July 27 2007 10:48:12.061 AM TEST_INT_PRB FORTRAN90 version Run the TEST_INT tests. TEST01 Composite midpoint rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.71828 1 1.64872 0.695606E-01 2 1.70051 0.177691E-01 4 1.71382 0.446655E-02 8 1.71716 0.111816E-02 16 1.71800 0.279636E-03 32 1.71821 0.699151E-04 64 1.71826 0.174791E-04 128 1.71828 0.436981E-05 2 .700000 1 1.00000 .300000 2 .500000 .200000 4 .750000 0.500000E-01 8 .750000 0.500000E-01 16 .687500 0.125000E-01 32 .687500 0.125000E-01 64 .703125 0.312500E-02 128 .703125 0.312500E-02 3 .666667 1 .707107 0.404401E-01 2 .683013 0.163460E-01 4 .672977 0.631073E-02 8 .669032 0.236551E-02 16 .667537 0.870009E-03 32 .666983 0.316020E-03 64 .666781 0.113837E-03 128 .666707 0.407740E-04 4 .479428 1 -.160000 .639428 2 .319667 .159762 4 .439407 0.400208E-01 8 .469417 0.100116E-01 16 .476925 0.250332E-02 32 .478802 0.625856E-03 64 .479272 0.156466E-03 128 .479389 0.391165E-04 5 1.58223 1 2.22222 .639989 2 1.64948 0.672516E-01 4 1.59690 0.146717E-01 8 1.58594 0.370973E-02 16 1.58316 0.928631E-03 32 1.58247 0.232219E-03 64 1.58229 0.580584E-04 128 1.58225 0.145148E-04 6 1.46045 1 1.41421 0.462336E-01 2 1.00000 .460447 4 1.49203 0.315826E-01 8 1.47277 0.123277E-01 16 1.46510 0.465635E-02 32 1.46217 0.172127E-02 64 1.46107 0.627348E-03 128 1.46067 0.226500E-03 7 2.00000 1 1.41421 .585786 2 1.57735 .422650 4 1.69884 .301156 8 1.78646 .213539 16 1.84886 .151143 32 1.89309 .106912 64 1.92439 0.756072E-01 128 1.94654 0.534647E-01 8 .866973 1 .941176 0.742035E-01 2 .877876 0.109034E-01 4 .869605 0.263242E-02 8 .867626 0.652821E-03 16 .867136 0.162872E-03 32 .867014 0.406974E-04 64 .866983 0.101733E-04 128 .866976 0.254350E-05 9 1.15470 1 1.00000 .154701 2 1.33333 .178633 4 1.14286 0.118434E-01 8 1.15464 0.613647E-04 16 1.15470 0.325132E-08 32 1.15470 0.162075E-08 64 1.15470 0.162075E-08 128 1.15470 0.162075E-08 10 .693147 1 .666667 0.264805E-01 2 .685714 0.743289E-02 4 .691220 0.192729E-02 8 .692661 0.486627E-03 16 .693025 0.121966E-03 32 .693117 0.305111E-04 64 .693140 0.762899E-05 128 .693145 0.190732E-05 11 .379885 1 .377541 0.234482E-02 2 .379322 0.563090E-03 4 .379746 0.139456E-03 8 .379851 0.347815E-04 16 .379877 0.868809E-05 32 .379883 0.216943E-05 64 .379885 0.540056E-06 128 .379885 0.132732E-06 12 .777505 1 .770747 0.675759E-02 2 .775822 0.168250E-02 4 .777084 0.420197E-03 8 .777400 0.105020E-03 16 .777478 0.262502E-04 32 .777498 0.655936E-05 64 .777503 0.163675E-05 128 .777504 0.406103E-06 13 1.65835 1 -1.91785 3.57620 2 1.82228 .163930 4 1.68215 0.238016E-01 8 1.66365 0.530061E-02 16 1.65964 0.128888E-02 32 1.65867 0.320013E-03 64 1.65843 0.798663E-04 128 1.65837 0.199580E-04 14 .500000 1 .000000 .500000 2 .000000 .500000 4 .000000 .500000 8 .000000 .500000 16 0.962434E-06 .499999 32 0.477350E-01 .452265 64 .423773 0.762275E-01 128 .499966 0.340341E-04 15 1.00000 1 0.129161E-51 1.00000 2 0.898473E-25 1.00000 4 0.167563E-11 1.00000 8 0.511680E-05 .999995 16 0.632258E-02 .993677 32 .157218 .842782 64 .565397 .434603 128 .857119 .142881 16 .499364 1 0.254241E-01 .473940 2 0.562605E-01 .443103 4 .116750 .382614 8 .225744 .273620 16 .375544 .123820 32 .476020 0.233435E-01 64 .493313 0.605043E-02 128 .493635 0.572922E-02 17 .500000 1 0.241176E-30 .500000 2 1.00000 .500000 4 .500000 0.999201E-15 8 .500000 0.888178E-15 16 .500000 0.499600E-15 32 .500000 0.111022E-15 64 .500000 .000000 128 .500000 0.333067E-15 18 .170557 1 .188770 0.182130E-01 2 .175036 0.447858E-02 4 .171673 0.111519E-02 8 .170836 0.278522E-03 16 .170627 0.696129E-04 32 .170575 0.174017E-04 64 .170562 0.434991E-05 128 .170558 0.108703E-05 19 -1.00000 1 -.693147 .306853 2 -.836988 .163012 4 -.915951 0.840485E-01 8 -.957329 0.426712E-01 16 -.978502 0.214981E-01 32 -.989210 0.107897E-01 64 -.994595 0.540504E-02 128 -.997295 0.270506E-02 20 1.56440 1 1.99005 .425653 2 1.59363 0.292291E-01 4 1.57473 0.103302E-01 8 1.56699 0.259103E-02 16 1.56504 0.647800E-03 32 1.56456 0.161951E-03 64 1.56444 0.404885E-04 128 1.56441 0.101229E-04 21 .210803 1 0.986604E-02 .200937 2 .393257 .182455 4 .177981 0.328217E-01 8 .199073 0.117297E-01 16 .226581 0.157785E-01 32 .203178 0.762437E-02 64 .212309 0.150656E-02 128 .209728 0.107450E-02 22 .728103 1 .761905 0.338018E-01 2 .734977 0.687382E-02 4 .729839 0.173559E-02 8 .728537 0.434020E-03 16 .728211 0.108507E-03 32 .728130 0.271267E-04 64 .728110 0.678168E-05 128 .728105 0.169542E-05 23 .195248 1 0.644769E-01 .130771 2 0.697785E-01 .125469 4 0.950946E-01 .100153 8 0.969539E-01 0.982936E-01 16 .119024 0.762234E-01 32 .119540 0.757076E-01 64 .136295 0.589522E-01 128 .136428 0.588198E-01 24 .325109 1 0.617193E-01 .263389 2 0.653679E-01 .259741 4 0.935137E-01 .231595 8 0.947748E-01 .230334 16 .122431 .202677 32 .122781 .202328 64 .146614 .178495 128 .146704 .178405 25 13.6280 1 0.536404E-01 13.5744 2 0.541904E-01 13.5738 4 0.925750E-01 13.5354 8 0.927710E-01 13.5352 16 .146767 13.4812 32 .146826 13.4812 64 .214557 13.4134 128 .214573 13.4134 26 -0.469840E-02 1 0.323978E-01 0.370962E-01 2 0.327915E-01 0.374899E-01 4 0.202251E-01 0.249235E-01 8 0.205652E-01 0.252636E-01 16 -0.246714E-01 0.199730E-01 32 -0.245117E-01 0.198133E-01 64 0.713247E-02 0.118309E-01 128 0.715606E-02 0.118545E-01 27 0.158973E-02 1 -.125033 .126623 2 0.456752E-01 0.440855E-01 4 -0.645945E-01 0.661842E-01 8 0.122445E-02 0.365276E-03 16 -0.936751E-16 0.158973E-02 32 0.151686E-02 0.728677E-04 64 0.151686E-02 0.728677E-04 128 0.157511E-02 0.146182E-04 28 0.561037E-03 1 0.261259E-03 0.299779E-03 2 0.463475E-03 0.975618E-04 4 0.465279E-03 0.957585E-04 8 0.535686E-03 0.253510E-04 16 0.535688E-03 0.253494E-04 32 0.554611E-03 0.642565E-05 64 0.554611E-03 0.642565E-05 128 0.559425E-03 0.161192E-05 29 .162669 1 .120744 0.419246E-01 2 .131984 0.306850E-01 4 .168187 0.551836E-02 8 .177557 0.148879E-01 16 .135761 0.269080E-01 32 .142785 0.198842E-01 64 .158357 0.431192E-02 128 .163343 0.673596E-03 30 0.583349E-01 1 0.302561E-01 0.280788E-01 2 0.306464E-01 0.276885E-01 4 0.456290E-01 0.127059E-01 8 0.457855E-01 0.125494E-01 16 0.559159E-01 0.241901E-02 32 0.559669E-01 0.236800E-02 64 0.582492E-01 0.857052E-04 128 0.582627E-01 0.721531E-04 31 1.06346 1 .675665 .387797 2 .705075 .358386 4 .936504 .126958 8 .932906 .130556 16 1.04957 0.138947E-01 32 1.04645 0.170120E-01 64 1.06442 0.956214E-03 128 1.06346 0.615561E-06 32 1.57080 1 .800000 .770796 2 .790588 .780208 4 1.10879 .462009 8 1.10756 .463232 16 1.32589 .244907 32 1.32584 .244961 64 1.44644 .124353 128 1.44644 .124354 33 3.14159 1 .942809 2.19878 2 1.12991 2.01168 4 1.46612 1.67547 8 1.60149 1.54010 16 1.90488 1.23671 32 1.99786 1.14373 64 2.24546 .896129 128 2.30976 .831832 34 .500000 1 .532281 0.322807E-01 2 .550108 0.501076E-01 4 .579791 0.797910E-01 8 .587248 0.872482E-01 16 .496374 0.362560E-02 32 .498387 0.161316E-02 64 .499539 0.461099E-03 128 .500028 0.275998E-04 35 1.57080 1 .958851 .611945 2 .949234 .621563 4 1.60997 0.391701E-01 8 1.60655 0.357516E-01 16 1.75851 .187709 32 1.75828 .187482 64 1.57421 0.341242E-02 128 1.57419 0.339597E-02 36 .624713 1 1.81859 1.19388 2 -.865646 1.49036 4 2.94334 2.31863 8 -.265766 .890479 16 1.05719 .432480 32 3.04553 2.42081 64 1.56902 .944307 128 -1.79113 2.41584 37 -0.675475E-02 1 .112539 .119294 2 -0.346577E-01 0.279030E-01 4 -0.285088E-01 0.217540E-01 8 -0.172141E-01 0.104593E-01 16 -0.549740E-02 0.125734E-02 32 -0.668040E-02 0.743424E-04 64 -0.665077E-02 0.103973E-03 128 -0.681738E-02 0.626371E-04 38 -1.61086 1 -1.60944 0.142639E-02 2 -1.89712 .286256 4 -1.50264 .108226 8 -1.67409 0.632291E-01 16 -1.58156 0.293022E-01 32 -1.62610 0.152315E-01 64 -1.60339 0.747050E-02 128 -1.61464 0.377158E-02 39 7.95493 1 2.31145 5.64347 2 6.28319 1.67174 4 7.92053 0.343944E-01 8 7.95493 0.125169E-05 16 7.95493 0.266454E-14 32 7.95493 0.444089E-14 64 7.95493 0.532907E-14 128 7.95493 0.177636E-14 40 .841117 1 .666308 .174809 2 .724249 .116868 4 .764438 0.766788E-01 8 .791275 0.498421E-01 16 .808885 0.322321E-01 32 .820343 0.207743E-01 64 .827762 0.133553E-01 128 .832549 0.856742E-02 41 0.199547E-01 1 0.266686E-15 0.199547E-01 2 0.387556E-16 0.199547E-01 4 .591821 .571866 8 .451165 .431210 16 -.412133 .432088 32 -0.993940E-01 .119349 64 0.768649E-01 0.569102E-01 128 0.260090E-01 0.605430E-02 42 .306853 1 .400000 0.931472E-01 2 .222222 0.846306E-01 4 .318148 0.112955E-01 8 .318377 0.115243E-01 16 .295446 0.114068E-01 32 .307020 0.167549E-03 64 .307024 0.171049E-03 128 .307025 0.171924E-03 43 7.95493 1 2.31145 5.64347 2 6.28319 1.67174 4 7.92053 0.343944E-01 8 7.95493 0.125169E-05 16 7.95493 0.266454E-14 32 7.95493 0.444089E-14 64 7.95493 0.532907E-14 128 7.95493 0.177636E-14 44 2.65164 1 8.00000 5.34836 2 1.60000 1.05164 4 2.40000 .251635 8 2.64219 0.944525E-02 16 2.65219 0.552195E-03 32 2.65178 0.144012E-03 64 2.65167 0.360336E-04 128 2.65164 0.901032E-05 45 -12.0703 1 0.925377E-15 12.0703 2 -9.28279 2.78756 4 -11.4283 .642044 8 -11.9138 .156501 16 -12.0315 0.388662E-01 32 -12.0606 0.970023E-02 64 -12.0679 0.242404E-02 128 -12.0697 0.605945E-03 46 .886227 1 .832555 0.536723E-01 2 .856885 0.293419E-01 4 .870846 0.153812E-01 8 .878377 0.785022E-02 16 .882289 0.393745E-02 32 .884275 0.195217E-02 64 .885267 0.960397E-03 128 .885757 0.470070E-03 47 1085.25 1 219.336 865.917 2 814.086 271.167 4 1014.04 71.2096 8 1067.24 18.0160 16 1080.74 4.51736 32 1084.12 1.13017 64 1084.97 .282596 128 1085.18 0.706522E-01 48 26.0000 1 16.1592 9.84076 2 19.1472 6.85282 4 23.9735 2.02645 8 24.6537 1.34628 16 24.6682 1.33183 32 25.5508 .449172 64 25.0640 .936004 128 26.8277 .827707 49 100.000 1 1.29346 98.7065 2 2.60003 97.4000 4 4.18787 95.8121 8 6.00422 93.9958 16 8.00816 91.9918 32 10.1655 89.8345 64 12.4466 87.5534 128 14.8250 85.1750 50 3.13580 1 0.119893E-01 3.12381 2 .391087 2.74471 4 0.419041E-01 3.09389 8 .188576 2.94722 16 3.40688 .271079 32 .361297 2.77450 64 1.28441 1.85139 128 7.93948 4.80368 51 .539257 1 -.457102 .996359 2 2.54527 2.00601 4 -.864262 1.40352 8 .538767 0.490129E-03 16 .539257 0.444089E-15 32 .539257 0.555112E-15 64 .539257 0.111022E-15 128 .539257 0.111022E-15 52 2.78769 1 2.44949 .338204 2 2.50665 .281046 4 2.57506 .212633 8 2.63340 .154297 16 2.67756 .110134 32 2.70956 0.781367E-01 64 2.73238 0.553163E-01 128 2.74856 0.391309E-01 53 2.69896 1 1.87186 .827092 2 3.34087 .641914 4 2.15729 .541669 8 2.44645 .252509 16 2.94122 .242265 32 2.50065 .198310 64 2.59919 0.997649E-01 128 2.94320 .244240 54 6.09559 1 1.77778 4.31781 2 2.55811 3.53748 4 3.38470 2.71088 8 4.14022 1.95536 16 4.73426 1.36132 32 5.15477 .940810 64 5.44153 .654058 128 5.63770 .457888 55 3.98079 1 2.00208 1.97871 2 2.36867 1.61211 4 2.67031 1.31048 8 2.91613 1.06465 16 3.11597 .864811 32 3.27833 .702454 64 3.41021 .570572 128 3.51734 .463449 56 2.99157 1 1.29248 1.69909 2 1.59381 1.39776 4 1.85063 1.14094 8 2.06307 .928499 16 2.23681 .754761 32 2.37831 .613263 64 2.49337 .498201 128 2.58687 .404696 57 -0.300997E-01 1 0.412820E-04 0.301410E-01 2 0.475558E-03 0.305753E-01 4 -0.711483E-02 0.229849E-01 8 -0.206782E-01 0.942150E-02 16 -0.273605E-01 0.273917E-02 32 -0.293871E-01 0.712613E-03 64 -0.299197E-01 0.179960E-03 128 -0.300546E-01 0.451041E-04 58 -.292707 1 -.832294 .539587 2 -.519258 .226551 4 -.421685 .128978 8 -.374867 0.821608E-01 16 -.347869 0.551623E-01 32 -.330715 0.380086E-01 64 -.319237 0.265303E-01 128 -.311345 0.186387E-01 59 1.37604 1 1.09526 .280786 2 1.26042 .115619 4 1.32010 0.559467E-01 8 1.44772 0.716763E-01 16 .986746 .389297 32 1.07713 .298916 64 1.20643 .169613 128 1.26952 .106525 60 16.0000 1 .194700 15.8053 2 .220878 15.7791 4 1.27737 14.7226 8 1.28292 14.7171 16 5.17319 10.8268 32 5.17318 10.8268 64 12.1905 3.80946 128 12.1904 3.80961 61 .496729 1 0.392837E-01 .457446 2 0.896237E-01 .407106 4 0.931819E-01 .403548 8 .170275 .326454 16 .171684 .325045 32 .258173 .238557 64 .258691 .238038 128 .331831 .164899 62 -2.39368 1 -.666667 1.72701 2 -.815824 1.57785 4 -3.11326 .719584 8 -3.39150 .997824 16 -2.41151 0.178366E-01 32 -2.41079 0.171094E-01 64 -2.38089 0.127857E-01 128 -2.38069 0.129894E-01 63 6.17660 1 4.65698 1.51962 2 5.86229 .314310 4 6.06545 .111156 8 6.06909 .107512 16 6.06909 .107511 32 6.06909 .107511 64 6.06909 .107511 128 6.06909 .107511 64 -.444444 1 -.490129 0.456846E-01 2 -.471144 0.266991E-01 4 -.458076 0.136316E-01 8 -.450859 0.641469E-02 16 -.447304 0.285994E-02 32 -.445672 0.122744E-02 64 -.444957 0.512182E-03 128 -.444654 0.209174E-03 65 -4.00000 1 -.980258 3.01974 2 -1.55239 2.44761 4 -2.05513 1.94487 8 -2.47535 1.52465 16 -2.81679 1.18321 32 -3.08915 .910847 64 -3.30351 .696495 128 -3.47044 .529561 66 52.7407 1 -11.7769 64.5177 2 42.7807 9.96007 4 50.4805 2.26021 8 52.4691 .271599 16 51.8217 .919077 32 52.8604 .119671 64 52.7964 0.556088E-01 128 52.7346 0.612517E-02 67 -.361689 1 -0.266595E-01 .335030 2 -0.981190E-01 .263570 4 -0.964988E-01 .265190 8 -.220962 .140728 16 -.218466 .143224 32 -.313817 0.478721E-01 64 -.311702 0.499876E-01 128 -.343183 0.185066E-01 68 -.128137 1 -0.424430E-15 .128137 2 -.549306 .421169 4 .434294 .562430 8 -.233903 .105766 16 -.151016 0.228792E-01 32 -.134366 0.622943E-02 64 -.129889 0.175260E-02 128 -.128628 0.491628E-03 69 1.00000 1 1.00000 .000000 2 1.14482 .144822 4 .624487 .375513 8 .754231 .245769 16 .673585 .326415 32 .762571 .237429 64 .777277 .222723 128 .839998 .160002 70 .197814 1 -.316254 .514068 2 -.203886 .401699 4 -.193089 .390902 8 -.190257 .388070 16 -.189535 .387348 32 -.189346 .387159 64 -.189295 .387109 128 -.189281 .387095 71 -0.899440E-01 1 0.652174E-01 .155161 2 .909550 .999494 4 -.931213 .841269 8 .862596 .952540 16 -.971462 .881518 32 .828247 .918191 64 -.992841 .902897 128 .818136 .908080 72 1.32152 1 1.15470 .166820 2 2.41703 1.09551 4 1.19237 .129149 8 1.29604 0.254824E-01 16 1.41033 0.888090E-01 32 1.57604 .254522 64 1.43081 .109293 128 1.47347 .151952 73 1.15470 1 1.00000 .154701 2 1.33333 .178633 4 1.14286 0.118434E-01 8 1.15464 0.613631E-04 16 1.15470 0.163057E-08 32 1.15470 0.222045E-15 64 1.15470 0.444089E-15 128 1.15470 0.444089E-15 74 .505059 1 .569783 0.647242E-01 2 .552700 0.476410E-01 4 .512356 0.729694E-02 8 .506807 0.174792E-02 16 .505491 0.432640E-03 32 .505167 0.107895E-03 64 .505086 0.269573E-04 128 .505065 0.673830E-05 75 1.99225 1 2.22222 .229972 2 2.18430 .192050 4 2.03847 0.462221E-01 8 2.00115 0.889651E-02 16 1.99443 0.218141E-02 32 1.99279 0.544361E-03 64 1.99239 0.137723E-03 128 1.99229 0.362260E-04 76 .400000 1 .353553 0.464466E-01 2 .387260 0.127405E-01 4 .396607 0.339318E-02 8 .399114 0.885662E-03 16 .399772 0.228059E-03 32 .399942 0.581915E-04 64 .399985 0.147560E-04 128 .399996 0.372582E-05 TEST02 Composite Simpson rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.71828 1 1.71886 0.579323E-03 2 1.71832 0.370135E-04 4 1.71828 0.232624E-05 8 1.71828 0.145593E-06 16 1.71828 0.910273E-08 32 1.71828 0.568970E-09 64 1.71828 0.355609E-10 128 1.71828 0.222311E-11 2 .700000 1 .833333 .133333 2 .583333 .116667 4 .708333 0.833333E-02 8 .729167 0.291667E-01 16 .697917 0.208333E-02 32 .692708 0.729167E-02 64 .700521 0.520833E-03 128 .701823 0.182292E-02 3 .666667 1 .638071 0.285955E-01 2 .656526 0.101404E-01 4 .663079 0.358739E-02 8 .665398 0.126848E-02 16 .666218 0.448484E-03 32 .666508 0.158564E-03 64 .666611 0.560607E-04 128 .666647 0.198205E-04 4 .479428 1 .479555 0.126359E-03 2 .479555 0.126834E-03 4 .479438 0.978384E-05 8 .479429 0.640566E-06 16 .479428 0.404899E-07 32 .479428 0.253754E-08 64 .479428 0.158521E-09 128 .479428 0.972356E-11 5 1.58223 1 1.71137 .129134 2 1.58497 0.273629E-02 4 1.58217 0.592977E-04 8 1.58223 0.178421E-05 16 1.58223 0.928413E-07 32 1.58223 0.552189E-08 64 1.58223 0.340781E-09 128 1.58223 0.212310E-10 6 1.46045 1 1.58676 .126312 2 1.22434 .236103 4 1.44019 0.202552E-01 8 1.45327 0.717288E-02 16 1.45791 0.253683E-02 32 1.45955 0.896960E-03 64 1.46013 0.317127E-03 128 1.46034 0.112121E-03 7 2.00000 1 1.10948 .890524 2 1.37060 .629398 4 1.55497 .445028 8 1.68532 .314681 16 1.77749 .222513 32 1.84266 .157340 64 1.88874 .111256 128 1.92133 0.786701E-01 8 .866973 1 .877451 0.104780E-01 2 .867114 0.140714E-03 4 .866981 0.806199E-05 8 .866973 0.508704E-06 16 .866973 0.321281E-07 32 .866973 0.232673E-08 64 .866973 0.464087E-09 128 .866973 0.347672E-09 9 1.15470 1 1.00000 .154701 2 1.22222 0.675217E-01 4 1.15079 0.390689E-02 8 1.15468 0.204549E-04 16 1.15470 0.216427E-08 32 1.15470 0.162075E-08 64 1.15470 0.162075E-08 128 1.15470 0.162075E-08 10 .693147 1 .694444 0.129726E-02 2 .693254 0.106788E-03 4 .693155 0.735009E-05 8 .693148 0.472259E-06 16 .693147 0.297299E-07 32 .693147 0.186151E-08 64 .693147 0.116398E-09 128 .693147 0.727574E-11 11 .379885 1 .379851 0.348072E-04 2 .379883 0.199344E-05 4 .379885 0.119353E-06 8 .379885 0.457197E-08 16 .379885 0.256642E-08 32 .379885 0.301203E-08 64 .379885 0.303987E-08 128 .379885 0.304161E-08 12 .777505 1 .777494 0.104847E-04 2 .777504 0.641933E-06 4 .777505 0.361216E-07 8 .777505 0.159987E-08 16 .777505 0.395526E-08 32 .777505 0.410244E-08 64 .777505 0.411164E-08 128 .777505 0.411221E-08 13 1.65835 1 .297431 1.36092 2 1.68321 0.248610E-01 4 1.65932 0.976569E-03 8 1.65840 0.550876E-04 16 1.65835 0.335878E-05 32 1.65835 0.208639E-06 64 1.65835 0.130200E-07 128 1.65835 0.813440E-09 14 .500000 1 11.7851 11.2851 2 5.89256 5.39256 4 2.94628 2.44628 8 1.47314 .973139 16 .736570 .236570 32 .400108 0.998920E-01 64 .474613 0.253867E-01 128 .499989 0.114855E-04 15 1.00000 1 41.6667 40.6667 2 20.8333 19.8333 4 10.4167 9.41667 8 5.20834 4.20834 16 2.60838 1.60838 32 1.40795 .407950 64 1.05470 0.547035E-01 128 1.00453 0.453143E-02 16 .499364 1 2.67059 2.17123 2 1.36857 .869202 4 .752740 .253376 8 .507408 0.804372E-02 16 .466443 0.329212E-01 32 .487977 0.113864E-01 64 .493528 0.583622E-02 128 .493635 0.572919E-02 17 .500000 1 0.321568E-30 .500000 2 .666667 .166667 4 .500000 0.721645E-15 8 .500000 0.832667E-15 16 .500000 0.610623E-15 32 .500000 0.111022E-15 64 .500000 0.111022E-15 128 .500000 0.333067E-15 18 .170557 1 .170670 0.113110E-03 2 .170564 0.677421E-05 4 .170558 0.418452E-06 8 .170557 0.255257E-07 16 .170557 0.103409E-08 32 .170557 0.495600E-09 64 .170557 0.591190E-09 128 .170557 0.597164E-09 19 -1.00000 1 -.462098 .537902 2 -.673517 .326483 4 -.807895 .192105 8 -.889508 .110492 16 -.937534 0.624663E-01 32 -.965157 0.348433E-01 64 -.980773 0.192267E-01 128 -.989484 0.105159E-01 20 1.56440 1 1.65920 0.948055E-01 2 1.56034 0.405345E-02 4 1.56439 0.114061E-04 8 1.56440 0.536257E-07 16 1.56440 0.115717E-08 32 1.56440 0.112944E-08 64 1.56440 0.107368E-08 128 1.56440 0.106935E-08 21 .210803 1 0.183526E-01 .192450 2 .269703 0.589007E-01 4 .187963 0.228399E-01 8 .197033 0.137695E-01 16 .216392 0.558924E-02 32 .205885 0.491805E-02 64 .210619 0.183925E-03 128 .209743 0.105939E-02 22 .728103 1 .730159 0.205582E-02 2 .728080 0.231851E-04 4 .728103 0.167247E-06 8 .728103 0.249305E-08 16 .728103 0.384831E-10 32 .728103 0.599409E-12 64 .728103 0.910383E-14 128 .728103 0.222045E-15 23 .195248 1 0.726876E-01 .122560 2 0.721166E-01 .123131 4 0.976822E-01 0.975654E-01 8 0.976279E-01 0.976196E-01 16 .119720 0.755279E-01 32 .119716 0.755318E-01 64 .136472 0.587751E-01 128 .136472 0.587753E-01 24 .325109 1 0.672186E-01 .257890 2 0.669013E-01 .258207 4 0.952534E-01 .229855 8 0.952243E-01 .229884 16 .122901 .202207 32 .122899 .202209 64 .146734 .178375 128 .146734 .178375 25 13.6280 1 0.543968E-01 13.5736 2 0.543852E-01 13.5736 4 0.928382E-01 13.5352 8 0.928372E-01 13.5352 16 .146846 13.4812 32 .146846 13.4812 64 .214578 13.4134 128 .214578 13.4134 26 -0.469840E-02 1 0.329145E-01 0.376129E-01 2 0.329186E-01 0.376170E-01 4 0.206771E-01 0.253755E-01 8 0.206779E-01 0.253763E-01 16 -0.244586E-01 0.197602E-01 32 -0.244585E-01 0.197601E-01 64 0.716392E-02 0.118623E-01 128 0.716392E-02 0.118623E-01 27 0.158973E-02 1 -0.607998E-01 0.623895E-01 2 0.208892E-01 0.192994E-01 4 -0.205071E-01 0.220968E-01 8 0.132849E-02 0.261236E-03 16 0.102438E-02 0.565348E-03 32 0.152343E-02 0.662974E-04 64 0.155697E-02 0.327637E-04 128 0.157575E-02 0.139827E-04 28 0.561037E-03 1 0.590081E-03 0.290443E-04 2 0.560481E-03 0.555978E-06 4 0.563184E-03 0.214723E-05 8 0.561170E-03 0.132702E-06 16 0.561172E-03 0.134559E-06 32 0.561046E-03 0.841621E-08 64 0.561046E-03 0.841621E-08 128 0.561038E-03 0.535496E-09 29 .162669 Skip to avoid singularity. 30 0.583349E-01 1 0.307770E-01 0.275579E-01 2 0.307768E-01 0.275581E-01 4 0.458378E-01 0.124971E-01 8 0.458377E-01 0.124972E-01 16 0.559839E-01 0.235099E-02 32 0.559839E-01 0.235099E-02 64 0.582673E-01 0.676348E-04 128 0.582673E-01 0.676353E-04 31 1.06346 1 .664770 .398691 2 .689825 .373637 4 .924054 .139408 8 .927880 .135582 16 1.04485 0.186158E-01 32 1.04513 0.183334E-01 64 1.06311 0.353579E-03 128 1.06313 0.336569E-03 32 1.57080 1 .783333 .787463 2 .785392 .785404 4 1.10714 .463656 8 1.10715 .463648 16 1.32582 .244979 32 1.32582 .244979 64 1.44644 .124355 128 1.44644 .124355 33 3.14159 1 .711873 2.42972 2 .952078 2.18951 4 1.29195 1.84964 8 1.46928 1.67231 16 1.77295 1.36864 32 1.90090 1.24069 64 2.14852 .993071 128 2.23986 .901735 34 .500000 1 .554648 0.546482E-01 2 .555349 0.553490E-01 4 .589639 0.896391E-01 8 .589686 0.896865E-01 16 .499053 0.947408E-03 32 .499055 0.944879E-03 64 .500190 0.190182E-03 128 .500190 0.190341E-03 35 1.57080 1 .946146 .624650 2 .946087 .624709 4 1.60542 0.346218E-01 8 1.60541 0.346170E-01 16 1.75820 .187407 32 1.75820 .187407 64 1.57419 0.339050E-02 128 1.57419 0.339050E-02 36 .624713 1 1.35264 .727929 2 -.203876 .828589 4 2.00457 1.37985 8 .334548 .290165 16 .916364 .291651 32 2.31233 1.68762 64 1.69459 1.06988 128 -.608292 1.23300 37 -0.675475E-02 1 .101552 .108307 2 0.891432E-02 0.156691E-01 4 -0.877240E-02 0.201765E-02 8 -0.111108E-01 0.435605E-02 16 -0.635132E-02 0.403428E-03 32 -0.671303E-02 0.417187E-04 64 -0.667696E-02 0.777840E-04 128 -0.677494E-02 0.201948E-04 38 -1.61086 1 -1.33307 .277798 2 -1.66304 0.521760E-01 4 -1.51709 0.937722E-01 8 -1.62417 0.133043E-01 16 -1.58744 0.234208E-01 32 -1.61419 0.332766E-02 64 -1.60501 0.585509E-02 128 -1.61170 0.831922E-03 39 7.95493 1 7.23413 .720801 2 7.42061 .534316 4 7.94346 0.114640E-01 8 7.95493 0.417230E-06 16 7.95493 0.444089E-14 32 7.95493 0.621725E-14 64 7.95493 0.355271E-14 128 7.95493 0.532907E-14 40 .841117 1 .527539 .313578 2 .635551 .205566 4 .706693 .134424 8 .753456 0.876604E-01 16 .784106 0.570113E-01 32 .804134 0.369832E-01 64 .817184 0.239327E-01 128 .825665 0.154521E-01 41 0.199547E-01 1 0.181632E-15 0.199547E-01 2 0.722055E-16 0.199547E-01 4 .394547 .374593 8 .399413 .379459 16 -.150243 .170198 32 -0.726952E-01 0.926499E-01 64 0.314613E-01 0.115066E-01 128 0.202592E-01 0.304486E-03 42 .306853 1 .350000 0.431472E-01 2 .256481 0.503713E-01 4 .303303 0.355024E-02 8 .310878 0.402518E-02 16 .299340 0.751264E-02 32 .305109 0.174349E-02 64 .306067 0.785639E-03 128 .306546 0.306711E-03 43 7.95493 1 7.23413 .720801 2 7.42061 .534316 4 7.94346 0.114640E-01 8 7.95493 0.417230E-06 16 7.95493 0.444089E-14 32 7.95493 0.621725E-14 64 7.95493 0.355271E-14 128 7.95493 0.532907E-14 44 2.65164 1 5.49020 2.83856 2 2.47843 .173204 4 2.57255 0.790863E-01 8 2.64773 0.390076E-02 16 2.65163 0.804438E-05 32 2.65164 0.466730E-07 64 2.65164 0.292119E-08 128 2.65164 0.182664E-09 45 -12.0703 1 -11.5928 .477507 2 -11.9849 0.854023E-01 4 -12.0642 0.613736E-02 8 -12.0700 0.394993E-03 16 -12.0703 0.248603E-04 32 -12.0703 0.155646E-05 64 -12.0703 0.973205E-07 128 -12.0703 0.608319E-08 46 .886227 1 .555036 .331191 2 .710016 .176211 4 .792758 0.934694E-01 8 .836822 0.494046E-01 16 .860208 0.260189E-01 32 .872572 0.136547E-01 64 .879085 0.714224E-02 128 .882502 0.372443E-02 47 1085.25 1 1168.59 83.3333 2 1090.46 5.20833 4 1085.58 .325521 8 1085.27 0.203451E-01 16 1085.25 0.127157E-02 32 1085.25 0.794729E-04 64 1085.25 0.496705E-05 128 1085.25 0.310441E-06 48 26.0000 1 18.6450 7.35495 2 19.3941 6.60590 4 22.4882 3.51178 8 23.6843 2.31567 16 24.1787 1.82134 32 25.0119 .988147 64 24.9568 1.04321 128 26.1862 .186198 49 100.000 1 .862306 99.1377 2 1.94893 98.0511 4 3.33304 96.6670 8 4.97136 95.0286 16 6.82375 93.1763 32 8.85420 91.1458 64 11.0306 88.9694 128 13.3242 86.6758 50 3.13580 1 0.117908E-01 3.12401 2 .264622 2.87118 4 0.950659E-01 3.04073 8 .166266 2.96953 16 2.32296 .812843 32 .834530 2.30127 64 1.21332 1.92248 128 5.68558 2.54978 51 .539257 1 .742463 .203206 2 2.14426 1.60500 4 0.717440E-01 .467513 8 .539094 0.163376E-03 16 .539257 0.222045E-15 32 .539257 0.444089E-15 64 .539257 0.111022E-15 128 .539257 0.333067E-15 52 2.78769 1 2.12579 .661901 2 2.32575 .461947 4 2.46181 .325888 8 2.55732 .230370 16 2.62480 .162891 32 2.67251 .115181 64 2.70625 0.814453E-01 128 2.73010 0.575905E-01 53 2.69896 1 1.79575 .903208 2 2.81314 .114187 4 2.28795 .411005 8 2.41539 .283563 16 2.76077 0.618128E-01 32 2.55728 .141677 64 2.59466 .104297 128 2.82626 .127305 54 6.09559 Skip to avoid singularity. 55 3.98079 Skip to avoid singularity. 56 2.99157 Skip to avoid singularity. 57 -0.300997E-01 1 -.126106 0.960065E-01 2 -0.627430E-01 0.326433E-01 4 -0.361940E-01 0.609425E-02 8 -0.306966E-01 0.596941E-03 16 -0.301423E-01 0.426078E-04 32 -0.301025E-01 0.275693E-05 64 -0.300999E-01 0.173824E-06 128 -0.300997E-01 0.108879E-07 58 -.292707 Skip to avoid singularity. 59 1.37604 Skip to avoid singularity. 60 16.0000 1 .230889 15.7691 2 .230246 15.7698 4 1.28488 14.7151 8 1.28483 14.7152 16 5.17318 10.8268 32 5.17318 10.8268 64 12.1903 3.80965 128 12.1903 3.80965 61 .496729 Skip to avoid singularity. 62 -2.39368 Skip to avoid singularity. 63 6.17660 1 5.74112 .435486 2 6.00259 .174012 4 6.06788 .108725 8 6.06909 .107511 16 6.06909 .107511 32 6.06909 .107511 64 6.06909 .107511 128 6.06909 .107511 64 -.444444 Skip to avoid singularity. 65 -4.00000 Skip to avoid singularity. 66 52.7407 1 46.4910 6.24977 2 53.7288 .988013 4 53.3880 .647210 8 53.2600 .519241 16 52.4329 .307831 32 52.8198 0.790446E-01 64 52.7974 0.566497E-01 128 52.7557 0.149733E-01 67 -.361689 Skip to avoid singularity. 68 -.128137 1 -0.282953E-15 .128137 2 -.366204 .238067 4 .197978 .326115 8 -.129329 0.119172E-02 16 -.126358 0.177901E-02 32 -.127587 0.549761E-03 64 -.127992 0.144721E-03 128 -.128100 0.367076E-04 69 1.00000 Skip to avoid singularity. 70 .197814 1 -.210836 .408650 2 -.188633 .386446 4 -.189061 .386875 8 -.189187 .387000 16 -.189240 .387054 32 -.189262 .387075 64 -.189270 .387083 128 -.189273 .387087 71 -0.899440E-01 1 -.956205 .866261 2 .117395 .207339 4 -.713703 .623759 8 .373414 .463358 16 -.604700 .514756 32 .411725 .501669 64 -.594073 .504129 128 .413861 .503805 72 1.32152 1 1.05432 .267203 2 1.94606 .624541 4 1.36511 0.435866E-01 8 1.34785 0.263298E-01 16 1.39814 0.766180E-01 32 1.51471 .193189 64 1.44856 .127036 128 1.46812 .146604 73 1.15470 1 1.00000 .154701 2 1.22222 0.675217E-01 4 1.15079 0.390689E-02 8 1.15468 0.204533E-04 16 1.15470 0.543522E-09 32 1.15470 .000000 64 1.15470 0.444089E-15 128 1.15470 .000000 74 .505059 1 .475874 0.291847E-01 2 .511440 0.638096E-02 4 .505174 0.114941E-03 8 .505065 0.659279E-05 16 .505059 0.403280E-06 32 .505059 0.250707E-07 64 .505059 0.156483E-08 128 .505059 0.977695E-10 75 1.99225 1 1.83236 .159891 2 2.00201 0.975919E-02 4 1.99594 0.368591E-02 8 1.99232 0.702891E-04 16 1.99226 0.666298E-05 32 1.99225 0.267134E-05 64 1.99225 0.242437E-05 128 1.99225 0.240898E-05 76 .400000 1 .402369 0.236893E-02 2 .400432 0.431916E-03 4 .400077 0.772494E-04 8 .400014 0.137135E-04 16 .400002 0.242785E-05 32 .400000 0.429413E-06 64 .400000 0.759245E-07 128 .400000 0.134226E-07 TEST03 Monte Carlo rule, for 1D finite interval problems. Problem Exact Pts Approx Error 1 1.71828 1 2.67487 .956587 2 1.66530 0.529844E-01 4 2.00618 .287895 8 1.93613 .217850 16 1.89192 .173639 32 1.67193 0.463509E-01 64 1.87807 .159792 128 1.70135 0.169287E-01 256 1.73196 0.136761E-01 512 1.70869 0.959434E-02 1024 1.70448 0.138001E-01 2 .700000 1 .000000 .700000 2 1.00000 .300000 4 .250000 .450000 8 .750000 0.500000E-01 16 .875000 .175000 32 .656250 0.437500E-01 64 .687500 0.125000E-01 128 .726562 0.265625E-01 256 .667969 0.320312E-01 512 .675781 0.242187E-01 1024 .702148 0.214844E-02 3 .666667 1 .662409 0.425816E-02 2 .431550 .235117 4 .646973 0.196932E-01 8 .688449 0.217820E-01 16 .655367 0.112992E-01 32 .669317 0.264989E-02 64 .646958 0.197085E-01 128 .675086 0.841901E-02 256 .648310 0.183563E-01 512 .668444 0.177745E-02 1024 .663879 0.278786E-02 4 .479428 1 1.08565 .606227 2 .280185 .199243 4 .158568 .320860 8 .428685 0.507429E-01 16 .533014 0.535855E-01 32 .438414 0.410146E-01 64 .534266 0.548376E-01 128 .463699 0.157294E-01 256 .471787 0.764102E-02 512 .481209 0.178123E-02 1024 .461446 0.179826E-01 5 1.58223 1 1.29370 .288533 2 1.48299 0.992472E-01 4 1.19779 .384444 8 1.88228 .300043 16 1.45096 .131271 32 1.42995 .152287 64 1.48415 0.980875E-01 128 1.58017 0.206567E-02 256 1.61918 0.369476E-01 512 1.56810 0.141295E-01 1024 1.57618 0.605750E-02 6 1.46045 1 1.35827 .102179 2 1.02419 .436261 4 1.51246 0.520129E-01 8 1.84732 .386871 16 1.35402 .106428 32 1.37061 0.898380E-01 64 1.47634 0.158899E-01 128 1.40566 0.547859E-01 256 1.44287 0.175803E-01 512 1.42944 0.310042E-01 1024 1.44393 0.165201E-01 7 2.00000 1 1.10460 .895396 2 1.38277 .617229 4 1.33529 .664714 8 1.57753 .422466 16 1.50862 .491376 32 2.11651 .116507 64 2.13763 .137635 128 1.87955 .120451 256 1.84716 .152842 512 1.82072 .179276 1024 1.88770 .112305 8 .866973 1 .747835 .119138 2 .890782 0.238095E-01 4 .849842 0.171311E-01 8 .897934 0.309613E-01 16 .882345 0.153718E-01 32 .852520 0.144534E-01 64 .868499 0.152579E-02 128 .861819 0.515419E-02 256 .880163 0.131902E-01 512 .863681 0.329203E-02 1024 .861954 0.501864E-02 9 1.15470 1 1.06130 0.933994E-01 2 .929592 .225109 4 1.31526 .160557 8 .847240 .307461 16 1.11564 0.390646E-01 32 1.28405 .129353 64 1.11105 0.436555E-01 128 1.19359 0.388919E-01 256 1.08730 0.673974E-01 512 1.14031 0.143915E-01 1024 1.15378 0.917896E-03 10 .693147 1 .930179 .237032 2 .753537 0.603893E-01 4 .697871 0.472393E-02 8 .594282 0.988654E-01 16 .681326 0.118210E-01 32 .724228 0.310810E-01 64 .677382 0.157656E-01 128 .676213 0.169344E-01 256 .687330 0.581711E-02 512 .690486 0.266069E-02 1024 .692458 0.689280E-03 11 .379885 1 .469856 0.899703E-01 2 .364550 0.153353E-01 4 .393993 0.141080E-01 8 .411146 0.312602E-01 16 .383449 0.356334E-02 32 .381270 0.138463E-02 64 .384635 0.474984E-02 128 .375086 0.479941E-02 256 .377461 0.242431E-02 512 .378367 0.151895E-02 1024 .380921 0.103586E-02 12 .777505 1 .793463 0.159579E-01 2 .656828 .120677 4 .763593 0.139112E-01 8 .831835 0.543307E-01 16 .748008 0.294970E-01 32 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0.481413E-01 128 -.636002 .274313 256 -0.894839E-01 .272205 512 -.433114 0.714252E-01 1024 -.336186 0.255032E-01 68 -.128137 1 -.371443 .243306 2 -.860285 .732148 4 -.371273 .243136 8 -.265854 .137717 16 -.294167 .166030 32 -.299547 .171410 64 -.262093 .133956 128 -.253904 .125767 256 -0.826248E-01 0.455121E-01 512 -.134704 0.656701E-02 1024 -.171330 0.431933E-01 69 1.00000 1 .903276 0.967241E-01 2 .792379 .207621 4 1.70525 .705253 8 1.68235 .682350 16 .956307 0.436926E-01 32 1.07976 0.797580E-01 64 4.26246 3.26246 128 2.80514 1.80514 256 .454339 .545661 512 .296857 .703143 1024 .891627 .108373 70 .197814 1 -0.915538E-01 .289367 2 -0.910195E-01 .288833 4 -.163454 .361268 8 -.194317 .392130 16 -.207151 .404964 32 -.177628 .375441 64 -.186192 .384005 128 -.176981 .374794 256 -.185797 .383611 512 -.187262 .385075 1024 -.187694 .385508 71 -0.899440E-01 1 0.193151E-01 .109259 2 3.01215 3.10209 4 .133086 .223030 8 1.16461 1.25455 16 .645834 .735778 32 -.303040 .213096 64 -.272163 .182219 128 .640729 .730673 256 -1.79830 1.70836 512 -.876757 .786813 1024 .192069 .282013 72 1.32152 1 1.18106 .140465 2 1.02112 .300403 4 1.13390 .187625 8 2.81277 1.49125 16 1.32913 0.760589E-02 32 1.42591 .104391 64 1.99774 .676223 128 2.01258 .691064 256 1.45430 .132776 512 1.47279 .151268 1024 1.60972 .288203 73 1.15470 1 1.90652 .751821 2 .765628 .389072 4 1.24377 0.890674E-01 8 .952254 .202447 16 1.32126 .166558 32 1.11385 0.408465E-01 64 1.19326 0.385553E-01 128 1.13302 0.216819E-01 256 1.20612 0.514167E-01 512 1.16516 0.104585E-01 1024 1.16240 0.770215E-02 74 .505059 1 .244448 .260611 2 .365778 .139281 4 .493568 0.114909E-01 8 .230950 .274109 16 .608327 .103269 32 .495956 0.910258E-02 64 .475662 0.293969E-01 128 .548600 0.435410E-01 256 .507488 0.242915E-02 512 .504550 0.508248E-03 1024 .496732 0.832653E-02 75 1.99225 1 2.18085 .188596 2 1.68964 .302605 4 2.22185 .229595 8 2.11315 .120903 16 2.05771 0.654599E-01 32 1.98489 0.736144E-02 64 1.93919 0.530563E-01 128 2.00063 0.838142E-02 256 1.98895 0.329883E-02 512 2.00515 0.129029E-01 1024 2.01869 0.264404E-01 76 .400000 1 .125893 .274107 2 .619627 .219627 4 .631193 .231193 8 .407240 0.724004E-02 16 .514901 .114901 32 .349461 0.505388E-01 64 .376342 0.236584E-01 128 .338056 0.619444E-01 256 .417203 0.172028E-01 512 .381225 0.187747E-01 1024 .413079 0.130794E-01 TEST04 Use a composite 4 point Gauss-Legendre rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.71828 1 1.71828 0.112491E-08 2 1.71828 0.180678E-09 4 1.71828 0.173125E-09 8 1.71828 0.172149E-09 16 1.71828 0.171908E-09 32 1.71828 0.171848E-09 64 1.71828 0.171833E-09 128 1.71828 0.171829E-09 2 .700000 1 .826073 .126073 2 .750000 0.500000E-01 4 .706518 0.651814E-02 8 .687500 0.125000E-01 16 .698370 0.162954E-02 32 .703125 0.312500E-02 64 .700407 0.407384E-03 128 .699219 0.781250E-03 3 .666667 1 .667828 0.116098E-02 2 .667077 0.410474E-03 4 .666812 0.145124E-03 8 .666718 0.513092E-04 16 .666685 0.181405E-04 32 .666673 0.641359E-05 64 .666669 0.226750E-05 128 .666667 0.801641E-06 4 .479428 1 .479428 0.916743E-08 2 .479428 0.287087E-09 4 .479428 0.606055E-10 8 .479428 0.510179E-10 16 .479428 0.488594E-10 32 .479428 0.483205E-10 64 .479428 0.481858E-10 128 .479428 0.481518E-10 5 1.58223 1 1.58506 0.282752E-02 2 1.58221 0.193087E-04 4 1.58223 0.364086E-07 8 1.58223 0.124111E-09 16 1.58223 0.157811E-09 32 1.58223 0.158157E-09 64 1.58223 0.158207E-09 128 1.58223 0.158218E-09 6 1.46045 1 1.47344 0.129970E-01 2 1.48618 0.257291E-01 4 1.46127 0.820942E-03 8 1.46074 0.290249E-03 16 1.46055 0.102618E-03 32 1.46048 0.362810E-04 64 1.46046 0.128272E-04 128 1.46045 0.453499E-05 7 2.00000 1 1.80634 .193657 2 1.86306 .136937 4 1.90317 0.968288E-01 8 1.93153 0.684683E-01 16 1.95159 0.484144E-01 32 1.96577 0.342342E-01 64 1.97579 0.242072E-01 128 1.98288 0.171171E-01 8 .866973 1 .866956 0.173296E-04 2 .866973 0.558794E-07 4 .866973 0.421947E-09 8 .866973 0.253959E-09 16 .866973 0.253263E-09 32 .866973 0.253226E-09 64 .866973 0.253217E-09 128 .866973 0.253215E-09 9 1.15470 1 1.19781 0.431128E-01 2 1.24661 0.919063E-01 4 1.14775 0.695461E-02 8 1.15466 0.357517E-04 16 1.15470 0.268614E-08 32 1.15470 0.173622E-08 64 1.15470 0.173622E-08 128 1.15470 0.173622E-08 10 .693147 1 .693146 0.763192E-06 2 .693147 0.687786E-08 4 .693147 0.107104E-09 8 .693147 0.696163E-10 16 .693147 0.693503E-10 32 .693147 0.693235E-10 64 .693147 0.693161E-10 128 .693147 0.693159E-10 11 .379885 1 .379885 0.427600E-08 2 .379885 0.300741E-08 4 .379885 0.300371E-08 8 .379885 0.300372E-08 16 .379885 0.300373E-08 32 .379885 0.300373E-08 64 .379885 0.300373E-08 128 .379885 0.300373E-08 12 .777505 1 .777505 0.404618E-08 2 .777505 0.403407E-08 4 .777505 0.403438E-08 8 .777505 0.403447E-08 16 .777505 0.403449E-08 32 .777505 0.403450E-08 64 .777505 0.403450E-08 128 .777505 0.403450E-08 13 1.65835 1 1.66610 0.775417E-02 2 1.65834 0.947065E-05 4 1.65835 0.267356E-07 8 1.65835 0.258713E-09 16 1.65835 0.165827E-09 32 1.65835 0.165745E-09 64 1.65835 0.165814E-09 128 1.65835 0.165831E-09 14 .500000 1 .000000 .500000 2 0.369083E-07 .500000 4 0.270625E-01 .472938 8 .470876 0.291239E-01 16 .573638 0.736378E-01 32 .493226 0.677446E-02 64 .500077 0.769705E-04 128 .500000 0.175108E-06 15 1.00000 1 0.125847E-05 .999999 2 0.369866E-02 .996301 4 .141785 .858215 8 .621078 .378922 16 .947909 0.520906E-01 32 .998223 0.177698E-02 64 .999981 0.189316E-04 128 1.00000 0.104646E-06 16 .499364 1 .236976 .262388 2 .400596 0.987676E-01 4 .509088 0.972390E-02 8 .503719 0.435566E-02 16 .493170 0.619385E-02 32 .493618 0.574619E-02 64 .493635 0.572882E-02 128 .493635 0.572915E-02 17 .500000 1 .997235 .497235 2 .515987 0.159871E-01 4 .500000 0.500000E-10 8 .500000 0.500006E-10 16 .500000 0.499983E-10 32 .500000 0.500005E-10 64 .500000 0.499996E-10 128 .500000 0.499997E-10 18 .170557 1 .170557 0.128440E-08 2 .170557 0.616461E-09 4 .170557 0.614310E-09 8 .170557 0.614538E-09 16 .170557 0.614598E-09 32 .170557 0.614613E-09 64 .170557 0.614616E-09 128 .170557 0.614617E-09 19 -1.00000 1 -.968536 0.314640E-01 2 -.984268 0.157321E-01 4 -.992134 0.786604E-02 8 -.996067 0.393302E-02 16 -.998033 0.196651E-02 32 -.999017 0.983255E-03 64 -.999508 0.491628E-03 128 -.999754 0.245814E-03 20 1.56440 1 1.56227 0.212929E-02 2 1.56441 0.949464E-05 4 1.56440 0.231599E-07 8 1.56440 0.913063E-09 16 1.56440 0.912796E-09 32 1.56440 0.912657E-09 64 1.56440 0.912622E-09 128 1.56440 0.912613E-09 21 .210803 1 .128374 0.824283E-01 2 .197150 0.136530E-01 4 .197678 0.131248E-01 8 .197680 0.131224E-01 16 .210842 0.389964E-04 32 .209812 0.990258E-03 64 .209975 0.827246E-03 128 .210004 0.799021E-03 22 .728103 1 .728090 0.133961E-04 2 .728103 0.390468E-07 4 .728103 0.510577E-10 8 .728103 0.726021E-10 16 .728103 0.727791E-10 32 .728103 0.728023E-10 64 .728103 0.728084E-10 128 .728103 0.728089E-10 23 .195248 1 0.720594E-01 .123188 2 0.720601E-01 .123187 4 0.976238E-01 0.976238E-01 8 0.976238E-01 0.976238E-01 16 .119715 0.755320E-01 32 .119715 0.755320E-01 64 .136472 0.587754E-01 128 .136472 0.587754E-01 24 .325109 1 0.668710E-01 .258238 2 0.668713E-01 .258237 4 0.952221E-01 .229886 8 0.952221E-01 .229886 16 .122899 .202209 32 .122899 .202209 64 .146734 .178375 128 .146734 .178375 25 13.6280 1 0.543844E-01 13.5736 2 0.543844E-01 13.5736 4 0.928372E-01 13.5352 8 0.928372E-01 13.5352 16 .146846 13.4812 32 .146846 13.4812 64 .214578 13.4134 128 .214578 13.4134 26 -0.469840E-02 1 0.329189E-01 0.376173E-01 2 0.329189E-01 0.376173E-01 4 0.206779E-01 0.253763E-01 8 0.206779E-01 0.253763E-01 16 -0.244585E-01 0.197601E-01 32 -0.244585E-01 0.197601E-01 64 0.716392E-02 0.118623E-01 128 0.716392E-02 0.118623E-01 27 0.158973E-02 1 0.167797E-01 0.151900E-01 2 0.158967E-01 0.143070E-01 4 0.143665E-02 0.153079E-03 8 0.137676E-02 0.212969E-03 16 0.152750E-02 0.622280E-04 32 0.152632E-02 0.634093E-04 64 0.157605E-02 0.136820E-04 128 0.157602E-02 0.137116E-04 28 0.561037E-03 1 0.558394E-03 0.264347E-05 2 0.558388E-03 0.264945E-05 4 0.561035E-03 0.181856E-08 8 0.561035E-03 0.183762E-08 16 0.561037E-03 0.100645E-10 32 0.561037E-03 0.102312E-10 64 0.561037E-03 0.102312E-10 128 0.561037E-03 0.100888E-10 29 .162669 1 .149501 0.131677E-01 2 .154043 0.862580E-02 4 .190552 0.278827E-01 8 .193773 0.311037E-01 16 .152142 0.105273E-01 32 .154422 0.824659E-02 64 .169977 0.730759E-02 128 .171590 0.892139E-02 30 0.583349E-01 1 0.307767E-01 0.275582E-01 2 0.307767E-01 0.275582E-01 4 0.458377E-01 0.124972E-01 8 0.458377E-01 0.124972E-01 16 0.559839E-01 0.235099E-02 32 0.559839E-01 0.235099E-02 64 0.582673E-01 0.676353E-04 128 0.582673E-01 0.676353E-04 31 1.06346 1 .694035 .369427 2 .693966 .369495 4 .928177 .135284 8 .928181 .135281 16 1.04515 0.183154E-01 32 1.04515 0.183153E-01 64 1.06313 0.335463E-03 128 1.06313 0.335463E-03 32 1.57080 1 .785403 .785393 2 .785398 .785398 4 1.10715 .463648 8 1.10715 .463648 16 1.32582 .244979 32 1.32582 .244979 64 1.44644 .124355 128 1.44644 .124355 33 3.14159 1 1.37592 1.76567 2 1.43344 1.70815 4 1.77328 1.36832 8 1.81366 1.32793 16 2.11732 1.02427 32 2.14578 .995815 64 2.39340 .748194 128 2.41349 .728106 34 .500000 1 .555397 0.553969E-01 2 .555397 0.553969E-01 4 .589690 0.896897E-01 8 .589690 0.896897E-01 16 .499055 0.944710E-03 32 .499055 0.944710E-03 64 .500190 0.190351E-03 128 .500190 0.190351E-03 35 1.57080 1 .946083 .624713 2 .946083 .624713 4 1.60541 0.346166E-01 8 1.60541 0.346166E-01 16 1.75820 .187407 32 1.75820 .187407 64 1.57419 0.339049E-02 128 1.57419 0.339049E-02 36 .624713 1 3.17665 2.55194 2 -.594889 1.21960 4 2.25275 1.62804 8 1.84406 1.21934 16 -3.18856 3.81327 32 2.45470 1.82999 64 -2.14491 2.76963 128 1.29187 .667160 37 -0.675475E-02 1 0.365511E-02 0.104099E-01 2 0.152656E-01 0.220203E-01 4 0.479136E-02 0.115461E-01 8 -0.561279E-02 0.114195E-02 16 -0.659449E-02 0.160254E-03 32 -0.651672E-02 0.238021E-03 64 -0.678865E-02 0.339057E-04 128 -0.673083E-02 0.239155E-04 38 -1.61086 1 -1.80289 .192024 2 -1.57279 0.380774E-01 4 -1.56576 0.451066E-01 8 -1.60134 0.951960E-02 16 -1.59959 0.112767E-01 32 -1.60848 0.237990E-02 64 -1.60805 0.281916E-02 128 -1.61027 0.594975E-03 39 7.95493 1 7.94092 0.140102E-01 2 7.95263 0.229410E-02 4 7.95496 0.365707E-04 8 7.95493 0.541108E-09 16 7.95493 0.795488E-09 32 7.95493 0.795493E-09 64 7.95493 0.795489E-09 128 7.95493 0.795497E-09 40 .841117 1 .797664 0.434532E-01 2 .813100 0.280170E-01 4 .823093 0.180237E-01 8 .829546 0.115708E-01 16 .833703 0.741397E-02 32 .836375 0.474222E-02 64 .838088 0.302846E-02 128 .839186 0.193124E-02 41 0.199547E-01 1 .124191 .104236 2 -.177256 .197210 4 0.948975E-01 0.749428E-01 8 .227422 .207467 16 .354106 .334151 32 0.225451E-01 0.259046E-02 64 0.199424E-01 0.123037E-04 128 0.199547E-01 0.183805E-07 42 .306853 1 .346116 0.392629E-01 2 .318629 0.117765E-01 4 .302542 0.431111E-02 8 .310523 0.367009E-02 16 .307028 0.175026E-03 32 .307025 0.172216E-03 64 .307025 0.172216E-03 128 .307025 0.172216E-03 43 7.95493 1 7.94092 0.140102E-01 2 7.95263 0.229410E-02 4 7.95496 0.365707E-04 8 7.95493 0.541108E-09 16 7.95493 0.795488E-09 32 7.95493 0.795493E-09 64 7.95493 0.795489E-09 128 7.95493 0.795497E-09 44 2.65164 1 2.04729 .604350 2 2.65543 0.379112E-02 4 2.65082 0.817563E-03 8 2.65165 0.980452E-05 16 2.65164 0.231236E-07 32 2.65164 0.265039E-09 64 2.65164 0.265149E-09 128 2.65164 0.265159E-09 45 -12.0703 1 -12.0702 0.156831E-03 2 -12.0703 0.324036E-05 4 -12.0703 0.164037E-07 8 -12.0703 0.131258E-08 16 -12.0703 0.121842E-08 32 -12.0703 0.120983E-08 64 -12.0703 0.120773E-08 128 -12.0703 0.120721E-08 46 .886227 1 .880399 0.582799E-02 2 .883352 0.287455E-02 4 .884818 0.140888E-02 8 .885539 0.687677E-03 16 .885892 0.334806E-03 32 .886064 0.162779E-03 64 .886148 0.790953E-04 128 .886188 0.384321E-04 47 1085.25 1 1085.25 0.379683E-06 2 1085.25 0.187751E-06 4 1085.25 0.129046E-06 8 1085.25 0.113700E-06 16 1085.25 0.109822E-06 32 1085.25 0.108850E-06 64 1085.25 0.108607E-06 128 1085.25 0.108546E-06 48 26.0000 1 29.1002 3.10021 2 21.4437 4.55633 4 121.740 95.7402 8 32.2505 6.25050 16 30.6850 4.68495 32 26.5430 .543024 64 25.8498 .150151 128 25.4518 .548202 49 100.000 1 6.29854 93.7015 2 8.34127 91.6587 4 10.5306 89.4694 8 12.8378 87.1622 16 15.2372 84.7628 32 17.7061 82.2939 64 20.2245 79.7755 128 22.7746 77.2254 50 3.13580 1 0.338325E-01 3.10197 2 0.818374E-01 3.05396 4 .197291 2.93851 8 1.21299 1.92280 16 .643995 2.49180 32 1.64518 1.49062 64 3.23778 .101980 128 2.59874 .537061 51 .539257 1 1.51305 .973790 2 .406660 .132597 4 .540695 0.143763E-02 8 .539257 0.523323E-06 16 .539257 0.539268E-10 32 .539257 0.539266E-10 64 .539257 0.539259E-10 128 .539257 0.539255E-10 52 2.78769 1 6.78140 3.99370 2 5.61163 2.82394 4 4.78452 1.99683 8 4.19966 1.41197 16 3.78611 .998413 32 3.49368 .705985 64 3.28690 .499207 128 3.14069 .352992 53 2.69896 1 2.10507 .593885 2 2.28468 .414276 4 2.41720 .281753 8 2.65152 0.474357E-01 16 2.54806 .150898 32 2.60573 0.932308E-01 64 2.65617 0.427867E-01 128 2.63761 0.613442E-01 54 6.09559 1 4.29442 1.80117 2 4.86748 1.22810 4 5.25298 .842609 8 5.50856 .587030 16 5.68314 .412447 32 5.80479 .290793 64 5.89025 .205332 128 5.95049 .145091 55 3.98079 1 2.96736 1.01342 2 3.15764 .823142 4 3.31219 .668596 8 3.43772 .543068 16 3.53968 .441108 32 3.62250 .358291 64 3.68976 .291023 128 3.74440 .236384 56 2.99157 1 2.10711 .884460 2 2.27296 .718612 4 2.40779 .583781 8 2.51735 .474215 16 2.60637 .385199 32 2.67868 .312886 64 2.73742 .254146 128 2.78514 .206432 57 -0.300997E-01 1 -0.236000E-01 0.649971E-02 2 -0.297061E-01 0.393636E-03 4 -0.300941E-01 0.559488E-05 8 -0.300997E-01 0.333874E-07 16 -0.300997E-01 0.149265E-09 32 -0.300997E-01 0.379894E-11 64 -0.300997E-01 0.306397E-11 128 -0.300997E-01 0.302295E-11 58 -.292707 1 -.362859 0.701522E-01 2 -.341268 0.485615E-01 4 -.326652 0.339448E-01 8 -.316566 0.238597E-01 16 -.309527 0.168202E-01 32 -.304582 0.118755E-01 64 -.301097 0.839079E-02 128 -.298638 0.593090E-02 59 1.37604 1 1.49105 .115006 2 1.54794 .171894 4 1.61450 .238460 8 1.65467 .278630 16 1.19496 .181081 32 1.22335 .152697 64 1.35250 0.235436E-01 128 1.37256 0.348150E-02 60 16.0000 1 .230203 15.7698 2 .230203 15.7698 4 1.28482 14.7152 8 1.28482 14.7152 16 5.17318 10.8268 32 5.17318 10.8268 64 12.1903 3.80965 128 12.1903 3.80965 61 .496729 1 .269045 .227684 2 .342396 .154333 4 .346118 .150612 8 .394072 .102657 16 .395486 .101243 32 .426320 0.704097E-01 64 .426838 0.698910E-01 128 .447646 0.490838E-01 62 -2.39368 1 -.840717 1.55296 2 -.841093 1.55258 4 -3.99263 1.59895 8 -4.26988 1.87621 16 -2.41053 0.168572E-01 32 -2.41053 0.168572E-01 64 -2.38062 0.130576E-01 128 -2.38062 0.130576E-01 63 6.17660 1 6.06337 .113230 2 6.06890 .107698 4 6.06909 .107507 8 6.06909 .107511 16 6.06909 .107511 32 6.06909 .107511 64 6.06909 .107511 128 6.06909 .107511 64 -.444444 1 -.448878 0.443311E-02 2 -.446296 0.185187E-02 4 -.445200 0.755327E-03 8 -.444747 0.302613E-03 16 -.444564 0.119564E-03 32 -.444491 0.467179E-04 64 -.444463 0.180890E-04 128 -.444451 0.695109E-05 65 -4.00000 1 -2.56246 1.43754 2 -2.88859 1.11141 4 -3.14700 .853003 8 -3.34938 .650623 16 -3.50638 .493618 32 -3.62723 .372770 64 -3.71963 .280367 128 -3.78989 .210114 66 52.7407 1 52.4911 .249654 2 50.7370 2.00374 4 52.2435 .497236 8 52.5621 .178668 16 52.6861 0.546064E-01 32 52.6314 .109398 64 52.7231 0.175987E-01 128 52.6833 0.574527E-01 67 -.361689 1 -.346421 0.152683E-01 2 -.361009 0.680579E-03 4 -.359481 0.220804E-02 8 -.362167 0.477701E-03 16 -.359670 0.201892E-02 32 -.363727 0.203749E-02 64 -.361611 0.782089E-04 128 -.363573 0.188382E-02 68 -.128137 1 -.183037 0.549001E-01 2 0.679213E-01 .196058 4 -.131315 0.317850E-02 8 -.128444 0.307245E-03 16 -.128216 0.790615E-04 32 -.128157 0.198788E-04 64 -.128142 0.497690E-05 128 -.128138 0.124467E-05 69 1.00000 1 1.36619 .366190 2 1.42286 .422861 4 .920857 0.791426E-01 8 .960956 0.390437E-01 16 .879680 .120320 32 .908039 0.919612E-01 64 .922771 0.772286E-01 128 .942825 0.571750E-01 70 .197814 1 -.189169 .386983 2 -.189298 .387111 4 -.189284 .387097 8 -.189278 .387092 16 -.189276 .387090 32 -.189276 .387089 64 -.189275 .387089 128 -.189275 .387089 71 -0.899440E-01 1 -.165815 0.758712E-01 2 -16.4350 16.3450 4 16.2832 16.3732 8 -16.4536 16.3636 16 16.2758 16.3657 32 -16.4554 16.3655 64 16.2755 16.3655 128 -16.4554 16.3655 72 1.32152 1 1.33515 0.136293E-01 2 1.24434 0.771774E-01 4 2.13839 .816865 8 1.39627 0.747458E-01 16 1.49550 .173982 32 1.45047 .128950 64 1.46529 .143767 128 1.51214 .190615 73 1.15470 1 1.19781 0.431128E-01 2 1.24661 0.919063E-01 4 1.14775 0.695461E-02 8 1.15466 0.357501E-04 16 1.15470 0.106539E-08 32 1.15470 0.115471E-09 64 1.15470 0.115471E-09 128 1.15470 0.115470E-09 74 .505059 1 .506864 0.180534E-02 2 .505046 0.125893E-04 4 .505059 0.138984E-08 8 .505059 0.583599E-10 16 .505059 0.504152E-10 32 .505059 0.504748E-10 64 .505059 0.504983E-10 128 .505059 0.505039E-10 75 1.99225 1 1.97870 0.135454E-01 2 1.99302 0.769721E-03 4 1.99224 0.617004E-05 8 1.99225 0.241650E-05 16 1.99225 0.240776E-05 32 1.99225 0.240775E-05 64 1.99225 0.240775E-05 128 1.99225 0.240775E-05 76 .400000 1 .399950 0.496150E-04 2 .399991 0.877181E-05 4 .399998 0.155069E-05 8 .400000 0.274159E-06 16 .400000 0.484979E-07 32 .400000 0.860624E-08 64 .400000 0.155431E-08 128 .400000 0.307696E-09 TEST05 Composite trapezoid rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.71828 1 1.85914 .140859 2 1.75393 0.356493E-01 4 1.72722 0.894008E-02 8 1.72052 0.223676E-02 16 1.71884 0.559300E-03 32 1.71842 0.139832E-03 64 1.71832 0.349584E-04 128 1.71829 0.873962E-05 2 .700000 1 .500000 .200000 2 .750000 0.500000E-01 4 .625000 0.750000E-01 8 .687500 0.125000E-01 16 .718750 0.187500E-01 32 .703125 0.312500E-02 64 .695312 0.468750E-02 128 .699219 0.781250E-03 3 .666667 1 .500000 .166667 2 .603553 0.631133E-01 4 .643283 0.233836E-01 8 .658130 0.853645E-02 16 .663581 0.308547E-02 32 .665559 0.110773E-02 64 .666271 0.395855E-03 128 .666526 0.141009E-03 4 .479428 1 1.75866 1.27924 2 .799332 .319904 4 .559499 0.800710E-01 8 .499453 0.200251E-01 16 .484435 0.500675E-02 32 .480680 0.125172E-02 64 .479741 0.312932E-03 128 .479506 0.782330E-04 5 1.58223 1 .689655 .892578 2 1.45594 .126294 4 1.55271 0.295213E-01 8 1.57481 0.742481E-02 16 1.58038 0.185754E-02 32 1.58177 0.464455E-03 64 1.58212 0.116118E-03 128 1.58220 0.290297E-04 6 1.46045 1 1.93185 .471405 2 1.67303 .212585 4 1.33652 .123931 8 1.41427 0.461741E-01 16 1.44352 0.169232E-01 32 1.45431 0.613342E-02 64 1.45824 0.220608E-02 128 1.45966 0.789364E-03 7 2.00000 1 .500000 1.50000 2 .957107 1.04289 4 1.26723 .732771 8 1.48304 .516964 16 1.63475 .365251 32 1.74180 .258197 64 1.81745 .182554 128 1.87092 .129081 8 .866973 1 .750000 .116973 2 .845588 0.213848E-01 4 .861732 0.524065E-02 8 .865669 0.130412E-02 16 .866647 0.325648E-03 32 .866892 0.813878E-04 64 .866953 0.203452E-04 128 .866968 0.508595E-05 9 1.15470 1 1.00000 .154701 2 1.00000 .154701 4 1.16667 0.119661E-01 8 1.15476 0.613648E-04 16 1.15470 0.981815E-11 32 1.15470 0.162075E-08 64 1.15470 0.162075E-08 128 1.15470 0.162075E-08 10 .693147 1 .750000 0.568528E-01 2 .708333 0.151862E-01 4 .697024 0.387663E-02 8 .694122 0.974670E-03 16 .693391 0.244022E-03 32 .693208 0.610277E-04 64 .693162 0.152583E-04 128 .693151 0.381467E-05 11 .379885 1 .384471 0.458522E-02 2 .381006 0.112020E-02 4 .380164 0.278555E-03 8 .379955 0.695492E-04 16 .379903 0.173839E-04 32 .379890 0.434789E-05 64 .379887 0.108923E-05 128 .379886 0.274588E-06 12 .777505 1 .790988 0.134837E-01 2 .780868 0.336307E-02 4 .778345 0.840285E-03 8 .777715 0.210044E-03 16 .777557 0.525123E-04 32 .777518 0.131310E-04 64 .777508 0.328583E-05 128 .777505 0.824542E-06 13 1.65835 1 4.72799 3.06964 2 1.40507 .253277 4 1.61367 0.446736E-01 8 1.64791 0.104360E-01 16 1.65578 0.256768E-02 32 1.65771 0.639400E-03 64 1.65819 0.159693E-03 128 1.65831 0.399136E-04 14 .500000 1 35.3553 34.8553 2 17.6777 17.1777 4 8.83883 8.33883 8 4.41942 3.91942 16 2.20971 1.70971 32 1.10485 .604855 64 .576295 0.762947E-01 128 .500034 0.336118E-04 15 1.00000 1 125.000 124.000 2 62.5000 61.5000 4 31.2500 30.2500 8 15.6250 14.6250 16 7.81250 6.81250 32 3.90941 2.90941 64 2.03332 1.03332 128 1.29936 .299356 16 .499364 1 7.96093 7.46157 2 3.99318 3.49381 4 2.02472 1.52535 8 1.07073 .571371 16 .648239 .148875 32 .511892 0.125279E-01 64 .493956 0.540780E-02 128 .493635 0.572911E-02 17 .500000 1 0.482352E-30 .500000 2 0.361764E-30 .500000 4 .500000 .000000 8 .500000 0.555112E-15 16 .500000 0.721645E-15 32 .500000 0.499600E-15 64 .500000 0.222045E-15 128 .500000 .000000 18 .170557 1 .134471 0.360866E-01 2 .161621 0.893683E-02 4 .168328 0.222913E-02 8 .170000 0.556968E-03 16 .170418 0.139223E-03 32 .170523 0.348049E-04 64 .170549 0.870160E-05 128 .170555 0.217584E-05 19 -1.00000 1 .000000 1.00000 2 -.346574 .653426 4 -.591781 .408219 8 -.753866 .246134 16 -.855597 .144403 32 -.917050 0.829503E-01 64 -.953130 0.468700E-01 128 -.973862 0.261375E-01 20 1.56440 1 .997506 .566890 2 1.49378 0.706185E-01 4 1.54370 0.206947E-01 8 1.55921 0.518223E-02 16 1.56310 0.129560E-02 32 1.56407 0.323898E-03 64 1.56432 0.809738E-04 128 1.56438 0.202426E-04 21 .210803 1 0.353256E-01 .175477 2 0.225958E-01 .188207 4 .207927 0.287618E-02 8 .192954 0.178489E-01 16 .196013 0.147893E-01 32 .211297 0.494597E-03 64 .207238 0.356489E-02 128 .209774 0.102917E-02 22 .728103 1 .666667 0.614362E-01 2 .714286 0.138172E-01 4 .724631 0.347169E-02 8 .727235 0.868048E-03 16 .727886 0.217014E-03 32 .728049 0.542535E-04 64 .728089 0.135634E-04 128 .728100 0.339084E-05 23 .195248 1 0.891090E-01 .106139 2 0.767930E-01 .118455 4 .102857 0.923901E-01 8 0.989760E-01 0.962715E-01 16 .121111 0.741368E-01 32 .120067 0.751801E-01 64 .136827 0.584208E-01 128 .136561 0.586865E-01 24 .325109 1 0.782172E-01 .246891 2 0.699682E-01 .255140 4 0.987327E-01 .226376 8 0.961232E-01 .228985 16 .123841 .201267 32 .123136 .201972 64 .146974 .178135 128 .146794 .178315 25 13.6280 1 0.559095E-01 13.5721 2 0.547750E-01 13.5732 4 0.933646E-01 13.5346 8 0.929698E-01 13.5350 16 .147003 13.4810 32 .146885 13.4811 64 .214620 13.4134 128 .214588 13.4134 26 -0.469840E-02 1 0.339481E-01 0.386465E-01 2 0.331729E-01 0.378713E-01 4 0.215812E-01 0.262796E-01 8 0.209031E-01 0.256015E-01 16 -0.240331E-01 0.193347E-01 32 -0.243522E-01 0.196538E-01 64 0.722683E-02 0.119252E-01 128 0.717965E-02 0.118780E-01 27 0.158973E-02 1 0.676676E-01 0.660779E-01 2 -0.286829E-01 0.302727E-01 4 0.676676E-01 0.660779E-01 8 0.153657E-02 0.531568E-04