), (x'358637be'),
(x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
(x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
-- format crossover at 1e-04
(x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
(x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
(x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
(x'38d1b71d'),
--
(x'38dffffe'), (x'38dfffff'), (x'38e00000'),
(x'38efffff'), (x'38f00000'), (x'38f00001'),
(x'3a83126e'), (x'3a83126f'), (x'3a831270'),
(x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
(x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
-- chosen to need 9 digits for 3dcccd70
(x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
--
(x'3effffff'), (x'3f000000'), (x'3f000001'),
(x'3f333332'), (x'3f333333'), (x'3f333334'),
-- approach 1.0 with increasing numbers of 9s
(x'3f666665'), (x'3f666666'), (x'3f666667'),
(x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
(x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
(x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
(x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
(x'3f7fffee'), (x'3f7fffef'),
-- values very close to 1
(x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
(x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
(x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
(x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
(x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
(x'3f7fffff'),
(x'3f800000'),
(x'3f800001'), (x'3f800002'), (x'3f800003'),
(x'3f800004'), (x'3f800005'), (x'3f800006'),
(x'3f800007'), (x'3f800008'), (x'3f800009'),
-- values 1 to 1.1
(x'3f80000f'), (x'3f800010'), (x'3f800011'),
(x'3f800012'), (x'3f800013'), (x'3f800014'),
(x'3f800017'), (x'3f800018'), (x'3f800019'),
(x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
(x'3f800029'), (x'3f80002a'), (x'3f80002b'),
(x'3f800053'), (x'3f800054'), (x'3f800055'),
(x'3f800346'), (x'3f800347'), (x'3f800348'),
(x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
(x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
(x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
--
(x'3fc90fdb'), -- pi/2
(x'402df854'), -- e
(x'40490fdb'), -- pi
--
(x'409fffff'), (x'40a00000'), (x'40a00001'),
(x'40afffff'), (x'40b00000'), (x'40b00001'),
(x'411fffff'), (x'41200000'), (x'41200001'),
(x'42c7ffff'), (x'42c80000'), (x'42c80001'),
(x'4479ffff'), (x'447a0000'), (x'447a0001'),
(x'461c3fff'), (x'461c4000'), (x'461c4001'),
(x'47c34fff'), (x'47c35000'), (x'47c35001'),
(x'497423ff'), (x'49742400'), (x'49742401'),
(x'4b18967f'), (x'4b189680'), (x'4b189681'),
(x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
(x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
(x'501502f8'), (x'501502f9'), (x'501502fa'),
(x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
-- stress values
(x'1f6c1e4a'), -- 5e-20
(x'59be6cea'), -- 67e14
(x'5d5ab6c4'), -- 985e15
(x'2cc4a9bd'), -- 55895e-16
(x'15ae43fd'), -- 7038531e-32
(x'2cf757ca'), -- 702990899e-20
(x'665ba998'), -- 25933168707e13
(x'743c3324'), -- 596428896559e20
-- exercise fixed-point memmoves
(x'47f1205a'),
(x'4640e6ae'),
(x'449a5225'),
(x'42f6e9d5'),
(x'414587dd'),
(x'3f9e064b'),
-- these cases come from the upstream's testsuite
-- BoundaryRoundEven
(x'4c000004'),
(x'50061c46'),
(x'510006a8'),
-- ExactValueRoundEven
(x'48951f84'),
(x'45fd1840'),
-- LotsOfTrailingZeros
(x'39800000'),
(x'3b200000'),
(x'3b900000'),
(x'3bd00000'),
-- Regression
(x'63800000'),
(x'4b000000'),
(x'4b800000'),
(x'4c000001'),
(x'4c800b0d'),
(x'00d24584'),
(x'00d90b88'),
(x'45803f34'),
(x'4f9f24f7'),
(x'3a8722c3'),
(x'5c800041'),
(x'15ae43fd'),
(x'5d4cccfb'),
(x'4c800001'),
(x'57800ed8'),
(x'5f000000'),
(x'700000f0'),
(x'5f23e9ac'),
(x'5e9502f9'),
(x'5e8012b1'),
(x'3c000028'),
(x'60cde861'),
(x'03aa2a50'),
(x'43480000'),
(x'4c000000'),
-- LooksLikePow5
(x'5D1502F9'),
(x'5D9502F9'),
(x'5E1502F9'),
-- OutputLength
(x'3f99999a'),
(x'3f9d70a4'),
(x'3f9df3b6'),
(x'3f9e0419'),
(x'3f9e0610'),
(x'3f9e064b'),
(x'3f9e0651'),
(x'03d20cfe')
)
select float4send(flt) as ibits,
flt,
flt::text::float4 as r_flt,
float4send(flt::text::float4) as obits,
float4send(flt::text::float4) = float4send(flt) as correct
from (select bits::integer::xfloat4::float4 as flt
from testdata
offset 0) s;
-- clean up, lest opr_sanity complain
drop type xfloat4 cascade;