diff options
Diffstat (limited to 'src/test/regress/expected/numeric.out')
| -rw-r--r-- | src/test/regress/expected/numeric.out | 3345 |
1 files changed, 3345 insertions, 0 deletions
diff --git a/src/test/regress/expected/numeric.out b/src/test/regress/expected/numeric.out new file mode 100644 index 0000000..ea11fee --- /dev/null +++ b/src/test/regress/expected/numeric.out @@ -0,0 +1,3345 @@ +-- +-- NUMERIC +-- +CREATE TABLE num_data (id int4, val numeric(210,10)); +CREATE TABLE num_exp_add (id1 int4, id2 int4, expected numeric(210,10)); +CREATE TABLE num_exp_sub (id1 int4, id2 int4, expected numeric(210,10)); +CREATE TABLE num_exp_div (id1 int4, id2 int4, expected numeric(210,10)); +CREATE TABLE num_exp_mul (id1 int4, id2 int4, expected numeric(210,10)); +CREATE TABLE num_exp_sqrt (id int4, expected numeric(210,10)); +CREATE TABLE num_exp_ln (id int4, expected numeric(210,10)); +CREATE TABLE num_exp_log10 (id int4, expected numeric(210,10)); +CREATE TABLE num_exp_power_10_ln (id int4, expected numeric(210,10)); +CREATE TABLE num_result (id1 int4, id2 int4, result numeric(210,10)); +-- ****************************** +-- * The following EXPECTED results are computed by bc(1) +-- * with a scale of 200 +-- ****************************** +BEGIN TRANSACTION; +INSERT INTO num_exp_add VALUES (0,0,'0'); +INSERT INTO num_exp_sub VALUES (0,0,'0'); +INSERT INTO num_exp_mul VALUES (0,0,'0'); +INSERT INTO num_exp_div VALUES (0,0,'NaN'); +INSERT INTO num_exp_add VALUES (0,1,'0'); +INSERT INTO num_exp_sub VALUES (0,1,'0'); +INSERT INTO num_exp_mul VALUES (0,1,'0'); +INSERT INTO num_exp_div VALUES (0,1,'NaN'); +INSERT INTO num_exp_add VALUES (0,2,'-34338492.215397047'); +INSERT INTO num_exp_sub VALUES (0,2,'34338492.215397047'); +INSERT INTO num_exp_mul VALUES (0,2,'0'); +INSERT INTO num_exp_div VALUES (0,2,'0'); +INSERT INTO num_exp_add VALUES (0,3,'4.31'); +INSERT INTO num_exp_sub VALUES (0,3,'-4.31'); +INSERT INTO num_exp_mul VALUES (0,3,'0'); +INSERT INTO num_exp_div VALUES (0,3,'0'); +INSERT INTO num_exp_add VALUES (0,4,'7799461.4119'); +INSERT INTO num_exp_sub VALUES (0,4,'-7799461.4119'); +INSERT INTO num_exp_mul VALUES (0,4,'0'); +INSERT INTO num_exp_div VALUES (0,4,'0'); +INSERT INTO num_exp_add VALUES (0,5,'16397.038491'); +INSERT INTO num_exp_sub VALUES (0,5,'-16397.038491'); +INSERT INTO num_exp_mul VALUES (0,5,'0'); +INSERT INTO num_exp_div VALUES (0,5,'0'); +INSERT INTO num_exp_add VALUES (0,6,'93901.57763026'); +INSERT INTO num_exp_sub VALUES (0,6,'-93901.57763026'); +INSERT INTO num_exp_mul VALUES (0,6,'0'); +INSERT INTO num_exp_div VALUES (0,6,'0'); +INSERT INTO num_exp_add VALUES (0,7,'-83028485'); +INSERT INTO num_exp_sub VALUES (0,7,'83028485'); +INSERT INTO num_exp_mul VALUES (0,7,'0'); +INSERT INTO num_exp_div VALUES (0,7,'0'); +INSERT INTO num_exp_add VALUES (0,8,'74881'); +INSERT INTO num_exp_sub VALUES (0,8,'-74881'); +INSERT INTO num_exp_mul VALUES (0,8,'0'); +INSERT INTO num_exp_div VALUES (0,8,'0'); +INSERT INTO num_exp_add VALUES (0,9,'-24926804.045047420'); +INSERT INTO num_exp_sub VALUES (0,9,'24926804.045047420'); +INSERT INTO num_exp_mul VALUES (0,9,'0'); +INSERT INTO num_exp_div VALUES (0,9,'0'); +INSERT INTO num_exp_add VALUES (1,0,'0'); +INSERT INTO num_exp_sub VALUES (1,0,'0'); +INSERT INTO num_exp_mul VALUES (1,0,'0'); +INSERT INTO num_exp_div VALUES (1,0,'NaN'); +INSERT INTO num_exp_add VALUES (1,1,'0'); +INSERT INTO num_exp_sub VALUES (1,1,'0'); +INSERT INTO num_exp_mul VALUES (1,1,'0'); +INSERT INTO num_exp_div VALUES (1,1,'NaN'); +INSERT INTO num_exp_add VALUES (1,2,'-34338492.215397047'); +INSERT INTO num_exp_sub VALUES (1,2,'34338492.215397047'); +INSERT INTO num_exp_mul VALUES (1,2,'0'); +INSERT INTO num_exp_div VALUES (1,2,'0'); +INSERT INTO num_exp_add VALUES (1,3,'4.31'); +INSERT INTO num_exp_sub VALUES (1,3,'-4.31'); +INSERT INTO num_exp_mul VALUES (1,3,'0'); +INSERT INTO num_exp_div VALUES (1,3,'0'); +INSERT INTO num_exp_add VALUES (1,4,'7799461.4119'); +INSERT INTO num_exp_sub VALUES (1,4,'-7799461.4119'); +INSERT INTO num_exp_mul VALUES (1,4,'0'); +INSERT INTO num_exp_div VALUES (1,4,'0'); +INSERT INTO num_exp_add VALUES (1,5,'16397.038491'); +INSERT INTO num_exp_sub VALUES (1,5,'-16397.038491'); +INSERT INTO num_exp_mul VALUES (1,5,'0'); +INSERT INTO num_exp_div VALUES (1,5,'0'); +INSERT INTO num_exp_add VALUES (1,6,'93901.57763026'); +INSERT INTO num_exp_sub VALUES (1,6,'-93901.57763026'); +INSERT INTO num_exp_mul VALUES (1,6,'0'); +INSERT INTO num_exp_div VALUES (1,6,'0'); +INSERT INTO num_exp_add VALUES (1,7,'-83028485'); +INSERT INTO num_exp_sub VALUES (1,7,'83028485'); +INSERT INTO num_exp_mul VALUES (1,7,'0'); +INSERT INTO num_exp_div VALUES (1,7,'0'); +INSERT INTO num_exp_add VALUES (1,8,'74881'); +INSERT INTO num_exp_sub VALUES (1,8,'-74881'); +INSERT INTO num_exp_mul VALUES (1,8,'0'); +INSERT INTO num_exp_div VALUES (1,8,'0'); +INSERT INTO num_exp_add VALUES (1,9,'-24926804.045047420'); +INSERT INTO num_exp_sub VALUES (1,9,'24926804.045047420'); +INSERT INTO num_exp_mul VALUES (1,9,'0'); +INSERT INTO num_exp_div VALUES (1,9,'0'); +INSERT INTO num_exp_add VALUES (2,0,'-34338492.215397047'); +INSERT INTO num_exp_sub VALUES (2,0,'-34338492.215397047'); +INSERT INTO num_exp_mul VALUES (2,0,'0'); +INSERT INTO num_exp_div VALUES (2,0,'NaN'); +INSERT INTO num_exp_add VALUES (2,1,'-34338492.215397047'); +INSERT INTO num_exp_sub VALUES (2,1,'-34338492.215397047'); +INSERT INTO num_exp_mul VALUES (2,1,'0'); +INSERT INTO num_exp_div VALUES (2,1,'NaN'); +INSERT INTO num_exp_add VALUES (2,2,'-68676984.430794094'); +INSERT INTO num_exp_sub VALUES (2,2,'0'); +INSERT INTO num_exp_mul VALUES (2,2,'1179132047626883.596862135856320209'); +INSERT INTO num_exp_div VALUES (2,2,'1.00000000000000000000'); +INSERT INTO num_exp_add VALUES (2,3,'-34338487.905397047'); +INSERT INTO num_exp_sub VALUES (2,3,'-34338496.525397047'); +INSERT INTO num_exp_mul VALUES (2,3,'-147998901.44836127257'); +INSERT INTO num_exp_div VALUES (2,3,'-7967167.56737750510440835266'); +INSERT INTO num_exp_add VALUES (2,4,'-26539030.803497047'); +INSERT INTO num_exp_sub VALUES (2,4,'-42137953.627297047'); +INSERT INTO num_exp_mul VALUES (2,4,'-267821744976817.8111137106593'); +INSERT INTO num_exp_div VALUES (2,4,'-4.40267480046830116685'); +INSERT INTO num_exp_add VALUES (2,5,'-34322095.176906047'); +INSERT INTO num_exp_sub VALUES (2,5,'-34354889.253888047'); +INSERT INTO num_exp_mul VALUES (2,5,'-563049578578.769242506736077'); +INSERT INTO num_exp_div VALUES (2,5,'-2094.18866914563535496429'); +INSERT INTO num_exp_add VALUES (2,6,'-34244590.637766787'); +INSERT INTO num_exp_sub VALUES (2,6,'-34432393.793027307'); +INSERT INTO num_exp_mul VALUES (2,6,'-3224438592470.18449811926184222'); +INSERT INTO num_exp_div VALUES (2,6,'-365.68599891479766440940'); +INSERT INTO num_exp_add VALUES (2,7,'-117366977.215397047'); +INSERT INTO num_exp_sub VALUES (2,7,'48689992.784602953'); +INSERT INTO num_exp_mul VALUES (2,7,'2851072985828710.485883795'); +INSERT INTO num_exp_div VALUES (2,7,'.41357483778485235518'); +INSERT INTO num_exp_add VALUES (2,8,'-34263611.215397047'); +INSERT INTO num_exp_sub VALUES (2,8,'-34413373.215397047'); +INSERT INTO num_exp_mul VALUES (2,8,'-2571300635581.146276407'); +INSERT INTO num_exp_div VALUES (2,8,'-458.57416721727870888476'); +INSERT INTO num_exp_add VALUES (2,9,'-59265296.260444467'); +INSERT INTO num_exp_sub VALUES (2,9,'-9411688.170349627'); +INSERT INTO num_exp_mul VALUES (2,9,'855948866655588.453741509242968740'); +INSERT INTO num_exp_div VALUES (2,9,'1.37757299946438931811'); +INSERT INTO num_exp_add VALUES (3,0,'4.31'); +INSERT INTO num_exp_sub VALUES (3,0,'4.31'); +INSERT INTO num_exp_mul VALUES (3,0,'0'); +INSERT INTO num_exp_div VALUES (3,0,'NaN'); +INSERT INTO num_exp_add VALUES (3,1,'4.31'); +INSERT INTO num_exp_sub VALUES (3,1,'4.31'); +INSERT INTO num_exp_mul VALUES (3,1,'0'); +INSERT INTO num_exp_div VALUES (3,1,'NaN'); +INSERT INTO num_exp_add VALUES (3,2,'-34338487.905397047'); +INSERT INTO num_exp_sub VALUES (3,2,'34338496.525397047'); +INSERT INTO num_exp_mul VALUES (3,2,'-147998901.44836127257'); +INSERT INTO num_exp_div VALUES (3,2,'-.00000012551512084352'); +INSERT INTO num_exp_add VALUES (3,3,'8.62'); +INSERT INTO num_exp_sub VALUES (3,3,'0'); +INSERT INTO num_exp_mul VALUES (3,3,'18.5761'); +INSERT INTO num_exp_div VALUES (3,3,'1.00000000000000000000'); +INSERT INTO num_exp_add VALUES (3,4,'7799465.7219'); +INSERT INTO num_exp_sub VALUES (3,4,'-7799457.1019'); +INSERT INTO num_exp_mul VALUES (3,4,'33615678.685289'); +INSERT INTO num_exp_div VALUES (3,4,'.00000055260225961552'); +INSERT INTO num_exp_add VALUES (3,5,'16401.348491'); +INSERT INTO num_exp_sub VALUES (3,5,'-16392.728491'); +INSERT INTO num_exp_mul VALUES (3,5,'70671.23589621'); +INSERT INTO num_exp_div VALUES (3,5,'.00026285234387695504'); +INSERT INTO num_exp_add VALUES (3,6,'93905.88763026'); +INSERT INTO num_exp_sub VALUES (3,6,'-93897.26763026'); +INSERT INTO num_exp_mul VALUES (3,6,'404715.7995864206'); +INSERT INTO num_exp_div VALUES (3,6,'.00004589912234457595'); +INSERT INTO num_exp_add VALUES (3,7,'-83028480.69'); +INSERT INTO num_exp_sub VALUES (3,7,'83028489.31'); +INSERT INTO num_exp_mul VALUES (3,7,'-357852770.35'); +INSERT INTO num_exp_div VALUES (3,7,'-.00000005190989574240'); +INSERT INTO num_exp_add VALUES (3,8,'74885.31'); +INSERT INTO num_exp_sub VALUES (3,8,'-74876.69'); +INSERT INTO num_exp_mul VALUES (3,8,'322737.11'); +INSERT INTO num_exp_div VALUES (3,8,'.00005755799201399553'); +INSERT INTO num_exp_add VALUES (3,9,'-24926799.735047420'); 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+INSERT INTO num_exp_div VALUES (7,8,'-1108.80577182462841041118'); +INSERT INTO num_exp_add VALUES (7,9,'-107955289.045047420'); +INSERT INTO num_exp_sub VALUES (7,9,'-58101680.954952580'); +INSERT INTO num_exp_mul VALUES (7,9,'2069634775752159.035758700'); +INSERT INTO num_exp_div VALUES (7,9,'3.33089171198810413382'); +INSERT INTO num_exp_add VALUES (8,0,'74881'); +INSERT INTO num_exp_sub VALUES (8,0,'74881'); +INSERT INTO num_exp_mul VALUES (8,0,'0'); +INSERT INTO num_exp_div VALUES (8,0,'NaN'); +INSERT INTO num_exp_add VALUES (8,1,'74881'); +INSERT INTO num_exp_sub VALUES (8,1,'74881'); +INSERT INTO num_exp_mul VALUES (8,1,'0'); +INSERT INTO num_exp_div VALUES (8,1,'NaN'); +INSERT INTO num_exp_add VALUES (8,2,'-34263611.215397047'); +INSERT INTO num_exp_sub VALUES (8,2,'34413373.215397047'); +INSERT INTO num_exp_mul VALUES (8,2,'-2571300635581.146276407'); +INSERT INTO num_exp_div VALUES (8,2,'-.00218067233500788615'); +INSERT INTO num_exp_add VALUES (8,3,'74885.31'); +INSERT INTO num_exp_sub VALUES (8,3,'74876.69'); +INSERT INTO num_exp_mul VALUES (8,3,'322737.11'); +INSERT INTO num_exp_div VALUES (8,3,'17373.78190255220417633410'); +INSERT INTO num_exp_add VALUES (8,4,'7874342.4119'); +INSERT INTO num_exp_sub VALUES (8,4,'-7724580.4119'); +INSERT INTO num_exp_mul VALUES (8,4,'584031469984.4839'); +INSERT INTO num_exp_div VALUES (8,4,'.00960079113741758956'); +INSERT INTO num_exp_add VALUES (8,5,'91278.038491'); +INSERT INTO num_exp_sub VALUES (8,5,'58483.961509'); +INSERT INTO num_exp_mul VALUES (8,5,'1227826639.244571'); +INSERT INTO num_exp_div VALUES (8,5,'4.56673929509287019456'); +INSERT INTO num_exp_add VALUES (8,6,'168782.57763026'); +INSERT INTO num_exp_sub VALUES (8,6,'-19020.57763026'); +INSERT INTO num_exp_mul VALUES (8,6,'7031444034.53149906'); +INSERT INTO num_exp_div VALUES (8,6,'.79744134113322314424'); +INSERT INTO num_exp_add VALUES (8,7,'-82953604'); +INSERT INTO num_exp_sub VALUES (8,7,'83103366'); +INSERT INTO num_exp_mul VALUES (8,7,'-6217255985285'); +INSERT INTO num_exp_div VALUES (8,7,'-.00090187120721280172'); +INSERT INTO num_exp_add VALUES (8,8,'149762'); +INSERT INTO num_exp_sub VALUES (8,8,'0'); +INSERT INTO num_exp_mul VALUES (8,8,'5607164161'); +INSERT INTO num_exp_div VALUES (8,8,'1.00000000000000000000'); +INSERT INTO num_exp_add VALUES (8,9,'-24851923.045047420'); +INSERT INTO num_exp_sub VALUES (8,9,'25001685.045047420'); +INSERT INTO num_exp_mul VALUES (8,9,'-1866544013697.195857020'); +INSERT INTO num_exp_div VALUES (8,9,'-.00300403532938582735'); +INSERT INTO num_exp_add VALUES (9,0,'-24926804.045047420'); +INSERT INTO num_exp_sub VALUES (9,0,'-24926804.045047420'); +INSERT INTO num_exp_mul VALUES (9,0,'0'); +INSERT INTO num_exp_div VALUES (9,0,'NaN'); +INSERT INTO num_exp_add VALUES (9,1,'-24926804.045047420'); +INSERT INTO num_exp_sub VALUES (9,1,'-24926804.045047420'); +INSERT INTO num_exp_mul VALUES (9,1,'0'); +INSERT INTO num_exp_div VALUES (9,1,'NaN'); +INSERT INTO num_exp_add VALUES (9,2,'-59265296.260444467'); +INSERT INTO num_exp_sub VALUES (9,2,'9411688.170349627'); +INSERT INTO num_exp_mul VALUES (9,2,'855948866655588.453741509242968740'); +INSERT INTO num_exp_div VALUES (9,2,'.72591434384152961526'); +INSERT INTO num_exp_add VALUES (9,3,'-24926799.735047420'); +INSERT INTO num_exp_sub VALUES (9,3,'-24926808.355047420'); +INSERT INTO num_exp_mul VALUES (9,3,'-107434525.43415438020'); +INSERT INTO num_exp_div VALUES (9,3,'-5783481.21694835730858468677'); +INSERT INTO num_exp_add VALUES (9,4,'-17127342.633147420'); +INSERT INTO num_exp_sub VALUES (9,4,'-32726265.456947420'); +INSERT INTO num_exp_mul VALUES (9,4,'-194415646271340.1815956522980'); +INSERT INTO num_exp_div VALUES (9,4,'-3.19596478892958416484'); +INSERT INTO num_exp_add VALUES (9,5,'-24910407.006556420'); +INSERT INTO num_exp_sub VALUES (9,5,'-24943201.083538420'); +INSERT INTO num_exp_mul VALUES (9,5,'-408725765384.257043660243220'); +INSERT INTO num_exp_div VALUES (9,5,'-1520.20159364322004505807'); +INSERT INTO num_exp_add VALUES (9,6,'-24832902.467417160'); +INSERT INTO num_exp_sub VALUES (9,6,'-25020705.622677680'); +INSERT INTO num_exp_mul VALUES (9,6,'-2340666225110.29929521292692920'); +INSERT INTO num_exp_div VALUES (9,6,'-265.45671195426965751280'); +INSERT INTO num_exp_add VALUES (9,7,'-107955289.045047420'); +INSERT INTO num_exp_sub VALUES (9,7,'58101680.954952580'); +INSERT INTO num_exp_mul VALUES (9,7,'2069634775752159.035758700'); +INSERT INTO num_exp_div VALUES (9,7,'.30021990699995814689'); +INSERT INTO num_exp_add VALUES (9,8,'-24851923.045047420'); +INSERT INTO num_exp_sub VALUES (9,8,'-25001685.045047420'); +INSERT INTO num_exp_mul VALUES (9,8,'-1866544013697.195857020'); +INSERT INTO num_exp_div VALUES (9,8,'-332.88556569820675471748'); +INSERT INTO num_exp_add VALUES (9,9,'-49853608.090094840'); +INSERT INTO num_exp_sub VALUES (9,9,'0'); +INSERT INTO num_exp_mul VALUES (9,9,'621345559900192.420120630048656400'); +INSERT INTO num_exp_div VALUES (9,9,'1.00000000000000000000'); +COMMIT TRANSACTION; +BEGIN TRANSACTION; +INSERT INTO num_exp_sqrt VALUES (0,'0'); +INSERT INTO num_exp_sqrt VALUES (1,'0'); +INSERT INTO num_exp_sqrt VALUES (2,'5859.90547836712524903505'); +INSERT INTO num_exp_sqrt VALUES (3,'2.07605394920266944396'); +INSERT INTO num_exp_sqrt VALUES (4,'2792.75158435189147418923'); +INSERT INTO num_exp_sqrt VALUES (5,'128.05092147657509145473'); +INSERT INTO num_exp_sqrt VALUES (6,'306.43364311096782703406'); +INSERT INTO num_exp_sqrt VALUES (7,'9111.99676251039939975230'); +INSERT INTO num_exp_sqrt VALUES (8,'273.64392922189960397542'); +INSERT INTO num_exp_sqrt VALUES (9,'4992.67503899937593364766'); +COMMIT TRANSACTION; +BEGIN TRANSACTION; +INSERT INTO num_exp_ln VALUES (0,'NaN'); +INSERT INTO num_exp_ln VALUES (1,'NaN'); +INSERT INTO num_exp_ln VALUES (2,'17.35177750493897715514'); +INSERT INTO num_exp_ln VALUES (3,'1.46093790411565641971'); +INSERT INTO num_exp_ln VALUES (4,'15.86956523951936572464'); +INSERT INTO num_exp_ln VALUES (5,'9.70485601768871834038'); +INSERT INTO num_exp_ln VALUES (6,'11.45000246622944403127'); +INSERT INTO num_exp_ln VALUES (7,'18.23469429965478772991'); +INSERT INTO num_exp_ln VALUES (8,'11.22365546576315513668'); +INSERT INTO num_exp_ln VALUES (9,'17.03145425013166006962'); +COMMIT TRANSACTION; +BEGIN TRANSACTION; +INSERT INTO num_exp_log10 VALUES (0,'NaN'); +INSERT INTO num_exp_log10 VALUES (1,'NaN'); +INSERT INTO num_exp_log10 VALUES (2,'7.53578122160797276459'); +INSERT INTO num_exp_log10 VALUES (3,'.63447727016073160075'); +INSERT INTO num_exp_log10 VALUES (4,'6.89206461372691743345'); +INSERT INTO num_exp_log10 VALUES (5,'4.21476541614777768626'); +INSERT INTO num_exp_log10 VALUES (6,'4.97267288886207207671'); +INSERT INTO num_exp_log10 VALUES (7,'7.91922711353275546914'); +INSERT INTO num_exp_log10 VALUES (8,'4.87437163556421004138'); +INSERT INTO num_exp_log10 VALUES (9,'7.39666659961986567059'); +COMMIT TRANSACTION; +BEGIN TRANSACTION; +INSERT INTO num_exp_power_10_ln VALUES (0,'NaN'); +INSERT INTO num_exp_power_10_ln VALUES (1,'NaN'); +INSERT INTO num_exp_power_10_ln VALUES (2,'224790267919917955.13261618583642653184'); +INSERT INTO num_exp_power_10_ln VALUES (3,'28.90266599445155957393'); +INSERT INTO num_exp_power_10_ln VALUES (4,'7405685069594999.07733999469386277636'); +INSERT INTO num_exp_power_10_ln VALUES (5,'5068226527.32127265408584640098'); +INSERT INTO num_exp_power_10_ln VALUES (6,'281839893606.99372343357047819067'); +INSERT INTO num_exp_power_10_ln VALUES (7,'1716699575118597095.42330819910640247627'); +INSERT INTO num_exp_power_10_ln VALUES (8,'167361463828.07491320069016125952'); +INSERT INTO num_exp_power_10_ln VALUES (9,'107511333880052007.04141124673540337457'); +COMMIT TRANSACTION; +BEGIN TRANSACTION; +INSERT INTO num_data VALUES (0, '0'); +INSERT INTO num_data VALUES (1, '0'); +INSERT INTO num_data VALUES (2, '-34338492.215397047'); +INSERT INTO num_data VALUES (3, '4.31'); +INSERT INTO num_data VALUES (4, '7799461.4119'); +INSERT INTO num_data VALUES (5, '16397.038491'); +INSERT INTO num_data VALUES (6, '93901.57763026'); +INSERT INTO num_data VALUES (7, '-83028485'); +INSERT INTO num_data VALUES (8, '74881'); +INSERT INTO num_data VALUES (9, '-24926804.045047420'); +COMMIT TRANSACTION; +-- ****************************** +-- * Create indices for faster checks +-- ****************************** +CREATE UNIQUE INDEX num_exp_add_idx ON num_exp_add (id1, id2); +CREATE UNIQUE INDEX num_exp_sub_idx ON num_exp_sub (id1, id2); +CREATE UNIQUE INDEX num_exp_div_idx ON num_exp_div (id1, id2); +CREATE UNIQUE INDEX num_exp_mul_idx ON num_exp_mul (id1, id2); +CREATE UNIQUE INDEX num_exp_sqrt_idx ON num_exp_sqrt (id); +CREATE UNIQUE INDEX num_exp_ln_idx ON num_exp_ln (id); +CREATE UNIQUE INDEX num_exp_log10_idx ON num_exp_log10 (id); +CREATE UNIQUE INDEX num_exp_power_10_ln_idx ON num_exp_power_10_ln (id); +VACUUM ANALYZE num_exp_add; +VACUUM ANALYZE num_exp_sub; +VACUUM ANALYZE num_exp_div; +VACUUM ANALYZE num_exp_mul; +VACUUM ANALYZE num_exp_sqrt; +VACUUM ANALYZE num_exp_ln; +VACUUM ANALYZE num_exp_log10; +VACUUM ANALYZE num_exp_power_10_ln; +-- ****************************** +-- * Now check the behaviour of the NUMERIC type +-- ****************************** +-- ****************************** +-- * Addition check +-- ****************************** +DELETE FROM num_result; +INSERT INTO num_result SELECT t1.id, t2.id, t1.val + t2.val + FROM num_data t1, num_data t2; +SELECT t1.id1, t1.id2, t1.result, t2.expected + FROM num_result t1, num_exp_add t2 + WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2 + AND t1.result != t2.expected; + id1 | id2 | result | expected +-----+-----+--------+---------- +(0 rows) + +DELETE FROM num_result; +INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val + t2.val, 10) + FROM num_data t1, num_data t2; +SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 10) as expected + FROM num_result t1, num_exp_add t2 + WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2 + AND t1.result != round(t2.expected, 10); + id1 | id2 | result | expected +-----+-----+--------+---------- +(0 rows) + +-- ****************************** +-- * Subtraction check +-- ****************************** +DELETE FROM num_result; +INSERT INTO num_result SELECT t1.id, t2.id, t1.val - t2.val + FROM num_data t1, num_data t2; +SELECT t1.id1, t1.id2, t1.result, t2.expected + FROM num_result t1, num_exp_sub t2 + WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2 + AND t1.result != t2.expected; + id1 | id2 | result | expected +-----+-----+--------+---------- +(0 rows) + +DELETE FROM num_result; +INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val - t2.val, 40) + FROM num_data t1, num_data t2; +SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 40) + FROM num_result t1, num_exp_sub t2 + WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2 + AND t1.result != round(t2.expected, 40); + id1 | id2 | result | round +-----+-----+--------+------- +(0 rows) + +-- ****************************** +-- * Multiply check +-- ****************************** +DELETE FROM num_result; +INSERT INTO num_result SELECT t1.id, t2.id, t1.val * t2.val + FROM num_data t1, num_data t2; +SELECT t1.id1, t1.id2, t1.result, t2.expected + FROM num_result t1, num_exp_mul t2 + WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2 + AND t1.result != t2.expected; + id1 | id2 | result | expected +-----+-----+--------+---------- +(0 rows) + +DELETE FROM num_result; +INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val * t2.val, 30) + FROM num_data t1, num_data t2; +SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 30) as expected + FROM num_result t1, num_exp_mul t2 + WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2 + AND t1.result != round(t2.expected, 30); + id1 | id2 | result | expected +-----+-----+--------+---------- +(0 rows) + +-- ****************************** +-- * Division check +-- ****************************** +DELETE FROM num_result; +INSERT INTO num_result SELECT t1.id, t2.id, t1.val / t2.val + FROM num_data t1, num_data t2 + WHERE t2.val != '0.0'; +SELECT t1.id1, t1.id2, t1.result, t2.expected + FROM num_result t1, num_exp_div t2 + WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2 + AND t1.result != t2.expected; + id1 | id2 | result | expected +-----+-----+--------+---------- +(0 rows) + +DELETE FROM num_result; +INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val / t2.val, 80) + FROM num_data t1, num_data t2 + WHERE t2.val != '0.0'; +SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 80) as expected + FROM num_result t1, num_exp_div t2 + WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2 + AND t1.result != round(t2.expected, 80); + id1 | id2 | result | expected +-----+-----+--------+---------- +(0 rows) + +-- ****************************** +-- * Square root check +-- ****************************** +DELETE FROM num_result; +INSERT INTO num_result SELECT id, 0, SQRT(ABS(val)) + FROM num_data; +SELECT t1.id1, t1.result, t2.expected + FROM num_result t1, num_exp_sqrt t2 + WHERE t1.id1 = t2.id + AND t1.result != t2.expected; + id1 | result | expected +-----+--------+---------- +(0 rows) + +-- ****************************** +-- * Natural logarithm check +-- ****************************** +DELETE FROM num_result; +INSERT INTO num_result SELECT id, 0, LN(ABS(val)) + FROM num_data + WHERE val != '0.0'; +SELECT t1.id1, t1.result, t2.expected + FROM num_result t1, num_exp_ln t2 + WHERE t1.id1 = t2.id + AND t1.result != t2.expected; + id1 | result | expected +-----+--------+---------- +(0 rows) + +-- ****************************** +-- * Logarithm base 10 check +-- ****************************** +DELETE FROM num_result; +INSERT INTO num_result SELECT id, 0, LOG(numeric '10', ABS(val)) + FROM num_data + WHERE val != '0.0'; +SELECT t1.id1, t1.result, t2.expected + FROM num_result t1, num_exp_log10 t2 + WHERE t1.id1 = t2.id + AND t1.result != t2.expected; + id1 | result | expected +-----+--------+---------- +(0 rows) + +-- ****************************** +-- * POWER(10, LN(value)) check +-- ****************************** +DELETE FROM num_result; +INSERT INTO num_result SELECT id, 0, POWER(numeric '10', LN(ABS(round(val,200)))) + FROM num_data + WHERE val != '0.0'; +SELECT t1.id1, t1.result, t2.expected + FROM num_result t1, num_exp_power_10_ln t2 + WHERE t1.id1 = t2.id + AND t1.result != t2.expected; + id1 | result | expected +-----+--------+---------- +(0 rows) + +-- ****************************** +-- * Check behavior with Inf and NaN inputs. It's easiest to handle these +-- * separately from the num_data framework used above, because some input +-- * combinations will throw errors. +-- ****************************** +WITH v(x) AS + (VALUES('0'::numeric),('1'),('-1'),('4.2'),('inf'),('-inf'),('nan')) +SELECT x1, x2, + x1 + x2 AS sum, + x1 - x2 AS diff, + x1 * x2 AS prod +FROM v AS v1(x1), v AS v2(x2); + x1 | x2 | sum | diff | prod +-----------+-----------+-----------+-----------+----------- + 0 | 0 | 0 | 0 | 0 + 0 | 1 | 1 | -1 | 0 + 0 | -1 | -1 | 1 | 0 + 0 | 4.2 | 4.2 | -4.2 | 0.0 + 0 | Infinity | Infinity | -Infinity | NaN + 0 | -Infinity | -Infinity | Infinity | NaN + 0 | NaN | NaN | NaN | NaN + 1 | 0 | 1 | 1 | 0 + 1 | 1 | 2 | 0 | 1 + 1 | -1 | 0 | 2 | -1 + 1 | 4.2 | 5.2 | -3.2 | 4.2 + 1 | Infinity | Infinity | -Infinity | Infinity + 1 | -Infinity | -Infinity | Infinity | -Infinity + 1 | NaN | NaN | NaN | NaN + -1 | 0 | -1 | -1 | 0 + -1 | 1 | 0 | -2 | -1 + -1 | -1 | -2 | 0 | 1 + -1 | 4.2 | 3.2 | -5.2 | -4.2 + -1 | Infinity | Infinity | -Infinity | -Infinity + -1 | -Infinity | -Infinity | Infinity | Infinity + -1 | NaN | NaN | NaN | NaN + 4.2 | 0 | 4.2 | 4.2 | 0.0 + 4.2 | 1 | 5.2 | 3.2 | 4.2 + 4.2 | -1 | 3.2 | 5.2 | -4.2 + 4.2 | 4.2 | 8.4 | 0.0 | 17.64 + 4.2 | Infinity | Infinity | -Infinity | Infinity + 4.2 | -Infinity | -Infinity | Infinity | -Infinity + 4.2 | NaN | NaN | NaN | NaN + Infinity | 0 | Infinity | Infinity | NaN + Infinity | 1 | Infinity | Infinity | Infinity + Infinity | -1 | Infinity | Infinity | -Infinity + Infinity | 4.2 | Infinity | Infinity | Infinity + Infinity | Infinity | Infinity | NaN | Infinity + Infinity | -Infinity | NaN | Infinity | -Infinity + Infinity | NaN | NaN | NaN | NaN + -Infinity | 0 | -Infinity | -Infinity | NaN + -Infinity | 1 | -Infinity | -Infinity | -Infinity + -Infinity | -1 | -Infinity | -Infinity | Infinity + -Infinity | 4.2 | -Infinity | -Infinity | -Infinity + -Infinity | Infinity | NaN | -Infinity | -Infinity + -Infinity | -Infinity | -Infinity | NaN | Infinity + -Infinity | NaN | NaN | NaN | NaN + NaN | 0 | NaN | NaN | NaN + NaN | 1 | NaN | NaN | NaN + NaN | -1 | NaN | NaN | NaN + NaN | 4.2 | NaN | NaN | NaN + NaN | Infinity | NaN | NaN | NaN + NaN | -Infinity | NaN | NaN | NaN + NaN | NaN | NaN | NaN | NaN +(49 rows) + +WITH v(x) AS + (VALUES('0'::numeric),('1'),('-1'),('4.2'),('inf'),('-inf'),('nan')) +SELECT x1, x2, + x1 / x2 AS quot, + x1 % x2 AS mod, + div(x1, x2) AS div +FROM v AS v1(x1), v AS v2(x2) WHERE x2 != 0; + x1 | x2 | quot | mod | div +-----------+-----------+-------------------------+------+----------- + 0 | 1 | 0.00000000000000000000 | 0 | 0 + 1 | 1 | 1.00000000000000000000 | 0 | 1 + -1 | 1 | -1.00000000000000000000 | 0 | -1 + 4.2 | 1 | 4.2000000000000000 | 0.2 | 4 + Infinity | 1 | Infinity | NaN | Infinity + -Infinity | 1 | -Infinity | NaN | -Infinity + NaN | 1 | NaN | NaN | NaN + 0 | -1 | 0.00000000000000000000 | 0 | 0 + 1 | -1 | -1.00000000000000000000 | 0 | -1 + -1 | -1 | 1.00000000000000000000 | 0 | 1 + 4.2 | -1 | -4.2000000000000000 | 0.2 | -4 + Infinity | -1 | -Infinity | NaN | -Infinity + -Infinity | -1 | Infinity | NaN | Infinity + NaN | -1 | NaN | NaN | NaN + 0 | 4.2 | 0.00000000000000000000 | 0.0 | 0 + 1 | 4.2 | 0.23809523809523809524 | 1.0 | 0 + -1 | 4.2 | -0.23809523809523809524 | -1.0 | 0 + 4.2 | 4.2 | 1.00000000000000000000 | 0.0 | 1 + Infinity | 4.2 | Infinity | NaN | Infinity + -Infinity | 4.2 | -Infinity | NaN | -Infinity + NaN | 4.2 | NaN | NaN | NaN + 0 | Infinity | 0 | 0 | 0 + 1 | Infinity | 0 | 1 | 0 + -1 | Infinity | 0 | -1 | 0 + 4.2 | Infinity | 0 | 4.2 | 0 + Infinity | Infinity | NaN | NaN | NaN + -Infinity | Infinity | NaN | NaN | NaN + NaN | Infinity | NaN | NaN | NaN + 0 | -Infinity | 0 | 0 | 0 + 1 | -Infinity | 0 | 1 | 0 + -1 | -Infinity | 0 | -1 | 0 + 4.2 | -Infinity | 0 | 4.2 | 0 + Infinity | -Infinity | NaN | NaN | NaN + -Infinity | -Infinity | NaN | NaN | NaN + NaN | -Infinity | NaN | NaN | NaN + 0 | NaN | NaN | NaN | NaN + 1 | NaN | NaN | NaN | NaN + -1 | NaN | NaN | NaN | NaN + 4.2 | NaN | NaN | NaN | NaN + Infinity | NaN | NaN | NaN | NaN + -Infinity | NaN | NaN | NaN | NaN + NaN | NaN | NaN | NaN | NaN +(42 rows) + +SELECT 'inf'::numeric / '0'; +ERROR: division by zero +SELECT '-inf'::numeric / '0'; +ERROR: division by zero +SELECT 'nan'::numeric / '0'; + ?column? +---------- + NaN +(1 row) + +SELECT '0'::numeric / '0'; +ERROR: division by zero +SELECT 'inf'::numeric % '0'; +ERROR: division by zero +SELECT '-inf'::numeric % '0'; +ERROR: division by zero +SELECT 'nan'::numeric % '0'; + ?column? +---------- + NaN +(1 row) + +SELECT '0'::numeric % '0'; +ERROR: division by zero +SELECT div('inf'::numeric, '0'); +ERROR: division by zero +SELECT div('-inf'::numeric, '0'); +ERROR: division by zero +SELECT div('nan'::numeric, '0'); + div +----- + NaN +(1 row) + +SELECT div('0'::numeric, '0'); +ERROR: division by zero +WITH v(x) AS + (VALUES('0'::numeric),('1'),('-1'),('4.2'),('-7.777'),('inf'),('-inf'),('nan')) +SELECT x, -x as minusx, abs(x), floor(x), ceil(x), sign(x), numeric_inc(x) as inc +FROM v; + x | minusx | abs | floor | ceil | sign | inc +-----------+-----------+----------+-----------+-----------+------+----------- + 0 | 0 | 0 | 0 | 0 | 0 | 1 + 1 | -1 | 1 | 1 | 1 | 1 | 2 + -1 | 1 | 1 | -1 | -1 | -1 | 0 + 4.2 | -4.2 | 4.2 | 4 | 5 | 1 | 5.2 + -7.777 | 7.777 | 7.777 | -8 | -7 | -1 | -6.777 + Infinity | -Infinity | Infinity | Infinity | Infinity | 1 | Infinity + -Infinity | Infinity | Infinity | -Infinity | -Infinity | -1 | -Infinity + NaN | NaN | NaN | NaN | NaN | NaN | NaN +(8 rows) + +WITH v(x) AS + (VALUES('0'::numeric),('1'),('-1'),('4.2'),('-7.777'),('inf'),('-inf'),('nan')) +SELECT x, round(x), round(x,1) as round1, trunc(x), trunc(x,1) as trunc1 +FROM v; + x | round | round1 | trunc | trunc1 +-----------+-----------+-----------+-----------+----------- + 0 | 0 | 0.0 | 0 | 0.0 + 1 | 1 | 1.0 | 1 | 1.0 + -1 | -1 | -1.0 | -1 | -1.0 + 4.2 | 4 | 4.2 | 4 | 4.2 + -7.777 | -8 | -7.8 | -7 | -7.7 + Infinity | Infinity | Infinity | Infinity | Infinity + -Infinity | -Infinity | -Infinity | -Infinity | -Infinity + NaN | NaN | NaN | NaN | NaN +(8 rows) + +-- the large values fall into the numeric abbreviation code's maximal classes +WITH v(x) AS + (VALUES('0'::numeric),('1'),('-1'),('4.2'),('-7.777'),('1e340'),('-1e340'), + ('inf'),('-inf'),('nan'), + ('inf'),('-inf'),('nan')) +SELECT substring(x::text, 1, 32) +FROM v ORDER BY x; + substring +---------------------------------- + -Infinity + -Infinity + -1000000000000000000000000000000 + -7.777 + -1 + 0 + 1 + 4.2 + 10000000000000000000000000000000 + Infinity + Infinity + NaN + NaN +(13 rows) + +WITH v(x) AS + (VALUES('0'::numeric),('1'),('4.2'),('inf'),('nan')) +SELECT x, sqrt(x) +FROM v; + x | sqrt +----------+------------------- + 0 | 0.000000000000000 + 1 | 1.000000000000000 + 4.2 | 2.049390153191920 + Infinity | Infinity + NaN | NaN +(5 rows) + +SELECT sqrt('-1'::numeric); +ERROR: cannot take square root of a negative number +SELECT sqrt('-inf'::numeric); +ERROR: cannot take square root of a negative number +WITH v(x) AS + (VALUES('1'::numeric),('4.2'),('inf'),('nan')) +SELECT x, + log(x), + log10(x), + ln(x) +FROM v; + x | log | log10 | ln +----------+--------------------+--------------------+-------------------- + 1 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000 + 4.2 | 0.6232492903979005 | 0.6232492903979005 | 1.4350845252893226 + Infinity | Infinity | Infinity | Infinity + NaN | NaN | NaN | NaN +(4 rows) + +SELECT ln('0'::numeric); +ERROR: cannot take logarithm of zero +SELECT ln('-1'::numeric); +ERROR: cannot take logarithm of a negative number +SELECT ln('-inf'::numeric); +ERROR: cannot take logarithm of a negative number +WITH v(x) AS + (VALUES('2'::numeric),('4.2'),('inf'),('nan')) +SELECT x1, x2, + log(x1, x2) +FROM v AS v1(x1), v AS v2(x2); + x1 | x2 | log +----------+----------+-------------------- + 2 | 2 | 1.0000000000000000 + 2 | 4.2 | 2.0703893278913979 + 2 | Infinity | Infinity + 2 | NaN | NaN + 4.2 | 2 | 0.4830009440873890 + 4.2 | 4.2 | 1.0000000000000000 + 4.2 | Infinity | Infinity + 4.2 | NaN | NaN + Infinity | 2 | 0 + Infinity | 4.2 | 0 + Infinity | Infinity | NaN + Infinity | NaN | NaN + NaN | 2 | NaN + NaN | 4.2 | NaN + NaN | Infinity | NaN + NaN | NaN | NaN +(16 rows) + +SELECT log('0'::numeric, '10'); +ERROR: cannot take logarithm of zero +SELECT log('10'::numeric, '0'); +ERROR: cannot take logarithm of zero +SELECT log('-inf'::numeric, '10'); +ERROR: cannot take logarithm of a negative number +SELECT log('10'::numeric, '-inf'); +ERROR: cannot take logarithm of a negative number +SELECT log('inf'::numeric, '0'); +ERROR: cannot take logarithm of zero +SELECT log('inf'::numeric, '-inf'); +ERROR: cannot take logarithm of a negative number +SELECT log('-inf'::numeric, 'inf'); +ERROR: cannot take logarithm of a negative number +WITH v(x) AS + (VALUES('0'::numeric),('1'),('2'),('4.2'),('inf'),('nan')) +SELECT x1, x2, + power(x1, x2) +FROM v AS v1(x1), v AS v2(x2) WHERE x1 != 0 OR x2 >= 0; + x1 | x2 | power +----------+----------+--------------------- + 0 | 0 | 1.0000000000000000 + 0 | 1 | 0.0000000000000000 + 0 | 2 | 0.0000000000000000 + 0 | 4.2 | 0.0000000000000000 + 0 | Infinity | 0 + 0 | NaN | NaN + 1 | 0 | 1.0000000000000000 + 1 | 1 | 1.0000000000000000 + 1 | 2 | 1.0000000000000000 + 1 | 4.2 | 1.0000000000000000 + 1 | Infinity | 1 + 1 | NaN | 1 + 2 | 0 | 1.0000000000000000 + 2 | 1 | 2.0000000000000000 + 2 | 2 | 4.0000000000000000 + 2 | 4.2 | 18.379173679952560 + 2 | Infinity | Infinity + 2 | NaN | NaN + 4.2 | 0 | 1.0000000000000000 + 4.2 | 1 | 4.2000000000000000 + 4.2 | 2 | 17.6400000000000000 + 4.2 | 4.2 | 414.61691860129675 + 4.2 | Infinity | Infinity + 4.2 | NaN | NaN + Infinity | 0 | 1 + Infinity | 1 | Infinity + Infinity | 2 | Infinity + Infinity | 4.2 | Infinity + Infinity | Infinity | Infinity + Infinity | NaN | NaN + NaN | 0 | 1 + NaN | 1 | NaN + NaN | 2 | NaN + NaN | 4.2 | NaN + NaN | Infinity | NaN + NaN | NaN | NaN +(36 rows) + +SELECT power('0'::numeric, '-1'); +ERROR: zero raised to a negative power is undefined +SELECT power('0'::numeric, '-inf'); +ERROR: zero raised to a negative power is undefined +SELECT power('-1'::numeric, 'inf'); + power +------- + 1 +(1 row) + +SELECT power('-2'::numeric, '3'); + power +--------------------- + -8.0000000000000000 +(1 row) + +SELECT power('-2'::numeric, '3.3'); +ERROR: a negative number raised to a non-integer power yields a complex result +SELECT power('-2'::numeric, '-1'); + power +--------------------- + -0.5000000000000000 +(1 row) + +SELECT power('-2'::numeric, '-1.5'); +ERROR: a negative number raised to a non-integer power yields a complex result +SELECT power('-2'::numeric, 'inf'); + power +---------- + Infinity +(1 row) + +SELECT power('-2'::numeric, '-inf'); + power +------- + 0 +(1 row) + +SELECT power('inf'::numeric, '-2'); + power +------- + 0 +(1 row) + +SELECT power('inf'::numeric, '-inf'); + power +------- + 0 +(1 row) + +SELECT power('-inf'::numeric, '2'); + power +---------- + Infinity +(1 row) + +SELECT power('-inf'::numeric, '3'); + power +----------- + -Infinity +(1 row) + +SELECT power('-inf'::numeric, '4.5'); +ERROR: a negative number raised to a non-integer power yields a complex result +SELECT power('-inf'::numeric, '-2'); + power +------- + 0 +(1 row) + +SELECT power('-inf'::numeric, '-3'); + power +------- + 0 +(1 row) + +SELECT power('-inf'::numeric, '0'); + power +------- + 1 +(1 row) + +SELECT power('-inf'::numeric, 'inf'); + power +---------- + Infinity +(1 row) + +SELECT power('-inf'::numeric, '-inf'); + power +------- + 0 +(1 row) + +-- ****************************** +-- * miscellaneous checks for things that have been broken in the past... +-- ****************************** +-- numeric AVG used to fail on some platforms +SELECT AVG(val) FROM num_data; + avg +------------------------ + -13430913.592242320700 +(1 row) + +SELECT MAX(val) FROM num_data; + max +-------------------- + 7799461.4119000000 +(1 row) + +SELECT MIN(val) FROM num_data; + min +---------------------- + -83028485.0000000000 +(1 row) + +SELECT STDDEV(val) FROM num_data; + stddev +------------------------------- + 27791203.28758835329805617386 +(1 row) + +SELECT VARIANCE(val) FROM num_data; + variance +-------------------------------------- + 772350980172061.69659105821915863601 +(1 row) + +-- Check for appropriate rounding and overflow +CREATE TABLE fract_only (id int, val numeric(4,4)); +INSERT INTO fract_only VALUES (1, '0.0'); +INSERT INTO fract_only VALUES (2, '0.1'); +INSERT INTO fract_only VALUES (3, '1.0'); -- should fail +ERROR: numeric field overflow +DETAIL: A field with precision 4, scale 4 must round to an absolute value less than 1. +INSERT INTO fract_only VALUES (4, '-0.9999'); +INSERT INTO fract_only VALUES (5, '0.99994'); +INSERT INTO fract_only VALUES (6, '0.99995'); -- should fail +ERROR: numeric field overflow +DETAIL: A field with precision 4, scale 4 must round to an absolute value less than 1. +INSERT INTO fract_only VALUES (7, '0.00001'); +INSERT INTO fract_only VALUES (8, '0.00017'); +INSERT INTO fract_only VALUES (9, 'NaN'); +INSERT INTO fract_only VALUES (10, 'Inf'); -- should fail +ERROR: numeric field overflow +DETAIL: A field with precision 4, scale 4 cannot hold an infinite value. +INSERT INTO fract_only VALUES (11, '-Inf'); -- should fail +ERROR: numeric field overflow +DETAIL: A field with precision 4, scale 4 cannot hold an infinite value. +SELECT * FROM fract_only; + id | val +----+--------- + 1 | 0.0000 + 2 | 0.1000 + 4 | -0.9999 + 5 | 0.9999 + 7 | 0.0000 + 8 | 0.0002 + 9 | NaN +(7 rows) + +DROP TABLE fract_only; +-- Check conversion to integers +SELECT (-9223372036854775808.5)::int8; -- should fail +ERROR: bigint out of range +SELECT (-9223372036854775808.4)::int8; -- ok + int8 +---------------------- + -9223372036854775808 +(1 row) + +SELECT 9223372036854775807.4::int8; -- ok + int8 +--------------------- + 9223372036854775807 +(1 row) + +SELECT 9223372036854775807.5::int8; -- should fail +ERROR: bigint out of range +SELECT (-2147483648.5)::int4; -- should fail +ERROR: integer out of range +SELECT (-2147483648.4)::int4; -- ok + int4 +------------- + -2147483648 +(1 row) + +SELECT 2147483647.4::int4; -- ok + int4 +------------ + 2147483647 +(1 row) + +SELECT 2147483647.5::int4; -- should fail +ERROR: integer out of range +SELECT (-32768.5)::int2; -- should fail +ERROR: smallint out of range +SELECT (-32768.4)::int2; -- ok + int2 +-------- + -32768 +(1 row) + +SELECT 32767.4::int2; -- ok + int2 +------- + 32767 +(1 row) + +SELECT 32767.5::int2; -- should fail +ERROR: smallint out of range +-- Check inf/nan conversion behavior +SELECT 'NaN'::float8::numeric; + numeric +--------- + NaN +(1 row) + +SELECT 'Infinity'::float8::numeric; + numeric +---------- + Infinity +(1 row) + +SELECT '-Infinity'::float8::numeric; + numeric +----------- + -Infinity +(1 row) + +SELECT 'NaN'::numeric::float8; + float8 +-------- + NaN +(1 row) + +SELECT 'Infinity'::numeric::float8; + float8 +---------- + Infinity +(1 row) + +SELECT '-Infinity'::numeric::float8; + float8 +----------- + -Infinity +(1 row) + +SELECT 'NaN'::float4::numeric; + numeric +--------- + NaN +(1 row) + +SELECT 'Infinity'::float4::numeric; + numeric +---------- + Infinity +(1 row) + +SELECT '-Infinity'::float4::numeric; + numeric +----------- + -Infinity +(1 row) + +SELECT 'NaN'::numeric::float4; + float4 +-------- + NaN +(1 row) + +SELECT 'Infinity'::numeric::float4; + float4 +---------- + Infinity +(1 row) + +SELECT '-Infinity'::numeric::float4; + float4 +----------- + -Infinity +(1 row) + +SELECT '42'::int2::numeric; + numeric +--------- + 42 +(1 row) + +SELECT 'NaN'::numeric::int2; +ERROR: cannot convert NaN to smallint +SELECT 'Infinity'::numeric::int2; +ERROR: cannot convert infinity to smallint +SELECT '-Infinity'::numeric::int2; +ERROR: cannot convert infinity to smallint +SELECT 'NaN'::numeric::int4; +ERROR: cannot convert NaN to integer +SELECT 'Infinity'::numeric::int4; +ERROR: cannot convert infinity to integer +SELECT '-Infinity'::numeric::int4; +ERROR: cannot convert infinity to integer +SELECT 'NaN'::numeric::int8; +ERROR: cannot convert NaN to bigint +SELECT 'Infinity'::numeric::int8; +ERROR: cannot convert infinity to bigint +SELECT '-Infinity'::numeric::int8; +ERROR: cannot convert infinity to bigint +-- Simple check that ceil(), floor(), and round() work correctly +CREATE TABLE ceil_floor_round (a numeric); +INSERT INTO ceil_floor_round VALUES ('-5.5'); +INSERT INTO ceil_floor_round VALUES ('-5.499999'); +INSERT INTO ceil_floor_round VALUES ('9.5'); +INSERT INTO ceil_floor_round VALUES ('9.4999999'); +INSERT INTO ceil_floor_round VALUES ('0.0'); +INSERT INTO ceil_floor_round VALUES ('0.0000001'); +INSERT INTO ceil_floor_round VALUES ('-0.000001'); +SELECT a, ceil(a), ceiling(a), floor(a), round(a) FROM ceil_floor_round; + a | ceil | ceiling | floor | round +-----------+------+---------+-------+------- + -5.5 | -5 | -5 | -6 | -6 + -5.499999 | -5 | -5 | -6 | -5 + 9.5 | 10 | 10 | 9 | 10 + 9.4999999 | 10 | 10 | 9 | 9 + 0.0 | 0 | 0 | 0 | 0 + 0.0000001 | 1 | 1 | 0 | 0 + -0.000001 | 0 | 0 | -1 | 0 +(7 rows) + +DROP TABLE ceil_floor_round; +-- Check rounding, it should round ties away from zero. +SELECT i as pow, + round((-2.5 * 10 ^ i)::numeric, -i), + round((-1.5 * 10 ^ i)::numeric, -i), + round((-0.5 * 10 ^ i)::numeric, -i), + round((0.5 * 10 ^ i)::numeric, -i), + round((1.5 * 10 ^ i)::numeric, -i), + round((2.5 * 10 ^ i)::numeric, -i) +FROM generate_series(-5,5) AS t(i); + pow | round | round | round | round | round | round +-----+----------+----------+----------+---------+---------+--------- + -5 | -0.00003 | -0.00002 | -0.00001 | 0.00001 | 0.00002 | 0.00003 + -4 | -0.0003 | -0.0002 | -0.0001 | 0.0001 | 0.0002 | 0.0003 + -3 | -0.003 | -0.002 | -0.001 | 0.001 | 0.002 | 0.003 + -2 | -0.03 | -0.02 | -0.01 | 0.01 | 0.02 | 0.03 + -1 | -0.3 | -0.2 | -0.1 | 0.1 | 0.2 | 0.3 + 0 | -3 | -2 | -1 | 1 | 2 | 3 + 1 | -30 | -20 | -10 | 10 | 20 | 30 + 2 | -300 | -200 | -100 | 100 | 200 | 300 + 3 | -3000 | -2000 | -1000 | 1000 | 2000 | 3000 + 4 | -30000 | -20000 | -10000 | 10000 | 20000 | 30000 + 5 | -300000 | -200000 | -100000 | 100000 | 200000 | 300000 +(11 rows) + +-- Testing for width_bucket(). For convenience, we test both the +-- numeric and float8 versions of the function in this file. +-- errors +SELECT width_bucket(5.0, 3.0, 4.0, 0); +ERROR: count must be greater than zero +SELECT width_bucket(5.0, 3.0, 4.0, -5); +ERROR: count must be greater than zero +SELECT width_bucket(3.5, 3.0, 3.0, 888); +ERROR: lower bound cannot equal upper bound +SELECT width_bucket(5.0::float8, 3.0::float8, 4.0::float8, 0); +ERROR: count must be greater than zero +SELECT width_bucket(5.0::float8, 3.0::float8, 4.0::float8, -5); +ERROR: count must be greater than zero +SELECT width_bucket(3.5::float8, 3.0::float8, 3.0::float8, 888); +ERROR: lower bound cannot equal upper bound +SELECT width_bucket('NaN', 3.0, 4.0, 888); +ERROR: operand, lower bound, and upper bound cannot be NaN +SELECT width_bucket(0::float8, 'NaN', 4.0::float8, 888); +ERROR: operand, lower bound, and upper bound cannot be NaN +SELECT width_bucket(2.0, 3.0, '-inf', 888); +ERROR: lower and upper bounds must be finite +SELECT width_bucket(0::float8, '-inf', 4.0::float8, 888); +ERROR: lower and upper bounds must be finite +-- normal operation +CREATE TABLE width_bucket_test (operand_num numeric, operand_f8 float8); +COPY width_bucket_test (operand_num) FROM stdin; +UPDATE width_bucket_test SET operand_f8 = operand_num::float8; +SELECT + operand_num, + width_bucket(operand_num, 0, 10, 5) AS wb_1, + width_bucket(operand_f8, 0, 10, 5) AS wb_1f, + width_bucket(operand_num, 10, 0, 5) AS wb_2, + width_bucket(operand_f8, 10, 0, 5) AS wb_2f, + width_bucket(operand_num, 2, 8, 4) AS wb_3, + width_bucket(operand_f8, 2, 8, 4) AS wb_3f, + width_bucket(operand_num, 5.0, 5.5, 20) AS wb_4, + width_bucket(operand_f8, 5.0, 5.5, 20) AS wb_4f, + width_bucket(operand_num, -25, 25, 10) AS wb_5, + width_bucket(operand_f8, -25, 25, 10) AS wb_5f + FROM width_bucket_test; + operand_num | wb_1 | wb_1f | wb_2 | wb_2f | wb_3 | wb_3f | wb_4 | wb_4f | wb_5 | wb_5f +------------------+------+-------+------+-------+------+-------+------+-------+------+------- + -5.2 | 0 | 0 | 6 | 6 | 0 | 0 | 0 | 0 | 4 | 4 + -0.0000000001 | 0 | 0 | 6 | 6 | 0 | 0 | 0 | 0 | 5 | 5 + 0.000000000001 | 1 | 1 | 5 | 5 | 0 | 0 | 0 | 0 | 6 | 6 + 1 | 1 | 1 | 5 | 5 | 0 | 0 | 0 | 0 | 6 | 6 + 1.99999999999999 | 1 | 1 | 5 | 5 | 0 | 0 | 0 | 0 | 6 | 6 + 2 | 2 | 2 | 5 | 5 | 1 | 1 | 0 | 0 | 6 | 6 + 2.00000000000001 | 2 | 2 | 4 | 4 | 1 | 1 | 0 | 0 | 6 | 6 + 3 | 2 | 2 | 4 | 4 | 1 | 1 | 0 | 0 | 6 | 6 + 4 | 3 | 3 | 4 | 4 | 2 | 2 | 0 | 0 | 6 | 6 + 4.5 | 3 | 3 | 3 | 3 | 2 | 2 | 0 | 0 | 6 | 6 + 5 | 3 | 3 | 3 | 3 | 3 | 3 | 1 | 1 | 7 | 7 + 5.5 | 3 | 3 | 3 | 3 | 3 | 3 | 21 | 21 | 7 | 7 + 6 | 4 | 4 | 3 | 3 | 3 | 3 | 21 | 21 | 7 | 7 + 7 | 4 | 4 | 2 | 2 | 4 | 4 | 21 | 21 | 7 | 7 + 8 | 5 | 5 | 2 | 2 | 5 | 5 | 21 | 21 | 7 | 7 + 9 | 5 | 5 | 1 | 1 | 5 | 5 | 21 | 21 | 7 | 7 + 9.99999999999999 | 5 | 5 | 1 | 1 | 5 | 5 | 21 | 21 | 7 | 7 + 10 | 6 | 6 | 1 | 1 | 5 | 5 | 21 | 21 | 8 | 8 + 10.0000000000001 | 6 | 6 | 0 | 0 | 5 | 5 | 21 | 21 | 8 | 8 +(19 rows) + +-- Check positive and negative infinity: we require +-- finite bucket bounds, but allow an infinite operand +SELECT width_bucket(0.0::numeric, 'Infinity'::numeric, 5, 10); -- error +ERROR: lower and upper bounds must be finite +SELECT width_bucket(0.0::numeric, 5, '-Infinity'::numeric, 20); -- error +ERROR: lower and upper bounds must be finite +SELECT width_bucket('Infinity'::numeric, 1, 10, 10), + width_bucket('-Infinity'::numeric, 1, 10, 10); + width_bucket | width_bucket +--------------+-------------- + 11 | 0 +(1 row) + +SELECT width_bucket(0.0::float8, 'Infinity'::float8, 5, 10); -- error +ERROR: lower and upper bounds must be finite +SELECT width_bucket(0.0::float8, 5, '-Infinity'::float8, 20); -- error +ERROR: lower and upper bounds must be finite +SELECT width_bucket('Infinity'::float8, 1, 10, 10), + width_bucket('-Infinity'::float8, 1, 10, 10); + width_bucket | width_bucket +--------------+-------------- + 11 | 0 +(1 row) + +DROP TABLE width_bucket_test; +-- Simple test for roundoff error when results should be exact +SELECT x, width_bucket(x::float8, 10, 100, 9) as flt, + width_bucket(x::numeric, 10, 100, 9) as num +FROM generate_series(0, 110, 10) x; + x | flt | num +-----+-----+----- + 0 | 0 | 0 + 10 | 1 | 1 + 20 | 2 | 2 + 30 | 3 | 3 + 40 | 4 | 4 + 50 | 5 | 5 + 60 | 6 | 6 + 70 | 7 | 7 + 80 | 8 | 8 + 90 | 9 | 9 + 100 | 10 | 10 + 110 | 10 | 10 +(12 rows) + +SELECT x, width_bucket(x::float8, 100, 10, 9) as flt, + width_bucket(x::numeric, 100, 10, 9) as num +FROM generate_series(0, 110, 10) x; + x | flt | num +-----+-----+----- + 0 | 10 | 10 + 10 | 10 | 10 + 20 | 9 | 9 + 30 | 8 | 8 + 40 | 7 | 7 + 50 | 6 | 6 + 60 | 5 | 5 + 70 | 4 | 4 + 80 | 3 | 3 + 90 | 2 | 2 + 100 | 1 | 1 + 110 | 0 | 0 +(12 rows) + +-- +-- TO_CHAR() +-- +SELECT to_char(val, '9G999G999G999G999G999') + FROM num_data; + to_char +------------------------ + 0 + 0 + -34,338,492 + 4 + 7,799,461 + 16,397 + 93,902 + -83,028,485 + 74,881 + -24,926,804 +(10 rows) + +SELECT to_char(val, '9G999G999G999G999G999D999G999G999G999G999') + FROM num_data; + to_char +-------------------------------------------- + .000,000,000,000,000 + .000,000,000,000,000 + -34,338,492.215,397,047,000,000 + 4.310,000,000,000,000 + 7,799,461.411,900,000,000,000 + 16,397.038,491,000,000,000 + 93,901.577,630,260,000,000 + -83,028,485.000,000,000,000,000 + 74,881.000,000,000,000,000 + -24,926,804.045,047,420,000,000 +(10 rows) + +SELECT to_char(val, '9999999999999999.999999999999999PR') + FROM num_data; + to_char +------------------------------------ + .000000000000000 + .000000000000000 + <34338492.215397047000000> + 4.310000000000000 + 7799461.411900000000000 + 16397.038491000000000 + 93901.577630260000000 + <83028485.000000000000000> + 74881.000000000000000 + <24926804.045047420000000> +(10 rows) + +SELECT to_char(val, '9999999999999999.999999999999999S') + FROM num_data; + to_char +----------------------------------- + .000000000000000+ + .000000000000000+ + 34338492.215397047000000- + 4.310000000000000+ + 7799461.411900000000000+ + 16397.038491000000000+ + 93901.577630260000000+ + 83028485.000000000000000- + 74881.000000000000000+ + 24926804.045047420000000- +(10 rows) + +SELECT to_char(val, 'MI9999999999999999.999999999999999') FROM num_data; + to_char +----------------------------------- + .000000000000000 + .000000000000000 + - 34338492.215397047000000 + 4.310000000000000 + 7799461.411900000000000 + 16397.038491000000000 + 93901.577630260000000 + - 83028485.000000000000000 + 74881.000000000000000 + - 24926804.045047420000000 +(10 rows) + +SELECT to_char(val, 'FMS9999999999999999.999999999999999') FROM num_data; + to_char +--------------------- + +0. + +0. + -34338492.215397047 + +4.31 + +7799461.4119 + +16397.038491 + +93901.57763026 + -83028485. + +74881. + -24926804.04504742 +(10 rows) + +SELECT to_char(val, 'FM9999999999999999.999999999999999THPR') FROM num_data; + to_char +---------------------- + 0. + 0. + <34338492.215397047> + 4.31 + 7799461.4119 + 16397.038491 + 93901.57763026 + <83028485.> + 74881. + <24926804.04504742> +(10 rows) + +SELECT to_char(val, 'SG9999999999999999.999999999999999th') FROM num_data; + to_char +----------------------------------- + + .000000000000000 + + .000000000000000 + - 34338492.215397047000000 + + 4.310000000000000 + + 7799461.411900000000000 + + 16397.038491000000000 + + 93901.577630260000000 + - 83028485.000000000000000 + + 74881.000000000000000 + - 24926804.045047420000000 +(10 rows) + +SELECT to_char(val, '0999999999999999.999999999999999') FROM num_data; + to_char +----------------------------------- + 0000000000000000.000000000000000 + 0000000000000000.000000000000000 + -0000000034338492.215397047000000 + 0000000000000004.310000000000000 + 0000000007799461.411900000000000 + 0000000000016397.038491000000000 + 0000000000093901.577630260000000 + -0000000083028485.000000000000000 + 0000000000074881.000000000000000 + -0000000024926804.045047420000000 +(10 rows) + +SELECT to_char(val, 'S0999999999999999.999999999999999') FROM num_data; + to_char +----------------------------------- + +0000000000000000.000000000000000 + +0000000000000000.000000000000000 + -0000000034338492.215397047000000 + +0000000000000004.310000000000000 + +0000000007799461.411900000000000 + +0000000000016397.038491000000000 + +0000000000093901.577630260000000 + -0000000083028485.000000000000000 + +0000000000074881.000000000000000 + -0000000024926804.045047420000000 +(10 rows) + +SELECT to_char(val, 'FM0999999999999999.999999999999999') FROM num_data; + to_char +----------------------------- + 0000000000000000. + 0000000000000000. + -0000000034338492.215397047 + 0000000000000004.31 + 0000000007799461.4119 + 0000000000016397.038491 + 0000000000093901.57763026 + -0000000083028485. + 0000000000074881. + -0000000024926804.04504742 +(10 rows) + +SELECT to_char(val, 'FM9999999999999999.099999999999999') FROM num_data; + to_char +--------------------- + .0 + .0 + -34338492.215397047 + 4.31 + 7799461.4119 + 16397.038491 + 93901.57763026 + -83028485.0 + 74881.0 + -24926804.04504742 +(10 rows) + +SELECT to_char(val, 'FM9999999999990999.990999999999999') FROM num_data; + to_char +--------------------- + 0000.000 + 0000.000 + -34338492.215397047 + 0004.310 + 7799461.4119 + 16397.038491 + 93901.57763026 + -83028485.000 + 74881.000 + -24926804.04504742 +(10 rows) + +SELECT to_char(val, 'FM0999999999999999.999909999999999') FROM num_data; + to_char +----------------------------- + 0000000000000000.00000 + 0000000000000000.00000 + -0000000034338492.215397047 + 0000000000000004.31000 + 0000000007799461.41190 + 0000000000016397.038491 + 0000000000093901.57763026 + -0000000083028485.00000 + 0000000000074881.00000 + -0000000024926804.04504742 +(10 rows) + +SELECT to_char(val, 'FM9999999990999999.099999999999999') FROM num_data; + to_char +--------------------- + 0000000.0 + 0000000.0 + -34338492.215397047 + 0000004.31 + 7799461.4119 + 0016397.038491 + 0093901.57763026 + -83028485.0 + 0074881.0 + -24926804.04504742 +(10 rows) + +SELECT to_char(val, 'L9999999999999999.099999999999999') FROM num_data; + to_char +------------------------------------ + .000000000000000 + .000000000000000 + -34338492.215397047000000 + 4.310000000000000 + 7799461.411900000000000 + 16397.038491000000000 + 93901.577630260000000 + -83028485.000000000000000 + 74881.000000000000000 + -24926804.045047420000000 +(10 rows) + +SELECT to_char(val, 'FM9999999999999999.99999999999999') FROM num_data; + to_char +--------------------- + 0. + 0. + -34338492.215397047 + 4.31 + 7799461.4119 + 16397.038491 + 93901.57763026 + -83028485. + 74881. + -24926804.04504742 +(10 rows) + +SELECT to_char(val, 'S 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 . 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9') FROM num_data; + to_char +----------------------------------------------------------------------- + +. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + +. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + -3 4 3 3 8 4 9 2 . 2 1 5 3 9 7 0 4 7 0 0 0 0 0 0 0 0 + +4 . 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + +7 7 9 9 4 6 1 . 4 1 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 + +1 6 3 9 7 . 0 3 8 4 9 1 0 0 0 0 0 0 0 0 0 0 0 + +9 3 9 0 1 . 5 7 7 6 3 0 2 6 0 0 0 0 0 0 0 0 0 + -8 3 0 2 8 4 8 5 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + +7 4 8 8 1 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + -2 4 9 2 6 8 0 4 . 0 4 5 0 4 7 4 2 0 0 0 0 0 0 0 0 0 +(10 rows) + +SELECT to_char(val, 'FMS 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 . 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9') FROM num_data; + to_char +------------------------------------------------------- + +0 . + +0 . + -3 4 3 3 8 4 9 2 . 2 1 5 3 9 7 0 4 7 + +4 . 3 1 + +7 7 9 9 4 6 1 . 4 1 1 9 + +1 6 3 9 7 . 0 3 8 4 9 1 + +9 3 9 0 1 . 5 7 7 6 3 0 2 6 + -8 3 0 2 8 4 8 5 . + +7 4 8 8 1 . + -2 4 9 2 6 8 0 4 . 0 4 5 0 4 7 4 2 +(10 rows) + +SELECT to_char(val, E'99999 "text" 9999 "9999" 999 "\\"text between quote marks\\"" 9999') FROM num_data; + to_char +----------------------------------------------------------- + text 9999 "text between quote marks" 0 + text 9999 "text between quote marks" 0 + text -3 9999 433 "text between quote marks" 8492 + text 9999 "text between quote marks" 4 + text 9999 779 "text between quote marks" 9461 + text 9999 1 "text between quote marks" 6397 + text 9999 9 "text between quote marks" 3902 + text -8 9999 302 "text between quote marks" 8485 + text 9999 7 "text between quote marks" 4881 + text -2 9999 492 "text between quote marks" 6804 +(10 rows) + +SELECT to_char(val, '999999SG9999999999') FROM num_data; + to_char +------------------- + + 0 + + 0 + - 34338492 + + 4 + + 7799461 + + 16397 + + 93902 + - 83028485 + + 74881 + - 24926804 +(10 rows) + +SELECT to_char(val, 'FM9999999999999999.999999999999999') FROM num_data; + to_char +--------------------- + 0. + 0. + -34338492.215397047 + 4.31 + 7799461.4119 + 16397.038491 + 93901.57763026 + -83028485. + 74881. + -24926804.04504742 +(10 rows) + +SELECT to_char(val, '9.999EEEE') FROM num_data; + to_char +------------ + 0.000e+00 + 0.000e+00 + -3.434e+07 + 4.310e+00 + 7.799e+06 + 1.640e+04 + 9.390e+04 + -8.303e+07 + 7.488e+04 + -2.493e+07 +(10 rows) + +WITH v(val) AS + (VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan')) +SELECT val, + to_char(val, '9.999EEEE') as numeric, + to_char(val::float8, '9.999EEEE') as float8, + to_char(val::float4, '9.999EEEE') as float4 +FROM v; + val | numeric | float8 | float4 +------------+------------+------------+------------ + 0 | 0.000e+00 | 0.000e+00 | 0.000e+00 + -4.2 | -4.200e+00 | -4.200e+00 | -4.200e+00 + 4200000000 | 4.200e+09 | 4.200e+09 | 4.200e+09 + 0.000012 | 1.200e-05 | 1.200e-05 | 1.200e-05 + Infinity | #.####### | #.####### | #.####### + -Infinity | #.####### | #.####### | #.####### + NaN | #.####### | #.####### | #.####### +(7 rows) + +WITH v(exp) AS + (VALUES(-16379),(-16378),(-1234),(-789),(-45),(-5),(-4),(-3),(-2),(-1),(0), + (1),(2),(3),(4),(5),(38),(275),(2345),(45678),(131070),(131071)) +SELECT exp, + to_char(('1.2345e'||exp)::numeric, '9.999EEEE') as numeric +FROM v; + exp | numeric +--------+---------------- + -16379 | 1.235e-16379 + -16378 | 1.235e-16378 + -1234 | 1.235e-1234 + -789 | 1.235e-789 + -45 | 1.235e-45 + -5 | 1.235e-05 + -4 | 1.235e-04 + -3 | 1.235e-03 + -2 | 1.235e-02 + -1 | 1.235e-01 + 0 | 1.235e+00 + 1 | 1.235e+01 + 2 | 1.235e+02 + 3 | 1.235e+03 + 4 | 1.235e+04 + 5 | 1.235e+05 + 38 | 1.235e+38 + 275 | 1.235e+275 + 2345 | 1.235e+2345 + 45678 | 1.235e+45678 + 131070 | 1.235e+131070 + 131071 | 1.235e+131071 +(22 rows) + +WITH v(val) AS + (VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan')) +SELECT val, + to_char(val, 'MI9999999999.99') as numeric, + to_char(val::float8, 'MI9999999999.99') as float8, + to_char(val::float4, 'MI9999999999.99') as float4 +FROM v; + val | numeric | float8 | float4 +------------+----------------+----------------+---------------- + 0 | .00 | .00 | .00 + -4.2 | - 4.20 | - 4.20 | - 4.20 + 4200000000 | 4200000000.00 | 4200000000.00 | 4200000000 + 0.000012 | .00 | .00 | .00 + Infinity | Infinity | Infinity | Infinity + -Infinity | - Infinity | - Infinity | - Infinity + NaN | NaN | NaN | NaN +(7 rows) + +WITH v(val) AS + (VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan')) +SELECT val, + to_char(val, 'MI99.99') as numeric, + to_char(val::float8, 'MI99.99') as float8, + to_char(val::float4, 'MI99.99') as float4 +FROM v; + val | numeric | float8 | float4 +------------+---------+--------+-------- + 0 | .00 | .00 | .00 + -4.2 | - 4.20 | - 4.20 | - 4.20 + 4200000000 | ##.## | ##.## | ##. + 0.000012 | .00 | .00 | .00 + Infinity | ##.## | ##.## | ##. + -Infinity | -##.## | -##.## | -##. + NaN | ##.## | ##.## | ##.## +(7 rows) + +SELECT to_char('100'::numeric, 'FM999.9'); + to_char +--------- + 100. +(1 row) + +SELECT to_char('100'::numeric, 'FM999.'); + to_char +--------- + 100 +(1 row) + +SELECT to_char('100'::numeric, 'FM999'); + to_char +--------- + 100 +(1 row) + +SELECT to_char('12345678901'::float8, 'FM9999999999D9999900000000000000000'); + to_char +----------------- + ##########.#### +(1 row) + +-- Check parsing of literal text in a format string +SELECT to_char('100'::numeric, 'foo999'); + to_char +--------- + foo 100 +(1 row) + +SELECT to_char('100'::numeric, 'f\oo999'); + to_char +---------- + f\oo 100 +(1 row) + +SELECT to_char('100'::numeric, 'f\\oo999'); + to_char +----------- + f\\oo 100 +(1 row) + +SELECT to_char('100'::numeric, 'f\"oo999'); + to_char +---------- + f"oo 100 +(1 row) + +SELECT to_char('100'::numeric, 'f\\"oo999'); + to_char +----------- + f\"oo 100 +(1 row) + +SELECT to_char('100'::numeric, 'f"ool"999'); + to_char +---------- + fool 100 +(1 row) + +SELECT to_char('100'::numeric, 'f"\ool"999'); + to_char +---------- + fool 100 +(1 row) + +SELECT to_char('100'::numeric, 'f"\\ool"999'); + to_char +----------- + f\ool 100 +(1 row) + +SELECT to_char('100'::numeric, 'f"ool\"999'); + to_char +---------- + fool"999 +(1 row) + +SELECT to_char('100'::numeric, 'f"ool\\"999'); + to_char +----------- + fool\ 100 +(1 row) + +-- TO_NUMBER() +-- +SET lc_numeric = 'C'; +SELECT to_number('-34,338,492', '99G999G999'); + to_number +----------- + -34338492 +(1 row) + +SELECT to_number('-34,338,492.654,878', '99G999G999D999G999'); + to_number +------------------ + -34338492.654878 +(1 row) + +SELECT to_number('<564646.654564>', '999999.999999PR'); + to_number +---------------- + -564646.654564 +(1 row) + +SELECT to_number('0.00001-', '9.999999S'); + to_number +----------- + -0.00001 +(1 row) + +SELECT to_number('5.01-', 'FM9.999999S'); + to_number +----------- + -5.01 +(1 row) + +SELECT to_number('5.01-', 'FM9.999999MI'); + to_number +----------- + -5.01 +(1 row) + +SELECT to_number('5 4 4 4 4 8 . 7 8', '9 9 9 9 9 9 . 9 9'); + to_number +----------- + 544448.78 +(1 row) + +SELECT to_number('.01', 'FM9.99'); + to_number +----------- + 0.01 +(1 row) + +SELECT to_number('.0', '99999999.99999999'); + to_number +----------- + 0.0 +(1 row) + +SELECT to_number('0', '99.99'); + to_number +----------- + 0 +(1 row) + +SELECT to_number('.-01', 'S99.99'); + to_number +----------- + -0.01 +(1 row) + +SELECT to_number('.01-', '99.99S'); + to_number +----------- + -0.01 +(1 row) + +SELECT to_number(' . 0 1-', ' 9 9 . 9 9 S'); + to_number +----------- + -0.01 +(1 row) + +SELECT to_number('34,50','999,99'); + to_number +----------- + 3450 +(1 row) + +SELECT to_number('123,000','999G'); + to_number +----------- + 123 +(1 row) + +SELECT to_number('123456','999G999'); + to_number +----------- + 123456 +(1 row) + +SELECT to_number('$1234.56','L9,999.99'); + to_number +----------- + 1234.56 +(1 row) + +SELECT to_number('$1234.56','L99,999.99'); + to_number +----------- + 1234.56 +(1 row) + +SELECT to_number('$1,234.56','L99,999.99'); + to_number +----------- + 1234.56 +(1 row) + +SELECT to_number('1234.56','L99,999.99'); + to_number +----------- + 1234.56 +(1 row) + +SELECT to_number('1,234.56','L99,999.99'); + to_number +----------- + 1234.56 +(1 row) + +SELECT to_number('42nd', '99th'); + to_number +----------- + 42 +(1 row) + +RESET lc_numeric; +-- +-- Input syntax +-- +CREATE TABLE num_input_test (n1 numeric); +-- good inputs +INSERT INTO num_input_test(n1) VALUES (' 123'); +INSERT INTO num_input_test(n1) VALUES (' 3245874 '); +INSERT INTO num_input_test(n1) VALUES (' -93853'); +INSERT INTO num_input_test(n1) VALUES ('555.50'); +INSERT INTO num_input_test(n1) VALUES ('-555.50'); +INSERT INTO num_input_test(n1) VALUES ('NaN '); +INSERT INTO num_input_test(n1) VALUES (' nan'); +INSERT INTO num_input_test(n1) VALUES (' inf '); +INSERT INTO num_input_test(n1) VALUES (' +inf '); +INSERT INTO num_input_test(n1) VALUES (' -inf '); +INSERT INTO num_input_test(n1) VALUES (' Infinity '); +INSERT INTO num_input_test(n1) VALUES (' +inFinity '); +INSERT INTO num_input_test(n1) VALUES (' -INFINITY '); +-- bad inputs +INSERT INTO num_input_test(n1) VALUES (' '); +ERROR: invalid input syntax for type numeric: " " +LINE 1: INSERT INTO num_input_test(n1) VALUES (' '); + ^ +INSERT INTO num_input_test(n1) VALUES (' 1234 %'); +ERROR: invalid input syntax for type numeric: " 1234 %" +LINE 1: INSERT INTO num_input_test(n1) VALUES (' 1234 %'); + ^ +INSERT INTO num_input_test(n1) VALUES ('xyz'); +ERROR: invalid input syntax for type numeric: "xyz" +LINE 1: INSERT INTO num_input_test(n1) VALUES ('xyz'); + ^ +INSERT INTO num_input_test(n1) VALUES ('- 1234'); +ERROR: invalid input syntax for type numeric: "- 1234" +LINE 1: INSERT INTO num_input_test(n1) VALUES ('- 1234'); + ^ +INSERT INTO num_input_test(n1) VALUES ('5 . 0'); +ERROR: invalid input syntax for type numeric: "5 . 0" +LINE 1: INSERT INTO num_input_test(n1) VALUES ('5 . 0'); + ^ +INSERT INTO num_input_test(n1) VALUES ('5. 0 '); +ERROR: invalid input syntax for type numeric: "5. 0 " +LINE 1: INSERT INTO num_input_test(n1) VALUES ('5. 0 '); + ^ +INSERT INTO num_input_test(n1) VALUES (''); +ERROR: invalid input syntax for type numeric: "" +LINE 1: INSERT INTO num_input_test(n1) VALUES (''); + ^ +INSERT INTO num_input_test(n1) VALUES (' N aN '); +ERROR: invalid input syntax for type numeric: " N aN " +LINE 1: INSERT INTO num_input_test(n1) VALUES (' N aN '); + ^ +INSERT INTO num_input_test(n1) VALUES ('+ infinity'); +ERROR: invalid input syntax for type numeric: "+ infinity" +LINE 1: INSERT INTO num_input_test(n1) VALUES ('+ infinity'); + ^ +SELECT * FROM num_input_test; + n1 +----------- + 123 + 3245874 + -93853 + 555.50 + -555.50 + NaN + NaN + Infinity + Infinity + -Infinity + Infinity + Infinity + -Infinity +(13 rows) + +-- +-- Test precision and scale typemods +-- +CREATE TABLE num_typemod_test ( + millions numeric(3, -6), + thousands numeric(3, -3), + units numeric(3, 0), + thousandths numeric(3, 3), + millionths numeric(3, 6) +); +\d num_typemod_test + Table "public.num_typemod_test" + Column | Type | Collation | Nullable | Default +-------------+---------------+-----------+----------+--------- + millions | numeric(3,-6) | | | + thousands | numeric(3,-3) | | | + units | numeric(3,0) | | | + thousandths | numeric(3,3) | | | + millionths | numeric(3,6) | | | + +-- rounding of valid inputs +INSERT INTO num_typemod_test VALUES (123456, 123, 0.123, 0.000123, 0.000000123); +INSERT INTO num_typemod_test VALUES (654321, 654, 0.654, 0.000654, 0.000000654); +INSERT INTO num_typemod_test VALUES (2345678, 2345, 2.345, 0.002345, 0.000002345); +INSERT INTO num_typemod_test VALUES (7654321, 7654, 7.654, 0.007654, 0.000007654); +INSERT INTO num_typemod_test VALUES (12345678, 12345, 12.345, 0.012345, 0.000012345); +INSERT INTO num_typemod_test VALUES (87654321, 87654, 87.654, 0.087654, 0.000087654); +INSERT INTO num_typemod_test VALUES (123456789, 123456, 123.456, 0.123456, 0.000123456); +INSERT INTO num_typemod_test VALUES (987654321, 987654, 987.654, 0.987654, 0.000987654); +INSERT INTO num_typemod_test VALUES ('NaN', 'NaN', 'NaN', 'NaN', 'NaN'); +SELECT scale(millions), * FROM num_typemod_test ORDER BY millions; + scale | millions | thousands | units | thousandths | millionths +-------+-----------+-----------+-------+-------------+------------ + 0 | 0 | 0 | 0 | 0.000 | 0.000000 + 0 | 1000000 | 1000 | 1 | 0.001 | 0.000001 + 0 | 2000000 | 2000 | 2 | 0.002 | 0.000002 + 0 | 8000000 | 8000 | 8 | 0.008 | 0.000008 + 0 | 12000000 | 12000 | 12 | 0.012 | 0.000012 + 0 | 88000000 | 88000 | 88 | 0.088 | 0.000088 + 0 | 123000000 | 123000 | 123 | 0.123 | 0.000123 + 0 | 988000000 | 988000 | 988 | 0.988 | 0.000988 + | NaN | NaN | NaN | NaN | NaN +(9 rows) + +-- invalid inputs +INSERT INTO num_typemod_test (millions) VALUES ('inf'); +ERROR: numeric field overflow +DETAIL: A field with precision 3, scale -6 cannot hold an infinite value. +INSERT INTO num_typemod_test (millions) VALUES (999500000); +ERROR: numeric field overflow +DETAIL: A field with precision 3, scale -6 must round to an absolute value less than 10^9. +INSERT INTO num_typemod_test (thousands) VALUES (999500); +ERROR: numeric field overflow +DETAIL: A field with precision 3, scale -3 must round to an absolute value less than 10^6. +INSERT INTO num_typemod_test (units) VALUES (999.5); +ERROR: numeric field overflow +DETAIL: A field with precision 3, scale 0 must round to an absolute value less than 10^3. +INSERT INTO num_typemod_test (thousandths) VALUES (0.9995); +ERROR: numeric field overflow +DETAIL: A field with precision 3, scale 3 must round to an absolute value less than 1. +INSERT INTO num_typemod_test (millionths) VALUES (0.0009995); +ERROR: numeric field overflow +DETAIL: A field with precision 3, scale 6 must round to an absolute value less than 10^-3. +-- +-- Test some corner cases for multiplication +-- +select 4790999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999; + ?column? +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 47909999999999999999999999999999999999999999999999999999999999999999999999999999999999985209000000000000000000000000000000000000000000000000000000000000000000000000000000000001 +(1 row) + +select 4789999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999; + ?column? +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 47899999999999999999999999999999999999999999999999999999999999999999999999999999999999985210000000000000000000000000000000000000000000000000000000000000000000000000000000000001 +(1 row) + +select 4770999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999; + ?column? +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 47709999999999999999999999999999999999999999999999999999999999999999999999999999999999985229000000000000000000000000000000000000000000000000000000000000000000000000000000000001 +(1 row) + +select 4769999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999; + ?column? +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 47699999999999999999999999999999999999999999999999999999999999999999999999999999999999985230000000000000000000000000000000000000000000000000000000000000000000000000000000000001 +(1 row) + +select trim_scale((0.1 - 2e-16383) * (0.1 - 3e-16383)); + trim_scale +------------ + 0.01 +(1 row) + +-- +-- Test some corner cases for division +-- +select 999999999999999999999::numeric/1000000000000000000000; + ?column? +------------------------ + 1.00000000000000000000 +(1 row) + +select div(999999999999999999999::numeric,1000000000000000000000); + div +----- + 0 +(1 row) + +select mod(999999999999999999999::numeric,1000000000000000000000); + mod +----------------------- + 999999999999999999999 +(1 row) + +select div(-9999999999999999999999::numeric,1000000000000000000000); + div +----- + -9 +(1 row) + +select mod(-9999999999999999999999::numeric,1000000000000000000000); + mod +------------------------ + -999999999999999999999 +(1 row) + +select div(-9999999999999999999999::numeric,1000000000000000000000)*1000000000000000000000 + mod(-9999999999999999999999::numeric,1000000000000000000000); + ?column? +------------------------- + -9999999999999999999999 +(1 row) + +select mod (70.0,70) ; + mod +----- + 0.0 +(1 row) + +select div (70.0,70) ; + div +----- + 1 +(1 row) + +select 70.0 / 70 ; + ?column? +------------------------ + 1.00000000000000000000 +(1 row) + +select 12345678901234567890 % 123; + ?column? +---------- + 78 +(1 row) + +select 12345678901234567890 / 123; + ?column? +-------------------- + 100371373180768845 +(1 row) + +select div(12345678901234567890, 123); + div +-------------------- + 100371373180768844 +(1 row) + +select div(12345678901234567890, 123) * 123 + 12345678901234567890 % 123; + ?column? +---------------------- + 12345678901234567890 +(1 row) + +-- +-- Test some corner cases for square root +-- +select sqrt(1.000000000000003::numeric); + sqrt +------------------- + 1.000000000000001 +(1 row) + +select sqrt(1.000000000000004::numeric); + sqrt +------------------- + 1.000000000000002 +(1 row) + +select sqrt(96627521408608.56340355805::numeric); + sqrt +--------------------- + 9829929.87811248648 +(1 row) + +select sqrt(96627521408608.56340355806::numeric); + sqrt +--------------------- + 9829929.87811248649 +(1 row) + +select sqrt(515549506212297735.073688290367::numeric); + sqrt +------------------------ + 718017761.766585921184 +(1 row) + +select sqrt(515549506212297735.073688290368::numeric); + sqrt +------------------------ + 718017761.766585921185 +(1 row) + +select sqrt(8015491789940783531003294973900306::numeric); + sqrt +------------------- + 89529278953540017 +(1 row) + +select sqrt(8015491789940783531003294973900307::numeric); + sqrt +------------------- + 89529278953540018 +(1 row) + +-- +-- Test code path for raising to integer powers +-- +select 10.0 ^ -2147483648 as rounds_to_zero; + rounds_to_zero +-------------------- + 0.0000000000000000 +(1 row) + +select 10.0 ^ -2147483647 as rounds_to_zero; + rounds_to_zero +-------------------- + 0.0000000000000000 +(1 row) + +select 10.0 ^ 2147483647 as overflows; +ERROR: value overflows numeric format +select 117743296169.0 ^ 1000000000 as overflows; +ERROR: value overflows numeric format +-- cases that used to return inaccurate results +select 3.789 ^ 21; + ?column? +-------------------------------- + 1409343026052.8716016316022141 +(1 row) + +select 3.789 ^ 35; + ?column? +---------------------------------------- + 177158169650516670809.3820586142670135 +(1 row) + +select 1.2 ^ 345; + ?column? +----------------------------------------------- + 2077446682327378559843444695.5827049735727869 +(1 row) + +select 0.12 ^ (-20); + ?column? +-------------------------------------- + 2608405330458882702.5529619561355838 +(1 row) + +select 1.000000000123 ^ (-2147483648); + ?column? +-------------------- + 0.7678656556403084 +(1 row) + +select coalesce(nullif(0.9999999999 ^ 23300000000000, 0), 0) as rounds_to_zero; + rounds_to_zero +---------------- + 0 +(1 row) + +select round(((1 - 1.500012345678e-1000) ^ 1.45e1003) * 1e1000); + round +---------------------------------------------------------- + 25218976308958387188077465658068501556514992509509282366 +(1 row) + +-- cases that used to error out +select 0.12 ^ (-25); + ?column? +------------------------------------------- + 104825960103961013959336.4983657883169110 +(1 row) + +select 0.5678 ^ (-85); + ?column? +---------------------------------------- + 782333637740774446257.7719390061997396 +(1 row) + +select coalesce(nullif(0.9999999999 ^ 70000000000000, 0), 0) as underflows; + underflows +------------ + 0 +(1 row) + +-- negative base to integer powers +select (-1.0) ^ 2147483646; + ?column? +-------------------- + 1.0000000000000000 +(1 row) + +select (-1.0) ^ 2147483647; + ?column? +--------------------- + -1.0000000000000000 +(1 row) + +select (-1.0) ^ 2147483648; + ?column? +-------------------- + 1.0000000000000000 +(1 row) + +select (-1.0) ^ 1000000000000000; + ?column? +-------------------- + 1.0000000000000000 +(1 row) + +select (-1.0) ^ 1000000000000001; + ?column? +--------------------- + -1.0000000000000000 +(1 row) + +-- +-- Tests for raising to non-integer powers +-- +-- special cases +select 0.0 ^ 0.0; + ?column? +-------------------- + 1.0000000000000000 +(1 row) + +select (-12.34) ^ 0.0; + ?column? +-------------------- + 1.0000000000000000 +(1 row) + +select 12.34 ^ 0.0; + ?column? +-------------------- + 1.0000000000000000 +(1 row) + +select 0.0 ^ 12.34; + ?column? +-------------------- + 0.0000000000000000 +(1 row) + +-- NaNs +select 'NaN'::numeric ^ 'NaN'::numeric; + ?column? +---------- + NaN +(1 row) + +select 'NaN'::numeric ^ 0; + ?column? +---------- + 1 +(1 row) + +select 'NaN'::numeric ^ 1; + ?column? +---------- + NaN +(1 row) + +select 0 ^ 'NaN'::numeric; + ?column? +---------- + NaN +(1 row) + +select 1 ^ 'NaN'::numeric; + ?column? +---------- + 1 +(1 row) + +-- invalid inputs +select 0.0 ^ (-12.34); +ERROR: zero raised to a negative power is undefined +select (-12.34) ^ 1.2; +ERROR: a negative number raised to a non-integer power yields a complex result +-- cases that used to generate inaccurate results +select 32.1 ^ 9.8; + ?column? +-------------------- + 580429286790711.10 +(1 row) + +select 32.1 ^ (-9.8); + ?column? +---------------------------------- + 0.000000000000001722862754788209 +(1 row) + +select 12.3 ^ 45.6; + ?column? +------------------------------------------------------ + 50081010321492803393171165777624533697036806969694.9 +(1 row) + +select 12.3 ^ (-45.6); + ?column? +--------------------------------------------------------------------- + 0.00000000000000000000000000000000000000000000000001996764828785491 +(1 row) + +-- big test +select 1.234 ^ 5678; + ?column? +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 307239295662090741644584872593956173493568238595074141254349565406661439636598896798876823220904084953233015553994854875890890858118656468658643918169805277399402542281777901029346337707622181574346585989613344285010764501017625366742865066948856161360224801370482171458030533346309750557140549621313515752078638620714732831815297168231790779296290266207315344008883935010274044001522606235576584215999260117523114297033944018699691024106823438431754073086813382242140602291215149759520833200152654884259619588924545324.5973362312547382 +(1 row) + +-- +-- Tests for EXP() +-- +-- special cases +select exp(0.0); + exp +-------------------- + 1.0000000000000000 +(1 row) + +select exp(1.0); + exp +-------------------- + 2.7182818284590452 +(1 row) + +select exp(1.0::numeric(71,70)); + exp +-------------------------------------------------------------------------- + 2.7182818284590452353602874713526624977572470936999595749669676277240766 +(1 row) + +select exp('nan'::numeric); + exp +----- + NaN +(1 row) + +select exp('inf'::numeric); + exp +---------- + Infinity +(1 row) + +select exp('-inf'::numeric); + exp +----- + 0 +(1 row) + +select coalesce(nullif(exp(-5000::numeric), 0), 0) as rounds_to_zero; + rounds_to_zero +---------------- + 0 +(1 row) + +select coalesce(nullif(exp(-10000::numeric), 0), 0) as underflows; + underflows +------------ + 0 +(1 row) + +-- cases that used to generate inaccurate results +select exp(32.999); + exp +--------------------- + 214429043492155.053 +(1 row) + +select exp(-32.999); + exp +---------------------------------- + 0.000000000000004663547361468248 +(1 row) + +select exp(123.456); + exp +------------------------------------------------------------ + 413294435277809344957685441227343146614594393746575438.725 +(1 row) + +select exp(-123.456); + exp +------------------------------------------------------------------------- + 0.000000000000000000000000000000000000000000000000000002419582541264601 +(1 row) + +-- big test +select exp(1234.5678); + exp +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 146549072930959479983482138503979804217622199675223653966270157446954995433819741094410764947112047906012815540251009949604426069672532417736057033099274204598385314594846509975629046864798765888104789074984927709616261452461385220475510438783429612447831614003668421849727379202555580791042606170523016207262965336641214601082882495255771621327088265411334088968112458492660609809762865582162764292604697957813514621259353683899630997077707406305730694385703091201347848855199354307506425820147289848677003277208302716466011827836279231.9667 +(1 row) + +-- +-- Tests for generate_series +-- +select * from generate_series(0.0::numeric, 4.0::numeric); + generate_series +----------------- + 0.0 + 1.0 + 2.0 + 3.0 + 4.0 +(5 rows) + +select * from generate_series(0.1::numeric, 4.0::numeric, 1.3::numeric); + generate_series +----------------- + 0.1 + 1.4 + 2.7 + 4.0 +(4 rows) + +select * from generate_series(4.0::numeric, -1.5::numeric, -2.2::numeric); + generate_series +----------------- + 4.0 + 1.8 + -0.4 +(3 rows) + +-- Trigger errors +select * from generate_series(-100::numeric, 100::numeric, 0::numeric); +ERROR: step size cannot equal zero +select * from generate_series(-100::numeric, 100::numeric, 'nan'::numeric); +ERROR: step size cannot be NaN +select * from generate_series('nan'::numeric, 100::numeric, 10::numeric); +ERROR: start value cannot be NaN +select * from generate_series(0::numeric, 'nan'::numeric, 10::numeric); +ERROR: stop value cannot be NaN +select * from generate_series('inf'::numeric, 'inf'::numeric, 10::numeric); +ERROR: start value cannot be infinity +select * from generate_series(0::numeric, 'inf'::numeric, 10::numeric); +ERROR: stop value cannot be infinity +select * from generate_series(0::numeric, '42'::numeric, '-inf'::numeric); +ERROR: step size cannot be infinity +-- Checks maximum, output is truncated +select (i / (10::numeric ^ 131071))::numeric(1,0) + from generate_series(6 * (10::numeric ^ 131071), + 9 * (10::numeric ^ 131071), + 10::numeric ^ 131071) as a(i); + numeric +--------- + 6 + 7 + 8 + 9 +(4 rows) + +-- Check usage with variables +select * from generate_series(1::numeric, 3::numeric) i, generate_series(i,3) j; + i | j +---+--- + 1 | 1 + 1 | 2 + 1 | 3 + 2 | 2 + 2 | 3 + 3 | 3 +(6 rows) + +select * from generate_series(1::numeric, 3::numeric) i, generate_series(1,i) j; + i | j +---+--- + 1 | 1 + 2 | 1 + 2 | 2 + 3 | 1 + 3 | 2 + 3 | 3 +(6 rows) + +select * from generate_series(1::numeric, 3::numeric) i, generate_series(1,5,i) j; + i | j +---+--- + 1 | 1 + 1 | 2 + 1 | 3 + 1 | 4 + 1 | 5 + 2 | 1 + 2 | 3 + 2 | 5 + 3 | 1 + 3 | 4 +(10 rows) + +-- +-- Tests for LN() +-- +-- Invalid inputs +select ln(-12.34); +ERROR: cannot take logarithm of a negative number +select ln(0.0); +ERROR: cannot take logarithm of zero +-- Some random tests +select ln(1.2345678e-28); + ln +----------------------------------------- + -64.26166165451762991204894255882820859 +(1 row) + +select ln(0.0456789); + ln +--------------------- + -3.0861187944847439 +(1 row) + +select ln(0.349873948359354029493948309745709580730482050975); + ln +----------------------------------------------------- + -1.050182336912082775693991697979750253056317885460 +(1 row) + +select ln(0.99949452); + ln +------------------------- + -0.00050560779808326467 +(1 row) + +select ln(1.00049687395); + ln +------------------------ + 0.00049675054901370394 +(1 row) + +select ln(1234.567890123456789); + ln +-------------------- + 7.1184763012977896 +(1 row) + +select ln(5.80397490724e5); + ln +-------------------- + 13.271468476626518 +(1 row) + +select ln(9.342536355e34); + ln +-------------------- + 80.522470935524187 +(1 row) + +-- +-- Tests for LOG() (base 10) +-- +-- invalid inputs +select log(-12.34); +ERROR: cannot take logarithm of a negative number +CONTEXT: SQL function "log" statement 1 +select log(0.0); +ERROR: cannot take logarithm of zero +CONTEXT: SQL function "log" statement 1 +-- some random tests +select log(1.234567e-89); + log +----------------------------------------------------------------------------------------------------- + -88.90848533591373725637496492944925187293052336306443143312825869985819779294142441287021741054275 +(1 row) + +select log(3.4634998359873254962349856073435545); + log +-------------------------------------- + 0.5395151714070134409152404011959981 +(1 row) + +select log(9.999999999999999999); + log +---------------------- + 1.000000000000000000 +(1 row) + +select log(10.00000000000000000); + log +--------------------- + 1.00000000000000000 +(1 row) + +select log(10.00000000000000001); + log +--------------------- + 1.00000000000000000 +(1 row) + +select log(590489.45235237); + log +------------------- + 5.771212144411727 +(1 row) + +-- +-- Tests for LOG() (arbitrary base) +-- +-- invalid inputs +select log(-12.34, 56.78); +ERROR: cannot take logarithm of a negative number +select log(-12.34, -56.78); +ERROR: cannot take logarithm of a negative number +select log(12.34, -56.78); +ERROR: cannot take logarithm of a negative number +select log(0.0, 12.34); +ERROR: cannot take logarithm of zero +select log(12.34, 0.0); +ERROR: cannot take logarithm of zero +select log(1.0, 12.34); +ERROR: division by zero +-- some random tests +select log(1.23e-89, 6.4689e45); + log +------------------------------------------------------------------------------------------------ + -0.5152489207781856983977054971756484879653568168479201885425588841094788842469115325262329756 +(1 row) + +select log(0.99923, 4.58934e34); + log +--------------------- + -103611.55579544132 +(1 row) + +select log(1.000016, 8.452010e18); + log +-------------------- + 2723830.2877097365 +(1 row) + +select log(3.1954752e47, 9.4792021e-73); + log +------------------------------------------------------------------------------------- + -1.51613372350688302142917386143459361608600157692779164475351842333265418126982165 +(1 row) + +-- +-- Tests for scale() +-- +select scale(numeric 'NaN'); + scale +------- + +(1 row) + +select scale(numeric 'inf'); + scale +------- + +(1 row) + +select scale(NULL::numeric); + scale +------- + +(1 row) + +select scale(1.12); + scale +------- + 2 +(1 row) + +select scale(0); + scale +------- + 0 +(1 row) + +select scale(0.00); + scale +------- + 2 +(1 row) + +select scale(1.12345); + scale +------- + 5 +(1 row) + +select scale(110123.12475871856128); + scale +------- + 14 +(1 row) + +select scale(-1123.12471856128); + scale +------- + 11 +(1 row) + +select scale(-13.000000000000000); + scale +------- + 15 +(1 row) + +-- +-- Tests for min_scale() +-- +select min_scale(numeric 'NaN') is NULL; -- should be true + ?column? +---------- + t +(1 row) + +select min_scale(numeric 'inf') is NULL; -- should be true + ?column? +---------- + t +(1 row) + +select min_scale(0); -- no digits + min_scale +----------- + 0 +(1 row) + +select min_scale(0.00); -- no digits again + min_scale +----------- + 0 +(1 row) + +select min_scale(1.0); -- no scale + min_scale +----------- + 0 +(1 row) + +select min_scale(1.1); -- scale 1 + min_scale +----------- + 1 +(1 row) + +select min_scale(1.12); -- scale 2 + min_scale +----------- + 2 +(1 row) + +select min_scale(1.123); -- scale 3 + min_scale +----------- + 3 +(1 row) + +select min_scale(1.1234); -- scale 4, filled digit + min_scale +----------- + 4 +(1 row) + +select min_scale(1.12345); -- scale 5, 2 NDIGITS + min_scale +----------- + 5 +(1 row) + +select min_scale(1.1000); -- 1 pos in NDIGITS + min_scale +----------- + 1 +(1 row) + +select min_scale(1e100); -- very big number + min_scale +----------- + 0 +(1 row) + +-- +-- Tests for trim_scale() +-- +select trim_scale(numeric 'NaN'); + trim_scale +------------ + NaN +(1 row) + +select trim_scale(numeric 'inf'); + trim_scale +------------ + Infinity +(1 row) + +select trim_scale(1.120); + trim_scale +------------ + 1.12 +(1 row) + +select trim_scale(0); + trim_scale +------------ + 0 +(1 row) + +select trim_scale(0.00); + trim_scale +------------ + 0 +(1 row) + +select trim_scale(1.1234500); + trim_scale +------------ + 1.12345 +(1 row) + +select trim_scale(110123.12475871856128000); + trim_scale +----------------------- + 110123.12475871856128 +(1 row) + +select trim_scale(-1123.124718561280000000); + trim_scale +------------------- + -1123.12471856128 +(1 row) + +select trim_scale(-13.00000000000000000000); + trim_scale +------------ + -13 +(1 row) + +select trim_scale(1e100); + trim_scale +------------------------------------------------------------------------------------------------------- + 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 +(1 row) + +-- +-- Tests for SUM() +-- +-- cases that need carry propagation +SELECT SUM(9999::numeric) FROM generate_series(1, 100000); + sum +----------- + 999900000 +(1 row) + +SELECT SUM((-9999)::numeric) FROM generate_series(1, 100000); + sum +------------ + -999900000 +(1 row) + +-- +-- Tests for VARIANCE() +-- +CREATE TABLE num_variance (a numeric); +INSERT INTO num_variance VALUES (0); +INSERT INTO num_variance VALUES (3e-500); +INSERT INTO num_variance VALUES (-3e-500); +INSERT INTO num_variance VALUES (4e-500 - 1e-16383); +INSERT INTO num_variance VALUES (-4e-500 + 1e-16383); +-- variance is just under 12.5e-1000 and so should round down to 12e-1000 +SELECT trim_scale(variance(a) * 1e1000) FROM num_variance; + trim_scale +------------ + 12 +(1 row) + +-- check that parallel execution produces the same result +BEGIN; +ALTER TABLE num_variance SET (parallel_workers = 4); +SET LOCAL parallel_setup_cost = 0; +SET LOCAL max_parallel_workers_per_gather = 4; +SELECT trim_scale(variance(a) * 1e1000) FROM num_variance; + trim_scale +------------ + 12 +(1 row) + +ROLLBACK; +-- case where sum of squares would overflow but variance does not +DELETE FROM num_variance; +INSERT INTO num_variance SELECT 9e131071 + x FROM generate_series(1, 5) x; +SELECT variance(a) FROM num_variance; + variance +-------------------- + 2.5000000000000000 +(1 row) + +-- check that parallel execution produces the same result +BEGIN; +ALTER TABLE num_variance SET (parallel_workers = 4); +SET LOCAL parallel_setup_cost = 0; +SET LOCAL max_parallel_workers_per_gather = 4; +SELECT variance(a) FROM num_variance; + variance +-------------------- + 2.5000000000000000 +(1 row) + +ROLLBACK; +DROP TABLE num_variance; +-- +-- Tests for GCD() +-- +SELECT a, b, gcd(a, b), gcd(a, -b), gcd(-b, a), gcd(-b, -a) +FROM (VALUES (0::numeric, 0::numeric), + (0::numeric, numeric 'NaN'), + (0::numeric, 46375::numeric), + (433125::numeric, 46375::numeric), + (43312.5::numeric, 4637.5::numeric), + (4331.250::numeric, 463.75000::numeric), + ('inf', '0'), + ('inf', '42'), + ('inf', 'inf') + ) AS v(a, b); + a | b | gcd | gcd | gcd | gcd +----------+-----------+---------+---------+---------+--------- + 0 | 0 | 0 | 0 | 0 | 0 + 0 | NaN | NaN | NaN | NaN | NaN + 0 | 46375 | 46375 | 46375 | 46375 | 46375 + 433125 | 46375 | 875 | 875 | 875 | 875 + 43312.5 | 4637.5 | 87.5 | 87.5 | 87.5 | 87.5 + 4331.250 | 463.75000 | 8.75000 | 8.75000 | 8.75000 | 8.75000 + Infinity | 0 | NaN | NaN | NaN | NaN + Infinity | 42 | NaN | NaN | NaN | NaN + Infinity | Infinity | NaN | NaN | NaN | NaN +(9 rows) + +-- +-- Tests for LCM() +-- +SELECT a,b, lcm(a, b), lcm(a, -b), lcm(-b, a), lcm(-b, -a) +FROM (VALUES (0::numeric, 0::numeric), + (0::numeric, numeric 'NaN'), + (0::numeric, 13272::numeric), + (13272::numeric, 13272::numeric), + (423282::numeric, 13272::numeric), + (42328.2::numeric, 1327.2::numeric), + (4232.820::numeric, 132.72000::numeric), + ('inf', '0'), + ('inf', '42'), + ('inf', 'inf') + ) AS v(a, b); + a | b | lcm | lcm | lcm | lcm +----------+-----------+--------------+--------------+--------------+-------------- + 0 | 0 | 0 | 0 | 0 | 0 + 0 | NaN | NaN | NaN | NaN | NaN + 0 | 13272 | 0 | 0 | 0 | 0 + 13272 | 13272 | 13272 | 13272 | 13272 | 13272 + 423282 | 13272 | 11851896 | 11851896 | 11851896 | 11851896 + 42328.2 | 1327.2 | 1185189.6 | 1185189.6 | 1185189.6 | 1185189.6 + 4232.820 | 132.72000 | 118518.96000 | 118518.96000 | 118518.96000 | 118518.96000 + Infinity | 0 | NaN | NaN | NaN | NaN + Infinity | 42 | NaN | NaN | NaN | NaN + Infinity | Infinity | NaN | NaN | NaN | NaN +(10 rows) + +SELECT lcm(9999 * (10::numeric)^131068 + (10::numeric^131068 - 1), 2); -- overflow +ERROR: value overflows numeric format +-- +-- Tests for factorial +-- +SELECT factorial(4); + factorial +----------- + 24 +(1 row) + +SELECT factorial(15); + factorial +--------------- + 1307674368000 +(1 row) + +SELECT factorial(100000); +ERROR: value overflows numeric format +SELECT factorial(0); + factorial +----------- + 1 +(1 row) + +SELECT factorial(-4); +ERROR: factorial of a negative number is undefined +-- +-- Tests for pg_lsn() +-- +SELECT pg_lsn(23783416::numeric); + pg_lsn +----------- + 0/16AE7F8 +(1 row) + +SELECT pg_lsn(0::numeric); + pg_lsn +-------- + 0/0 +(1 row) + +SELECT pg_lsn(18446744073709551615::numeric); + pg_lsn +------------------- + FFFFFFFF/FFFFFFFF +(1 row) + +SELECT pg_lsn(-1::numeric); +ERROR: pg_lsn out of range +SELECT pg_lsn(18446744073709551616::numeric); +ERROR: pg_lsn out of range +SELECT pg_lsn('NaN'::numeric); +ERROR: cannot convert NaN to pg_lsn |