-- -- 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'); INSERT INTO num_exp_sub VALUES (3,9,'24926808.355047420'); INSERT INTO num_exp_mul VALUES (3,9,'-107434525.43415438020'); INSERT INTO num_exp_div VALUES (3,9,'-.00000017290624149854'); INSERT INTO num_exp_add VALUES (4,0,'7799461.4119'); INSERT INTO num_exp_sub VALUES (4,0,'7799461.4119'); 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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 | 17.640000000000000 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) -- Another roundoff-error hazard SELECT width_bucket(0, -1e100::numeric, 1, 10); width_bucket -------------- 10 (1 row) SELECT width_bucket(0, -1e100::float8, 1, 10); width_bucket -------------- 10 (1 row) SELECT width_bucket(1, 1e100::numeric, 0, 10); width_bucket -------------- 10 (1 row) SELECT width_bucket(1, 1e100::float8, 0, 10); width_bucket -------------- 10 (1 row) -- Check cases that could trigger overflow or underflow within the calculation SELECT oper, low, high, cnt, width_bucket(oper, low, high, cnt) FROM (SELECT 1.797e+308::float8 AS big, 5e-324::float8 AS tiny) as v, LATERAL (VALUES (10.5::float8, -big, big, 1), (10.5::float8, -big, big, 2), (10.5::float8, -big, big, 3), (big / 4, -big / 2, big / 2, 10), (10.5::float8, big, -big, 1), (10.5::float8, big, -big, 2), (10.5::float8, big, -big, 3), (big / 4, big / 2, -big / 2, 10), (0, 0, tiny, 4), (tiny, 0, tiny, 4), (0, 0, 1, 2147483647), (1, 1, 0, 2147483647) ) as sample(oper, low, high, cnt); oper | low | high | cnt | width_bucket -------------+-------------+-------------+------------+-------------- 10.5 | -1.797e+308 | 1.797e+308 | 1 | 1 10.5 | -1.797e+308 | 1.797e+308 | 2 | 2 10.5 | -1.797e+308 | 1.797e+308 | 3 | 2 4.4925e+307 | -8.985e+307 | 8.985e+307 | 10 | 8 10.5 | 1.797e+308 | -1.797e+308 | 1 | 1 10.5 | 1.797e+308 | -1.797e+308 | 2 | 2 10.5 | 1.797e+308 | -1.797e+308 | 3 | 2 4.4925e+307 | 8.985e+307 | -8.985e+307 | 10 | 3 0 | 0 | 5e-324 | 4 | 1 5e-324 | 0 | 5e-324 | 4 | 5 0 | 0 | 1 | 2147483647 | 1 1 | 1 | 0 | 2147483647 | 1 (12 rows) -- These fail because the result would be out of int32 range: SELECT width_bucket(1::float8, 0, 1, 2147483647); ERROR: integer out of range SELECT width_bucket(0::float8, 1, 0, 2147483647); ERROR: integer out of range -- -- 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 '); INSERT INTO num_input_test(n1) VALUES ('12_000_000_000'); INSERT INTO num_input_test(n1) VALUES ('12_000.123_456'); INSERT INTO num_input_test(n1) VALUES ('23_000_000_000e-1_0'); INSERT INTO num_input_test(n1) VALUES ('.000_000_000_123e1_0'); INSERT INTO num_input_test(n1) VALUES ('.000_000_000_123e+1_1'); INSERT INTO num_input_test(n1) VALUES ('0b10001110111100111100001001010'); INSERT INTO num_input_test(n1) VALUES (' -0B_1010_1011_0101_0100_1010_1001_1000_1100_1110_1011_0001_1111_0000_1010_1101_0010 '); INSERT INTO num_input_test(n1) VALUES (' +0o112402761777 '); INSERT INTO num_input_test(n1) VALUES ('-0O0012_5524_5230_6334_3167_0261'); INSERT INTO num_input_test(n1) VALUES ('-0x0000000000000000000000000deadbeef'); INSERT INTO num_input_test(n1) VALUES (' 0X_30b1_F33a_6DF0_bD4E_64DF_9BdA_7D15 '); -- 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 ('+NaN'); ERROR: invalid input syntax for type numeric: "+NaN" LINE 1: INSERT INTO num_input_test(n1) VALUES ('+NaN'); ^ INSERT INTO num_input_test(n1) VALUES ('-NaN'); ERROR: invalid input syntax for type numeric: "-NaN" LINE 1: INSERT INTO num_input_test(n1) VALUES ('-NaN'); ^ 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'); ^ INSERT INTO num_input_test(n1) VALUES ('_123'); ERROR: invalid input syntax for type numeric: "_123" LINE 1: INSERT INTO num_input_test(n1) VALUES ('_123'); ^ INSERT INTO num_input_test(n1) VALUES ('123_'); ERROR: invalid input syntax for type numeric: "123_" LINE 1: INSERT INTO num_input_test(n1) VALUES ('123_'); ^ INSERT INTO num_input_test(n1) VALUES ('12__34'); ERROR: invalid input syntax for type numeric: "12__34" LINE 1: INSERT INTO num_input_test(n1) VALUES ('12__34'); ^ INSERT INTO num_input_test(n1) VALUES ('123_.456'); ERROR: invalid input syntax for type numeric: "123_.456" LINE 1: INSERT INTO num_input_test(n1) VALUES ('123_.456'); ^ INSERT INTO num_input_test(n1) VALUES ('123._456'); ERROR: invalid input syntax for type numeric: "123._456" LINE 1: INSERT INTO num_input_test(n1) VALUES ('123._456'); ^ INSERT INTO num_input_test(n1) VALUES ('1.2e_34'); ERROR: invalid input syntax for type numeric: "1.2e_34" LINE 1: INSERT INTO num_input_test(n1) VALUES ('1.2e_34'); ^ INSERT INTO num_input_test(n1) VALUES ('1.2e34_'); ERROR: invalid input syntax for type numeric: "1.2e34_" LINE 1: INSERT INTO num_input_test(n1) VALUES ('1.2e34_'); ^ INSERT INTO num_input_test(n1) VALUES ('1.2e3__4'); ERROR: invalid input syntax for type numeric: "1.2e3__4" LINE 1: INSERT INTO num_input_test(n1) VALUES ('1.2e3__4'); ^ INSERT INTO num_input_test(n1) VALUES ('0b1112'); ERROR: invalid input syntax for type numeric: "0b1112" LINE 1: INSERT INTO num_input_test(n1) VALUES ('0b1112'); ^ INSERT INTO num_input_test(n1) VALUES ('0c1112'); ERROR: invalid input syntax for type numeric: "0c1112" LINE 1: INSERT INTO num_input_test(n1) VALUES ('0c1112'); ^ INSERT INTO num_input_test(n1) VALUES ('0o12345678'); ERROR: invalid input syntax for type numeric: "0o12345678" LINE 1: INSERT INTO num_input_test(n1) VALUES ('0o12345678'); ^ INSERT INTO num_input_test(n1) VALUES ('0x1eg'); ERROR: invalid input syntax for type numeric: "0x1eg" LINE 1: INSERT INTO num_input_test(n1) VALUES ('0x1eg'); ^ INSERT INTO num_input_test(n1) VALUES ('0x12.34'); ERROR: invalid input syntax for type numeric: "0x12.34" LINE 1: INSERT INTO num_input_test(n1) VALUES ('0x12.34'); ^ INSERT INTO num_input_test(n1) VALUES ('0x__1234'); ERROR: invalid input syntax for type numeric: "0x__1234" LINE 1: INSERT INTO num_input_test(n1) VALUES ('0x__1234'); ^ INSERT INTO num_input_test(n1) VALUES ('0x1234_'); ERROR: invalid input syntax for type numeric: "0x1234_" LINE 1: INSERT INTO num_input_test(n1) VALUES ('0x1234_'); ^ INSERT INTO num_input_test(n1) VALUES ('0x12__34'); ERROR: invalid input syntax for type numeric: "0x12__34" LINE 1: INSERT INTO num_input_test(n1) VALUES ('0x12__34'); ^ SELECT * FROM num_input_test; n1 ----------------------------------- 123 3245874 -93853 555.50 -555.50 NaN NaN Infinity Infinity -Infinity Infinity Infinity -Infinity 12000000000 12000.123456 2.3000000000 1.23 12.3 299792458 -12345678901234567890 9999999999 -12345678900987654321 -3735928559 987654321234567898765432123456789 (24 rows) -- Also try it with non-error-throwing API SELECT pg_input_is_valid('34.5', 'numeric'); pg_input_is_valid ------------------- t (1 row) SELECT pg_input_is_valid('34xyz', 'numeric'); pg_input_is_valid ------------------- f (1 row) SELECT pg_input_is_valid('1e400000', 'numeric'); pg_input_is_valid ------------------- f (1 row) SELECT * FROM pg_input_error_info('1e400000', 'numeric'); message | detail | hint | sql_error_code --------------------------------+--------+------+---------------- value overflows numeric format | | | 22003 (1 row) SELECT pg_input_is_valid('1234.567', 'numeric(8,4)'); pg_input_is_valid ------------------- t (1 row) SELECT pg_input_is_valid('1234.567', 'numeric(7,4)'); pg_input_is_valid ------------------- f (1 row) SELECT * FROM pg_input_error_info('1234.567', 'numeric(7,4)'); message | detail | hint | sql_error_code ------------------------+-----------------------------------------------------------------------------------+------+---------------- numeric field overflow | A field with precision 7, scale 4 must round to an absolute value less than 10^3. | | 22003 (1 row) SELECT * FROM pg_input_error_info('0x1234.567', 'numeric'); message | detail | hint | sql_error_code -----------------------------------------------------+--------+------+---------------- invalid input syntax for type numeric: "0x1234.567" | | | 22P02 (1 row) -- -- 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 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (1 row) select 10.0 ^ -2147483647 as rounds_to_zero; rounds_to_zero -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (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 ^ 21.0000000000000000; ?column? -------------------------------- 1409343026052.8716016316022141 (1 row) select 3.789 ^ 35.0000000000000000; ?column? ---------------------------------------- 177158169650516670809.3820586142670135 (1 row) select 1.2 ^ 345; ?column? -------------------------------- 2077446682327378559843444695.6 (1 row) select 0.12 ^ (-20); ?column? ------------------------ 2608405330458882702.55 (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? ----------------------------- 104825960103961013959336.50 (1 row) select 0.5678 ^ (-85); ?column? ---------------------------- 782333637740774446257.7719 (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) -- integer powers of 10 select n, 10.0 ^ n as "10^n", (10.0 ^ n) * (10.0 ^ (-n)) = 1 as ok from generate_series(-20, 20) n; n | 10^n | ok -----+----------------------------------------+---- -20 | 0.000000000000000000010000000000000000 | t -19 | 0.00000000000000000010000000000000000 | t -18 | 0.0000000000000000010000000000000000 | t -17 | 0.000000000000000010000000000000000 | t -16 | 0.00000000000000010000000000000000 | t -15 | 0.0000000000000010000000000000000 | t -14 | 0.000000000000010000000000000000 | t -13 | 0.00000000000010000000000000000 | t -12 | 0.0000000000010000000000000000 | t -11 | 0.000000000010000000000000000 | t -10 | 0.00000000010000000000000000 | t -9 | 0.0000000010000000000000000 | t -8 | 0.000000010000000000000000 | t -7 | 0.00000010000000000000000 | t -6 | 0.0000010000000000000000 | t -5 | 0.000010000000000000000 | t -4 | 0.00010000000000000000 | t -3 | 0.0010000000000000000 | t -2 | 0.010000000000000000 | t -1 | 0.10000000000000000 | t 0 | 1.0000000000000000 | t 1 | 10.000000000000000 | t 2 | 100.00000000000000 | t 3 | 1000.0000000000000 | t 4 | 10000.000000000000 | t 5 | 100000.00000000000 | t 6 | 1000000.0000000000 | t 7 | 10000000.000000000 | t 8 | 100000000.00000000 | t 9 | 1000000000.0000000 | t 10 | 10000000000.000000 | t 11 | 100000000000.00000 | t 12 | 1000000000000.0000 | t 13 | 10000000000000.000 | t 14 | 100000000000000.00 | t 15 | 1000000000000000.0 | t 16 | 10000000000000000.0 | t 17 | 100000000000000000.0 | t 18 | 1000000000000000000.0 | t 19 | 10000000000000000000.0 | t 20 | 100000000000000000000.0 | t (41 rows) -- -- 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? --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 307239295662090741644584872593956173493568238595074141254349565406661439636598896798876823220904084953233015553994854875890890858118656468658643918169805277399402542281777901029346337707622181574346585989613344285010764501017625366742865066948856161360224801370482171458030533346309750557140549621313515752078638620714732831815297168231790779296290266207315344008883935010274044001522606235576584215999260117523114297033944018699691024106823438431754073086813382242140602291215149759520833200152654884259619588924545324.597 (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