regress/sql/float8.sql

--
-- 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;
SELECT '-10e400'::float8;
SELECT '10e-400'::float8;
SELECT '-10e-400'::float8;

-- test smallest normalized input
SELECT float8send('2.2250738585072014E-308'::float8);

-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
INSERT INTO FLOAT8_TBL(f1) VALUES ('     ');
INSERT INTO FLOAT8_TBL(f1) VALUES ('xyz');
INSERT INTO FLOAT8_TBL(f1) VALUES ('5.0.0');
INSERT INTO FLOAT8_TBL(f1) VALUES ('5 . 0');
INSERT INTO FLOAT8_TBL(f1) VALUES ('5.   0');
INSERT INTO FLOAT8_TBL(f1) VALUES ('    - 3');
INSERT INTO FLOAT8_TBL(f1) VALUES ('123           5');

-- special inputs
SELECT 'NaN'::float8;
SELECT 'nan'::float8;
SELECT '   NAN  '::float8;
SELECT 'infinity'::float8;
SELECT '          -INFINiTY   '::float8;
-- bad special inputs
SELECT 'N A N'::float8;
SELECT 'NaN x'::float8;
SELECT ' INFINITY    x'::float8;

SELECT 'Infinity'::float8 + 100.0;
SELECT 'Infinity'::float8 / 'Infinity'::float8;
SELECT '42'::float8 / 'Infinity'::float8;
SELECT 'nan'::float8 / 'nan'::float8;
SELECT 'nan'::float8 / '0'::float8;
SELECT 'nan'::numeric::float8;

SELECT * FROM FLOAT8_TBL;

SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 <> '1004.3';

SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 = '1004.3';

SELECT f.* FROM FLOAT8_TBL f WHERE '1004.3' > f.f1;

SELECT f.* FROM FLOAT8_TBL f WHERE  f.f1 < '1004.3';

SELECT f.* FROM FLOAT8_TBL f WHERE '1004.3' >= f.f1;

SELECT f.* FROM FLOAT8_TBL f WHERE  f.f1 <= '1004.3';

SELECT f.f1, f.f1 * '-10' AS x
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';

SELECT f.f1, f.f1 + '-10' AS x
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';

SELECT f.f1, f.f1 / '-10' AS x
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';

SELECT f.f1, f.f1 - '-10' AS x
   FROM FLOAT8_TBL f
   WHERE f.f1 > '0.0';

SELECT f.f1 ^ '2.0' AS square_f1
   FROM FLOAT8_TBL f where f.f1 = '1004.3';

-- absolute value
SELECT f.f1, @f.f1 AS abs_f1
   FROM FLOAT8_TBL f;

-- truncate
SELECT f.f1, trunc(f.f1) AS trunc_f1
   FROM FLOAT8_TBL f;

-- round
SELECT f.f1, round(f.f1) AS round_f1
   FROM FLOAT8_TBL f;

-- ceil / ceiling
select ceil(f1) as ceil_f1 from float8_tbl f;
select ceiling(f1) as ceiling_f1 from float8_tbl f;

-- floor
select floor(f1) as floor_f1 from float8_tbl f;

-- sign
select sign(f1) as sign_f1 from float8_tbl f;

-- 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;

SELECT |/ float8 '64' AS eight;

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

-- power
SELECT power(float8 '144', float8 '0.5');
SELECT power(float8 'NaN', float8 '0.5');
SELECT power(float8 '144', float8 'NaN');
SELECT power(float8 'NaN', float8 'NaN');
SELECT power(float8 '-1', float8 'NaN');
SELECT power(float8 '1', float8 'NaN');
SELECT power(float8 'NaN', float8 '0');
SELECT power(float8 'inf', float8 '0');
SELECT power(float8 '-inf', float8 '0');
SELECT power(float8 '0', float8 'inf');
SELECT power(float8 '0', float8 '-inf');
SELECT power(float8 '1', float8 'inf');
SELECT power(float8 '1', float8 '-inf');
SELECT power(float8 '-1', float8 'inf');
SELECT power(float8 '-1', float8 '-inf');
SELECT power(float8 '0.1', float8 'inf');
SELECT power(float8 '-0.1', float8 'inf');
SELECT power(float8 '1.1', float8 'inf');
SELECT power(float8 '-1.1', float8 'inf');
SELECT power(float8 '0.1', float8 '-inf');
SELECT power(float8 '-0.1', float8 '-inf');
SELECT power(float8 '1.1', float8 '-inf');
SELECT power(float8 '-1.1', float8 '-inf');
SELECT power(float8 'inf', float8 '-2');
SELECT power(float8 'inf', float8 '2');
SELECT power(float8 'inf', float8 'inf');
SELECT power(float8 'inf', float8 '-inf');
-- 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';
SELECT power(float8 '-inf', float8 '-3');
SELECT power(float8 '-inf', float8 '2');
SELECT power(float8 '-inf', float8 '3');
SELECT power(float8 '-inf', float8 '3.5');
SELECT power(float8 '-inf', float8 'inf');
SELECT power(float8 '-inf', float8 '-inf');

-- 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';

-- check edge cases for exp
SELECT exp('inf'::float8), exp('-inf'::float8), exp('nan'::float8);

-- cube root
SELECT ||/ float8 '27' AS three;

SELECT f.f1, ||/f.f1 AS cbrt_f1 FROM FLOAT8_TBL f;


SELECT * FROM FLOAT8_TBL;

UPDATE FLOAT8_TBL
   SET f1 = FLOAT8_TBL.f1 * '-1'
   WHERE FLOAT8_TBL.f1 > '0.0';

SELECT f.f1 * '1e200' from FLOAT8_TBL f;

SELECT f.f1 ^ '1e200' from FLOAT8_TBL f;

SELECT 0 ^ 0 + 0 ^ 1 + 0 ^ 0.0 + 0 ^ 0.5;

SELECT ln(f.f1) from FLOAT8_TBL f where f.f1 = '0.0' ;

SELECT ln(f.f1) from FLOAT8_TBL f where f.f1 < '0.0' ;

SELECT exp(f.f1) from FLOAT8_TBL f;

SELECT f.f1 / '0.0' from FLOAT8_TBL f;

SELECT * FROM FLOAT8_TBL;

-- 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');
SELECT cosh(float8 '1');
SELECT tanh(float8 '1');
SELECT asinh(float8 '1');
SELECT acosh(float8 '2');
SELECT atanh(float8 '0.5');
-- test Inf/NaN cases for hyperbolic functions
SELECT sinh(float8 'infinity');
SELECT sinh(float8 '-infinity');
SELECT sinh(float8 'nan');
SELECT cosh(float8 'infinity');
SELECT cosh(float8 '-infinity');
SELECT cosh(float8 'nan');
SELECT tanh(float8 'infinity');
SELECT tanh(float8 '-infinity');
SELECT tanh(float8 'nan');
SELECT asinh(float8 'infinity');
SELECT asinh(float8 '-infinity');
SELECT asinh(float8 'nan');
-- acosh(Inf) should be Inf, but some mingw versions produce NaN, so skip test
-- SELECT acosh(float8 'infinity');
SELECT acosh(float8 '-infinity');
SELECT acosh(float8 'nan');
SELECT atanh(float8 'infinity');
SELECT atanh(float8 '-infinity');
SELECT atanh(float8 'nan');

RESET extra_float_digits;

-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');

INSERT INTO FLOAT8_TBL(f1) VALUES ('-10e400');

INSERT INTO FLOAT8_TBL(f1) VALUES ('10e-400');

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 * FROM FLOAT8_TBL;

-- test edge-case coercions to integer
SELECT '32767.4'::float8::int2;
SELECT '32767.6'::float8::int2;
SELECT '-32768.4'::float8::int2;
SELECT '-32768.6'::float8::int2;
SELECT '2147483647.4'::float8::int4;
SELECT '2147483647.6'::float8::int4;
SELECT '-2147483648.4'::float8::int4;
SELECT '-2147483648.6'::float8::int4;
SELECT '9223372036854773760'::float8::int8;
SELECT '9223372036854775807'::float8::int8;
SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;

-- 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);

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);

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);

SELECT x,
       asind(x),
       asind(x) IN (-90,-30,0,30,90) AS asind_exact,
       acosd(x),
       acosd(x) IN (0,60,90,120,180) AS acosd_exact
FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);

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);

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);

--
-- 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 xfloat8;
create function xfloat8in(cstring) returns xfloat8 immutable strict
  language internal as 'int8in';
create function xfloat8out(xfloat8) returns cstring immutable strict
  language internal as 'int8out';
create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
create cast (xfloat8 as float8) without function;
create cast (float8 as xfloat8) without function;
create cast (xfloat8 as bigint) without function;
create cast (bigint as xfloat8) without function;

-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)

-- 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'0000000000000001'),
  (x'0000000000000002'), (x'0000000000000003'),
  (x'0000000000001000'), (x'0000000100000000'),
  (x'0000010000000000'), (x'0000010100000000'),
  (x'0000400000000000'), (x'0000400100000000'),
  (x'0000800000000000'), (x'0000800000000001'),
  -- these values taken from upstream testsuite
  (x'00000000000f4240'),
  (x'00000000016e3600'),
  (x'0000008cdcdea440'),
  -- borderline between subnormal and normal
  (x'000ffffffffffff0'), (x'000ffffffffffff1'),
  (x'000ffffffffffffe'), (x'000fffffffffffff'))
select float8send(flt) as ibits,
       flt
  from (select bits::bigint::xfloat8::float8 as flt
          from testdata
	offset 0) s;

-- round-trip tests

with testdata(bits) as (values
  (x'0000000000000000'),
  -- smallest normal values
  (x'0010000000000000'), (x'0010000000000001'),
  (x'0010000000000002'), (x'0018000000000000'),
  --
  (x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
  (x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
  (x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
  (x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
  (x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
  (x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
  (x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
  (x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
  (x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
  (x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
  -- values very close to 1
  (x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
  (x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
  (x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
  (x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
  (x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
  (x'3fefffffffffffff'),
  (x'3ff0000000000000'),
  (x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
  (x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
  (x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
  --
  (x'3ff921fb54442d18'),
  (x'4005bf0a8b14576a'),
  (x'400921fb54442d18'),
  --
  (x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
  (x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
  (x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
  (x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
  (x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
  (x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
  (x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
  (x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
  (x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
  (x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
  (x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
  (x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
  (x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
  (x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
  (x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
  (x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
  (x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
  (x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
  (x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
  (x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
  (x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
  (x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
  (x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
  (x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
  (x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
  --
  (x'7feffffffffffffe'), (x'7fefffffffffffff'),
  -- round to even tests (+ve)
  (x'4350000000000002'),
  (x'4350000000002e06'),
  (x'4352000000000003'),
  (x'4352000000000004'),
  (x'4358000000000003'),
  (x'4358000000000004'),
  (x'435f000000000020'),
  -- round to even tests (-ve)
  (x'c350000000000002'),
  (x'c350000000002e06'),
  (x'c352000000000003'),
  (x'c352000000000004'),
  (x'c358000000000003'),
  (x'c358000000000004'),
  (x'c35f000000000020'),
  -- exercise fixed-point memmoves
  (x'42dc12218377de66'),
  (x'42a674e79c5fe51f'),
  (x'4271f71fb04cb74c'),
  (x'423cbe991a145879'),
  (x'4206fee0e1a9e061'),
  (x'41d26580b487e6b4'),
  (x'419d6f34540ca453'),
  (x'41678c29dcd6e9dc'),
  (x'4132d687e3df217d'),
  (x'40fe240c9fcb68c8'),
  (x'40c81cd6e63c53d3'),
  (x'40934a4584fd0fdc'),
  (x'405edd3c07fb4c93'),
  (x'4028b0fcd32f7076'),
  (x'3ff3c0ca428c59f8'),
  -- these cases come from the upstream's testsuite
  -- LotsOfTrailingZeros)
  (x'3e60000000000000'),
  -- Regression
  (x'c352bd2668e077c4'),
  (x'434018601510c000'),
  (x'43d055dc36f24000'),
  (x'43e052961c6f8000'),
  (x'3ff3c0ca2a5b1d5d'),
  -- LooksLikePow5
  (x'4830f0cf064dd592'),
  (x'4840f0cf064dd592'),
  (x'4850f0cf064dd592'),
  -- OutputLength
  (x'3ff3333333333333'),
  (x'3ff3ae147ae147ae'),
  (x'3ff3be76c8b43958'),
  (x'3ff3c083126e978d'),
  (x'3ff3c0c1fc8f3238'),
  (x'3ff3c0c9539b8887'),
  (x'3ff3c0ca2a5b1d5d'),
  (x'3ff3c0ca4283de1b'),
  (x'3ff3c0ca43db770a'),
  (x'3ff3c0ca428abd53'),
  (x'3ff3c0ca428c1d2b'),
  (x'3ff3c0ca428c51f2'),
  (x'3ff3c0ca428c58fc'),
  (x'3ff3c0ca428c59dd'),
  (x'3ff3c0ca428c59f8'),
  (x'3ff3c0ca428c59fb'),
  -- 32-bit chunking
  (x'40112e0be8047a7d'),
  (x'40112e0be815a889'),
  (x'40112e0be826d695'),
  (x'40112e0be83804a1'),
  (x'40112e0be84932ad'),
  -- MinMaxShift
  (x'0040000000000000'),
  (x'007fffffffffffff'),
  (x'0290000000000000'),
  (x'029fffffffffffff'),
  (x'4350000000000000'),
  (x'435fffffffffffff'),
  (x'1330000000000000'),
  (x'133fffffffffffff'),
  (x'3a6fa7161a4d6e0c')
)
select float8send(flt) as ibits,
       flt,
       flt::text::float8 as r_flt,
       float8send(flt::text::float8) as obits,
       float8send(flt::text::float8) = float8send(flt) as correct
  from (select bits::bigint::xfloat8::float8 as flt
          from testdata
	offset 0) s;

-- clean up, lest opr_sanity complain
drop type xfloat8 cascade;