set enable_seqscan=off;
CREATE TABLE test_float4 (
	i float4
);
INSERT INTO test_float4 VALUES (-2),(-1),(0),(1),(2),(3);
CREATE INDEX idx_float4 ON test_float4 USING gin (i);
SELECT * FROM test_float4 WHERE i<1::float4 ORDER BY i;
 i  
----
 -2
 -1
  0
(3 rows)

SELECT * FROM test_float4 WHERE i<=1::float4 ORDER BY i;
 i  
----
 -2
 -1
  0
  1
(4 rows)

SELECT * FROM test_float4 WHERE i=1::float4 ORDER BY i;
 i 
---
 1
(1 row)

SELECT * FROM test_float4 WHERE i>=1::float4 ORDER BY i;
 i 
---
 1
 2
 3
(3 rows)

SELECT * FROM test_float4 WHERE i>1::float4 ORDER BY i;
 i 
---
 2
 3
(2 rows)

explain (costs off)
SELECT * FROM test_float4 WHERE i<1::float8 ORDER BY i;
                      QUERY PLAN                       
-------------------------------------------------------
 Sort
   Sort Key: i
   ->  Bitmap Heap Scan on test_float4
         Recheck Cond: (i < '1'::double precision)
         ->  Bitmap Index Scan on idx_float4
               Index Cond: (i < '1'::double precision)
(6 rows)

SELECT * FROM test_float4 WHERE i<1::float8 ORDER BY i;
 i  
----
 -2
 -1
  0
(3 rows)

SELECT * FROM test_float4 WHERE i<=1::float8 ORDER BY i;
 i  
----
 -2
 -1
  0
  1
(4 rows)

SELECT * FROM test_float4 WHERE i=1::float8 ORDER BY i;
 i 
---
 1
(1 row)

SELECT * FROM test_float4 WHERE i>=1::float8 ORDER BY i;
 i 
---
 1
 2
 3
(3 rows)

SELECT * FROM test_float4 WHERE i>1::float8 ORDER BY i;
 i 
---
 2
 3
(2 rows)

-- Check endpoint and out-of-range cases
INSERT INTO test_float4 VALUES ('NaN'), ('Inf'), ('-Inf');
SELECT gin_clean_pending_list('idx_float4');
 gin_clean_pending_list 
------------------------
                      1
(1 row)

SELECT * FROM test_float4 WHERE i<'-Inf'::float8 ORDER BY i;
 i 
---
(0 rows)

SELECT * FROM test_float4 WHERE i<='-Inf'::float8 ORDER BY i;
     i     
-----------
 -Infinity
(1 row)

SELECT * FROM test_float4 WHERE i='-Inf'::float8 ORDER BY i;
     i     
-----------
 -Infinity
(1 row)

SELECT * FROM test_float4 WHERE i>='-Inf'::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
         0
         1
         2
         3
  Infinity
       NaN
(9 rows)

SELECT * FROM test_float4 WHERE i>'-Inf'::float8 ORDER BY i;
    i     
----------
       -2
       -1
        0
        1
        2
        3
 Infinity
      NaN
(8 rows)

SELECT * FROM test_float4 WHERE i<'Inf'::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
         0
         1
         2
         3
(7 rows)

SELECT * FROM test_float4 WHERE i<='Inf'::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
         0
         1
         2
         3
  Infinity
(8 rows)

SELECT * FROM test_float4 WHERE i='Inf'::float8 ORDER BY i;
    i     
----------
 Infinity
(1 row)

SELECT * FROM test_float4 WHERE i>='Inf'::float8 ORDER BY i;
    i     
----------
 Infinity
      NaN
(2 rows)

SELECT * FROM test_float4 WHERE i>'Inf'::float8 ORDER BY i;
  i  
-----
 NaN
(1 row)

SELECT * FROM test_float4 WHERE i<'1e300'::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
         0
         1
         2
         3
(7 rows)

SELECT * FROM test_float4 WHERE i<='1e300'::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
         0
         1
         2
         3
(7 rows)

SELECT * FROM test_float4 WHERE i='1e300'::float8 ORDER BY i;
 i 
---
(0 rows)

SELECT * FROM test_float4 WHERE i>='1e300'::float8 ORDER BY i;
    i     
----------
 Infinity
      NaN
(2 rows)

SELECT * FROM test_float4 WHERE i>'1e300'::float8 ORDER BY i;
    i     
----------
 Infinity
      NaN
(2 rows)

SELECT * FROM test_float4 WHERE i<'NaN'::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
         0
         1
         2
         3
  Infinity
(8 rows)

SELECT * FROM test_float4 WHERE i<='NaN'::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
         0
         1
         2
         3
  Infinity
       NaN
(9 rows)

SELECT * FROM test_float4 WHERE i='NaN'::float8 ORDER BY i;
  i  
-----
 NaN
(1 row)

SELECT * FROM test_float4 WHERE i>='NaN'::float8 ORDER BY i;
  i  
-----
 NaN
(1 row)

SELECT * FROM test_float4 WHERE i>'NaN'::float8 ORDER BY i;
 i 
---
(0 rows)

-- Check rounding cases
-- 1e-300 rounds to 0 for float4 but not for float8
SELECT * FROM test_float4 WHERE i < -1e-300::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
(3 rows)

SELECT * FROM test_float4 WHERE i <= -1e-300::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
(3 rows)

SELECT * FROM test_float4 WHERE i = -1e-300::float8 ORDER BY i;
 i 
---
(0 rows)

SELECT * FROM test_float4 WHERE i > -1e-300::float8 ORDER BY i;
    i     
----------
        0
        1
        2
        3
 Infinity
      NaN
(6 rows)

SELECT * FROM test_float4 WHERE i >= -1e-300::float8 ORDER BY i;
    i     
----------
        0
        1
        2
        3
 Infinity
      NaN
(6 rows)

SELECT * FROM test_float4 WHERE i < 1e-300::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
         0
(4 rows)

SELECT * FROM test_float4 WHERE i <= 1e-300::float8 ORDER BY i;
     i     
-----------
 -Infinity
        -2
        -1
         0
(4 rows)

SELECT * FROM test_float4 WHERE i = 1e-300::float8 ORDER BY i;
 i 
---
(0 rows)

SELECT * FROM test_float4 WHERE i > 1e-300::float8 ORDER BY i;
    i     
----------
        1
        2
        3
 Infinity
      NaN
(5 rows)

SELECT * FROM test_float4 WHERE i >= 1e-300::float8 ORDER BY i;
    i     
----------
        1
        2
        3
 Infinity
      NaN
(5 rows)