--
-- FLOAT8
--
CREATE 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;
ERROR:  "10e400" is out of range for type double precision
LINE 1: SELECT '10e400'::float8;
               ^
SELECT '-10e400'::float8;
ERROR:  "-10e400" is out of range for type double precision
LINE 1: SELECT '-10e400'::float8;
               ^
SELECT '10e-400'::float8;
ERROR:  "10e-400" is out of range for type double precision
LINE 1: SELECT '10e-400'::float8;
               ^
SELECT '-10e-400'::float8;
ERROR:  "-10e-400" is out of range for type double precision
LINE 1: SELECT '-10e-400'::float8;
               ^
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR:  invalid input syntax for type double precision: ""
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('');
                                           ^
INSERT INTO FLOAT8_TBL(f1) VALUES ('     ');
ERROR:  invalid input syntax for type double precision: "     "
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('     ');
                                           ^
INSERT INTO FLOAT8_TBL(f1) VALUES ('xyz');
ERROR:  invalid input syntax for type double precision: "xyz"
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('xyz');
                                           ^
INSERT INTO FLOAT8_TBL(f1) VALUES ('5.0.0');
ERROR:  invalid input syntax for type double precision: "5.0.0"
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('5.0.0');
                                           ^
INSERT INTO FLOAT8_TBL(f1) VALUES ('5 . 0');
ERROR:  invalid input syntax for type double precision: "5 . 0"
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('5 . 0');
                                           ^
INSERT INTO FLOAT8_TBL(f1) VALUES ('5.   0');
ERROR:  invalid input syntax for type double precision: "5.   0"
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('5.   0');
                                           ^
INSERT INTO FLOAT8_TBL(f1) VALUES ('    - 3');
ERROR:  invalid input syntax for type double precision: "    - 3"
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('    - 3');
                                           ^
INSERT INTO FLOAT8_TBL(f1) VALUES ('123           5');
ERROR:  invalid input syntax for type double precision: "123           5"
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('123           5');
                                           ^
-- special inputs
SELECT 'NaN'::float8;
 float8 
--------
    NaN
(1 row)

SELECT 'nan'::float8;
 float8 
--------
    NaN
(1 row)

SELECT '   NAN  '::float8;
 float8 
--------
    NaN
(1 row)

SELECT 'infinity'::float8;
  float8  
----------
 Infinity
(1 row)

SELECT '          -INFINiTY   '::float8;
  float8   
-----------
 -Infinity
(1 row)

-- bad special inputs
SELECT 'N A N'::float8;
ERROR:  invalid input syntax for type double precision: "N A N"
LINE 1: SELECT 'N A N'::float8;
               ^
SELECT 'NaN x'::float8;
ERROR:  invalid input syntax for type double precision: "NaN x"
LINE 1: SELECT 'NaN x'::float8;
               ^
SELECT ' INFINITY    x'::float8;
ERROR:  invalid input syntax for type double precision: " INFINITY    x"
LINE 1: SELECT ' INFINITY    x'::float8;
               ^
SELECT 'Infinity'::float8 + 100.0;
 ?column? 
----------
 Infinity
(1 row)

SELECT 'Infinity'::float8 / 'Infinity'::float8;
 ?column? 
----------
      NaN
(1 row)

SELECT 'nan'::float8 / 'nan'::float8;
 ?column? 
----------
      NaN
(1 row)

SELECT 'nan'::numeric::float8;
 float8 
--------
    NaN
(1 row)

SELECT '' AS five, * FROM FLOAT8_TBL;
 five |          f1          
------+----------------------
      |                    0
      |               1004.3
      |               -34.84
      | 1.2345678901234e+200
      | 1.2345678901234e-200
(5 rows)

SELECT '' AS four, f.* FROM FLOAT8_TBL f WHERE f.f1 <> '1004.3';
 four |          f1          
------+----------------------
      |                    0
      |               -34.84
      | 1.2345678901234e+200
      | 1.2345678901234e-200
(4 rows)

SELECT '' AS one, f.* FROM FLOAT8_TBL f WHERE f.f1 = '1004.3';
 one |   f1   
-----+--------
     | 1004.3
(1 row)

SELECT '' AS three, f.* FROM FLOAT8_TBL f WHERE '1004.3' > f.f1;
 three |          f1          
-------+----------------------
       |                    0
       |               -34.84
       | 1.2345678901234e-200
(3 rows)

SELECT '' AS three, f.* FROM FLOAT8_TBL f WHERE  f.f1 < '1004.3';
 three |          f1          
-------+----------------------
       |                    0
       |               -34.84
       | 1.2345678901234e-200
(3 rows)

SELECT '' AS four, f.* FROM FLOAT8_TBL f WHERE '1004.3' >= f.f1;
 four |          f1          
------+----------------------
      |                    0
      |               1004.3
      |               -34.84
      | 1.2345678901234e-200
(4 rows)

SELECT '' AS four, f.* FROM FLOAT8_TBL f WHERE  f.f1 <= '1004.3';
 four |          f1          
------+----------------------
      |                    0
      |               1004.3
      |               -34.84
      | 1.2345678901234e-200
(4 rows)

SELECT '' AS three, f.f1, f.f1 * '-10' AS x
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';
 three |          f1          |           x           
-------+----------------------+-----------------------
       |               1004.3 |                -10043
       | 1.2345678901234e+200 | -1.2345678901234e+201
       | 1.2345678901234e-200 | -1.2345678901234e-199
(3 rows)

SELECT '' AS three, f.f1, f.f1 + '-10' AS x
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';
 three |          f1          |          x           
-------+----------------------+----------------------
       |               1004.3 |                994.3
       | 1.2345678901234e+200 | 1.2345678901234e+200
       | 1.2345678901234e-200 |                  -10
(3 rows)

SELECT '' AS three, f.f1, f.f1 / '-10' AS x
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';
 three |          f1          |           x           
-------+----------------------+-----------------------
       |               1004.3 |               -100.43
       | 1.2345678901234e+200 | -1.2345678901234e+199
       | 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)

SELECT '' AS three, f.f1, f.f1 - '-10' AS x
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';
 three |          f1          |          x           
-------+----------------------+----------------------
       |               1004.3 |               1014.3
       | 1.2345678901234e+200 | 1.2345678901234e+200
       | 1.2345678901234e-200 |                   10
(3 rows)

SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
   FROM FLOAT8_TBL f where f.f1 = '1004.3';
 one | square_f1  
-----+------------
     | 1008618.49
(1 row)

-- absolute value
SELECT '' AS five, f.f1, @f.f1 AS abs_f1
   FROM FLOAT8_TBL f;
 five |          f1          |        abs_f1        
------+----------------------+----------------------
      |                    0 |                    0
      |               1004.3 |               1004.3
      |               -34.84 |                34.84
      | 1.2345678901234e+200 | 1.2345678901234e+200
      | 1.2345678901234e-200 | 1.2345678901234e-200
(5 rows)

-- truncate
SELECT '' AS five, f.f1, trunc(f.f1) AS trunc_f1
   FROM FLOAT8_TBL f;
 five |          f1          |       trunc_f1       
------+----------------------+----------------------
      |                    0 |                    0
      |               1004.3 |                 1004
      |               -34.84 |                  -34
      | 1.2345678901234e+200 | 1.2345678901234e+200
      | 1.2345678901234e-200 |                    0
(5 rows)

-- round
SELECT '' AS five, f.f1, round(f.f1) AS round_f1
   FROM FLOAT8_TBL f;
 five |          f1          |       round_f1       
------+----------------------+----------------------
      |                    0 |                    0
      |               1004.3 |                 1004
      |               -34.84 |                  -35
      | 1.2345678901234e+200 | 1.2345678901234e+200
      | 1.2345678901234e-200 |                    0
(5 rows)

-- ceil / ceiling
select ceil(f1) as ceil_f1 from float8_tbl f;
       ceil_f1        
----------------------
                    0
                 1005
                  -34
 1.2345678901234e+200
                    1
(5 rows)

select ceiling(f1) as ceiling_f1 from float8_tbl f;
      ceiling_f1      
----------------------
                    0
                 1005
                  -34
 1.2345678901234e+200
                    1
(5 rows)

-- floor
select floor(f1) as floor_f1 from float8_tbl f;
       floor_f1       
----------------------
                    0
                 1004
                  -35
 1.2345678901234e+200
                    0
(5 rows)

-- sign
select sign(f1) as sign_f1 from float8_tbl f;
 sign_f1 
---------
       0
       1
      -1
       1
       1
(5 rows)

-- square root
SELECT sqrt(float8 '64') AS eight;
 eight 
-------
     8
(1 row)

SELECT |/ float8 '64' AS eight;
 eight 
-------
     8
(1 row)

SELECT '' AS three, f.f1, |/f.f1 AS sqrt_f1
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';
 three |          f1          |        sqrt_f1        
-------+----------------------+-----------------------
       |               1004.3 |      31.6906926399535
       | 1.2345678901234e+200 | 1.11111110611109e+100
       | 1.2345678901234e-200 | 1.11111110611109e-100
(3 rows)

-- power
SELECT power(float8 '144', float8 '0.5');
 power 
-------
    12
(1 row)

-- take exp of ln(f.f1)
SELECT '' AS three, f.f1, exp(ln(f.f1)) AS exp_ln_f1
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';
 three |          f1          |       exp_ln_f1       
-------+----------------------+-----------------------
       |               1004.3 |                1004.3
       | 1.2345678901234e+200 | 1.23456789012338e+200
       | 1.2345678901234e-200 | 1.23456789012339e-200
(3 rows)

-- cube root
SELECT ||/ float8 '27' AS three;
 three 
-------
     3
(1 row)

SELECT '' AS five, f.f1, ||/f.f1 AS cbrt_f1 FROM FLOAT8_TBL f;
 five |          f1          |       cbrt_f1        
------+----------------------+----------------------
      |                    0 |                    0
      |               1004.3 |      10.014312837827
      |               -34.84 |    -3.26607421344208
      | 1.2345678901234e+200 | 4.97933859234765e+66
      | 1.2345678901234e-200 |  2.3112042409018e-67
(5 rows)

SELECT '' AS five, * FROM FLOAT8_TBL;
 five |          f1          
------+----------------------
      |                    0
      |               1004.3
      |               -34.84
      | 1.2345678901234e+200
      | 1.2345678901234e-200
(5 rows)

UPDATE FLOAT8_TBL
   SET f1 = FLOAT8_TBL.f1 * '-1'
   WHERE FLOAT8_TBL.f1 > '0.0';
SELECT '' AS bad, f.f1 * '1e200' from FLOAT8_TBL f;
ERROR:  value out of range: overflow
SELECT '' AS bad, f.f1 ^ '1e200' from FLOAT8_TBL f;
ERROR:  value out of range: overflow
SELECT 0 ^ 0 + 0 ^ 1 + 0 ^ 0.0 + 0 ^ 0.5;
 ?column? 
----------
        2
(1 row)

SELECT '' AS bad, ln(f.f1) from FLOAT8_TBL f where f.f1 = '0.0' ;
ERROR:  cannot take logarithm of zero
SELECT '' AS bad, ln(f.f1) from FLOAT8_TBL f where f.f1 < '0.0' ;
ERROR:  cannot take logarithm of a negative number
SELECT '' AS bad, exp(f.f1) from FLOAT8_TBL f;
ERROR:  value out of range: underflow
SELECT '' AS bad, f.f1 / '0.0' from FLOAT8_TBL f;
ERROR:  division by zero
SELECT '' AS five, * FROM FLOAT8_TBL;
 five |          f1           
------+-----------------------
      |                     0
      |                -34.84
      |               -1004.3
      | -1.2345678901234e+200
      | -1.2345678901234e-200
(5 rows)

-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR:  "10e400" is out of range for type double precision
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
                                           ^
INSERT INTO FLOAT8_TBL(f1) VALUES ('-10e400');
ERROR:  "-10e400" is out of range for type double precision
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('-10e400');
                                           ^
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e-400');
ERROR:  "10e-400" is out of range for type double precision
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('10e-400');
                                           ^
INSERT INTO FLOAT8_TBL(f1) VALUES ('-10e-400');
ERROR:  "-10e-400" is out of range for type double precision
LINE 1: INSERT INTO FLOAT8_TBL(f1) VALUES ('-10e-400');
                                           ^
-- maintain external table consistency across platforms
-- delete all values and reinsert well-behaved ones
DELETE FROM FLOAT8_TBL;
INSERT INTO FLOAT8_TBL(f1) VALUES ('0.0');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-34.84');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-1004.30');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-1.2345678901234e+200');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-1.2345678901234e-200');
SELECT '' AS five, * FROM FLOAT8_TBL;
 five |          f1           
------+-----------------------
      |                     0
      |                -34.84
      |               -1004.3
      | -1.2345678901234e+200
      | -1.2345678901234e-200
(5 rows)

-- test exact cases for trigonometric functions in degrees
SELECT x,
       CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
       CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
       CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
                             1,'Infinity'::float8) THEN tand(x) END AS tand,
       CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
                             1,'Infinity'::float8) THEN cotd(x) END AS cotd
FROM generate_series(0, 360, 15) AS t(x);
  x  | sind | cosd |   tand    |   cotd    
-----+------+------+-----------+-----------
   0 |    0 |    1 |         0 |  Infinity
  15 |      |      |           |          
  30 |  0.5 |      |           |          
  45 |      |      |         1 |         1
  60 |      |  0.5 |           |          
  75 |      |      |           |          
  90 |    1 |    0 |  Infinity |         0
 105 |      |      |           |          
 120 |      | -0.5 |           |          
 135 |      |      |        -1 |        -1
 150 |  0.5 |      |           |          
 165 |      |      |           |          
 180 |    0 |   -1 |         0 | -Infinity
 195 |      |      |           |          
 210 | -0.5 |      |           |          
 225 |      |      |         1 |         1
 240 |      | -0.5 |           |          
 255 |      |      |           |          
 270 |   -1 |    0 | -Infinity |         0
 285 |      |      |           |          
 300 |      |  0.5 |           |          
 315 |      |      |        -1 |        -1
 330 | -0.5 |      |           |          
 345 |      |      |           |          
 360 |    0 |    1 |         0 |  Infinity
(25 rows)

SELECT x,
       CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
       CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
       CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
  x   | asind | acosd | atand 
------+-------+-------+-------
   -1 |   -90 |   180 |   -45
 -0.5 |   -30 |   120 |      
    0 |     0 |    90 |     0
  0.5 |    30 |    60 |      
    1 |    90 |     0 |    45
(5 rows)

SELECT atand('-Infinity'::float8) = -90;
 ?column? 
----------
 t
(1 row)

SELECT atand('Infinity'::float8) = 90;
 ?column? 
----------
 t
(1 row)

SELECT x, y,
       CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
FROM (SELECT 10*cosd(a), 10*sind(a)
      FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
  x  |  y  | atan2d 
-----+-----+--------
  10 |   0 |      0
   0 |  10 |     90
 -10 |   0 |    180
   0 | -10 |    -90
  10 |   0 |      0
(5 rows)