-- -- 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; 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); -- ****************************** -- * 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; 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); -- ****************************** -- * 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; 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); -- ****************************** -- * 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; 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); -- ****************************** -- * 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; -- ****************************** -- * 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; -- ****************************** -- * 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; -- ****************************** -- * 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; -- ****************************** -- * 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); 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; SELECT 'inf'::numeric / '0'; SELECT '-inf'::numeric / '0'; SELECT 'nan'::numeric / '0'; SELECT '0'::numeric / '0'; SELECT 'inf'::numeric % '0'; SELECT '-inf'::numeric % '0'; SELECT 'nan'::numeric % '0'; SELECT '0'::numeric % '0'; SELECT div('inf'::numeric, '0'); SELECT div('-inf'::numeric, '0'); SELECT div('nan'::numeric, '0'); SELECT div('0'::numeric, '0'); 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; 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; -- 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; WITH v(x) AS (VALUES('0'::numeric),('1'),('4.2'),('inf'),('nan')) SELECT x, sqrt(x) FROM v; SELECT sqrt('-1'::numeric); SELECT sqrt('-inf'::numeric); WITH v(x) AS (VALUES('1'::numeric),('4.2'),('inf'),('nan')) SELECT x, log(x), log10(x), ln(x) FROM v; SELECT ln('0'::numeric); SELECT ln('-1'::numeric); SELECT ln('-inf'::numeric); 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); SELECT log('0'::numeric, '10'); SELECT log('10'::numeric, '0'); SELECT log('-inf'::numeric, '10'); SELECT log('10'::numeric, '-inf'); SELECT log('inf'::numeric, '0'); SELECT log('inf'::numeric, '-inf'); SELECT log('-inf'::numeric, 'inf'); 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; SELECT power('0'::numeric, '-1'); SELECT power('0'::numeric, '-inf'); SELECT power('-1'::numeric, 'inf'); SELECT power('-2'::numeric, '3'); SELECT power('-2'::numeric, '3.3'); SELECT power('-2'::numeric, '-1'); SELECT power('-2'::numeric, '-1.5'); SELECT power('-2'::numeric, 'inf'); SELECT power('-2'::numeric, '-inf'); SELECT power('inf'::numeric, '-2'); SELECT power('inf'::numeric, '-inf'); SELECT power('-inf'::numeric, '2'); SELECT power('-inf'::numeric, '3'); SELECT power('-inf'::numeric, '4.5'); SELECT power('-inf'::numeric, '-2'); SELECT power('-inf'::numeric, '-3'); SELECT power('-inf'::numeric, '0'); SELECT power('-inf'::numeric, 'inf'); SELECT power('-inf'::numeric, '-inf'); -- ****************************** -- * 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; SELECT MAX(val) FROM num_data; SELECT MIN(val) FROM num_data; SELECT STDDEV(val) FROM num_data; SELECT VARIANCE(val) FROM num_data; -- 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 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 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 INSERT INTO fract_only VALUES (11, '-Inf'); -- should fail SELECT * FROM fract_only; DROP TABLE fract_only; -- Check conversion to integers SELECT (-9223372036854775808.5)::int8; -- should fail SELECT (-9223372036854775808.4)::int8; -- ok SELECT 9223372036854775807.4::int8; -- ok SELECT 9223372036854775807.5::int8; -- should fail SELECT (-2147483648.5)::int4; -- should fail SELECT (-2147483648.4)::int4; -- ok SELECT 2147483647.4::int4; -- ok SELECT 2147483647.5::int4; -- should fail SELECT (-32768.5)::int2; -- should fail SELECT (-32768.4)::int2; -- ok SELECT 32767.4::int2; -- ok SELECT 32767.5::int2; -- should fail -- Check inf/nan conversion behavior SELECT 'NaN'::float8::numeric; SELECT 'Infinity'::float8::numeric; SELECT '-Infinity'::float8::numeric; SELECT 'NaN'::numeric::float8; SELECT 'Infinity'::numeric::float8; SELECT '-Infinity'::numeric::float8; SELECT 'NaN'::float4::numeric; SELECT 'Infinity'::float4::numeric; SELECT '-Infinity'::float4::numeric; SELECT 'NaN'::numeric::float4; SELECT 'Infinity'::numeric::float4; SELECT '-Infinity'::numeric::float4; SELECT '42'::int2::numeric; SELECT 'NaN'::numeric::int2; SELECT 'Infinity'::numeric::int2; SELECT '-Infinity'::numeric::int2; SELECT 'NaN'::numeric::int4; SELECT 'Infinity'::numeric::int4; SELECT '-Infinity'::numeric::int4; SELECT 'NaN'::numeric::int8; SELECT 'Infinity'::numeric::int8; SELECT '-Infinity'::numeric::int8; -- 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; 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); -- Check limits of rounding before the decimal point SELECT round(4.4e131071, -131071) = 4e131071; SELECT round(4.5e131071, -131071) = 5e131071; SELECT round(4.5e131071, -131072); -- loses all digits SELECT round(5.5e131071, -131072); -- rounds up and overflows SELECT round(5.5e131071, -131073); -- loses all digits SELECT round(5.5e131071, -1000000); -- loses all digits -- Check limits of rounding after the decimal point SELECT round(5e-16383, 1000000) = 5e-16383; SELECT round(5e-16383, 16383) = 5e-16383; SELECT round(5e-16383, 16382) = 1e-16382; SELECT round(5e-16383, 16381) = 0; -- Check limits of trunc() before the decimal point SELECT trunc(9.9e131071, -131071) = 9e131071; SELECT trunc(9.9e131071, -131072); -- loses all digits SELECT trunc(9.9e131071, -131073); -- loses all digits SELECT trunc(9.9e131071, -1000000); -- loses all digits -- Check limits of trunc() after the decimal point SELECT trunc(5e-16383, 1000000) = 5e-16383; SELECT trunc(5e-16383, 16383) = 5e-16383; SELECT trunc(5e-16383, 16382) = 0; -- 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); SELECT width_bucket(5.0, 3.0, 4.0, -5); SELECT width_bucket(3.5, 3.0, 3.0, 888); SELECT width_bucket(5.0::float8, 3.0::float8, 4.0::float8, 0); SELECT width_bucket(5.0::float8, 3.0::float8, 4.0::float8, -5); SELECT width_bucket(3.5::float8, 3.0::float8, 3.0::float8, 888); SELECT width_bucket('NaN', 3.0, 4.0, 888); SELECT width_bucket(0::float8, 'NaN', 4.0::float8, 888); SELECT width_bucket(2.0, 3.0, '-inf', 888); SELECT width_bucket(0::float8, '-inf', 4.0::float8, 888); -- normal operation CREATE TABLE width_bucket_test (operand_num numeric, operand_f8 float8); COPY width_bucket_test (operand_num) FROM stdin; -5.2 -0.0000000001 0.000000000001 1 1.99999999999999 2 2.00000000000001 3 4 4.5 5 5.5 6 7 8 9 9.99999999999999 10 10.0000000000001 \. 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; -- 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 SELECT width_bucket(0.0::numeric, 5, '-Infinity'::numeric, 20); -- error SELECT width_bucket('Infinity'::numeric, 1, 10, 10), width_bucket('-Infinity'::numeric, 1, 10, 10); SELECT width_bucket(0.0::float8, 'Infinity'::float8, 5, 10); -- error SELECT width_bucket(0.0::float8, 5, '-Infinity'::float8, 20); -- error SELECT width_bucket('Infinity'::float8, 1, 10, 10), width_bucket('-Infinity'::float8, 1, 10, 10); 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; 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; -- Another roundoff-error hazard SELECT width_bucket(0, -1e100::numeric, 1, 10); SELECT width_bucket(0, -1e100::float8, 1, 10); SELECT width_bucket(1, 1e100::numeric, 0, 10); SELECT width_bucket(1, 1e100::float8, 0, 10); -- 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); -- These fail because the result would be out of int32 range: SELECT width_bucket(1::float8, 0, 1, 2147483647); SELECT width_bucket(0::float8, 1, 0, 2147483647); -- -- TO_CHAR() -- SELECT to_char(val, '9G999G999G999G999G999') FROM num_data; SELECT to_char(val, '9G999G999G999G999G999D999G999G999G999G999') FROM num_data; SELECT to_char(val, '9999999999999999.999999999999999PR') FROM num_data; SELECT to_char(val, '9999999999999999.999999999999999S') FROM num_data; SELECT to_char(val, 'MI9999999999999999.999999999999999') FROM num_data; SELECT to_char(val, 'FMS9999999999999999.999999999999999') FROM num_data; SELECT to_char(val, 'FM9999999999999999.999999999999999THPR') FROM num_data; SELECT to_char(val, 'SG9999999999999999.999999999999999th') FROM num_data; SELECT to_char(val, '0999999999999999.999999999999999') FROM num_data; SELECT to_char(val, 'S0999999999999999.999999999999999') FROM num_data; SELECT to_char(val, 'FM0999999999999999.999999999999999') FROM num_data; SELECT to_char(val, 'FM9999999999999999.099999999999999') FROM num_data; SELECT to_char(val, 'FM9999999999990999.990999999999999') FROM num_data; SELECT to_char(val, 'FM0999999999999999.999909999999999') FROM num_data; SELECT to_char(val, 'FM9999999990999999.099999999999999') FROM num_data; SELECT to_char(val, 'L9999999999999999.099999999999999') FROM num_data; SELECT to_char(val, 'FM9999999999999999.99999999999999') FROM num_data; 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; 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; SELECT to_char(val, E'99999 "text" 9999 "9999" 999 "\\"text between quote marks\\"" 9999') FROM num_data; SELECT to_char(val, '999999SG9999999999') FROM num_data; SELECT to_char(val, 'FM9999999999999999.999999999999999') FROM num_data; SELECT to_char(val, '9.999EEEE') FROM num_data; 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; 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; 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; 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; SELECT to_char('100'::numeric, 'FM999.9'); SELECT to_char('100'::numeric, 'FM999.'); SELECT to_char('100'::numeric, 'FM999'); SELECT to_char('12345678901'::float8, 'FM9999999999D9999900000000000000000'); -- Check parsing of literal text in a format string SELECT to_char('100'::numeric, 'foo999'); SELECT to_char('100'::numeric, 'f\oo999'); SELECT to_char('100'::numeric, 'f\\oo999'); SELECT to_char('100'::numeric, 'f\"oo999'); SELECT to_char('100'::numeric, 'f\\"oo999'); SELECT to_char('100'::numeric, 'f"ool"999'); SELECT to_char('100'::numeric, 'f"\ool"999'); SELECT to_char('100'::numeric, 'f"\\ool"999'); SELECT to_char('100'::numeric, 'f"ool\"999'); SELECT to_char('100'::numeric, 'f"ool\\"999'); -- TO_NUMBER() -- SET lc_numeric = 'C'; SELECT to_number('-34,338,492', '99G999G999'); SELECT to_number('-34,338,492.654,878', '99G999G999D999G999'); SELECT to_number('<564646.654564>', '999999.999999PR'); SELECT to_number('0.00001-', '9.999999S'); SELECT to_number('5.01-', 'FM9.999999S'); SELECT to_number('5.01-', 'FM9.999999MI'); SELECT to_number('5 4 4 4 4 8 . 7 8', '9 9 9 9 9 9 . 9 9'); SELECT to_number('.01', 'FM9.99'); SELECT to_number('.0', '99999999.99999999'); SELECT to_number('0', '99.99'); SELECT to_number('.-01', 'S99.99'); SELECT to_number('.01-', '99.99S'); SELECT to_number(' . 0 1-', ' 9 9 . 9 9 S'); SELECT to_number('34,50','999,99'); SELECT to_number('123,000','999G'); SELECT to_number('123456','999G999'); SELECT to_number('$1234.56','L9,999.99'); SELECT to_number('$1234.56','L99,999.99'); SELECT to_number('$1,234.56','L99,999.99'); SELECT to_number('1234.56','L99,999.99'); SELECT to_number('1,234.56','L99,999.99'); SELECT to_number('42nd', '99th'); 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 (' '); INSERT INTO num_input_test(n1) VALUES (' 1234 %'); INSERT INTO num_input_test(n1) VALUES ('xyz'); INSERT INTO num_input_test(n1) VALUES ('- 1234'); INSERT INTO num_input_test(n1) VALUES ('5 . 0'); INSERT INTO num_input_test(n1) VALUES ('5. 0 '); INSERT INTO num_input_test(n1) VALUES (''); INSERT INTO num_input_test(n1) VALUES (' N aN '); INSERT INTO num_input_test(n1) VALUES ('+NaN'); INSERT INTO num_input_test(n1) VALUES ('-NaN'); INSERT INTO num_input_test(n1) VALUES ('+ infinity'); INSERT INTO num_input_test(n1) VALUES ('_123'); INSERT INTO num_input_test(n1) VALUES ('123_'); INSERT INTO num_input_test(n1) VALUES ('12__34'); INSERT INTO num_input_test(n1) VALUES ('123_.456'); INSERT INTO num_input_test(n1) VALUES ('123._456'); INSERT INTO num_input_test(n1) VALUES ('1.2e_34'); INSERT INTO num_input_test(n1) VALUES ('1.2e34_'); INSERT INTO num_input_test(n1) VALUES ('1.2e3__4'); INSERT INTO num_input_test(n1) VALUES ('0b1112'); INSERT INTO num_input_test(n1) VALUES ('0c1112'); INSERT INTO num_input_test(n1) VALUES ('0o12345678'); INSERT INTO num_input_test(n1) VALUES ('0x1eg'); INSERT INTO num_input_test(n1) VALUES ('0x12.34'); INSERT INTO num_input_test(n1) VALUES ('0x__1234'); INSERT INTO num_input_test(n1) VALUES ('0x1234_'); INSERT INTO num_input_test(n1) VALUES ('0x12__34'); SELECT * FROM num_input_test; -- Also try it with non-error-throwing API SELECT pg_input_is_valid('34.5', 'numeric'); SELECT pg_input_is_valid('34xyz', 'numeric'); SELECT pg_input_is_valid('1e400000', 'numeric'); SELECT * FROM pg_input_error_info('1e400000', 'numeric'); SELECT pg_input_is_valid('1234.567', 'numeric(8,4)'); SELECT pg_input_is_valid('1234.567', 'numeric(7,4)'); SELECT * FROM pg_input_error_info('1234.567', 'numeric(7,4)'); SELECT * FROM pg_input_error_info('0x1234.567', 'numeric'); -- -- 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 -- 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; -- invalid inputs INSERT INTO num_typemod_test (millions) VALUES ('inf'); INSERT INTO num_typemod_test (millions) VALUES (999500000); INSERT INTO num_typemod_test (thousands) VALUES (999500); INSERT INTO num_typemod_test (units) VALUES (999.5); INSERT INTO num_typemod_test (thousandths) VALUES (0.9995); INSERT INTO num_typemod_test (millionths) VALUES (0.0009995); -- -- Test some corner cases for multiplication -- select 4790999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999; select 4789999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999; select 4770999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999; select 4769999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999; select trim_scale((0.1 - 2e-16383) * (0.1 - 3e-16383)); -- -- Test some corner cases for division -- select 999999999999999999999::numeric/1000000000000000000000; select div(999999999999999999999::numeric,1000000000000000000000); select mod(999999999999999999999::numeric,1000000000000000000000); select div(-9999999999999999999999::numeric,1000000000000000000000); select mod(-9999999999999999999999::numeric,1000000000000000000000); select div(-9999999999999999999999::numeric,1000000000000000000000)*1000000000000000000000 + mod(-9999999999999999999999::numeric,1000000000000000000000); select mod (70.0,70) ; select div (70.0,70) ; select 70.0 / 70 ; select 12345678901234567890 % 123; select 12345678901234567890 / 123; select div(12345678901234567890, 123); select div(12345678901234567890, 123) * 123 + 12345678901234567890 % 123; -- -- Test some corner cases for square root -- select sqrt(1.000000000000003::numeric); select sqrt(1.000000000000004::numeric); select sqrt(96627521408608.56340355805::numeric); select sqrt(96627521408608.56340355806::numeric); select sqrt(515549506212297735.073688290367::numeric); select sqrt(515549506212297735.073688290368::numeric); select sqrt(8015491789940783531003294973900306::numeric); select sqrt(8015491789940783531003294973900307::numeric); -- -- Test code path for raising to integer powers -- select 10.0 ^ -2147483648 as rounds_to_zero; select 10.0 ^ -2147483647 as rounds_to_zero; select 10.0 ^ 2147483647 as overflows; select 117743296169.0 ^ 1000000000 as overflows; -- cases that used to return inaccurate results select 3.789 ^ 21.0000000000000000; select 3.789 ^ 35.0000000000000000; select 1.2 ^ 345; select 0.12 ^ (-20); select 1.000000000123 ^ (-2147483648); select coalesce(nullif(0.9999999999 ^ 23300000000000, 0), 0) as rounds_to_zero; select round(((1 - 1.500012345678e-1000) ^ 1.45e1003) * 1e1000); -- cases that used to error out select 0.12 ^ (-25); select 0.5678 ^ (-85); select coalesce(nullif(0.9999999999 ^ 70000000000000, 0), 0) as underflows; -- negative base to integer powers select (-1.0) ^ 2147483646; select (-1.0) ^ 2147483647; select (-1.0) ^ 2147483648; select (-1.0) ^ 1000000000000000; select (-1.0) ^ 1000000000000001; -- 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; -- -- Tests for raising to non-integer powers -- -- special cases select 0.0 ^ 0.0; select (-12.34) ^ 0.0; select 12.34 ^ 0.0; select 0.0 ^ 12.34; -- NaNs select 'NaN'::numeric ^ 'NaN'::numeric; select 'NaN'::numeric ^ 0; select 'NaN'::numeric ^ 1; select 0 ^ 'NaN'::numeric; select 1 ^ 'NaN'::numeric; -- invalid inputs select 0.0 ^ (-12.34); select (-12.34) ^ 1.2; -- cases that used to generate inaccurate results select 32.1 ^ 9.8; select 32.1 ^ (-9.8); select 12.3 ^ 45.6; select 12.3 ^ (-45.6); -- big test select 1.234 ^ 5678; -- -- Tests for EXP() -- -- special cases select exp(0.0); select exp(1.0); select exp(1.0::numeric(71,70)); select exp('nan'::numeric); select exp('inf'::numeric); select exp('-inf'::numeric); select coalesce(nullif(exp(-5000::numeric), 0), 0) as rounds_to_zero; select coalesce(nullif(exp(-10000::numeric), 0), 0) as underflows; -- cases that used to generate inaccurate results select exp(32.999); select exp(-32.999); select exp(123.456); select exp(-123.456); -- big test select exp(1234.5678); -- -- Tests for generate_series -- select * from generate_series(0.0::numeric, 4.0::numeric); select * from generate_series(0.1::numeric, 4.0::numeric, 1.3::numeric); select * from generate_series(4.0::numeric, -1.5::numeric, -2.2::numeric); -- Trigger errors select * from generate_series(-100::numeric, 100::numeric, 0::numeric); select * from generate_series(-100::numeric, 100::numeric, 'nan'::numeric); select * from generate_series('nan'::numeric, 100::numeric, 10::numeric); select * from generate_series(0::numeric, 'nan'::numeric, 10::numeric); select * from generate_series('inf'::numeric, 'inf'::numeric, 10::numeric); select * from generate_series(0::numeric, 'inf'::numeric, 10::numeric); select * from generate_series(0::numeric, '42'::numeric, '-inf'::numeric); -- 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); -- Check usage with variables select * from generate_series(1::numeric, 3::numeric) i, generate_series(i,3) j; select * from generate_series(1::numeric, 3::numeric) i, generate_series(1,i) j; select * from generate_series(1::numeric, 3::numeric) i, generate_series(1,5,i) j; -- -- Tests for LN() -- -- Invalid inputs select ln(-12.34); select ln(0.0); -- Some random tests select ln(1.2345678e-28); select ln(0.0456789); select ln(0.349873948359354029493948309745709580730482050975); select ln(0.99949452); select ln(1.00049687395); select ln(1234.567890123456789); select ln(5.80397490724e5); select ln(9.342536355e34); -- -- Tests for LOG() (base 10) -- -- invalid inputs select log(-12.34); select log(0.0); -- some random tests select log(1.234567e-89); select log(3.4634998359873254962349856073435545); select log(9.999999999999999999); select log(10.00000000000000000); select log(10.00000000000000001); select log(590489.45235237); -- -- Tests for LOG() (arbitrary base) -- -- invalid inputs select log(-12.34, 56.78); select log(-12.34, -56.78); select log(12.34, -56.78); select log(0.0, 12.34); select log(12.34, 0.0); select log(1.0, 12.34); -- some random tests select log(1.23e-89, 6.4689e45); select log(0.99923, 4.58934e34); select log(1.000016, 8.452010e18); select log(3.1954752e47, 9.4792021e-73); -- -- Tests for scale() -- select scale(numeric 'NaN'); select scale(numeric 'inf'); select scale(NULL::numeric); select scale(1.12); select scale(0); select scale(0.00); select scale(1.12345); select scale(110123.12475871856128); select scale(-1123.12471856128); select scale(-13.000000000000000); -- -- Tests for min_scale() -- select min_scale(numeric 'NaN') is NULL; -- should be true select min_scale(numeric 'inf') is NULL; -- should be true select min_scale(0); -- no digits select min_scale(0.00); -- no digits again select min_scale(1.0); -- no scale select min_scale(1.1); -- scale 1 select min_scale(1.12); -- scale 2 select min_scale(1.123); -- scale 3 select min_scale(1.1234); -- scale 4, filled digit select min_scale(1.12345); -- scale 5, 2 NDIGITS select min_scale(1.1000); -- 1 pos in NDIGITS select min_scale(1e100); -- very big number -- -- Tests for trim_scale() -- select trim_scale(numeric 'NaN'); select trim_scale(numeric 'inf'); select trim_scale(1.120); select trim_scale(0); select trim_scale(0.00); select trim_scale(1.1234500); select trim_scale(110123.12475871856128000); select trim_scale(-1123.124718561280000000); select trim_scale(-13.00000000000000000000); select trim_scale(1e100); -- -- Tests for SUM() -- -- cases that need carry propagation SELECT SUM(9999::numeric) FROM generate_series(1, 100000); SELECT SUM((-9999)::numeric) FROM generate_series(1, 100000); -- -- 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; -- 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; 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; -- 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; 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); -- -- 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); SELECT lcm(9999 * (10::numeric)^131068 + (10::numeric^131068 - 1), 2); -- overflow -- -- Tests for factorial -- SELECT factorial(4); SELECT factorial(15); SELECT factorial(100000); SELECT factorial(0); SELECT factorial(-4); -- -- Tests for pg_lsn() -- SELECT pg_lsn(23783416::numeric); SELECT pg_lsn(0::numeric); SELECT pg_lsn(18446744073709551615::numeric); SELECT pg_lsn(-1::numeric); SELECT pg_lsn(18446744073709551616::numeric); SELECT pg_lsn('NaN'::numeric);