--
-- 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');
INSERT INTO num_exp_mul VALUES (4,0,'0');
INSERT INTO num_exp_div VALUES (4,0,'NaN');
INSERT INTO num_exp_add VALUES (4,1,'7799461.4119');
INSERT INTO num_exp_sub VALUES (4,1,'7799461.4119');
INSERT INTO num_exp_mul VALUES (4,1,'0');
INSERT INTO num_exp_div VALUES (4,1,'NaN');
INSERT INTO num_exp_add VALUES (4,2,'-26539030.803497047');
INSERT INTO num_exp_sub VALUES (4,2,'42137953.627297047');
INSERT INTO num_exp_mul VALUES (4,2,'-267821744976817.8111137106593');
INSERT INTO num_exp_div VALUES (4,2,'-.22713465002993920385');
INSERT INTO num_exp_add VALUES (4,3,'7799465.7219');
INSERT INTO num_exp_sub VALUES (4,3,'7799457.1019');
INSERT INTO num_exp_mul VALUES (4,3,'33615678.685289');
INSERT INTO num_exp_div VALUES (4,3,'1809619.81714617169373549883');
INSERT INTO num_exp_add VALUES (4,4,'15598922.8238');
INSERT INTO num_exp_sub VALUES (4,4,'0');
INSERT INTO num_exp_mul VALUES (4,4,'60831598315717.14146161');
INSERT INTO num_exp_div VALUES (4,4,'1.00000000000000000000');
INSERT INTO num_exp_add VALUES (4,5,'7815858.450391');
INSERT INTO num_exp_sub VALUES (4,5,'7783064.373409');
INSERT INTO num_exp_mul VALUES (4,5,'127888068979.9935054429');
INSERT INTO num_exp_div VALUES (4,5,'475.66281046305802686061');
INSERT INTO num_exp_add VALUES (4,6,'7893362.98953026');
INSERT INTO num_exp_sub VALUES (4,6,'7705559.83426974');
INSERT INTO num_exp_mul VALUES (4,6,'732381731243.745115764094');
INSERT INTO num_exp_div VALUES (4,6,'83.05996138436129499606');
INSERT INTO num_exp_add VALUES (4,7,'-75229023.5881');
INSERT INTO num_exp_sub VALUES (4,7,'90827946.4119');
INSERT INTO num_exp_mul VALUES (4,7,'-647577464846017.9715');
INSERT INTO num_exp_div VALUES (4,7,'-.09393717604145131637');
INSERT INTO num_exp_add VALUES (4,8,'7874342.4119');
INSERT INTO num_exp_sub VALUES (4,8,'7724580.4119');
INSERT INTO num_exp_mul VALUES (4,8,'584031469984.4839');
INSERT INTO num_exp_div VALUES (4,8,'104.15808298366741897143');
INSERT INTO num_exp_add VALUES (4,9,'-17127342.633147420');
INSERT INTO num_exp_sub VALUES (4,9,'32726265.456947420');
INSERT INTO num_exp_mul VALUES (4,9,'-194415646271340.1815956522980');
INSERT INTO num_exp_div VALUES (4,9,'-.31289456112403769409');
INSERT INTO num_exp_add VALUES (5,0,'16397.038491');
INSERT INTO num_exp_sub VALUES (5,0,'16397.038491');
INSERT INTO num_exp_mul VALUES (5,0,'0');
INSERT INTO num_exp_div VALUES (5,0,'NaN');
INSERT INTO num_exp_add VALUES (5,1,'16397.038491');
INSERT INTO num_exp_sub VALUES (5,1,'16397.038491');
INSERT INTO num_exp_mul VALUES (5,1,'0');
INSERT INTO num_exp_div VALUES (5,1,'NaN');
INSERT INTO num_exp_add VALUES (5,2,'-34322095.176906047');
INSERT INTO num_exp_sub VALUES (5,2,'34354889.253888047');
INSERT INTO num_exp_mul VALUES (5,2,'-563049578578.769242506736077');
INSERT INTO num_exp_div VALUES (5,2,'-.00047751189505192446');
INSERT INTO num_exp_add VALUES (5,3,'16401.348491');
INSERT INTO num_exp_sub VALUES (5,3,'16392.728491');
INSERT INTO num_exp_mul VALUES (5,3,'70671.23589621');
INSERT INTO num_exp_div VALUES (5,3,'3804.41728329466357308584');
INSERT INTO num_exp_add VALUES (5,4,'7815858.450391');
INSERT INTO num_exp_sub VALUES (5,4,'-7783064.373409');
INSERT INTO num_exp_mul VALUES (5,4,'127888068979.9935054429');
INSERT INTO num_exp_div VALUES (5,4,'.00210232958726897192');
INSERT INTO num_exp_add VALUES (5,5,'32794.076982');
INSERT INTO num_exp_sub VALUES (5,5,'0');
INSERT INTO num_exp_mul VALUES (5,5,'268862871.275335557081');
INSERT INTO num_exp_div VALUES (5,5,'1.00000000000000000000');
INSERT INTO num_exp_add VALUES (5,6,'110298.61612126');
INSERT INTO num_exp_sub VALUES (5,6,'-77504.53913926');
INSERT INTO num_exp_mul VALUES (5,6,'1539707782.76899778633766');
INSERT INTO num_exp_div VALUES (5,6,'.17461941433576102689');
INSERT INTO num_exp_add VALUES (5,7,'-83012087.961509');
INSERT INTO num_exp_sub VALUES (5,7,'83044882.038491');
INSERT INTO num_exp_mul VALUES (5,7,'-1361421264394.416135');
INSERT INTO num_exp_div VALUES (5,7,'-.00019748690453643710');
INSERT INTO num_exp_add VALUES (5,8,'91278.038491');
INSERT INTO num_exp_sub VALUES (5,8,'-58483.961509');
INSERT INTO num_exp_mul VALUES (5,8,'1227826639.244571');
INSERT INTO num_exp_div VALUES (5,8,'.21897461960978085228');
INSERT INTO num_exp_add VALUES (5,9,'-24910407.006556420');
INSERT INTO num_exp_sub VALUES (5,9,'24943201.083538420');
INSERT INTO num_exp_mul VALUES (5,9,'-408725765384.257043660243220');
INSERT INTO num_exp_div VALUES (5,9,'-.00065780749354660427');
INSERT INTO num_exp_add VALUES (6,0,'93901.57763026');
INSERT INTO num_exp_sub VALUES (6,0,'93901.57763026');
INSERT INTO num_exp_mul VALUES (6,0,'0');
INSERT INTO num_exp_div VALUES (6,0,'NaN');
INSERT INTO num_exp_add VALUES (6,1,'93901.57763026');
INSERT INTO num_exp_sub VALUES (6,1,'93901.57763026');
INSERT INTO num_exp_mul VALUES (6,1,'0');
INSERT INTO num_exp_div VALUES (6,1,'NaN');
INSERT INTO num_exp_add VALUES (6,2,'-34244590.637766787');
INSERT INTO num_exp_sub VALUES (6,2,'34432393.793027307');
INSERT INTO num_exp_mul VALUES (6,2,'-3224438592470.18449811926184222');
INSERT INTO num_exp_div VALUES (6,2,'-.00273458651128995823');
INSERT INTO num_exp_add VALUES (6,3,'93905.88763026');
INSERT INTO num_exp_sub VALUES (6,3,'93897.26763026');
INSERT INTO num_exp_mul VALUES (6,3,'404715.7995864206');
INSERT INTO num_exp_div VALUES (6,3,'21786.90896293735498839907');
INSERT INTO num_exp_add VALUES (6,4,'7893362.98953026');
INSERT INTO num_exp_sub VALUES (6,4,'-7705559.83426974');
INSERT INTO num_exp_mul VALUES (6,4,'732381731243.745115764094');
INSERT INTO num_exp_div VALUES (6,4,'.01203949512295682469');
INSERT INTO num_exp_add VALUES (6,5,'110298.61612126');
INSERT INTO num_exp_sub VALUES (6,5,'77504.53913926');
INSERT INTO num_exp_mul VALUES (6,5,'1539707782.76899778633766');
INSERT INTO num_exp_div VALUES (6,5,'5.72674008674192359679');
INSERT INTO num_exp_add VALUES (6,6,'187803.15526052');
INSERT INTO num_exp_sub VALUES (6,6,'0');
INSERT INTO num_exp_mul VALUES (6,6,'8817506281.4517452372676676');
INSERT INTO num_exp_div VALUES (6,6,'1.00000000000000000000');
INSERT INTO num_exp_add VALUES (6,7,'-82934583.42236974');
INSERT INTO num_exp_sub VALUES (6,7,'83122386.57763026');
INSERT INTO num_exp_mul VALUES (6,7,'-7796505729750.37795610');
INSERT INTO num_exp_div VALUES (6,7,'-.00113095617281538980');
INSERT INTO num_exp_add VALUES (6,8,'168782.57763026');
INSERT INTO num_exp_sub VALUES (6,8,'19020.57763026');
INSERT INTO num_exp_mul VALUES (6,8,'7031444034.53149906');
INSERT INTO num_exp_div VALUES (6,8,'1.25401073209839612184');
INSERT INTO num_exp_add VALUES (6,9,'-24832902.467417160');
INSERT INTO num_exp_sub VALUES (6,9,'25020705.622677680');
INSERT INTO num_exp_mul VALUES (6,9,'-2340666225110.29929521292692920');
INSERT INTO num_exp_div VALUES (6,9,'-.00376709254265256789');
INSERT INTO num_exp_add VALUES (7,0,'-83028485');
INSERT INTO num_exp_sub VALUES (7,0,'-83028485');
INSERT INTO num_exp_mul VALUES (7,0,'0');
INSERT INTO num_exp_div VALUES (7,0,'NaN');
INSERT INTO num_exp_add VALUES (7,1,'-83028485');
INSERT INTO num_exp_sub VALUES (7,1,'-83028485');
INSERT INTO num_exp_mul VALUES (7,1,'0');
INSERT INTO num_exp_div VALUES (7,1,'NaN');
INSERT INTO num_exp_add VALUES (7,2,'-117366977.215397047');
INSERT INTO num_exp_sub VALUES (7,2,'-48689992.784602953');
INSERT INTO num_exp_mul VALUES (7,2,'2851072985828710.485883795');
INSERT INTO num_exp_div VALUES (7,2,'2.41794207151503385700');
INSERT INTO num_exp_add VALUES (7,3,'-83028480.69');
INSERT INTO num_exp_sub VALUES (7,3,'-83028489.31');
INSERT INTO num_exp_mul VALUES (7,3,'-357852770.35');
INSERT INTO num_exp_div VALUES (7,3,'-19264149.65197215777262180974');
INSERT INTO num_exp_add VALUES (7,4,'-75229023.5881');
INSERT INTO num_exp_sub VALUES (7,4,'-90827946.4119');
INSERT INTO num_exp_mul VALUES (7,4,'-647577464846017.9715');
INSERT INTO num_exp_div VALUES (7,4,'-10.64541262725136247686');
INSERT INTO num_exp_add VALUES (7,5,'-83012087.961509');
INSERT INTO num_exp_sub VALUES (7,5,'-83044882.038491');
INSERT INTO num_exp_mul VALUES (7,5,'-1361421264394.416135');
INSERT INTO num_exp_div VALUES (7,5,'-5063.62688881730941836574');
INSERT INTO num_exp_add VALUES (7,6,'-82934583.42236974');
INSERT INTO num_exp_sub VALUES (7,6,'-83122386.57763026');
INSERT INTO num_exp_mul VALUES (7,6,'-7796505729750.37795610');
INSERT INTO num_exp_div VALUES (7,6,'-884.20756174009028770294');
INSERT INTO num_exp_add VALUES (7,7,'-166056970');
INSERT INTO num_exp_sub VALUES (7,7,'0');
INSERT INTO num_exp_mul VALUES (7,7,'6893729321395225');
INSERT INTO num_exp_div VALUES (7,7,'1.00000000000000000000');
INSERT INTO num_exp_add VALUES (7,8,'-82953604');
INSERT INTO num_exp_sub VALUES (7,8,'-83103366');
INSERT INTO num_exp_mul VALUES (7,8,'-6217255985285');
INSERT INTO num_exp_div VALUES (7,8,'-1108.80577182462841041118');
INSERT INTO num_exp_add VALUES (7,9,'-107955289.045047420');
INSERT INTO num_exp_sub VALUES (7,9,'-58101680.954952580');
INSERT INTO num_exp_mul VALUES (7,9,'2069634775752159.035758700');
INSERT INTO num_exp_div VALUES (7,9,'3.33089171198810413382');
INSERT INTO num_exp_add VALUES (8,0,'74881');
INSERT INTO num_exp_sub VALUES (8,0,'74881');
INSERT INTO num_exp_mul VALUES (8,0,'0');
INSERT INTO num_exp_div VALUES (8,0,'NaN');
INSERT INTO num_exp_add VALUES (8,1,'74881');
INSERT INTO num_exp_sub VALUES (8,1,'74881');
INSERT INTO num_exp_mul VALUES (8,1,'0');
INSERT INTO num_exp_div VALUES (8,1,'NaN');
INSERT INTO num_exp_add VALUES (8,2,'-34263611.215397047');
INSERT INTO num_exp_sub VALUES (8,2,'34413373.215397047');
INSERT INTO num_exp_mul VALUES (8,2,'-2571300635581.146276407');
INSERT INTO num_exp_div VALUES (8,2,'-.00218067233500788615');
INSERT INTO num_exp_add VALUES (8,3,'74885.31');
INSERT INTO num_exp_sub VALUES (8,3,'74876.69');
INSERT INTO num_exp_mul VALUES (8,3,'322737.11');
INSERT INTO num_exp_div VALUES (8,3,'17373.78190255220417633410');
INSERT INTO num_exp_add VALUES (8,4,'7874342.4119');
INSERT INTO num_exp_sub VALUES (8,4,'-7724580.4119');
INSERT INTO num_exp_mul VALUES (8,4,'584031469984.4839');
INSERT INTO num_exp_div VALUES (8,4,'.00960079113741758956');
INSERT INTO num_exp_add VALUES (8,5,'91278.038491');
INSERT INTO num_exp_sub VALUES (8,5,'58483.961509');
INSERT INTO num_exp_mul VALUES (8,5,'1227826639.244571');
INSERT INTO num_exp_div VALUES (8,5,'4.56673929509287019456');
INSERT INTO num_exp_add VALUES (8,6,'168782.57763026');
INSERT INTO num_exp_sub VALUES (8,6,'-19020.57763026');
INSERT INTO num_exp_mul VALUES (8,6,'7031444034.53149906');
INSERT INTO num_exp_div VALUES (8,6,'.79744134113322314424');
INSERT INTO num_exp_add VALUES (8,7,'-82953604');
INSERT INTO num_exp_sub VALUES (8,7,'83103366');
INSERT INTO num_exp_mul VALUES (8,7,'-6217255985285');
INSERT INTO num_exp_div VALUES (8,7,'-.00090187120721280172');
INSERT INTO num_exp_add VALUES (8,8,'149762');
INSERT INTO num_exp_sub VALUES (8,8,'0');
INSERT INTO num_exp_mul VALUES (8,8,'5607164161');
INSERT INTO num_exp_div VALUES (8,8,'1.00000000000000000000');
INSERT INTO num_exp_add VALUES (8,9,'-24851923.045047420');
INSERT INTO num_exp_sub VALUES (8,9,'25001685.045047420');
INSERT INTO num_exp_mul VALUES (8,9,'-1866544013697.195857020');
INSERT INTO num_exp_div VALUES (8,9,'-.00300403532938582735');
INSERT INTO num_exp_add VALUES (9,0,'-24926804.045047420');
INSERT INTO num_exp_sub VALUES (9,0,'-24926804.045047420');
INSERT INTO num_exp_mul VALUES (9,0,'0');
INSERT INTO num_exp_div VALUES (9,0,'NaN');
INSERT INTO num_exp_add VALUES (9,1,'-24926804.045047420');
INSERT INTO num_exp_sub VALUES (9,1,'-24926804.045047420');
INSERT INTO num_exp_mul VALUES (9,1,'0');
INSERT INTO num_exp_div VALUES (9,1,'NaN');
INSERT INTO num_exp_add VALUES (9,2,'-59265296.260444467');
INSERT INTO num_exp_sub VALUES (9,2,'9411688.170349627');
INSERT INTO num_exp_mul VALUES (9,2,'855948866655588.453741509242968740');
INSERT INTO num_exp_div VALUES (9,2,'.72591434384152961526');
INSERT INTO num_exp_add VALUES (9,3,'-24926799.735047420');
INSERT INTO num_exp_sub VALUES (9,3,'-24926808.355047420');
INSERT INTO num_exp_mul VALUES (9,3,'-107434525.43415438020');
INSERT INTO num_exp_div VALUES (9,3,'-5783481.21694835730858468677');
INSERT INTO num_exp_add VALUES (9,4,'-17127342.633147420');
INSERT INTO num_exp_sub VALUES (9,4,'-32726265.456947420');
INSERT INTO num_exp_mul VALUES (9,4,'-194415646271340.1815956522980');
INSERT INTO num_exp_div VALUES (9,4,'-3.19596478892958416484');
INSERT INTO num_exp_add VALUES (9,5,'-24910407.006556420');
INSERT INTO num_exp_sub VALUES (9,5,'-24943201.083538420');
INSERT INTO num_exp_mul VALUES (9,5,'-408725765384.257043660243220');
INSERT INTO num_exp_div VALUES (9,5,'-1520.20159364322004505807');
INSERT INTO num_exp_add VALUES (9,6,'-24832902.467417160');
INSERT INTO num_exp_sub VALUES (9,6,'-25020705.622677680');
INSERT INTO num_exp_mul VALUES (9,6,'-2340666225110.29929521292692920');
INSERT INTO num_exp_div VALUES (9,6,'-265.45671195426965751280');
INSERT INTO num_exp_add VALUES (9,7,'-107955289.045047420');
INSERT INTO num_exp_sub VALUES (9,7,'58101680.954952580');
INSERT INTO num_exp_mul VALUES (9,7,'2069634775752159.035758700');
INSERT INTO num_exp_div VALUES (9,7,'.30021990699995814689');
INSERT INTO num_exp_add VALUES (9,8,'-24851923.045047420');
INSERT INTO num_exp_sub VALUES (9,8,'-25001685.045047420');
INSERT INTO num_exp_mul VALUES (9,8,'-1866544013697.195857020');
INSERT INTO num_exp_div VALUES (9,8,'-332.88556569820675471748');
INSERT INTO num_exp_add VALUES (9,9,'-49853608.090094840');
INSERT INTO num_exp_sub VALUES (9,9,'0');
INSERT INTO num_exp_mul VALUES (9,9,'621345559900192.420120630048656400');
INSERT INTO num_exp_div VALUES (9,9,'1.00000000000000000000');
COMMIT TRANSACTION;
BEGIN TRANSACTION;
INSERT INTO num_exp_sqrt VALUES (0,'0');
INSERT INTO num_exp_sqrt VALUES (1,'0');
INSERT INTO num_exp_sqrt VALUES (2,'5859.90547836712524903505');
INSERT INTO num_exp_sqrt VALUES (3,'2.07605394920266944396');
INSERT INTO num_exp_sqrt VALUES (4,'2792.75158435189147418923');
INSERT INTO num_exp_sqrt VALUES (5,'128.05092147657509145473');
INSERT INTO num_exp_sqrt VALUES (6,'306.43364311096782703406');
INSERT INTO num_exp_sqrt VALUES (7,'9111.99676251039939975230');
INSERT INTO num_exp_sqrt VALUES (8,'273.64392922189960397542');
INSERT INTO num_exp_sqrt VALUES (9,'4992.67503899937593364766');
COMMIT TRANSACTION;
BEGIN TRANSACTION;
INSERT INTO num_exp_ln VALUES (0,'NaN');
INSERT INTO num_exp_ln VALUES (1,'NaN');
INSERT INTO num_exp_ln VALUES (2,'17.35177750493897715514');
INSERT INTO num_exp_ln VALUES (3,'1.46093790411565641971');
INSERT INTO num_exp_ln VALUES (4,'15.86956523951936572464');
INSERT INTO num_exp_ln VALUES (5,'9.70485601768871834038');
INSERT INTO num_exp_ln VALUES (6,'11.45000246622944403127');
INSERT INTO num_exp_ln VALUES (7,'18.23469429965478772991');
INSERT INTO num_exp_ln VALUES (8,'11.22365546576315513668');
INSERT INTO num_exp_ln VALUES (9,'17.03145425013166006962');
COMMIT TRANSACTION;
BEGIN TRANSACTION;
INSERT INTO num_exp_log10 VALUES (0,'NaN');
INSERT INTO num_exp_log10 VALUES (1,'NaN');
INSERT INTO num_exp_log10 VALUES (2,'7.53578122160797276459');
INSERT INTO num_exp_log10 VALUES (3,'.63447727016073160075');
INSERT INTO num_exp_log10 VALUES (4,'6.89206461372691743345');
INSERT INTO num_exp_log10 VALUES (5,'4.21476541614777768626');
INSERT INTO num_exp_log10 VALUES (6,'4.97267288886207207671');
INSERT INTO num_exp_log10 VALUES (7,'7.91922711353275546914');
INSERT INTO num_exp_log10 VALUES (8,'4.87437163556421004138');
INSERT INTO num_exp_log10 VALUES (9,'7.39666659961986567059');
COMMIT TRANSACTION;
BEGIN TRANSACTION;
INSERT INTO num_exp_power_10_ln VALUES (0,'NaN');
INSERT INTO num_exp_power_10_ln VALUES (1,'NaN');
INSERT INTO num_exp_power_10_ln VALUES (2,'224790267919917955.13261618583642653184');
INSERT INTO num_exp_power_10_ln VALUES (3,'28.90266599445155957393');
INSERT INTO num_exp_power_10_ln VALUES (4,'7405685069594999.07733999469386277636');
INSERT INTO num_exp_power_10_ln VALUES (5,'5068226527.32127265408584640098');
INSERT INTO num_exp_power_10_ln VALUES (6,'281839893606.99372343357047819067');
INSERT INTO num_exp_power_10_ln VALUES (7,'1716699575118597095.42330819910640247627');
INSERT INTO num_exp_power_10_ln VALUES (8,'167361463828.07491320069016125952');
INSERT INTO num_exp_power_10_ln VALUES (9,'107511333880052007.04141124673540337457');
COMMIT TRANSACTION;
BEGIN TRANSACTION;
INSERT INTO num_data VALUES (0, '0');
INSERT INTO num_data VALUES (1, '0');
INSERT INTO num_data VALUES (2, '-34338492.215397047');
INSERT INTO num_data VALUES (3, '4.31');
INSERT INTO num_data VALUES (4, '7799461.4119');
INSERT INTO num_data VALUES (5, '16397.038491');
INSERT INTO num_data VALUES (6, '93901.57763026');
INSERT INTO num_data VALUES (7, '-83028485');
INSERT INTO num_data VALUES (8, '74881');
INSERT INTO num_data VALUES (9, '-24926804.045047420');
COMMIT TRANSACTION;
-- ******************************
-- * Create indices for faster checks
-- ******************************
CREATE UNIQUE INDEX num_exp_add_idx ON num_exp_add (id1, id2);
CREATE UNIQUE INDEX num_exp_sub_idx ON num_exp_sub (id1, id2);
CREATE UNIQUE INDEX num_exp_div_idx ON num_exp_div (id1, id2);
CREATE UNIQUE INDEX num_exp_mul_idx ON num_exp_mul (id1, id2);
CREATE UNIQUE INDEX num_exp_sqrt_idx ON num_exp_sqrt (id);
CREATE UNIQUE INDEX num_exp_ln_idx ON num_exp_ln (id);
CREATE UNIQUE INDEX num_exp_log10_idx ON num_exp_log10 (id);
CREATE UNIQUE INDEX num_exp_power_10_ln_idx ON num_exp_power_10_ln (id);
VACUUM ANALYZE num_exp_add;
VACUUM ANALYZE num_exp_sub;
VACUUM ANALYZE num_exp_div;
VACUUM ANALYZE num_exp_mul;
VACUUM ANALYZE num_exp_sqrt;
VACUUM ANALYZE num_exp_ln;
VACUUM ANALYZE num_exp_log10;
VACUUM ANALYZE num_exp_power_10_ln;
-- ******************************
-- * Now check the behaviour of the NUMERIC type
-- ******************************
-- ******************************
-- * Addition check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, t1.val + t2.val
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, t2.expected
FROM num_result t1, num_exp_add t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != t2.expected;
id1 | id2 | result | expected
-----+-----+--------+----------
(0 rows)
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val + t2.val, 10)
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 10) as expected
FROM num_result t1, num_exp_add t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != round(t2.expected, 10);
id1 | id2 | result | expected
-----+-----+--------+----------
(0 rows)
-- ******************************
-- * Subtraction check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, t1.val - t2.val
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, t2.expected
FROM num_result t1, num_exp_sub t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != t2.expected;
id1 | id2 | result | expected
-----+-----+--------+----------
(0 rows)
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val - t2.val, 40)
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 40)
FROM num_result t1, num_exp_sub t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != round(t2.expected, 40);
id1 | id2 | result | round
-----+-----+--------+-------
(0 rows)
-- ******************************
-- * Multiply check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, t1.val * t2.val
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, t2.expected
FROM num_result t1, num_exp_mul t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != t2.expected;
id1 | id2 | result | expected
-----+-----+--------+----------
(0 rows)
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val * t2.val, 30)
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 30) as expected
FROM num_result t1, num_exp_mul t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != round(t2.expected, 30);
id1 | id2 | result | expected
-----+-----+--------+----------
(0 rows)
-- ******************************
-- * Division check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, t1.val / t2.val
FROM num_data t1, num_data t2
WHERE t2.val != '0.0';
SELECT t1.id1, t1.id2, t1.result, t2.expected
FROM num_result t1, num_exp_div t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != t2.expected;
id1 | id2 | result | expected
-----+-----+--------+----------
(0 rows)
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val / t2.val, 80)
FROM num_data t1, num_data t2
WHERE t2.val != '0.0';
SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 80) as expected
FROM num_result t1, num_exp_div t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != round(t2.expected, 80);
id1 | id2 | result | expected
-----+-----+--------+----------
(0 rows)
-- ******************************
-- * Square root check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT id, 0, SQRT(ABS(val))
FROM num_data;
SELECT t1.id1, t1.result, t2.expected
FROM num_result t1, num_exp_sqrt t2
WHERE t1.id1 = t2.id
AND t1.result != t2.expected;
id1 | result | expected
-----+--------+----------
(0 rows)
-- ******************************
-- * Natural logarithm check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT id, 0, LN(ABS(val))
FROM num_data
WHERE val != '0.0';
SELECT t1.id1, t1.result, t2.expected
FROM num_result t1, num_exp_ln t2
WHERE t1.id1 = t2.id
AND t1.result != t2.expected;
id1 | result | expected
-----+--------+----------
(0 rows)
-- ******************************
-- * Logarithm base 10 check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT id, 0, LOG(numeric '10', ABS(val))
FROM num_data
WHERE val != '0.0';
SELECT t1.id1, t1.result, t2.expected
FROM num_result t1, num_exp_log10 t2
WHERE t1.id1 = t2.id
AND t1.result != t2.expected;
id1 | result | expected
-----+--------+----------
(0 rows)
-- ******************************
-- * POWER(10, LN(value)) check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT id, 0, POWER(numeric '10', LN(ABS(round(val,200))))
FROM num_data
WHERE val != '0.0';
SELECT t1.id1, t1.result, t2.expected
FROM num_result t1, num_exp_power_10_ln t2
WHERE t1.id1 = t2.id
AND t1.result != t2.expected;
id1 | result | expected
-----+--------+----------
(0 rows)
-- ******************************
-- * Check behavior with Inf and NaN inputs. It's easiest to handle these
-- * separately from the num_data framework used above, because some input
-- * combinations will throw errors.
-- ******************************
WITH v(x) AS
(VALUES('0'::numeric),('1'),('-1'),('4.2'),('inf'),('-inf'),('nan'))
SELECT x1, x2,
x1 + x2 AS sum,
x1 - x2 AS diff,
x1 * x2 AS prod
FROM v AS v1(x1), v AS v2(x2);
x1 | x2 | sum | diff | prod
-----------+-----------+-----------+-----------+-----------
0 | 0 | 0 | 0 | 0
0 | 1 | 1 | -1 | 0
0 | -1 | -1 | 1 | 0
0 | 4.2 | 4.2 | -4.2 | 0.0
0 | Infinity | Infinity | -Infinity | NaN
0 | -Infinity | -Infinity | Infinity | NaN
0 | NaN | NaN | NaN | NaN
1 | 0 | 1 | 1 | 0
1 | 1 | 2 | 0 | 1
1 | -1 | 0 | 2 | -1
1 | 4.2 | 5.2 | -3.2 | 4.2
1 | Infinity | Infinity | -Infinity | Infinity
1 | -Infinity | -Infinity | Infinity | -Infinity
1 | NaN | NaN | NaN | NaN
-1 | 0 | -1 | -1 | 0
-1 | 1 | 0 | -2 | -1
-1 | -1 | -2 | 0 | 1
-1 | 4.2 | 3.2 | -5.2 | -4.2
-1 | Infinity | Infinity | -Infinity | -Infinity
-1 | -Infinity | -Infinity | Infinity | Infinity
-1 | NaN | NaN | NaN | NaN
4.2 | 0 | 4.2 | 4.2 | 0.0
4.2 | 1 | 5.2 | 3.2 | 4.2
4.2 | -1 | 3.2 | 5.2 | -4.2
4.2 | 4.2 | 8.4 | 0.0 | 17.64
4.2 | Infinity | Infinity | -Infinity | Infinity
4.2 | -Infinity | -Infinity | Infinity | -Infinity
4.2 | NaN | NaN | NaN | NaN
Infinity | 0 | Infinity | Infinity | NaN
Infinity | 1 | Infinity | Infinity | Infinity
Infinity | -1 | Infinity | Infinity | -Infinity
Infinity | 4.2 | Infinity | Infinity | Infinity
Infinity | Infinity | Infinity | NaN | Infinity
Infinity | -Infinity | NaN | Infinity | -Infinity
Infinity | NaN | NaN | NaN | NaN
-Infinity | 0 | -Infinity | -Infinity | NaN
-Infinity | 1 | -Infinity | -Infinity | -Infinity
-Infinity | -1 | -Infinity | -Infinity | Infinity
-Infinity | 4.2 | -Infinity | -Infinity | -Infinity
-Infinity | Infinity | NaN | -Infinity | -Infinity
-Infinity | -Infinity | -Infinity | NaN | Infinity
-Infinity | NaN | NaN | NaN | NaN
NaN | 0 | NaN | NaN | NaN
NaN | 1 | NaN | NaN | NaN
NaN | -1 | NaN | NaN | NaN
NaN | 4.2 | NaN | NaN | NaN
NaN | Infinity | NaN | NaN | NaN
NaN | -Infinity | NaN | NaN | NaN
NaN | NaN | NaN | NaN | NaN
(49 rows)
WITH v(x) AS
(VALUES('0'::numeric),('1'),('-1'),('4.2'),('inf'),('-inf'),('nan'))
SELECT x1, x2,
x1 / x2 AS quot,
x1 % x2 AS mod,
div(x1, x2) AS div
FROM v AS v1(x1), v AS v2(x2) WHERE x2 != 0;
x1 | x2 | quot | mod | div
-----------+-----------+-------------------------+------+-----------
0 | 1 | 0.00000000000000000000 | 0 | 0
1 | 1 | 1.00000000000000000000 | 0 | 1
-1 | 1 | -1.00000000000000000000 | 0 | -1
4.2 | 1 | 4.2000000000000000 | 0.2 | 4
Infinity | 1 | Infinity | NaN | Infinity
-Infinity | 1 | -Infinity | NaN | -Infinity
NaN | 1 | NaN | NaN | NaN
0 | -1 | 0.00000000000000000000 | 0 | 0
1 | -1 | -1.00000000000000000000 | 0 | -1
-1 | -1 | 1.00000000000000000000 | 0 | 1
4.2 | -1 | -4.2000000000000000 | 0.2 | -4
Infinity | -1 | -Infinity | NaN | -Infinity
-Infinity | -1 | Infinity | NaN | Infinity
NaN | -1 | NaN | NaN | NaN
0 | 4.2 | 0.00000000000000000000 | 0.0 | 0
1 | 4.2 | 0.23809523809523809524 | 1.0 | 0
-1 | 4.2 | -0.23809523809523809524 | -1.0 | 0
4.2 | 4.2 | 1.00000000000000000000 | 0.0 | 1
Infinity | 4.2 | Infinity | NaN | Infinity
-Infinity | 4.2 | -Infinity | NaN | -Infinity
NaN | 4.2 | NaN | NaN | NaN
0 | Infinity | 0 | 0 | 0
1 | Infinity | 0 | 1 | 0
-1 | Infinity | 0 | -1 | 0
4.2 | Infinity | 0 | 4.2 | 0
Infinity | Infinity | NaN | NaN | NaN
-Infinity | Infinity | NaN | NaN | NaN
NaN | Infinity | NaN | NaN | NaN
0 | -Infinity | 0 | 0 | 0
1 | -Infinity | 0 | 1 | 0
-1 | -Infinity | 0 | -1 | 0
4.2 | -Infinity | 0 | 4.2 | 0
Infinity | -Infinity | NaN | NaN | NaN
-Infinity | -Infinity | NaN | NaN | NaN
NaN | -Infinity | NaN | NaN | NaN
0 | NaN | NaN | NaN | NaN
1 | NaN | NaN | NaN | NaN
-1 | NaN | NaN | NaN | NaN
4.2 | NaN | NaN | NaN | NaN
Infinity | NaN | NaN | NaN | NaN
-Infinity | NaN | NaN | NaN | NaN
NaN | NaN | NaN | NaN | NaN
(42 rows)
SELECT 'inf'::numeric / '0';
ERROR: division by zero
SELECT '-inf'::numeric / '0';
ERROR: division by zero
SELECT 'nan'::numeric / '0';
?column?
----------
NaN
(1 row)
SELECT '0'::numeric / '0';
ERROR: division by zero
SELECT 'inf'::numeric % '0';
ERROR: division by zero
SELECT '-inf'::numeric % '0';
ERROR: division by zero
SELECT 'nan'::numeric % '0';
?column?
----------
NaN
(1 row)
SELECT '0'::numeric % '0';
ERROR: division by zero
SELECT div('inf'::numeric, '0');
ERROR: division by zero
SELECT div('-inf'::numeric, '0');
ERROR: division by zero
SELECT div('nan'::numeric, '0');
div
-----
NaN
(1 row)
SELECT div('0'::numeric, '0');
ERROR: division by zero
WITH v(x) AS
(VALUES('0'::numeric),('1'),('-1'),('4.2'),('-7.777'),('inf'),('-inf'),('nan'))
SELECT x, -x as minusx, abs(x), floor(x), ceil(x), sign(x), numeric_inc(x) as inc
FROM v;
x | minusx | abs | floor | ceil | sign | inc
-----------+-----------+----------+-----------+-----------+------+-----------
0 | 0 | 0 | 0 | 0 | 0 | 1
1 | -1 | 1 | 1 | 1 | 1 | 2
-1 | 1 | 1 | -1 | -1 | -1 | 0
4.2 | -4.2 | 4.2 | 4 | 5 | 1 | 5.2
-7.777 | 7.777 | 7.777 | -8 | -7 | -1 | -6.777
Infinity | -Infinity | Infinity | Infinity | Infinity | 1 | Infinity
-Infinity | Infinity | Infinity | -Infinity | -Infinity | -1 | -Infinity
NaN | NaN | NaN | NaN | NaN | NaN | NaN
(8 rows)
WITH v(x) AS
(VALUES('0'::numeric),('1'),('-1'),('4.2'),('-7.777'),('inf'),('-inf'),('nan'))
SELECT x, round(x), round(x,1) as round1, trunc(x), trunc(x,1) as trunc1
FROM v;
x | round | round1 | trunc | trunc1
-----------+-----------+-----------+-----------+-----------
0 | 0 | 0.0 | 0 | 0.0
1 | 1 | 1.0 | 1 | 1.0
-1 | -1 | -1.0 | -1 | -1.0
4.2 | 4 | 4.2 | 4 | 4.2
-7.777 | -8 | -7.8 | -7 | -7.7
Infinity | Infinity | Infinity | Infinity | Infinity
-Infinity | -Infinity | -Infinity | -Infinity | -Infinity
NaN | NaN | NaN | NaN | NaN
(8 rows)
-- the large values fall into the numeric abbreviation code's maximal classes
WITH v(x) AS
(VALUES('0'::numeric),('1'),('-1'),('4.2'),('-7.777'),('1e340'),('-1e340'),
('inf'),('-inf'),('nan'),
('inf'),('-inf'),('nan'))
SELECT substring(x::text, 1, 32)
FROM v ORDER BY x;
substring
----------------------------------
-Infinity
-Infinity
-1000000000000000000000000000000
-7.777
-1
0
1
4.2
10000000000000000000000000000000
Infinity
Infinity
NaN
NaN
(13 rows)
WITH v(x) AS
(VALUES('0'::numeric),('1'),('4.2'),('inf'),('nan'))
SELECT x, sqrt(x)
FROM v;
x | sqrt
----------+-------------------
0 | 0.000000000000000
1 | 1.000000000000000
4.2 | 2.049390153191920
Infinity | Infinity
NaN | NaN
(5 rows)
SELECT sqrt('-1'::numeric);
ERROR: cannot take square root of a negative number
SELECT sqrt('-inf'::numeric);
ERROR: cannot take square root of a negative number
WITH v(x) AS
(VALUES('1'::numeric),('4.2'),('inf'),('nan'))
SELECT x,
log(x),
log10(x),
ln(x)
FROM v;
x | log | log10 | ln
----------+--------------------+--------------------+--------------------
1 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
4.2 | 0.6232492903979005 | 0.6232492903979005 | 1.4350845252893226
Infinity | Infinity | Infinity | Infinity
NaN | NaN | NaN | NaN
(4 rows)
SELECT ln('0'::numeric);
ERROR: cannot take logarithm of zero
SELECT ln('-1'::numeric);
ERROR: cannot take logarithm of a negative number
SELECT ln('-inf'::numeric);
ERROR: cannot take logarithm of a negative number
WITH v(x) AS
(VALUES('2'::numeric),('4.2'),('inf'),('nan'))
SELECT x1, x2,
log(x1, x2)
FROM v AS v1(x1), v AS v2(x2);
x1 | x2 | log
----------+----------+--------------------
2 | 2 | 1.0000000000000000
2 | 4.2 | 2.0703893278913979
2 | Infinity | Infinity
2 | NaN | NaN
4.2 | 2 | 0.4830009440873890
4.2 | 4.2 | 1.0000000000000000
4.2 | Infinity | Infinity
4.2 | NaN | NaN
Infinity | 2 | 0
Infinity | 4.2 | 0
Infinity | Infinity | NaN
Infinity | NaN | NaN
NaN | 2 | NaN
NaN | 4.2 | NaN
NaN | Infinity | NaN
NaN | NaN | NaN
(16 rows)
SELECT log('0'::numeric, '10');
ERROR: cannot take logarithm of zero
SELECT log('10'::numeric, '0');
ERROR: cannot take logarithm of zero
SELECT log('-inf'::numeric, '10');
ERROR: cannot take logarithm of a negative number
SELECT log('10'::numeric, '-inf');
ERROR: cannot take logarithm of a negative number
SELECT log('inf'::numeric, '0');
ERROR: cannot take logarithm of zero
SELECT log('inf'::numeric, '-inf');
ERROR: cannot take logarithm of a negative number
SELECT log('-inf'::numeric, 'inf');
ERROR: cannot take logarithm of a negative number
WITH v(x) AS
(VALUES('0'::numeric),('1'),('2'),('4.2'),('inf'),('nan'))
SELECT x1, x2,
power(x1, x2)
FROM v AS v1(x1), v AS v2(x2) WHERE x1 != 0 OR x2 >= 0;
x1 | x2 | power
----------+----------+---------------------
0 | 0 | 1.0000000000000000
0 | 1 | 0.0000000000000000
0 | 2 | 0.0000000000000000
0 | 4.2 | 0.0000000000000000
0 | Infinity | 0
0 | NaN | NaN
1 | 0 | 1.0000000000000000
1 | 1 | 1.0000000000000000
1 | 2 | 1.0000000000000000
1 | 4.2 | 1.0000000000000000
1 | Infinity | 1
1 | NaN | 1
2 | 0 | 1.0000000000000000
2 | 1 | 2.0000000000000000
2 | 2 | 4.0000000000000000
2 | 4.2 | 18.379173679952560
2 | Infinity | Infinity
2 | NaN | NaN
4.2 | 0 | 1.0000000000000000
4.2 | 1 | 4.2000000000000000
4.2 | 2 | 17.6400000000000000
4.2 | 4.2 | 414.61691860129675
4.2 | Infinity | Infinity
4.2 | NaN | NaN
Infinity | 0 | 1
Infinity | 1 | Infinity
Infinity | 2 | Infinity
Infinity | 4.2 | Infinity
Infinity | Infinity | Infinity
Infinity | NaN | NaN
NaN | 0 | 1
NaN | 1 | NaN
NaN | 2 | NaN
NaN | 4.2 | NaN
NaN | Infinity | NaN
NaN | NaN | NaN
(36 rows)
SELECT power('0'::numeric, '-1');
ERROR: zero raised to a negative power is undefined
SELECT power('0'::numeric, '-inf');
ERROR: zero raised to a negative power is undefined
SELECT power('-1'::numeric, 'inf');
power
-------
1
(1 row)
SELECT power('-2'::numeric, '3');
power
---------------------
-8.0000000000000000
(1 row)
SELECT power('-2'::numeric, '3.3');
ERROR: a negative number raised to a non-integer power yields a complex result
SELECT power('-2'::numeric, '-1');
power
---------------------
-0.5000000000000000
(1 row)
SELECT power('-2'::numeric, '-1.5');
ERROR: a negative number raised to a non-integer power yields a complex result
SELECT power('-2'::numeric, 'inf');
power
----------
Infinity
(1 row)
SELECT power('-2'::numeric, '-inf');
power
-------
0
(1 row)
SELECT power('inf'::numeric, '-2');
power
-------
0
(1 row)
SELECT power('inf'::numeric, '-inf');
power
-------
0
(1 row)
SELECT power('-inf'::numeric, '2');
power
----------
Infinity
(1 row)
SELECT power('-inf'::numeric, '3');
power
-----------
-Infinity
(1 row)
SELECT power('-inf'::numeric, '4.5');
ERROR: a negative number raised to a non-integer power yields a complex result
SELECT power('-inf'::numeric, '-2');
power
-------
0
(1 row)
SELECT power('-inf'::numeric, '-3');
power
-------
0
(1 row)
SELECT power('-inf'::numeric, '0');
power
-------
1
(1 row)
SELECT power('-inf'::numeric, 'inf');
power
----------
Infinity
(1 row)
SELECT power('-inf'::numeric, '-inf');
power
-------
0
(1 row)
-- ******************************
-- * miscellaneous checks for things that have been broken in the past...
-- ******************************
-- numeric AVG used to fail on some platforms
SELECT AVG(val) FROM num_data;
avg
------------------------
-13430913.592242320700
(1 row)
SELECT MAX(val) FROM num_data;
max
--------------------
7799461.4119000000
(1 row)
SELECT MIN(val) FROM num_data;
min
----------------------
-83028485.0000000000
(1 row)
SELECT STDDEV(val) FROM num_data;
stddev
-------------------------------
27791203.28758835329805617386
(1 row)
SELECT VARIANCE(val) FROM num_data;
variance
--------------------------------------
772350980172061.69659105821915863601
(1 row)
-- Check for appropriate rounding and overflow
CREATE TABLE fract_only (id int, val numeric(4,4));
INSERT INTO fract_only VALUES (1, '0.0');
INSERT INTO fract_only VALUES (2, '0.1');
INSERT INTO fract_only VALUES (3, '1.0'); -- should fail
ERROR: numeric field overflow
DETAIL: A field with precision 4, scale 4 must round to an absolute value less than 1.
INSERT INTO fract_only VALUES (4, '-0.9999');
INSERT INTO fract_only VALUES (5, '0.99994');
INSERT INTO fract_only VALUES (6, '0.99995'); -- should fail
ERROR: numeric field overflow
DETAIL: A field with precision 4, scale 4 must round to an absolute value less than 1.
INSERT INTO fract_only VALUES (7, '0.00001');
INSERT INTO fract_only VALUES (8, '0.00017');
INSERT INTO fract_only VALUES (9, 'NaN');
INSERT INTO fract_only VALUES (10, 'Inf'); -- should fail
ERROR: numeric field overflow
DETAIL: A field with precision 4, scale 4 cannot hold an infinite value.
INSERT INTO fract_only VALUES (11, '-Inf'); -- should fail
ERROR: numeric field overflow
DETAIL: A field with precision 4, scale 4 cannot hold an infinite value.
SELECT * FROM fract_only;
id | val
----+---------
1 | 0.0000
2 | 0.1000
4 | -0.9999
5 | 0.9999
7 | 0.0000
8 | 0.0002
9 | NaN
(7 rows)
DROP TABLE fract_only;
-- Check inf/nan conversion behavior
SELECT 'NaN'::float8::numeric;
numeric
---------
NaN
(1 row)
SELECT 'Infinity'::float8::numeric;
numeric
----------
Infinity
(1 row)
SELECT '-Infinity'::float8::numeric;
numeric
-----------
-Infinity
(1 row)
SELECT 'NaN'::numeric::float8;
float8
--------
NaN
(1 row)
SELECT 'Infinity'::numeric::float8;
float8
----------
Infinity
(1 row)
SELECT '-Infinity'::numeric::float8;
float8
-----------
-Infinity
(1 row)
SELECT 'NaN'::float4::numeric;
numeric
---------
NaN
(1 row)
SELECT 'Infinity'::float4::numeric;
numeric
----------
Infinity
(1 row)
SELECT '-Infinity'::float4::numeric;
numeric
-----------
-Infinity
(1 row)
SELECT 'NaN'::numeric::float4;
float4
--------
NaN
(1 row)
SELECT 'Infinity'::numeric::float4;
float4
----------
Infinity
(1 row)
SELECT '-Infinity'::numeric::float4;
float4
-----------
-Infinity
(1 row)
SELECT '42'::int2::numeric;
numeric
---------
42
(1 row)
SELECT 'NaN'::numeric::int2;
ERROR: cannot convert NaN to smallint
SELECT 'Infinity'::numeric::int2;
ERROR: cannot convert infinity to smallint
SELECT '-Infinity'::numeric::int2;
ERROR: cannot convert infinity to smallint
SELECT 'NaN'::numeric::int4;
ERROR: cannot convert NaN to integer
SELECT 'Infinity'::numeric::int4;
ERROR: cannot convert infinity to integer
SELECT '-Infinity'::numeric::int4;
ERROR: cannot convert infinity to integer
SELECT 'NaN'::numeric::int8;
ERROR: cannot convert NaN to bigint
SELECT 'Infinity'::numeric::int8;
ERROR: cannot convert infinity to bigint
SELECT '-Infinity'::numeric::int8;
ERROR: cannot convert infinity to bigint
-- Simple check that ceil(), floor(), and round() work correctly
CREATE TABLE ceil_floor_round (a numeric);
INSERT INTO ceil_floor_round VALUES ('-5.5');
INSERT INTO ceil_floor_round VALUES ('-5.499999');
INSERT INTO ceil_floor_round VALUES ('9.5');
INSERT INTO ceil_floor_round VALUES ('9.4999999');
INSERT INTO ceil_floor_round VALUES ('0.0');
INSERT INTO ceil_floor_round VALUES ('0.0000001');
INSERT INTO ceil_floor_round VALUES ('-0.000001');
SELECT a, ceil(a), ceiling(a), floor(a), round(a) FROM ceil_floor_round;
a | ceil | ceiling | floor | round
-----------+------+---------+-------+-------
-5.5 | -5 | -5 | -6 | -6
-5.499999 | -5 | -5 | -6 | -5
9.5 | 10 | 10 | 9 | 10
9.4999999 | 10 | 10 | 9 | 9
0.0 | 0 | 0 | 0 | 0
0.0000001 | 1 | 1 | 0 | 0
-0.000001 | 0 | 0 | -1 | 0
(7 rows)
DROP TABLE ceil_floor_round;
-- Check rounding, it should round ties away from zero.
SELECT i as pow,
round((-2.5 * 10 ^ i)::numeric, -i),
round((-1.5 * 10 ^ i)::numeric, -i),
round((-0.5 * 10 ^ i)::numeric, -i),
round((0.5 * 10 ^ i)::numeric, -i),
round((1.5 * 10 ^ i)::numeric, -i),
round((2.5 * 10 ^ i)::numeric, -i)
FROM generate_series(-5,5) AS t(i);
pow | round | round | round | round | round | round
-----+----------+----------+----------+---------+---------+---------
-5 | -0.00003 | -0.00002 | -0.00001 | 0.00001 | 0.00002 | 0.00003
-4 | -0.0003 | -0.0002 | -0.0001 | 0.0001 | 0.0002 | 0.0003
-3 | -0.003 | -0.002 | -0.001 | 0.001 | 0.002 | 0.003
-2 | -0.03 | -0.02 | -0.01 | 0.01 | 0.02 | 0.03
-1 | -0.3 | -0.2 | -0.1 | 0.1 | 0.2 | 0.3
0 | -3 | -2 | -1 | 1 | 2 | 3
1 | -30 | -20 | -10 | 10 | 20 | 30
2 | -300 | -200 | -100 | 100 | 200 | 300
3 | -3000 | -2000 | -1000 | 1000 | 2000 | 3000
4 | -30000 | -20000 | -10000 | 10000 | 20000 | 30000
5 | -300000 | -200000 | -100000 | 100000 | 200000 | 300000
(11 rows)
-- Testing for width_bucket(). For convenience, we test both the
-- numeric and float8 versions of the function in this file.
-- errors
SELECT width_bucket(5.0, 3.0, 4.0, 0);
ERROR: count must be greater than zero
SELECT width_bucket(5.0, 3.0, 4.0, -5);
ERROR: count must be greater than zero
SELECT width_bucket(3.5, 3.0, 3.0, 888);
ERROR: lower bound cannot equal upper bound
SELECT width_bucket(5.0::float8, 3.0::float8, 4.0::float8, 0);
ERROR: count must be greater than zero
SELECT width_bucket(5.0::float8, 3.0::float8, 4.0::float8, -5);
ERROR: count must be greater than zero
SELECT width_bucket(3.5::float8, 3.0::float8, 3.0::float8, 888);
ERROR: lower bound cannot equal upper bound
SELECT width_bucket('NaN', 3.0, 4.0, 888);
ERROR: operand, lower bound, and upper bound cannot be NaN
SELECT width_bucket(0::float8, 'NaN', 4.0::float8, 888);
ERROR: operand, lower bound, and upper bound cannot be NaN
SELECT width_bucket(2.0, 3.0, '-inf', 888);
ERROR: lower and upper bounds must be finite
SELECT width_bucket(0::float8, '-inf', 4.0::float8, 888);
ERROR: lower and upper bounds must be finite
-- normal operation
CREATE TABLE width_bucket_test (operand_num numeric, operand_f8 float8);
COPY width_bucket_test (operand_num) FROM stdin;
UPDATE width_bucket_test SET operand_f8 = operand_num::float8;
SELECT
operand_num,
width_bucket(operand_num, 0, 10, 5) AS wb_1,
width_bucket(operand_f8, 0, 10, 5) AS wb_1f,
width_bucket(operand_num, 10, 0, 5) AS wb_2,
width_bucket(operand_f8, 10, 0, 5) AS wb_2f,
width_bucket(operand_num, 2, 8, 4) AS wb_3,
width_bucket(operand_f8, 2, 8, 4) AS wb_3f,
width_bucket(operand_num, 5.0, 5.5, 20) AS wb_4,
width_bucket(operand_f8, 5.0, 5.5, 20) AS wb_4f,
width_bucket(operand_num, -25, 25, 10) AS wb_5,
width_bucket(operand_f8, -25, 25, 10) AS wb_5f
FROM width_bucket_test;
operand_num | wb_1 | wb_1f | wb_2 | wb_2f | wb_3 | wb_3f | wb_4 | wb_4f | wb_5 | wb_5f
------------------+------+-------+------+-------+------+-------+------+-------+------+-------
-5.2 | 0 | 0 | 6 | 6 | 0 | 0 | 0 | 0 | 4 | 4
-0.0000000001 | 0 | 0 | 6 | 6 | 0 | 0 | 0 | 0 | 5 | 5
0.000000000001 | 1 | 1 | 5 | 5 | 0 | 0 | 0 | 0 | 6 | 6
1 | 1 | 1 | 5 | 5 | 0 | 0 | 0 | 0 | 6 | 6
1.99999999999999 | 1 | 1 | 5 | 5 | 0 | 0 | 0 | 0 | 6 | 6
2 | 2 | 2 | 5 | 5 | 1 | 1 | 0 | 0 | 6 | 6
2.00000000000001 | 2 | 2 | 4 | 4 | 1 | 1 | 0 | 0 | 6 | 6
3 | 2 | 2 | 4 | 4 | 1 | 1 | 0 | 0 | 6 | 6
4 | 3 | 3 | 4 | 4 | 2 | 2 | 0 | 0 | 6 | 6
4.5 | 3 | 3 | 3 | 3 | 2 | 2 | 0 | 0 | 6 | 6
5 | 3 | 3 | 3 | 3 | 3 | 3 | 1 | 1 | 7 | 7
5.5 | 3 | 3 | 3 | 3 | 3 | 3 | 21 | 21 | 7 | 7
6 | 4 | 4 | 3 | 3 | 3 | 3 | 21 | 21 | 7 | 7
7 | 4 | 4 | 2 | 2 | 4 | 4 | 21 | 21 | 7 | 7
8 | 5 | 5 | 2 | 2 | 5 | 5 | 21 | 21 | 7 | 7
9 | 5 | 5 | 1 | 1 | 5 | 5 | 21 | 21 | 7 | 7
9.99999999999999 | 5 | 5 | 1 | 1 | 5 | 5 | 21 | 21 | 7 | 7
10 | 6 | 6 | 1 | 1 | 5 | 5 | 21 | 21 | 8 | 8
10.0000000000001 | 6 | 6 | 0 | 0 | 5 | 5 | 21 | 21 | 8 | 8
(19 rows)
-- Check positive and negative infinity: we require
-- finite bucket bounds, but allow an infinite operand
SELECT width_bucket(0.0::numeric, 'Infinity'::numeric, 5, 10); -- error
ERROR: lower and upper bounds must be finite
SELECT width_bucket(0.0::numeric, 5, '-Infinity'::numeric, 20); -- error
ERROR: lower and upper bounds must be finite
SELECT width_bucket('Infinity'::numeric, 1, 10, 10),
width_bucket('-Infinity'::numeric, 1, 10, 10);
width_bucket | width_bucket
--------------+--------------
11 | 0
(1 row)
SELECT width_bucket(0.0::float8, 'Infinity'::float8, 5, 10); -- error
ERROR: lower and upper bounds must be finite
SELECT width_bucket(0.0::float8, 5, '-Infinity'::float8, 20); -- error
ERROR: lower and upper bounds must be finite
SELECT width_bucket('Infinity'::float8, 1, 10, 10),
width_bucket('-Infinity'::float8, 1, 10, 10);
width_bucket | width_bucket
--------------+--------------
11 | 0
(1 row)
DROP TABLE width_bucket_test;
-- Simple test for roundoff error when results should be exact
SELECT x, width_bucket(x::float8, 10, 100, 9) as flt,
width_bucket(x::numeric, 10, 100, 9) as num
FROM generate_series(0, 110, 10) x;
x | flt | num
-----+-----+-----
0 | 0 | 0
10 | 1 | 1
20 | 2 | 2
30 | 3 | 3
40 | 4 | 4
50 | 5 | 5
60 | 6 | 6
70 | 7 | 7
80 | 8 | 8
90 | 9 | 9
100 | 10 | 10
110 | 10 | 10
(12 rows)
SELECT x, width_bucket(x::float8, 100, 10, 9) as flt,
width_bucket(x::numeric, 100, 10, 9) as num
FROM generate_series(0, 110, 10) x;
x | flt | num
-----+-----+-----
0 | 10 | 10
10 | 10 | 10
20 | 9 | 9
30 | 8 | 8
40 | 7 | 7
50 | 6 | 6
60 | 5 | 5
70 | 4 | 4
80 | 3 | 3
90 | 2 | 2
100 | 1 | 1
110 | 0 | 0
(12 rows)
--
-- TO_CHAR()
--
SELECT to_char(val, '9G999G999G999G999G999')
FROM num_data;
to_char
------------------------
0
0
-34,338,492
4
7,799,461
16,397
93,902
-83,028,485
74,881
-24,926,804
(10 rows)
SELECT to_char(val, '9G999G999G999G999G999D999G999G999G999G999')
FROM num_data;
to_char
--------------------------------------------
.000,000,000,000,000
.000,000,000,000,000
-34,338,492.215,397,047,000,000
4.310,000,000,000,000
7,799,461.411,900,000,000,000
16,397.038,491,000,000,000
93,901.577,630,260,000,000
-83,028,485.000,000,000,000,000
74,881.000,000,000,000,000
-24,926,804.045,047,420,000,000
(10 rows)
SELECT to_char(val, '9999999999999999.999999999999999PR')
FROM num_data;
to_char
------------------------------------
.000000000000000
.000000000000000
<34338492.215397047000000>
4.310000000000000
7799461.411900000000000
16397.038491000000000
93901.577630260000000
<83028485.000000000000000>
74881.000000000000000
<24926804.045047420000000>
(10 rows)
SELECT to_char(val, '9999999999999999.999999999999999S')
FROM num_data;
to_char
-----------------------------------
.000000000000000+
.000000000000000+
34338492.215397047000000-
4.310000000000000+
7799461.411900000000000+
16397.038491000000000+
93901.577630260000000+
83028485.000000000000000-
74881.000000000000000+
24926804.045047420000000-
(10 rows)
SELECT to_char(val, 'MI9999999999999999.999999999999999') FROM num_data;
to_char
-----------------------------------
.000000000000000
.000000000000000
- 34338492.215397047000000
4.310000000000000
7799461.411900000000000
16397.038491000000000
93901.577630260000000
- 83028485.000000000000000
74881.000000000000000
- 24926804.045047420000000
(10 rows)
SELECT to_char(val, 'FMS9999999999999999.999999999999999') FROM num_data;
to_char
---------------------
+0.
+0.
-34338492.215397047
+4.31
+7799461.4119
+16397.038491
+93901.57763026
-83028485.
+74881.
-24926804.04504742
(10 rows)
SELECT to_char(val, 'FM9999999999999999.999999999999999THPR') FROM num_data;
to_char
----------------------
0.
0.
<34338492.215397047>
4.31
7799461.4119
16397.038491
93901.57763026
<83028485.>
74881.
<24926804.04504742>
(10 rows)
SELECT to_char(val, 'SG9999999999999999.999999999999999th') FROM num_data;
to_char
-----------------------------------
+ .000000000000000
+ .000000000000000
- 34338492.215397047000000
+ 4.310000000000000
+ 7799461.411900000000000
+ 16397.038491000000000
+ 93901.577630260000000
- 83028485.000000000000000
+ 74881.000000000000000
- 24926804.045047420000000
(10 rows)
SELECT to_char(val, '0999999999999999.999999999999999') FROM num_data;
to_char
-----------------------------------
0000000000000000.000000000000000
0000000000000000.000000000000000
-0000000034338492.215397047000000
0000000000000004.310000000000000
0000000007799461.411900000000000
0000000000016397.038491000000000
0000000000093901.577630260000000
-0000000083028485.000000000000000
0000000000074881.000000000000000
-0000000024926804.045047420000000
(10 rows)
SELECT to_char(val, 'S0999999999999999.999999999999999') FROM num_data;
to_char
-----------------------------------
+0000000000000000.000000000000000
+0000000000000000.000000000000000
-0000000034338492.215397047000000
+0000000000000004.310000000000000
+0000000007799461.411900000000000
+0000000000016397.038491000000000
+0000000000093901.577630260000000
-0000000083028485.000000000000000
+0000000000074881.000000000000000
-0000000024926804.045047420000000
(10 rows)
SELECT to_char(val, 'FM0999999999999999.999999999999999') FROM num_data;
to_char
-----------------------------
0000000000000000.
0000000000000000.
-0000000034338492.215397047
0000000000000004.31
0000000007799461.4119
0000000000016397.038491
0000000000093901.57763026
-0000000083028485.
0000000000074881.
-0000000024926804.04504742
(10 rows)
SELECT to_char(val, 'FM9999999999999999.099999999999999') FROM num_data;
to_char
---------------------
.0
.0
-34338492.215397047
4.31
7799461.4119
16397.038491
93901.57763026
-83028485.0
74881.0
-24926804.04504742
(10 rows)
SELECT to_char(val, 'FM9999999999990999.990999999999999') FROM num_data;
to_char
---------------------
0000.000
0000.000
-34338492.215397047
0004.310
7799461.4119
16397.038491
93901.57763026
-83028485.000
74881.000
-24926804.04504742
(10 rows)
SELECT to_char(val, 'FM0999999999999999.999909999999999') FROM num_data;
to_char
-----------------------------
0000000000000000.00000
0000000000000000.00000
-0000000034338492.215397047
0000000000000004.31000
0000000007799461.41190
0000000000016397.038491
0000000000093901.57763026
-0000000083028485.00000
0000000000074881.00000
-0000000024926804.04504742
(10 rows)
SELECT to_char(val, 'FM9999999990999999.099999999999999') FROM num_data;
to_char
---------------------
0000000.0
0000000.0
-34338492.215397047
0000004.31
7799461.4119
0016397.038491
0093901.57763026
-83028485.0
0074881.0
-24926804.04504742
(10 rows)
SELECT to_char(val, 'L9999999999999999.099999999999999') FROM num_data;
to_char
------------------------------------
.000000000000000
.000000000000000
-34338492.215397047000000
4.310000000000000
7799461.411900000000000
16397.038491000000000
93901.577630260000000
-83028485.000000000000000
74881.000000000000000
-24926804.045047420000000
(10 rows)
SELECT to_char(val, 'FM9999999999999999.99999999999999') FROM num_data;
to_char
---------------------
0.
0.
-34338492.215397047
4.31
7799461.4119
16397.038491
93901.57763026
-83028485.
74881.
-24926804.04504742
(10 rows)
SELECT to_char(val, 'S 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 . 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9') FROM num_data;
to_char
-----------------------------------------------------------------------
+. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-3 4 3 3 8 4 9 2 . 2 1 5 3 9 7 0 4 7 0 0 0 0 0 0 0 0
+4 . 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+7 7 9 9 4 6 1 . 4 1 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0
+1 6 3 9 7 . 0 3 8 4 9 1 0 0 0 0 0 0 0 0 0 0 0
+9 3 9 0 1 . 5 7 7 6 3 0 2 6 0 0 0 0 0 0 0 0 0
-8 3 0 2 8 4 8 5 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+7 4 8 8 1 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 4 9 2 6 8 0 4 . 0 4 5 0 4 7 4 2 0 0 0 0 0 0 0 0 0
(10 rows)
SELECT to_char(val, 'FMS 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 . 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9') FROM num_data;
to_char
-------------------------------------------------------
+0 .
+0 .
-3 4 3 3 8 4 9 2 . 2 1 5 3 9 7 0 4 7
+4 . 3 1
+7 7 9 9 4 6 1 . 4 1 1 9
+1 6 3 9 7 . 0 3 8 4 9 1
+9 3 9 0 1 . 5 7 7 6 3 0 2 6
-8 3 0 2 8 4 8 5 .
+7 4 8 8 1 .
-2 4 9 2 6 8 0 4 . 0 4 5 0 4 7 4 2
(10 rows)
SELECT to_char(val, E'99999 "text" 9999 "9999" 999 "\\"text between quote marks\\"" 9999') FROM num_data;
to_char
-----------------------------------------------------------
text 9999 "text between quote marks" 0
text 9999 "text between quote marks" 0
text -3 9999 433 "text between quote marks" 8492
text 9999 "text between quote marks" 4
text 9999 779 "text between quote marks" 9461
text 9999 1 "text between quote marks" 6397
text 9999 9 "text between quote marks" 3902
text -8 9999 302 "text between quote marks" 8485
text 9999 7 "text between quote marks" 4881
text -2 9999 492 "text between quote marks" 6804
(10 rows)
SELECT to_char(val, '999999SG9999999999') FROM num_data;
to_char
-------------------
+ 0
+ 0
- 34338492
+ 4
+ 7799461
+ 16397
+ 93902
- 83028485
+ 74881
- 24926804
(10 rows)
SELECT to_char(val, 'FM9999999999999999.999999999999999') FROM num_data;
to_char
---------------------
0.
0.
-34338492.215397047
4.31
7799461.4119
16397.038491
93901.57763026
-83028485.
74881.
-24926804.04504742
(10 rows)
SELECT to_char(val, '9.999EEEE') FROM num_data;
to_char
------------
0.000e+00
0.000e+00
-3.434e+07
4.310e+00
7.799e+06
1.640e+04
9.390e+04
-8.303e+07
7.488e+04
-2.493e+07
(10 rows)
WITH v(val) AS
(VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan'))
SELECT val,
to_char(val, '9.999EEEE') as numeric,
to_char(val::float8, '9.999EEEE') as float8,
to_char(val::float4, '9.999EEEE') as float4
FROM v;
val | numeric | float8 | float4
------------+------------+------------+------------
0 | 0.000e+00 | 0.000e+00 | 0.000e+00
-4.2 | -4.200e+00 | -4.200e+00 | -4.200e+00
4200000000 | 4.200e+09 | 4.200e+09 | 4.200e+09
0.000012 | 1.200e-05 | 1.200e-05 | 1.200e-05
Infinity | #.####### | #.####### | #.#######
-Infinity | #.####### | #.####### | #.#######
NaN | #.####### | #.####### | #.#######
(7 rows)
WITH v(exp) AS
(VALUES(-16379),(-16378),(-1234),(-789),(-45),(-5),(-4),(-3),(-2),(-1),(0),
(1),(2),(3),(4),(5),(38),(275),(2345),(45678),(131070),(131071))
SELECT exp,
to_char(('1.2345e'||exp)::numeric, '9.999EEEE') as numeric
FROM v;
exp | numeric
--------+----------------
-16379 | 1.235e-16379
-16378 | 1.235e-16378
-1234 | 1.235e-1234
-789 | 1.235e-789
-45 | 1.235e-45
-5 | 1.235e-05
-4 | 1.235e-04
-3 | 1.235e-03
-2 | 1.235e-02
-1 | 1.235e-01
0 | 1.235e+00
1 | 1.235e+01
2 | 1.235e+02
3 | 1.235e+03
4 | 1.235e+04
5 | 1.235e+05
38 | 1.235e+38
275 | 1.235e+275
2345 | 1.235e+2345
45678 | 1.235e+45678
131070 | 1.235e+131070
131071 | 1.235e+131071
(22 rows)
WITH v(val) AS
(VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan'))
SELECT val,
to_char(val, 'MI9999999999.99') as numeric,
to_char(val::float8, 'MI9999999999.99') as float8,
to_char(val::float4, 'MI9999999999.99') as float4
FROM v;
val | numeric | float8 | float4
------------+----------------+----------------+----------------
0 | .00 | .00 | .00
-4.2 | - 4.20 | - 4.20 | - 4.20
4200000000 | 4200000000.00 | 4200000000.00 | 4200000000
0.000012 | .00 | .00 | .00
Infinity | Infinity | Infinity | Infinity
-Infinity | - Infinity | - Infinity | - Infinity
NaN | NaN | NaN | NaN
(7 rows)
WITH v(val) AS
(VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan'))
SELECT val,
to_char(val, 'MI99.99') as numeric,
to_char(val::float8, 'MI99.99') as float8,
to_char(val::float4, 'MI99.99') as float4
FROM v;
val | numeric | float8 | float4
------------+---------+--------+--------
0 | .00 | .00 | .00
-4.2 | - 4.20 | - 4.20 | - 4.20
4200000000 | ##.## | ##.## | ##.
0.000012 | .00 | .00 | .00
Infinity | ##.## | ##.## | ##.
-Infinity | -##.## | -##.## | -##.
NaN | ##.## | ##.## | ##.##
(7 rows)
SELECT to_char('100'::numeric, 'FM999.9');
to_char
---------
100.
(1 row)
SELECT to_char('100'::numeric, 'FM999.');
to_char
---------
100
(1 row)
SELECT to_char('100'::numeric, 'FM999');
to_char
---------
100
(1 row)
-- Check parsing of literal text in a format string
SELECT to_char('100'::numeric, 'foo999');
to_char
---------
foo 100
(1 row)
SELECT to_char('100'::numeric, 'f\oo999');
to_char
----------
f\oo 100
(1 row)
SELECT to_char('100'::numeric, 'f\\oo999');
to_char
-----------
f\\oo 100
(1 row)
SELECT to_char('100'::numeric, 'f\"oo999');
to_char
----------
f"oo 100
(1 row)
SELECT to_char('100'::numeric, 'f\\"oo999');
to_char
-----------
f\"oo 100
(1 row)
SELECT to_char('100'::numeric, 'f"ool"999');
to_char
----------
fool 100
(1 row)
SELECT to_char('100'::numeric, 'f"\ool"999');
to_char
----------
fool 100
(1 row)
SELECT to_char('100'::numeric, 'f"\\ool"999');
to_char
-----------
f\ool 100
(1 row)
SELECT to_char('100'::numeric, 'f"ool\"999');
to_char
----------
fool"999
(1 row)
SELECT to_char('100'::numeric, 'f"ool\\"999');
to_char
-----------
fool\ 100
(1 row)
-- TO_NUMBER()
--
SET lc_numeric = 'C';
SELECT to_number('-34,338,492', '99G999G999');
to_number
-----------
-34338492
(1 row)
SELECT to_number('-34,338,492.654,878', '99G999G999D999G999');
to_number
------------------
-34338492.654878
(1 row)
SELECT to_number('<564646.654564>', '999999.999999PR');
to_number
----------------
-564646.654564
(1 row)
SELECT to_number('0.00001-', '9.999999S');
to_number
-----------
-0.00001
(1 row)
SELECT to_number('5.01-', 'FM9.999999S');
to_number
-----------
-5.01
(1 row)
SELECT to_number('5.01-', 'FM9.999999MI');
to_number
-----------
-5.01
(1 row)
SELECT to_number('5 4 4 4 4 8 . 7 8', '9 9 9 9 9 9 . 9 9');
to_number
-----------
544448.78
(1 row)
SELECT to_number('.01', 'FM9.99');
to_number
-----------
0.01
(1 row)
SELECT to_number('.0', '99999999.99999999');
to_number
-----------
0.0
(1 row)
SELECT to_number('0', '99.99');
to_number
-----------
0
(1 row)
SELECT to_number('.-01', 'S99.99');
to_number
-----------
-0.01
(1 row)
SELECT to_number('.01-', '99.99S');
to_number
-----------
-0.01
(1 row)
SELECT to_number(' . 0 1-', ' 9 9 . 9 9 S');
to_number
-----------
-0.01
(1 row)
SELECT to_number('34,50','999,99');
to_number
-----------
3450
(1 row)
SELECT to_number('123,000','999G');
to_number
-----------
123
(1 row)
SELECT to_number('123456','999G999');
to_number
-----------
123456
(1 row)
SELECT to_number('$1234.56','L9,999.99');
to_number
-----------
1234.56
(1 row)
SELECT to_number('$1234.56','L99,999.99');
to_number
-----------
1234.56
(1 row)
SELECT to_number('$1,234.56','L99,999.99');
to_number
-----------
1234.56
(1 row)
SELECT to_number('1234.56','L99,999.99');
to_number
-----------
1234.56
(1 row)
SELECT to_number('1,234.56','L99,999.99');
to_number
-----------
1234.56
(1 row)
SELECT to_number('42nd', '99th');
to_number
-----------
42
(1 row)
RESET lc_numeric;
--
-- Input syntax
--
CREATE TABLE num_input_test (n1 numeric);
-- good inputs
INSERT INTO num_input_test(n1) VALUES (' 123');
INSERT INTO num_input_test(n1) VALUES (' 3245874 ');
INSERT INTO num_input_test(n1) VALUES (' -93853');
INSERT INTO num_input_test(n1) VALUES ('555.50');
INSERT INTO num_input_test(n1) VALUES ('-555.50');
INSERT INTO num_input_test(n1) VALUES ('NaN ');
INSERT INTO num_input_test(n1) VALUES (' nan');
INSERT INTO num_input_test(n1) VALUES (' inf ');
INSERT INTO num_input_test(n1) VALUES (' +inf ');
INSERT INTO num_input_test(n1) VALUES (' -inf ');
INSERT INTO num_input_test(n1) VALUES (' Infinity ');
INSERT INTO num_input_test(n1) VALUES (' +inFinity ');
INSERT INTO num_input_test(n1) VALUES (' -INFINITY ');
-- bad inputs
INSERT INTO num_input_test(n1) VALUES (' ');
ERROR: invalid input syntax for type numeric: " "
LINE 1: INSERT INTO num_input_test(n1) VALUES (' ');
^
INSERT INTO num_input_test(n1) VALUES (' 1234 %');
ERROR: invalid input syntax for type numeric: " 1234 %"
LINE 1: INSERT INTO num_input_test(n1) VALUES (' 1234 %');
^
INSERT INTO num_input_test(n1) VALUES ('xyz');
ERROR: invalid input syntax for type numeric: "xyz"
LINE 1: INSERT INTO num_input_test(n1) VALUES ('xyz');
^
INSERT INTO num_input_test(n1) VALUES ('- 1234');
ERROR: invalid input syntax for type numeric: "- 1234"
LINE 1: INSERT INTO num_input_test(n1) VALUES ('- 1234');
^
INSERT INTO num_input_test(n1) VALUES ('5 . 0');
ERROR: invalid input syntax for type numeric: "5 . 0"
LINE 1: INSERT INTO num_input_test(n1) VALUES ('5 . 0');
^
INSERT INTO num_input_test(n1) VALUES ('5. 0 ');
ERROR: invalid input syntax for type numeric: "5. 0 "
LINE 1: INSERT INTO num_input_test(n1) VALUES ('5. 0 ');
^
INSERT INTO num_input_test(n1) VALUES ('');
ERROR: invalid input syntax for type numeric: ""
LINE 1: INSERT INTO num_input_test(n1) VALUES ('');
^
INSERT INTO num_input_test(n1) VALUES (' N aN ');
ERROR: invalid input syntax for type numeric: " N aN "
LINE 1: INSERT INTO num_input_test(n1) VALUES (' N aN ');
^
INSERT INTO num_input_test(n1) VALUES ('+ infinity');
ERROR: invalid input syntax for type numeric: "+ infinity"
LINE 1: INSERT INTO num_input_test(n1) VALUES ('+ infinity');
^
SELECT * FROM num_input_test;
n1
-----------
123
3245874
-93853
555.50
-555.50
NaN
NaN
Infinity
Infinity
-Infinity
Infinity
Infinity
-Infinity
(13 rows)
--
-- Test some corner cases for multiplication
--
select 4790999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
?column?
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
47909999999999999999999999999999999999999999999999999999999999999999999999999999999999985209000000000000000000000000000000000000000000000000000000000000000000000000000000000001
(1 row)
select 4789999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
?column?
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
47899999999999999999999999999999999999999999999999999999999999999999999999999999999999985210000000000000000000000000000000000000000000000000000000000000000000000000000000000001
(1 row)
select 4770999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
?column?
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
47709999999999999999999999999999999999999999999999999999999999999999999999999999999999985229000000000000000000000000000000000000000000000000000000000000000000000000000000000001
(1 row)
select 4769999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
?column?
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
47699999999999999999999999999999999999999999999999999999999999999999999999999999999999985230000000000000000000000000000000000000000000000000000000000000000000000000000000000001
(1 row)
select trim_scale((0.1 - 2e-16383) * (0.1 - 3e-16383));
trim_scale
------------
0.01
(1 row)
--
-- Test some corner cases for division
--
select 999999999999999999999::numeric/1000000000000000000000;
?column?
------------------------
1.00000000000000000000
(1 row)
select div(999999999999999999999::numeric,1000000000000000000000);
div
-----
0
(1 row)
select mod(999999999999999999999::numeric,1000000000000000000000);
mod
-----------------------
999999999999999999999
(1 row)
select div(-9999999999999999999999::numeric,1000000000000000000000);
div
-----
-9
(1 row)
select mod(-9999999999999999999999::numeric,1000000000000000000000);
mod
------------------------
-999999999999999999999
(1 row)
select div(-9999999999999999999999::numeric,1000000000000000000000)*1000000000000000000000 + mod(-9999999999999999999999::numeric,1000000000000000000000);
?column?
-------------------------
-9999999999999999999999
(1 row)
select mod (70.0,70) ;
mod
-----
0.0
(1 row)
select div (70.0,70) ;
div
-----
1
(1 row)
select 70.0 / 70 ;
?column?
------------------------
1.00000000000000000000
(1 row)
select 12345678901234567890 % 123;
?column?
----------
78
(1 row)
select 12345678901234567890 / 123;
?column?
--------------------
100371373180768845
(1 row)
select div(12345678901234567890, 123);
div
--------------------
100371373180768844
(1 row)
select div(12345678901234567890, 123) * 123 + 12345678901234567890 % 123;
?column?
----------------------
12345678901234567890
(1 row)
--
-- Test some corner cases for square root
--
select sqrt(1.000000000000003::numeric);
sqrt
-------------------
1.000000000000001
(1 row)
select sqrt(1.000000000000004::numeric);
sqrt
-------------------
1.000000000000002
(1 row)
select sqrt(96627521408608.56340355805::numeric);
sqrt
---------------------
9829929.87811248648
(1 row)
select sqrt(96627521408608.56340355806::numeric);
sqrt
---------------------
9829929.87811248649
(1 row)
select sqrt(515549506212297735.073688290367::numeric);
sqrt
------------------------
718017761.766585921184
(1 row)
select sqrt(515549506212297735.073688290368::numeric);
sqrt
------------------------
718017761.766585921185
(1 row)
select sqrt(8015491789940783531003294973900306::numeric);
sqrt
-------------------
89529278953540017
(1 row)
select sqrt(8015491789940783531003294973900307::numeric);
sqrt
-------------------
89529278953540018
(1 row)
--
-- Test code path for raising to integer powers
--
select 10.0 ^ -2147483648 as rounds_to_zero;
rounds_to_zero
--------------------
0.0000000000000000
(1 row)
select 10.0 ^ -2147483647 as rounds_to_zero;
rounds_to_zero
--------------------
0.0000000000000000
(1 row)
select 10.0 ^ 2147483647 as overflows;
ERROR: value overflows numeric format
select 117743296169.0 ^ 1000000000 as overflows;
ERROR: value overflows numeric format
-- cases that used to return inaccurate results
select 3.789 ^ 21;
?column?
--------------------------------
1409343026052.8716016316022141
(1 row)
select 3.789 ^ 35;
?column?
----------------------------------------
177158169650516670809.3820586142670135
(1 row)
select 1.2 ^ 345;
?column?
-----------------------------------------------
2077446682327378559843444695.5827049735727869
(1 row)
select 0.12 ^ (-20);
?column?
--------------------------------------
2608405330458882702.5529619561355838
(1 row)
select 1.000000000123 ^ (-2147483648);
?column?
--------------------
0.7678656556403084
(1 row)
select 0.9999999999 ^ 23300000000000 = 0 as rounds_to_zero;
rounds_to_zero
----------------
t
(1 row)
-- cases that used to error out
select 0.12 ^ (-25);
?column?
-------------------------------------------
104825960103961013959336.4983657883169110
(1 row)
select 0.5678 ^ (-85);
?column?
----------------------------------------
782333637740774446257.7719390061997396
(1 row)
select 0.9999999999 ^ 70000000000000 = 0 as underflows;
underflows
------------
t
(1 row)
-- negative base to integer powers
select (-1.0) ^ 2147483646;
?column?
--------------------
1.0000000000000000
(1 row)
select (-1.0) ^ 2147483647;
?column?
---------------------
-1.0000000000000000
(1 row)
select (-1.0) ^ 2147483648;
?column?
--------------------
1.0000000000000000
(1 row)
select (-1.0) ^ 1000000000000000;
?column?
--------------------
1.0000000000000000
(1 row)
select (-1.0) ^ 1000000000000001;
?column?
---------------------
-1.0000000000000000
(1 row)
--
-- Tests for raising to non-integer powers
--
-- special cases
select 0.0 ^ 0.0;
?column?
--------------------
1.0000000000000000
(1 row)
select (-12.34) ^ 0.0;
?column?
--------------------
1.0000000000000000
(1 row)
select 12.34 ^ 0.0;
?column?
--------------------
1.0000000000000000
(1 row)
select 0.0 ^ 12.34;
?column?
--------------------
0.0000000000000000
(1 row)
-- NaNs
select 'NaN'::numeric ^ 'NaN'::numeric;
?column?
----------
NaN
(1 row)
select 'NaN'::numeric ^ 0;
?column?
----------
1
(1 row)
select 'NaN'::numeric ^ 1;
?column?
----------
NaN
(1 row)
select 0 ^ 'NaN'::numeric;
?column?
----------
NaN
(1 row)
select 1 ^ 'NaN'::numeric;
?column?
----------
1
(1 row)
-- invalid inputs
select 0.0 ^ (-12.34);
ERROR: zero raised to a negative power is undefined
select (-12.34) ^ 1.2;
ERROR: a negative number raised to a non-integer power yields a complex result
-- cases that used to generate inaccurate results
select 32.1 ^ 9.8;
?column?
--------------------
580429286790711.10
(1 row)
select 32.1 ^ (-9.8);
?column?
----------------------------------
0.000000000000001722862754788209
(1 row)
select 12.3 ^ 45.6;
?column?
------------------------------------------------------
50081010321492803393171165777624533697036806969694.9
(1 row)
select 12.3 ^ (-45.6);
?column?
---------------------------------------------------------------------
0.00000000000000000000000000000000000000000000000001996764828785491
(1 row)
-- big test
select 1.234 ^ 5678;
?column?
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
307239295662090741644584872593956173493568238595074141254349565406661439636598896798876823220904084953233015553994854875890890858118656468658643918169805277399402542281777901029346337707622181574346585989613344285010764501017625366742865066948856161360224801370482171458030533346309750557140549621313515752078638620714732831815297168231790779296290266207315344008883935010274044001522606235576584215999260117523114297033944018699691024106823438431754073086813382242140602291215149759520833200152654884259619588924545324.5973362312547382
(1 row)
--
-- Tests for EXP()
--
-- special cases
select exp(0.0);
exp
--------------------
1.0000000000000000
(1 row)
select exp(1.0);
exp
--------------------
2.7182818284590452
(1 row)
select exp(1.0::numeric(71,70));
exp
--------------------------------------------------------------------------
2.7182818284590452353602874713526624977572470936999595749669676277240766
(1 row)
select exp('nan'::numeric);
exp
-----
NaN
(1 row)
select exp('inf'::numeric);
exp
----------
Infinity
(1 row)
select exp('-inf'::numeric);
exp
-----
0
(1 row)
select exp(-5000::numeric) = 0 as rounds_to_zero;
rounds_to_zero
----------------
t
(1 row)
select exp(-10000::numeric) = 0 as underflows;
underflows
------------
t
(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 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