Performance testing of a FORTRAN library of mathematical function routines - a case study in the application of testing techniques

Thi s pape r describes a n app lication of tes ting methodology a nd te c hniques de ve loped by th e a uthors to a id in impro vi ng the qu a lity of mathem ati ca l soft wa re. These techni q ues diffe r rad ica ll y in se vera l as pects from techni q ues pre vious ly used . the most import a nt d iffere nce be ing th at th e testin g is not based e xc lus ivel y Oil random a rgume nt s. Ins tead , throughou t the range of eac h fun c tio n use is ma de of s pec ia l a rgum e nt s that a re des ig ned to d etec t progra mming e rrors and to tes t the pe rfnrm a nce of an algorithm in diffe re nt regions. T he fu nction values a re tes ted aga ins t refe re nce valu es whic h are s tored o n re fe re nce tapes ge ne ra ted b y a hi ghl y au the nti ca ted s yste m of s ubro utin es. S ince the eff ec tive ness of s uch a tes tin g sys te m in di scove ring e rrors and pe rform a nce limit ati ons can be fu ll y ascert a ined o nl y th rough ac tu a l use , we report the res ult s of e m ploying our s ys tem to tes t an exi stin g FORTRAN library of ma the matica l fun c tion routines. S pec if, c a s pects of the num e ri ca l accurac y of the libJ·a ry used in thi s te st case are di sc ussed in orde r to ill :~5tra t e the e ffec ti ve ness of a we ll -d es igned tes ting s yste m as a n ana lyti c tool for the e valuation of mathe matica l so ft wa re. S ince docum e nt ati on prov ides information necessary to perform testing and cont ain s s pecifications th at re flect the result s of testin g, our stud y inc ludes com me nts on th e doc ume nt at ion. No information on timing or storage re quire me nts is present ed in thi s case s tud y.