(FILECREATED " 6-Jun-86 17:14:15" ("compiled on " {QV}LISP>PROBFNCTS.;1) "12-Nov-85 14:59:23" recompiled ALL in "INTERLISP-D 11-May-86 ..." dated "11-May-86 15:19:08") (FILECREATED " 6-Jun-86 17:12:10" {QV}LISP>PROBFNCTS.;1 31493 changes to: (FNS PTDIS ALNREL GAMMA PNORMS R91GMC HORNER BETA) (MACROS HORNER) previous date: "24-Feb-86 18:27:28" {QV}LISP>DINDEPROBFNS.;1) ALBETA D1 (P 3 SumOfArguments P 2 NaturalLogSquareRootTwoPi P 1 LargerArgument P 0 SmallerArgument I 1 B I 0 A) Á@bAb@A @A oHoó§o oHó³@HIÔI oÖJH I K HoÕHK× ÖIH K× ÖÔÔÔÔÔÔoIó²H I HIÔ ×Ö HIÔH I K ÕHd K ÖIoÔH K× ÖÔÔÔÔ(271Q ALNREL 264Q MINUS 251Q LOG 245Q MINUS 237Q R91GMC 233Q R91GMC 227Q ALNGAM 214Q LOG 207Q GAMMA 201Q GAMMA 175Q GAMMA 151Q ALNREL 144Q MINUS 136Q LOG 122Q MINUS 117Q R91GMC 113Q R91GMC 107Q R91GMC 75Q LOG 52Q ERROR 25Q MAX 20Q MIN) (11Q FLOATP 3 FLOATP) ( 257Q -.5 165Q 10.0 127Q .5 101Q -.5 57Q 10.0 47Q "ERROR in function ALBETA - Both arguments must be positive." 41Q 0.0 31Q .9189386) ALNGAM D1 (P 5 SinePiTimesAbsoluteX P 4 XMaximum P 3 RelativeDX P 2 NaturalLogSquareRootTwoPi P 1 NaturalLogSquareRootPiOverTwo P 0 AbsoluteX I 0 X) Ã@bd ooooHdoó«¿@ Ló—o @oó²J@oÕ@ Ö@ H ÔÔÔHoÖi Mjð³(Mµ@doÕjØÕ@× Kýó²o ²áo I@oÕH Ö@ M H ÔÔÔÔ(274Q MINUS 271Q R91GMC 265Q MINUS 262Q LOG 256Q MINUS 251Q LOG 235Q ERROR 224Q \FZEROP 220Q ERROR 204Q ABS 150Q ABS 145Q SIN 127Q R91GMC 123Q MINUS 116Q LOG 72Q ERROR 57Q LOG 54Q ABS 51Q GAMMA 11Q ABS) (3 FLOATP) ( 244Q .5 232Q "ERROR in function ALNGAM - X is a negative integer." 215Q "ERROR in function ALNGAM - Answer under half precision." 173Q .5 140Q 3.141593 111Q .5 100Q 0.0 67Q "ERROR in function ALNGAM - ABS(X) out of range." 42Q 10.0 31Q 3.835341E36 25Q .0004882813 21Q .9189386 15Q .2257914) ALNREL D1 (P 3 XMinimum P 2 NumberOfChebyshevTerms P 0 Coefficients I 0 X F 4 \IEEE.SHORT.MACHEPS) v@booYd³HlToÖi¿Io»@oó§o K@ó—o @ oó³@o@do×HJÖÕÖ@oÔ (163Q LOG 146Q CSEVL 116Q ABS 111Q ERROR 75Q ERROR 41Q INITS) (3 FLOATP) ( 157Q 1.0 140Q .375 132Q 1.0 122Q .375 106Q "ERROR in function ALNREL - Answer under half precision." 72Q "ERROR in function ALNREL - X must be greater than -1." 64Q -1.0 56Q -.9995118 35Q .1 20Q (NIL) 11Q (MAKE-ARRAY 27Q (QUOTE :ELEMENT-TYPE) (QUOTE FLOAT) (QUOTE :INITIAL-CONTENTS) (QUOTE (1.037869 -.133643 .1940825 -.003010755 .0004869461 -.00008105488 .00001377885 -2.380221E-6 4.164042E-7 -7.359583E-8 1.311761E-8 -2.354671E-9 4.252277E-10 -7.71909E-11 1.407575E-11 -2.576907E-12 4.734241E-13 -8.7249E-14 1.6124E-14 -2.987E-15 5.54E-16 -1.03E-16 1.9E-17)))) BETA D1 (P 36Q FinalResult P 35Q I P 33Q E P 32Q FiniteSum P 31Q ModifiedP P 30Q D P 27Q TermValue P 26Q IB P 25Q Betai P 14Q C P 13Q F P 12Q B P 11Q XB P 6 PQXCondition2 P 5 Q P 4 P P 3 Y P 2 PQXCondition1 P 1 NaturalLogSmall P 0 NaturalLogMachinePrecisionValue I 2 QInputValue I 1 PInputValue I 0 X) ï@bAbBbj@ó¦@oó—o Aoó§o Boó§o oo¹BAó™o@óhðµ o@óhðZ–o@Õ€@»J‘B€A¼J‘A€B½K@ hðµ LA hð¾oLMÔKÖLoÔ×ó²KLKo ÖL LM ÔÔ OIóžKo ¥O ƒo_¿N—oOÕOMdjØÕ Ojð©Odš ”oOLK ÖOL L ÔÔ IOó’±O Oo ³xHK ×o jØkOíLíìOíOíKíLín?€jÑOOó³@bAµo‚bdoó§o @oó¤oo@A× Õ(72Q ANTILOG 67Q MINUS 40Q ERROR) (20Q FLOATP 3 FLOATP) ( 61Q 1.0 54Q 0.0 46Q 0.0 35Q "ERROR in function PEXPT - Mu must be positive." 27Q 0.0 14Q 1.0) PFDIS D1 (P 0 TemporaryResult I 2 DenominatorDF I 1 NumeratorDF I 0 X) y@bAµo‚bBµo‚bj@ó—o Aoó§o Boó§o @o ”o@AB×ÖHdoÔ×Ao×Bo×(166Q PBETA 121Q EQP 110Q ERROR 71Q ERROR 52Q ERROR) (35Q FLOATP 20Q FLOATP 3 FLOATP) ( 162Q 2.0 154Q 2.0 145Q 1.0 126Q 0.0 116Q 0.0 105Q "ERROR in function PFDIS - DenominatorDF must be positive." 77Q 0.0 66Q "ERROR in function PFDIS - NumeratorDF must be positive." 60Q 0.0 47Q "ERROR in function PFDIS - Quantile must be positive." 31Q 1.0 14Q 1.0) PGAMM D1 (P 5 Scratch P 4 I P 2 TotalSum P 1 SeriesTerm P 0 CopyOfEta I 1 Eta I 0 X) @bAµo‚b@oó§o Adoó¨¿o ooA@ó³|o@ó³to@ó•@AmÿÔ‚Al ÔjØkLKó³HoÕ¸IHÖ@×¹JIÔºLkÔ\°çIHoÕÖ¹JI@H oÔÔ×Ôºo@ AoÕ@ ÖJ A ÔÔÔ ÕHoÔ¸@H×½IMÖ¹JIÔºMoó³çIJ×oó³ÝA@ Ö@ J A ÔÔÔ A×(377Q ANTILOG 371Q MINUS 366Q GAMLOG 362Q LOG 356Q MINUS 351Q LOG 272Q ANTILOG 264Q MINUS 261Q GAMLOG 255Q LOG 250Q LOG 236Q MINUS 215Q MINUS 61Q ERROR 40Q ERROR) (20Q FLOATP 3 FLOATP) ( 341Q 1.192093E-7 327Q .5 304Q 1.0 243Q 1.0 232Q 1.0 221Q 2.0 203Q 1.0 153Q 1.0 116Q 11.0 106Q 7.0 72Q 1.0 66Q 1.0 56Q "ERROR in function PGAMM - Eta must be positive." 47Q 0.0 35Q "ERROR in function PGAMM - Quantile must be positive." 27Q 0.0 14Q 1.0) PLNORM D1 (I 2 Sigma I 1 Mu I 0 X) Y@bAµo‚bBµo‚bo@ó—o Boó§o @o ”o@ AÕB× (126Q PNORMS 117Q LOG 105Q EQP 74Q ERROR 55Q ERROR) (35Q FLOATP 20Q FLOATP 3 FLOATP) ( 112Q 0.0 102Q 0.0 71Q "ERROR in function PLNORM - Sigma must be positive." 63Q 0.0 52Q "ERROR in function PLNORM - Quantile must be positive." 43Q 0.0 31Q 1.0 14Q 0.0) PLOGI D1 (I 2 Sigma I 1 Mu I 0 X) C@bAµo‚bBµo‚bdoó§o oA@ÕB× oÔ×(72Q ANTILOG 55Q ERROR) (35Q FLOATP 20Q FLOATP 3 FLOATP) ( 76Q 1.0 62Q 1.0 52Q "ERROR in function PLOGI - Sigma must be positive." 44Q 0.0 31Q 1.0 14Q 0.0) PNORM D1 (I 2 Sigma I 1 Mu I 0 X) 9@bAµo‚bBµo‚bdoó§o @AÕB× (66Q PNORMS 55Q ERROR) (35Q FLOATP 20Q FLOATP 3 FLOATP) ( 52Q "ERROR in function PNORM - Sigma must be positive." 44Q 0.0 31Q 1.0 14Q 0.0) PNORMS D1 (P 12Q FinalResult P 11Q Coefficients P 10Q Center P 7 Bound P 3 XAdjustedBySqrtOf2 P 2 ListOfCoefficients P 1 Centers P 0 Bounds I 0 X) ©@booo@o ”o@o× JIH3 Nµ°_¿Mµ‡_¿Lµh³/o@ó²"o_¿KOó¦O³i°ãN¾M½L¼°ÀoKíOíìO l 2í o@ó•O OoÔ(236Q MINUS 211Q ARRAYBASE 53Q ABS 34Q EQP) (3 FLOATP) ( 245Q .5 226Q 0.0 172Q 1.0 132Q 0.0 122Q 0.0 47Q 1.414214 41Q .5 31Q 0.0 21Q (LIST (MAKE-ARRAY 12Q (QUOTE :ELEMENT-TYPE) (QUOTE FLOAT) (QUOTE :INITIAL-CONTENTS) (QUOTE (.000679824 .005102864 -.006016087 -.02272561 .03355577 .07270331 -.140939 -.1546891 .5156305 .1643134))) (MAKE-ARRAY 12Q (QUOTE :ELEMENT-TYPE) (QUOTE FLOAT) (QUOTE :INITIAL-CONTENTS) (QUOTE (-.001270975 -.001482265 .008771896 -.002020042 -.03468168 .0476424 .05685029 -.2218062 .2397904 .4045884))) (MAKE-ARRAY 12Q (QUOTE :ELEMENT-TYPE) (QUOTE FLOAT) (QUOTE :INITIAL-CONTENTS) (QUOTE (.0006796452 -.0003458989 -.00308834 .007214109 -.001067704 -.02485975 .05742032 -.0653837 .04023613 .4892219))) (MAKE-ARRAY 12Q (QUOTE :ELEMENT-TYPE) (QUOTE FLOAT) (QUOTE :INITIAL-CONTENTS) (QUOTE (-.00008850032 .0005682608 -.0004501553 -.001387239 .005542219 -.01022113 .0118502 -.008886404 .003993889 .4991742))) (MAKE-ARRAY 12Q (QUOTE :ELEMENT-TYPE) (QUOTE FLOAT) (QUOTE :INITIAL-CONTENTS) (QUOTE (1.479155E-7 -.00006196501 .0002226671 -.0004439002 .0006297875 -.0006638263 .0005126568 -.0002765716 .00009375142 .4999849))) (MAKE-ARRAY 12Q (QUOTE :ELEMENT-TYPE) (QUOTE FLOAT) (QUOTE :INITIAL-CONTENTS) (QUOTE (5.487908E-7 -8.665614E-7 6.687777E-7 -6.408465E-7 6.247178E-7 -4.210501E-7 2.074213E-7 -7.685604E-8 1.872202E-8 .5)))) 15Q (.3 .925 1.625 2.225 2.95 4.15) 11Q (.625 1.25 2.0 2.45 3.5 4.62)) PTDIS D1 (P 14Q F P 13Q E P 12Q A P 11Q D P 10Q C P 7 B P 6 A P 1 XSquared P 0 IntegerDegreesOfFreedom I 1 DegreesOfFreedom I 0 X) û @bAµo‚bddoó©¿o ¿AjØ@dÖBoAHÕ ó²lHó£AIó§HlÈó¢±IA×AoÕOdoÖÖONdoó—oÔ Ö OoÖoÕOÖoÕOÖoÕOdoÖÖOoÔÔ×OoÔÔO×oÔO Ö ºo@ó‘JoJÕ AIA×OoÔ o_¿lHó²#oIó²O __¿Hk ²qo_°kO _AÖ_¿jOlÔ_¿O_¿OOkÕÖOOÖ×_¿OOOOÔ×Ô_OÕ oó³ËOoÔ_¿o_¿o_¿O _Oo¼¿OoÕ_¿O»OOOoÕOOÖ×ÖÔ_¿OdLó³Ú¿K_¿OO oó²OkiOO×ÔoÖ‡OO ×ÕoÖ½o@ó‘MoMÕ(741Q SQRT 716Q ARCTAN2 700Q ABS 577Q MINUS 533Q ABS 440Q SQRT 421Q EQP 407Q SQRT 305Q PNORMS 302Q MINUS 276Q SQRT 167Q LOG 66Q ABS 42Q ERROR) (20Q FLOATP 3 FLOATP) ( 766Q 1.0 755Q 0.0 747Q .5 730Q .6366197 704Q 1.175494E-38 641Q 1.0 620Q 2.0 610Q 1.0 567Q 0.0 560Q 0.0 550Q 2.0 537Q 1.175494E-38 427Q 0.0 376Q 4.0 361Q 1.0 351Q 1.0 323Q 1.0 312Q 0.0 270Q 1.0 257Q 3.0 246Q 100.0 236Q .8 226Q 85.5 216Q 24.0 206Q 3.3 201Q -.4 163Q 1.0 155Q 1.0E-6 140Q 48.0 125Q .5 60Q 1.0E-6 37Q "ERROR in function PTDIS - DegreesOfFreedom must be positive." 30Q 0.0 14Q 1.0) PUNIF D1 (I 2 BoundHigh I 1 BoundLow I 0 X) B@bAµo‚bBµo‚bdAó§o @Aó”@dBó”oAÕBAÕ×(52Q ERROR) (35Q FLOATP 20Q FLOATP 3 FLOATP) ( 70Q 0.0 47Q "ERROR in function PUNIF - No effective calculation range." 31Q 1.0 14Q 0.0) R91GMC D1 (P 5 TemporaryResult P 4 XMaximum P 3 NumberOfChebyshevTerms P 1 CutOffPoint P 0 Coefficients I 0 X F 6 \IEEE.SHORT.MACHEPS) z@bo!o¹oZd«HlVi¿Jo¼o@ó—o L@ó§o I@ó² o@×MdoÖÖoÕHK@×o@oÖ×(151Q CSEVL 110Q ERROR 74Q ERROR 40Q INITS) (3 FLOATP) ( 165Q 12.0 160Q 1.0 143Q 1.0 135Q 2.0 122Q 10.0 105Q "ERROR in function R91GMC - X out of range." 71Q "ERROR in function R91GMC - X must be greater/equal to 10." 62Q 10.0 55Q 2.835686E37 25Q (NIL) 20Q 2896.309 11Q (MAKE-ARRAY 6 (QUOTE :ELEMENT-TYPE) (QUOTE FLOAT) (QUOTE :INITIAL-CONTENTS) (QUOTE (.1666389 -.00001384948 9.810826E-9 -1.80912E-11 6.22E-14 -3.0E-16)))) (PRETTYCOMPRINT PROBFNCTSCOMS) (RPAQQ PROBFNCTSCOMS ((FNS ALBETA ALNGAM ALNREL BETA CSEVL GAMLOG GAMMA HORNER INITS PBETA PCAUC PCHIS PEXPT PFDIS PGAMM PLNORM PLOGI PNORM PNORMS PTDIS PUNIF R91GMC) (CONSTANTS (\IEEE.SHORT.MACHEPS (EXPT 2.0 -23)) (\IEEE.SHORT.LEAST.NORMAL (EXPT 2.0 -126)) (\IEEE.SHORT.BASE 2) (\IEEE.SHORT.MANTISSA 23) ( \IEEE.SHORT.EXPONENT 8) (\IEEE.SHORT.LEAST.EXPONENT -126) (\IEEE.SHORT.GREATEST.EXPONENT 127) ( \IEEE.SHORT.EXPONENT.BIAS 127) (\IEEE.SHORT.PI 3.141593)) (MACROS HORNER))) (RPAQ \IEEE.SHORT.MACHEPS (EXPT 2.0 -23)) (RPAQ \IEEE.SHORT.LEAST.NORMAL (EXPT 2.0 -126)) (RPAQQ \IEEE.SHORT.BASE 2) (RPAQQ \IEEE.SHORT.MANTISSA 23) (RPAQQ \IEEE.SHORT.EXPONENT 8) (RPAQQ \IEEE.SHORT.LEAST.EXPONENT -126) (RPAQQ \IEEE.SHORT.GREATEST.EXPONENT 127) (RPAQQ \IEEE.SHORT.EXPONENT.BIAS 127) (RPAQQ \IEEE.SHORT.PI 3.141593) (CONSTANTS (\IEEE.SHORT.MACHEPS (EXPT 2.0 -23)) (\IEEE.SHORT.LEAST.NORMAL (EXPT 2.0 -126)) ( \IEEE.SHORT.BASE 2) (\IEEE.SHORT.MANTISSA 23) (\IEEE.SHORT.EXPONENT 8) (\IEEE.SHORT.LEAST.EXPONENT -126) (\IEEE.SHORT.GREATEST.EXPONENT 127) (\IEEE.SHORT.EXPONENT.BIAS 127) (\IEEE.SHORT.PI 3.141593)) (PUTPROPS HORNER DMACRO ((X POLY DEGREE) (\FLOATBOX ((OPCODES UBFLOAT3 0) (\FLOATUNBOX X) (ARRAYBASE POLY) DEGREE)))) (PUTPROPS PROBFNCTS COPYRIGHT ("Massachusetts Institute of Technology" 1986)) NIL