--
-- 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');
ERROR:  "10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
ERROR:  "-10e70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
ERROR:  "10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
ERROR:  "-10e-70" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e70'::float8);
ERROR:  value out of range: overflow
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e70'::float8);
ERROR:  value out of range: overflow
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-70'::float8);
ERROR:  value out of range: underflow
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-70'::float8);
ERROR:  value out of range: underflow
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
ERROR:  "10e400" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e400');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
ERROR:  "-10e400" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e400');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
ERROR:  "10e-400" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('10e-400');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
ERROR:  "-10e-400" is out of range for type real
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('-10e-400');
                                           ^
-- bad input
INSERT INTO FLOAT4_TBL(f1) VALUES ('');
ERROR:  invalid input syntax for type real: ""
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('       ');
ERROR:  invalid input syntax for type real: "       "
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('       ');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
ERROR:  invalid input syntax for type real: "xyz"
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('xyz');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
ERROR:  invalid input syntax for type real: "5.0.0"
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5.0.0');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
ERROR:  invalid input syntax for type real: "5 . 0"
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5 . 0');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('5.   0');
ERROR:  invalid input syntax for type real: "5.   0"
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('5.   0');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('     - 3.0');
ERROR:  invalid input syntax for type real: "     - 3.0"
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('     - 3.0');
                                           ^
INSERT INTO FLOAT4_TBL(f1) VALUES ('123            5');
ERROR:  invalid input syntax for type real: "123            5"
LINE 1: INSERT INTO FLOAT4_TBL(f1) VALUES ('123            5');
                                           ^
-- special inputs
SELECT 'NaN'::float4;
 float4 
--------
    NaN
(1 row)

SELECT 'nan'::float4;
 float4 
--------
    NaN
(1 row)

SELECT '   NAN  '::float4;
 float4 
--------
    NaN
(1 row)

SELECT 'infinity'::float4;
  float4  
----------
 Infinity
(1 row)

SELECT '          -INFINiTY   '::float4;
  float4   
-----------
 -Infinity
(1 row)

-- bad special inputs
SELECT 'N A N'::float4;
ERROR:  invalid input syntax for type real: "N A N"
LINE 1: SELECT 'N A N'::float4;
               ^
SELECT 'NaN x'::float4;
ERROR:  invalid input syntax for type real: "NaN x"
LINE 1: SELECT 'NaN x'::float4;
               ^
SELECT ' INFINITY    x'::float4;
ERROR:  invalid input syntax for type real: " INFINITY    x"
LINE 1: SELECT ' INFINITY    x'::float4;
               ^
SELECT 'Infinity'::float4 + 100.0;
 ?column? 
----------
 Infinity
(1 row)

SELECT 'Infinity'::float4 / 'Infinity'::float4;
 ?column? 
----------
      NaN
(1 row)

SELECT 'nan'::float4 / 'nan'::float4;
 ?column? 
----------
      NaN
(1 row)

SELECT 'nan'::numeric::float4;
 float4 
--------
    NaN
(1 row)

SELECT '' AS five, * FROM FLOAT4_TBL;
 five |      f1       
------+---------------
      |             0
      |        1004.3
      |        -34.84
      | 1.2345679e+20
      | 1.2345679e-20
(5 rows)

SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
 four |      f1       
------+---------------
      |             0
      |        -34.84
      | 1.2345679e+20
      | 1.2345679e-20
(4 rows)

SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
 one |   f1   
-----+--------
     | 1004.3
(1 row)

SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
 three |      f1       
-------+---------------
       |             0
       |        -34.84
       | 1.2345679e-20
(3 rows)

SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE  f.f1 < '1004.3';
 three |      f1       
-------+---------------
       |             0
       |        -34.84
       | 1.2345679e-20
(3 rows)

SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
 four |      f1       
------+---------------
      |             0
      |        1004.3
      |        -34.84
      | 1.2345679e-20
(4 rows)

SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE  f.f1 <= '1004.3';
 four |      f1       
------+---------------
      |             0
      |        1004.3
      |        -34.84
      | 1.2345679e-20
(4 rows)

SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
   WHERE f.f1 > '0.0';
 three |      f1       |       x        
-------+---------------+----------------
       |        1004.3 |         -10043
       | 1.2345679e+20 | -1.2345678e+21
       | 1.2345679e-20 | -1.2345678e-19
(3 rows)

SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
   WHERE f.f1 > '0.0';
 three |      f1       |       x       
-------+---------------+---------------
       |        1004.3 |         994.3
       | 1.2345679e+20 | 1.2345679e+20
       | 1.2345679e-20 |           -10
(3 rows)

SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
   WHERE f.f1 > '0.0';
 three |      f1       |       x        
-------+---------------+----------------
       |        1004.3 |        -100.43
       | 1.2345679e+20 | -1.2345679e+19
       | 1.2345679e-20 | -1.2345679e-21
(3 rows)

SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
   WHERE f.f1 > '0.0';
 three |      f1       |       x       
-------+---------------+---------------
       |        1004.3 |        1014.3
       | 1.2345679e+20 | 1.2345679e+20
       | 1.2345679e-20 |            10
(3 rows)

-- test divide by zero
SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
ERROR:  division by zero
SELECT '' AS five, * FROM FLOAT4_TBL;
 five |      f1       
------+---------------
      |             0
      |        1004.3
      |        -34.84
      | 1.2345679e+20
      | 1.2345679e-20
(5 rows)

-- test the unary float4abs operator
SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
 five |      f1       |    abs_f1     
------+---------------+---------------
      |             0 |             0
      |        1004.3 |        1004.3
      |        -34.84 |         34.84
      | 1.2345679e+20 | 1.2345679e+20
      | 1.2345679e-20 | 1.2345679e-20
(5 rows)

UPDATE FLOAT4_TBL
   SET f1 = FLOAT4_TBL.f1 * '-1'
   WHERE FLOAT4_TBL.f1 > '0.0';
SELECT '' AS five, * FROM FLOAT4_TBL;
 five |       f1       
------+----------------
      |              0
      |         -34.84
      |        -1004.3
      | -1.2345679e+20
      | -1.2345679e-20
(5 rows)

-- test edge-case coercions to integer
SELECT '32767.4'::float4::int2;
 int2  
-------
 32767
(1 row)

SELECT '32767.6'::float4::int2;
ERROR:  smallint out of range
SELECT '-32768.4'::float4::int2;
  int2  
--------
 -32768
(1 row)

SELECT '-32768.6'::float4::int2;
ERROR:  smallint out of range
SELECT '2147483520'::float4::int4;
    int4    
------------
 2147483520
(1 row)

SELECT '2147483647'::float4::int4;
ERROR:  integer out of range
SELECT '-2147483648.5'::float4::int4;
    int4     
-------------
 -2147483648
(1 row)

SELECT '-2147483900'::float4::int4;
ERROR:  integer out of range
SELECT '9223369837831520256'::float4::int8;
        int8         
---------------------
 9223369837831520256
(1 row)

SELECT '9223372036854775807'::float4::int8;
ERROR:  bigint out of range
SELECT '-9223372036854775808.5'::float4::int8;
         int8         
----------------------
 -9223372036854775808
(1 row)

SELECT '-9223380000000000000'::float4::int8;
ERROR:  bigint out of range
-- 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);
 float4send 
------------
 \x1f6c1e4a
(1 row)

SELECT float4send('67e14'::float4);
 float4send 
------------
 \x59be6cea
(1 row)

SELECT float4send('985e15'::float4);
 float4send 
------------
 \x5d5ab6c4
(1 row)

SELECT float4send('55895e-16'::float4);
 float4send 
------------
 \x2cc4a9bd
(1 row)

SELECT float4send('7038531e-32'::float4);
 float4send 
------------
 \x15ae43fe
(1 row)

SELECT float4send('702990899e-20'::float4);
 float4send 
------------
 \x2cf757ca
(1 row)

SELECT float4send('3e-23'::float4);
 float4send 
------------
 \x1a111234
(1 row)

SELECT float4send('57e18'::float4);
 float4send 
------------
 \x6045c22c
(1 row)

SELECT float4send('789e-35'::float4);
 float4send 
------------
 \x0a23de70
(1 row)

SELECT float4send('2539e-18'::float4);
 float4send 
------------
 \x2736f449
(1 row)

SELECT float4send('76173e28'::float4);
 float4send 
------------
 \x7616398a
(1 row)

SELECT float4send('887745e-11'::float4);
 float4send 
------------
 \x3714f05c
(1 row)

SELECT float4send('5382571e-37'::float4);
 float4send 
------------
 \x0d2eaca7
(1 row)

SELECT float4send('82381273e-35'::float4);
 float4send 
------------
 \x128289d0
(1 row)

SELECT float4send('750486563e-38'::float4);
 float4send 
------------
 \x0f18377e
(1 row)

-- 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);
 float4send 
------------
 \x00800000
(1 row)

SELECT float4send('1.1754944e-38'::float4);
 float4send 
------------
 \x00800000
(1 row)

-- 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';
NOTICE:  return type xfloat4 is only a shell
create function xfloat4out(xfloat4) returns cstring immutable strict
  language internal as 'int4out';
NOTICE:  argument type xfloat4 is only a shell
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;
   ibits    |      flt      
------------+---------------
 \x00000001 |         1e-45
 \x00000002 |         3e-45
 \x00000003 |         4e-45
 \x00000010 |       2.2e-44
 \x00000011 |       2.4e-44
 \x00000100 |      3.59e-43
 \x00000101 |       3.6e-43
 \x00004000 |    2.2959e-41
 \x00004001 |     2.296e-41
 \x00080000 |   7.34684e-40
 \x00080001 |   7.34685e-40
 \x0053c4f4 |     7.693e-39
 \x006c85c4 |   9.96622e-39
 \x0041ca76 |  6.041937e-39
 \x004b7678 |  6.930161e-39
 \x00000007 |         1e-44
 \x00424fe2 |    6.0898e-39
 \x007ffff0 | 1.1754921e-38
 \x007ffff1 | 1.1754922e-38
 \x007ffffe | 1.1754941e-38
 \x007fffff | 1.1754942e-38
(21 rows)

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;
   ibits    |      flt       |     r_flt      |   obits    | correct 
------------+----------------+----------------+------------+---------
 \x00000000 |              0 |              0 | \x00000000 | t
 \x00800000 |  1.1754944e-38 |  1.1754944e-38 | \x00800000 | t
 \x00800001 |  1.1754945e-38 |  1.1754945e-38 | \x00800001 | t
 \x00800004 |  1.1754949e-38 |  1.1754949e-38 | \x00800004 | t
 \x00800005 |   1.175495e-38 |   1.175495e-38 | \x00800005 | t
 \x00800006 |  1.1754952e-38 |  1.1754952e-38 | \x00800006 | t
 \x008002f1 |  1.1755999e-38 |  1.1755999e-38 | \x008002f1 | t
 \x008002f2 |     1.1756e-38 |     1.1756e-38 | \x008002f2 | t
 \x008002f3 |  1.1756001e-38 |  1.1756001e-38 | \x008002f3 | t
 \x00800e17 |  1.1759998e-38 |  1.1759998e-38 | \x00800e17 | t
 \x00800e18 |      1.176e-38 |      1.176e-38 | \x00800e18 | t
 \x00800e19 |  1.1760001e-38 |  1.1760001e-38 | \x00800e19 | t
 \x01000001 |   2.350989e-38 |   2.350989e-38 | \x01000001 | t
 \x01102843 |   2.647751e-38 |   2.647751e-38 | \x01102843 | t
 \x01a52c98 |  6.0675416e-38 |  6.0675416e-38 | \x01a52c98 | t
 \x0219c229 |  1.1296386e-37 |  1.1296386e-37 | \x0219c229 | t
 \x02e4464d |   3.354194e-37 |   3.354194e-37 | \x02e4464d | t
 \x037343c1 |   7.148906e-37 |   7.148906e-37 | \x037343c1 | t
 \x03a91b36 |   9.939175e-37 |   9.939175e-37 | \x03a91b36 | t
 \x047ada65 |   2.948764e-36 |   2.948764e-36 | \x047ada65 | t
 \x0496fe87 |  3.5498577e-36 |  3.5498577e-36 | \x0496fe87 | t
 \x0550844f |   9.804414e-36 |   9.804414e-36 | \x0550844f | t
 \x05999da3 |  1.4445957e-35 |  1.4445957e-35 | \x05999da3 | t
 \x060ea5e2 |  2.6829103e-35 |  2.6829103e-35 | \x060ea5e2 | t
 \x06e63c45 |   8.660494e-35 |   8.660494e-35 | \x06e63c45 | t
 \x07f1e548 |   3.639641e-34 |   3.639641e-34 | \x07f1e548 | t
 \x0fc5282b |  1.9441172e-29 |  1.9441172e-29 | \x0fc5282b | t
 \x1f850283 |  5.6331846e-20 |  5.6331846e-20 | \x1f850283 | t
 \x2874a9d6 |  1.3581548e-14 |  1.3581548e-14 | \x2874a9d6 | t
 \x3356bf94 |  4.9999997e-08 |  4.9999997e-08 | \x3356bf94 | t
 \x3356bf95 |          5e-08 |          5e-08 | \x3356bf95 | t
 \x3356bf96 |  5.0000004e-08 |  5.0000004e-08 | \x3356bf96 | t
 \x33d6bf94 |  9.9999994e-08 |  9.9999994e-08 | \x33d6bf94 | t
 \x33d6bf95 |          1e-07 |          1e-07 | \x33d6bf95 | t
 \x33d6bf96 |  1.0000001e-07 |  1.0000001e-07 | \x33d6bf96 | t
 \x34a10faf |  2.9999998e-07 |  2.9999998e-07 | \x34a10faf | t
 \x34a10fb0 |          3e-07 |          3e-07 | \x34a10fb0 | t
 \x34a10fb1 |  3.0000004e-07 |  3.0000004e-07 | \x34a10fb1 | t
 \x350637bc |  4.9999994e-07 |  4.9999994e-07 | \x350637bc | t
 \x350637bd |          5e-07 |          5e-07 | \x350637bd | t
 \x350637be |  5.0000006e-07 |  5.0000006e-07 | \x350637be | t
 \x35719786 |   8.999999e-07 |   8.999999e-07 | \x35719786 | t
 \x35719787 |          9e-07 |          9e-07 | \x35719787 | t
 \x35719788 |  9.0000003e-07 |  9.0000003e-07 | \x35719788 | t
 \x358637bc |   9.999999e-07 |   9.999999e-07 | \x358637bc | t
 \x358637bd |          1e-06 |          1e-06 | \x358637bd | t
 \x358637be |  1.0000001e-06 |  1.0000001e-06 | \x358637be | t
 \x36a7c5ab |  4.9999994e-06 |  4.9999994e-06 | \x36a7c5ab | t
 \x36a7c5ac |          5e-06 |          5e-06 | \x36a7c5ac | t
 \x36a7c5ad |  5.0000003e-06 |  5.0000003e-06 | \x36a7c5ad | t
 \x3727c5ab |   9.999999e-06 |   9.999999e-06 | \x3727c5ab | t
 \x3727c5ac |          1e-05 |          1e-05 | \x3727c5ac | t
 \x3727c5ad |  1.0000001e-05 |  1.0000001e-05 | \x3727c5ad | t
 \x38d1b714 |  9.9999976e-05 |  9.9999976e-05 | \x38d1b714 | t
 \x38d1b715 |   9.999998e-05 |   9.999998e-05 | \x38d1b715 | t
 \x38d1b716 |   9.999999e-05 |   9.999999e-05 | \x38d1b716 | t
 \x38d1b717 |         0.0001 |         0.0001 | \x38d1b717 | t
 \x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
 \x38d1b719 |  0.00010000001 |  0.00010000001 | \x38d1b719 | t
 \x38d1b71a |  0.00010000002 |  0.00010000002 | \x38d1b71a | t
 \x38d1b71b |  0.00010000003 |  0.00010000003 | \x38d1b71b | t
 \x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
 \x38d1b71d |  0.00010000004 |  0.00010000004 | \x38d1b71d | t
 \x38dffffe |  0.00010681151 |  0.00010681151 | \x38dffffe | t
 \x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
 \x38e00000 |  0.00010681152 |  0.00010681152 | \x38e00000 | t
 \x38efffff |  0.00011444091 |  0.00011444091 | \x38efffff | t
 \x38f00000 |  0.00011444092 |  0.00011444092 | \x38f00000 | t
 \x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
 \x3a83126e |   0.0009999999 |   0.0009999999 | \x3a83126e | t
 \x3a83126f |          0.001 |          0.001 | \x3a83126f | t
 \x3a831270 |   0.0010000002 |   0.0010000002 | \x3a831270 | t
 \x3c23d709 |    0.009999999 |    0.009999999 | \x3c23d709 | t
 \x3c23d70a |           0.01 |           0.01 | \x3c23d70a | t
 \x3c23d70b |    0.010000001 |    0.010000001 | \x3c23d70b | t
 \x3dcccccc |    0.099999994 |    0.099999994 | \x3dcccccc | t
 \x3dcccccd |            0.1 |            0.1 | \x3dcccccd | t
 \x3dccccce |     0.10000001 |     0.10000001 | \x3dccccce | t
 \x3dcccd6f |     0.10000121 |     0.10000121 | \x3dcccd6f | t
 \x3dcccd70 |    0.100001216 |    0.100001216 | \x3dcccd70 | t
 \x3dcccd71 |     0.10000122 |     0.10000122 | \x3dcccd71 | t
 \x3effffff |     0.49999997 |     0.49999997 | \x3effffff | t
 \x3f000000 |            0.5 |            0.5 | \x3f000000 | t
 \x3f000001 |     0.50000006 |     0.50000006 | \x3f000001 | t
 \x3f333332 |      0.6999999 |      0.6999999 | \x3f333332 | t
 \x3f333333 |            0.7 |            0.7 | \x3f333333 | t
 \x3f333334 |     0.70000005 |     0.70000005 | \x3f333334 | t
 \x3f666665 |      0.8999999 |      0.8999999 | \x3f666665 | t
 \x3f666666 |            0.9 |            0.9 | \x3f666666 | t
 \x3f666667 |     0.90000004 |     0.90000004 | \x3f666667 | t
 \x3f7d70a3 |     0.98999995 |     0.98999995 | \x3f7d70a3 | t
 \x3f7d70a4 |           0.99 |           0.99 | \x3f7d70a4 | t
 \x3f7d70a5 |     0.99000007 |     0.99000007 | \x3f7d70a5 | t
 \x3f7fbe76 |     0.99899995 |     0.99899995 | \x3f7fbe76 | t
 \x3f7fbe77 |          0.999 |          0.999 | \x3f7fbe77 | t
 \x3f7fbe78 |      0.9990001 |      0.9990001 | \x3f7fbe78 | t
 \x3f7ff971 |      0.9998999 |      0.9998999 | \x3f7ff971 | t
 \x3f7ff972 |         0.9999 |         0.9999 | \x3f7ff972 | t
 \x3f7ff973 |     0.99990004 |     0.99990004 | \x3f7ff973 | t
 \x3f7fff57 |      0.9999899 |      0.9999899 | \x3f7fff57 | t
 \x3f7fff58 |        0.99999 |        0.99999 | \x3f7fff58 | t
 \x3f7fff59 |     0.99999005 |     0.99999005 | \x3f7fff59 | t
 \x3f7fffee |      0.9999989 |      0.9999989 | \x3f7fffee | t
 \x3f7fffef |       0.999999 |       0.999999 | \x3f7fffef | t
 \x3f7ffff0 |     0.99999905 |     0.99999905 | \x3f7ffff0 | t
 \x3f7ffff1 |      0.9999991 |      0.9999991 | \x3f7ffff1 | t
 \x3f7ffff2 |     0.99999917 |     0.99999917 | \x3f7ffff2 | t
 \x3f7ffff3 |      0.9999992 |      0.9999992 | \x3f7ffff3 | t
 \x3f7ffff4 |      0.9999993 |      0.9999993 | \x3f7ffff4 | t
 \x3f7ffff5 |     0.99999934 |     0.99999934 | \x3f7ffff5 | t
 \x3f7ffff6 |      0.9999994 |      0.9999994 | \x3f7ffff6 | t
 \x3f7ffff7 |     0.99999946 |     0.99999946 | \x3f7ffff7 | t
 \x3f7ffff8 |      0.9999995 |      0.9999995 | \x3f7ffff8 | t
 \x3f7ffff9 |      0.9999996 |      0.9999996 | \x3f7ffff9 | t
 \x3f7ffffa |     0.99999964 |     0.99999964 | \x3f7ffffa | t
 \x3f7ffffb |      0.9999997 |      0.9999997 | \x3f7ffffb | t
 \x3f7ffffc |     0.99999976 |     0.99999976 | \x3f7ffffc | t
 \x3f7ffffd |      0.9999998 |      0.9999998 | \x3f7ffffd | t
 \x3f7ffffe |      0.9999999 |      0.9999999 | \x3f7ffffe | t
 \x3f7fffff |     0.99999994 |     0.99999994 | \x3f7fffff | t
 \x3f800000 |              1 |              1 | \x3f800000 | t
 \x3f800001 |      1.0000001 |      1.0000001 | \x3f800001 | t
 \x3f800002 |      1.0000002 |      1.0000002 | \x3f800002 | t
 \x3f800003 |      1.0000004 |      1.0000004 | \x3f800003 | t
 \x3f800004 |      1.0000005 |      1.0000005 | \x3f800004 | t
 \x3f800005 |      1.0000006 |      1.0000006 | \x3f800005 | t
 \x3f800006 |      1.0000007 |      1.0000007 | \x3f800006 | t
 \x3f800007 |      1.0000008 |      1.0000008 | \x3f800007 | t
 \x3f800008 |       1.000001 |       1.000001 | \x3f800008 | t
 \x3f800009 |      1.0000011 |      1.0000011 | \x3f800009 | t
 \x3f80000f |      1.0000018 |      1.0000018 | \x3f80000f | t
 \x3f800010 |      1.0000019 |      1.0000019 | \x3f800010 | t
 \x3f800011 |       1.000002 |       1.000002 | \x3f800011 | t
 \x3f800012 |      1.0000021 |      1.0000021 | \x3f800012 | t
 \x3f800013 |      1.0000023 |      1.0000023 | \x3f800013 | t
 \x3f800014 |      1.0000024 |      1.0000024 | \x3f800014 | t
 \x3f800017 |      1.0000027 |      1.0000027 | \x3f800017 | t
 \x3f800018 |      1.0000029 |      1.0000029 | \x3f800018 | t
 \x3f800019 |       1.000003 |       1.000003 | \x3f800019 | t
 \x3f80001a |      1.0000031 |      1.0000031 | \x3f80001a | t
 \x3f80001b |      1.0000032 |      1.0000032 | \x3f80001b | t
 \x3f80001c |      1.0000033 |      1.0000033 | \x3f80001c | t
 \x3f800029 |      1.0000049 |      1.0000049 | \x3f800029 | t
 \x3f80002a |       1.000005 |       1.000005 | \x3f80002a | t
 \x3f80002b |      1.0000051 |      1.0000051 | \x3f80002b | t
 \x3f800053 |      1.0000099 |      1.0000099 | \x3f800053 | t
 \x3f800054 |        1.00001 |        1.00001 | \x3f800054 | t
 \x3f800055 |      1.0000101 |      1.0000101 | \x3f800055 | t
 \x3f800346 |      1.0000999 |      1.0000999 | \x3f800346 | t
 \x3f800347 |         1.0001 |         1.0001 | \x3f800347 | t
 \x3f800348 |      1.0001001 |      1.0001001 | \x3f800348 | t
 \x3f8020c4 |      1.0009999 |      1.0009999 | \x3f8020c4 | t
 \x3f8020c5 |          1.001 |          1.001 | \x3f8020c5 | t
 \x3f8020c6 |      1.0010002 |      1.0010002 | \x3f8020c6 | t
 \x3f8147ad |      1.0099999 |      1.0099999 | \x3f8147ad | t
 \x3f8147ae |           1.01 |           1.01 | \x3f8147ae | t
 \x3f8147af |      1.0100001 |      1.0100001 | \x3f8147af | t
 \x3f8ccccc |      1.0999999 |      1.0999999 | \x3f8ccccc | t
 \x3f8ccccd |            1.1 |            1.1 | \x3f8ccccd | t
 \x3f8cccce |      1.1000001 |      1.1000001 | \x3f8cccce | t
 \x3fc90fdb |      1.5707964 |      1.5707964 | \x3fc90fdb | t
 \x402df854 |      2.7182817 |      2.7182817 | \x402df854 | t
 \x40490fdb |      3.1415927 |      3.1415927 | \x40490fdb | t
 \x409fffff |      4.9999995 |      4.9999995 | \x409fffff | t
 \x40a00000 |              5 |              5 | \x40a00000 | t
 \x40a00001 |      5.0000005 |      5.0000005 | \x40a00001 | t
 \x40afffff |      5.4999995 |      5.4999995 | \x40afffff | t
 \x40b00000 |            5.5 |            5.5 | \x40b00000 | t
 \x40b00001 |      5.5000005 |      5.5000005 | \x40b00001 | t
 \x411fffff |       9.999999 |       9.999999 | \x411fffff | t
 \x41200000 |             10 |             10 | \x41200000 | t
 \x41200001 |      10.000001 |      10.000001 | \x41200001 | t
 \x42c7ffff |       99.99999 |       99.99999 | \x42c7ffff | t
 \x42c80000 |            100 |            100 | \x42c80000 | t
 \x42c80001 |      100.00001 |      100.00001 | \x42c80001 | t
 \x4479ffff |      999.99994 |      999.99994 | \x4479ffff | t
 \x447a0000 |           1000 |           1000 | \x447a0000 | t
 \x447a0001 |     1000.00006 |     1000.00006 | \x447a0001 | t
 \x461c3fff |       9999.999 |       9999.999 | \x461c3fff | t
 \x461c4000 |          10000 |          10000 | \x461c4000 | t
 \x461c4001 |      10000.001 |      10000.001 | \x461c4001 | t
 \x47c34fff |       99999.99 |       99999.99 | \x47c34fff | t
 \x47c35000 |         100000 |         100000 | \x47c35000 | t
 \x47c35001 |      100000.01 |      100000.01 | \x47c35001 | t
 \x497423ff |      999999.94 |      999999.94 | \x497423ff | t
 \x49742400 |          1e+06 |          1e+06 | \x49742400 | t
 \x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
 \x4b18967f |   9.999999e+06 |   9.999999e+06 | \x4b18967f | t
 \x4b189680 |          1e+07 |          1e+07 | \x4b189680 | t
 \x4b189681 |  1.0000001e+07 |  1.0000001e+07 | \x4b189681 | t
 \x4cbebc1f |   9.999999e+07 |   9.999999e+07 | \x4cbebc1f | t
 \x4cbebc20 |          1e+08 |          1e+08 | \x4cbebc20 | t
 \x4cbebc21 |  1.0000001e+08 |  1.0000001e+08 | \x4cbebc21 | t
 \x4e6e6b27 |  9.9999994e+08 |  9.9999994e+08 | \x4e6e6b27 | t
 \x4e6e6b28 |          1e+09 |          1e+09 | \x4e6e6b28 | t
 \x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
 \x501502f8 |   9.999999e+09 |   9.999999e+09 | \x501502f8 | t
 \x501502f9 |          1e+10 |          1e+10 | \x501502f9 | t
 \x501502fa |  1.0000001e+10 |  1.0000001e+10 | \x501502fa | t
 \x51ba43b6 |   9.999999e+10 |   9.999999e+10 | \x51ba43b6 | t
 \x51ba43b7 |          1e+11 |          1e+11 | \x51ba43b7 | t
 \x51ba43b8 |  1.0000001e+11 |  1.0000001e+11 | \x51ba43b8 | t
 \x1f6c1e4a |          5e-20 |          5e-20 | \x1f6c1e4a | t
 \x59be6cea |        6.7e+15 |        6.7e+15 | \x59be6cea | t
 \x5d5ab6c4 |       9.85e+17 |       9.85e+17 | \x5d5ab6c4 | t
 \x2cc4a9bd |     5.5895e-12 |     5.5895e-12 | \x2cc4a9bd | t
 \x15ae43fd |   7.038531e-26 |  7.0385313e-26 | \x15ae43fe | f
 \x2cf757ca |  7.0299088e-12 |  7.0299088e-12 | \x2cf757ca | t
 \x665ba998 |  2.5933168e+23 |  2.5933168e+23 | \x665ba998 | t
 \x743c3324 |  5.9642887e+31 |  5.9642887e+31 | \x743c3324 | t
 \x47f1205a |       123456.7 |       123456.7 | \x47f1205a | t
 \x4640e6ae |       12345.67 |       12345.67 | \x4640e6ae | t
 \x449a5225 |       1234.567 |       1234.567 | \x449a5225 | t
 \x42f6e9d5 |       123.4567 |       123.4567 | \x42f6e9d5 | t
 \x414587dd |       12.34567 |       12.34567 | \x414587dd | t
 \x3f9e064b |       1.234567 |       1.234567 | \x3f9e064b | t
 \x4c000004 |  3.3554448e+07 |  3.3554448e+07 | \x4c000004 | t
 \x50061c46 |   8.999999e+09 |   8.999999e+09 | \x50061c46 | t
 \x510006a8 |  3.4366718e+10 |  3.4366718e+10 | \x510006a8 | t
 \x48951f84 |      305404.12 |      305404.12 | \x48951f84 | t
 \x45fd1840 |      8099.0312 |      8099.0312 | \x45fd1840 | t
 \x39800000 |  0.00024414062 |  0.00024414062 | \x39800000 | t
 \x3b200000 |   0.0024414062 |   0.0024414062 | \x3b200000 | t
 \x3b900000 |   0.0043945312 |   0.0043945312 | \x3b900000 | t
 \x3bd00000 |   0.0063476562 |   0.0063476562 | \x3bd00000 | t
 \x63800000 |  4.7223665e+21 |  4.7223665e+21 | \x63800000 | t
 \x4b000000 |   8.388608e+06 |   8.388608e+06 | \x4b000000 | t
 \x4b800000 |  1.6777216e+07 |  1.6777216e+07 | \x4b800000 | t
 \x4c000001 |  3.3554436e+07 |  3.3554436e+07 | \x4c000001 | t
 \x4c800b0d |  6.7131496e+07 |  6.7131496e+07 | \x4c800b0d | t
 \x00d24584 |  1.9310392e-38 |  1.9310392e-38 | \x00d24584 | t
 \x00d90b88 |   1.993244e-38 |   1.993244e-38 | \x00d90b88 | t
 \x45803f34 |      4103.9004 |      4103.9004 | \x45803f34 | t
 \x4f9f24f7 |  5.3399997e+09 |  5.3399997e+09 | \x4f9f24f7 | t
 \x3a8722c3 |   0.0010310042 |   0.0010310042 | \x3a8722c3 | t
 \x5c800041 |   2.882326e+17 |   2.882326e+17 | \x5c800041 | t
 \x15ae43fd |   7.038531e-26 |  7.0385313e-26 | \x15ae43fe | f
 \x5d4cccfb |   9.223404e+17 |   9.223404e+17 | \x5d4cccfb | t
 \x4c800001 |   6.710887e+07 |   6.710887e+07 | \x4c800001 | t
 \x57800ed8 |   2.816025e+14 |   2.816025e+14 | \x57800ed8 | t
 \x5f000000 |   9.223372e+18 |   9.223372e+18 | \x5f000000 | t
 \x700000f0 |  1.5846086e+29 |  1.5846086e+29 | \x700000f0 | t
 \x5f23e9ac |  1.1811161e+19 |  1.1811161e+19 | \x5f23e9ac | t
 \x5e9502f9 |   5.368709e+18 |   5.368709e+18 | \x5e9502f9 | t
 \x5e8012b1 |  4.6143166e+18 |  4.6143166e+18 | \x5e8012b1 | t
 \x3c000028 |    0.007812537 |    0.007812537 | \x3c000028 | t
 \x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
 \x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
 \x43480000 |            200 |            200 | \x43480000 | t
 \x4c000000 |  3.3554432e+07 |  3.3554432e+07 | \x4c000000 | t
 \x5d1502f9 |  6.7108864e+17 |  6.7108864e+17 | \x5d1502f9 | t
 \x5d9502f9 |  1.3421773e+18 |  1.3421773e+18 | \x5d9502f9 | t
 \x5e1502f9 |  2.6843546e+18 |  2.6843546e+18 | \x5e1502f9 | t
 \x3f99999a |            1.2 |            1.2 | \x3f99999a | t
 \x3f9d70a4 |           1.23 |           1.23 | \x3f9d70a4 | t
 \x3f9df3b6 |          1.234 |          1.234 | \x3f9df3b6 | t
 \x3f9e0419 |         1.2345 |         1.2345 | \x3f9e0419 | t
 \x3f9e0610 |        1.23456 |        1.23456 | \x3f9e0610 | t
 \x3f9e064b |       1.234567 |       1.234567 | \x3f9e064b | t
 \x3f9e0651 |      1.2345678 |      1.2345678 | \x3f9e0651 | t
 \x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
(261 rows)

-- clean up, lest opr_sanity complain
drop type xfloat4 cascade;
NOTICE:  drop cascades to 6 other objects
DETAIL:  drop cascades to function xfloat4in(cstring)
drop cascades to function xfloat4out(xfloat4)
drop cascades to cast from xfloat4 to real
drop cascades to cast from real to xfloat4
drop cascades to cast from xfloat4 to integer
drop cascades to cast from integer to xfloat4