text: --
  -- 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 'nan'::float8 / 'nan'::float8;
  SELECT 'nan'::numeric::float8;
  
  SELECT '' AS five, * FROM FLOAT8_TBL;
  
  SELECT '' AS four, f.* FROM FLOAT8_TBL f WHERE f.f1 <> '1004.3';
  
  SELECT '' AS one, f.* FROM FLOAT8_TBL f WHERE f.f1 = '1004.3';
  
  SELECT '' AS three, f.* FROM FLOAT8_TBL f WHERE '1004.3' > f.f1;
  
  SELECT '' AS three, f.* FROM FLOAT8_TBL f WHERE  f.f1 < '1004.3';
  
  SELECT '' AS four, f.* FROM FLOAT8_TBL f WHERE '1004.3' >= f.f1;
  
  SELECT '' AS four, f.* FROM FLOAT8_TBL f WHERE  f.f1 <= '1004.3';
  
  SELECT '' AS three, f.f1, f.f1 * '-10' AS x
     FROM FLOAT8_TBL f
     WHERE f.f1 > '0.0';
  
  SELECT '' AS three, f.f1, f.f1 + '-10' AS x
     FROM FLOAT8_TBL f
     WHERE f.f1 > '0.0';
  
  SELECT '' AS three, f.f1, f.f1 / '-10' AS x
     FROM FLOAT8_TBL f
     WHERE f.f1 > '0.0';
  
  SELECT '' AS three, f.f1, f.f1 - '-10' AS x
     FROM FLOAT8_TBL f
     WHERE f.f1 > '0.0';
  
  SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
     FROM FLOAT8_TBL f where f.f1 = '1004.3';
  
  -- absolute value
  SELECT '' AS five, f.f1, @f.f1 AS abs_f1
     FROM FLOAT8_TBL f;
  
  -- truncate
  SELECT '' AS five, f.f1, trunc(f.f1) AS trunc_f1
     FROM FLOAT8_TBL f;
  
  -- round
  SELECT '' AS five, 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 '' AS three, 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 '' AS three, 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 '' AS five, f.f1, ||/f.f1 AS cbrt_f1 FROM FLOAT8_TBL f;
  
  
  SELECT '' AS five, * FROM FLOAT8_TBL;
  
  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;
  
  SELECT '' AS bad, f.f1 ^ '1e200' from FLOAT8_TBL f;
  
  SELECT 0 ^ 0 + 0 ^ 1 + 0 ^ 0.0 + 0 ^ 0.5;
  
  SELECT '' AS bad, ln(f.f1) from FLOAT8_TBL f where f.f1 = '0.0' ;
  
  SELECT '' AS bad, ln(f.f1) from FLOAT8_TBL f where f.f1 < '0.0' ;
  
  SELECT '' AS bad, exp(f.f1) from FLOAT8_TBL f;
  
  SELECT '' AS bad, f.f1 / '0.0' from FLOAT8_TBL f;
  
  SELECT '' AS five, * 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 '' AS five, * 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;
  