locating overlow/underflow

• To: mathgroup at smc.vnet.net
• Subject: [mg112176] locating overlow/underflow
• From: Leslaw Bieniasz <nbbienia at cyf-kr.edu.pl>
• Date: Fri, 3 Sep 2010 06:10:12 -0400 (EDT)

```
Hi,

I am not very much familiar with MATHEMATICA, but
I have to tabulate a certain mathematical expression in a possibly large
range of independent variable, and with the highest possible number of
accurate digits. I have a notebook file that does the job (included
below in text form, together with the results) but during the cell
evaluation I obtain error messages stating that underflow or overflow occurred.
My question is: is there any way to rewrite the code in such a way so
that I can obtain an information where exactly (that is for which values
of independent variable) the errors actually occur?
Or, is there any way to rewrite the code or change the program settings
in such a way so that the errors do not occur at all?
I am using MATHEMATICA 6.0.

One more question: I also need a special function representing
the so-called Dawson integral (related to error functions).
Is such a function available in MATHEMATICA?

Leslaw

-----------------

In[1]:= Table[{N[y],
SetPrecision[
2 ((y - 1) Exp[y] Erfc[Sqrt[y]] + (y/3 - 1) 2 Sqrt[y/Pi] +
1)/(y y), 70],
Precision[
2 ((y - 1) Exp[y] Erfc[Sqrt[y]] + (y/3 - 1) 2 Sqrt[y/Pi] +
1)/(y y)]
},
{y,  {
1/10^19, 2/10^19, 5/10^19,
1/10^18, 2/10^18, 5/10^18,
1/10^17, 2/10^17, 5/10^17,
1/10^16, 2/10^16, 5/10^16,
1/10^15, 2/10^15, 5/10^15,
1/10^14, 2/10^14, 5/10^14,
1/10^13, 2/10^13, 5/10^13,
1/10^12, 2/10^12, 5/10^12,
1/10^11, 2/10^11, 5/10^11,
1/10^10, 2/10^10, 5/10^10,
1/10^9,  2/10^9,    5/10^9,
1/10^8,  2/10^8,    5/10^8,
1/10^7,  2/10^7,    5/10^7,
1/10^6,  2/10^6,    5/10^6,
1/10^5,  2/10^5,    5/10^5,
1/10^4,  2/10^4,    5/10^4,
1/10^3,  2/10^3,    5/10^3,
1/10^2,  2/10^2,    5/10^2,
1/10^1,  2/10^1,    5/10^1,
10^0,        2 10^0,    5 10^0,
10^1,        2 10^1,    5 10^1,
10^2,        2 10^2,    5 10^2,
10^3,        2 10^3,    5 10^3,
10^4,        2 10^4,    5 10^4,
10^5,        2 10^5,    5 10^5,
10^6,        2 10^6,    5 10^6,
10^7,        2 10^7,    5 10^7,
10^8,        2 10^8,    5 10^8,
10^9,        2 10^9,    5 10^9,
10^10,      2 10^10, 5 10^10,
10^11,      2 10^11, 5 10^11,
10^12,      2 10^12, 5 10^12,
10^13,      2 10^13, 5 10^13,
10^14,      2 10^14, 5 10^14,
10^15,      2 10^15, 5 10^15

}}]
TableForm[%]

During evaluation of In[1]:= General::ovfl: Overflow occurred in computation. >>
During evaluation of In[1]:= General::unfl: Underflow occurred in computation. >>
During evaluation of In[1]:= General::ovfl: Overflow occurred in computation. >>
During evaluation of In[1]:= General::unfl: Underflow occurred in computation. >>
During evaluation of In[1]:= General::ovfl: Overflow occurred in computation. >>
During evaluation of In[1]:= General::stop: Further output of General::ovfl will be suppressed \
during this calculation. >>
During evaluation of In[1]:= General::unfl: Underflow occurred in computation. >>
During evaluation of In[1]:= General::stop: Further output of General::unfl will be suppressed \
during this calculation. >>
Out[1]= {{1.*10^-19,
0.9999999997145401414822232883268, \[Infinity]}, {2.*10^-19,
0.9999999995962987966101077255753, \[Infinity]}, {5.*10^-19,
0.99999999936169235169104104847744, \[Infinity]}, {1.*10^-18,
0.999999999097296666990256607119881, \[Infinity]}, {2.*10^-18,
0.999999998723384704048748762709682, \[Infinity]}, {5.*10^-18,
0.9999999979814939857172052899296470, \[Infinity]}, {1.*10^-17,
0.99999999714540142082223286981099390, \[Infinity]}, {2.*10^-17,
0.99999999596298797810107721769016053, \[Infinity]}, {5.*10^-17,
0.999999993616923546910410334316185418, \[Infinity]}, {1.*10^-16,
0.9999999909729667299025656456386676196, \[Infinity]}, {2.*10^-16,
0.9999999872338471604874864234309767634, \[Infinity]}, {5.*10^-16,
0.99999997981494015717204814138949104458, \[Infinity]}, {1.*10^-15,
0.999999971454014808222315240716855446413, \[Infinity]}, {2.*10^-15,
0.999999959629880981010734113646272096829, \[Infinity]}, \
{5.*10^-15,
0.9999999361692384691039528849366322454328, \[Infinity]}, \
{1.*10^-14,
0.99999990972967329902523089626863231557756, \[Infinity]}, \
{2.*10^-14,
0.99999987233848360487366056855794216146181, \[Infinity]}, \
{5.*10^-14,
0.999999798149431571715723507477761640655816, \[Infinity]}, \
{1.*10^-13,
0.9999997145402080822096950163327874248582992, \[Infinity]}, \
{2.*10^-13,
0.9999995962989298100692778901205287332143837, \[Infinity]}, \
{5.*10^-13,
0.99999936169268469088907068033811563428191196, \[Infinity]}, \
{1.*10^-12,
0.999999097297332989826749069417310407519066954, \[Infinity]}, \
{2.*10^-12,
0.999998723386036047532940832853199726877995106, \[Infinity]}, \
{5.*10^-12,
0.9999979814973157123993342769964108375782037344, \[Infinity]}, \
{1.*10^-11,
0.99999714540808080863958180501897178805571422797, \[Infinity]}, \
{2.*10^-11,
0.99999596300129806262962246877623843211942468409, \[Infinity]}, \
{5.*10^-11,
0.999993616956846758433099710334117289408922294795, \[Infinity]}, \
{1.*10^-10,
0.9999909730333294727098451619220974886096584308203, \[Infinity]}, \
{2.*10^-10,
0.9999872339803592716735465274233676888555754834793, \[Infinity]}, \
{5.*10^-10,
0.99997981527315236614873799872200298660421599112079, \[Infinity]}, \
{1.*10^-9,
0.999971454680794629252230555027937586208375206273895, \
\[Infinity]}, {2.*10^-9,
0.999959631212942564038868577810708150105882262021567, \
\[Infinity]}, {5.*10^-9,
0.9999361725683171323430450418935382232030480963633574, \
\[Infinity]}, {1.*10^-8,
0.99990973633286919192909560231769338552621527844005465, \
\[Infinity]}, {2.*10^-8,
0.99987235180238915077617597090031017455487299571323293, \
\[Infinity]}, {5.*10^-8,
0.999798182726766378746112583033893508505423363651441785, \
\[Infinity]}, {1.*10^-7,
0.9997146067944913962662443861381550812129566065971701181, \
\[Infinity]}, {2.*10^-7,
0.9995964320913723716649649533249490727923551184325208368, \
\[Infinity]}, {5.*10^-7,
0.99936202553277550583443780378864879173919378767298350956, \
\[Infinity]}, {1.*10^-6,
0.999097962903381392618257918169808186133578565612905041807, \
\[Infinity]}, {2.*10^-6,
0.998724716821223900132151301649431782912244457614617752179, \
\[Infinity]}, {5.*10^-6,
0.9979848225159930290612974417133409969991182485096079390572, \
\[Infinity]}, {0.00001,
0.99715205451245340984272072402376554746735097950171503191800, \
\[Infinity]}, {0.00002,
0.99597628295012871025175184133716000186655058157832590725788, \
\[Infinity]}, {0.00005,
0.993650105491543032373266408651022396609428946524109448862154, \
\[Infinity]}, {0.0001,
0.9910392059578652166795069631112683822179123631575592632039850, \
\[Infinity]}, {0.0002,
0.9873659744612733772583124002782906358336022836617031938910022, \
\[Infinity]}, {0.0005,
0.98014352895111543381382637050340393731816757683943978354872738, \
\[Infinity]}, {0.001,
0.972107333318279894078855918414228411392356971871252393881957589, \
\[Infinity]}, {0.002,
0.960925741846674240019638473110302681634263594240453539524316569, \
\[Infinity]}, {0.005,
0.9393566121127200498908648890246331681521689289144646538210050146, \
\[Infinity]}, {0.01,
0.9159902009040924490250299590163413654635346369396778873520195889, \
\[Infinity]}, {0.02,
0.8845489144448704427280817404061389113644987295066944272551439941, \
\[Infinity]}, {0.05,
0.82723454417674794029046907957368671185022940780693788453724800037,\
\[Infinity]}, {0.1,
0.769748582788727344538491837757160790299606272079824730272354026215\
, \[Infinity]}, {0.2,
0.699232242525341506949772819117642562815375532716177178907138434103\
7, \[Infinity]}, {0.5,
0.588143259726577320679301839443053773222030917216494297935021239844\
33, \[Infinity]}, {1.,
0.495494443872649901471788129171273104415864988456003048415771408771\
620, \[Infinity]}, {2.,
0.402140480955548821133851740739495786058744699228268255193373584174\
60, \[Infinity]}, {5.,
0.288911482041544026351044834721976387733419669000343513698745282192\
, \[Infinity]}, {10.,
0.2172222401396003819699281665905984026748849752211952762443786524, \
\[Infinity]}, {20.,
0.159682833889492164165276148953035239355107803536204179301335, \
\[Infinity]}, {50.,
0.103898856438174453901130042254777276403821295925701001674896046826\
4487, \[Infinity]}, {100.,
0.074280111128504166978597120002158527004820661741654346725511978095\
5073, \[Infinity]}, {200.,
0.052840382044123199631462541766374044290452985187147781191204691936\
3881, \[Infinity]}, {500.,
0.033548539386005934478949701602134509526379532531957500468075086230\
3655, \[Infinity]}, {1000.,
0.023754585587166811032652812370733379184448439544392165425468126451\
3817, \[Infinity]}, {2000.,
0.016808758359715603635767774844392236608100743804294132512009896293\
3174, \[Infinity]}, {5000.,
0.010635348315159696919776357112721673103593889162191241340002282113\
68411, \[Infinity]}, {10000.,
0.007521419232226881694285320256609641558690025685331124462521775358\
92807, \[Infinity]}, {20000.,
0.005318836433152609806824908867860117033202568088113139797523807695\
85166, \[Infinity]}, {50000.,
0.003364076567698290692034556074814691590610990159037322908916949765\
51381, \[Infinity]}, {100000.,
0.002378796671852805656000459926141396168102735040314336789405930067\
58431, \[Infinity]}, {200000.,
0.001682075782256212856024086228569462951010275705207774046173766787\
05007, \[Infinity]}, {500000.,
0.001063842897522669330939755783504367122329615797119676515766230784\
462375, \[Infinity]}, {1.*10^6,
0.000752251651682815386411359767278213838037055070919378369497456335\
765897, \[Infinity]}, {2.*10^6,
0.000531922642092663962568285063847383265111997405192167429802686793\
128027, \[Infinity]}, {5.*10^6,
0.000336417568757356848041333360766808363214193818969988566716986874\
026595, \[Infinity]}, {1.*10^7,
0.000237883179824548473177870798184711650639486725296508177959537387\
265020, \[Infinity]}, {2.*10^7,
0.000168208822190680446941020059970130276635534860948672447590320829\
019214, \[Infinity]}, {5.*10^7,
0.000106384604916310375159711825221478563296699198272857096813639705\
4260506, \[Infinity]}, {1.*10^8,
0.000075225276678188320905210654259981758159131350353428366909503619\
2342803, \[Infinity]}, {2.*10^8,
0.000053192303654632073665159706174172569621308032205289040073382595\
7980036, \[Infinity]}, {5.*10^8,
0.000033641766859351499459713022897197101554901804981600259808868366\
7584749, \[Infinity]}, {1.*10^9,
0.000023788321513023132483940405903441743127938158022647462615222027\
1704841, \[Infinity]}, {2.*10^9,
Indeterminate, \[Infinity]}, {5.*10^9,
Indeterminate, \[Infinity]}, {1.*10^10,
Indeterminate, \[Infinity]}, {2.*10^10,
Indeterminate, \[Infinity]}, {5.*10^10,
Indeterminate, \[Infinity]}, {1.*10^11,
Indeterminate, \[Infinity]}, {2.*10^11,
Indeterminate, \[Infinity]}, {5.*10^11,
Indeterminate, \[Infinity]}, {1.*10^12,
Indeterminate, \[Infinity]}, {2.*10^12,
Indeterminate, \[Infinity]}, {5.*10^12,
Indeterminate, \[Infinity]}, {1.*10^13,
Indeterminate, \[Infinity]}, {2.*10^13,
Indeterminate, \[Infinity]}, {5.*10^13,
Indeterminate, \[Infinity]}, {1.*10^14,
Indeterminate, \[Infinity]}, {2.*10^14,
Indeterminate, \[Infinity]}, {5.*10^14,
Indeterminate, \[Infinity]}, {1.*10^15,
Indeterminate, \[Infinity]}, {2.*10^15,
Indeterminate, \[Infinity]}, {5.*10^15, Indeterminate, \[Infinity]}}
Out[2]//TableForm= \!\(\*
TagBox[GridBox[{
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397940007947568", "\[Infinity]"},
{"2.`*^-19",
"0.999999999596298796610107725575341676095945272569`31.\
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{"5.`*^-19",
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{"1.`*^-18",
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{"2.`*^-18",
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999999996760074", "\[Infinity]"},
{"5.`*^-18",
"0.999999997981493985717205289929647013080957505254`34.\
795880012221296", "\[Infinity]"},
{"1.`*^-17",
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"Columns" -> {{Left}}, "ColumnsIndexed" -> {},
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GridBoxSpacings->{"Columns" -> {
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Function[BoxForm`e\$,
TableForm[BoxForm`e\$]]]\)

```

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