From a41f002ab7a54485867d5574187b557117b1f94b Mon Sep 17 00:00:00 2001
From: Daniel Gustafsson <dgustafsson@postgresql.org>
Date: Mon, 19 Feb 2024 13:25:44 +0100
Subject: [PATCH v1] Remove numeric_big test suite

The numeric_big testsuite has never been connected with make check,
and has thus never been frequently executed. As it doesn't add any
additional coverage, remove it and the associated bespoke targets
to run it.
---
 doc/src/sgml/regress.sgml                 |    9 +-
 src/test/regress/GNUmakefile              |    7 -
 src/test/regress/expected/numeric_big.out | 2082 ---------------------
 src/test/regress/sql/numeric_big.sql      | 1366 --------------
 4 files changed, 5 insertions(+), 3459 deletions(-)
 delete mode 100644 src/test/regress/expected/numeric_big.out
 delete mode 100644 src/test/regress/sql/numeric_big.sql

diff --git a/doc/src/sgml/regress.sgml b/doc/src/sgml/regress.sgml
index 6a27aae319..5843f9ce33 100644
--- a/doc/src/sgml/regress.sgml
+++ b/doc/src/sgml/regress.sgml
@@ -437,12 +437,13 @@ make check EXTRA_REGRESS_OPTS="--temp-config=test_postgresql.conf"
 
    <para>
     The core regression test suite contains a few test files that are not
-    run by default, because they might be platform-dependent or take a
-    very long time to run.  You can run these or other extra test
+    run by default, because they might be platform-dependent, take a
+    very long time to run or be unreliable when run in conjunction with
+    other tests.  You can run these or other extra test
     files by setting the variable <envar>EXTRA_TESTS</envar>.  For
-    example, to run the <literal>numeric_big</literal> test:
+    example, to run the <literal>reindex_catalog</literal> test:
 <screen>
-make check EXTRA_TESTS=numeric_big
+make check EXTRA_TESTS=reindex_catalog
 </screen>
    </para>
   </sect2>
diff --git a/src/test/regress/GNUmakefile b/src/test/regress/GNUmakefile
index 9003435aab..9621cb253a 100644
--- a/src/test/regress/GNUmakefile
+++ b/src/test/regress/GNUmakefile
@@ -135,13 +135,6 @@ runcheck: check
 runtest: installcheck
 runtest-parallel: installcheck-parallel
 
-bigtest: all
-	$(pg_regress_installcheck) $(REGRESS_OPTS) --schedule=$(srcdir)/parallel_schedule --max-connections=1 numeric_big
-
-bigcheck: all | temp-install
-	$(pg_regress_check) $(REGRESS_OPTS) --schedule=$(srcdir)/parallel_schedule $(MAXCONNOPT) numeric_big
-
-
 ##
 ## Clean up
 ##
diff --git a/src/test/regress/expected/numeric_big.out b/src/test/regress/expected/numeric_big.out
deleted file mode 100644
index 12ff35b583..0000000000
--- a/src/test/regress/expected/numeric_big.out
+++ /dev/null
@@ -1,2082 +0,0 @@
--- ******************************
--- * Test suite for the Postgres NUMERIC data type
--- ******************************
--- Must drop tables created by short numeric test.
-DROP TABLE num_data;
-DROP TABLE num_exp_add;
-DROP TABLE num_exp_sub;
-DROP TABLE num_exp_div;
-DROP TABLE num_exp_mul;
-DROP TABLE num_exp_sqrt;
-DROP TABLE num_exp_ln;
-DROP TABLE num_exp_log10;
-DROP TABLE num_exp_power_10_ln;
-DROP TABLE num_result;
-CREATE TABLE num_data (id int4, val numeric(1000,800));
-CREATE TABLE num_exp_add (id1 int4, id2 int4, expected numeric(1000,800));
-CREATE TABLE num_exp_sub (id1 int4, id2 int4, expected numeric(1000,800));
-CREATE TABLE num_exp_div (id1 int4, id2 int4, expected numeric(1000,800));
-CREATE TABLE num_exp_mul (id1 int4, id2 int4, expected numeric(1000,800));
-CREATE TABLE num_exp_sqrt (id int4, expected numeric(1000,800));
-CREATE TABLE num_exp_ln (id int4, expected numeric(1000,800));
-CREATE TABLE num_exp_log10 (id int4, expected numeric(1000,800));
-CREATE TABLE num_exp_power_10_ln (id int4, expected numeric(1000,800));
-CREATE TABLE num_result (id1 int4, id2 int4, result numeric(1000,800));
--- ******************************
--- * The following EXPECTED results are computed by bc(1)
--- * with a scale of 1000
--- ******************************
-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,'85243.39540024977626076239847863600785982737155858270959890014613035727868293618673807776733416230953723818527101593495895350807775607346277892835514324320448949370623441059033804864158715021903312693889518990256881059434042443507529601095150710777634743301398926463888783847290873199395304998050753365215426971278237920063435565949203678024225270616295573678510929020831006146661747271783837653203039829647102027431761129518881525935216608429897041525858540380754759125150233053469999022855035');
-INSERT INTO num_exp_sub VALUES (0,1,'-85243.39540024977626076239847863600785982737155858270959890014613035727868293618673807776733416230953723818527101593495895350807775607346277892835514324320448949370623441059033804864158715021903312693889518990256881059434042443507529601095150710777634743301398926463888783847290873199395304998050753365215426971278237920063435565949203678024225270616295573678510929020831006146661747271783837653203039829647102027431761129518881525935216608429897041525858540380754759125150233053469999022855035');
-INSERT INTO num_exp_mul VALUES (0,1,'0');
-INSERT INTO num_exp_div VALUES (0,1,'0');
-INSERT INTO num_exp_add VALUES (0,2,'-994877526002806872754342148749241.04353023451866590387054959174736129501310680280823383331007646306243540953499740615246583399296334239109936336446284803020643582102868247857009494139535009572740621288230740389545481395');
-INSERT INTO num_exp_sub VALUES (0,2,'994877526002806872754342148749241.04353023451866590387054959174736129501310680280823383331007646306243540953499740615246583399296334239109936336446284803020643582102868247857009494139535009572740621288230740389545481395');
-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,'-60302029489319384367663884408085757480.2322712404088283093870869198708849258097125725036189625900174440196153781995220721511009855207486224837798752903681993777275846325950111427710563453217985216966456785944859989497422927661683538629473170704026975786513125842675604577233871570629808699803522400038975396500769162308448069085909755023233588510630417065084295051270219462289785473643946404281422516357503746700705970360169619852905053433235726497292406142332833');
-INSERT INTO num_exp_sub VALUES (0,3,'60302029489319384367663884408085757480.2322712404088283093870869198708849258097125725036189625900174440196153781995220721511009855207486224837798752903681993777275846325950111427710563453217985216966456785944859989497422927661683538629473170704026975786513125842675604577233871570629808699803522400038975396500769162308448069085909755023233588510630417065084295051270219462289785473643946404281422516357503746700705970360169619852905053433235726497292406142332833');
-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,'5329378275943663322215245.24931765987630429629836382184742348353920297283690739124220773955591340709935970062776650204659187764581615597720798385015942389765692769739983054442503547211560297249686289665792078548480268091496050883021187158502798880896590227542729659940394038802461081290690995869705131152889309663639310553909874081663091069118126221594338242710530718836025225507189149221049928936955230868771875644038572888630664890573507822342998964954667474300944699078658989010257103569231493090050659723450626338923049035040974032671138430612839043269997482582763267536489504794826476836323549796385028155416935072959933315468068930689064483178204550825728947252440604703474049780550458442808479096492346910001692358508618202898514895453589357');
-INSERT INTO num_exp_sub VALUES (0,4,'-5329378275943663322215245.24931765987630429629836382184742348353920297283690739124220773955591340709935970062776650204659187764581615597720798385015942389765692769739983054442503547211560297249686289665792078548480268091496050883021187158502798880896590227542729659940394038802461081290690995869705131152889309663639310553909874081663091069118126221594338242710530718836025225507189149221049928936955230868771875644038572888630664890573507822342998964954667474300944699078658989010257103569231493090050659723450626338923049035040974032671138430612839043269997482582763267536489504794826476836323549796385028155416935072959933315468068930689064483178204550825728947252440604703474049780550458442808479096492346910001692358508618202898514895453589357');
-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,'-652755630.43456071828048833552593835051449845484289562110789582081210403487973096161149072377955192388469356112505543620695003436531392789029513380101663750625024853263344909355177280161504414335005574882649025508632900995595004153086358670541462762210415346958050909878501048483523600711486406055424807840429541335391538322886495085448421556770991545781035298449067051916630343957356635391594362639819978677032855590055900561501350354631803808000307050416047072513406855040715556454205065332997338225626635780147287003130754254277103928406089109802521803537038957372612837169223905290912251006321930223154562110264217937');
-INSERT INTO num_exp_sub VALUES (0,5,'652755630.43456071828048833552593835051449845484289562110789582081210403487973096161149072377955192388469356112505543620695003436531392789029513380101663750625024853263344909355177280161504414335005574882649025508632900995595004153086358670541462762210415346958050909878501048483523600711486406055424807840429541335391538322886495085448421556770991545781035298449067051916630343957356635391594362639819978677032855590055900561501350354631803808000307050416047072513406855040715556454205065332997338225626635780147287003130754254277103928406089109802521803537038957372612837169223905290912251006321930223154562110264217937');
-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,'.0469370721950711508944806393077762204079964905145503836835397203739563036579760026190241480514409364');
-INSERT INTO num_exp_sub VALUES (0,6,'-.0469370721950711508944806393077762204079964905145503836835397203739563036579760026190241480514409364');
-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,'-818934540071845742');
-INSERT INTO num_exp_sub VALUES (0,7,'818934540071845742');
-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,'8496986223.64063724353165506167988570717591150432282238795309964705925283285060558038824227595710139960766584401003765241409149793494330798800');
-INSERT INTO num_exp_sub VALUES (0,8,'-8496986223.64063724353165506167988570717591150432282238795309964705925283285060558038824227595710139960766584401003765241409149793494330798800');
-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,'54863480.34685027005508022756223282084742813020271603840941647350440860843570182437301045468670059279379903480024743452620396345637401505220786389930600883087012615993343976556472498552535317826554614696684732913955544753638726438705858481670766245958647367500212800073774509075408148134050353551558174813940258910304990570172170811882520915334358633');
-INSERT INTO num_exp_sub VALUES (0,9,'-54863480.34685027005508022756223282084742813020271603840941647350440860843570182437301045468670059279379903480024743452620396345637401505220786389930600883087012615993343976556472498552535317826554614696684732913955544753638726438705858481670766245958647367500212800073774509075408148134050353551558174813940258910304990570172170811882520915334358633');
-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,'85243.39540024977626076239847863600785982737155858270959890014613035727868293618673807776733416230953723818527101593495895350807775607346277892835514324320448949370623441059033804864158715021903312693889518990256881059434042443507529601095150710777634743301398926463888783847290873199395304998050753365215426971278237920063435565949203678024225270616295573678510929020831006146661747271783837653203039829647102027431761129518881525935216608429897041525858540380754759125150233053469999022855035');
-INSERT INTO num_exp_sub VALUES (1,0,'85243.39540024977626076239847863600785982737155858270959890014613035727868293618673807776733416230953723818527101593495895350807775607346277892835514324320448949370623441059033804864158715021903312693889518990256881059434042443507529601095150710777634743301398926463888783847290873199395304998050753365215426971278237920063435565949203678024225270616295573678510929020831006146661747271783837653203039829647102027431761129518881525935216608429897041525858540380754759125150233053469999022855035');
-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,'170486.79080049955252152479695727201571965474311716541919780029226071455736587237347615553466832461907447637054203186991790701615551214692555785671028648640897898741246882118067609728317430043806625387779037980513762118868084887015059202190301421555269486602797852927777567694581746398790609996101506730430853942556475840126871131898407356048450541232591147357021858041662012293323494543567675306406079659294204054863522259037763051870433216859794083051717080761509518250300466106939998045710070');
-INSERT INTO num_exp_sub VALUES (1,1,'0');
-INSERT INTO num_exp_mul VALUES (1,1,'7266436459.363324713115467666113895787027372854351303425444968800459979742082292257107107767894843498525848597439323325297125474674300428669958003640228730876886174255457103020291514229439701871032118057857763809224712818579091741996335014138185389554630910658876423205103697147288306070059640369158894028731728589073730895396494400175420670713113234800826523252075036892246807434088405522834549449664122407363485486902219500109237667016524913027290777216477989904700729228025571098410870506256758678625928245828210775042611512394316804583459576285681159178280400209217948833631961377519855502763611693070238579591463373484424582723121059964236704135695706864890193388054537703767833595331866551990460050750959493829603581882430597105627056085260296454181999581594565113210481151487049158699087454047624433576922179904629');
-INSERT INTO num_exp_div VALUES (1,1,'1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000');
-INSERT INTO num_exp_add VALUES (1,2,'-994877526002806872754342148663997.64812998474240514147207095573950146764154822009863493316394610578375247334825932838513167168342610420582834742950389452212867974756590355021495169819086060202117180229196935525386766373096687306110481009743118940565957556492470398904849289222365256698601073536111216152709126800604695001949246634784573028721762079936564434050796321975774729383704426321489070979168993853338252728216162346796960170352897972568238870481118474064783391570102958474141459619245240874849766946530000977144965');
-INSERT INTO num_exp_sub VALUES (1,2,'994877526002806872754342148834484.43893048429492666626902822775522112238466538551783273345620682034111834572173548391979999630250058057637037929942180153828419189449146140692523818459983958943364062347264545253704196416903312693889518990256881059434042443507529601095150710777634743301398926463888783847290873199395304998050753365215426971278237920063435565949203678024225270616295573678510929020831006146661747271783837653203039829647102027431761129518881525935216608429897041525858540380754759125150233053469999022855035');
-INSERT INTO num_exp_mul VALUES (1,2,'-84806738323879544552397401815149740513.8505875535743013876823142649666132764556588225959336097903898464616542203793600590311980154402068027051522932586050753865288419084437796768749509032177577451738712965496693249429231838833655025794915864261585848007162358912070811805298210095333433397862313304655108809804359760907473898420016370058274978588765092161529583480924554820756527238472641797198545539410039895140087686344382628317530286295498797849942258314364503000942821309916954725689781458590617068629906894951122301020797266469357701283289275708774593896770378558232444454118891917258610753077932026885574920166837998049508644891327208474213193224700658584824407382455480657734911543930195324144216374573825');
-INSERT INTO num_exp_div VALUES (1,2,'-.000000000000000000000000000085682300757901809257711279577127388124986344391495296640171942990079130291883279872719240502687189411421655284515420074848478500192127657883342858267913417679786356766341637336955924836847768457039175660279784295612167899455618405343686908907695358239088351870495830739180518509859269437015797489301844593920484927630172344269378248455657186218762679357609204333669024237648538465053048724383898528808961206696787294681884412485427843796696788390072124570957047672341581447744981862017791206857428430183366004980966398716823512288330174863890117558744630102020144500158878244146399686532935435591262767487823942606452349972401012308378888947381934278131785907155692007064636085000405504866631011593239041758448995933095907216863744502344014999804306234830774259496097549717476344048');
-INSERT INTO num_exp_add VALUES (1,3,'-60302029489319384367663884408085672236.83687099063256754698860828386302509843815398979402006244388708674093244201278399438376682321121138429850885935540924586964982855913223221441591310211730902799041126800414795030815514254713522692405212716783388698431088814919226444677188004928663343696636297536500970117716818423689175692808344185016908913828066250587407384563498516598672584120143890364303296142744031320345312431817858545326010704685255237541162931904446804064783391570102958474141459619245240874849766946530000977144965');
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-INSERT INTO num_exp_power_10_ln VALUES (6,'.000873076977206566818052116526263730226812004454463281371489634779519089200224205946321120805055212090024554381349223642352209212670470260295303361873760972918129853308169576675500721645609379420329169271088810484607337679253503247351324049221970104335289487989027621978310506220905131150125321713385148268584530413680037620544212746920563790371941626294733473967065607791756894237438288480748407449237446113996117912144587258434808327522518688617394025018756570740098795745692805352377041347367240475846033282850136270250633825482156304826383360291164928049344226886150285595932088884965511963310715773499733217615863523253012606066583814112265708693122563204149232245895551314975524172504103194858904869273185785182598234060315036187756490539352752560361560286717869643902435677448962235275054804452967413005');
-INSERT INTO num_exp_power_10_ln VALUES (7,'176514565873872717825163931126806100435750.096278384530154766967061948052237623936423931849868926020451465515367348890410352640552194499619062823622476972850692557798609619250753020363520533767813563613425606228355802781302735485038377521515850536680425059519814786118919994914180918228654298075183514200191737597656810036850772127169441661576862538643715648802139886576391427423689320082366572297580054381937437005879583216745596935643579262248665490169331304003204939561361718554509909313409421397022626924406091551900222555950699170864234411017062042057683304265485826061096835531732950909546314722726990314852356462874701181085379772134121978510387397276859318242238150439474660772561390798432890789762504242822787017140808209820627435991445529404692793744568204608385843245177656436105160780897472099970336514833257055017279707999437302548655364559');
-INSERT INTO num_exp_power_10_ln VALUES (8,'72941951052009383458167.300747500436981484566111756088702608000390737594784514635592222758882092500858797317505303492923829092720870826490477962201959426813271424853341826896270963213736922458746003100613943600855942721319226948714369219316345322636075285343544788982588956431405042577296229122673590336976893594798942025893296105815818487227300314490440902574022885833779324177053242170024559675073866612316965636832258283516275906085642459351367507561963945012828379111856700009391438637054015804558386733558956649061672420804826896303889067785497738203077050774825608647969196321506624991188638449047860249367840775936911749905927108478444112230174584693363226143549933224252679398881354887872642908328737917862751077365602631600279486028043329404269490375935308156815477700961014566228692743960491745353377403533037122586797765130');
-INSERT INTO num_exp_power_10_ln VALUES (9,'661239032819374816.097553651299556484820492272269662685578275493609248662925676004753503494252951243895572437264999063878330704584509915845096232798927524470286655554736724913758600775591269525423912692080421094644542553026831758426157681271572808657664918053119324646138457659418857926209701677786068580819823633713337632456905824562235373422309621872998037966404189020165296080436871220718574009921789858751384547836431858428729570977259373272041837411903005303672798845573379758630607982213326716018594073712340609488043353995410508475153538231445235003980586600882223782814368245305160648543466496726973755388826656879616734762068443462618454921858705377028522664844761719759342490380417060255776725333319537746890406213693117052223545525717132695297770810635066731941724108167146710297146989770382041617889670713111888375717');
-COMMIT TRANSACTION;
-BEGIN TRANSACTION;
-INSERT INTO num_data VALUES (0, '0');
-INSERT INTO num_data VALUES (1, '85243.39540024977626076239847863600785982737155858270959890014613035727868293618673807776733416230953723818527101593495895350807775607346277892835514324320448949370623441059033804864158715021903312693889518990256881059434042443507529601095150710777634743301398926463888783847290873199395304998050753365215426971278237920063435565949203678024225270616295573678510929020831006146661747271783837653203039829647102027431761129518881525935216608429897041525858540380754759125150233053469999022855035');
-INSERT INTO num_data VALUES (2, '-994877526002806872754342148749241.04353023451866590387054959174736129501310680280823383331007646306243540953499740615246583399296334239109936336446284803020643582102868247857009494139535009572740621288230740389545481395');
-INSERT INTO num_data VALUES (3, '-60302029489319384367663884408085757480.2322712404088283093870869198708849258097125725036189625900174440196153781995220721511009855207486224837798752903681993777275846325950111427710563453217985216966456785944859989497422927661683538629473170704026975786513125842675604577233871570629808699803522400038975396500769162308448069085909755023233588510630417065084295051270219462289785473643946404281422516357503746700705970360169619852905053433235726497292406142332833');
-INSERT INTO num_data VALUES (4, '5329378275943663322215245.24931765987630429629836382184742348353920297283690739124220773955591340709935970062776650204659187764581615597720798385015942389765692769739983054442503547211560297249686289665792078548480268091496050883021187158502798880896590227542729659940394038802461081290690995869705131152889309663639310553909874081663091069118126221594338242710530718836025225507189149221049928936955230868771875644038572888630664890573507822342998964954667474300944699078658989010257103569231493090050659723450626338923049035040974032671138430612839043269997482582763267536489504794826476836323549796385028155416935072959933315468068930689064483178204550825728947252440604703474049780550458442808479096492346910001692358508618202898514895453589357');
-INSERT INTO num_data VALUES (5, '-652755630.43456071828048833552593835051449845484289562110789582081210403487973096161149072377955192388469356112505543620695003436531392789029513380101663750625024853263344909355177280161504414335005574882649025508632900995595004153086358670541462762210415346958050909878501048483523600711486406055424807840429541335391538322886495085448421556770991545781035298449067051916630343957356635391594362639819978677032855590055900561501350354631803808000307050416047072513406855040715556454205065332997338225626635780147287003130754254277103928406089109802521803537038957372612837169223905290912251006321930223154562110264217937');
-INSERT INTO num_data VALUES (6, '0.0469370721950711508944806393077762204079964905145503836835397203739563036579760026190241480514409364');
-INSERT INTO num_data VALUES (7, '-818934540071845742');
-INSERT INTO num_data VALUES (8, '8496986223.64063724353165506167988570717591150432282238795309964705925283285060558038824227595710139960766584401003765241409149793494330798800');
-INSERT INTO num_data VALUES (9, '054863480.34685027005508022756223282084742813020271603840941647350440860843570182437301045468670059279379903480024743452620396345637401505220786389930600883087012615993343976556472498552535317826554614696684732913955544753638726438705858481670766245958647367500212800073774509075408148134050353551558174813940258910304990570172170811882520915334358633');
-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('10'::numeric, 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)
-
--- ******************************
--- * POW(10, LN(value)) check
--- ******************************
-DELETE FROM num_result;
-INSERT INTO num_result SELECT id, 0, POW(numeric '10', LN(ABS(round(val,1000))))
-    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)
-
---
--- Test code path for raising to integer powers
---
--- base less than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of POW():
---
--- for p in {-20..20}
--- do
---   b="0.084738"
---   r=$(bc -ql <<< "scale=500 ; $b^$p" | head -n 1)
---   echo "($b, $p, $r),"
--- done
-WITH t(b, p, bc_result) AS (VALUES
-(0.084738, -20, 2744326694304960114888.785913),
-(0.084738, -19, 232548755422013710215.445941),
-(0.084738, -18, 19705716436950597776.236458),
-(0.084738, -17, 1669822999434319754.362725),
-(0.084738, -16, 141497461326065387.345189),
-(0.084738, -15, 11990211877848128.792857),
-(0.084738, -14, 1016026574105094.737649),
-(0.084738, -13, 86096059836517.517879),
-(0.084738, -12, 7295607918426.821430),
-(0.084738, -11, 618215223791.651994),
-(0.084738, -10, 52386321633.657007),
-(0.084738, -9, 4439112122.5928274),
-(0.084738, -8, 376161483.04427101),
-(0.084738, -7, 31875171.750205437),
-(0.084738, -6, 2701038.3037689083),
-(0.084738, -5, 228880.58378476975),
-(0.084738, -4, 19394.882908753819),
-(0.084738, -3, 1643.4835879219811),
-(0.084738, -2, 139.26551227333284),
-(0.084738, -1, 11.801080979017678),
-(0.084738, 0, 1),
-(0.084738, 1, .084738),
-(0.084738, 2, .007180528644),
-(0.084738, 3, .000608463636235272),
-(0.084738, 4, .00005155999160730448),
-(0.084738, 5, .000004369090568819767),
-(0.084738, 6, .0000003702279966206494),
-(0.084738, 7, .00000003137237997764059),
-(0.084738, 8, .000000002658432734545308),
-(0.084738, 9, .0000000002252702730599003),
-(0.084738, 10, .00000000001908895239854983),
-(0.084738, 11, .000000000001617559648348316),
-(0.084738, 12, .0000000000001370687694817396),
-(0.084738, 13, .00000000000001161493338834365),
-(0.084738, 14, .0000000000000009842262254614642),
-(0.084738, 15, .00000000000000008340136189315355),
-(0.084738, 16, .000000000000000007067264604102046),
-(0.084738, 17, .0000000000000000005988658680223991),
-(0.084738, 18, .00000000000000000005074669592448206),
-(0.084738, 19, .000000000000000000004300173519248761),
-(0.084738, 20, .0000000000000000000003643881036741015))
-SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
-    b     |  p  |                bc_result                |                  power                  |                  diff                   
-----------+-----+-----------------------------------------+-----------------------------------------+-----------------------------------------
- 0.084738 | -20 |           2744326694304960114888.785913 |           2744326694304960114888.785913 |                                0.000000
- 0.084738 | -19 |            232548755422013710215.445941 |            232548755422013710215.445941 |                                0.000000
- 0.084738 | -18 |             19705716436950597776.236458 |             19705716436950597776.236458 |                                0.000000
- 0.084738 | -17 |              1669822999434319754.362725 |              1669822999434319754.362725 |                                0.000000
- 0.084738 | -16 |               141497461326065387.345189 |               141497461326065387.345189 |                                0.000000
- 0.084738 | -15 |                11990211877848128.792857 |                11990211877848128.792857 |                                0.000000
- 0.084738 | -14 |                 1016026574105094.737649 |                 1016026574105094.737649 |                                0.000000
- 0.084738 | -13 |                   86096059836517.517879 |                   86096059836517.517879 |                                0.000000
- 0.084738 | -12 |                    7295607918426.821430 |                    7295607918426.821430 |                                0.000000
- 0.084738 | -11 |                     618215223791.651994 |                     618215223791.651994 |                                0.000000
- 0.084738 | -10 |                      52386321633.657007 |                      52386321633.657007 |                                0.000000
- 0.084738 |  -9 |                      4439112122.5928274 |                      4439112122.5928274 |                               0.0000000
- 0.084738 |  -8 |                      376161483.04427101 |                      376161483.04427101 |                              0.00000000
- 0.084738 |  -7 |                      31875171.750205437 |                      31875171.750205437 |                             0.000000000
- 0.084738 |  -6 |                      2701038.3037689083 |                      2701038.3037689083 |                            0.0000000000
- 0.084738 |  -5 |                      228880.58378476975 |                      228880.58378476975 |                           0.00000000000
- 0.084738 |  -4 |                      19394.882908753819 |                      19394.882908753819 |                          0.000000000000
- 0.084738 |  -3 |                      1643.4835879219811 |                      1643.4835879219811 |                         0.0000000000000
- 0.084738 |  -2 |                      139.26551227333284 |                      139.26551227333284 |                        0.00000000000000
- 0.084738 |  -1 |                      11.801080979017678 |                      11.801080979017678 |                       0.000000000000000
- 0.084738 |   0 |                                       1 |                      1.0000000000000000 |                      0.0000000000000000
- 0.084738 |   1 |                                0.084738 |                     0.08473800000000000 |                     0.00000000000000000
- 0.084738 |   2 |                          0.007180528644 |                    0.007180528644000000 |                    0.000000000000000000
- 0.084738 |   3 |                    0.000608463636235272 |                   0.0006084636362352720 |                   0.0000000000000000000
- 0.084738 |   4 |                  0.00005155999160730448 |                  0.00005155999160730448 |                  0.00000000000000000000
- 0.084738 |   5 |                 0.000004369090568819767 |                 0.000004369090568819767 |                 0.000000000000000000000
- 0.084738 |   6 |                0.0000003702279966206494 |                0.0000003702279966206494 |                0.0000000000000000000000
- 0.084738 |   7 |               0.00000003137237997764059 |               0.00000003137237997764059 |               0.00000000000000000000000
- 0.084738 |   8 |              0.000000002658432734545308 |              0.000000002658432734545308 |              0.000000000000000000000000
- 0.084738 |   9 |             0.0000000002252702730599003 |             0.0000000002252702730599003 |             0.0000000000000000000000000
- 0.084738 |  10 |            0.00000000001908895239854983 |            0.00000000001908895239854983 |            0.00000000000000000000000000
- 0.084738 |  11 |           0.000000000001617559648348316 |           0.000000000001617559648348316 |           0.000000000000000000000000000
- 0.084738 |  12 |          0.0000000000001370687694817396 |          0.0000000000001370687694817396 |          0.0000000000000000000000000000
- 0.084738 |  13 |         0.00000000000001161493338834365 |         0.00000000000001161493338834365 |         0.00000000000000000000000000000
- 0.084738 |  14 |       0.0000000000000009842262254614642 |       0.0000000000000009842262254614642 |       0.0000000000000000000000000000000
- 0.084738 |  15 |      0.00000000000000008340136189315355 |      0.00000000000000008340136189315355 |      0.00000000000000000000000000000000
- 0.084738 |  16 |     0.000000000000000007067264604102046 |     0.000000000000000007067264604102046 |     0.000000000000000000000000000000000
- 0.084738 |  17 |    0.0000000000000000005988658680223991 |    0.0000000000000000005988658680223991 |    0.0000000000000000000000000000000000
- 0.084738 |  18 |   0.00000000000000000005074669592448206 |   0.00000000000000000005074669592448206 |   0.00000000000000000000000000000000000
- 0.084738 |  19 |  0.000000000000000000004300173519248761 |  0.000000000000000000004300173519248761 |  0.000000000000000000000000000000000000
- 0.084738 |  20 | 0.0000000000000000000003643881036741015 | 0.0000000000000000000003643881036741015 | 0.0000000000000000000000000000000000000
-(41 rows)
-
--- base greater than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of POW():
---
--- for p in {-20..20}
--- do
---   b="37.821637"
---   r=$(bc -ql <<< "scale=500 ; $b^$p" | head -n 1)
---   echo "($b, $p, $r),"
--- done
-WITH t(b, p, bc_result) AS (VALUES
-(37.821637, -20, .00000000000000000000000000000002787363175065101),
-(37.821637, -19, .000000000000000000000000000001054226381944797),
-(37.821637, -18, .00000000000000000000000000003987256753373947),
-(37.821637, -17, .000000000000000000000000001508045775519079),
-(37.821637, -16, .00000000000000000000000005703675990106610),
-(37.821637, -15, .000000000000000000000002157223628634278),
-(37.821637, -14, .00000000000000000000008158972901002847),
-(37.821637, -13, .000000000000000000003085857113545666),
-(37.821637, -12, .0000000000000000001167121675823920),
-(37.821637, -11, .000000000000000004414245235784397),
-(37.821637, -10, .0000000000000001669539809368169),
-(37.821637, -9, .000000000000006314472862697207),
-(37.821637, -8, .0000000000002388237004592846),
-(37.821637, -7, .000000000009032703305767796),
-(37.821637, -6, .0000000003416316255594496),
-(37.821637, -5, .00000001292106732962942),
-(37.821637, -4, .0000004886959181938034),
-(37.821637, -3, .00001848327962130773),
-(37.821637, -2, .0006990678924065984),
-(37.821637, -1, .02643989206495742),
-(37.821637, 0, 1),
-(37.821637, 1, 37.821637),
-(37.821637, 2, 1430.476225359769),
-(37.821637, 3, 54102.952532687378),
-(37.821637, 4, 2046262.2313195326),
-(37.821637, 5, 77392987.319777394),
-(37.821637, 6, 2927129472.7542235),
-(37.821637, 7, 110708828370.511632),
-(37.821637, 8, 4187189119324.792454),
-(37.821637, 9, 158366346921451.985294),
-(37.821637, 10, 5989674486279224.500736),
-(37.821637, 11, 226539294168214309.708325),
-(37.821637, 12, 8568086950266418559.993831),
-(37.821637, 13, 324059074417413536066.149409),
-(37.821637, 14, 12256444679171401239980.310926),
-(37.821637, 15, 463558801566202198479885.206986),
-(37.821637, 16, 17532552720991931019508170.100286),
-(37.821637, 17, 663109844696719094948877928.067252),
-(37.821637, 18, 25079899837245684700124994552.671731),
-(37.821637, 19, 948562867640665366544581398598.127577),
-(37.821637, 20, 35876200451584291931921101974730.690104))
-SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
-     b     |  p  |                     bc_result                     |                       power                       |                       diff                        
------------+-----+---------------------------------------------------+---------------------------------------------------+---------------------------------------------------
- 37.821637 | -20 | 0.00000000000000000000000000000002787363175065101 | 0.00000000000000000000000000000002787363175065101 | 0.00000000000000000000000000000000000000000000000
- 37.821637 | -19 |   0.000000000000000000000000000001054226381944797 |   0.000000000000000000000000000001054226381944797 |   0.000000000000000000000000000000000000000000000
- 37.821637 | -18 |    0.00000000000000000000000000003987256753373947 |    0.00000000000000000000000000003987256753373947 |    0.00000000000000000000000000000000000000000000
- 37.821637 | -17 |      0.000000000000000000000000001508045775519079 |      0.000000000000000000000000001508045775519079 |      0.000000000000000000000000000000000000000000
- 37.821637 | -16 |       0.00000000000000000000000005703675990106610 |       0.00000000000000000000000005703675990106610 |       0.00000000000000000000000000000000000000000
- 37.821637 | -15 |         0.000000000000000000000002157223628634278 |         0.000000000000000000000002157223628634278 |         0.000000000000000000000000000000000000000
- 37.821637 | -14 |          0.00000000000000000000008158972901002847 |          0.00000000000000000000008158972901002847 |          0.00000000000000000000000000000000000000
- 37.821637 | -13 |            0.000000000000000000003085857113545666 |            0.000000000000000000003085857113545666 |            0.000000000000000000000000000000000000
- 37.821637 | -12 |              0.0000000000000000001167121675823920 |              0.0000000000000000001167121675823920 |              0.0000000000000000000000000000000000
- 37.821637 | -11 |               0.000000000000000004414245235784397 |               0.000000000000000004414245235784397 |               0.000000000000000000000000000000000
- 37.821637 | -10 |                 0.0000000000000001669539809368169 |                 0.0000000000000001669539809368169 |                 0.0000000000000000000000000000000
- 37.821637 |  -9 |                  0.000000000000006314472862697207 |                  0.000000000000006314472862697207 |                  0.000000000000000000000000000000
- 37.821637 |  -8 |                    0.0000000000002388237004592846 |                    0.0000000000002388237004592846 |                    0.0000000000000000000000000000
- 37.821637 |  -7 |                     0.000000000009032703305767796 |                     0.000000000009032703305767796 |                     0.000000000000000000000000000
- 37.821637 |  -6 |                       0.0000000003416316255594496 |                       0.0000000003416316255594496 |                       0.0000000000000000000000000
- 37.821637 |  -5 |                         0.00000001292106732962942 |                         0.00000001292106732962942 |                         0.00000000000000000000000
- 37.821637 |  -4 |                          0.0000004886959181938034 |                          0.0000004886959181938034 |                          0.0000000000000000000000
- 37.821637 |  -3 |                            0.00001848327962130773 |                            0.00001848327962130773 |                            0.00000000000000000000
- 37.821637 |  -2 |                             0.0006990678924065984 |                             0.0006990678924065984 |                             0.0000000000000000000
- 37.821637 |  -1 |                               0.02643989206495742 |                               0.02643989206495742 |                               0.00000000000000000
- 37.821637 |   0 |                                                 1 |                                1.0000000000000000 |                                0.0000000000000000
- 37.821637 |   1 |                                         37.821637 |                                37.821637000000000 |                                 0.000000000000000
- 37.821637 |   2 |                                 1430.476225359769 |                                1430.4762253597690 |                                   0.0000000000000
- 37.821637 |   3 |                                54102.952532687378 |                                54102.952532687378 |                                    0.000000000000
- 37.821637 |   4 |                                2046262.2313195326 |                                2046262.2313195326 |                                      0.0000000000
- 37.821637 |   5 |                                77392987.319777394 |                                77392987.319777394 |                                       0.000000000
- 37.821637 |   6 |                                2927129472.7542235 |                                2927129472.7542235 |                                         0.0000000
- 37.821637 |   7 |                               110708828370.511632 |                               110708828370.511632 |                                          0.000000
- 37.821637 |   8 |                              4187189119324.792454 |                              4187189119324.792454 |                                          0.000000
- 37.821637 |   9 |                            158366346921451.985294 |                            158366346921451.985294 |                                          0.000000
- 37.821637 |  10 |                           5989674486279224.500736 |                           5989674486279224.500736 |                                          0.000000
- 37.821637 |  11 |                         226539294168214309.708325 |                         226539294168214309.708325 |                                          0.000000
- 37.821637 |  12 |                        8568086950266418559.993831 |                        8568086950266418559.993831 |                                          0.000000
- 37.821637 |  13 |                      324059074417413536066.149409 |                      324059074417413536066.149409 |                                          0.000000
- 37.821637 |  14 |                    12256444679171401239980.310926 |                    12256444679171401239980.310926 |                                          0.000000
- 37.821637 |  15 |                   463558801566202198479885.206986 |                   463558801566202198479885.206986 |                                          0.000000
- 37.821637 |  16 |                 17532552720991931019508170.100286 |                 17532552720991931019508170.100286 |                                          0.000000
- 37.821637 |  17 |                663109844696719094948877928.067252 |                663109844696719094948877928.067252 |                                          0.000000
- 37.821637 |  18 |              25079899837245684700124994552.671731 |              25079899837245684700124994552.671731 |                                          0.000000
- 37.821637 |  19 |             948562867640665366544581398598.127577 |             948562867640665366544581398598.127577 |                                          0.000000
- 37.821637 |  20 |           35876200451584291931921101974730.690104 |           35876200451584291931921101974730.690104 |                                          0.000000
-(41 rows)
-
---
--- Tests for raising to non-integer powers
---
--- base less than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of POW():
---
--- for n in {-20..20}
--- do
---   b="0.06933247"
---   p="$n.342987"
---   r=$(bc -ql <<< "scale=500 ; e($p*l($b))" | head -n 1)
---   echo "($b, $p, $r),"
--- done
-WITH t(b, p, bc_result) AS (VALUES
-(0.06933247, -20.342987, 379149253615977128356318.39406340),
-(0.06933247, -19.342987, 26287354251852125772450.59436685),
-(0.06933247, -18.342987, 1822567200045909954554.65766042),
-(0.06933247, -17.342987, 126363085720167050546.86216560),
-(0.06933247, -16.342987, 8761064849800910427.02880469),
-(0.06933247, -15.342987, 607426265866876128.15466179),
-(0.06933247, -14.342987, 42114363355427213.14899924),
-(0.06933247, -13.342987, 2919892833909256.59283660),
-(0.06933247, -12.342987, 202443382310228.51544515),
-(0.06933247, -11.342987, 14035899730722.44924025),
-(0.06933247, -10.342987, 973143597003.32229028),
-(0.06933247, -9.342987, 67470449244.92493259),
-(0.06933247, -8.342987, 4677892898.16028054),
-(0.06933247, -7.342987, 324329869.02491071),
-(0.06933247, -6.342987, 22486590.914273551),
-(0.06933247, -5.342987, 1559050.8899661435),
-(0.06933247, -4.342987, 108092.84905705095),
-(0.06933247, -3.342987, 7494.3442144625131),
-(0.06933247, -2.342987, 519.60139541889576),
-(0.06933247, -1.342987, 36.025248159838727),
-(0.06933247, 0.342987, .40036522320023350),
-(0.06933247, 1.342987, .02775830982657349),
-(0.06933247, 2.342987, .001924552183301612),
-(0.06933247, 3.342987, .0001334339565121935),
-(0.06933247, 4.342987, .000009251305786862961),
-(0.06933247, 5.342987, .0000006414158809285026),
-(0.06933247, 6.342987, .00000004447094732199898),
-(0.06933247, 7.342987, .000000003083280621074075),
-(0.06933247, 8.342987, .0000000002137714611621997),
-(0.06933247, 9.342987, .00000000001482130341788437),
-(0.06933247, 10.342987, .000000000001027597574581366),
-(0.06933247, 11.342987, .00000000000007124587801173530),
-(0.06933247, 12.342987, .000000000000004939652699872298),
-(0.06933247, 13.342987, .0000000000000003424783226243151),
-(0.06933247, 14.342987, .00000000000000002374486802900065),
-(0.06933247, 15.342987, .000000000000000001646290350274646),
-(0.06933247, 16.342987, .0000000000000000001141413763217064),
-(0.06933247, 17.342987, .000000000000000000007913703549583420),
-(0.06933247, 18.342987, .0000000000000000000005486766139403860),
-(0.06933247, 19.342987, .00000000000000000000003804110487572339),
-(0.06933247, 20.342987, .000000000000000000000002637483762562946))
-SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
-     b      |     p      |                 bc_result                 |                   power                   |                   diff                    
-------------+------------+-------------------------------------------+-------------------------------------------+-------------------------------------------
- 0.06933247 | -20.342987 |         379149253615977128356318.39406340 |         379149253615977128356318.39406340 |                                0.00000000
- 0.06933247 | -19.342987 |          26287354251852125772450.59436685 |          26287354251852125772450.59436685 |                                0.00000000
- 0.06933247 | -18.342987 |           1822567200045909954554.65766042 |           1822567200045909954554.65766042 |                                0.00000000
- 0.06933247 | -17.342987 |            126363085720167050546.86216560 |            126363085720167050546.86216560 |                                0.00000000
- 0.06933247 | -16.342987 |              8761064849800910427.02880469 |              8761064849800910427.02880469 |                                0.00000000
- 0.06933247 | -15.342987 |               607426265866876128.15466179 |               607426265866876128.15466179 |                                0.00000000
- 0.06933247 | -14.342987 |                42114363355427213.14899924 |                42114363355427213.14899924 |                                0.00000000
- 0.06933247 | -13.342987 |                 2919892833909256.59283660 |                 2919892833909256.59283660 |                                0.00000000
- 0.06933247 | -12.342987 |                  202443382310228.51544515 |                  202443382310228.51544515 |                                0.00000000
- 0.06933247 | -11.342987 |                   14035899730722.44924025 |                   14035899730722.44924025 |                                0.00000000
- 0.06933247 | -10.342987 |                     973143597003.32229028 |                     973143597003.32229028 |                                0.00000000
- 0.06933247 |  -9.342987 |                      67470449244.92493259 |                      67470449244.92493259 |                                0.00000000
- 0.06933247 |  -8.342987 |                       4677892898.16028054 |                       4677892898.16028054 |                                0.00000000
- 0.06933247 |  -7.342987 |                        324329869.02491071 |                        324329869.02491071 |                                0.00000000
- 0.06933247 |  -6.342987 |                        22486590.914273551 |                        22486590.914273551 |                               0.000000000
- 0.06933247 |  -5.342987 |                        1559050.8899661435 |                        1559050.8899661435 |                              0.0000000000
- 0.06933247 |  -4.342987 |                        108092.84905705095 |                        108092.84905705095 |                             0.00000000000
- 0.06933247 |  -3.342987 |                        7494.3442144625131 |                        7494.3442144625131 |                           0.0000000000000
- 0.06933247 |  -2.342987 |                        519.60139541889576 |                        519.60139541889576 |                          0.00000000000000
- 0.06933247 |  -1.342987 |                        36.025248159838727 |                        36.025248159838727 |                         0.000000000000000
- 0.06933247 |   0.342987 |                       0.40036522320023350 |                        0.4003652232002335 |                       0.00000000000000000
- 0.06933247 |   1.342987 |                       0.02775830982657349 |                       0.02775830982657349 |                       0.00000000000000000
- 0.06933247 |   2.342987 |                      0.001924552183301612 |                      0.001924552183301612 |                      0.000000000000000000
- 0.06933247 |   3.342987 |                     0.0001334339565121935 |                     0.0001334339565121935 |                     0.0000000000000000000
- 0.06933247 |   4.342987 |                   0.000009251305786862961 |                   0.000009251305786862961 |                   0.000000000000000000000
- 0.06933247 |   5.342987 |                  0.0000006414158809285026 |                  0.0000006414158809285026 |                  0.0000000000000000000000
- 0.06933247 |   6.342987 |                 0.00000004447094732199898 |                 0.00000004447094732199898 |                 0.00000000000000000000000
- 0.06933247 |   7.342987 |                0.000000003083280621074075 |                0.000000003083280621074075 |                0.000000000000000000000000
- 0.06933247 |   8.342987 |               0.0000000002137714611621997 |               0.0000000002137714611621997 |               0.0000000000000000000000000
- 0.06933247 |   9.342987 |              0.00000000001482130341788437 |              0.00000000001482130341788437 |              0.00000000000000000000000000
- 0.06933247 |  10.342987 |             0.000000000001027597574581366 |             0.000000000001027597574581366 |             0.000000000000000000000000000
- 0.06933247 |  11.342987 |           0.00000000000007124587801173530 |           0.00000000000007124587801173530 |           0.00000000000000000000000000000
- 0.06933247 |  12.342987 |          0.000000000000004939652699872298 |          0.000000000000004939652699872298 |          0.000000000000000000000000000000
- 0.06933247 |  13.342987 |         0.0000000000000003424783226243151 |         0.0000000000000003424783226243151 |         0.0000000000000000000000000000000
- 0.06933247 |  14.342987 |        0.00000000000000002374486802900065 |        0.00000000000000002374486802900065 |        0.00000000000000000000000000000000
- 0.06933247 |  15.342987 |       0.000000000000000001646290350274646 |       0.000000000000000001646290350274646 |       0.000000000000000000000000000000000
- 0.06933247 |  16.342987 |      0.0000000000000000001141413763217064 |      0.0000000000000000001141413763217064 |      0.0000000000000000000000000000000000
- 0.06933247 |  17.342987 |    0.000000000000000000007913703549583420 |    0.000000000000000000007913703549583420 |    0.000000000000000000000000000000000000
- 0.06933247 |  18.342987 |   0.0000000000000000000005486766139403860 |   0.0000000000000000000005486766139403860 |   0.0000000000000000000000000000000000000
- 0.06933247 |  19.342987 |  0.00000000000000000000003804110487572339 |  0.00000000000000000000003804110487572339 |  0.00000000000000000000000000000000000000
- 0.06933247 |  20.342987 | 0.000000000000000000000002637483762562946 | 0.000000000000000000000002637483762562946 | 0.000000000000000000000000000000000000000
-(41 rows)
-
--- base greater than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of POW():
---
--- for n in {-20..20}
--- do
---   b="27.234987"
---   p="$n.230957"
---   r=$(bc -ql <<< "scale=500 ; e($p*l($b))" | head -n 1)
---   echo "($b, $p, $r),"
--- done
-WITH t(b, p, bc_result) AS (VALUES
-(27.234987, -20.230957, .000000000000000000000000000009247064512095633),
-(27.234987, -19.230957, .0000000000000000000000000002518436817750859),
-(27.234987, -18.230957, .000000000000000000000000006858959399176602),
-(27.234987, -17.230957, .0000000000000000000000001868036700701026),
-(27.234987, -16.230957, .000000000000000000000005087595525911532),
-(27.234987, -15.230957, .0000000000000000000001385605980094587),
-(27.234987, -14.230957, .000000000000000000003773696085499835),
-(27.234987, -13.230957, .0000000000000000001027765638305389),
-(27.234987, -12.230957, .000000000000000002799118379829397),
-(27.234987, -11.230957, .00000000000000007623395268611469),
-(27.234987, -10.230957, .000000000000002076230710364949),
-(27.234987, -9.230957, .00000000000005654611640579014),
-(27.234987, -8.230957, .000000000001540032745212181),
-(27.234987, -7.230957, .00000000004194277179542807),
-(27.234987, -6.230957, .000000001142310844592450),
-(27.234987, -5.230957, .00000003111082100243440),
-(27.234987, -4.230957, .0000008473028055606278),
-(27.234987, -3.230957, .00002307628089450723),
-(27.234987, -2.230957, .0006284822101702527),
-(27.234987, -1.230957, .01711670482371810),
-(27.234987, 0.230957, 2.1451253063142300),
-(27.234987, 1.230957, 58.422459830839071),
-(27.234987, 2.230957, 1591.1349340009243),
-(27.234987, 3.230957, 43334.539242761031),
-(27.234987, 4.230957, 1180215.6129275865),
-(27.234987, 5.230957, 32143156.875279851),
-(27.234987, 6.230957, 875418459.63720737),
-(27.234987, 7.230957, 23842010367.779367),
-(27.234987, 8.230957, 649336842420.336290),
-(27.234987, 9.230957, 17684680461938.907402),
-(27.234987, 10.230957, 481642042480060.137900),
-(27.234987, 11.230957, 13117514765597885.614921),
-(27.234987, 12.230957, 357255344113366461.949871),
-(27.234987, 13.230957, 9729844652608062117.440722),
-(27.234987, 14.230957, 264992192625800087863.690528),
-(27.234987, 15.230957, 7217058921265161257566.469315),
-(27.234987, 16.230957, 196556505898890690402726.443417),
-(27.234987, 17.230957, 5353213882921711267539279.451015),
-(27.234987, 18.230957, 145794710509592328389185797.837767),
-(27.234987, 19.230957, 3970717045397510438979206144.696206),
-(27.234987, 20.230957, 108142427112079606637962972621.121293))
-SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
-     b     |     p      |                    bc_result                    |                      power                      |                      diff                       
------------+------------+-------------------------------------------------+-------------------------------------------------+-------------------------------------------------
- 27.234987 | -20.230957 | 0.000000000000000000000000000009247064512095633 | 0.000000000000000000000000000009247064512095633 | 0.000000000000000000000000000000000000000000000
- 27.234987 | -19.230957 |   0.0000000000000000000000000002518436817750859 |   0.0000000000000000000000000002518436817750859 |   0.0000000000000000000000000000000000000000000
- 27.234987 | -18.230957 |    0.000000000000000000000000006858959399176602 |    0.000000000000000000000000006858959399176602 |    0.000000000000000000000000000000000000000000
- 27.234987 | -17.230957 |      0.0000000000000000000000001868036700701026 |      0.0000000000000000000000001868036700701026 |      0.0000000000000000000000000000000000000000
- 27.234987 | -16.230957 |       0.000000000000000000000005087595525911532 |       0.000000000000000000000005087595525911532 |       0.000000000000000000000000000000000000000
- 27.234987 | -15.230957 |         0.0000000000000000000001385605980094587 |         0.0000000000000000000001385605980094587 |         0.0000000000000000000000000000000000000
- 27.234987 | -14.230957 |          0.000000000000000000003773696085499835 |          0.000000000000000000003773696085499835 |          0.000000000000000000000000000000000000
- 27.234987 | -13.230957 |            0.0000000000000000001027765638305389 |            0.0000000000000000001027765638305389 |            0.0000000000000000000000000000000000
- 27.234987 | -12.230957 |             0.000000000000000002799118379829397 |             0.000000000000000002799118379829397 |             0.000000000000000000000000000000000
- 27.234987 | -11.230957 |              0.00000000000000007623395268611469 |              0.00000000000000007623395268611469 |              0.00000000000000000000000000000000
- 27.234987 | -10.230957 |                0.000000000000002076230710364949 |                0.000000000000002076230710364949 |                0.000000000000000000000000000000
- 27.234987 |  -9.230957 |                 0.00000000000005654611640579014 |                 0.00000000000005654611640579014 |                 0.00000000000000000000000000000
- 27.234987 |  -8.230957 |                   0.000000000001540032745212181 |                   0.000000000001540032745212181 |                   0.000000000000000000000000000
- 27.234987 |  -7.230957 |                    0.00000000004194277179542807 |                    0.00000000004194277179542807 |                    0.00000000000000000000000000
- 27.234987 |  -6.230957 |                      0.000000001142310844592450 |                      0.000000001142310844592450 |                      0.000000000000000000000000
- 27.234987 |  -5.230957 |                       0.00000003111082100243440 |                       0.00000003111082100243440 |                       0.00000000000000000000000
- 27.234987 |  -4.230957 |                        0.0000008473028055606278 |                        0.0000008473028055606278 |                        0.0000000000000000000000
- 27.234987 |  -3.230957 |                          0.00002307628089450723 |                          0.00002307628089450723 |                          0.00000000000000000000
- 27.234987 |  -2.230957 |                           0.0006284822101702527 |                           0.0006284822101702527 |                           0.0000000000000000000
- 27.234987 |  -1.230957 |                             0.01711670482371810 |                             0.01711670482371810 |                             0.00000000000000000
- 27.234987 |   0.230957 |                              2.1451253063142300 |                              2.1451253063142300 |                              0.0000000000000000
- 27.234987 |   1.230957 |                              58.422459830839071 |                              58.422459830839071 |                               0.000000000000000
- 27.234987 |   2.230957 |                              1591.1349340009243 |                              1591.1349340009243 |                                 0.0000000000000
- 27.234987 |   3.230957 |                              43334.539242761031 |                              43334.539242761031 |                                  0.000000000000
- 27.234987 |   4.230957 |                              1180215.6129275865 |                              1180215.6129275865 |                                    0.0000000000
- 27.234987 |   5.230957 |                              32143156.875279851 |                              32143156.875279851 |                                     0.000000000
- 27.234987 |   6.230957 |                              875418459.63720737 |                              875418459.63720737 |                                      0.00000000
- 27.234987 |   7.230957 |                              23842010367.779367 |                              23842010367.779367 |                                        0.000000
- 27.234987 |   8.230957 |                             649336842420.336290 |                             649336842420.336290 |                                        0.000000
- 27.234987 |   9.230957 |                           17684680461938.907402 |                           17684680461938.907402 |                                        0.000000
- 27.234987 |  10.230957 |                          481642042480060.137900 |                          481642042480060.137900 |                                        0.000000
- 27.234987 |  11.230957 |                        13117514765597885.614921 |                        13117514765597885.614921 |                                        0.000000
- 27.234987 |  12.230957 |                       357255344113366461.949871 |                       357255344113366461.949871 |                                        0.000000
- 27.234987 |  13.230957 |                      9729844652608062117.440722 |                      9729844652608062117.440722 |                                        0.000000
- 27.234987 |  14.230957 |                    264992192625800087863.690528 |                    264992192625800087863.690528 |                                        0.000000
- 27.234987 |  15.230957 |                   7217058921265161257566.469315 |                   7217058921265161257566.469315 |                                        0.000000
- 27.234987 |  16.230957 |                 196556505898890690402726.443417 |                 196556505898890690402726.443417 |                                        0.000000
- 27.234987 |  17.230957 |                5353213882921711267539279.451015 |                5353213882921711267539279.451015 |                                        0.000000
- 27.234987 |  18.230957 |              145794710509592328389185797.837767 |              145794710509592328389185797.837767 |                                        0.000000
- 27.234987 |  19.230957 |             3970717045397510438979206144.696206 |             3970717045397510438979206144.696206 |                                        0.000000
- 27.234987 |  20.230957 |           108142427112079606637962972621.121293 |           108142427112079606637962972621.121293 |                                        0.000000
-(41 rows)
-
--- Inputs close to overflow
---
--- bc(1) results computed with a scale of 2700 and truncated to 4 decimal
--- places.
-WITH t(b, p, bc_result) AS (VALUES
-(0.12, -2829.8369, 58463948950011752465280493160293790845494328939320966633018493248607815580903065923369555885857984675501574162389726507612128133630191173383130639968378879506624785786843501848666498440326970769604109017960864573408272864266102690849952650095786874354625921641729880352858506454246180842452983243549491658464046163869265572232996388827878976066830374513768599285647145439771472435206769249126377164951470622827631950210853282324510655982757098065657709137845327135766013147354253426364240746381620690117663724329288646510198895137275207992825719846135857839292915100523542874885080351683587865157015032404901182924720371819942957083390475846809517968191151435281268695782594904484795360890092607679215675240583291240729468370895035823777914792823688291214492607109455017754453939895630226174304357121900605689015734289765672740769194115142607443713769825894380064727556869268488695795705030158832909348803019429370973064732712469794182891757241046263341655894972953512257981661670321890336672832647028099324621932563236459127918144141230217523147304565594514812518826936144181257723061181656522095236928347413997136815409159361412494284201481609684892562646522086577634100783077813105675590737823924220663206479031113753135119759722725207724879578900186075841393115040465401462266086907464970054073340036852442184414587772177753008511913377364966775792477387717262694468450099866775550614257191941835797445874557362115814601886902749237439492398087966544817154173072811937702110580330775581851211123491341435883319798273456296794954514173820352334127081705706502510709179711510240917772628308487366740741280043704807717608366220401933596364641284631036907635403895053036499618723044314773148779735006542501244942039455169872946018271985844759209768927953340447524637670938413827595013338859796135512187473850161303598087634723542727044978083220970836296653305188470017342167913572166172051819741354902582606590658382067039498769674611071582171914886494269818475850690414812481252963932223686078322390396586222238852602472958831686564971334200490182175112490433364675164900946902818404704835106260174052265784055642968397240262737313737007322288203637798365320295080314524864099419556398713380156353062937736280885716820226469419928595465390700629307079710611273715705695938635644841913194091407807776191951797748706106000922803167645881087385311847268311361092838264814899353459146959869764278464187826798546290981492648723002412475976344071283321798061003719251864595518596639432393032991023409676558943539937377229130132816883146259468718344018277257037013406135980469482324577407154032999045733141275895.3432),
-(1.2, 32908.8896, 58463467728170833376633133695001863276259293590926929026251227859007891876739460057725441400966420577009060860805883032969522911803372870882799865787473726926215148161529632590083389287080925059682489116446754279752928005457087175157581627230586554364417068189211136840990661174760199073702207450133797324318403866058202372178813998850887986769280847189341565507156189065295823921162851958925352114220880236114784962150135485415106748467247897246441194126125699204912883449386043559785865023459356275014504597646990160571664166410683323036984805434677654413174177920726210827006973855410386789516533036723888687725436216478665958434776205940192130053647653715221076841771578099896259902368829351569726536927952661429685419815305418450230567773264738536471211804481206474781470237730069753206249915908804615495060673071058534441654604668770343616386612119048579369195201590008082689834456232255266932976831478404670192731621439902738547169253818323045451045749609624500171633897705543164388470746657118050314064066768449450440405619135824055131398727045420324382226572368236570500391463795989258779677208133531636928003546809249007993065200108076924439703799231711400266122025052209803513232429907231051873161206025860851056337427740362763618748092029386371493898291580557004812947013231371383576580415676519066503391905962989205397824064923920045371823949776899815750413244195402085917098964452866825666226141169411712884994564949174271056284898570445214367063763956186792886147126466387576513166370247576466566827375268334148320298849218878848928271566491769458471357076035396330179659440244425914213309776100351793665960978678576150833311810944729586040624059867137538839913141142139636023129691775489034134511666020819676247950267220131499463010350308195762769192775344260909521732256844149916046793599150786757764962585268686580124987490115873389726527572428003433405659445349155536369077209682951123806333170190998931670309088422483075609203671527331975811507450670132060984691061148836994322505371265263690017938762760088575875666254883673433331627055180154954694693433502522592907190906966067656027637884202418119121728966267936832338377284832958974299187166554160783467156478554899314000348357280306042140481751668215838656488457943830180819301102535170705017482946779698265096226184239631924271857062033454725540956591929965181603262502135610768915716020374362368495244256420143645126927013882334008435586481691725030031204304273292938132599127402133470745819213047706793887965197191137237066440328777206799072470374264316425913530947082957300047105685634407092811630672103242089966046839626911122.7149))
-SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
-  b   |     p      |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      bc_result                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        power                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |  diff  
-------+------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------
- 0.12 | -2829.8369 | 58463948950011752465280493160293790845494328939320966633018493248607815580903065923369555885857984675501574162389726507612128133630191173383130639968378879506624785786843501848666498440326970769604109017960864573408272864266102690849952650095786874354625921641729880352858506454246180842452983243549491658464046163869265572232996388827878976066830374513768599285647145439771472435206769249126377164951470622827631950210853282324510655982757098065657709137845327135766013147354253426364240746381620690117663724329288646510198895137275207992825719846135857839292915100523542874885080351683587865157015032404901182924720371819942957083390475846809517968191151435281268695782594904484795360890092607679215675240583291240729468370895035823777914792823688291214492607109455017754453939895630226174304357121900605689015734289765672740769194115142607443713769825894380064727556869268488695795705030158832909348803019429370973064732712469794182891757241046263341655894972953512257981661670321890336672832647028099324621932563236459127918144141230217523147304565594514812518826936144181257723061181656522095236928347413997136815409159361412494284201481609684892562646522086577634100783077813105675590737823924220663206479031113753135119759722725207724879578900186075841393115040465401462266086907464970054073340036852442184414587772177753008511913377364966775792477387717262694468450099866775550614257191941835797445874557362115814601886902749237439492398087966544817154173072811937702110580330775581851211123491341435883319798273456296794954514173820352334127081705706502510709179711510240917772628308487366740741280043704807717608366220401933596364641284631036907635403895053036499618723044314773148779735006542501244942039455169872946018271985844759209768927953340447524637670938413827595013338859796135512187473850161303598087634723542727044978083220970836296653305188470017342167913572166172051819741354902582606590658382067039498769674611071582171914886494269818475850690414812481252963932223686078322390396586222238852602472958831686564971334200490182175112490433364675164900946902818404704835106260174052265784055642968397240262737313737007322288203637798365320295080314524864099419556398713380156353062937736280885716820226469419928595465390700629307079710611273715705695938635644841913194091407807776191951797748706106000922803167645881087385311847268311361092838264814899353459146959869764278464187826798546290981492648723002412475976344071283321798061003719251864595518596639432393032991023409676558943539937377229130132816883146259468718344018277257037013406135980469482324577407154032999045733141275895.3432 | 58463948950011752465280493160293790845494328939320966633018493248607815580903065923369555885857984675501574162389726507612128133630191173383130639968378879506624785786843501848666498440326970769604109017960864573408272864266102690849952650095786874354625921641729880352858506454246180842452983243549491658464046163869265572232996388827878976066830374513768599285647145439771472435206769249126377164951470622827631950210853282324510655982757098065657709137845327135766013147354253426364240746381620690117663724329288646510198895137275207992825719846135857839292915100523542874885080351683587865157015032404901182924720371819942957083390475846809517968191151435281268695782594904484795360890092607679215675240583291240729468370895035823777914792823688291214492607109455017754453939895630226174304357121900605689015734289765672740769194115142607443713769825894380064727556869268488695795705030158832909348803019429370973064732712469794182891757241046263341655894972953512257981661670321890336672832647028099324621932563236459127918144141230217523147304565594514812518826936144181257723061181656522095236928347413997136815409159361412494284201481609684892562646522086577634100783077813105675590737823924220663206479031113753135119759722725207724879578900186075841393115040465401462266086907464970054073340036852442184414587772177753008511913377364966775792477387717262694468450099866775550614257191941835797445874557362115814601886902749237439492398087966544817154173072811937702110580330775581851211123491341435883319798273456296794954514173820352334127081705706502510709179711510240917772628308487366740741280043704807717608366220401933596364641284631036907635403895053036499618723044314773148779735006542501244942039455169872946018271985844759209768927953340447524637670938413827595013338859796135512187473850161303598087634723542727044978083220970836296653305188470017342167913572166172051819741354902582606590658382067039498769674611071582171914886494269818475850690414812481252963932223686078322390396586222238852602472958831686564971334200490182175112490433364675164900946902818404704835106260174052265784055642968397240262737313737007322288203637798365320295080314524864099419556398713380156353062937736280885716820226469419928595465390700629307079710611273715705695938635644841913194091407807776191951797748706106000922803167645881087385311847268311361092838264814899353459146959869764278464187826798546290981492648723002412475976344071283321798061003719251864595518596639432393032991023409676558943539937377229130132816883146259468718344018277257037013406135980469482324577407154032999045733141275895.3432 | 0.0000
-  1.2 | 32908.8896 | 58463467728170833376633133695001863276259293590926929026251227859007891876739460057725441400966420577009060860805883032969522911803372870882799865787473726926215148161529632590083389287080925059682489116446754279752928005457087175157581627230586554364417068189211136840990661174760199073702207450133797324318403866058202372178813998850887986769280847189341565507156189065295823921162851958925352114220880236114784962150135485415106748467247897246441194126125699204912883449386043559785865023459356275014504597646990160571664166410683323036984805434677654413174177920726210827006973855410386789516533036723888687725436216478665958434776205940192130053647653715221076841771578099896259902368829351569726536927952661429685419815305418450230567773264738536471211804481206474781470237730069753206249915908804615495060673071058534441654604668770343616386612119048579369195201590008082689834456232255266932976831478404670192731621439902738547169253818323045451045749609624500171633897705543164388470746657118050314064066768449450440405619135824055131398727045420324382226572368236570500391463795989258779677208133531636928003546809249007993065200108076924439703799231711400266122025052209803513232429907231051873161206025860851056337427740362763618748092029386371493898291580557004812947013231371383576580415676519066503391905962989205397824064923920045371823949776899815750413244195402085917098964452866825666226141169411712884994564949174271056284898570445214367063763956186792886147126466387576513166370247576466566827375268334148320298849218878848928271566491769458471357076035396330179659440244425914213309776100351793665960978678576150833311810944729586040624059867137538839913141142139636023129691775489034134511666020819676247950267220131499463010350308195762769192775344260909521732256844149916046793599150786757764962585268686580124987490115873389726527572428003433405659445349155536369077209682951123806333170190998931670309088422483075609203671527331975811507450670132060984691061148836994322505371265263690017938762760088575875666254883673433331627055180154954694693433502522592907190906966067656027637884202418119121728966267936832338377284832958974299187166554160783467156478554899314000348357280306042140481751668215838656488457943830180819301102535170705017482946779698265096226184239631924271857062033454725540956591929965181603262502135610768915716020374362368495244256420143645126927013882334008435586481691725030031204304273292938132599127402133470745819213047706793887965197191137237066440328777206799072470374264316425913530947082957300047105685634407092811630672103242089966046839626911122.7149 | 58463467728170833376633133695001863276259293590926929026251227859007891876739460057725441400966420577009060860805883032969522911803372870882799865787473726926215148161529632590083389287080925059682489116446754279752928005457087175157581627230586554364417068189211136840990661174760199073702207450133797324318403866058202372178813998850887986769280847189341565507156189065295823921162851958925352114220880236114784962150135485415106748467247897246441194126125699204912883449386043559785865023459356275014504597646990160571664166410683323036984805434677654413174177920726210827006973855410386789516533036723888687725436216478665958434776205940192130053647653715221076841771578099896259902368829351569726536927952661429685419815305418450230567773264738536471211804481206474781470237730069753206249915908804615495060673071058534441654604668770343616386612119048579369195201590008082689834456232255266932976831478404670192731621439902738547169253818323045451045749609624500171633897705543164388470746657118050314064066768449450440405619135824055131398727045420324382226572368236570500391463795989258779677208133531636928003546809249007993065200108076924439703799231711400266122025052209803513232429907231051873161206025860851056337427740362763618748092029386371493898291580557004812947013231371383576580415676519066503391905962989205397824064923920045371823949776899815750413244195402085917098964452866825666226141169411712884994564949174271056284898570445214367063763956186792886147126466387576513166370247576466566827375268334148320298849218878848928271566491769458471357076035396330179659440244425914213309776100351793665960978678576150833311810944729586040624059867137538839913141142139636023129691775489034134511666020819676247950267220131499463010350308195762769192775344260909521732256844149916046793599150786757764962585268686580124987490115873389726527572428003433405659445349155536369077209682951123806333170190998931670309088422483075609203671527331975811507450670132060984691061148836994322505371265263690017938762760088575875666254883673433331627055180154954694693433502522592907190906966067656027637884202418119121728966267936832338377284832958974299187166554160783467156478554899314000348357280306042140481751668215838656488457943830180819301102535170705017482946779698265096226184239631924271857062033454725540956591929965181603262502135610768915716020374362368495244256420143645126927013882334008435586481691725030031204304273292938132599127402133470745819213047706793887965197191137237066440328777206799072470374264316425913530947082957300047105685634407092811630672103242089966046839626911122.7149 | 0.0000
-(2 rows)
-
---
--- Tests for EXP()
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of EXP():
---
--- for n in {-20..20}
--- do
---   x="$n.29837"
---   r=$(bc -ql <<< "scale=500 ; e($x)" | head -n 1)
---   echo "($x, $r),"
--- done
-WITH t(x, bc_result) AS (VALUES
-(-20.29837, .000000001529431101152222),
-(-19.29837, .000000004157424770142192),
-(-18.29837, .00000001130105220586304),
-(-17.29837, .00000003071944485366452),
-(-16.29837, .00000008350410872606600),
-(-15.29837, .0000002269877013517336),
-(-14.29837, .0000006170165438681061),
-(-13.29837, .000001677224859055276),
-(-12.29837, .000004559169856609741),
-(-11.29837, .00001239310857408049),
-(-10.29837, .00003368796183504298),
-(-9.29837, .00009157337449401917),
-(-8.29837, .0002489222398577673),
-(-7.29837, .0006766408013046928),
-(-6.29837, .001839300394580514),
-(-5.29837, .004999736839665763),
-(-4.29837, .01359069379834070),
-(-3.29837, .03694333598818056),
-(-2.29837, .1004223988993283),
-(-1.29837, .2729763820983097),
-(0.29837, 1.3476603299656679),
-(1.29837, 3.6633205858807959),
-(2.29837, 9.9579377804197108),
-(3.29837, 27.068481317440698),
-(4.29837, 73.579760889182206),
-(5.29837, 200.01052696742555),
-(6.29837, 543.68498095607070),
-(7.29837, 1477.8890041389891),
-(8.29837, 4017.3188244304487),
-(9.29837, 10920.204759575742),
-(10.29837, 29684.194161006717),
-(11.29837, 80690.005580314652),
-(12.29837, 219338.17590722828),
-(13.29837, 596222.97785597218),
-(14.29837, 1620702.0864156289),
-(15.29837, 4405525.0308492653),
-(16.29837, 11975458.636179032),
-(17.29837, 32552671.598188404),
-(18.29837, 88487335.673150406),
-(19.29837, 240533516.60908059),
-(20.29837, 653837887.33381570))
-SELECT x, bc_result, exp(x), exp(x)-bc_result AS diff FROM t;
-     x     |         bc_result          |            exp             |            diff            
------------+----------------------------+----------------------------+----------------------------
- -20.29837 | 0.000000001529431101152222 | 0.000000001529431101152222 | 0.000000000000000000000000
- -19.29837 | 0.000000004157424770142192 | 0.000000004157424770142192 | 0.000000000000000000000000
- -18.29837 |  0.00000001130105220586304 |  0.00000001130105220586304 |  0.00000000000000000000000
- -17.29837 |  0.00000003071944485366452 |  0.00000003071944485366452 |  0.00000000000000000000000
- -16.29837 |  0.00000008350410872606600 |  0.00000008350410872606600 |  0.00000000000000000000000
- -15.29837 |   0.0000002269877013517336 |   0.0000002269877013517336 |   0.0000000000000000000000
- -14.29837 |   0.0000006170165438681061 |   0.0000006170165438681061 |   0.0000000000000000000000
- -13.29837 |    0.000001677224859055276 |    0.000001677224859055276 |    0.000000000000000000000
- -12.29837 |    0.000004559169856609741 |    0.000004559169856609741 |    0.000000000000000000000
- -11.29837 |     0.00001239310857408049 |     0.00001239310857408049 |     0.00000000000000000000
- -10.29837 |     0.00003368796183504298 |     0.00003368796183504298 |     0.00000000000000000000
-  -9.29837 |     0.00009157337449401917 |     0.00009157337449401917 |     0.00000000000000000000
-  -8.29837 |      0.0002489222398577673 |      0.0002489222398577673 |      0.0000000000000000000
-  -7.29837 |      0.0006766408013046928 |      0.0006766408013046928 |      0.0000000000000000000
-  -6.29837 |       0.001839300394580514 |       0.001839300394580514 |       0.000000000000000000
-  -5.29837 |       0.004999736839665763 |       0.004999736839665763 |       0.000000000000000000
-  -4.29837 |        0.01359069379834070 |        0.01359069379834070 |        0.00000000000000000
-  -3.29837 |        0.03694333598818056 |        0.03694333598818056 |        0.00000000000000000
-  -2.29837 |         0.1004223988993283 |         0.1004223988993283 |         0.0000000000000000
-  -1.29837 |         0.2729763820983097 |         0.2729763820983097 |         0.0000000000000000
-   0.29837 |         1.3476603299656679 |         1.3476603299656679 |         0.0000000000000000
-   1.29837 |         3.6633205858807959 |         3.6633205858807959 |         0.0000000000000000
-   2.29837 |         9.9579377804197108 |         9.9579377804197108 |         0.0000000000000000
-   3.29837 |         27.068481317440698 |         27.068481317440698 |          0.000000000000000
-   4.29837 |         73.579760889182206 |         73.579760889182206 |          0.000000000000000
-   5.29837 |         200.01052696742555 |         200.01052696742555 |           0.00000000000000
-   6.29837 |         543.68498095607070 |         543.68498095607070 |           0.00000000000000
-   7.29837 |         1477.8890041389891 |         1477.8890041389891 |            0.0000000000000
-   8.29837 |         4017.3188244304487 |         4017.3188244304487 |            0.0000000000000
-   9.29837 |         10920.204759575742 |         10920.204759575742 |             0.000000000000
-  10.29837 |         29684.194161006717 |         29684.194161006717 |             0.000000000000
-  11.29837 |         80690.005580314652 |         80690.005580314652 |             0.000000000000
-  12.29837 |         219338.17590722828 |         219338.17590722828 |              0.00000000000
-  13.29837 |         596222.97785597218 |         596222.97785597218 |              0.00000000000
-  14.29837 |         1620702.0864156289 |         1620702.0864156289 |               0.0000000000
-  15.29837 |         4405525.0308492653 |         4405525.0308492653 |               0.0000000000
-  16.29837 |         11975458.636179032 |         11975458.636179032 |                0.000000000
-  17.29837 |         32552671.598188404 |         32552671.598188404 |                0.000000000
-  18.29837 |         88487335.673150406 |         88487335.673150406 |                0.000000000
-  19.29837 |         240533516.60908059 |         240533516.60908059 |                 0.00000000
-  20.29837 |         653837887.33381570 |         653837887.33381570 |                 0.00000000
-(41 rows)
-
---
--- Tests for LN()
---
--- input very small
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40}
--- do
---   l=$(bc -ql <<< "scale=500 ; l(10^-$p)" | head -n 1)
---   echo "('1.0e-$p', $l),"
--- done
-WITH t(x, bc_result) AS (VALUES
-('1.0e-1', -2.3025850929940457),
-('1.0e-2', -4.6051701859880914),
-('1.0e-3', -6.9077552789821371),
-('1.0e-4', -9.2103403719761827),
-('1.0e-5', -11.512925464970228),
-('1.0e-6', -13.815510557964274),
-('1.0e-7', -16.118095650958320),
-('1.0e-8', -18.420680743952365),
-('1.0e-9', -20.723265836946411),
-('1.0e-10', -23.025850929940457),
-('1.0e-11', -25.328436022934503),
-('1.0e-12', -27.631021115928548),
-('1.0e-13', -29.933606208922594),
-('1.0e-14', -32.236191301916640),
-('1.0e-15', -34.5387763949106853),
-('1.0e-16', -36.84136148790473094),
-('1.0e-17', -39.143946580898776628),
-('1.0e-18', -41.4465316738928223123),
-('1.0e-19', -43.74911676688686799634),
-('1.0e-20', -46.051701859880913680360),
-('1.0e-21', -48.3542869528749593643778),
-('1.0e-22', -50.65687204586900504839581),
-('1.0e-23', -52.959457138863050732413803),
-('1.0e-24', -55.2620422318570964164317949),
-('1.0e-25', -57.56462732485114210044978637),
-('1.0e-26', -59.867212417845187784467777822),
-('1.0e-27', -62.1697975108392334684857692765),
-('1.0e-28', -64.47238260383327915250376073116),
-('1.0e-29', -66.774967696827324836521752185847),
-('1.0e-30', -69.0775527898213705205397436405309),
-('1.0e-31', -71.38013788281541620455773509521529),
-('1.0e-32', -73.682722975809461888575726549899655),
-('1.0e-33', -75.9853080688035075725937180045840189),
-('1.0e-34', -78.28789316179755325661170945926838306),
-('1.0e-35', -80.590478254791598940629700913952747266),
-('1.0e-36', -82.8930633477856446246476923686371114736),
-('1.0e-37', -85.19564844077969030866568382332147568124),
-('1.0e-38', -87.498233533773735992683675278005839888842),
-('1.0e-39', -89.8008186267677816767016667326902040964430),
-('1.0e-40', -92.10340371976182736071965818737456830404406))
-SELECT x, bc_result, ln(x::numeric), ln(x::numeric)-bc_result AS diff FROM t;
-    x    |                   bc_result                   |                      ln                       |                    diff                     
----------+-----------------------------------------------+-----------------------------------------------+---------------------------------------------
- 1.0e-1  |                           -2.3025850929940457 |                           -2.3025850929940457 |                          0.0000000000000000
- 1.0e-2  |                           -4.6051701859880914 |                           -4.6051701859880914 |                          0.0000000000000000
- 1.0e-3  |                           -6.9077552789821371 |                           -6.9077552789821371 |                          0.0000000000000000
- 1.0e-4  |                           -9.2103403719761827 |                           -9.2103403719761827 |                          0.0000000000000000
- 1.0e-5  |                           -11.512925464970228 |                           -11.512925464970228 |                           0.000000000000000
- 1.0e-6  |                           -13.815510557964274 |                           -13.815510557964274 |                           0.000000000000000
- 1.0e-7  |                           -16.118095650958320 |                           -16.118095650958320 |                           0.000000000000000
- 1.0e-8  |                           -18.420680743952365 |                           -18.420680743952365 |                           0.000000000000000
- 1.0e-9  |                           -20.723265836946411 |                           -20.723265836946411 |                           0.000000000000000
- 1.0e-10 |                           -23.025850929940457 |                           -23.025850929940457 |                           0.000000000000000
- 1.0e-11 |                           -25.328436022934503 |                           -25.328436022934503 |                           0.000000000000000
- 1.0e-12 |                           -27.631021115928548 |                           -27.631021115928548 |                           0.000000000000000
- 1.0e-13 |                           -29.933606208922594 |                           -29.933606208922594 |                           0.000000000000000
- 1.0e-14 |                           -32.236191301916640 |                           -32.236191301916640 |                           0.000000000000000
- 1.0e-15 |                          -34.5387763949106853 |                          -34.5387763949106853 |                          0.0000000000000000
- 1.0e-16 |                         -36.84136148790473094 |                         -36.84136148790473094 |                         0.00000000000000000
- 1.0e-17 |                        -39.143946580898776628 |                        -39.143946580898776628 |                        0.000000000000000000
- 1.0e-18 |                       -41.4465316738928223123 |                       -41.4465316738928223123 |                       0.0000000000000000000
- 1.0e-19 |                      -43.74911676688686799634 |                      -43.74911676688686799634 |                      0.00000000000000000000
- 1.0e-20 |                     -46.051701859880913680360 |                     -46.051701859880913680360 |                     0.000000000000000000000
- 1.0e-21 |                    -48.3542869528749593643778 |                    -48.3542869528749593643778 |                    0.0000000000000000000000
- 1.0e-22 |                   -50.65687204586900504839581 |                   -50.65687204586900504839581 |                   0.00000000000000000000000
- 1.0e-23 |                  -52.959457138863050732413803 |                  -52.959457138863050732413803 |                  0.000000000000000000000000
- 1.0e-24 |                 -55.2620422318570964164317949 |                 -55.2620422318570964164317949 |                 0.0000000000000000000000000
- 1.0e-25 |                -57.56462732485114210044978637 |                -57.56462732485114210044978637 |                0.00000000000000000000000000
- 1.0e-26 |               -59.867212417845187784467777822 |               -59.867212417845187784467777822 |               0.000000000000000000000000000
- 1.0e-27 |              -62.1697975108392334684857692765 |              -62.1697975108392334684857692765 |              0.0000000000000000000000000000
- 1.0e-28 |             -64.47238260383327915250376073116 |             -64.47238260383327915250376073116 |             0.00000000000000000000000000000
- 1.0e-29 |            -66.774967696827324836521752185847 |            -66.774967696827324836521752185847 |            0.000000000000000000000000000000
- 1.0e-30 |           -69.0775527898213705205397436405309 |           -69.0775527898213705205397436405309 |           0.0000000000000000000000000000000
- 1.0e-31 |          -71.38013788281541620455773509521529 |          -71.38013788281541620455773509521529 |          0.00000000000000000000000000000000
- 1.0e-32 |         -73.682722975809461888575726549899655 |         -73.682722975809461888575726549899655 |         0.000000000000000000000000000000000
- 1.0e-33 |        -75.9853080688035075725937180045840189 |        -75.9853080688035075725937180045840189 |        0.0000000000000000000000000000000000
- 1.0e-34 |       -78.28789316179755325661170945926838306 |       -78.28789316179755325661170945926838306 |       0.00000000000000000000000000000000000
- 1.0e-35 |      -80.590478254791598940629700913952747266 |      -80.590478254791598940629700913952747266 |      0.000000000000000000000000000000000000
- 1.0e-36 |     -82.8930633477856446246476923686371114736 |     -82.8930633477856446246476923686371114736 |     0.0000000000000000000000000000000000000
- 1.0e-37 |    -85.19564844077969030866568382332147568124 |    -85.19564844077969030866568382332147568124 |    0.00000000000000000000000000000000000000
- 1.0e-38 |   -87.498233533773735992683675278005839888842 |   -87.498233533773735992683675278005839888842 |   0.000000000000000000000000000000000000000
- 1.0e-39 |  -89.8008186267677816767016667326902040964430 |  -89.8008186267677816767016667326902040964430 |  0.0000000000000000000000000000000000000000
- 1.0e-40 | -92.10340371976182736071965818737456830404406 | -92.10340371976182736071965818737456830404406 | 0.00000000000000000000000000000000000000000
-(40 rows)
-
--- input very close to but smaller than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40}
--- do
---   l=$(bc -ql <<< "scale=500 ; l(1-10^-$p)" | head -n 1)
---   echo "('1.0e-$p', $l),"
--- done
-WITH t(x, bc_result) AS (VALUES
-('1.0e-1', -.10536051565782630),
-('1.0e-2', -.010050335853501441),
-('1.0e-3', -.0010005003335835335),
-('1.0e-4', -.00010000500033335834),
-('1.0e-5', -.000010000050000333336),
-('1.0e-6', -.0000010000005000003333),
-('1.0e-7', -.00000010000000500000033),
-('1.0e-8', -.000000010000000050000000),
-('1.0e-9', -.0000000010000000005000000),
-('1.0e-10', -.00000000010000000000500000),
-('1.0e-11', -.000000000010000000000050000),
-('1.0e-12', -.0000000000010000000000005000),
-('1.0e-13', -.00000000000010000000000000500),
-('1.0e-14', -.000000000000010000000000000050),
-('1.0e-15', -.0000000000000010000000000000005),
-('1.0e-16', -.00000000000000010000000000000001),
-('1.0e-17', -.000000000000000010000000000000000),
-('1.0e-18', -.0000000000000000010000000000000000),
-('1.0e-19', -.00000000000000000010000000000000000),
-('1.0e-20', -.000000000000000000010000000000000000),
-('1.0e-21', -.0000000000000000000010000000000000000),
-('1.0e-22', -.00000000000000000000010000000000000000),
-('1.0e-23', -.000000000000000000000010000000000000000),
-('1.0e-24', -.0000000000000000000000010000000000000000),
-('1.0e-25', -.00000000000000000000000010000000000000000),
-('1.0e-26', -.000000000000000000000000010000000000000000),
-('1.0e-27', -.0000000000000000000000000010000000000000000),
-('1.0e-28', -.00000000000000000000000000010000000000000000),
-('1.0e-29', -.000000000000000000000000000010000000000000000),
-('1.0e-30', -.0000000000000000000000000000010000000000000000),
-('1.0e-31', -.00000000000000000000000000000010000000000000000),
-('1.0e-32', -.000000000000000000000000000000010000000000000000),
-('1.0e-33', -.0000000000000000000000000000000010000000000000000),
-('1.0e-34', -.00000000000000000000000000000000010000000000000000),
-('1.0e-35', -.000000000000000000000000000000000010000000000000000),
-('1.0e-36', -.0000000000000000000000000000000000010000000000000000),
-('1.0e-37', -.00000000000000000000000000000000000010000000000000000),
-('1.0e-38', -.000000000000000000000000000000000000010000000000000000),
-('1.0e-39', -.0000000000000000000000000000000000000010000000000000000),
-('1.0e-40', -.00000000000000000000000000000000000000010000000000000000))
-SELECT '1-'||x, bc_result, ln(1.0-x::numeric), ln(1.0-x::numeric)-bc_result AS diff FROM t;
- ?column?  |                          bc_result                          |                             ln                              |                            diff                            
------------+-------------------------------------------------------------+-------------------------------------------------------------+------------------------------------------------------------
- 1-1.0e-1  |                                        -0.10536051565782630 |                                        -0.10536051565782630 |                                        0.00000000000000000
- 1-1.0e-2  |                                       -0.010050335853501441 |                                       -0.010050335853501441 |                                       0.000000000000000000
- 1-1.0e-3  |                                      -0.0010005003335835335 |                                      -0.0010005003335835335 |                                      0.0000000000000000000
- 1-1.0e-4  |                                     -0.00010000500033335834 |                                     -0.00010000500033335834 |                                     0.00000000000000000000
- 1-1.0e-5  |                                    -0.000010000050000333336 |                                    -0.000010000050000333336 |                                    0.000000000000000000000
- 1-1.0e-6  |                                   -0.0000010000005000003333 |                                   -0.0000010000005000003333 |                                   0.0000000000000000000000
- 1-1.0e-7  |                                  -0.00000010000000500000033 |                                  -0.00000010000000500000033 |                                  0.00000000000000000000000
- 1-1.0e-8  |                                 -0.000000010000000050000000 |                                 -0.000000010000000050000000 |                                 0.000000000000000000000000
- 1-1.0e-9  |                                -0.0000000010000000005000000 |                                -0.0000000010000000005000000 |                                0.0000000000000000000000000
- 1-1.0e-10 |                               -0.00000000010000000000500000 |                               -0.00000000010000000000500000 |                               0.00000000000000000000000000
- 1-1.0e-11 |                              -0.000000000010000000000050000 |                              -0.000000000010000000000050000 |                              0.000000000000000000000000000
- 1-1.0e-12 |                             -0.0000000000010000000000005000 |                             -0.0000000000010000000000005000 |                             0.0000000000000000000000000000
- 1-1.0e-13 |                            -0.00000000000010000000000000500 |                            -0.00000000000010000000000000500 |                            0.00000000000000000000000000000
- 1-1.0e-14 |                           -0.000000000000010000000000000050 |                           -0.000000000000010000000000000050 |                           0.000000000000000000000000000000
- 1-1.0e-15 |                          -0.0000000000000010000000000000005 |                          -0.0000000000000010000000000000005 |                          0.0000000000000000000000000000000
- 1-1.0e-16 |                         -0.00000000000000010000000000000001 |                         -0.00000000000000010000000000000001 |                         0.00000000000000000000000000000000
- 1-1.0e-17 |                        -0.000000000000000010000000000000000 |                        -0.000000000000000010000000000000000 |                        0.000000000000000000000000000000000
- 1-1.0e-18 |                       -0.0000000000000000010000000000000000 |                       -0.0000000000000000010000000000000000 |                       0.0000000000000000000000000000000000
- 1-1.0e-19 |                      -0.00000000000000000010000000000000000 |                      -0.00000000000000000010000000000000000 |                      0.00000000000000000000000000000000000
- 1-1.0e-20 |                     -0.000000000000000000010000000000000000 |                     -0.000000000000000000010000000000000000 |                     0.000000000000000000000000000000000000
- 1-1.0e-21 |                    -0.0000000000000000000010000000000000000 |                    -0.0000000000000000000010000000000000000 |                    0.0000000000000000000000000000000000000
- 1-1.0e-22 |                   -0.00000000000000000000010000000000000000 |                   -0.00000000000000000000010000000000000000 |                   0.00000000000000000000000000000000000000
- 1-1.0e-23 |                  -0.000000000000000000000010000000000000000 |                  -0.000000000000000000000010000000000000000 |                  0.000000000000000000000000000000000000000
- 1-1.0e-24 |                 -0.0000000000000000000000010000000000000000 |                 -0.0000000000000000000000010000000000000000 |                 0.0000000000000000000000000000000000000000
- 1-1.0e-25 |                -0.00000000000000000000000010000000000000000 |                -0.00000000000000000000000010000000000000000 |                0.00000000000000000000000000000000000000000
- 1-1.0e-26 |               -0.000000000000000000000000010000000000000000 |               -0.000000000000000000000000010000000000000000 |               0.000000000000000000000000000000000000000000
- 1-1.0e-27 |              -0.0000000000000000000000000010000000000000000 |              -0.0000000000000000000000000010000000000000000 |              0.0000000000000000000000000000000000000000000
- 1-1.0e-28 |             -0.00000000000000000000000000010000000000000000 |             -0.00000000000000000000000000010000000000000000 |             0.00000000000000000000000000000000000000000000
- 1-1.0e-29 |            -0.000000000000000000000000000010000000000000000 |            -0.000000000000000000000000000010000000000000000 |            0.000000000000000000000000000000000000000000000
- 1-1.0e-30 |           -0.0000000000000000000000000000010000000000000000 |           -0.0000000000000000000000000000010000000000000000 |           0.0000000000000000000000000000000000000000000000
- 1-1.0e-31 |          -0.00000000000000000000000000000010000000000000000 |          -0.00000000000000000000000000000010000000000000000 |          0.00000000000000000000000000000000000000000000000
- 1-1.0e-32 |         -0.000000000000000000000000000000010000000000000000 |         -0.000000000000000000000000000000010000000000000000 |         0.000000000000000000000000000000000000000000000000
- 1-1.0e-33 |        -0.0000000000000000000000000000000010000000000000000 |        -0.0000000000000000000000000000000010000000000000000 |        0.0000000000000000000000000000000000000000000000000
- 1-1.0e-34 |       -0.00000000000000000000000000000000010000000000000000 |       -0.00000000000000000000000000000000010000000000000000 |       0.00000000000000000000000000000000000000000000000000
- 1-1.0e-35 |      -0.000000000000000000000000000000000010000000000000000 |      -0.000000000000000000000000000000000010000000000000000 |      0.000000000000000000000000000000000000000000000000000
- 1-1.0e-36 |     -0.0000000000000000000000000000000000010000000000000000 |     -0.0000000000000000000000000000000000010000000000000000 |     0.0000000000000000000000000000000000000000000000000000
- 1-1.0e-37 |    -0.00000000000000000000000000000000000010000000000000000 |    -0.00000000000000000000000000000000000010000000000000000 |    0.00000000000000000000000000000000000000000000000000000
- 1-1.0e-38 |   -0.000000000000000000000000000000000000010000000000000000 |   -0.000000000000000000000000000000000000010000000000000000 |   0.000000000000000000000000000000000000000000000000000000
- 1-1.0e-39 |  -0.0000000000000000000000000000000000000010000000000000000 |  -0.0000000000000000000000000000000000000010000000000000000 |  0.0000000000000000000000000000000000000000000000000000000
- 1-1.0e-40 | -0.00000000000000000000000000000000000000010000000000000000 | -0.00000000000000000000000000000000000000010000000000000000 | 0.00000000000000000000000000000000000000000000000000000000
-(40 rows)
-
--- input very close to but larger than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40}
--- do
---   l=$(bc -ql <<< "scale=500 ; l(1+10^-$p)" | head -n 1)
---   echo "('1.0e-$p', $l),"
--- done
-WITH t(x, bc_result) AS (VALUES
-('1.0e-1', .09531017980432486),
-('1.0e-2', .009950330853168083),
-('1.0e-3', .0009995003330835332),
-('1.0e-4', .00009999500033330834),
-('1.0e-5', .000009999950000333331),
-('1.0e-6', .0000009999995000003333),
-('1.0e-7', .00000009999999500000033),
-('1.0e-8', .000000009999999950000000),
-('1.0e-9', .0000000009999999995000000),
-('1.0e-10', .00000000009999999999500000),
-('1.0e-11', .000000000009999999999950000),
-('1.0e-12', .0000000000009999999999995000),
-('1.0e-13', .00000000000009999999999999500),
-('1.0e-14', .000000000000009999999999999950),
-('1.0e-15', .0000000000000009999999999999995),
-('1.0e-16', .00000000000000010000000000000000),
-('1.0e-17', .000000000000000010000000000000000),
-('1.0e-18', .0000000000000000010000000000000000),
-('1.0e-19', .00000000000000000010000000000000000),
-('1.0e-20', .000000000000000000010000000000000000),
-('1.0e-21', .0000000000000000000010000000000000000),
-('1.0e-22', .00000000000000000000010000000000000000),
-('1.0e-23', .000000000000000000000010000000000000000),
-('1.0e-24', .0000000000000000000000010000000000000000),
-('1.0e-25', .00000000000000000000000010000000000000000),
-('1.0e-26', .000000000000000000000000010000000000000000),
-('1.0e-27', .0000000000000000000000000010000000000000000),
-('1.0e-28', .00000000000000000000000000010000000000000000),
-('1.0e-29', .000000000000000000000000000010000000000000000),
-('1.0e-30', .0000000000000000000000000000010000000000000000),
-('1.0e-31', .00000000000000000000000000000010000000000000000),
-('1.0e-32', .000000000000000000000000000000010000000000000000),
-('1.0e-33', .0000000000000000000000000000000010000000000000000),
-('1.0e-34', .00000000000000000000000000000000010000000000000000),
-('1.0e-35', .000000000000000000000000000000000010000000000000000),
-('1.0e-36', .0000000000000000000000000000000000010000000000000000),
-('1.0e-37', .00000000000000000000000000000000000010000000000000000),
-('1.0e-38', .000000000000000000000000000000000000010000000000000000),
-('1.0e-39', .0000000000000000000000000000000000000010000000000000000),
-('1.0e-40', .00000000000000000000000000000000000000010000000000000000))
-SELECT '1+'||x, bc_result, ln(1.0+x::numeric), ln(1.0+x::numeric)-bc_result AS diff FROM t;
- ?column?  |                         bc_result                          |                             ln                             |                            diff                            
------------+------------------------------------------------------------+------------------------------------------------------------+------------------------------------------------------------
- 1+1.0e-1  |                                        0.09531017980432486 |                                        0.09531017980432486 |                                        0.00000000000000000
- 1+1.0e-2  |                                       0.009950330853168083 |                                       0.009950330853168083 |                                       0.000000000000000000
- 1+1.0e-3  |                                      0.0009995003330835332 |                                      0.0009995003330835332 |                                      0.0000000000000000000
- 1+1.0e-4  |                                     0.00009999500033330834 |                                     0.00009999500033330834 |                                     0.00000000000000000000
- 1+1.0e-5  |                                    0.000009999950000333331 |                                    0.000009999950000333331 |                                    0.000000000000000000000
- 1+1.0e-6  |                                   0.0000009999995000003333 |                                   0.0000009999995000003333 |                                   0.0000000000000000000000
- 1+1.0e-7  |                                  0.00000009999999500000033 |                                  0.00000009999999500000033 |                                  0.00000000000000000000000
- 1+1.0e-8  |                                 0.000000009999999950000000 |                                 0.000000009999999950000000 |                                 0.000000000000000000000000
- 1+1.0e-9  |                                0.0000000009999999995000000 |                                0.0000000009999999995000000 |                                0.0000000000000000000000000
- 1+1.0e-10 |                               0.00000000009999999999500000 |                               0.00000000009999999999500000 |                               0.00000000000000000000000000
- 1+1.0e-11 |                              0.000000000009999999999950000 |                              0.000000000009999999999950000 |                              0.000000000000000000000000000
- 1+1.0e-12 |                             0.0000000000009999999999995000 |                             0.0000000000009999999999995000 |                             0.0000000000000000000000000000
- 1+1.0e-13 |                            0.00000000000009999999999999500 |                            0.00000000000009999999999999500 |                            0.00000000000000000000000000000
- 1+1.0e-14 |                           0.000000000000009999999999999950 |                           0.000000000000009999999999999950 |                           0.000000000000000000000000000000
- 1+1.0e-15 |                          0.0000000000000009999999999999995 |                          0.0000000000000009999999999999995 |                          0.0000000000000000000000000000000
- 1+1.0e-16 |                         0.00000000000000010000000000000000 |                         0.00000000000000010000000000000000 |                         0.00000000000000000000000000000000
- 1+1.0e-17 |                        0.000000000000000010000000000000000 |                        0.000000000000000010000000000000000 |                        0.000000000000000000000000000000000
- 1+1.0e-18 |                       0.0000000000000000010000000000000000 |                       0.0000000000000000010000000000000000 |                       0.0000000000000000000000000000000000
- 1+1.0e-19 |                      0.00000000000000000010000000000000000 |                      0.00000000000000000010000000000000000 |                      0.00000000000000000000000000000000000
- 1+1.0e-20 |                     0.000000000000000000010000000000000000 |                     0.000000000000000000010000000000000000 |                     0.000000000000000000000000000000000000
- 1+1.0e-21 |                    0.0000000000000000000010000000000000000 |                    0.0000000000000000000010000000000000000 |                    0.0000000000000000000000000000000000000
- 1+1.0e-22 |                   0.00000000000000000000010000000000000000 |                   0.00000000000000000000010000000000000000 |                   0.00000000000000000000000000000000000000
- 1+1.0e-23 |                  0.000000000000000000000010000000000000000 |                  0.000000000000000000000010000000000000000 |                  0.000000000000000000000000000000000000000
- 1+1.0e-24 |                 0.0000000000000000000000010000000000000000 |                 0.0000000000000000000000010000000000000000 |                 0.0000000000000000000000000000000000000000
- 1+1.0e-25 |                0.00000000000000000000000010000000000000000 |                0.00000000000000000000000010000000000000000 |                0.00000000000000000000000000000000000000000
- 1+1.0e-26 |               0.000000000000000000000000010000000000000000 |               0.000000000000000000000000010000000000000000 |               0.000000000000000000000000000000000000000000
- 1+1.0e-27 |              0.0000000000000000000000000010000000000000000 |              0.0000000000000000000000000010000000000000000 |              0.0000000000000000000000000000000000000000000
- 1+1.0e-28 |             0.00000000000000000000000000010000000000000000 |             0.00000000000000000000000000010000000000000000 |             0.00000000000000000000000000000000000000000000
- 1+1.0e-29 |            0.000000000000000000000000000010000000000000000 |            0.000000000000000000000000000010000000000000000 |            0.000000000000000000000000000000000000000000000
- 1+1.0e-30 |           0.0000000000000000000000000000010000000000000000 |           0.0000000000000000000000000000010000000000000000 |           0.0000000000000000000000000000000000000000000000
- 1+1.0e-31 |          0.00000000000000000000000000000010000000000000000 |          0.00000000000000000000000000000010000000000000000 |          0.00000000000000000000000000000000000000000000000
- 1+1.0e-32 |         0.000000000000000000000000000000010000000000000000 |         0.000000000000000000000000000000010000000000000000 |         0.000000000000000000000000000000000000000000000000
- 1+1.0e-33 |        0.0000000000000000000000000000000010000000000000000 |        0.0000000000000000000000000000000010000000000000000 |        0.0000000000000000000000000000000000000000000000000
- 1+1.0e-34 |       0.00000000000000000000000000000000010000000000000000 |       0.00000000000000000000000000000000010000000000000000 |       0.00000000000000000000000000000000000000000000000000
- 1+1.0e-35 |      0.000000000000000000000000000000000010000000000000000 |      0.000000000000000000000000000000000010000000000000000 |      0.000000000000000000000000000000000000000000000000000
- 1+1.0e-36 |     0.0000000000000000000000000000000000010000000000000000 |     0.0000000000000000000000000000000000010000000000000000 |     0.0000000000000000000000000000000000000000000000000000
- 1+1.0e-37 |    0.00000000000000000000000000000000000010000000000000000 |    0.00000000000000000000000000000000000010000000000000000 |    0.00000000000000000000000000000000000000000000000000000
- 1+1.0e-38 |   0.000000000000000000000000000000000000010000000000000000 |   0.000000000000000000000000000000000000010000000000000000 |   0.000000000000000000000000000000000000000000000000000000
- 1+1.0e-39 |  0.0000000000000000000000000000000000000010000000000000000 |  0.0000000000000000000000000000000000000010000000000000000 |  0.0000000000000000000000000000000000000000000000000000000
- 1+1.0e-40 | 0.00000000000000000000000000000000000000010000000000000000 | 0.00000000000000000000000000000000000000010000000000000000 | 0.00000000000000000000000000000000000000000000000000000000
-(40 rows)
-
--- input very large
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40}
--- do
---   l=$(bc -ql <<< "scale=500 ; l(10^$p)" | head -n 1)
---   echo "('1.0e$p', $l),"
--- done
-WITH t(x, bc_result) AS (VALUES
-('1.0e1', 2.3025850929940457),
-('1.0e2', 4.6051701859880914),
-('1.0e3', 6.9077552789821371),
-('1.0e4', 9.2103403719761827),
-('1.0e5', 11.512925464970228),
-('1.0e6', 13.815510557964274),
-('1.0e7', 16.118095650958320),
-('1.0e8', 18.420680743952365),
-('1.0e9', 20.723265836946411),
-('1.0e10', 23.025850929940457),
-('1.0e11', 25.328436022934503),
-('1.0e12', 27.631021115928548),
-('1.0e13', 29.933606208922594),
-('1.0e14', 32.236191301916640),
-('1.0e15', 34.538776394910685),
-('1.0e16', 36.841361487904731),
-('1.0e17', 39.143946580898777),
-('1.0e18', 41.446531673892822),
-('1.0e19', 43.749116766886868),
-('1.0e20', 46.051701859880914),
-('1.0e21', 48.354286952874959),
-('1.0e22', 50.656872045869005),
-('1.0e23', 52.959457138863051),
-('1.0e24', 55.262042231857096),
-('1.0e25', 57.564627324851142),
-('1.0e26', 59.867212417845188),
-('1.0e27', 62.169797510839233),
-('1.0e28', 64.472382603833279),
-('1.0e29', 66.774967696827325),
-('1.0e30', 69.077552789821371),
-('1.0e31', 71.380137882815416),
-('1.0e32', 73.682722975809462),
-('1.0e33', 75.985308068803508),
-('1.0e34', 78.287893161797553),
-('1.0e35', 80.590478254791599),
-('1.0e36', 82.893063347785645),
-('1.0e37', 85.195648440779690),
-('1.0e38', 87.498233533773736),
-('1.0e39', 89.800818626767782),
-('1.0e40', 92.103403719761827))
-SELECT x, bc_result, ln(x::numeric), ln(x::numeric)-bc_result AS diff FROM t;
-   x    |     bc_result      |         ln         |        diff        
---------+--------------------+--------------------+--------------------
- 1.0e1  | 2.3025850929940457 | 2.3025850929940457 | 0.0000000000000000
- 1.0e2  | 4.6051701859880914 | 4.6051701859880914 | 0.0000000000000000
- 1.0e3  | 6.9077552789821371 | 6.9077552789821371 | 0.0000000000000000
- 1.0e4  | 9.2103403719761827 | 9.2103403719761827 | 0.0000000000000000
- 1.0e5  | 11.512925464970228 | 11.512925464970228 |  0.000000000000000
- 1.0e6  | 13.815510557964274 | 13.815510557964274 |  0.000000000000000
- 1.0e7  | 16.118095650958320 | 16.118095650958320 |  0.000000000000000
- 1.0e8  | 18.420680743952365 | 18.420680743952365 |  0.000000000000000
- 1.0e9  | 20.723265836946411 | 20.723265836946411 |  0.000000000000000
- 1.0e10 | 23.025850929940457 | 23.025850929940457 |  0.000000000000000
- 1.0e11 | 25.328436022934503 | 25.328436022934503 |  0.000000000000000
- 1.0e12 | 27.631021115928548 | 27.631021115928548 |  0.000000000000000
- 1.0e13 | 29.933606208922594 | 29.933606208922594 |  0.000000000000000
- 1.0e14 | 32.236191301916640 | 32.236191301916640 |  0.000000000000000
- 1.0e15 | 34.538776394910685 | 34.538776394910685 |  0.000000000000000
- 1.0e16 | 36.841361487904731 | 36.841361487904731 |  0.000000000000000
- 1.0e17 | 39.143946580898777 | 39.143946580898777 |  0.000000000000000
- 1.0e18 | 41.446531673892822 | 41.446531673892822 |  0.000000000000000
- 1.0e19 | 43.749116766886868 | 43.749116766886868 |  0.000000000000000
- 1.0e20 | 46.051701859880914 | 46.051701859880914 |  0.000000000000000
- 1.0e21 | 48.354286952874959 | 48.354286952874959 |  0.000000000000000
- 1.0e22 | 50.656872045869005 | 50.656872045869005 |  0.000000000000000
- 1.0e23 | 52.959457138863051 | 52.959457138863051 |  0.000000000000000
- 1.0e24 | 55.262042231857096 | 55.262042231857096 |  0.000000000000000
- 1.0e25 | 57.564627324851142 | 57.564627324851142 |  0.000000000000000
- 1.0e26 | 59.867212417845188 | 59.867212417845188 |  0.000000000000000
- 1.0e27 | 62.169797510839233 | 62.169797510839233 |  0.000000000000000
- 1.0e28 | 64.472382603833279 | 64.472382603833279 |  0.000000000000000
- 1.0e29 | 66.774967696827325 | 66.774967696827325 |  0.000000000000000
- 1.0e30 | 69.077552789821371 | 69.077552789821371 |  0.000000000000000
- 1.0e31 | 71.380137882815416 | 71.380137882815416 |  0.000000000000000
- 1.0e32 | 73.682722975809462 | 73.682722975809462 |  0.000000000000000
- 1.0e33 | 75.985308068803508 | 75.985308068803508 |  0.000000000000000
- 1.0e34 | 78.287893161797553 | 78.287893161797553 |  0.000000000000000
- 1.0e35 | 80.590478254791599 | 80.590478254791599 |  0.000000000000000
- 1.0e36 | 82.893063347785645 | 82.893063347785645 |  0.000000000000000
- 1.0e37 | 85.195648440779690 | 85.195648440779690 |  0.000000000000000
- 1.0e38 | 87.498233533773736 | 87.498233533773736 |  0.000000000000000
- 1.0e39 | 89.800818626767782 | 89.800818626767782 |  0.000000000000000
- 1.0e40 | 92.103403719761827 | 92.103403719761827 |  0.000000000000000
-(40 rows)
-
--- input huge
---
--- bc(1) results computed with a scale of 1000 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..10}
--- do
---   l=$(bc -ql <<< "scale=1000 ; l(10^${p}00)" | head -n 1)
---  echo "('1.0e${p}00', $l),"
--- done
-WITH t(x, bc_result) AS (VALUES
-('1.0e100', 230.25850929940457),
-('1.0e200', 460.51701859880914),
-('1.0e300', 690.77552789821371),
-('1.0e400', 921.03403719761827),
-('1.0e500', 1151.2925464970228),
-('1.0e600', 1381.5510557964274),
-('1.0e700', 1611.8095650958320),
-('1.0e800', 1842.0680743952365),
-('1.0e900', 2072.3265836946411),
-('1.0e1000', 2302.5850929940457))
-SELECT x, bc_result, ln(x::numeric), ln(x::numeric)-bc_result AS diff FROM t;
-    x     |     bc_result      |         ln         |       diff       
-----------+--------------------+--------------------+------------------
- 1.0e100  | 230.25850929940457 | 230.25850929940457 | 0.00000000000000
- 1.0e200  | 460.51701859880914 | 460.51701859880914 | 0.00000000000000
- 1.0e300  | 690.77552789821371 | 690.77552789821371 | 0.00000000000000
- 1.0e400  | 921.03403719761827 | 921.03403719761827 | 0.00000000000000
- 1.0e500  | 1151.2925464970228 | 1151.2925464970228 |  0.0000000000000
- 1.0e600  | 1381.5510557964274 | 1381.5510557964274 |  0.0000000000000
- 1.0e700  | 1611.8095650958320 | 1611.8095650958320 |  0.0000000000000
- 1.0e800  | 1842.0680743952365 | 1842.0680743952365 |  0.0000000000000
- 1.0e900  | 2072.3265836946411 | 2072.3265836946411 |  0.0000000000000
- 1.0e1000 | 2302.5850929940457 | 2302.5850929940457 |  0.0000000000000
-(10 rows)
-
--- inputs with 1000 decimal places
---
--- bc(1) results computed with a scale of 2000 and rounded to 1000 decimal
--- places
-WITH t(x, bc_result) AS (VALUES
-(484990182159328900690402236933516249572671683638747490717351807610531884491845416923860371219625151551889257298200816555016472471293780254009492949585031653913930735918829139712249577547959394351523545901788627247613322896296041868431769047433229466634098452564756860190085118463828382895145244362033728480588969626012192733802377468089120757046364393407262957242230928854711898925295251902007136232994524624903257456111389508582206404271734668422903183500589303866613158037169610592539145461637447957948521714058034772237111009429638870236361143304703683377693378577075353794118557951847394763531830696578809001981568860219578880229402696449243344235099860421846016326538272155937175661905904288335499593232232926636205909086901191153907183842087577811871344870731324067822883041265129394268082883745408414994.8967939438561591657171240282983703914075472645212002662497023142663831371447287624846942598424990784971781730103682951722370983277124599054059027055336437808366784501932987082321905202623642371063626378290734289114618092750984153422293450048717769065428713836637664433167768445609659527458911187829232316677137895259433038764404970599325009178297626038331436654541552998098529141205301472138026818453893127265938030066392881979113522757891639646670670272542401773230506961559808927249585675430838495658225557294666522469887436551840596777627408780618586500922973500018513068499587683746133637919751545157547095670767246977244726331271787622126889459658539988980096764323712767863722912919120929339399753431689512753214200090670880647731689804555417871258907716687575767185444541243606329768784843125926070743277339790277626515824924290352180761378846035233155198504033292692893297993698953705472933411199778880561376633444249703838589180474329586470353212010427945060694794274109764269805332803290229,
- 1864.3702986939570026328504202935192533137907736189919154633800554877738455118081651650863235106905871352085850240570561347180517240105510505203972860921397909573687877993477806728098306202020229409548306695695574102950949468160529713610952021974630774784174851619325758380143625473386495586347322798415543385655090746985183329114860118551572428921774322172798724455202876781611633419444058398798142214904998877857425038669920064728855823072107227506485770367799671977282350083029452784747350395161797215115525867416898416360638482342253129160308632504217096916335590470843180746834864303790913372081974355613359678634194879425862536147988835528973291020680020540866655622823550861337486588647231688134992810403147262346312159819432914207194632564009749236609081399504118359354620598232725290537215007867979331582119891661859015726276335168158288396939655310210558566592649049602925182137256134162660116182293851038854455437841571331011002023088829768308520393956515509475418031437505751407687618234418262),
-(87190145885430429849953615409019208993240447426362428988181639909267773304254748257120061524000254226856815085523676417146197197996896030672521334101413071112068202429835905642444187493717977611730127126387257253646790849384975208460867137315507010888782632024640844766297185244443116696943912406389670302370461137850160539373600494054874979342373255280815156048999900951842673141766630630919020492255966628630634124452614590400422133958133100159154995520080124736657520969784129924799670552560034302960877087853678350801769339861812435411200669026902417951572668727488315537985378304242438181615160041688723201917323705450185975141141262578884689500612295576288125956289035673242989906973367691922065122033180281670221390667818909912035903387888639331486823729897326624516015340.0330856710565117793999512551468220085711713631167607285185762046751452975325645379302403715842570486302993296501788672462090620871511446272026693318239212657949496275318383141403236705902077406660768573015707706831878445598837931116223956945944726162551477136715847593742032488181481888084716920605114101902724395659898621880016853548602514706686907951229872573180602614761229992106144727082722940736406782659562775289407005631298246624198606031298081220736931229256511054595028182057216042683060059115371651410352645266000330509331097811566633211452233019461903115970558624057877018778178814946285827512359903934291318219271464841957435711594154280905473802599888081783098187210283997106131616471807951265003903143099667366508222327805543948921694362089860577380749774036318574113007382111997454202845559941557812813566442364810680529092880773126707073967537693927177460459341763934709686530005721141046645111784404932103241501569571235364365556796422998363930810983452790309019295181282099408260156,
- 1793.5767085750017553306932533574391150814202249805881581227430032600579405884415934520704053351781361105595296647510475380766428668443641914861849764330704062323054023252886955844207807229267936432730818329225450152491146839618683772020068682795388746108876393249306737841247788224204701299467519965182171772253974884845661168860422489046657965359832930382114760565628765599962013955588754803194908990025689040598990346417563277021386852342928910383706995866844541160576254266641602065102228267316550706943783591722246885978355472097314691737807509436806788803362444745551013400341861820755594413819894154786253014501454443272120342005711761286524843010157182464200556865694401941794983935172457481497909987740544409272349152397774548604845897687504977786762391359552407068124283290504752932824699865504970420939586707791994870941813718246825616335675307740641350673558328821461530563823677144691877374809441673507467507447891562257806191361453045937798278733402269265623588493124129181374135958668436774),
-(93936642222690597390233191619858485419795942047468396309991947772747208870873993801669373075421461116465960407843923269693395211616591453397070258466704654943689268224479477016161636938138334729982904232438440955361656138189836032891825113139184685132178764873033678116450665758561650355252211196676137179184043639278410827092182700922151290703747496962700158844772453483316974221113826173404445159281421213715669245417896170368554410830320000019029956317336703559699859949692222685614036912057150632902650913831404804982509990655560731349634628713944739168096272097122388116038119844786988276635032016787352796502360718569977397214936366251320294621522016.6483354941025384161536675750898007896744690911429670830432784905421638721478353275821072200938900938046264210604940707974410950770029535636602548377806284157951164875821446035013896786653932045182167021839184824627082391478016195098055107001433336586881395912782883663046617432598969149948351689103230162742769845955320418573803127107923535948653168889411316007796459064267436246637115946581149511513369842911210359447262641996566147462977170742544980481275049898092152042927981394239266559286915303786701737610786594006685748456635797125029722684151298695274097006242412384086302106763844070230264910503179385988626477852818174114043927841085089058972074427820150462261941575665882880501074676800316585217150509780489224388148722603385921057007086785238310735038314861960410473809826927329368597558806004392175746233568789445929554890241140656324160187253042639339549705859147930476532359840809944163908006480881926041259363654863689570520534301207043189181147254153307163555433328278834311658232337,
- 1510.4332713542154696529645934345554302578243896764921637693542962119938599884313210100957753316832762996428481801312323020427109678979117469716796746760060470871840325255146954580681101106876674367471955788143763250819168311353856748872452260808797135108102729064040463343792765872545182299889360257515315869180266759715933989413256377582681707188367254513700731642913479683031478361835565783219287780434673712341147656477670848734998849030451414278832848680301511646182446524915091598080243532068451726548537866633622180283865668708517173065893429240665300584705585310049892047293928733753369421499719516009692095913169665213597158441636480707309244604139865130782756488091268094213446272360006907802989573582755585110277620911226015342778471352130366770729972784317323917141031824334355639769512749560550167491709646539950725523461943580211843652293561678342656010571108219244870234329176123205423872844099992204896411752620881541000940129833754169391528449211839693800724450201835161044717173715867437))
-SELECT trim_scale(ln(x::numeric)-bc_result) AS diff FROM t;
- diff 
-------
-    0
-    0
-    0
-(3 rows)
-
---
--- Tests for LOG() (base 10)
---
--- input very small, exact result known
-WITH t(x) AS (SELECT '1e-'||n FROM generate_series(1, 100) g(n))
-SELECT x, log(x::numeric) FROM t;
-   x    |                                                    log                                                    
---------+-----------------------------------------------------------------------------------------------------------
- 1e-1   |                                                                                       -1.0000000000000000
- 1e-2   |                                                                                       -2.0000000000000000
- 1e-3   |                                                                                       -3.0000000000000000
- 1e-4   |                                                                                       -4.0000000000000000
- 1e-5   |                                                                                        -5.000000000000000
- 1e-6   |                                                                                        -6.000000000000000
- 1e-7   |                                                                                        -7.000000000000000
- 1e-8   |                                                                                        -8.000000000000000
- 1e-9   |                                                                                        -9.000000000000000
- 1e-10  |                                                                                       -10.000000000000000
- 1e-11  |                                                                                       -11.000000000000000
- 1e-12  |                                                                                       -12.000000000000000
- 1e-13  |                                                                                       -13.000000000000000
- 1e-14  |                                                                                       -14.000000000000000
- 1e-15  |                                                                                       -15.000000000000000
- 1e-16  |                                                                                      -16.0000000000000000
- 1e-17  |                                                                                     -17.00000000000000000
- 1e-18  |                                                                                    -18.000000000000000000
- 1e-19  |                                                                                   -19.0000000000000000000
- 1e-20  |                                                                                  -20.00000000000000000000
- 1e-21  |                                                                                 -21.000000000000000000000
- 1e-22  |                                                                                -22.0000000000000000000000
- 1e-23  |                                                                               -23.00000000000000000000000
- 1e-24  |                                                                              -24.000000000000000000000000
- 1e-25  |                                                                             -25.0000000000000000000000000
- 1e-26  |                                                                            -26.00000000000000000000000000
- 1e-27  |                                                                           -27.000000000000000000000000000
- 1e-28  |                                                                          -28.0000000000000000000000000000
- 1e-29  |                                                                         -29.00000000000000000000000000000
- 1e-30  |                                                                        -30.000000000000000000000000000000
- 1e-31  |                                                                       -31.0000000000000000000000000000000
- 1e-32  |                                                                      -32.00000000000000000000000000000000
- 1e-33  |                                                                     -33.000000000000000000000000000000000
- 1e-34  |                                                                    -34.0000000000000000000000000000000000
- 1e-35  |                                                                   -35.00000000000000000000000000000000000
- 1e-36  |                                                                  -36.000000000000000000000000000000000000
- 1e-37  |                                                                 -37.0000000000000000000000000000000000000
- 1e-38  |                                                                -38.00000000000000000000000000000000000000
- 1e-39  |                                                               -39.000000000000000000000000000000000000000
- 1e-40  |                                                              -40.0000000000000000000000000000000000000000
- 1e-41  |                                                             -41.00000000000000000000000000000000000000000
- 1e-42  |                                                            -42.000000000000000000000000000000000000000000
- 1e-43  |                                                           -43.0000000000000000000000000000000000000000000
- 1e-44  |                                                          -44.00000000000000000000000000000000000000000000
- 1e-45  |                                                         -45.000000000000000000000000000000000000000000000
- 1e-46  |                                                        -46.0000000000000000000000000000000000000000000000
- 1e-47  |                                                       -47.00000000000000000000000000000000000000000000000
- 1e-48  |                                                      -48.000000000000000000000000000000000000000000000000
- 1e-49  |                                                     -49.0000000000000000000000000000000000000000000000000
- 1e-50  |                                                    -50.00000000000000000000000000000000000000000000000000
- 1e-51  |                                                   -51.000000000000000000000000000000000000000000000000000
- 1e-52  |                                                  -52.0000000000000000000000000000000000000000000000000000
- 1e-53  |                                                 -53.00000000000000000000000000000000000000000000000000000
- 1e-54  |                                                -54.000000000000000000000000000000000000000000000000000000
- 1e-55  |                                               -55.0000000000000000000000000000000000000000000000000000000
- 1e-56  |                                              -56.00000000000000000000000000000000000000000000000000000000
- 1e-57  |                                             -57.000000000000000000000000000000000000000000000000000000000
- 1e-58  |                                            -58.0000000000000000000000000000000000000000000000000000000000
- 1e-59  |                                           -59.00000000000000000000000000000000000000000000000000000000000
- 1e-60  |                                          -60.000000000000000000000000000000000000000000000000000000000000
- 1e-61  |                                         -61.0000000000000000000000000000000000000000000000000000000000000
- 1e-62  |                                        -62.00000000000000000000000000000000000000000000000000000000000000
- 1e-63  |                                       -63.000000000000000000000000000000000000000000000000000000000000000
- 1e-64  |                                      -64.0000000000000000000000000000000000000000000000000000000000000000
- 1e-65  |                                     -65.00000000000000000000000000000000000000000000000000000000000000000
- 1e-66  |                                    -66.000000000000000000000000000000000000000000000000000000000000000000
- 1e-67  |                                   -67.0000000000000000000000000000000000000000000000000000000000000000000
- 1e-68  |                                  -68.00000000000000000000000000000000000000000000000000000000000000000000
- 1e-69  |                                 -69.000000000000000000000000000000000000000000000000000000000000000000000
- 1e-70  |                                -70.0000000000000000000000000000000000000000000000000000000000000000000000
- 1e-71  |                               -71.00000000000000000000000000000000000000000000000000000000000000000000000
- 1e-72  |                              -72.000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-73  |                             -73.0000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-74  |                            -74.00000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-75  |                           -75.000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-76  |                          -76.0000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-77  |                         -77.00000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-78  |                        -78.000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-79  |                       -79.0000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-80  |                      -80.00000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-81  |                     -81.000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-82  |                    -82.0000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-83  |                   -83.00000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-84  |                  -84.000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-85  |                 -85.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-86  |                -86.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-87  |               -87.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-88  |              -88.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-89  |             -89.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-90  |            -90.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-91  |           -91.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-92  |          -92.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-93  |         -93.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-94  |        -94.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-95  |       -95.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-96  |      -96.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-97  |     -97.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-98  |    -98.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-99  |   -99.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- 1e-100 | -100.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-(100 rows)
-
--- input very small, non-exact results
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..50..7}
--- do
---   for d in {9..1..3}
---   do
---     l=$(bc -ql <<< "scale=500 ; l($d*10^-$p) / l(10)" | head -n 1)
---     echo "('${d}.0e-$p', $l),"
---   done
--- done
-WITH t(x, bc_result) AS (VALUES
-('9.0e-1', -.04575749056067513),
-('6.0e-1', -.2218487496163564),
-('3.0e-1', -.5228787452803376),
-('9.0e-8', -7.045757490560675),
-('6.0e-8', -7.221848749616356),
-('3.0e-8', -7.522878745280338),
-('9.0e-15', -14.0457574905606751),
-('6.0e-15', -14.2218487496163564),
-('3.0e-15', -14.5228787452803376),
-('9.0e-22', -21.04575749056067512540994),
-('6.0e-22', -21.22184874961635636749123),
-('3.0e-22', -21.52287874528033756270497),
-('9.0e-29', -28.045757490560675125409944193490),
-('6.0e-29', -28.221848749616356367491233202020),
-('3.0e-29', -28.522878745280337562704972096745),
-('9.0e-36', -35.0457574905606751254099441934897693816),
-('6.0e-36', -35.2218487496163563674912332020203916640),
-('3.0e-36', -35.5228787452803375627049720967448846908),
-('9.0e-43', -42.04575749056067512540994419348976938159974227),
-('6.0e-43', -42.22184874961635636749123320202039166403168125),
-('3.0e-43', -42.52287874528033756270497209674488469079987114),
-('9.0e-50', -49.045757490560675125409944193489769381599742271618608),
-('6.0e-50', -49.221848749616356367491233202020391664031681254347196),
-('3.0e-50', -49.522878745280337562704972096744884690799871135809304))
-SELECT x, bc_result, log(x::numeric), log(x::numeric)-bc_result AS diff FROM t;
-    x    |                        bc_result                        |                           log                           |                         diff                          
----------+---------------------------------------------------------+---------------------------------------------------------+-------------------------------------------------------
- 9.0e-1  |                                    -0.04575749056067513 |                                    -0.04575749056067513 |                                   0.00000000000000000
- 6.0e-1  |                                     -0.2218487496163564 |                                     -0.2218487496163564 |                                    0.0000000000000000
- 3.0e-1  |                                     -0.5228787452803376 |                                     -0.5228787452803376 |                                    0.0000000000000000
- 9.0e-8  |                                      -7.045757490560675 |                                      -7.045757490560675 |                                     0.000000000000000
- 6.0e-8  |                                      -7.221848749616356 |                                      -7.221848749616356 |                                     0.000000000000000
- 3.0e-8  |                                      -7.522878745280338 |                                      -7.522878745280338 |                                     0.000000000000000
- 9.0e-15 |                                    -14.0457574905606751 |                                    -14.0457574905606751 |                                    0.0000000000000000
- 6.0e-15 |                                    -14.2218487496163564 |                                    -14.2218487496163564 |                                    0.0000000000000000
- 3.0e-15 |                                    -14.5228787452803376 |                                    -14.5228787452803376 |                                    0.0000000000000000
- 9.0e-22 |                             -21.04575749056067512540994 |                             -21.04575749056067512540994 |                             0.00000000000000000000000
- 6.0e-22 |                             -21.22184874961635636749123 |                             -21.22184874961635636749123 |                             0.00000000000000000000000
- 3.0e-22 |                             -21.52287874528033756270497 |                             -21.52287874528033756270497 |                             0.00000000000000000000000
- 9.0e-29 |                      -28.045757490560675125409944193490 |                      -28.045757490560675125409944193490 |                      0.000000000000000000000000000000
- 6.0e-29 |                      -28.221848749616356367491233202020 |                      -28.221848749616356367491233202020 |                      0.000000000000000000000000000000
- 3.0e-29 |                      -28.522878745280337562704972096745 |                      -28.522878745280337562704972096745 |                      0.000000000000000000000000000000
- 9.0e-36 |               -35.0457574905606751254099441934897693816 |               -35.0457574905606751254099441934897693816 |               0.0000000000000000000000000000000000000
- 6.0e-36 |               -35.2218487496163563674912332020203916640 |               -35.2218487496163563674912332020203916640 |               0.0000000000000000000000000000000000000
- 3.0e-36 |               -35.5228787452803375627049720967448846908 |               -35.5228787452803375627049720967448846908 |               0.0000000000000000000000000000000000000
- 9.0e-43 |        -42.04575749056067512540994419348976938159974227 |        -42.04575749056067512540994419348976938159974227 |        0.00000000000000000000000000000000000000000000
- 6.0e-43 |        -42.22184874961635636749123320202039166403168125 |        -42.22184874961635636749123320202039166403168125 |        0.00000000000000000000000000000000000000000000
- 3.0e-43 |        -42.52287874528033756270497209674488469079987114 |        -42.52287874528033756270497209674488469079987114 |        0.00000000000000000000000000000000000000000000
- 9.0e-50 | -49.045757490560675125409944193489769381599742271618608 | -49.045757490560675125409944193489769381599742271618608 | 0.000000000000000000000000000000000000000000000000000
- 6.0e-50 | -49.221848749616356367491233202020391664031681254347196 | -49.221848749616356367491233202020391664031681254347196 | 0.000000000000000000000000000000000000000000000000000
- 3.0e-50 | -49.522878745280337562704972096744884690799871135809304 | -49.522878745280337562704972096744884690799871135809304 | 0.000000000000000000000000000000000000000000000000000
-(24 rows)
-
--- input very close to but smaller than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40..7}
--- do
---   for d in {9..1..3}
---   do
---     l=$(bc -ql <<< "scale=500 ; l(1-$d*10^-$p) / l(10)" | head -n 1)
---     echo "('${d}.0e-$p', $l),"
---   done
--- done
-WITH t(x, bc_result) AS (VALUES
-('9.0e-1', -1.0000000000000000),
-('6.0e-1', -.3979400086720376),
-('3.0e-1', -.1549019599857432),
-('9.0e-8', -.000000039086505130185422),
-('6.0e-8', -.000000026057669695925208),
-('3.0e-8', -.000000013028834652530076),
-('9.0e-15', -.0000000000000039086503371292840),
-('6.0e-15', -.0000000000000026057668914195188),
-('3.0e-15', -.0000000000000013028834457097574),
-('9.0e-22', -.00000000000000000000039086503371292664),
-('6.0e-22', -.00000000000000000000026057668914195110),
-('3.0e-22', -.00000000000000000000013028834457097555),
-('9.0e-29', -.000000000000000000000000000039086503371292664),
-('6.0e-29', -.000000000000000000000000000026057668914195110),
-('3.0e-29', -.000000000000000000000000000013028834457097555),
-('9.0e-36', -.0000000000000000000000000000000000039086503371292664),
-('6.0e-36', -.0000000000000000000000000000000000026057668914195110),
-('3.0e-36', -.0000000000000000000000000000000000013028834457097555))
-SELECT '1-'||x, bc_result, log(1.0-x::numeric), log(1.0-x::numeric)-bc_result AS diff FROM t;
- ?column?  |                        bc_result                        |                           log                           |                          diff                          
------------+---------------------------------------------------------+---------------------------------------------------------+--------------------------------------------------------
- 1-9.0e-1  |                                     -1.0000000000000000 |                                     -1.0000000000000000 |                                     0.0000000000000000
- 1-6.0e-1  |                                     -0.3979400086720376 |                                     -0.3979400086720376 |                                     0.0000000000000000
- 1-3.0e-1  |                                     -0.1549019599857432 |                                     -0.1549019599857432 |                                     0.0000000000000000
- 1-9.0e-8  |                             -0.000000039086505130185422 |                             -0.000000039086505130185422 |                             0.000000000000000000000000
- 1-6.0e-8  |                             -0.000000026057669695925208 |                             -0.000000026057669695925208 |                             0.000000000000000000000000
- 1-3.0e-8  |                             -0.000000013028834652530076 |                             -0.000000013028834652530076 |                             0.000000000000000000000000
- 1-9.0e-15 |                      -0.0000000000000039086503371292840 |                      -0.0000000000000039086503371292840 |                      0.0000000000000000000000000000000
- 1-6.0e-15 |                      -0.0000000000000026057668914195188 |                      -0.0000000000000026057668914195188 |                      0.0000000000000000000000000000000
- 1-3.0e-15 |                      -0.0000000000000013028834457097574 |                      -0.0000000000000013028834457097574 |                      0.0000000000000000000000000000000
- 1-9.0e-22 |               -0.00000000000000000000039086503371292664 |               -0.00000000000000000000039086503371292664 |               0.00000000000000000000000000000000000000
- 1-6.0e-22 |               -0.00000000000000000000026057668914195110 |               -0.00000000000000000000026057668914195110 |               0.00000000000000000000000000000000000000
- 1-3.0e-22 |               -0.00000000000000000000013028834457097555 |               -0.00000000000000000000013028834457097555 |               0.00000000000000000000000000000000000000
- 1-9.0e-29 |        -0.000000000000000000000000000039086503371292664 |        -0.000000000000000000000000000039086503371292664 |        0.000000000000000000000000000000000000000000000
- 1-6.0e-29 |        -0.000000000000000000000000000026057668914195110 |        -0.000000000000000000000000000026057668914195110 |        0.000000000000000000000000000000000000000000000
- 1-3.0e-29 |        -0.000000000000000000000000000013028834457097555 |        -0.000000000000000000000000000013028834457097555 |        0.000000000000000000000000000000000000000000000
- 1-9.0e-36 | -0.0000000000000000000000000000000000039086503371292664 | -0.0000000000000000000000000000000000039086503371292664 | 0.0000000000000000000000000000000000000000000000000000
- 1-6.0e-36 | -0.0000000000000000000000000000000000026057668914195110 | -0.0000000000000000000000000000000000026057668914195110 | 0.0000000000000000000000000000000000000000000000000000
- 1-3.0e-36 | -0.0000000000000000000000000000000000013028834457097555 | -0.0000000000000000000000000000000000013028834457097555 | 0.0000000000000000000000000000000000000000000000000000
-(18 rows)
-
--- input very close to but larger than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40..7}
--- do
---   for d in {9..1..3}
---   do
---     l=$(bc -ql <<< "scale=500 ; l(1+$d*10^-$p) / l(10)" | head -n 1)
---     echo "('${d}.0e-$p', $l),"
---   done
--- done
-WITH t(x, bc_result) AS (VALUES
-('9.0e-1', .2787536009528290),
-('6.0e-1', .2041199826559248),
-('3.0e-1', .1139433523068368),
-('9.0e-8', .000000039086501612400118),
-('6.0e-8', .000000026057668132465074),
-('3.0e-8', .000000013028834261665042),
-('9.0e-15', .0000000000000039086503371292489),
-('6.0e-15', .0000000000000026057668914195031),
-('3.0e-15', .0000000000000013028834457097535),
-('9.0e-22', .00000000000000000000039086503371292664),
-('6.0e-22', .00000000000000000000026057668914195110),
-('3.0e-22', .00000000000000000000013028834457097555),
-('9.0e-29', .000000000000000000000000000039086503371292664),
-('6.0e-29', .000000000000000000000000000026057668914195110),
-('3.0e-29', .000000000000000000000000000013028834457097555),
-('9.0e-36', .0000000000000000000000000000000000039086503371292664),
-('6.0e-36', .0000000000000000000000000000000000026057668914195110),
-('3.0e-36', .0000000000000000000000000000000000013028834457097555))
-SELECT '1+'||x, bc_result, log(1.0+x::numeric), log(1.0+x::numeric)-bc_result AS diff FROM t;
- ?column?  |                       bc_result                        |                          log                           |                          diff                          
------------+--------------------------------------------------------+--------------------------------------------------------+--------------------------------------------------------
- 1+9.0e-1  |                                     0.2787536009528290 |                                     0.2787536009528290 |                                     0.0000000000000000
- 1+6.0e-1  |                                     0.2041199826559248 |                                     0.2041199826559248 |                                     0.0000000000000000
- 1+3.0e-1  |                                     0.1139433523068368 |                                     0.1139433523068368 |                                     0.0000000000000000
- 1+9.0e-8  |                             0.000000039086501612400118 |                             0.000000039086501612400118 |                             0.000000000000000000000000
- 1+6.0e-8  |                             0.000000026057668132465074 |                             0.000000026057668132465074 |                             0.000000000000000000000000
- 1+3.0e-8  |                             0.000000013028834261665042 |                             0.000000013028834261665042 |                             0.000000000000000000000000
- 1+9.0e-15 |                      0.0000000000000039086503371292489 |                      0.0000000000000039086503371292489 |                      0.0000000000000000000000000000000
- 1+6.0e-15 |                      0.0000000000000026057668914195031 |                      0.0000000000000026057668914195031 |                      0.0000000000000000000000000000000
- 1+3.0e-15 |                      0.0000000000000013028834457097535 |                      0.0000000000000013028834457097535 |                      0.0000000000000000000000000000000
- 1+9.0e-22 |               0.00000000000000000000039086503371292664 |               0.00000000000000000000039086503371292664 |               0.00000000000000000000000000000000000000
- 1+6.0e-22 |               0.00000000000000000000026057668914195110 |               0.00000000000000000000026057668914195110 |               0.00000000000000000000000000000000000000
- 1+3.0e-22 |               0.00000000000000000000013028834457097555 |               0.00000000000000000000013028834457097555 |               0.00000000000000000000000000000000000000
- 1+9.0e-29 |        0.000000000000000000000000000039086503371292664 |        0.000000000000000000000000000039086503371292664 |        0.000000000000000000000000000000000000000000000
- 1+6.0e-29 |        0.000000000000000000000000000026057668914195110 |        0.000000000000000000000000000026057668914195110 |        0.000000000000000000000000000000000000000000000
- 1+3.0e-29 |        0.000000000000000000000000000013028834457097555 |        0.000000000000000000000000000013028834457097555 |        0.000000000000000000000000000000000000000000000
- 1+9.0e-36 | 0.0000000000000000000000000000000000039086503371292664 | 0.0000000000000000000000000000000000039086503371292664 | 0.0000000000000000000000000000000000000000000000000000
- 1+6.0e-36 | 0.0000000000000000000000000000000000026057668914195110 | 0.0000000000000000000000000000000000026057668914195110 | 0.0000000000000000000000000000000000000000000000000000
- 1+3.0e-36 | 0.0000000000000000000000000000000000013028834457097555 | 0.0000000000000000000000000000000000013028834457097555 | 0.0000000000000000000000000000000000000000000000000000
-(18 rows)
-
--- input very large, exact result known
-WITH t(x) AS (SELECT '1e'||n FROM generate_series(1, 100) g(n))
-SELECT x, log(x::numeric) FROM t;
-   x   |        log         
--------+--------------------
- 1e1   | 1.0000000000000000
- 1e2   | 2.0000000000000000
- 1e3   | 3.0000000000000000
- 1e4   | 4.0000000000000000
- 1e5   |  5.000000000000000
- 1e6   |  6.000000000000000
- 1e7   |  7.000000000000000
- 1e8   |  8.000000000000000
- 1e9   |  9.000000000000000
- 1e10  | 10.000000000000000
- 1e11  | 11.000000000000000
- 1e12  | 12.000000000000000
- 1e13  | 13.000000000000000
- 1e14  | 14.000000000000000
- 1e15  | 15.000000000000000
- 1e16  | 16.000000000000000
- 1e17  | 17.000000000000000
- 1e18  | 18.000000000000000
- 1e19  | 19.000000000000000
- 1e20  | 20.000000000000000
- 1e21  | 21.000000000000000
- 1e22  | 22.000000000000000
- 1e23  | 23.000000000000000
- 1e24  | 24.000000000000000
- 1e25  | 25.000000000000000
- 1e26  | 26.000000000000000
- 1e27  | 27.000000000000000
- 1e28  | 28.000000000000000
- 1e29  | 29.000000000000000
- 1e30  | 30.000000000000000
- 1e31  | 31.000000000000000
- 1e32  | 32.000000000000000
- 1e33  | 33.000000000000000
- 1e34  | 34.000000000000000
- 1e35  | 35.000000000000000
- 1e36  | 36.000000000000000
- 1e37  | 37.000000000000000
- 1e38  | 38.000000000000000
- 1e39  | 39.000000000000000
- 1e40  | 40.000000000000000
- 1e41  | 41.000000000000000
- 1e42  | 42.000000000000000
- 1e43  | 43.000000000000000
- 1e44  |  44.00000000000000
- 1e45  |  45.00000000000000
- 1e46  |  46.00000000000000
- 1e47  |  47.00000000000000
- 1e48  |  48.00000000000000
- 1e49  |  49.00000000000000
- 1e50  |  50.00000000000000
- 1e51  |  51.00000000000000
- 1e52  |  52.00000000000000
- 1e53  |  53.00000000000000
- 1e54  |  54.00000000000000
- 1e55  |  55.00000000000000
- 1e56  |  56.00000000000000
- 1e57  |  57.00000000000000
- 1e58  |  58.00000000000000
- 1e59  |  59.00000000000000
- 1e60  |  60.00000000000000
- 1e61  |  61.00000000000000
- 1e62  |  62.00000000000000
- 1e63  |  63.00000000000000
- 1e64  |  64.00000000000000
- 1e65  |  65.00000000000000
- 1e66  |  66.00000000000000
- 1e67  |  67.00000000000000
- 1e68  |  68.00000000000000
- 1e69  |  69.00000000000000
- 1e70  |  70.00000000000000
- 1e71  |  71.00000000000000
- 1e72  |  72.00000000000000
- 1e73  |  73.00000000000000
- 1e74  |  74.00000000000000
- 1e75  |  75.00000000000000
- 1e76  |  76.00000000000000
- 1e77  |  77.00000000000000
- 1e78  |  78.00000000000000
- 1e79  |  79.00000000000000
- 1e80  |  80.00000000000000
- 1e81  |  81.00000000000000
- 1e82  |  82.00000000000000
- 1e83  |  83.00000000000000
- 1e84  |  84.00000000000000
- 1e85  |  85.00000000000000
- 1e86  |  86.00000000000000
- 1e87  |  87.00000000000000
- 1e88  |  88.00000000000000
- 1e89  |  89.00000000000000
- 1e90  |  90.00000000000000
- 1e91  |  91.00000000000000
- 1e92  |  92.00000000000000
- 1e93  |  93.00000000000000
- 1e94  |  94.00000000000000
- 1e95  |  95.00000000000000
- 1e96  |  96.00000000000000
- 1e97  |  97.00000000000000
- 1e98  |  98.00000000000000
- 1e99  |  99.00000000000000
- 1e100 | 100.00000000000000
-(100 rows)
-
--- input very large, non-exact results
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {10..50..7}
---   do
---   for d in {2..9..3}
---   do
---     l=$(bc -ql <<< "scale=500 ; l($d*10^$p) / l(10)" | head -n 1)
---     echo "('${d}.0e$p', $l),"
---   done
--- done
-WITH t(x, bc_result) AS (VALUES
-('2.0e10', 10.301029995663981),
-('5.0e10', 10.698970004336019),
-('8.0e10', 10.903089986991944),
-('2.0e17', 17.301029995663981),
-('5.0e17', 17.698970004336019),
-('8.0e17', 17.903089986991944),
-('2.0e24', 24.301029995663981),
-('5.0e24', 24.698970004336019),
-('8.0e24', 24.903089986991944),
-('2.0e31', 31.301029995663981),
-('5.0e31', 31.698970004336019),
-('8.0e31', 31.903089986991944),
-('2.0e38', 38.301029995663981),
-('5.0e38', 38.698970004336019),
-('8.0e38', 38.903089986991944),
-('2.0e45', 45.30102999566398),
-('5.0e45', 45.69897000433602),
-('8.0e45', 45.90308998699194))
-SELECT x, bc_result, log(x::numeric), log(x::numeric)-bc_result AS diff FROM t;
-   x    |     bc_result      |        log         |       diff        
---------+--------------------+--------------------+-------------------
- 2.0e10 | 10.301029995663981 | 10.301029995663981 | 0.000000000000000
- 5.0e10 | 10.698970004336019 | 10.698970004336019 | 0.000000000000000
- 8.0e10 | 10.903089986991944 | 10.903089986991944 | 0.000000000000000
- 2.0e17 | 17.301029995663981 | 17.301029995663981 | 0.000000000000000
- 5.0e17 | 17.698970004336019 | 17.698970004336019 | 0.000000000000000
- 8.0e17 | 17.903089986991944 | 17.903089986991944 | 0.000000000000000
- 2.0e24 | 24.301029995663981 | 24.301029995663981 | 0.000000000000000
- 5.0e24 | 24.698970004336019 | 24.698970004336019 | 0.000000000000000
- 8.0e24 | 24.903089986991944 | 24.903089986991944 | 0.000000000000000
- 2.0e31 | 31.301029995663981 | 31.301029995663981 | 0.000000000000000
- 5.0e31 | 31.698970004336019 | 31.698970004336019 | 0.000000000000000
- 8.0e31 | 31.903089986991944 | 31.903089986991944 | 0.000000000000000
- 2.0e38 | 38.301029995663981 | 38.301029995663981 | 0.000000000000000
- 5.0e38 | 38.698970004336019 | 38.698970004336019 | 0.000000000000000
- 8.0e38 | 38.903089986991944 | 38.903089986991944 | 0.000000000000000
- 2.0e45 |  45.30102999566398 |  45.30102999566398 |  0.00000000000000
- 5.0e45 |  45.69897000433602 |  45.69897000433602 |  0.00000000000000
- 8.0e45 |  45.90308998699194 |  45.90308998699194 |  0.00000000000000
-(18 rows)
-
diff --git a/src/test/regress/sql/numeric_big.sql b/src/test/regress/sql/numeric_big.sql
deleted file mode 100644
index d67d9e88f9..0000000000
--- a/src/test/regress/sql/numeric_big.sql
+++ /dev/null
@@ -1,1366 +0,0 @@
--- ******************************
--- * Test suite for the Postgres NUMERIC data type
--- ******************************
-
--- Must drop tables created by short numeric test.
-DROP TABLE num_data;
-DROP TABLE num_exp_add;
-DROP TABLE num_exp_sub;
-DROP TABLE num_exp_div;
-DROP TABLE num_exp_mul;
-DROP TABLE num_exp_sqrt;
-DROP TABLE num_exp_ln;
-DROP TABLE num_exp_log10;
-DROP TABLE num_exp_power_10_ln;
-DROP TABLE num_result;
-
-CREATE TABLE num_data (id int4, val numeric(1000,800));
-CREATE TABLE num_exp_add (id1 int4, id2 int4, expected numeric(1000,800));
-CREATE TABLE num_exp_sub (id1 int4, id2 int4, expected numeric(1000,800));
-CREATE TABLE num_exp_div (id1 int4, id2 int4, expected numeric(1000,800));
-CREATE TABLE num_exp_mul (id1 int4, id2 int4, expected numeric(1000,800));
-CREATE TABLE num_exp_sqrt (id int4, expected numeric(1000,800));
-CREATE TABLE num_exp_ln (id int4, expected numeric(1000,800));
-CREATE TABLE num_exp_log10 (id int4, expected numeric(1000,800));
-CREATE TABLE num_exp_power_10_ln (id int4, expected numeric(1000,800));
-
-CREATE TABLE num_result (id1 int4, id2 int4, result numeric(1000,800));
-
-
--- ******************************
--- * The following EXPECTED results are computed by bc(1)
--- * with a scale of 1000
--- ******************************
-
-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,'85243.39540024977626076239847863600785982737155858270959890014613035727868293618673807776733416230953723818527101593495895350807775607346277892835514324320448949370623441059033804864158715021903312693889518990256881059434042443507529601095150710777634743301398926463888783847290873199395304998050753365215426971278237920063435565949203678024225270616295573678510929020831006146661747271783837653203039829647102027431761129518881525935216608429897041525858540380754759125150233053469999022855035');
-INSERT INTO num_exp_sub VALUES (0,1,'-85243.39540024977626076239847863600785982737155858270959890014613035727868293618673807776733416230953723818527101593495895350807775607346277892835514324320448949370623441059033804864158715021903312693889518990256881059434042443507529601095150710777634743301398926463888783847290873199395304998050753365215426971278237920063435565949203678024225270616295573678510929020831006146661747271783837653203039829647102027431761129518881525935216608429897041525858540380754759125150233053469999022855035');
-INSERT INTO num_exp_mul VALUES (0,1,'0');
-INSERT INTO num_exp_div VALUES (0,1,'0');
-INSERT INTO num_exp_add VALUES (0,2,'-994877526002806872754342148749241.04353023451866590387054959174736129501310680280823383331007646306243540953499740615246583399296334239109936336446284803020643582102868247857009494139535009572740621288230740389545481395');
-INSERT INTO num_exp_sub VALUES (0,2,'994877526002806872754342148749241.04353023451866590387054959174736129501310680280823383331007646306243540953499740615246583399296334239109936336446284803020643582102868247857009494139535009572740621288230740389545481395');
-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,'-60302029489319384367663884408085757480.2322712404088283093870869198708849258097125725036189625900174440196153781995220721511009855207486224837798752903681993777275846325950111427710563453217985216966456785944859989497422927661683538629473170704026975786513125842675604577233871570629808699803522400038975396500769162308448069085909755023233588510630417065084295051270219462289785473643946404281422516357503746700705970360169619852905053433235726497292406142332833');
-INSERT INTO num_exp_sub VALUES (0,3,'60302029489319384367663884408085757480.2322712404088283093870869198708849258097125725036189625900174440196153781995220721511009855207486224837798752903681993777275846325950111427710563453217985216966456785944859989497422927661683538629473170704026975786513125842675604577233871570629808699803522400038975396500769162308448069085909755023233588510630417065084295051270219462289785473643946404281422516357503746700705970360169619852905053433235726497292406142332833');
-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,'5329378275943663322215245.24931765987630429629836382184742348353920297283690739124220773955591340709935970062776650204659187764581615597720798385015942389765692769739983054442503547211560297249686289665792078548480268091496050883021187158502798880896590227542729659940394038802461081290690995869705131152889309663639310553909874081663091069118126221594338242710530718836025225507189149221049928936955230868771875644038572888630664890573507822342998964954667474300944699078658989010257103569231493090050659723450626338923049035040974032671138430612839043269997482582763267536489504794826476836323549796385028155416935072959933315468068930689064483178204550825728947252440604703474049780550458442808479096492346910001692358508618202898514895453589357');
-INSERT INTO num_exp_sub VALUES (0,4,'-5329378275943663322215245.24931765987630429629836382184742348353920297283690739124220773955591340709935970062776650204659187764581615597720798385015942389765692769739983054442503547211560297249686289665792078548480268091496050883021187158502798880896590227542729659940394038802461081290690995869705131152889309663639310553909874081663091069118126221594338242710530718836025225507189149221049928936955230868771875644038572888630664890573507822342998964954667474300944699078658989010257103569231493090050659723450626338923049035040974032671138430612839043269997482582763267536489504794826476836323549796385028155416935072959933315468068930689064483178204550825728947252440604703474049780550458442808479096492346910001692358508618202898514895453589357');
-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,'-652755630.43456071828048833552593835051449845484289562110789582081210403487973096161149072377955192388469356112505543620695003436531392789029513380101663750625024853263344909355177280161504414335005574882649025508632900995595004153086358670541462762210415346958050909878501048483523600711486406055424807840429541335391538322886495085448421556770991545781035298449067051916630343957356635391594362639819978677032855590055900561501350354631803808000307050416047072513406855040715556454205065332997338225626635780147287003130754254277103928406089109802521803537038957372612837169223905290912251006321930223154562110264217937');
-INSERT INTO num_exp_sub VALUES (0,5,'652755630.43456071828048833552593835051449845484289562110789582081210403487973096161149072377955192388469356112505543620695003436531392789029513380101663750625024853263344909355177280161504414335005574882649025508632900995595004153086358670541462762210415346958050909878501048483523600711486406055424807840429541335391538322886495085448421556770991545781035298449067051916630343957356635391594362639819978677032855590055900561501350354631803808000307050416047072513406855040715556454205065332997338225626635780147287003130754254277103928406089109802521803537038957372612837169223905290912251006321930223154562110264217937');
-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,'.0469370721950711508944806393077762204079964905145503836835397203739563036579760026190241480514409364');
-INSERT INTO num_exp_sub VALUES (0,6,'-.0469370721950711508944806393077762204079964905145503836835397203739563036579760026190241480514409364');
-INSERT INTO num_exp_mul VALUES (0,6,'0');
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-COMMIT TRANSACTION;
-BEGIN TRANSACTION;
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-COMMIT TRANSACTION;
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-INSERT INTO num_exp_log10 VALUES (3,'37.780331928743475574895606142114739140772838801045013007323050327909196792739138159615327729728110344767302636436234256468332011934881494997184865617793179255006442447189720642997935223133982347184994174261506212652322213673745795726283311685835974151422721233207287206894148660531800622455957268888702309499182978182878524951883775154983702898237404558813230370364953160102391101897560104513279410610948028599674950811462114131673380477843456965645417025376374320207504913806546872166094337441573669261285052323206348035827948287081776955945081345131570610652073053464020209215624179904586956137079321655773178387441622685682721151900601340680061607114354850640946256225260430676099781727317540719923791064452012925902993317349390523278687089530234444415688602090547516647302454865526291471706301790881694022223');
-INSERT INTO num_exp_log10 VALUES (4,'24.726676547286224970759328746582840552419566534667446425423046931401641497155587075591229106937829957279943690528061985864558314570189069764367933957499905044566413640017549478921384160584906257607957223101377816440084188042395098536074479064548620374152344954289432050971466476174493306432228880930006524504974367146536665170956555486181410864034862861231267121149652317599303804477688621597163730470970207231328339082779056152481480926452142005969020950341307977091850953883445808399574256295803245530993204179747743812544604144379381347499056545148243304041538981954204310612049423688645476667184129189153715486929216331980316967699254518020077226689317148303152585009031597809279387172427408557115400021035692880631275593381822805377317270568779655383061987766693697518921188619814204902583361096973421134004');
-INSERT INTO num_exp_log10 VALUES (5,'8.814750626578650238811431417807018895270298639823442501111235973209197727215795256506525221092818797578008152140054383421240180435087611869193019443372556081555311825248667278358330916098378127100899126895012782320751838528480712942601038190627182482614147263228588284866661508052724762701223357327343090598060805245853527435948381893458352744679795853650453594546267600486696643924152372736774331080527157374379043696696647158270918245668579680394279565181670004245143555617589138267976417280970718829942998800499312890580011246294669585429723974582350357991472101919333996770115834067969654217063942059882195268353998096891812525364797586486311202350700339609637274043915687880562465121559531284337603363356183320193656553931871200575467929714875483123706358278876389849119105053294688326141759401230994901405');
-INSERT INTO num_exp_log10 VALUES (6,'-1.328484003982869642690619298690906747763234110040562640557173509402512757735587333095924652711056556491908059708986413635120656426593745303715671199761364516107844087845783714418487426723538440387069985879601248897538855843115404484229652166941838283489828419407478748732927617251897244190697443966424660881366993754577233476597163021768156814527570512834684713730559883782625870597080940193303268818336816535968869931456641949301731046034660616615392129109391145214470757259042172416816936479713743188047425796931722546185493217275537303458837771965375448968719169174136287532752370175863826715450565025635651343928205805494319778539652563499901671319955144823432132740582617949774638538594081514904904341299199113721131520557004571803778698005652464301037962272085633628653321081368256925971558076970172779715');
-INSERT INTO num_exp_log10 VALUES (7,'17.913249188669140643510654105014358282516966474257460687880559542190804665566625978925406311113121982595279826214959603627387555578965653325278444455875162277940655989601428868642914577248262147833499137348602966573601719040813549936948178463592211685237720748377879836890106515699728652218324794927458352954247096536337594789471529493944292143186953509162522579060020018226817623648563806559917579317916242706559131476179714031602207057714677845347616752450567251644277767418397621490301286115159509360375419599968738067461569666699939732107480135216621373057421990702923042287910730395998082514702629760389192370666675364405730936537832803383367187639209534697198515928978064543150195911463663617683085348965065679311986715357338675515370634753254774665197233934933271954463040729779956682570415317734489164385');
-INSERT INTO num_exp_log10 VALUES (8,'9.929264914121995501917993119394933531225401243275938207624866270551448544301376913376130982251708700134720886862945040266148728213253651323129942781577143957084726727561987639140151337848818195806259935747329665025823709044567138449084349729747202164413995795609659711723455165142329822773177102845804114214340046404641970845707372809306219463962664551623665322610139794354769767829380018857313559373283673392337954610346290037758389035140213224696023751541663171574697035012610534455189013755134090933979479069288110010954211669067225249755249337768792642303351914884187159646984708862430789018895140670365476746734456807215043628059581947593694929159076346249490593187993386780521089745819640214783614157516171005086731241769146397577246387886107367648843380733370112546792442909347322732196805316614555689762');
-INSERT INTO num_exp_log10 VALUES (9,'7.739283354261751283625223433456284905560931805428759681411970457812279544250432389511382263439324085689734710188041049046660480575958686859942980599595036769090747781359217248301544587434077376812293034848418204834388504169166350770257248896025815531248627658465029806509131631454856186387892627989218208026727504548130018922325585619738185507999433763118148418722504204066578294826264005398891049629199412773138457218976050467479292777172717500219850781664314597312411301296201533610562886229900497272268364496763758868455934979903774531992886483396489868888731578355541611359130188566524240259770918423445785338175040098706500034487703124623745259139247432324145633151895802637182446905097253961951018926565652497920605819785424451050191604602898777804133717341512568151920576684198443843944721398831404081859');
-COMMIT TRANSACTION;
-BEGIN TRANSACTION;
-INSERT INTO num_exp_power_10_ln VALUES (0,'NaN');
-INSERT INTO num_exp_power_10_ln VALUES (1,'225561990715.277245515991117670624124484084762557459065170589803293759247930753528436379932442146759103295277479258327642314622036941865221478746258727236601688778946696303277607709407496616423493315166963938393760548678730128692212077086588682984700837334554241405763691119669847463520746595280034536307041368063462023793177898200220207765205127584303464304601759554817607633012272490650155253979182893585119965271975927569080191838676053084168631217591768468344106219831174026139608715965691941366334940196517120885214887008671956523579678156919416435031020452971977153991139145404842034138317592877675821045409772456977018293365238179815614004574330200783530118851005077771478448804470170641452481992602803877112958872108069738434946694089025321283178188028224338756015337492913115267362635647236447601252924834642796058');
-INSERT INTO num_exp_power_10_ln VALUES (2,'9553718264533556311125292459627965006385666643531070061102266984368939757379.536714147420215784125170401370065894858487440153494392538261078415409784085960333028254155527328359894197540839556987826344995348426293585457768226283066583722499658006242709930685932246087653832230889613022921575445199055131152661556678809191264086381976922223866204038615136758192929883317207903579770917317641181652055458721731297347443662717939116561947785705140374908203404860090658919334137955075887697259604047657534191202566335372150375993361370075961180728155127447781364264047857624746079509591666068708743260905728661917791822925979235918475633100283148558978385583805341715868143937062092264994833222352433299015979561976964779350640064096690062929265992966564232453102431600199173711947391200249130712039686700111791790265309426741120465259677894665532560198051256215915373145226284270408649736509');
-INSERT INTO num_exp_power_10_ln VALUES (3,'982718444846268846508445482774217796844461660819285525931206164100817251856409365450682.362683768066405322653747385034480250394145008573806022660379219602846285813744865438912887625784087005970975437905783802114553690522787857272953842288090141945268495451006273685577260054069522075046955466204804067271437138871789034722069934693546671607506851844248427950939791205412350536883779850165603116191193657054604569586553874805856647223849267039531773072343908345333155562072887754900969504551717514980465801806565999410206735831440712124661645970935112535081991606671600328471264697018198676317466846450405861359235297846597981143547119390922405594115478086038680663368675222949247096131378724350715530605691796680604309063173515781378545860473572389718345696107553363715518601596249508215455106779522851210398208919496668879040223859884166805448827948087400426315425231119801173387715922086154065273');
-INSERT INTO num_exp_power_10_ln VALUES (4,'861542720105376650266753999919217194383259935058507531116.774511336660822591851369622743235084609149542494189385785321912210129989390054947787009383210009523204976629456268332186620016067379702483800883493431423160815760933380418976582725913410929214462739708321325884209636272001805871036779154087677637129248122540412937033791526383240502286607736226090213753913654673523613612439527815137888202973659987501649474772884055648603290154867585312925699571949539600328906295652872654314913539778815035321695215634102441494403825526533235061083947035338872599854931230001361227174477274708230470794066733245241594719912710139298949856243576688344051439047966427547889756037265151798639614843866387316916203238068277912991427278268083231579195846744438643659745041780103653332041031419793815914447232121937821142169172566753399257291244398531365781832297786941359729799400');
-INSERT INTO num_exp_power_10_ln VALUES (5,'198021976607570296508.271597639984889464620426933601643322058775615235389194561064983706229795978402690473201671702614911129095149240715527556855309177671128442458698638704394974473956869419481315262823632891676087912529523219333012290621046361106033860210270638559271706082115529424772192777643046125905852037759566224116373416253787241195450409652089019290072319861181399387753223422998872180810295299831487867222464355713552301775702554189470264147325049133532522718679336524769566984150923939420759804463781082299907043016120177416779442865059261387111806785876531152192378576258351599534512031062777609734092707165605364139201322351960602280089186180302246827234844736393745487324460438448807241887783263546165171099497316415863122023114646876909575845860402164818094500541234974716577550807551946414081410743197768993152975501');
-INSERT INTO num_exp_power_10_ln VALUES (6,'.000873076977206566818052116526263730226812004454463281371489634779519089200224205946321120805055212090024554381349223642352209212670470260295303361873760972918129853308169576675500721645609379420329169271088810484607337679253503247351324049221970104335289487989027621978310506220905131150125321713385148268584530413680037620544212746920563790371941626294733473967065607791756894237438288480748407449237446113996117912144587258434808327522518688617394025018756570740098795745692805352377041347367240475846033282850136270250633825482156304826383360291164928049344226886150285595932088884965511963310715773499733217615863523253012606066583814112265708693122563204149232245895551314975524172504103194858904869273185785182598234060315036187756490539352752560361560286717869643902435677448962235275054804452967413005');
-INSERT INTO num_exp_power_10_ln VALUES (7,'176514565873872717825163931126806100435750.096278384530154766967061948052237623936423931849868926020451465515367348890410352640552194499619062823622476972850692557798609619250753020363520533767813563613425606228355802781302735485038377521515850536680425059519814786118919994914180918228654298075183514200191737597656810036850772127169441661576862538643715648802139886576391427423689320082366572297580054381937437005879583216745596935643579262248665490169331304003204939561361718554509909313409421397022626924406091551900222555950699170864234411017062042057683304265485826061096835531732950909546314722726990314852356462874701181085379772134121978510387397276859318242238150439474660772561390798432890789762504242822787017140808209820627435991445529404692793744568204608385843245177656436105160780897472099970336514833257055017279707999437302548655364559');
-INSERT INTO num_exp_power_10_ln VALUES (8,'72941951052009383458167.300747500436981484566111756088702608000390737594784514635592222758882092500858797317505303492923829092720870826490477962201959426813271424853341826896270963213736922458746003100613943600855942721319226948714369219316345322636075285343544788982588956431405042577296229122673590336976893594798942025893296105815818487227300314490440902574022885833779324177053242170024559675073866612316965636832258283516275906085642459351367507561963945012828379111856700009391438637054015804558386733558956649061672420804826896303889067785497738203077050774825608647969196321506624991188638449047860249367840775936911749905927108478444112230174584693363226143549933224252679398881354887872642908328737917862751077365602631600279486028043329404269490375935308156815477700961014566228692743960491745353377403533037122586797765130');
-INSERT INTO num_exp_power_10_ln VALUES (9,'661239032819374816.097553651299556484820492272269662685578275493609248662925676004753503494252951243895572437264999063878330704584509915845096232798927524470286655554736724913758600775591269525423912692080421094644542553026831758426157681271572808657664918053119324646138457659418857926209701677786068580819823633713337632456905824562235373422309621872998037966404189020165296080436871220718574009921789858751384547836431858428729570977259373272041837411903005303672798845573379758630607982213326716018594073712340609488043353995410508475153538231445235003980586600882223782814368245305160648543466496726973755388826656879616734762068443462618454921858705377028522664844761719759342490380417060255776725333319537746890406213693117052223545525717132695297770810635066731941724108167146710297146989770382041617889670713111888375717');
-COMMIT TRANSACTION;
-BEGIN TRANSACTION;
-INSERT INTO num_data VALUES (0, '0');
-INSERT INTO num_data VALUES (1, '85243.39540024977626076239847863600785982737155858270959890014613035727868293618673807776733416230953723818527101593495895350807775607346277892835514324320448949370623441059033804864158715021903312693889518990256881059434042443507529601095150710777634743301398926463888783847290873199395304998050753365215426971278237920063435565949203678024225270616295573678510929020831006146661747271783837653203039829647102027431761129518881525935216608429897041525858540380754759125150233053469999022855035');
-INSERT INTO num_data VALUES (2, '-994877526002806872754342148749241.04353023451866590387054959174736129501310680280823383331007646306243540953499740615246583399296334239109936336446284803020643582102868247857009494139535009572740621288230740389545481395');
-INSERT INTO num_data VALUES (3, '-60302029489319384367663884408085757480.2322712404088283093870869198708849258097125725036189625900174440196153781995220721511009855207486224837798752903681993777275846325950111427710563453217985216966456785944859989497422927661683538629473170704026975786513125842675604577233871570629808699803522400038975396500769162308448069085909755023233588510630417065084295051270219462289785473643946404281422516357503746700705970360169619852905053433235726497292406142332833');
-INSERT INTO num_data VALUES (4, '5329378275943663322215245.24931765987630429629836382184742348353920297283690739124220773955591340709935970062776650204659187764581615597720798385015942389765692769739983054442503547211560297249686289665792078548480268091496050883021187158502798880896590227542729659940394038802461081290690995869705131152889309663639310553909874081663091069118126221594338242710530718836025225507189149221049928936955230868771875644038572888630664890573507822342998964954667474300944699078658989010257103569231493090050659723450626338923049035040974032671138430612839043269997482582763267536489504794826476836323549796385028155416935072959933315468068930689064483178204550825728947252440604703474049780550458442808479096492346910001692358508618202898514895453589357');
-INSERT INTO num_data VALUES (5, '-652755630.43456071828048833552593835051449845484289562110789582081210403487973096161149072377955192388469356112505543620695003436531392789029513380101663750625024853263344909355177280161504414335005574882649025508632900995595004153086358670541462762210415346958050909878501048483523600711486406055424807840429541335391538322886495085448421556770991545781035298449067051916630343957356635391594362639819978677032855590055900561501350354631803808000307050416047072513406855040715556454205065332997338225626635780147287003130754254277103928406089109802521803537038957372612837169223905290912251006321930223154562110264217937');
-INSERT INTO num_data VALUES (6, '0.0469370721950711508944806393077762204079964905145503836835397203739563036579760026190241480514409364');
-INSERT INTO num_data VALUES (7, '-818934540071845742');
-INSERT INTO num_data VALUES (8, '8496986223.64063724353165506167988570717591150432282238795309964705925283285060558038824227595710139960766584401003765241409149793494330798800');
-INSERT INTO num_data VALUES (9, '054863480.34685027005508022756223282084742813020271603840941647350440860843570182437301045468670059279379903480024743452620396345637401505220786389930600883087012615993343976556472498552535317826554614696684732913955544753638726438705858481670766245958647367500212800073774509075408148134050353551558174813940258910304990570172170811882520915334358633');
-COMMIT TRANSACTION;
-
--- ******************************
--- * Create indices for faster checks
--- ******************************
-
-CREATE UNIQUE INDEX num_exp_add_idx ON num_exp_add (id1, id2);
-CREATE UNIQUE INDEX num_exp_sub_idx ON num_exp_sub (id1, id2);
-CREATE UNIQUE INDEX num_exp_div_idx ON num_exp_div (id1, id2);
-CREATE UNIQUE INDEX num_exp_mul_idx ON num_exp_mul (id1, id2);
-CREATE UNIQUE INDEX num_exp_sqrt_idx ON num_exp_sqrt (id);
-CREATE UNIQUE INDEX num_exp_ln_idx ON num_exp_ln (id);
-CREATE UNIQUE INDEX num_exp_log10_idx ON num_exp_log10 (id);
-CREATE UNIQUE INDEX num_exp_power_10_ln_idx ON num_exp_power_10_ln (id);
-
-VACUUM ANALYZE num_exp_add;
-VACUUM ANALYZE num_exp_sub;
-VACUUM ANALYZE num_exp_div;
-VACUUM ANALYZE num_exp_mul;
-VACUUM ANALYZE num_exp_sqrt;
-VACUUM ANALYZE num_exp_ln;
-VACUUM ANALYZE num_exp_log10;
-VACUUM ANALYZE num_exp_power_10_ln;
-
--- ******************************
--- * Now check the behaviour of the NUMERIC type
--- ******************************
-
--- ******************************
--- * Addition check
--- ******************************
-DELETE FROM num_result;
-INSERT INTO num_result SELECT t1.id, t2.id, t1.val + t2.val
-    FROM num_data t1, num_data t2;
-SELECT t1.id1, t1.id2, t1.result, t2.expected
-    FROM num_result t1, num_exp_add t2
-    WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
-    AND t1.result != t2.expected;
-
-DELETE FROM num_result;
-INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val + t2.val, 10)
-    FROM num_data t1, num_data t2;
-SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 10) as expected
-    FROM num_result t1, num_exp_add t2
-    WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
-    AND t1.result != round(t2.expected, 10);
-
--- ******************************
--- * Subtraction check
--- ******************************
-DELETE FROM num_result;
-INSERT INTO num_result SELECT t1.id, t2.id, t1.val - t2.val
-    FROM num_data t1, num_data t2;
-SELECT t1.id1, t1.id2, t1.result, t2.expected
-    FROM num_result t1, num_exp_sub t2
-    WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
-    AND t1.result != t2.expected;
-
-DELETE FROM num_result;
-INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val - t2.val, 40)
-    FROM num_data t1, num_data t2;
-SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 40)
-    FROM num_result t1, num_exp_sub t2
-    WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
-    AND t1.result != round(t2.expected, 40);
-
--- ******************************
--- * Multiply check
--- ******************************
-DELETE FROM num_result;
-INSERT INTO num_result SELECT t1.id, t2.id, t1.val * t2.val
-    FROM num_data t1, num_data t2;
-SELECT t1.id1, t1.id2, t1.result, t2.expected
-    FROM num_result t1, num_exp_mul t2
-    WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
-    AND t1.result != t2.expected;
-
-DELETE FROM num_result;
-INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val * t2.val, 30)
-    FROM num_data t1, num_data t2;
-SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 30) as expected
-    FROM num_result t1, num_exp_mul t2
-    WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
-    AND t1.result != round(t2.expected, 30);
-
--- ******************************
--- * Division check
--- ******************************
-DELETE FROM num_result;
-INSERT INTO num_result SELECT t1.id, t2.id, t1.val / t2.val
-    FROM num_data t1, num_data t2
-    WHERE t2.val != '0.0';
-SELECT t1.id1, t1.id2, t1.result, t2.expected
-    FROM num_result t1, num_exp_div t2
-    WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
-    AND t1.result != t2.expected;
-
-DELETE FROM num_result;
-INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val / t2.val, 80)
-    FROM num_data t1, num_data t2
-    WHERE t2.val != '0.0';
-SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 80) as expected
-    FROM num_result t1, num_exp_div t2
-    WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
-    AND t1.result != round(t2.expected, 80);
-
--- ******************************
--- * Square root check
--- ******************************
-DELETE FROM num_result;
-INSERT INTO num_result SELECT id, 0, SQRT(ABS(val))
-    FROM num_data;
-SELECT t1.id1, t1.result, t2.expected
-    FROM num_result t1, num_exp_sqrt t2
-    WHERE t1.id1 = t2.id
-    AND t1.result != t2.expected;
-
--- ******************************
--- * Natural logarithm check
--- ******************************
-DELETE FROM num_result;
-INSERT INTO num_result SELECT id, 0, LN(ABS(val))
-    FROM num_data
-    WHERE val != '0.0';
-SELECT t1.id1, t1.result, t2.expected
-    FROM num_result t1, num_exp_ln t2
-    WHERE t1.id1 = t2.id
-    AND t1.result != t2.expected;
-
--- ******************************
--- * Logarithm base 10 check
--- ******************************
-DELETE FROM num_result;
-INSERT INTO num_result SELECT id, 0, LOG('10'::numeric, 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;
-
--- ******************************
--- * POW(10, LN(value)) check
--- ******************************
-DELETE FROM num_result;
-INSERT INTO num_result SELECT id, 0, POW(numeric '10', LN(ABS(round(val,1000))))
-    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;
-
-
---
--- Test code path for raising to integer powers
---
-
--- base less than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of POW():
---
--- for p in {-20..20}
--- do
---   b="0.084738"
---   r=$(bc -ql <<< "scale=500 ; $b^$p" | head -n 1)
---   echo "($b, $p, $r),"
--- done
-
-WITH t(b, p, bc_result) AS (VALUES
-(0.084738, -20, 2744326694304960114888.785913),
-(0.084738, -19, 232548755422013710215.445941),
-(0.084738, -18, 19705716436950597776.236458),
-(0.084738, -17, 1669822999434319754.362725),
-(0.084738, -16, 141497461326065387.345189),
-(0.084738, -15, 11990211877848128.792857),
-(0.084738, -14, 1016026574105094.737649),
-(0.084738, -13, 86096059836517.517879),
-(0.084738, -12, 7295607918426.821430),
-(0.084738, -11, 618215223791.651994),
-(0.084738, -10, 52386321633.657007),
-(0.084738, -9, 4439112122.5928274),
-(0.084738, -8, 376161483.04427101),
-(0.084738, -7, 31875171.750205437),
-(0.084738, -6, 2701038.3037689083),
-(0.084738, -5, 228880.58378476975),
-(0.084738, -4, 19394.882908753819),
-(0.084738, -3, 1643.4835879219811),
-(0.084738, -2, 139.26551227333284),
-(0.084738, -1, 11.801080979017678),
-(0.084738, 0, 1),
-(0.084738, 1, .084738),
-(0.084738, 2, .007180528644),
-(0.084738, 3, .000608463636235272),
-(0.084738, 4, .00005155999160730448),
-(0.084738, 5, .000004369090568819767),
-(0.084738, 6, .0000003702279966206494),
-(0.084738, 7, .00000003137237997764059),
-(0.084738, 8, .000000002658432734545308),
-(0.084738, 9, .0000000002252702730599003),
-(0.084738, 10, .00000000001908895239854983),
-(0.084738, 11, .000000000001617559648348316),
-(0.084738, 12, .0000000000001370687694817396),
-(0.084738, 13, .00000000000001161493338834365),
-(0.084738, 14, .0000000000000009842262254614642),
-(0.084738, 15, .00000000000000008340136189315355),
-(0.084738, 16, .000000000000000007067264604102046),
-(0.084738, 17, .0000000000000000005988658680223991),
-(0.084738, 18, .00000000000000000005074669592448206),
-(0.084738, 19, .000000000000000000004300173519248761),
-(0.084738, 20, .0000000000000000000003643881036741015))
-SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
-
--- base greater than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of POW():
---
--- for p in {-20..20}
--- do
---   b="37.821637"
---   r=$(bc -ql <<< "scale=500 ; $b^$p" | head -n 1)
---   echo "($b, $p, $r),"
--- done
-
-WITH t(b, p, bc_result) AS (VALUES
-(37.821637, -20, .00000000000000000000000000000002787363175065101),
-(37.821637, -19, .000000000000000000000000000001054226381944797),
-(37.821637, -18, .00000000000000000000000000003987256753373947),
-(37.821637, -17, .000000000000000000000000001508045775519079),
-(37.821637, -16, .00000000000000000000000005703675990106610),
-(37.821637, -15, .000000000000000000000002157223628634278),
-(37.821637, -14, .00000000000000000000008158972901002847),
-(37.821637, -13, .000000000000000000003085857113545666),
-(37.821637, -12, .0000000000000000001167121675823920),
-(37.821637, -11, .000000000000000004414245235784397),
-(37.821637, -10, .0000000000000001669539809368169),
-(37.821637, -9, .000000000000006314472862697207),
-(37.821637, -8, .0000000000002388237004592846),
-(37.821637, -7, .000000000009032703305767796),
-(37.821637, -6, .0000000003416316255594496),
-(37.821637, -5, .00000001292106732962942),
-(37.821637, -4, .0000004886959181938034),
-(37.821637, -3, .00001848327962130773),
-(37.821637, -2, .0006990678924065984),
-(37.821637, -1, .02643989206495742),
-(37.821637, 0, 1),
-(37.821637, 1, 37.821637),
-(37.821637, 2, 1430.476225359769),
-(37.821637, 3, 54102.952532687378),
-(37.821637, 4, 2046262.2313195326),
-(37.821637, 5, 77392987.319777394),
-(37.821637, 6, 2927129472.7542235),
-(37.821637, 7, 110708828370.511632),
-(37.821637, 8, 4187189119324.792454),
-(37.821637, 9, 158366346921451.985294),
-(37.821637, 10, 5989674486279224.500736),
-(37.821637, 11, 226539294168214309.708325),
-(37.821637, 12, 8568086950266418559.993831),
-(37.821637, 13, 324059074417413536066.149409),
-(37.821637, 14, 12256444679171401239980.310926),
-(37.821637, 15, 463558801566202198479885.206986),
-(37.821637, 16, 17532552720991931019508170.100286),
-(37.821637, 17, 663109844696719094948877928.067252),
-(37.821637, 18, 25079899837245684700124994552.671731),
-(37.821637, 19, 948562867640665366544581398598.127577),
-(37.821637, 20, 35876200451584291931921101974730.690104))
-SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
-
---
--- Tests for raising to non-integer powers
---
-
--- base less than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of POW():
---
--- for n in {-20..20}
--- do
---   b="0.06933247"
---   p="$n.342987"
---   r=$(bc -ql <<< "scale=500 ; e($p*l($b))" | head -n 1)
---   echo "($b, $p, $r),"
--- done
-
-WITH t(b, p, bc_result) AS (VALUES
-(0.06933247, -20.342987, 379149253615977128356318.39406340),
-(0.06933247, -19.342987, 26287354251852125772450.59436685),
-(0.06933247, -18.342987, 1822567200045909954554.65766042),
-(0.06933247, -17.342987, 126363085720167050546.86216560),
-(0.06933247, -16.342987, 8761064849800910427.02880469),
-(0.06933247, -15.342987, 607426265866876128.15466179),
-(0.06933247, -14.342987, 42114363355427213.14899924),
-(0.06933247, -13.342987, 2919892833909256.59283660),
-(0.06933247, -12.342987, 202443382310228.51544515),
-(0.06933247, -11.342987, 14035899730722.44924025),
-(0.06933247, -10.342987, 973143597003.32229028),
-(0.06933247, -9.342987, 67470449244.92493259),
-(0.06933247, -8.342987, 4677892898.16028054),
-(0.06933247, -7.342987, 324329869.02491071),
-(0.06933247, -6.342987, 22486590.914273551),
-(0.06933247, -5.342987, 1559050.8899661435),
-(0.06933247, -4.342987, 108092.84905705095),
-(0.06933247, -3.342987, 7494.3442144625131),
-(0.06933247, -2.342987, 519.60139541889576),
-(0.06933247, -1.342987, 36.025248159838727),
-(0.06933247, 0.342987, .40036522320023350),
-(0.06933247, 1.342987, .02775830982657349),
-(0.06933247, 2.342987, .001924552183301612),
-(0.06933247, 3.342987, .0001334339565121935),
-(0.06933247, 4.342987, .000009251305786862961),
-(0.06933247, 5.342987, .0000006414158809285026),
-(0.06933247, 6.342987, .00000004447094732199898),
-(0.06933247, 7.342987, .000000003083280621074075),
-(0.06933247, 8.342987, .0000000002137714611621997),
-(0.06933247, 9.342987, .00000000001482130341788437),
-(0.06933247, 10.342987, .000000000001027597574581366),
-(0.06933247, 11.342987, .00000000000007124587801173530),
-(0.06933247, 12.342987, .000000000000004939652699872298),
-(0.06933247, 13.342987, .0000000000000003424783226243151),
-(0.06933247, 14.342987, .00000000000000002374486802900065),
-(0.06933247, 15.342987, .000000000000000001646290350274646),
-(0.06933247, 16.342987, .0000000000000000001141413763217064),
-(0.06933247, 17.342987, .000000000000000000007913703549583420),
-(0.06933247, 18.342987, .0000000000000000000005486766139403860),
-(0.06933247, 19.342987, .00000000000000000000003804110487572339),
-(0.06933247, 20.342987, .000000000000000000000002637483762562946))
-SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
-
--- base greater than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of POW():
---
--- for n in {-20..20}
--- do
---   b="27.234987"
---   p="$n.230957"
---   r=$(bc -ql <<< "scale=500 ; e($p*l($b))" | head -n 1)
---   echo "($b, $p, $r),"
--- done
-
-WITH t(b, p, bc_result) AS (VALUES
-(27.234987, -20.230957, .000000000000000000000000000009247064512095633),
-(27.234987, -19.230957, .0000000000000000000000000002518436817750859),
-(27.234987, -18.230957, .000000000000000000000000006858959399176602),
-(27.234987, -17.230957, .0000000000000000000000001868036700701026),
-(27.234987, -16.230957, .000000000000000000000005087595525911532),
-(27.234987, -15.230957, .0000000000000000000001385605980094587),
-(27.234987, -14.230957, .000000000000000000003773696085499835),
-(27.234987, -13.230957, .0000000000000000001027765638305389),
-(27.234987, -12.230957, .000000000000000002799118379829397),
-(27.234987, -11.230957, .00000000000000007623395268611469),
-(27.234987, -10.230957, .000000000000002076230710364949),
-(27.234987, -9.230957, .00000000000005654611640579014),
-(27.234987, -8.230957, .000000000001540032745212181),
-(27.234987, -7.230957, .00000000004194277179542807),
-(27.234987, -6.230957, .000000001142310844592450),
-(27.234987, -5.230957, .00000003111082100243440),
-(27.234987, -4.230957, .0000008473028055606278),
-(27.234987, -3.230957, .00002307628089450723),
-(27.234987, -2.230957, .0006284822101702527),
-(27.234987, -1.230957, .01711670482371810),
-(27.234987, 0.230957, 2.1451253063142300),
-(27.234987, 1.230957, 58.422459830839071),
-(27.234987, 2.230957, 1591.1349340009243),
-(27.234987, 3.230957, 43334.539242761031),
-(27.234987, 4.230957, 1180215.6129275865),
-(27.234987, 5.230957, 32143156.875279851),
-(27.234987, 6.230957, 875418459.63720737),
-(27.234987, 7.230957, 23842010367.779367),
-(27.234987, 8.230957, 649336842420.336290),
-(27.234987, 9.230957, 17684680461938.907402),
-(27.234987, 10.230957, 481642042480060.137900),
-(27.234987, 11.230957, 13117514765597885.614921),
-(27.234987, 12.230957, 357255344113366461.949871),
-(27.234987, 13.230957, 9729844652608062117.440722),
-(27.234987, 14.230957, 264992192625800087863.690528),
-(27.234987, 15.230957, 7217058921265161257566.469315),
-(27.234987, 16.230957, 196556505898890690402726.443417),
-(27.234987, 17.230957, 5353213882921711267539279.451015),
-(27.234987, 18.230957, 145794710509592328389185797.837767),
-(27.234987, 19.230957, 3970717045397510438979206144.696206),
-(27.234987, 20.230957, 108142427112079606637962972621.121293))
-SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
-
--- Inputs close to overflow
---
--- bc(1) results computed with a scale of 2700 and truncated to 4 decimal
--- places.
-
-WITH t(b, p, bc_result) AS (VALUES
-(0.12, -2829.8369, 58463948950011752465280493160293790845494328939320966633018493248607815580903065923369555885857984675501574162389726507612128133630191173383130639968378879506624785786843501848666498440326970769604109017960864573408272864266102690849952650095786874354625921641729880352858506454246180842452983243549491658464046163869265572232996388827878976066830374513768599285647145439771472435206769249126377164951470622827631950210853282324510655982757098065657709137845327135766013147354253426364240746381620690117663724329288646510198895137275207992825719846135857839292915100523542874885080351683587865157015032404901182924720371819942957083390475846809517968191151435281268695782594904484795360890092607679215675240583291240729468370895035823777914792823688291214492607109455017754453939895630226174304357121900605689015734289765672740769194115142607443713769825894380064727556869268488695795705030158832909348803019429370973064732712469794182891757241046263341655894972953512257981661670321890336672832647028099324621932563236459127918144141230217523147304565594514812518826936144181257723061181656522095236928347413997136815409159361412494284201481609684892562646522086577634100783077813105675590737823924220663206479031113753135119759722725207724879578900186075841393115040465401462266086907464970054073340036852442184414587772177753008511913377364966775792477387717262694468450099866775550614257191941835797445874557362115814601886902749237439492398087966544817154173072811937702110580330775581851211123491341435883319798273456296794954514173820352334127081705706502510709179711510240917772628308487366740741280043704807717608366220401933596364641284631036907635403895053036499618723044314773148779735006542501244942039455169872946018271985844759209768927953340447524637670938413827595013338859796135512187473850161303598087634723542727044978083220970836296653305188470017342167913572166172051819741354902582606590658382067039498769674611071582171914886494269818475850690414812481252963932223686078322390396586222238852602472958831686564971334200490182175112490433364675164900946902818404704835106260174052265784055642968397240262737313737007322288203637798365320295080314524864099419556398713380156353062937736280885716820226469419928595465390700629307079710611273715705695938635644841913194091407807776191951797748706106000922803167645881087385311847268311361092838264814899353459146959869764278464187826798546290981492648723002412475976344071283321798061003719251864595518596639432393032991023409676558943539937377229130132816883146259468718344018277257037013406135980469482324577407154032999045733141275895.3432),
-(1.2, 32908.8896, 58463467728170833376633133695001863276259293590926929026251227859007891876739460057725441400966420577009060860805883032969522911803372870882799865787473726926215148161529632590083389287080925059682489116446754279752928005457087175157581627230586554364417068189211136840990661174760199073702207450133797324318403866058202372178813998850887986769280847189341565507156189065295823921162851958925352114220880236114784962150135485415106748467247897246441194126125699204912883449386043559785865023459356275014504597646990160571664166410683323036984805434677654413174177920726210827006973855410386789516533036723888687725436216478665958434776205940192130053647653715221076841771578099896259902368829351569726536927952661429685419815305418450230567773264738536471211804481206474781470237730069753206249915908804615495060673071058534441654604668770343616386612119048579369195201590008082689834456232255266932976831478404670192731621439902738547169253818323045451045749609624500171633897705543164388470746657118050314064066768449450440405619135824055131398727045420324382226572368236570500391463795989258779677208133531636928003546809249007993065200108076924439703799231711400266122025052209803513232429907231051873161206025860851056337427740362763618748092029386371493898291580557004812947013231371383576580415676519066503391905962989205397824064923920045371823949776899815750413244195402085917098964452866825666226141169411712884994564949174271056284898570445214367063763956186792886147126466387576513166370247576466566827375268334148320298849218878848928271566491769458471357076035396330179659440244425914213309776100351793665960978678576150833311810944729586040624059867137538839913141142139636023129691775489034134511666020819676247950267220131499463010350308195762769192775344260909521732256844149916046793599150786757764962585268686580124987490115873389726527572428003433405659445349155536369077209682951123806333170190998931670309088422483075609203671527331975811507450670132060984691061148836994322505371265263690017938762760088575875666254883673433331627055180154954694693433502522592907190906966067656027637884202418119121728966267936832338377284832958974299187166554160783467156478554899314000348357280306042140481751668215838656488457943830180819301102535170705017482946779698265096226184239631924271857062033454725540956591929965181603262502135610768915716020374362368495244256420143645126927013882334008435586481691725030031204304273292938132599127402133470745819213047706793887965197191137237066440328777206799072470374264316425913530947082957300047105685634407092811630672103242089966046839626911122.7149))
-SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
-
---
--- Tests for EXP()
---
-
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of EXP():
---
--- for n in {-20..20}
--- do
---   x="$n.29837"
---   r=$(bc -ql <<< "scale=500 ; e($x)" | head -n 1)
---   echo "($x, $r),"
--- done
-
-WITH t(x, bc_result) AS (VALUES
-(-20.29837, .000000001529431101152222),
-(-19.29837, .000000004157424770142192),
-(-18.29837, .00000001130105220586304),
-(-17.29837, .00000003071944485366452),
-(-16.29837, .00000008350410872606600),
-(-15.29837, .0000002269877013517336),
-(-14.29837, .0000006170165438681061),
-(-13.29837, .000001677224859055276),
-(-12.29837, .000004559169856609741),
-(-11.29837, .00001239310857408049),
-(-10.29837, .00003368796183504298),
-(-9.29837, .00009157337449401917),
-(-8.29837, .0002489222398577673),
-(-7.29837, .0006766408013046928),
-(-6.29837, .001839300394580514),
-(-5.29837, .004999736839665763),
-(-4.29837, .01359069379834070),
-(-3.29837, .03694333598818056),
-(-2.29837, .1004223988993283),
-(-1.29837, .2729763820983097),
-(0.29837, 1.3476603299656679),
-(1.29837, 3.6633205858807959),
-(2.29837, 9.9579377804197108),
-(3.29837, 27.068481317440698),
-(4.29837, 73.579760889182206),
-(5.29837, 200.01052696742555),
-(6.29837, 543.68498095607070),
-(7.29837, 1477.8890041389891),
-(8.29837, 4017.3188244304487),
-(9.29837, 10920.204759575742),
-(10.29837, 29684.194161006717),
-(11.29837, 80690.005580314652),
-(12.29837, 219338.17590722828),
-(13.29837, 596222.97785597218),
-(14.29837, 1620702.0864156289),
-(15.29837, 4405525.0308492653),
-(16.29837, 11975458.636179032),
-(17.29837, 32552671.598188404),
-(18.29837, 88487335.673150406),
-(19.29837, 240533516.60908059),
-(20.29837, 653837887.33381570))
-SELECT x, bc_result, exp(x), exp(x)-bc_result AS diff FROM t;
-
---
--- Tests for LN()
---
-
--- input very small
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40}
--- do
---   l=$(bc -ql <<< "scale=500 ; l(10^-$p)" | head -n 1)
---   echo "('1.0e-$p', $l),"
--- done
-
-WITH t(x, bc_result) AS (VALUES
-('1.0e-1', -2.3025850929940457),
-('1.0e-2', -4.6051701859880914),
-('1.0e-3', -6.9077552789821371),
-('1.0e-4', -9.2103403719761827),
-('1.0e-5', -11.512925464970228),
-('1.0e-6', -13.815510557964274),
-('1.0e-7', -16.118095650958320),
-('1.0e-8', -18.420680743952365),
-('1.0e-9', -20.723265836946411),
-('1.0e-10', -23.025850929940457),
-('1.0e-11', -25.328436022934503),
-('1.0e-12', -27.631021115928548),
-('1.0e-13', -29.933606208922594),
-('1.0e-14', -32.236191301916640),
-('1.0e-15', -34.5387763949106853),
-('1.0e-16', -36.84136148790473094),
-('1.0e-17', -39.143946580898776628),
-('1.0e-18', -41.4465316738928223123),
-('1.0e-19', -43.74911676688686799634),
-('1.0e-20', -46.051701859880913680360),
-('1.0e-21', -48.3542869528749593643778),
-('1.0e-22', -50.65687204586900504839581),
-('1.0e-23', -52.959457138863050732413803),
-('1.0e-24', -55.2620422318570964164317949),
-('1.0e-25', -57.56462732485114210044978637),
-('1.0e-26', -59.867212417845187784467777822),
-('1.0e-27', -62.1697975108392334684857692765),
-('1.0e-28', -64.47238260383327915250376073116),
-('1.0e-29', -66.774967696827324836521752185847),
-('1.0e-30', -69.0775527898213705205397436405309),
-('1.0e-31', -71.38013788281541620455773509521529),
-('1.0e-32', -73.682722975809461888575726549899655),
-('1.0e-33', -75.9853080688035075725937180045840189),
-('1.0e-34', -78.28789316179755325661170945926838306),
-('1.0e-35', -80.590478254791598940629700913952747266),
-('1.0e-36', -82.8930633477856446246476923686371114736),
-('1.0e-37', -85.19564844077969030866568382332147568124),
-('1.0e-38', -87.498233533773735992683675278005839888842),
-('1.0e-39', -89.8008186267677816767016667326902040964430),
-('1.0e-40', -92.10340371976182736071965818737456830404406))
-SELECT x, bc_result, ln(x::numeric), ln(x::numeric)-bc_result AS diff FROM t;
-
--- input very close to but smaller than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40}
--- do
---   l=$(bc -ql <<< "scale=500 ; l(1-10^-$p)" | head -n 1)
---   echo "('1.0e-$p', $l),"
--- done
-
-WITH t(x, bc_result) AS (VALUES
-('1.0e-1', -.10536051565782630),
-('1.0e-2', -.010050335853501441),
-('1.0e-3', -.0010005003335835335),
-('1.0e-4', -.00010000500033335834),
-('1.0e-5', -.000010000050000333336),
-('1.0e-6', -.0000010000005000003333),
-('1.0e-7', -.00000010000000500000033),
-('1.0e-8', -.000000010000000050000000),
-('1.0e-9', -.0000000010000000005000000),
-('1.0e-10', -.00000000010000000000500000),
-('1.0e-11', -.000000000010000000000050000),
-('1.0e-12', -.0000000000010000000000005000),
-('1.0e-13', -.00000000000010000000000000500),
-('1.0e-14', -.000000000000010000000000000050),
-('1.0e-15', -.0000000000000010000000000000005),
-('1.0e-16', -.00000000000000010000000000000001),
-('1.0e-17', -.000000000000000010000000000000000),
-('1.0e-18', -.0000000000000000010000000000000000),
-('1.0e-19', -.00000000000000000010000000000000000),
-('1.0e-20', -.000000000000000000010000000000000000),
-('1.0e-21', -.0000000000000000000010000000000000000),
-('1.0e-22', -.00000000000000000000010000000000000000),
-('1.0e-23', -.000000000000000000000010000000000000000),
-('1.0e-24', -.0000000000000000000000010000000000000000),
-('1.0e-25', -.00000000000000000000000010000000000000000),
-('1.0e-26', -.000000000000000000000000010000000000000000),
-('1.0e-27', -.0000000000000000000000000010000000000000000),
-('1.0e-28', -.00000000000000000000000000010000000000000000),
-('1.0e-29', -.000000000000000000000000000010000000000000000),
-('1.0e-30', -.0000000000000000000000000000010000000000000000),
-('1.0e-31', -.00000000000000000000000000000010000000000000000),
-('1.0e-32', -.000000000000000000000000000000010000000000000000),
-('1.0e-33', -.0000000000000000000000000000000010000000000000000),
-('1.0e-34', -.00000000000000000000000000000000010000000000000000),
-('1.0e-35', -.000000000000000000000000000000000010000000000000000),
-('1.0e-36', -.0000000000000000000000000000000000010000000000000000),
-('1.0e-37', -.00000000000000000000000000000000000010000000000000000),
-('1.0e-38', -.000000000000000000000000000000000000010000000000000000),
-('1.0e-39', -.0000000000000000000000000000000000000010000000000000000),
-('1.0e-40', -.00000000000000000000000000000000000000010000000000000000))
-SELECT '1-'||x, bc_result, ln(1.0-x::numeric), ln(1.0-x::numeric)-bc_result AS diff FROM t;
-
--- input very close to but larger than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40}
--- do
---   l=$(bc -ql <<< "scale=500 ; l(1+10^-$p)" | head -n 1)
---   echo "('1.0e-$p', $l),"
--- done
-
-WITH t(x, bc_result) AS (VALUES
-('1.0e-1', .09531017980432486),
-('1.0e-2', .009950330853168083),
-('1.0e-3', .0009995003330835332),
-('1.0e-4', .00009999500033330834),
-('1.0e-5', .000009999950000333331),
-('1.0e-6', .0000009999995000003333),
-('1.0e-7', .00000009999999500000033),
-('1.0e-8', .000000009999999950000000),
-('1.0e-9', .0000000009999999995000000),
-('1.0e-10', .00000000009999999999500000),
-('1.0e-11', .000000000009999999999950000),
-('1.0e-12', .0000000000009999999999995000),
-('1.0e-13', .00000000000009999999999999500),
-('1.0e-14', .000000000000009999999999999950),
-('1.0e-15', .0000000000000009999999999999995),
-('1.0e-16', .00000000000000010000000000000000),
-('1.0e-17', .000000000000000010000000000000000),
-('1.0e-18', .0000000000000000010000000000000000),
-('1.0e-19', .00000000000000000010000000000000000),
-('1.0e-20', .000000000000000000010000000000000000),
-('1.0e-21', .0000000000000000000010000000000000000),
-('1.0e-22', .00000000000000000000010000000000000000),
-('1.0e-23', .000000000000000000000010000000000000000),
-('1.0e-24', .0000000000000000000000010000000000000000),
-('1.0e-25', .00000000000000000000000010000000000000000),
-('1.0e-26', .000000000000000000000000010000000000000000),
-('1.0e-27', .0000000000000000000000000010000000000000000),
-('1.0e-28', .00000000000000000000000000010000000000000000),
-('1.0e-29', .000000000000000000000000000010000000000000000),
-('1.0e-30', .0000000000000000000000000000010000000000000000),
-('1.0e-31', .00000000000000000000000000000010000000000000000),
-('1.0e-32', .000000000000000000000000000000010000000000000000),
-('1.0e-33', .0000000000000000000000000000000010000000000000000),
-('1.0e-34', .00000000000000000000000000000000010000000000000000),
-('1.0e-35', .000000000000000000000000000000000010000000000000000),
-('1.0e-36', .0000000000000000000000000000000000010000000000000000),
-('1.0e-37', .00000000000000000000000000000000000010000000000000000),
-('1.0e-38', .000000000000000000000000000000000000010000000000000000),
-('1.0e-39', .0000000000000000000000000000000000000010000000000000000),
-('1.0e-40', .00000000000000000000000000000000000000010000000000000000))
-SELECT '1+'||x, bc_result, ln(1.0+x::numeric), ln(1.0+x::numeric)-bc_result AS diff FROM t;
-
--- input very large
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40}
--- do
---   l=$(bc -ql <<< "scale=500 ; l(10^$p)" | head -n 1)
---   echo "('1.0e$p', $l),"
--- done
-
-WITH t(x, bc_result) AS (VALUES
-('1.0e1', 2.3025850929940457),
-('1.0e2', 4.6051701859880914),
-('1.0e3', 6.9077552789821371),
-('1.0e4', 9.2103403719761827),
-('1.0e5', 11.512925464970228),
-('1.0e6', 13.815510557964274),
-('1.0e7', 16.118095650958320),
-('1.0e8', 18.420680743952365),
-('1.0e9', 20.723265836946411),
-('1.0e10', 23.025850929940457),
-('1.0e11', 25.328436022934503),
-('1.0e12', 27.631021115928548),
-('1.0e13', 29.933606208922594),
-('1.0e14', 32.236191301916640),
-('1.0e15', 34.538776394910685),
-('1.0e16', 36.841361487904731),
-('1.0e17', 39.143946580898777),
-('1.0e18', 41.446531673892822),
-('1.0e19', 43.749116766886868),
-('1.0e20', 46.051701859880914),
-('1.0e21', 48.354286952874959),
-('1.0e22', 50.656872045869005),
-('1.0e23', 52.959457138863051),
-('1.0e24', 55.262042231857096),
-('1.0e25', 57.564627324851142),
-('1.0e26', 59.867212417845188),
-('1.0e27', 62.169797510839233),
-('1.0e28', 64.472382603833279),
-('1.0e29', 66.774967696827325),
-('1.0e30', 69.077552789821371),
-('1.0e31', 71.380137882815416),
-('1.0e32', 73.682722975809462),
-('1.0e33', 75.985308068803508),
-('1.0e34', 78.287893161797553),
-('1.0e35', 80.590478254791599),
-('1.0e36', 82.893063347785645),
-('1.0e37', 85.195648440779690),
-('1.0e38', 87.498233533773736),
-('1.0e39', 89.800818626767782),
-('1.0e40', 92.103403719761827))
-SELECT x, bc_result, ln(x::numeric), ln(x::numeric)-bc_result AS diff FROM t;
-
--- input huge
---
--- bc(1) results computed with a scale of 1000 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..10}
--- do
---   l=$(bc -ql <<< "scale=1000 ; l(10^${p}00)" | head -n 1)
---  echo "('1.0e${p}00', $l),"
--- done
-
-WITH t(x, bc_result) AS (VALUES
-('1.0e100', 230.25850929940457),
-('1.0e200', 460.51701859880914),
-('1.0e300', 690.77552789821371),
-('1.0e400', 921.03403719761827),
-('1.0e500', 1151.2925464970228),
-('1.0e600', 1381.5510557964274),
-('1.0e700', 1611.8095650958320),
-('1.0e800', 1842.0680743952365),
-('1.0e900', 2072.3265836946411),
-('1.0e1000', 2302.5850929940457))
-SELECT x, bc_result, ln(x::numeric), ln(x::numeric)-bc_result AS diff FROM t;
-
--- inputs with 1000 decimal places
---
--- bc(1) results computed with a scale of 2000 and rounded to 1000 decimal
--- places
-
-WITH t(x, bc_result) AS (VALUES
-(484990182159328900690402236933516249572671683638747490717351807610531884491845416923860371219625151551889257298200816555016472471293780254009492949585031653913930735918829139712249577547959394351523545901788627247613322896296041868431769047433229466634098452564756860190085118463828382895145244362033728480588969626012192733802377468089120757046364393407262957242230928854711898925295251902007136232994524624903257456111389508582206404271734668422903183500589303866613158037169610592539145461637447957948521714058034772237111009429638870236361143304703683377693378577075353794118557951847394763531830696578809001981568860219578880229402696449243344235099860421846016326538272155937175661905904288335499593232232926636205909086901191153907183842087577811871344870731324067822883041265129394268082883745408414994.8967939438561591657171240282983703914075472645212002662497023142663831371447287624846942598424990784971781730103682951722370983277124599054059027055336437808366784501932987082321905202623642371063626378290734289114618092750984153422293450048717769065428713836637664433167768445609659527458911187829232316677137895259433038764404970599325009178297626038331436654541552998098529141205301472138026818453893127265938030066392881979113522757891639646670670272542401773230506961559808927249585675430838495658225557294666522469887436551840596777627408780618586500922973500018513068499587683746133637919751545157547095670767246977244726331271787622126889459658539988980096764323712767863722912919120929339399753431689512753214200090670880647731689804555417871258907716687575767185444541243606329768784843125926070743277339790277626515824924290352180761378846035233155198504033292692893297993698953705472933411199778880561376633444249703838589180474329586470353212010427945060694794274109764269805332803290229,
- 1864.3702986939570026328504202935192533137907736189919154633800554877738455118081651650863235106905871352085850240570561347180517240105510505203972860921397909573687877993477806728098306202020229409548306695695574102950949468160529713610952021974630774784174851619325758380143625473386495586347322798415543385655090746985183329114860118551572428921774322172798724455202876781611633419444058398798142214904998877857425038669920064728855823072107227506485770367799671977282350083029452784747350395161797215115525867416898416360638482342253129160308632504217096916335590470843180746834864303790913372081974355613359678634194879425862536147988835528973291020680020540866655622823550861337486588647231688134992810403147262346312159819432914207194632564009749236609081399504118359354620598232725290537215007867979331582119891661859015726276335168158288396939655310210558566592649049602925182137256134162660116182293851038854455437841571331011002023088829768308520393956515509475418031437505751407687618234418262),
-(87190145885430429849953615409019208993240447426362428988181639909267773304254748257120061524000254226856815085523676417146197197996896030672521334101413071112068202429835905642444187493717977611730127126387257253646790849384975208460867137315507010888782632024640844766297185244443116696943912406389670302370461137850160539373600494054874979342373255280815156048999900951842673141766630630919020492255966628630634124452614590400422133958133100159154995520080124736657520969784129924799670552560034302960877087853678350801769339861812435411200669026902417951572668727488315537985378304242438181615160041688723201917323705450185975141141262578884689500612295576288125956289035673242989906973367691922065122033180281670221390667818909912035903387888639331486823729897326624516015340.0330856710565117793999512551468220085711713631167607285185762046751452975325645379302403715842570486302993296501788672462090620871511446272026693318239212657949496275318383141403236705902077406660768573015707706831878445598837931116223956945944726162551477136715847593742032488181481888084716920605114101902724395659898621880016853548602514706686907951229872573180602614761229992106144727082722940736406782659562775289407005631298246624198606031298081220736931229256511054595028182057216042683060059115371651410352645266000330509331097811566633211452233019461903115970558624057877018778178814946285827512359903934291318219271464841957435711594154280905473802599888081783098187210283997106131616471807951265003903143099667366508222327805543948921694362089860577380749774036318574113007382111997454202845559941557812813566442364810680529092880773126707073967537693927177460459341763934709686530005721141046645111784404932103241501569571235364365556796422998363930810983452790309019295181282099408260156,
- 1793.5767085750017553306932533574391150814202249805881581227430032600579405884415934520704053351781361105595296647510475380766428668443641914861849764330704062323054023252886955844207807229267936432730818329225450152491146839618683772020068682795388746108876393249306737841247788224204701299467519965182171772253974884845661168860422489046657965359832930382114760565628765599962013955588754803194908990025689040598990346417563277021386852342928910383706995866844541160576254266641602065102228267316550706943783591722246885978355472097314691737807509436806788803362444745551013400341861820755594413819894154786253014501454443272120342005711761286524843010157182464200556865694401941794983935172457481497909987740544409272349152397774548604845897687504977786762391359552407068124283290504752932824699865504970420939586707791994870941813718246825616335675307740641350673558328821461530563823677144691877374809441673507467507447891562257806191361453045937798278733402269265623588493124129181374135958668436774),
-(93936642222690597390233191619858485419795942047468396309991947772747208870873993801669373075421461116465960407843923269693395211616591453397070258466704654943689268224479477016161636938138334729982904232438440955361656138189836032891825113139184685132178764873033678116450665758561650355252211196676137179184043639278410827092182700922151290703747496962700158844772453483316974221113826173404445159281421213715669245417896170368554410830320000019029956317336703559699859949692222685614036912057150632902650913831404804982509990655560731349634628713944739168096272097122388116038119844786988276635032016787352796502360718569977397214936366251320294621522016.6483354941025384161536675750898007896744690911429670830432784905421638721478353275821072200938900938046264210604940707974410950770029535636602548377806284157951164875821446035013896786653932045182167021839184824627082391478016195098055107001433336586881395912782883663046617432598969149948351689103230162742769845955320418573803127107923535948653168889411316007796459064267436246637115946581149511513369842911210359447262641996566147462977170742544980481275049898092152042927981394239266559286915303786701737610786594006685748456635797125029722684151298695274097006242412384086302106763844070230264910503179385988626477852818174114043927841085089058972074427820150462261941575665882880501074676800316585217150509780489224388148722603385921057007086785238310735038314861960410473809826927329368597558806004392175746233568789445929554890241140656324160187253042639339549705859147930476532359840809944163908006480881926041259363654863689570520534301207043189181147254153307163555433328278834311658232337,
- 1510.4332713542154696529645934345554302578243896764921637693542962119938599884313210100957753316832762996428481801312323020427109678979117469716796746760060470871840325255146954580681101106876674367471955788143763250819168311353856748872452260808797135108102729064040463343792765872545182299889360257515315869180266759715933989413256377582681707188367254513700731642913479683031478361835565783219287780434673712341147656477670848734998849030451414278832848680301511646182446524915091598080243532068451726548537866633622180283865668708517173065893429240665300584705585310049892047293928733753369421499719516009692095913169665213597158441636480707309244604139865130782756488091268094213446272360006907802989573582755585110277620911226015342778471352130366770729972784317323917141031824334355639769512749560550167491709646539950725523461943580211843652293561678342656010571108219244870234329176123205423872844099992204896411752620881541000940129833754169391528449211839693800724450201835161044717173715867437))
-SELECT trim_scale(ln(x::numeric)-bc_result) AS diff FROM t;
-
---
--- Tests for LOG() (base 10)
---
-
--- input very small, exact result known
-WITH t(x) AS (SELECT '1e-'||n FROM generate_series(1, 100) g(n))
-SELECT x, log(x::numeric) FROM t;
-
--- input very small, non-exact results
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..50..7}
--- do
---   for d in {9..1..3}
---   do
---     l=$(bc -ql <<< "scale=500 ; l($d*10^-$p) / l(10)" | head -n 1)
---     echo "('${d}.0e-$p', $l),"
---   done
--- done
-
-WITH t(x, bc_result) AS (VALUES
-('9.0e-1', -.04575749056067513),
-('6.0e-1', -.2218487496163564),
-('3.0e-1', -.5228787452803376),
-('9.0e-8', -7.045757490560675),
-('6.0e-8', -7.221848749616356),
-('3.0e-8', -7.522878745280338),
-('9.0e-15', -14.0457574905606751),
-('6.0e-15', -14.2218487496163564),
-('3.0e-15', -14.5228787452803376),
-('9.0e-22', -21.04575749056067512540994),
-('6.0e-22', -21.22184874961635636749123),
-('3.0e-22', -21.52287874528033756270497),
-('9.0e-29', -28.045757490560675125409944193490),
-('6.0e-29', -28.221848749616356367491233202020),
-('3.0e-29', -28.522878745280337562704972096745),
-('9.0e-36', -35.0457574905606751254099441934897693816),
-('6.0e-36', -35.2218487496163563674912332020203916640),
-('3.0e-36', -35.5228787452803375627049720967448846908),
-('9.0e-43', -42.04575749056067512540994419348976938159974227),
-('6.0e-43', -42.22184874961635636749123320202039166403168125),
-('3.0e-43', -42.52287874528033756270497209674488469079987114),
-('9.0e-50', -49.045757490560675125409944193489769381599742271618608),
-('6.0e-50', -49.221848749616356367491233202020391664031681254347196),
-('3.0e-50', -49.522878745280337562704972096744884690799871135809304))
-SELECT x, bc_result, log(x::numeric), log(x::numeric)-bc_result AS diff FROM t;
-
--- input very close to but smaller than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40..7}
--- do
---   for d in {9..1..3}
---   do
---     l=$(bc -ql <<< "scale=500 ; l(1-$d*10^-$p) / l(10)" | head -n 1)
---     echo "('${d}.0e-$p', $l),"
---   done
--- done
-
-WITH t(x, bc_result) AS (VALUES
-('9.0e-1', -1.0000000000000000),
-('6.0e-1', -.3979400086720376),
-('3.0e-1', -.1549019599857432),
-('9.0e-8', -.000000039086505130185422),
-('6.0e-8', -.000000026057669695925208),
-('3.0e-8', -.000000013028834652530076),
-('9.0e-15', -.0000000000000039086503371292840),
-('6.0e-15', -.0000000000000026057668914195188),
-('3.0e-15', -.0000000000000013028834457097574),
-('9.0e-22', -.00000000000000000000039086503371292664),
-('6.0e-22', -.00000000000000000000026057668914195110),
-('3.0e-22', -.00000000000000000000013028834457097555),
-('9.0e-29', -.000000000000000000000000000039086503371292664),
-('6.0e-29', -.000000000000000000000000000026057668914195110),
-('3.0e-29', -.000000000000000000000000000013028834457097555),
-('9.0e-36', -.0000000000000000000000000000000000039086503371292664),
-('6.0e-36', -.0000000000000000000000000000000000026057668914195110),
-('3.0e-36', -.0000000000000000000000000000000000013028834457097555))
-SELECT '1-'||x, bc_result, log(1.0-x::numeric), log(1.0-x::numeric)-bc_result AS diff FROM t;
-
--- input very close to but larger than 1
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {1..40..7}
--- do
---   for d in {9..1..3}
---   do
---     l=$(bc -ql <<< "scale=500 ; l(1+$d*10^-$p) / l(10)" | head -n 1)
---     echo "('${d}.0e-$p', $l),"
---   done
--- done
-
-WITH t(x, bc_result) AS (VALUES
-('9.0e-1', .2787536009528290),
-('6.0e-1', .2041199826559248),
-('3.0e-1', .1139433523068368),
-('9.0e-8', .000000039086501612400118),
-('6.0e-8', .000000026057668132465074),
-('3.0e-8', .000000013028834261665042),
-('9.0e-15', .0000000000000039086503371292489),
-('6.0e-15', .0000000000000026057668914195031),
-('3.0e-15', .0000000000000013028834457097535),
-('9.0e-22', .00000000000000000000039086503371292664),
-('6.0e-22', .00000000000000000000026057668914195110),
-('3.0e-22', .00000000000000000000013028834457097555),
-('9.0e-29', .000000000000000000000000000039086503371292664),
-('6.0e-29', .000000000000000000000000000026057668914195110),
-('3.0e-29', .000000000000000000000000000013028834457097555),
-('9.0e-36', .0000000000000000000000000000000000039086503371292664),
-('6.0e-36', .0000000000000000000000000000000000026057668914195110),
-('3.0e-36', .0000000000000000000000000000000000013028834457097555))
-SELECT '1+'||x, bc_result, log(1.0+x::numeric), log(1.0+x::numeric)-bc_result AS diff FROM t;
-
--- input very large, exact result known
-WITH t(x) AS (SELECT '1e'||n FROM generate_series(1, 100) g(n))
-SELECT x, log(x::numeric) FROM t;
-
--- input very large, non-exact results
---
--- bc(1) results computed with a scale of 500 and truncated using the script
--- below, and then rounded by hand to match the precision of LN():
---
--- for p in {10..50..7}
---   do
---   for d in {2..9..3}
---   do
---     l=$(bc -ql <<< "scale=500 ; l($d*10^$p) / l(10)" | head -n 1)
---     echo "('${d}.0e$p', $l),"
---   done
--- done
-
-WITH t(x, bc_result) AS (VALUES
-('2.0e10', 10.301029995663981),
-('5.0e10', 10.698970004336019),
-('8.0e10', 10.903089986991944),
-('2.0e17', 17.301029995663981),
-('5.0e17', 17.698970004336019),
-('8.0e17', 17.903089986991944),
-('2.0e24', 24.301029995663981),
-('5.0e24', 24.698970004336019),
-('8.0e24', 24.903089986991944),
-('2.0e31', 31.301029995663981),
-('5.0e31', 31.698970004336019),
-('8.0e31', 31.903089986991944),
-('2.0e38', 38.301029995663981),
-('5.0e38', 38.698970004336019),
-('8.0e38', 38.903089986991944),
-('2.0e45', 45.30102999566398),
-('5.0e45', 45.69897000433602),
-('8.0e45', 45.90308998699194))
-SELECT x, bc_result, log(x::numeric), log(x::numeric)-bc_result AS diff FROM t;
-- 
2.32.1 (Apple Git-133)

