--
-- 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;
               ^
-- test smallest normalized input
SELECT float8send('2.2250738585072014E-308'::float8);
     float8send     
--------------------
 \x0010000000000000
(1 row)

-- 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 '42'::float8 / 'Infinity'::float8;
 ?column? 
----------
        0
(1 row)

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

SELECT 'nan'::float8 / '0'::float8;
 ?column? 
----------
      NaN
(1 row)

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

SELECT * FROM FLOAT8_TBL;
          f1          
----------------------
                    0
               1004.3
               -34.84
 1.2345678901234e+200
 1.2345678901234e-200
(5 rows)

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

SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 = '1004.3';
   f1   
--------
 1004.3
(1 row)

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

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

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

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

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

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

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

-- absolute value
SELECT f.f1, @f.f1 AS abs_f1
   FROM FLOAT8_TBL f;
          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 f.f1, trunc(f.f1) AS trunc_f1
   FROM FLOAT8_TBL f;
          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 f.f1, round(f.f1) AS round_f1
   FROM FLOAT8_TBL f;
          f1          |       round_f1       
----------------------+----------------------
                    0 |                    0
               1004.3 |                 1004
               -34.84 |                  -35
 1.2345678901234e+200 | 1.2345678901234e+200
 1.2345678901234e-200 |                    0
(5 rows)

-- 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;
 eight 
-------
     8
(1 row)

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

SELECT f.f1, |/f.f1 AS sqrt_f1
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';
          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)

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

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

SELECT power(float8 'NaN', float8 'NaN');
 power 
-------
   NaN
(1 row)

SELECT power(float8 '-1', float8 'NaN');
 power 
-------
   NaN
(1 row)

SELECT power(float8 '1', float8 'NaN');
 power 
-------
     1
(1 row)

SELECT power(float8 'NaN', float8 '0');
 power 
-------
     1
(1 row)

SELECT power(float8 'inf', float8 '0');
 power 
-------
     1
(1 row)

SELECT power(float8 '-inf', float8 '0');
 power 
-------
     1
(1 row)

SELECT power(float8 '0', float8 'inf');
 power 
-------
     0
(1 row)

SELECT power(float8 '0', float8 '-inf');
ERROR:  zero raised to a negative power is undefined
SELECT power(float8 '1', float8 'inf');
 power 
-------
     1
(1 row)

SELECT power(float8 '1', float8 '-inf');
 power 
-------
     1
(1 row)

SELECT power(float8 '-1', float8 'inf');
 power 
-------
     1
(1 row)

SELECT power(float8 '-1', float8 '-inf');
 power 
-------
     1
(1 row)

SELECT power(float8 '0.1', float8 'inf');
 power 
-------
     0
(1 row)

SELECT power(float8 '-0.1', float8 'inf');
 power 
-------
     0
(1 row)

SELECT power(float8 '1.1', float8 'inf');
  power   
----------
 Infinity
(1 row)

SELECT power(float8 '-1.1', float8 'inf');
  power   
----------
 Infinity
(1 row)

SELECT power(float8 '0.1', float8 '-inf');
  power   
----------
 Infinity
(1 row)

SELECT power(float8 '-0.1', float8 '-inf');
  power   
----------
 Infinity
(1 row)

SELECT power(float8 '1.1', float8 '-inf');
 power 
-------
     0
(1 row)

SELECT power(float8 '-1.1', float8 '-inf');
 power 
-------
     0
(1 row)

SELECT power(float8 'inf', float8 '-2');
 power 
-------
     0
(1 row)

SELECT power(float8 'inf', float8 '2');
  power   
----------
 Infinity
(1 row)

SELECT power(float8 'inf', float8 'inf');
  power   
----------
 Infinity
(1 row)

SELECT power(float8 'inf', float8 '-inf');
 power 
-------
     0
(1 row)

-- 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';
 ?column? 
----------
 t
(1 row)

SELECT power(float8 '-inf', float8 '-3');
 power 
-------
    -0
(1 row)

SELECT power(float8 '-inf', float8 '2');
  power   
----------
 Infinity
(1 row)

SELECT power(float8 '-inf', float8 '3');
   power   
-----------
 -Infinity
(1 row)

SELECT power(float8 '-inf', float8 '3.5');
ERROR:  a negative number raised to a non-integer power yields a complex result
SELECT power(float8 '-inf', float8 'inf');
  power   
----------
 Infinity
(1 row)

SELECT power(float8 '-inf', float8 '-inf');
 power 
-------
     0
(1 row)

-- 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';
          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 f.f1, ||/f.f1 AS cbrt_f1 FROM FLOAT8_TBL f;
          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 * FROM FLOAT8_TBL;
          f1          
----------------------
                    0
               1004.3
               -34.84
 1.2345678901234e+200
 1.2345678901234e-200
(5 rows)

SELECT f.f1 * '1e200' from FLOAT8_TBL f;
ERROR:  value out of range: overflow
SELECT 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 ln(f.f1) from FLOAT8_TBL f where f.f1 = '0.0' ;
ERROR:  cannot take logarithm of zero
SELECT ln(f.f1) from FLOAT8_TBL f where f.f1 < '0.0' ;
ERROR:  cannot take logarithm of a negative number
SELECT f.f1 / '0.0' from FLOAT8_TBL f;
ERROR:  division by zero
-- 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');
      sinh       
-----------------
 1.1752011936438
(1 row)

SELECT cosh(float8 '1');
       cosh       
------------------
 1.54308063481524
(1 row)

SELECT tanh(float8 '1');
       tanh        
-------------------
 0.761594155955765
(1 row)

SELECT asinh(float8 '1');
       asinh       
-------------------
 0.881373587019543
(1 row)

SELECT acosh(float8 '2');
      acosh       
------------------
 1.31695789692482
(1 row)

SELECT atanh(float8 '0.5');
       atanh       
-------------------
 0.549306144334055
(1 row)

-- test Inf/NaN cases for hyperbolic functions
SELECT sinh(float8 'infinity');
   sinh   
----------
 Infinity
(1 row)

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

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

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

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

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

SELECT tanh(float8 'infinity');
 tanh 
------
    1
(1 row)

SELECT tanh(float8 '-infinity');
 tanh 
------
   -1
(1 row)

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

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

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

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

-- acosh(Inf) should be Inf, but some mingw versions produce NaN, so skip test
-- SELECT acosh(float8 'infinity');
SELECT acosh(float8 '-infinity');
ERROR:  input is out of range
SELECT acosh(float8 'nan');
 acosh 
-------
   NaN
(1 row)

SELECT atanh(float8 'infinity');
ERROR:  input is out of range
SELECT atanh(float8 '-infinity');
ERROR:  input is out of range
SELECT atanh(float8 'nan');
 atanh 
-------
   NaN
(1 row)

RESET extra_float_digits;
-- 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');
                                           ^
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');
-- test edge-case coercions to integer
SELECT '32767.4'::float8::int2;
 int2  
-------
 32767
(1 row)

SELECT '32767.6'::float8::int2;
ERROR:  smallint out of range
SELECT '-32768.4'::float8::int2;
  int2  
--------
 -32768
(1 row)

SELECT '-32768.6'::float8::int2;
ERROR:  smallint out of range
SELECT '2147483647.4'::float8::int4;
    int4    
------------
 2147483647
(1 row)

SELECT '2147483647.6'::float8::int4;
ERROR:  integer out of range
SELECT '-2147483648.4'::float8::int4;
    int4     
-------------
 -2147483648
(1 row)

SELECT '-2147483648.6'::float8::int4;
ERROR:  integer out of range
SELECT '9223372036854773760'::float8::int8;
        int8         
---------------------
 9223372036854773760
(1 row)

SELECT '9223372036854775807'::float8::int8;
ERROR:  bigint out of range
SELECT '-9223372036854775808.5'::float8::int8;
         int8         
----------------------
 -9223372036854775808
(1 row)

SELECT '-9223372036854780000'::float8::int8;
ERROR:  bigint out of range
-- 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);
  x  | sind | sind_exact 
-----+------+------------
   0 |    0 | t
  30 |  0.5 | t
  90 |    1 | t
 150 |  0.5 | t
 180 |    0 | t
 210 | -0.5 | t
 270 |   -1 | t
 330 | -0.5 | t
 360 |    0 | t
(9 rows)

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);
  x  | cosd | cosd_exact 
-----+------+------------
   0 |    1 | t
  60 |  0.5 | t
  90 |    0 | t
 120 | -0.5 | t
 180 |   -1 | t
 240 | -0.5 | t
 270 |    0 | t
 300 |  0.5 | t
 360 |    1 | t
(9 rows)

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);
  x  |   tand    | tand_exact |   cotd    | cotd_exact 
-----+-----------+------------+-----------+------------
   0 |         0 | t          |  Infinity | t
  45 |         1 | t          |         1 | t
  90 |  Infinity | t          |         0 | t
 135 |        -1 | t          |        -1 | t
 180 |         0 | t          | -Infinity | t
 225 |         1 | t          |         1 | t
 270 | -Infinity | t          |         0 | t
 315 |        -1 | t          |        -1 | t
 360 |         0 | t          |  Infinity | t
(9 rows)

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);
     x     | atand | atand_exact 
-----------+-------+-------------
 -Infinity |   -90 | t
        -1 |   -45 | t
         0 |     0 | t
         1 |    45 | t
  Infinity |    90 | t
(5 rows)

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);
  x  |  y  | atan2d | atan2d_exact 
-----+-----+--------+--------------
  10 |   0 |      0 | t
   0 |  10 |     90 | t
 -10 |   0 |    180 | t
   0 | -10 |    -90 | t
  10 |   0 |      0 | t
(5 rows)