Merge pull request #11788 from ydb-platform/mergelibs-241120-1113

Library import 241120-1113

1 files changed, 2383 insertions, 0 deletions

diff --git a/yql/essentials/tests/postgresql/cases/numeric.out b/yql/essentials/tests/postgresql/cases/numeric.out
new file mode 100644
index 0000000000..e9970b3d37
--- /dev/null
+++ b/yql/essentials/tests/postgresql/cases/numeric.out
@@ -0,0 +1,2383 @@
+--
+-- 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');
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+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');
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+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');
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+INSERT INTO num_exp_mul VALUES (6,6,'8817506281.4517452372676676');
+INSERT INTO num_exp_div VALUES (6,6,'1.00000000000000000000');
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+INSERT INTO num_exp_mul VALUES (6,8,'7031444034.53149906');
+INSERT INTO num_exp_div VALUES (6,8,'1.25401073209839612184');
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+INSERT INTO num_exp_mul VALUES (6,9,'-2340666225110.29929521292692920');
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+INSERT INTO num_exp_div VALUES (7,0,'NaN');
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+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');
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+INSERT INTO num_exp_div VALUES (7,3,'-19264149.65197215777262180974');
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+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');
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+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');
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+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;
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+INSERT INTO num_result SELECT id, 0, SQRT(ABS(val))
+    FROM num_data;
+INSERT INTO num_result SELECT id, 0, LN(ABS(val))
+    FROM num_data
+    WHERE val != '0.0';
+INSERT INTO num_result SELECT id, 0, LOG(numeric '10', ABS(val))
+    FROM num_data
+    WHERE val != '0.0';
+INSERT INTO num_result SELECT id, 0, POWER(numeric '10', LN(ABS(round(val,200))))
+    FROM num_data
+    WHERE val != '0.0';
+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
+-- 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)
+
+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
+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
+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
+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('-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, '0');
+ power 
+-------
+     1
+(1 row)
+
+SELECT power('-inf'::numeric, 'inf');
+  power   
+----------
+ Infinity
+(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)
+
+-- 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 (4, '-0.9999');
+INSERT INTO fract_only VALUES (5, '0.99994');
+INSERT INTO fract_only VALUES (7, '0.00001');
+INSERT INTO fract_only VALUES (8, '0.00017');
+INSERT INTO fract_only VALUES (9, 'NaN');
+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');
+DROP TABLE ceil_floor_round;
+-- 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);
+-- 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(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
+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)
+
+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)
+
+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('.-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)
+
+--
+-- 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)
+
+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 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)
+
+-- cases that used to error out
+select 0.12 ^ (-25);
+                 ?column?                  
+-------------------------------------------
+ 104825960103961013959336.4983657883169110
+(1 row)
+
+select 0.5678 ^ (-85);
+                ?column?                
+----------------------------------------
+ 782333637740774446257.7719390061997396
+(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)
+
+--
+-- 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)
+
+-- 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)
+
+--
+-- 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
+--
+-- 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(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)
+
+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