ydb/yql/essentials/tests/postgresql/original/cases/numeric.out

--
-- 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 conversion to integers
SELECT (-9223372036854775808.5)::int8; -- should fail
ERROR:  bigint out of range
SELECT (-9223372036854775808.4)::int8; -- ok
         int8         
----------------------
 -9223372036854775808
(1 row)

SELECT 9223372036854775807.4::int8; -- ok
        int8         
---------------------
 9223372036854775807
(1 row)

SELECT 9223372036854775807.5::int8; -- should fail
ERROR:  bigint out of range
SELECT (-2147483648.5)::int4; -- should fail
ERROR:  integer out of range
SELECT (-2147483648.4)::int4; -- ok
    int4     
-------------
 -2147483648
(1 row)

SELECT 2147483647.4::int4; -- ok
    int4    
------------
 2147483647
(1 row)

SELECT 2147483647.5::int4; -- should fail
ERROR:  integer out of range
SELECT (-32768.5)::int2; -- should fail
ERROR:  smallint out of range
SELECT (-32768.4)::int2; -- ok
  int2  
--------
 -32768
(1 row)

SELECT 32767.4::int2; -- ok
 int2  
-------
 32767
(1 row)

SELECT 32767.5::int2; -- should fail
ERROR:  smallint out of range
-- Check inf/nan conversion behavior
SELECT 'NaN'::float8::numeric;
 numeric 
---------
     NaN
(1 row)

SELECT 'Infinity'::float8::numeric;
 numeric  
----------
 Infinity
(1 row)

SELECT '-Infinity'::float8::numeric;
  numeric  
-----------
 -Infinity
(1 row)

SELECT 'NaN'::numeric::float8;
 float8 
--------
    NaN
(1 row)

SELECT 'Infinity'::numeric::float8;
  float8  
----------
 Infinity
(1 row)

SELECT '-Infinity'::numeric::float8;
  float8   
-----------
 -Infinity
(1 row)

SELECT 'NaN'::float4::numeric;
 numeric 
---------
     NaN
(1 row)

SELECT 'Infinity'::float4::numeric;
 numeric  
----------
 Infinity
(1 row)

SELECT '-Infinity'::float4::numeric;
  numeric  
-----------
 -Infinity
(1 row)

SELECT 'NaN'::numeric::float4;
 float4 
--------
    NaN
(1 row)

SELECT 'Infinity'::numeric::float4;
  float4  
----------
 Infinity
(1 row)

SELECT '-Infinity'::numeric::float4;
  float4   
-----------
 -Infinity
(1 row)

SELECT '42'::int2::numeric;
 numeric 
---------
      42
(1 row)

SELECT 'NaN'::numeric::int2;
ERROR:  cannot convert NaN to smallint
SELECT 'Infinity'::numeric::int2;
ERROR:  cannot convert infinity to smallint
SELECT '-Infinity'::numeric::int2;
ERROR:  cannot convert infinity to smallint
SELECT 'NaN'::numeric::int4;
ERROR:  cannot convert NaN to integer
SELECT 'Infinity'::numeric::int4;
ERROR:  cannot convert infinity to integer
SELECT '-Infinity'::numeric::int4;
ERROR:  cannot convert infinity to integer
SELECT 'NaN'::numeric::int8;
ERROR:  cannot convert NaN to bigint
SELECT 'Infinity'::numeric::int8;
ERROR:  cannot convert infinity to bigint
SELECT '-Infinity'::numeric::int8;
ERROR:  cannot convert infinity to bigint
-- Simple check that ceil(), floor(), and round() work correctly
CREATE TABLE ceil_floor_round (a numeric);
INSERT INTO ceil_floor_round VALUES ('-5.5');
INSERT INTO ceil_floor_round VALUES ('-5.499999');
INSERT INTO ceil_floor_round VALUES ('9.5');
INSERT INTO ceil_floor_round VALUES ('9.4999999');
INSERT INTO ceil_floor_round VALUES ('0.0');
INSERT INTO ceil_floor_round VALUES ('0.0000001');
INSERT INTO ceil_floor_round VALUES ('-0.000001');
SELECT a, ceil(a), ceiling(a), floor(a), round(a) FROM ceil_floor_round;
     a     | ceil | ceiling | floor | round 
-----------+------+---------+-------+-------
      -5.5 |   -5 |      -5 |    -6 |    -6
 -5.499999 |   -5 |      -5 |    -6 |    -5
       9.5 |   10 |      10 |     9 |    10
 9.4999999 |   10 |      10 |     9 |     9
       0.0 |    0 |       0 |     0 |     0
 0.0000001 |    1 |       1 |     0 |     0
 -0.000001 |    0 |       0 |    -1 |     0
(7 rows)

DROP TABLE ceil_floor_round;
-- Check rounding, it should round ties away from zero.
SELECT i as pow,
	round((-2.5 * 10 ^ i)::numeric, -i),
	round((-1.5 * 10 ^ i)::numeric, -i),
	round((-0.5 * 10 ^ i)::numeric, -i),
	round((0.5 * 10 ^ i)::numeric, -i),
	round((1.5 * 10 ^ i)::numeric, -i),
	round((2.5 * 10 ^ i)::numeric, -i)
FROM generate_series(-5,5) AS t(i);
 pow |  round   |  round   |  round   |  round  |  round  |  round  
-----+----------+----------+----------+---------+---------+---------
  -5 | -0.00003 | -0.00002 | -0.00001 | 0.00001 | 0.00002 | 0.00003
  -4 |  -0.0003 |  -0.0002 |  -0.0001 |  0.0001 |  0.0002 |  0.0003
  -3 |   -0.003 |   -0.002 |   -0.001 |   0.001 |   0.002 |   0.003
  -2 |    -0.03 |    -0.02 |    -0.01 |    0.01 |    0.02 |    0.03
  -1 |     -0.3 |     -0.2 |     -0.1 |     0.1 |     0.2 |     0.3
   0 |       -3 |       -2 |       -1 |       1 |       2 |       3
   1 |      -30 |      -20 |      -10 |      10 |      20 |      30
   2 |     -300 |     -200 |     -100 |     100 |     200 |     300
   3 |    -3000 |    -2000 |    -1000 |    1000 |    2000 |    3000
   4 |   -30000 |   -20000 |   -10000 |   10000 |   20000 |   30000
   5 |  -300000 |  -200000 |  -100000 |  100000 |  200000 |  300000
(11 rows)

-- Testing for width_bucket(). For convenience, we test both the
-- numeric and float8 versions of the function in this file.
-- errors
SELECT width_bucket(5.0, 3.0, 4.0, 0);
ERROR:  count must be greater than zero
SELECT width_bucket(5.0, 3.0, 4.0, -5);
ERROR:  count must be greater than zero
SELECT width_bucket(3.5, 3.0, 3.0, 888);
ERROR:  lower bound cannot equal upper bound
SELECT width_bucket(5.0::float8, 3.0::float8, 4.0::float8, 0);
ERROR:  count must be greater than zero
SELECT width_bucket(5.0::float8, 3.0::float8, 4.0::float8, -5);
ERROR:  count must be greater than zero
SELECT width_bucket(3.5::float8, 3.0::float8, 3.0::float8, 888);
ERROR:  lower bound cannot equal upper bound
SELECT width_bucket('NaN', 3.0, 4.0, 888);
ERROR:  operand, lower bound, and upper bound cannot be NaN
SELECT width_bucket(0::float8, 'NaN', 4.0::float8, 888);
ERROR:  operand, lower bound, and upper bound cannot be NaN
SELECT width_bucket(2.0, 3.0, '-inf', 888);
ERROR:  lower and upper bounds must be finite
SELECT width_bucket(0::float8, '-inf', 4.0::float8, 888);
ERROR:  lower and upper bounds must be finite
-- normal operation
CREATE TABLE width_bucket_test (operand_num numeric, operand_f8 float8);
COPY width_bucket_test (operand_num) FROM stdin;
UPDATE width_bucket_test SET operand_f8 = operand_num::float8;
SELECT
    operand_num,
    width_bucket(operand_num, 0, 10, 5) AS wb_1,
    width_bucket(operand_f8, 0, 10, 5) AS wb_1f,
    width_bucket(operand_num, 10, 0, 5) AS wb_2,
    width_bucket(operand_f8, 10, 0, 5) AS wb_2f,
    width_bucket(operand_num, 2, 8, 4) AS wb_3,
    width_bucket(operand_f8, 2, 8, 4) AS wb_3f,
    width_bucket(operand_num, 5.0, 5.5, 20) AS wb_4,
    width_bucket(operand_f8, 5.0, 5.5, 20) AS wb_4f,
    width_bucket(operand_num, -25, 25, 10) AS wb_5,
    width_bucket(operand_f8, -25, 25, 10) AS wb_5f
    FROM width_bucket_test;
   operand_num    | wb_1 | wb_1f | wb_2 | wb_2f | wb_3 | wb_3f | wb_4 | wb_4f | wb_5 | wb_5f 
------------------+------+-------+------+-------+------+-------+------+-------+------+-------
             -5.2 |    0 |     0 |    6 |     6 |    0 |     0 |    0 |     0 |    4 |     4
    -0.0000000001 |    0 |     0 |    6 |     6 |    0 |     0 |    0 |     0 |    5 |     5
   0.000000000001 |    1 |     1 |    5 |     5 |    0 |     0 |    0 |     0 |    6 |     6
                1 |    1 |     1 |    5 |     5 |    0 |     0 |    0 |     0 |    6 |     6
 1.99999999999999 |    1 |     1 |    5 |     5 |    0 |     0 |    0 |     0 |    6 |     6
                2 |    2 |     2 |    5 |     5 |    1 |     1 |    0 |     0 |    6 |     6
 2.00000000000001 |    2 |     2 |    4 |     4 |    1 |     1 |    0 |     0 |    6 |     6
                3 |    2 |     2 |    4 |     4 |    1 |     1 |    0 |     0 |    6 |     6
                4 |    3 |     3 |    4 |     4 |    2 |     2 |    0 |     0 |    6 |     6
              4.5 |    3 |     3 |    3 |     3 |    2 |     2 |    0 |     0 |    6 |     6
                5 |    3 |     3 |    3 |     3 |    3 |     3 |    1 |     1 |    7 |     7
              5.5 |    3 |     3 |    3 |     3 |    3 |     3 |   21 |    21 |    7 |     7
                6 |    4 |     4 |    3 |     3 |    3 |     3 |   21 |    21 |    7 |     7
                7 |    4 |     4 |    2 |     2 |    4 |     4 |   21 |    21 |    7 |     7
                8 |    5 |     5 |    2 |     2 |    5 |     5 |   21 |    21 |    7 |     7
                9 |    5 |     5 |    1 |     1 |    5 |     5 |   21 |    21 |    7 |     7
 9.99999999999999 |    5 |     5 |    1 |     1 |    5 |     5 |   21 |    21 |    7 |     7
               10 |    6 |     6 |    1 |     1 |    5 |     5 |   21 |    21 |    8 |     8
 10.0000000000001 |    6 |     6 |    0 |     0 |    5 |     5 |   21 |    21 |    8 |     8
(19 rows)

-- Check positive and negative infinity: we require
-- finite bucket bounds, but allow an infinite operand
SELECT width_bucket(0.0::numeric, 'Infinity'::numeric, 5, 10); -- error
ERROR:  lower and upper bounds must be finite
SELECT width_bucket(0.0::numeric, 5, '-Infinity'::numeric, 20); -- error
ERROR:  lower and upper bounds must be finite
SELECT width_bucket('Infinity'::numeric, 1, 10, 10),
       width_bucket('-Infinity'::numeric, 1, 10, 10);
 width_bucket | width_bucket 
--------------+--------------
           11 |            0
(1 row)

SELECT width_bucket(0.0::float8, 'Infinity'::float8, 5, 10); -- error
ERROR:  lower and upper bounds must be finite
SELECT width_bucket(0.0::float8, 5, '-Infinity'::float8, 20); -- error
ERROR:  lower and upper bounds must be finite
SELECT width_bucket('Infinity'::float8, 1, 10, 10),
       width_bucket('-Infinity'::float8, 1, 10, 10);
 width_bucket | width_bucket 
--------------+--------------
           11 |            0
(1 row)

DROP TABLE width_bucket_test;
-- Simple test for roundoff error when results should be exact
SELECT x, width_bucket(x::float8, 10, 100, 9) as flt,
       width_bucket(x::numeric, 10, 100, 9) as num
FROM generate_series(0, 110, 10) x;
  x  | flt | num 
-----+-----+-----
   0 |   0 |   0
  10 |   1 |   1
  20 |   2 |   2
  30 |   3 |   3
  40 |   4 |   4
  50 |   5 |   5
  60 |   6 |   6
  70 |   7 |   7
  80 |   8 |   8
  90 |   9 |   9
 100 |  10 |  10
 110 |  10 |  10
(12 rows)

SELECT x, width_bucket(x::float8, 100, 10, 9) as flt,
       width_bucket(x::numeric, 100, 10, 9) as num
FROM generate_series(0, 110, 10) x;
  x  | flt | num 
-----+-----+-----
   0 |  10 |  10
  10 |  10 |  10
  20 |   9 |   9
  30 |   8 |   8
  40 |   7 |   7
  50 |   6 |   6
  60 |   5 |   5
  70 |   4 |   4
  80 |   3 |   3
  90 |   2 |   2
 100 |   1 |   1
 110 |   0 |   0
(12 rows)

--
-- TO_CHAR()
--
SELECT to_char(val, '9G999G999G999G999G999')
	FROM num_data;
        to_char         
------------------------
                      0
                      0
            -34,338,492
                      4
              7,799,461
                 16,397
                 93,902
            -83,028,485
                 74,881
            -24,926,804
(10 rows)

SELECT to_char(val, '9G999G999G999G999G999D999G999G999G999G999')
	FROM num_data;
                  to_char                   
--------------------------------------------
                       .000,000,000,000,000
                       .000,000,000,000,000
            -34,338,492.215,397,047,000,000
                      4.310,000,000,000,000
              7,799,461.411,900,000,000,000
                 16,397.038,491,000,000,000
                 93,901.577,630,260,000,000
            -83,028,485.000,000,000,000,000
                 74,881.000,000,000,000,000
            -24,926,804.045,047,420,000,000
(10 rows)

SELECT to_char(val, '9999999999999999.999999999999999PR')
	FROM num_data;
              to_char               
------------------------------------
                  .000000000000000 
                  .000000000000000 
         <34338492.215397047000000>
                 4.310000000000000 
           7799461.411900000000000 
             16397.038491000000000 
             93901.577630260000000 
         <83028485.000000000000000>
             74881.000000000000000 
         <24926804.045047420000000>
(10 rows)

SELECT to_char(val, '9999999999999999.999999999999999S')
	FROM num_data;
              to_char              
-----------------------------------
                 .000000000000000+
                 .000000000000000+
         34338492.215397047000000-
                4.310000000000000+
          7799461.411900000000000+
            16397.038491000000000+
            93901.577630260000000+
         83028485.000000000000000-
            74881.000000000000000+
         24926804.045047420000000-
(10 rows)

SELECT to_char(val, 'MI9999999999999999.999999999999999')     FROM num_data;
              to_char              
-----------------------------------
                  .000000000000000
                  .000000000000000
 -        34338492.215397047000000
                 4.310000000000000
           7799461.411900000000000
             16397.038491000000000
             93901.577630260000000
 -        83028485.000000000000000
             74881.000000000000000
 -        24926804.045047420000000
(10 rows)

SELECT to_char(val, 'FMS9999999999999999.999999999999999')    FROM num_data;
       to_char       
---------------------
 +0.
 +0.
 -34338492.215397047
 +4.31
 +7799461.4119
 +16397.038491
 +93901.57763026
 -83028485.
 +74881.
 -24926804.04504742
(10 rows)

SELECT to_char(val, 'FM9999999999999999.999999999999999THPR') FROM num_data;
       to_char        
----------------------
 0.
 0.
 <34338492.215397047>
 4.31
 7799461.4119
 16397.038491
 93901.57763026
 <83028485.>
 74881.
 <24926804.04504742>
(10 rows)

SELECT to_char(val, 'SG9999999999999999.999999999999999th')   FROM num_data;
              to_char              
-----------------------------------
 +                .000000000000000
 +                .000000000000000
 -        34338492.215397047000000
 +               4.310000000000000
 +         7799461.411900000000000
 +           16397.038491000000000
 +           93901.577630260000000
 -        83028485.000000000000000
 +           74881.000000000000000
 -        24926804.045047420000000
(10 rows)

SELECT to_char(val, '0999999999999999.999999999999999')       FROM num_data;
              to_char              
-----------------------------------
  0000000000000000.000000000000000
  0000000000000000.000000000000000
 -0000000034338492.215397047000000
  0000000000000004.310000000000000
  0000000007799461.411900000000000
  0000000000016397.038491000000000
  0000000000093901.577630260000000
 -0000000083028485.000000000000000
  0000000000074881.000000000000000
 -0000000024926804.045047420000000
(10 rows)

SELECT to_char(val, 'S0999999999999999.999999999999999')      FROM num_data;
              to_char              
-----------------------------------
 +0000000000000000.000000000000000
 +0000000000000000.000000000000000
 -0000000034338492.215397047000000
 +0000000000000004.310000000000000
 +0000000007799461.411900000000000
 +0000000000016397.038491000000000
 +0000000000093901.577630260000000
 -0000000083028485.000000000000000
 +0000000000074881.000000000000000
 -0000000024926804.045047420000000
(10 rows)

SELECT to_char(val, 'FM0999999999999999.999999999999999')     FROM num_data;
           to_char           
-----------------------------
 0000000000000000.
 0000000000000000.
 -0000000034338492.215397047
 0000000000000004.31
 0000000007799461.4119
 0000000000016397.038491
 0000000000093901.57763026
 -0000000083028485.
 0000000000074881.
 -0000000024926804.04504742
(10 rows)

SELECT to_char(val, 'FM9999999999999999.099999999999999') 	FROM num_data;
       to_char       
---------------------
 .0
 .0
 -34338492.215397047
 4.31
 7799461.4119
 16397.038491
 93901.57763026
 -83028485.0
 74881.0
 -24926804.04504742
(10 rows)

SELECT to_char(val, 'FM9999999999990999.990999999999999') 	FROM num_data;
       to_char       
---------------------
 0000.000
 0000.000
 -34338492.215397047
 0004.310
 7799461.4119
 16397.038491
 93901.57763026
 -83028485.000
 74881.000
 -24926804.04504742
(10 rows)

SELECT to_char(val, 'FM0999999999999999.999909999999999') 	FROM num_data;
           to_char           
-----------------------------
 0000000000000000.00000
 0000000000000000.00000
 -0000000034338492.215397047
 0000000000000004.31000
 0000000007799461.41190
 0000000000016397.038491
 0000000000093901.57763026
 -0000000083028485.00000
 0000000000074881.00000
 -0000000024926804.04504742
(10 rows)

SELECT to_char(val, 'FM9999999990999999.099999999999999') 	FROM num_data;
       to_char       
---------------------
 0000000.0
 0000000.0
 -34338492.215397047
 0000004.31
 7799461.4119
 0016397.038491
 0093901.57763026
 -83028485.0
 0074881.0
 -24926804.04504742
(10 rows)

SELECT to_char(val, 'L9999999999999999.099999999999999')	FROM num_data;
              to_char               
------------------------------------
                   .000000000000000
                   .000000000000000
          -34338492.215397047000000
                  4.310000000000000
            7799461.411900000000000
              16397.038491000000000
              93901.577630260000000
          -83028485.000000000000000
              74881.000000000000000
          -24926804.045047420000000
(10 rows)

SELECT to_char(val, 'FM9999999999999999.99999999999999')	FROM num_data;
       to_char       
---------------------
 0.
 0.
 -34338492.215397047
 4.31
 7799461.4119
 16397.038491
 93901.57763026
 -83028485.
 74881.
 -24926804.04504742
(10 rows)

SELECT to_char(val, 'S 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 . 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9') FROM num_data;
                                to_char                                
-----------------------------------------------------------------------
                                  +. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                                  +. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                  -3 4 3 3 8 4 9 2 . 2 1 5 3 9 7 0 4 7 0 0 0 0 0 0 0 0
                                +4 . 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                    +7 7 9 9 4 6 1 . 4 1 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0
                        +1 6 3 9 7 . 0 3 8 4 9 1 0 0 0 0 0 0 0 0 0 0 0
                        +9 3 9 0 1 . 5 7 7 6 3 0 2 6 0 0 0 0 0 0 0 0 0
                  -8 3 0 2 8 4 8 5 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                        +7 4 8 8 1 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                  -2 4 9 2 6 8 0 4 . 0 4 5 0 4 7 4 2 0 0 0 0 0 0 0 0 0
(10 rows)

SELECT to_char(val, 'FMS 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 . 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9') FROM num_data;
                        to_char                        
-------------------------------------------------------
                 +0 .                 
                 +0 .                 
          -3 4 3 3 8 4 9 2 . 2 1 5 3 9 7 0 4 7        
                 +4 . 3 1               
           +7 7 9 9 4 6 1 . 4 1 1 9             
             +1 6 3 9 7 . 0 3 8 4 9 1           
             +9 3 9 0 1 . 5 7 7 6 3 0 2 6         
          -8 3 0 2 8 4 8 5 .                 
             +7 4 8 8 1 .                 
          -2 4 9 2 6 8 0 4 . 0 4 5 0 4 7 4 2         
(10 rows)

SELECT to_char(val, E'99999 "text" 9999 "9999" 999 "\\"text between quote marks\\"" 9999') FROM num_data;
                          to_char                          
-----------------------------------------------------------
       text      9999     "text between quote marks"     0
       text      9999     "text between quote marks"     0
       text    -3 9999 433 "text between quote marks" 8492
       text      9999     "text between quote marks"     4
       text      9999  779 "text between quote marks" 9461
       text      9999    1 "text between quote marks" 6397
       text      9999    9 "text between quote marks" 3902
       text    -8 9999 302 "text between quote marks" 8485
       text      9999    7 "text between quote marks" 4881
       text    -2 9999 492 "text between quote marks" 6804
(10 rows)

SELECT to_char(val, '999999SG9999999999')			FROM num_data;
      to_char      
-------------------
       +         0
       +         0
       -  34338492
       +         4
       +   7799461
       +     16397
       +     93902
       -  83028485
       +     74881
       -  24926804
(10 rows)

SELECT to_char(val, 'FM9999999999999999.999999999999999')	FROM num_data;
       to_char       
---------------------
 0.
 0.
 -34338492.215397047
 4.31
 7799461.4119
 16397.038491
 93901.57763026
 -83028485.
 74881.
 -24926804.04504742
(10 rows)

SELECT to_char(val, '9.999EEEE')				FROM num_data;
  to_char   
------------
  0.000e+00
  0.000e+00
 -3.434e+07
  4.310e+00
  7.799e+06
  1.640e+04
  9.390e+04
 -8.303e+07
  7.488e+04
 -2.493e+07
(10 rows)

WITH v(val) AS
  (VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan'))
SELECT val,
  to_char(val, '9.999EEEE') as numeric,
  to_char(val::float8, '9.999EEEE') as float8,
  to_char(val::float4, '9.999EEEE') as float4
FROM v;
    val     |  numeric   |   float8   |   float4   
------------+------------+------------+------------
          0 |  0.000e+00 |  0.000e+00 |  0.000e+00
       -4.2 | -4.200e+00 | -4.200e+00 | -4.200e+00
 4200000000 |  4.200e+09 |  4.200e+09 |  4.200e+09
   0.000012 |  1.200e-05 |  1.200e-05 |  1.200e-05
   Infinity |  #.####### |  #.####### |  #.#######
  -Infinity |  #.####### |  #.####### |  #.#######
        NaN |  #.####### |  #.####### |  #.#######
(7 rows)

WITH v(exp) AS
  (VALUES(-16379),(-16378),(-1234),(-789),(-45),(-5),(-4),(-3),(-2),(-1),(0),
         (1),(2),(3),(4),(5),(38),(275),(2345),(45678),(131070),(131071))
SELECT exp,
  to_char(('1.2345e'||exp)::numeric, '9.999EEEE') as numeric
FROM v;
  exp   |    numeric     
--------+----------------
 -16379 |  1.235e-16379
 -16378 |  1.235e-16378
  -1234 |  1.235e-1234
   -789 |  1.235e-789
    -45 |  1.235e-45
     -5 |  1.235e-05
     -4 |  1.235e-04
     -3 |  1.235e-03
     -2 |  1.235e-02
     -1 |  1.235e-01
      0 |  1.235e+00
      1 |  1.235e+01
      2 |  1.235e+02
      3 |  1.235e+03
      4 |  1.235e+04
      5 |  1.235e+05
     38 |  1.235e+38
    275 |  1.235e+275
   2345 |  1.235e+2345
  45678 |  1.235e+45678
 131070 |  1.235e+131070
 131071 |  1.235e+131071
(22 rows)

WITH v(val) AS
  (VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan'))
SELECT val,
  to_char(val, 'MI9999999999.99') as numeric,
  to_char(val::float8, 'MI9999999999.99') as float8,
  to_char(val::float4, 'MI9999999999.99') as float4
FROM v;
    val     |    numeric     |     float8     |     float4     
------------+----------------+----------------+----------------
          0 |            .00 |            .00 |            .00
       -4.2 | -         4.20 | -         4.20 | -         4.20
 4200000000 |  4200000000.00 |  4200000000.00 |  4200000000
   0.000012 |            .00 |            .00 |            .00
   Infinity |    Infinity    |    Infinity    |    Infinity
  -Infinity | -  Infinity    | -  Infinity    | -  Infinity
        NaN |         NaN    |         NaN    |         NaN
(7 rows)

WITH v(val) AS
  (VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan'))
SELECT val,
  to_char(val, 'MI99.99') as numeric,
  to_char(val::float8, 'MI99.99') as float8,
  to_char(val::float4, 'MI99.99') as float4
FROM v;
    val     | numeric | float8 | float4 
------------+---------+--------+--------
          0 |    .00  |    .00 |    .00
       -4.2 | - 4.20  | - 4.20 | - 4.20
 4200000000 |  ##.##  |  ##.## |  ##.
   0.000012 |    .00  |    .00 |    .00
   Infinity |  ##.##  |  ##.## |  ##.
  -Infinity | -##.##  | -##.## | -##.
        NaN |  ##.##  |  ##.## |  ##.##
(7 rows)

SELECT to_char('100'::numeric, 'FM999.9');
 to_char 
---------
 100.
(1 row)

SELECT to_char('100'::numeric, 'FM999.');
 to_char 
---------
 100
(1 row)

SELECT to_char('100'::numeric, 'FM999');
 to_char 
---------
 100
(1 row)

-- 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 coalesce(nullif(0.9999999999 ^ 23300000000000, 0), 0) as rounds_to_zero;
 rounds_to_zero 
----------------
              0
(1 row)

select round(((1 - 1.500012345678e-1000) ^ 1.45e1003) * 1e1000);
                          round                           
----------------------------------------------------------
 25218976308958387188077465658068501556514992509509282366
(1 row)

-- cases that used to error out
select 0.12 ^ (-25);
                 ?column?                  
-------------------------------------------
 104825960103961013959336.4983657883169110
(1 row)

select 0.5678 ^ (-85);
                ?column?                
----------------------------------------
 782333637740774446257.7719390061997396
(1 row)

select coalesce(nullif(0.9999999999 ^ 70000000000000, 0), 0) as underflows;
 underflows 
------------
          0
(1 row)

-- negative base to integer powers
select (-1.0) ^ 2147483646;
      ?column?      
--------------------
 1.0000000000000000
(1 row)

select (-1.0) ^ 2147483647;
      ?column?       
---------------------
 -1.0000000000000000
(1 row)

select (-1.0) ^ 2147483648;
      ?column?      
--------------------
 1.0000000000000000
(1 row)

select (-1.0) ^ 1000000000000000;
      ?column?      
--------------------
 1.0000000000000000
(1 row)

select (-1.0) ^ 1000000000000001;
      ?column?       
---------------------
 -1.0000000000000000
(1 row)

--
-- Tests for raising to non-integer powers
--
-- special cases
select 0.0 ^ 0.0;
      ?column?      
--------------------
 1.0000000000000000
(1 row)

select (-12.34) ^ 0.0;
      ?column?      
--------------------
 1.0000000000000000
(1 row)

select 12.34 ^ 0.0;
      ?column?      
--------------------
 1.0000000000000000
(1 row)

select 0.0 ^ 12.34;
      ?column?      
--------------------
 0.0000000000000000
(1 row)

-- NaNs
select 'NaN'::numeric ^ 'NaN'::numeric;
 ?column? 
----------
      NaN
(1 row)

select 'NaN'::numeric ^ 0;
 ?column? 
----------
        1
(1 row)

select 'NaN'::numeric ^ 1;
 ?column? 
----------
      NaN
(1 row)

select 0 ^ 'NaN'::numeric;
 ?column? 
----------
      NaN
(1 row)

select 1 ^ 'NaN'::numeric;
 ?column? 
----------
        1
(1 row)

-- invalid inputs
select 0.0 ^ (-12.34);
ERROR:  zero raised to a negative power is undefined
select (-12.34) ^ 1.2;
ERROR:  a negative number raised to a non-integer power yields a complex result
-- cases that used to generate inaccurate results
select 32.1 ^ 9.8;
      ?column?      
--------------------
 580429286790711.10
(1 row)

select 32.1 ^ (-9.8);
             ?column?             
----------------------------------
 0.000000000000001722862754788209
(1 row)

select 12.3 ^ 45.6;
                       ?column?                       
------------------------------------------------------
 50081010321492803393171165777624533697036806969694.9
(1 row)

select 12.3 ^ (-45.6);
                              ?column?                               
---------------------------------------------------------------------
 0.00000000000000000000000000000000000000000000000001996764828785491
(1 row)

-- big test
select 1.234 ^ 5678;
                                                                                                                                                                                                                                                                         ?column?                                                                                                                                                                                                                                                                         
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 307239295662090741644584872593956173493568238595074141254349565406661439636598896798876823220904084953233015553994854875890890858118656468658643918169805277399402542281777901029346337707622181574346585989613344285010764501017625366742865066948856161360224801370482171458030533346309750557140549621313515752078638620714732831815297168231790779296290266207315344008883935010274044001522606235576584215999260117523114297033944018699691024106823438431754073086813382242140602291215149759520833200152654884259619588924545324.5973362312547382
(1 row)

--
-- Tests for EXP()
--
-- special cases
select exp(0.0);
        exp         
--------------------
 1.0000000000000000
(1 row)

select exp(1.0);
        exp         
--------------------
 2.7182818284590452
(1 row)

select exp(1.0::numeric(71,70));
                                   exp                                    
--------------------------------------------------------------------------
 2.7182818284590452353602874713526624977572470936999595749669676277240766
(1 row)

select exp('nan'::numeric);
 exp 
-----
 NaN
(1 row)

select exp('inf'::numeric);
   exp    
----------
 Infinity
(1 row)

select exp('-inf'::numeric);
 exp 
-----
   0
(1 row)

select coalesce(nullif(exp(-5000::numeric), 0), 0) as rounds_to_zero;
 rounds_to_zero 
----------------
              0
(1 row)

select coalesce(nullif(exp(-10000::numeric), 0), 0) as underflows;
 underflows 
------------
          0
(1 row)

-- cases that used to generate inaccurate results
select exp(32.999);
         exp         
---------------------
 214429043492155.053
(1 row)

select exp(-32.999);
               exp                
----------------------------------
 0.000000000000004663547361468248
(1 row)

select exp(123.456);
                            exp                             
------------------------------------------------------------
 413294435277809344957685441227343146614594393746575438.725
(1 row)

select exp(-123.456);
                                   exp                                   
-------------------------------------------------------------------------
 0.000000000000000000000000000000000000000000000000000002419582541264601
(1 row)

-- big test
select exp(1234.5678);
                                                                                                                                                                                                                                                                              exp                                                                                                                                                                                                                                                                               
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 146549072930959479983482138503979804217622199675223653966270157446954995433819741094410764947112047906012815540251009949604426069672532417736057033099274204598385314594846509975629046864798765888104789074984927709616261452461385220475510438783429612447831614003668421849727379202555580791042606170523016207262965336641214601082882495255771621327088265411334088968112458492660609809762865582162764292604697957813514621259353683899630997077707406305730694385703091201347848855199354307506425820147289848677003277208302716466011827836279231.9667
(1 row)

--
-- Tests for generate_series
--
select * from generate_series(0.0::numeric, 4.0::numeric);
 generate_series 
-----------------
             0.0
             1.0
             2.0
             3.0
             4.0
(5 rows)

select * from generate_series(0.1::numeric, 4.0::numeric, 1.3::numeric);
 generate_series 
-----------------
             0.1
             1.4
             2.7
             4.0
(4 rows)

select * from generate_series(4.0::numeric, -1.5::numeric, -2.2::numeric);
 generate_series 
-----------------
             4.0
             1.8
            -0.4
(3 rows)

-- Trigger errors
select * from generate_series(-100::numeric, 100::numeric, 0::numeric);
ERROR:  step size cannot equal zero
select * from generate_series(-100::numeric, 100::numeric, 'nan'::numeric);
ERROR:  step size cannot be NaN
select * from generate_series('nan'::numeric, 100::numeric, 10::numeric);
ERROR:  start value cannot be NaN
select * from generate_series(0::numeric, 'nan'::numeric, 10::numeric);
ERROR:  stop value cannot be NaN
select * from generate_series('inf'::numeric, 'inf'::numeric, 10::numeric);
ERROR:  start value cannot be infinity
select * from generate_series(0::numeric, 'inf'::numeric, 10::numeric);
ERROR:  stop value cannot be infinity
select * from generate_series(0::numeric, '42'::numeric, '-inf'::numeric);
ERROR:  step size cannot be infinity
-- Checks maximum, output is truncated
select (i / (10::numeric ^ 131071))::numeric(1,0)
	from generate_series(6 * (10::numeric ^ 131071),
			     9 * (10::numeric ^ 131071),
			     10::numeric ^ 131071) as a(i);
 numeric 
---------
       6
       7
       8
       9
(4 rows)

-- Check usage with variables
select * from generate_series(1::numeric, 3::numeric) i, generate_series(i,3) j;
 i | j 
---+---
 1 | 1
 1 | 2
 1 | 3
 2 | 2
 2 | 3
 3 | 3
(6 rows)

select * from generate_series(1::numeric, 3::numeric) i, generate_series(1,i) j;
 i | j 
---+---
 1 | 1
 2 | 1
 2 | 2
 3 | 1
 3 | 2
 3 | 3
(6 rows)

select * from generate_series(1::numeric, 3::numeric) i, generate_series(1,5,i) j;
 i | j 
---+---
 1 | 1
 1 | 2
 1 | 3
 1 | 4
 1 | 5
 2 | 1
 2 | 3
 2 | 5
 3 | 1
 3 | 4
(10 rows)

--
-- Tests for LN()
--
-- Invalid inputs
select ln(-12.34);
ERROR:  cannot take logarithm of a negative number
select ln(0.0);
ERROR:  cannot take logarithm of zero
-- Some random tests
select ln(1.2345678e-28);
                   ln                    
-----------------------------------------
 -64.26166165451762991204894255882820859
(1 row)

select ln(0.0456789);
         ln          
---------------------
 -3.0861187944847439
(1 row)

select ln(0.349873948359354029493948309745709580730482050975);
                         ln                          
-----------------------------------------------------
 -1.050182336912082775693991697979750253056317885460
(1 row)

select ln(0.99949452);
           ln            
-------------------------
 -0.00050560779808326467
(1 row)

select ln(1.00049687395);
           ln           
------------------------
 0.00049675054901370394
(1 row)

select ln(1234.567890123456789);
         ln         
--------------------
 7.1184763012977896
(1 row)

select ln(5.80397490724e5);
         ln         
--------------------
 13.271468476626518
(1 row)

select ln(9.342536355e34);
         ln         
--------------------
 80.522470935524187
(1 row)

--
-- Tests for LOG() (base 10)
--
-- invalid inputs
select log(-12.34);
ERROR:  cannot take logarithm of a negative number
CONTEXT:  SQL function "log" statement 1
select log(0.0);
ERROR:  cannot take logarithm of zero
CONTEXT:  SQL function "log" statement 1
-- some random tests
select log(1.234567e-89);
                                                 log                                                 
-----------------------------------------------------------------------------------------------------
 -88.90848533591373725637496492944925187293052336306443143312825869985819779294142441287021741054275
(1 row)

select log(3.4634998359873254962349856073435545);
                 log                  
--------------------------------------
 0.5395151714070134409152404011959981
(1 row)

select log(9.999999999999999999);
         log          
----------------------
 1.000000000000000000
(1 row)

select log(10.00000000000000000);
         log         
---------------------
 1.00000000000000000
(1 row)

select log(10.00000000000000001);
         log         
---------------------
 1.00000000000000000
(1 row)

select log(590489.45235237);
        log        
-------------------
 5.771212144411727
(1 row)

--
-- Tests for LOG() (arbitrary base)
--
-- invalid inputs
select log(-12.34, 56.78);
ERROR:  cannot take logarithm of a negative number
select log(-12.34, -56.78);
ERROR:  cannot take logarithm of a negative number
select log(12.34, -56.78);
ERROR:  cannot take logarithm of a negative number
select log(0.0, 12.34);
ERROR:  cannot take logarithm of zero
select log(12.34, 0.0);
ERROR:  cannot take logarithm of zero
select log(1.0, 12.34);
ERROR:  division by zero
-- some random tests
select log(1.23e-89, 6.4689e45);
                                              log                                               
------------------------------------------------------------------------------------------------
 -0.5152489207781856983977054971756484879653568168479201885425588841094788842469115325262329756
(1 row)

select log(0.99923, 4.58934e34);
         log         
---------------------
 -103611.55579544132
(1 row)

select log(1.000016, 8.452010e18);
        log         
--------------------
 2723830.2877097365
(1 row)

select log(3.1954752e47, 9.4792021e-73);
                                         log                                         
-------------------------------------------------------------------------------------
 -1.51613372350688302142917386143459361608600157692779164475351842333265418126982165
(1 row)

--
-- Tests for scale()
--
select scale(numeric 'NaN');
 scale 
-------
      
(1 row)

select scale(numeric 'inf');
 scale 
-------
      
(1 row)

select scale(NULL::numeric);
 scale 
-------
      
(1 row)

select scale(1.12);
 scale 
-------
     2
(1 row)

select scale(0);
 scale 
-------
     0
(1 row)

select scale(0.00);
 scale 
-------
     2
(1 row)

select scale(1.12345);
 scale 
-------
     5
(1 row)

select scale(110123.12475871856128);
 scale 
-------
    14
(1 row)

select scale(-1123.12471856128);
 scale 
-------
    11
(1 row)

select scale(-13.000000000000000);
 scale 
-------
    15
(1 row)

--
-- Tests for min_scale()
--
select min_scale(numeric 'NaN') is NULL; -- should be true
 ?column? 
----------
 t
(1 row)

select min_scale(numeric 'inf') is NULL; -- should be true
 ?column? 
----------
 t
(1 row)

select min_scale(0);                     -- no digits
 min_scale 
-----------
         0
(1 row)

select min_scale(0.00);                  -- no digits again
 min_scale 
-----------
         0
(1 row)

select min_scale(1.0);                   -- no scale
 min_scale 
-----------
         0
(1 row)

select min_scale(1.1);                   -- scale 1
 min_scale 
-----------
         1
(1 row)

select min_scale(1.12);                  -- scale 2
 min_scale 
-----------
         2
(1 row)

select min_scale(1.123);                 -- scale 3
 min_scale 
-----------
         3
(1 row)

select min_scale(1.1234);                -- scale 4, filled digit
 min_scale 
-----------
         4
(1 row)

select min_scale(1.12345);               -- scale 5, 2 NDIGITS
 min_scale 
-----------
         5
(1 row)

select min_scale(1.1000);                -- 1 pos in NDIGITS
 min_scale 
-----------
         1
(1 row)

select min_scale(1e100);                 -- very big number
 min_scale 
-----------
         0
(1 row)

--
-- Tests for trim_scale()
--
select trim_scale(numeric 'NaN');
 trim_scale 
------------
        NaN
(1 row)

select trim_scale(numeric 'inf');
 trim_scale 
------------
   Infinity
(1 row)

select trim_scale(1.120);
 trim_scale 
------------
       1.12
(1 row)

select trim_scale(0);
 trim_scale 
------------
          0
(1 row)

select trim_scale(0.00);
 trim_scale 
------------
          0
(1 row)

select trim_scale(1.1234500);
 trim_scale 
------------
    1.12345
(1 row)

select trim_scale(110123.12475871856128000);
      trim_scale       
-----------------------
 110123.12475871856128
(1 row)

select trim_scale(-1123.124718561280000000);
    trim_scale     
-------------------
 -1123.12471856128
(1 row)

select trim_scale(-13.00000000000000000000);
 trim_scale 
------------
        -13
(1 row)

select trim_scale(1e100);
                                              trim_scale                                               
-------------------------------------------------------------------------------------------------------
 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
(1 row)

--
-- Tests for SUM()
--
-- cases that need carry propagation
SELECT SUM(9999::numeric) FROM generate_series(1, 100000);
    sum    
-----------
 999900000
(1 row)

SELECT SUM((-9999)::numeric) FROM generate_series(1, 100000);
    sum     
------------
 -999900000
(1 row)

--
-- Tests for 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