Fix corner-case loss of precision in numeric pow() calculation

Commit 7d9a4737c268f61fb8800957631f12d3f13be218 greatly improved the
accuracy of the numeric transcendental functions, however it failed to
consider the case where the result from pow() is close to the overflow
threshold, for example 0.12 ^ -2345.6. For such inputs, where the
result has more than 2000 digits before the decimal point, the decimal
result weight estimate was being clamped to 2000, leading to a loss of
precision in the final calculation.

Fix this by replacing the clamping code with an overflow test that
aborts the calculation early if the final result is sure to overflow,
based on the overflow limit in exp_var(). This provides the same
protection against integer overflow in the subsequent result scale
computation as the original clamping code, but it also ensures that
precision is never lost and saves compute cycles in cases that are
sure to overflow.

The new early overflow test works with the initial low-precision
result (expected to be accurate to around 8 significant digits) and
includes a small fuzz factor to ensure that it doesn't kick in for
values that would not overflow exp_var(), so the overall overflow
threshold of pow() is unchanged and consistent for all inputs with
non-integer exponents.

Author: Dean Rasheed
Reviewed-by: Tom Lane
Discussion: http://www.postgresql.org/message-id/CAEZATCUj3U-cQj0jjoia=qgs0SjE3auroxh8swvNKvZWUqegrg@mail.gmail.com
See-also: http://www.postgresql.org/message-id/CAEZATCV7w+8iB=07dJ8Q0zihXQT1semcQuTeK+4_rogC_zq5Hw@mail.gmail.com

diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
index 3ba373a15b9f693919282f5398848b4a57860bc6..3d21e33a26b8b8b246bde5ec19ce500bbbb6328a 100644 (file)
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -7591,6 +7591,7 @@ exp_var(NumericVar *arg, NumericVar *result, int rscale)
        val = numericvar_to_double_no_overflow(&x);
 
        /* Guard against overflow */
+       /* If you change this limit, see also power_var()'s limit */
        if (Abs(val) >= NUMERIC_MAX_RESULT_SCALE * 3)
                ereport(ERROR,
                                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
@@ -7992,6 +7993,15 @@ power_var(NumericVar *base, NumericVar *exp, NumericVar *result)
         *
         * We want result = e ^ (exp * ln(base))
         * so result dweight = log10(result) = exp * ln(base) * log10(e)
+        *
+        * We also perform a crude overflow test here so that we can exit early if
+        * the full-precision result is sure to overflow, and to guard against
+        * integer overflow when determining the scale for the real calculation.
+        * exp_var() supports inputs up to NUMERIC_MAX_RESULT_SCALE * 3, so the
+        * result will overflow if exp * ln(base) >= NUMERIC_MAX_RESULT_SCALE * 3.
+        * Since the values here are only approximations, we apply a small fuzz
+        * factor to this overflow test and let exp_var() determine the exact
+        * overflow threshold so that it is consistent for all inputs.
         *----------
         */
        ln_dweight = estimate_ln_dweight(base);
@@ -8006,11 +8016,13 @@ power_var(NumericVar *base, NumericVar *exp, NumericVar *result)
 
        val = numericvar_to_double_no_overflow(&ln_num);
 
-       val *= 0.434294481903252;       /* approximate decimal result weight */
+       /* initial overflow test with fuzz factor */
+       if (Abs(val) > NUMERIC_MAX_RESULT_SCALE * 3.01)
+               ereport(ERROR,
+                               (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+                                errmsg("value overflows numeric format")));
 
-       /* limit to something that won't cause integer overflow */
-       val = Max(val, -NUMERIC_MAX_RESULT_SCALE);
-       val = Min(val, NUMERIC_MAX_RESULT_SCALE);
+       val *= 0.434294481903252;       /* approximate decimal result weight */
 
        /* choose the result scale */
        rscale = NUMERIC_MIN_SIG_DIGITS - (int) val;

diff --git a/src/test/regress/expected/numeric_big.out b/src/test/regress/expected/numeric_big.out
index 1b3608ad535a88913027bf715aec622319d6eceb..8bb09c98dbf50177f27c0a342c96aff4a7fd99fc 100644 (file)
--- a/src/test/regress/expected/numeric_big.out
+++ b/src/test/regress/expected/numeric_big.out
@@ -1075,6 +1075,20 @@ SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
  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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |  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()
 --

diff --git a/src/test/regress/sql/numeric_big.sql b/src/test/regress/sql/numeric_big.sql
index 60080e85a50ddbc8786ab703c2e0d2aebdc1ca80..6dbcf9651e997f7fce07fb20f2248a9c512b9bda 100644 (file)
--- a/src/test/regress/sql/numeric_big.sql
+++ b/src/test/regress/sql/numeric_big.sql
@@ -881,6 +881,16 @@ WITH t(b, p, bc_result) AS (VALUES
 (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()
 --