Fix corner-case loss of precision in numeric ln().

When deciding on the local rscale to use for the Taylor series
expansion, ln_var() neglected to account for the fact that the result
is subsequently multiplied by a factor of 2^(nsqrt+1), where nsqrt is
the number of square root operations performed in the range reduction
step, which can be as high as 22 for very large inputs. This could
result in a loss of precision, particularly when combined with large
rscale values, for which a large number of Taylor series terms is
required (up to around 400).

Fix by computing a few extra digits in the Taylor series, based on the
weight of the multiplicative factor log10(2^(nsqrt+1)). It remains to
be proven whether or not the other 8 extra digits used for the Taylor
series is appropriate, but this at least deals with the obvious
oversight of failing to account for the effects of the final
multiplication.

Per report from Justin AnyhowStep. Reviewed by Tom Lane.

Discussion: https://postgr.es/m/16280-279f299d9c06e56f@postgresql.org

diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
index bd00f23b9464e189775592a14ff457cc2cdba58f..10229eb37e95bc53db9f4c3f507e44197073d16f 100644 (file)
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -8500,6 +8500,7 @@ ln_var(const NumericVar *arg, NumericVar *result, int rscale)
    NumericVar  ni;
    NumericVar  elem;
    NumericVar  fact;
+   int         nsqrt;
    int         local_rscale;
    int         cmp;
 
@@ -8530,12 +8531,14 @@ ln_var(const NumericVar *arg, NumericVar *result, int rscale)
     * rscale as we work so that we keep this many significant digits at each
     * step (plus a few more for good measure).
     */
+   nsqrt = 0;
    while (cmp_var(&x, &const_zero_point_nine) <= 0)
    {
        local_rscale = rscale - x.weight * DEC_DIGITS / 2 + 8;
        local_rscale = Max(local_rscale, NUMERIC_MIN_DISPLAY_SCALE);
        sqrt_var(&x, &x, local_rscale);
        mul_var(&fact, &const_two, &fact, 0);
+       nsqrt++;
    }
    while (cmp_var(&x, &const_one_point_one) >= 0)
    {
@@ -8543,6 +8546,7 @@ ln_var(const NumericVar *arg, NumericVar *result, int rscale)
        local_rscale = Max(local_rscale, NUMERIC_MIN_DISPLAY_SCALE);
        sqrt_var(&x, &x, local_rscale);
        mul_var(&fact, &const_two, &fact, 0);
+       nsqrt++;
    }
 
    /*
@@ -8555,8 +8559,12 @@ ln_var(const NumericVar *arg, NumericVar *result, int rscale)
     *
     * The convergence of this is not as fast as one would like, but is
     * tolerable given that z is small.
+    *
+    * The Taylor series result will be multiplied by 2^(nsqrt+1), which has a
+    * decimal weight of (nsqrt+1) * log10(2), so work with this many extra
+    * digits of precision (plus a few more for good measure).
     */
-   local_rscale = rscale + 8;
+   local_rscale = rscale + (int) ((nsqrt + 1) * 0.301029995663981) + 8;
 
    sub_var(&x, &const_one, result);
    add_var(&x, &const_one, &elem);

diff --git a/src/test/regress/expected/numeric_big.out b/src/test/regress/expected/numeric_big.out
index 8bb09c98dbf50177f27c0a342c96aff4a7fd99fc..468c6026bcde85a70db6683a94467ed94e6e83bf 100644 (file)
--- a/src/test/regress/expected/numeric_big.out
+++ b/src/test/regress/expected/numeric_big.out
@@ -1612,6 +1612,25 @@ SELECT x, bc_result, ln(x::numeric), ln(x::numeric)-bc_result AS diff FROM t;
  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)
 --

diff --git a/src/test/regress/sql/numeric_big.sql b/src/test/regress/sql/numeric_big.sql
index 6dbcf9651e997f7fce07fb20f2248a9c512b9bda..c9d52d08b4455f699a6b75d060d5ad2d6cdf0805 100644 (file)
--- a/src/test/regress/sql/numeric_big.sql
+++ b/src/test/regress/sql/numeric_big.sql
@@ -1193,6 +1193,20 @@ WITH t(x, bc_result) AS (VALUES
 ('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),
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+ 1510.4332713542154696529645934345554302578243896764921637693542962119938599884313210100957753316832762996428481801312323020427109678979117469716796746760060470871840325255146954580681101106876674367471955788143763250819168311353856748872452260808797135108102729064040463343792765872545182299889360257515315869180266759715933989413256377582681707188367254513700731642913479683031478361835565783219287780434673712341147656477670848734998849030451414278832848680301511646182446524915091598080243532068451726548537866633622180283865668708517173065893429240665300584705585310049892047293928733753369421499719516009692095913169665213597158441636480707309244604139865130782756488091268094213446272360006907802989573582755585110277620911226015342778471352130366770729972784317323917141031824334355639769512749560550167491709646539950725523461943580211843652293561678342656010571108219244870234329176123205423872844099992204896411752620881541000940129833754169391528449211839693800724450201835161044717173715867437))
+SELECT trim_scale(ln(x::numeric)-bc_result) AS diff FROM t;
+
 --
 -- Tests for LOG() (base 10)
 --