21 March 2018 1:23:08.299 PM TANH_QUAD_TEST FORTRAN90 version Test the TANH_QUAD library. TEST01 TANH_M_TO_H determines the spacing H from level M TANH_H_TO_N determines the quadrature order N from the spacing H and tolerance TOL. All tests use TOL = 0.22204460E-15 M H N -2 4.0000000 10 -1 2.0000000 19 0 1.0000000 37 1 0.50000000 73 2 0.25000000 142 3 0.12500000 278 4 0.62500000E-01 544 5 0.31250000E-01 1065 6 0.15625000E-01 2085 7 0.78125000E-02 4082 8 0.39062500E-02 7986 TEST012 Determine nested midpoint quadrature rules W, X by choosing N = 0, 1, 3, 7. M = 1 ORDER = 1 N = 0 H = 1.0000000 I Wi Xi 0 2.0000000 0.0000000 M = 2 ORDER = 3 N = 1 H = 0.50000000 I Wi Xi -1 0.75000000 -0.50000000 0 0.50000000 0.0000000 1 0.75000000 0.50000000 M = 3 ORDER = 7 N = 3 H = 0.25000000 I Wi Xi -3 0.37500000 -0.75000000 -2 0.25000000 -0.50000000 -1 0.25000000 -0.25000000 0 0.25000000 0.0000000 1 0.25000000 0.25000000 2 0.25000000 0.50000000 3 0.37500000 0.75000000 M = 4 ORDER = 15 N = 7 H = 0.12500000 I Wi Xi -7 0.18750000 -0.87500000 -6 0.12500000 -0.75000000 -5 0.12500000 -0.62500000 -4 0.12500000 -0.50000000 -3 0.12500000 -0.37500000 -2 0.12500000 -0.25000000 -1 0.12500000 -0.12500000 0 0.12500000 0.0000000 1 0.12500000 0.12500000 2 0.12500000 0.25000000 3 0.12500000 0.37500000 4 0.12500000 0.50000000 5 0.12500000 0.62500000 6 0.12500000 0.75000000 7 0.18750000 0.87500000 TEST02 Determine specific tanh quadrature rules W, X by choosing N = 5, 10, 20. The rule for N = 5 appears in the reference Kahaner, Moler and Nash. Also note that the rule for H(N) means that rules for doubled N do not nest. Quadrature order N = 5 H = 0.14853971-312 I Wi Xi -5 0.47073634E-03 -0.99973653 -4 0.28070981E-02 -0.99842785 -3 0.16631008E-01 -0.99064919 -2 0.94844191E-01 -0.94543431 -1 0.43912730 -0.71309791 0 0.89345883 0.0000000 1 0.43912730 0.71309791 2 0.94844191E-01 0.94543431 3 0.16631008E-01 0.99064919 4 0.28070981E-02 0.99842785 5 0.47073634E-03 0.99973653 Quadrature order N = 10 H = 1.7869177 I Wi Xi -10 0.56136359E-05 -0.99999570 -9 0.20700338E-04 -0.99998414 -8 0.76330326E-04 -0.99994151 -7 0.28142784E-03 -0.99978432 -6 0.10371786E-02 -0.99920489 -5 0.38164907E-02 -0.99707111 -4 0.13963380E-01 -0.98924192 -3 0.50033623E-01 -0.96089434 -2 0.16653875 -0.86299534 -1 0.43799999 -0.57333811 0 0.65248147 0.0000000 1 0.43799999 0.57333811 2 0.16653875 0.86299534 3 0.50033623E-01 0.96089434 4 0.13963380E-01 0.98924192 5 0.38164907E-02 0.99707111 6 0.10371786E-02 0.99920489 7 0.28142784E-03 0.99978432 8 0.76330326E-04 0.99994151 9 0.20700338E-04 0.99998414 10 0.56136359E-05 0.99999570 Quadrature order N = 20 H = 1.3049629 I Wi Xi -20 0.12049630E-07 -0.99999999 -19 0.30953706E-07 -0.99999997 -18 0.79515463E-07 -0.99999992 -17 0.20426337E-06 -0.99999978 -16 0.52472204E-06 -0.99999944 -15 0.13479317E-05 -0.99999857 -14 0.34626284E-05 -0.99999633 -13 0.88949261E-05 -0.99999057 -12 0.22849404E-04 -0.99997578 -11 0.58694491E-04 -0.99993779 -10 0.15076270E-03 -0.99984019 -9 0.38718988E-03 -0.99958952 -8 0.99399301E-03 -0.99894588 -7 0.25492027E-02 -0.99729436 -6 0.65208141E-02 -0.99306434 -5 0.16570211E-01 -0.98227974 -4 0.41407265E-01 -0.95510336 -3 0.99254868E-01 -0.88859082 -2 0.21563455 -0.73680737 -1 0.38057040 -0.43959559 0 0.47172941 0.0000000 1 0.38057040 0.43959559 2 0.21563455 0.73680737 3 0.99254868E-01 0.88859082 4 0.41407265E-01 0.95510336 5 0.16570211E-01 0.98227974 6 0.65208141E-02 0.99306434 7 0.25492027E-02 0.99729436 8 0.99399301E-03 0.99894588 9 0.38718988E-03 0.99958952 10 0.15076270E-03 0.99984019 11 0.58694491E-04 0.99993779 12 0.22849404E-04 0.99997578 13 0.88949261E-05 0.99999057 14 0.34626284E-05 0.99999633 15 0.13479317E-05 0.99999857 16 0.52472204E-06 0.99999944 17 0.20426337E-06 0.99999978 18 0.79515463E-07 0.99999992 19 0.30953706E-07 0.99999997 20 0.12049630E-07 0.99999999 Note that, especially for low N, the weights need not sum to 2!: N H sum(W) 5 1.78692 2.0012195 10 1.30496 2.0000284 20 0.943459 2.0000001 40 0.677481 2.0000000 80 0.484229 2.0000000 160 0.344991 2.0000000 320 0.245240 2.0000000 640 0.174058 2.0000000 1280 0.123401 2.0000000 2560 0.874196E-01 2.0000000 TEST025 Determine tanh-sinh quadrature rules W, X for N = 0, 1, 3, 7, 15, 31, 63. M = -3 ORDER = 1 N = 0 H = 2.0000000 I Wi Xi 0 3.1415927 0.0000000 M = -2 ORDER = 3 N = 1 H = 1.0000000 I Wi Xi -1 0.23002239 -0.95136796 0 1.5707963 0.0000000 1 0.23002239 0.95136796 M = -1 ORDER = 7 N = 3 H = 0.50000000 I Wi Xi -3 0.91715835E-02 -0.99751486 -2 0.11501120 -0.95136796 -1 0.48298829 -0.67427149 0 0.78539816 0.0000000 1 0.48298829 0.67427149 2 0.11501120 0.95136796 3 0.91715835E-02 0.99751486 M = 0 ORDER = 15 N = 7 H = 0.25000000 I Wi Xi -7 0.72562944E-03 -0.99968826 -6 0.45857917E-02 -0.99751486 -5 0.19096436E-01 -0.98704056 -4 0.57505599E-01 -0.95136796 -3 0.13276957 -0.85956906 -2 0.24149414 -0.67427149 -1 0.34740369 -0.37720974 0 0.39269908 0.0000000 1 0.34740369 0.37720974 2 0.24149414 0.67427149 3 0.13276957 0.85956906 4 0.57505599E-01 0.95136796 5 0.19096436E-01 0.98704056 6 0.45857917E-02 0.99751486 7 0.72562944E-03 0.99968826 M = 1 ORDER = 31 N = 15 H = 0.12500000 I Wi Xi -15 0.11874335E-03 -0.99990938 -14 0.36281472E-03 -0.99968826 -13 0.96782513E-03 -0.99906520 -12 0.22928959E-02 -0.99751486 -11 0.48968757E-02 -0.99405551 -10 0.95482179E-02 -0.98704056 -9 0.17177763E-01 -0.97396687 -8 0.28752799E-01 -0.95136796 -7 0.45057677E-01 -0.91487926 -6 0.66384784E-01 -0.85956906 -5 0.92179731E-01 -0.78060744 -4 0.12074707 -0.67427149 -3 0.14918288 -0.53914671 -2 0.17370184 -0.37720974 -1 0.19041046 -0.19435700 0 0.19634954 0.0000000 1 0.19041046 0.19435700 2 0.17370184 0.37720974 3 0.14918288 0.53914671 4 0.12074707 0.67427149 5 0.92179731E-01 0.78060744 6 0.66384784E-01 0.85956906 7 0.45057677E-01 0.91487926 8 0.28752799E-01 0.95136796 9 0.17177763E-01 0.97396687 10 0.95482179E-02 0.98704056 11 0.48968757E-02 0.99405551 12 0.22928959E-02 0.99751486 13 0.96782513E-03 0.99906520 14 0.36281472E-03 0.99968826 15 0.11874335E-03 0.99990938 M = 2 ORDER = 63 N = 31 H = 0.62500000E-01 I Wi Xi -31 0.32087114E-04 -0.99995387 -30 0.59371675E-04 -0.99990938 -29 0.10567962E-03 -0.99982882 -28 0.18140736E-03 -0.99968826 -27 0.30101863E-03 -0.99945143 -26 0.48391256E-03 -0.99906520 -25 0.75522147E-03 -0.99845421 -24 0.11464479E-02 -0.99751486 -23 0.16958444E-02 -0.99610867 -22 0.24484378E-02 -0.99405551 -21 0.34556052E-02 -0.99112699 -20 0.47741090E-02 -0.98704056 -19 0.64645096E-02 -0.98145483 -18 0.85888817E-02 -0.97396687 -17 0.11207776E-01 -0.96411216 -16 0.14376400E-01 -0.95136796 -15 0.18140042E-01 -0.93516086 -14 0.22528839E-01 -0.91487926 -13 0.27552077E-01 -0.88989140 -12 0.33192392E-01 -0.85956906 -11 0.39400321E-01 -0.82331701 -10 0.46089866E-01 -0.78060744 -9 0.53135804E-01 -0.73101803 -8 0.60373536E-01 -0.67427149 -7 0.67602187E-01 -0.61027366 -6 0.74591439E-01 -0.53914671 -5 0.81092234E-01 -0.46125354 -4 0.86850922E-01 -0.37720974 -3 0.91625902E-01 -0.28787993 -2 0.95205232E-01 -0.19435700 -1 0.97423335E-01 -0.97923885E-01 0 0.98174770E-01 0.0000000 1 0.97423335E-01 0.97923885E-01 2 0.95205232E-01 0.19435700 3 0.91625902E-01 0.28787993 4 0.86850922E-01 0.37720974 5 0.81092234E-01 0.46125354 6 0.74591439E-01 0.53914671 7 0.67602187E-01 0.61027366 8 0.60373536E-01 0.67427149 9 0.53135804E-01 0.73101803 10 0.46089866E-01 0.78060744 11 0.39400321E-01 0.82331701 12 0.33192392E-01 0.85956906 13 0.27552077E-01 0.88989140 14 0.22528839E-01 0.91487926 15 0.18140042E-01 0.93516086 16 0.14376400E-01 0.95136796 17 0.11207776E-01 0.96411216 18 0.85888817E-02 0.97396687 19 0.64645096E-02 0.98145483 20 0.47741090E-02 0.98704056 21 0.34556052E-02 0.99112699 22 0.24484378E-02 0.99405551 23 0.16958444E-02 0.99610867 24 0.11464479E-02 0.99751486 25 0.75522147E-03 0.99845421 26 0.48391256E-03 0.99906520 27 0.30101863E-03 0.99945143 28 0.18140736E-03 0.99968826 29 0.10567962E-03 0.99982882 30 0.59371675E-04 0.99990938 31 0.32087114E-04 0.99995387 M = 3 ORDER = 127 N = 63 H = 0.31250000E-01 I Wi Xi -63 0.11614592E-04 -0.99996759 -62 0.16043557E-04 -0.99995387 -61 0.21933110E-04 -0.99993502 -60 0.29685838E-04 -0.99990938 -59 0.39791498E-04 -0.99987487 -58 0.52839812E-04 -0.99982882 -57 0.69533835E-04 -0.99976797 -56 0.90703680E-04 -0.99968826 -55 0.11732034E-03 -0.99958475 -54 0.15050932E-03 -0.99945143 -53 0.19156368E-03 -0.99928111 -52 0.24195628E-03 -0.99906520 -51 0.30335074E-03 -0.99879353 -50 0.37761074E-03 -0.99845421 -49 0.46680735E-03 -0.99803334 -48 0.57322397E-03 -0.99751486 -47 0.69935847E-03 -0.99688032 -46 0.84792219E-03 -0.99610867 -45 0.10218354E-02 -0.99517603 -44 0.12242189E-02 -0.99405551 -43 0.14583815E-02 -0.99271700 -42 0.17278026E-02 -0.99112699 -41 0.20361104E-02 -0.98924843 -40 0.23870545E-02 -0.98704056 -39 0.27844731E-02 -0.98445883 -38 0.32322548E-02 -0.98145483 -37 0.37342941E-02 -0.97797624 -36 0.42944409E-02 -0.97396687 -35 0.49164439E-02 -0.96936673 -34 0.56038879E-02 -0.96411216 -33 0.63601250E-02 -0.95813602 -32 0.71881998E-02 -0.95136796 -31 0.80907700E-02 -0.94373479 -30 0.90700212E-02 -0.93516086 -29 0.10127579E-01 -0.92556863 -28 0.11264419E-01 -0.91487926 -27 0.12480773E-01 -0.90301328 -26 0.13776039E-01 -0.88989140 -25 0.15148690E-01 -0.87543540 -24 0.16596196E-01 -0.85956906 -23 0.18114941E-01 -0.84221925 -22 0.19700160E-01 -0.82331701 -21 0.21345891E-01 -0.80279874 -20 0.23044933E-01 -0.78060744 -19 0.24788834E-01 -0.75669391 -18 0.26567902E-01 -0.73101803 -17 0.28371231E-01 -0.70355001 -16 0.30186768E-01 -0.67427149 -15 0.32001404E-01 -0.64317676 -14 0.33801093E-01 -0.61027366 -13 0.35571008E-01 -0.57558449 -12 0.37295720E-01 -0.53914671 -11 0.38959413E-01 -0.50101339 -10 0.40546117E-01 -0.46125354 -9 0.42039965E-01 -0.41995211 -8 0.43425461E-01 -0.37720974 -7 0.44687761E-01 -0.33314226 -6 0.45812951E-01 -0.28787993 -5 0.46788319E-01 -0.24156632 -4 0.47602616E-01 -0.19435700 -3 0.48246285E-01 -0.14641798 -2 0.48711667E-01 -0.97923885E-01 -1 0.48993170E-01 -0.49055967E-01 0 0.49087385E-01 0.0000000 1 0.48993170E-01 0.49055967E-01 2 0.48711667E-01 0.97923885E-01 3 0.48246285E-01 0.14641798 4 0.47602616E-01 0.19435700 5 0.46788319E-01 0.24156632 6 0.45812951E-01 0.28787993 7 0.44687761E-01 0.33314226 8 0.43425461E-01 0.37720974 9 0.42039965E-01 0.41995211 10 0.40546117E-01 0.46125354 11 0.38959413E-01 0.50101339 12 0.37295720E-01 0.53914671 13 0.35571008E-01 0.57558449 14 0.33801093E-01 0.61027366 15 0.32001404E-01 0.64317676 16 0.30186768E-01 0.67427149 17 0.28371231E-01 0.70355001 18 0.26567902E-01 0.73101803 19 0.24788834E-01 0.75669391 20 0.23044933E-01 0.78060744 21 0.21345891E-01 0.80279874 22 0.19700160E-01 0.82331701 23 0.18114941E-01 0.84221925 24 0.16596196E-01 0.85956906 25 0.15148690E-01 0.87543540 26 0.13776039E-01 0.88989140 27 0.12480773E-01 0.90301328 28 0.11264419E-01 0.91487926 29 0.10127579E-01 0.92556863 30 0.90700212E-02 0.93516086 31 0.80907700E-02 0.94373479 32 0.71881998E-02 0.95136796 33 0.63601250E-02 0.95813602 34 0.56038879E-02 0.96411216 35 0.49164439E-02 0.96936673 36 0.42944409E-02 0.97396687 37 0.37342941E-02 0.97797624 38 0.32322548E-02 0.98145483 39 0.27844731E-02 0.98445883 40 0.23870545E-02 0.98704056 41 0.20361104E-02 0.98924843 42 0.17278026E-02 0.99112699 43 0.14583815E-02 0.99271700 44 0.12242189E-02 0.99405551 45 0.10218354E-02 0.99517603 46 0.84792219E-03 0.99610867 47 0.69935847E-03 0.99688032 48 0.57322397E-03 0.99751486 49 0.46680735E-03 0.99803334 50 0.37761074E-03 0.99845421 51 0.30335074E-03 0.99879353 52 0.24195628E-03 0.99906520 53 0.19156368E-03 0.99928111 54 0.15050932E-03 0.99945143 55 0.11732034E-03 0.99958475 56 0.90703680E-04 0.99968826 57 0.69533835E-04 0.99976797 58 0.52839812E-04 0.99982882 59 0.39791498E-04 0.99987487 60 0.29685838E-04 0.99990938 61 0.21933110E-04 0.99993502 62 0.16043557E-04 0.99995387 63 0.11614592E-04 0.99996759 Note that, especially for low N, the weights need not sum to 2!: N H sum(W) 0 8.0000000 12.566371 1 4.0000000 6.2831853 3 2.0000000 3.1426575 7 1.0000000 2.0313735 15 0.50000000 2.0000067 31 0.25000000 2.0000000 63 0.12500000 2.0000000 127 0.62500000E-01 2.0000000 255 0.31250000E-01 2.0000000 511 0.15625000E-01 2.0000000 1023 0.78125000E-02 2.0000000 2047 0.39062500E-02 2.0000000 4095 0.19531250E-02 2.0000000 8191 0.97656250E-03 2.0000000 TEST03 Determine a quadrature rule W, X by specifying a tolerance. Tolerance TOL = 0.22204460E-15 Level M = -1 Spacing H = 2.0000000 Quadrature order N = 19 I Wi Xi -19 0.12556531E-15 -1.0000000 -18 0.92780913E-15 -1.0000000 -17 0.68556337E-14 -1.0000000 -16 0.50656662E-13 -1.0000000 -15 0.37430492E-12 -1.0000000 -14 0.27657600E-11 -1.0000000 -13 0.20436356E-10 -1.0000000 -12 0.15100538E-09 -1.0000000 -11 0.11157872E-08 -1.0000000 -10 0.82446145E-08 -1.0000000 -9 0.60919917E-07 -0.99999997 -8 0.45014060E-06 -0.99999977 -7 0.33261093E-05 -0.99999834 -6 0.24576547E-04 -0.99998771 -5 0.18158323E-03 -0.99990920 -4 0.13409507E-02 -0.99932930 -3 0.98660372E-02 -0.99505475 -2 0.70650825E-01 -0.96402758 -1 0.41997434 -0.76159416 0 1.0000000 0.0000000 1 0.41997434 0.76159416 2 0.70650825E-01 0.96402758 3 0.98660372E-02 0.99505475 4 0.13409507E-02 0.99932930 5 0.18158323E-03 0.99990920 6 0.24576547E-04 0.99998771 7 0.33261093E-05 0.99999834 8 0.45014060E-06 0.99999977 9 0.60919917E-07 0.99999997 10 0.82446145E-08 1.0000000 11 0.11157872E-08 1.0000000 12 0.15100538E-09 1.0000000 13 0.20436356E-10 1.0000000 14 0.27657600E-11 1.0000000 15 0.37430492E-12 1.0000000 16 0.50656662E-13 1.0000000 17 0.68556337E-14 1.0000000 18 0.92780913E-15 1.0000000 19 0.12556531E-15 1.0000000 Level M = 0 Spacing H = 1.0000000 Quadrature order N = 37 I Wi Xi -37 0.17066095E-15 -1.0000000 -36 0.46390457E-15 -1.0000000 -35 0.12610234E-14 -1.0000000 -34 0.34278169E-14 -1.0000000 -33 0.93177723E-14 -1.0000000 -32 0.25328331E-13 -1.0000000 -31 0.68849542E-13 -1.0000000 -30 0.18715246E-12 -1.0000000 -29 0.50873313E-12 -1.0000000 -28 0.13828800E-11 -1.0000000 -27 0.37590576E-11 -1.0000000 -26 0.10218178E-10 -1.0000000 -25 0.27775888E-10 -1.0000000 -24 0.75502691E-10 -1.0000000 -23 0.20523759E-09 -1.0000000 -22 0.55789362E-09 -1.0000000 -21 0.15165121E-08 -1.0000000 -20 0.41223072E-08 -1.0000000 -19 0.11205593E-07 -0.99999999 -18 0.30459959E-07 -0.99999997 -17 0.82798748E-07 -0.99999992 -16 0.22507030E-06 -0.99999977 -15 0.61180427E-06 -0.99999939 -14 0.16630547E-05 -0.99999834 -13 0.45206384E-05 -0.99999548 -12 0.12288274E-04 -0.99998771 -11 0.33402286E-04 -0.99996660 -10 0.90791615E-04 -0.99990920 -9 0.24675870E-03 -0.99975321 -8 0.67047534E-03 -0.99932930 -7 0.18204424E-02 -0.99817790 -6 0.49330186E-02 -0.99505475 -5 0.13296113E-01 -0.98661430 -4 0.35325412E-01 -0.96402758 -3 0.90353319E-01 -0.90514825 -2 0.20998717 -0.76159416 -1 0.39322387 -0.46211716 0 0.50000000 0.0000000 1 0.39322387 0.46211716 2 0.20998717 0.76159416 3 0.90353319E-01 0.90514825 4 0.35325412E-01 0.96402758 5 0.13296113E-01 0.98661430 6 0.49330186E-02 0.99505475 7 0.18204424E-02 0.99817790 8 0.67047534E-03 0.99932930 9 0.24675870E-03 0.99975321 10 0.90791615E-04 0.99990920 11 0.33402286E-04 0.99996660 12 0.12288274E-04 0.99998771 13 0.45206384E-05 0.99999548 14 0.16630547E-05 0.99999834 15 0.61180427E-06 0.99999939 16 0.22507030E-06 0.99999977 17 0.82798748E-07 0.99999992 18 0.30459959E-07 0.99999997 19 0.11205593E-07 0.99999999 20 0.41223072E-08 1.0000000 21 0.15165121E-08 1.0000000 22 0.55789362E-09 1.0000000 23 0.20523759E-09 1.0000000 24 0.75502691E-10 1.0000000 25 0.27775888E-10 1.0000000 26 0.10218178E-10 1.0000000 27 0.37590576E-11 1.0000000 28 0.13828800E-11 1.0000000 29 0.50873313E-12 1.0000000 30 0.18715246E-12 1.0000000 31 0.68849542E-13 1.0000000 32 0.25328331E-13 1.0000000 33 0.93177723E-14 1.0000000 34 0.34278169E-14 1.0000000 35 0.12610234E-14 1.0000000 36 0.46390457E-15 1.0000000 37 0.17066095E-15 1.0000000 Level M = 1 Spacing H = 0.50000000 Quadrature order N = 73 I Wi Xi -73 0.14068617E-15 -1.0000000 -72 0.23195228E-15 -1.0000000 -71 0.38242466E-15 -1.0000000 -70 0.63051168E-15 -1.0000000 -69 0.10395380E-14 -1.0000000 -68 0.17139084E-14 -1.0000000 -67 0.28257573E-14 -1.0000000 -66 0.46588861E-14 -1.0000000 -65 0.76812047E-14 -1.0000000 -64 0.12664166E-13 -1.0000000 -63 0.20879679E-13 -1.0000000 -62 0.34424771E-13 -1.0000000 -61 0.56756852E-13 -1.0000000 -60 0.93576230E-13 -1.0000000 -59 0.15428112E-12 -1.0000000 -58 0.25436656E-12 -1.0000000 -57 0.41937957E-12 -1.0000000 -56 0.69144001E-12 -1.0000000 -55 0.11399919E-11 -1.0000000 -54 0.18795288E-11 -1.0000000 -53 0.30988191E-11 -1.0000000 -52 0.51090890E-11 -1.0000000 -51 0.84234638E-11 -1.0000000 -50 0.13887944E-10 -1.0000000 -49 0.22897348E-10 -1.0000000 -48 0.37751345E-10 -1.0000000 -47 0.62241446E-10 -1.0000000 -46 0.10261880E-09 -1.0000000 -45 0.16918979E-09 -1.0000000 -44 0.27894681E-09 -1.0000000 -43 0.45990554E-09 -1.0000000 -42 0.75825604E-09 -1.0000000 -41 0.12501529E-08 -1.0000000 -40 0.20611536E-08 -1.0000000 -39 0.33982678E-08 -0.99999999 -38 0.56027964E-08 -0.99999999 -37 0.92374495E-08 -0.99999998 -36 0.15229979E-07 -0.99999997 -35 0.25109990E-07 -0.99999995 -34 0.41399374E-07 -0.99999992 -33 0.68256024E-07 -0.99999986 -32 0.11253515E-06 -0.99999977 -31 0.18553907E-06 -0.99999963 -30 0.30590213E-06 -0.99999939 -29 0.50434715E-06 -0.99999899 -28 0.83152734E-06 -0.99999834 -27 0.13709553E-05 -0.99999726 -26 0.22603192E-05 -0.99999548 -25 0.37266254E-05 -0.99999255 -24 0.61441369E-05 -0.99998771 -23 0.10129888E-04 -0.99997974 -22 0.16701143E-04 -0.99996660 -21 0.27534933E-04 -0.99994493 -20 0.45395808E-04 -0.99990920 -19 0.74840626E-04 -0.99985031 -18 0.12337935E-03 -0.99975321 -17 0.20338560E-03 -0.99959315 -16 0.33523767E-03 -0.99932930 -15 0.55247307E-03 -0.99889444 -14 0.91022118E-03 -0.99817790 -13 0.14989287E-02 -0.99699764 -12 0.24665093E-02 -0.99505475 -11 0.40535717E-02 -0.99185972 -10 0.66480567E-02 -0.98661430 -9 0.10866230E-01 -0.97802611 -8 0.17662706E-01 -0.96402758 -7 0.28453024E-01 -0.94137554 -6 0.45176660E-01 -0.90514825 -5 0.70103717E-01 -0.84828364 -4 0.10499359 -0.76159416 -3 0.14914645 -0.63514895 -2 0.19661193 -0.46211716 -1 0.23500371 -0.24491866 0 0.25000000 0.0000000 1 0.23500371 0.24491866 2 0.19661193 0.46211716 3 0.14914645 0.63514895 4 0.10499359 0.76159416 5 0.70103717E-01 0.84828364 6 0.45176660E-01 0.90514825 7 0.28453024E-01 0.94137554 8 0.17662706E-01 0.96402758 9 0.10866230E-01 0.97802611 10 0.66480567E-02 0.98661430 11 0.40535717E-02 0.99185972 12 0.24665093E-02 0.99505475 13 0.14989287E-02 0.99699764 14 0.91022118E-03 0.99817790 15 0.55247307E-03 0.99889444 16 0.33523767E-03 0.99932930 17 0.20338560E-03 0.99959315 18 0.12337935E-03 0.99975321 19 0.74840626E-04 0.99985031 20 0.45395808E-04 0.99990920 21 0.27534933E-04 0.99994493 22 0.16701143E-04 0.99996660 23 0.10129888E-04 0.99997974 24 0.61441369E-05 0.99998771 25 0.37266254E-05 0.99999255 26 0.22603192E-05 0.99999548 27 0.13709553E-05 0.99999726 28 0.83152734E-06 0.99999834 29 0.50434715E-06 0.99999899 30 0.30590213E-06 0.99999939 31 0.18553907E-06 0.99999963 32 0.11253515E-06 0.99999977 33 0.68256024E-07 0.99999986 34 0.41399374E-07 0.99999992 35 0.25109990E-07 0.99999995 36 0.15229979E-07 0.99999997 37 0.92374495E-08 0.99999998 38 0.56027964E-08 0.99999999 39 0.33982678E-08 0.99999999 40 0.20611536E-08 1.0000000 41 0.12501529E-08 1.0000000 42 0.75825604E-09 1.0000000 43 0.45990554E-09 1.0000000 44 0.27894681E-09 1.0000000 45 0.16918979E-09 1.0000000 46 0.10261880E-09 1.0000000 47 0.62241446E-10 1.0000000 48 0.37751345E-10 1.0000000 49 0.22897348E-10 1.0000000 50 0.13887944E-10 1.0000000 51 0.84234638E-11 1.0000000 52 0.51090890E-11 1.0000000 53 0.30988191E-11 1.0000000 54 0.18795288E-11 1.0000000 55 0.11399919E-11 1.0000000 56 0.69144001E-12 1.0000000 57 0.41937957E-12 1.0000000 58 0.25436656E-12 1.0000000 59 0.15428112E-12 1.0000000 60 0.93576230E-13 1.0000000 61 0.56756852E-13 1.0000000 62 0.34424771E-13 1.0000000 63 0.20879679E-13 1.0000000 64 0.12664166E-13 1.0000000 65 0.76812047E-14 1.0000000 66 0.46588861E-14 1.0000000 67 0.28257573E-14 1.0000000 68 0.17139084E-14 1.0000000 69 0.10395380E-14 1.0000000 70 0.63051168E-15 1.0000000 71 0.38242466E-15 1.0000000 72 0.23195228E-15 1.0000000 73 0.14068617E-15 1.0000000 Level M = 2 Spacing H = 0.25000000 Quadrature order N = 142 I Wi Xi -142 0.19121233E-15 -1.0000000 -141 0.24552149E-15 -1.0000000 -140 0.31525584E-15 -1.0000000 -139 0.40479651E-15 -1.0000000 -138 0.51976901E-15 -1.0000000 -137 0.66739661E-15 -1.0000000 -136 0.85695422E-15 -1.0000000 -135 0.11003510E-14 -1.0000000 -134 0.14128786E-14 -1.0000000 -133 0.18141721E-14 -1.0000000 -132 0.23294431E-14 -1.0000000 -131 0.29910641E-14 -1.0000000 -130 0.38406023E-14 -1.0000000 -129 0.49314310E-14 -1.0000000 -128 0.63320828E-14 -1.0000000 -127 0.81305552E-14 -1.0000000 -126 0.10439840E-13 -1.0000000 -125 0.13405019E-13 -1.0000000 -124 0.17212386E-13 -1.0000000 -123 0.22101141E-13 -1.0000000 -122 0.28378426E-13 -1.0000000 -121 0.36438620E-13 -1.0000000 -120 0.46788115E-13 -1.0000000 -119 0.60077129E-13 -1.0000000 -118 0.77140560E-13 -1.0000000 -117 0.99050440E-13 -1.0000000 -116 0.12718328E-12 -1.0000000 -115 0.16330657E-12 -1.0000000 -114 0.20968978E-12 -1.0000000 -113 0.26924701E-12 -1.0000000 -112 0.34572001E-12 -1.0000000 -111 0.44391327E-12 -1.0000000 -110 0.56999593E-12 -1.0000000 -109 0.73188926E-12 -1.0000000 -108 0.93976441E-12 -1.0000000 -107 0.12066814E-11 -1.0000000 -106 0.15494096E-11 -1.0000000 -105 0.19894813E-11 -1.0000000 -104 0.25545445E-11 -1.0000000 -103 0.32801001E-11 -1.0000000 -102 0.42117319E-11 -1.0000000 -101 0.54079708E-11 -1.0000000 -100 0.69439719E-11 -1.0000000 -99 0.89162365E-11 -1.0000000 -98 0.11448674E-10 -1.0000000 -97 0.14700389E-10 -1.0000000 -96 0.18875673E-10 -1.0000000 -95 0.24236844E-10 -1.0000000 -94 0.31120723E-10 -1.0000000 -93 0.39959799E-10 -1.0000000 -92 0.51309398E-10 -1.0000000 -91 0.65882571E-10 -1.0000000 -90 0.84594896E-10 -1.0000000 -89 0.10862200E-09 -1.0000000 -88 0.13947340E-09 -1.0000000 -87 0.17908740E-09 -1.0000000 -86 0.22995277E-09 -1.0000000 -85 0.29526520E-09 -1.0000000 -84 0.37912802E-09 -1.0000000 -83 0.48681001E-09 -1.0000000 -82 0.62507643E-09 -1.0000000 -81 0.80261403E-09 -1.0000000 -80 0.10305768E-08 -1.0000000 -79 0.13232868E-08 -0.99999999 -78 0.16991339E-08 -0.99999999 -77 0.21817311E-08 -0.99999999 -76 0.28013982E-08 -0.99999999 -75 0.35970665E-08 -0.99999999 -74 0.46187247E-08 -0.99999998 -73 0.59305599E-08 -0.99999998 -72 0.76149896E-08 -0.99999997 -71 0.97778402E-08 -0.99999996 -70 0.12554995E-07 -0.99999995 -69 0.16120933E-07 -0.99999994 -68 0.20699687E-07 -0.99999992 -67 0.26578923E-07 -0.99999989 -66 0.34128012E-07 -0.99999986 -65 0.43821233E-07 -0.99999982 -64 0.56267575E-07 -0.99999977 -63 0.72248991E-07 -0.99999971 -62 0.92769534E-07 -0.99999963 -61 0.11911843E-06 -0.99999952 -60 0.15295107E-06 -0.99999939 -59 0.19639302E-06 -0.99999921 -58 0.25217358E-06 -0.99999899 -57 0.32379719E-06 -0.99999870 -56 0.41576367E-06 -0.99999834 -55 0.53385087E-06 -0.99999786 -54 0.68547766E-06 -0.99999726 -53 0.88017006E-06 -0.99999648 -52 0.11301596E-05 -0.99999548 -51 0.14511518E-05 -0.99999420 -50 0.18633127E-05 -0.99999255 -49 0.23925358E-05 -0.99999043 -48 0.30720684E-05 -0.99998771 -47 0.39446002E-05 -0.99998422 -46 0.50649442E-05 -0.99997974 -45 0.65034796E-05 -0.99997399 -44 0.83505715E-05 -0.99996660 -43 0.10722244E-04 -0.99995711 -42 0.13767466E-04 -0.99994493 -41 0.17677500E-04 -0.99992929 -40 0.22697904E-04 -0.99990920 -39 0.29143934E-04 -0.99988342 -38 0.37420313E-04 -0.99985031 -37 0.48046590E-04 -0.99980780 -36 0.61689675E-04 -0.99975321 -35 0.79205559E-04 -0.99968313 -34 0.10169280E-03 -0.99959315 -33 0.13056105E-03 -0.99947762 -32 0.16761884E-03 -0.99932930 -31 0.21518585E-03 -0.99913889 -30 0.27623654E-03 -0.99889444 -29 0.35458338E-03 -0.99858066 -28 0.45511059E-03 -0.99817790 -27 0.58407126E-03 -0.99766098 -26 0.74946435E-03 -0.99699764 -25 0.96151118E-03 -0.99614653 -24 0.12332546E-02 -0.99505475 -23 0.15813085E-02 -0.99365463 -22 0.20267858E-02 -0.99185972 -21 0.25964380E-02 -0.98955975 -20 0.33240283E-02 -0.98661430 -19 0.42519561E-02 -0.98284503 -18 0.54331149E-02 -0.97802611 -17 0.69329207E-02 -0.97187275 -16 0.88313531E-02 -0.96402758 -15 0.11224705E-01 -0.95404526 -14 0.14226512E-01 -0.94137554 -13 0.17966795E-01 -0.92534623 -12 0.22588330E-01 -0.90514825 -11 0.28238122E-01 -0.87982670 -10 0.35051858E-01 -0.84828364 -9 0.43128972E-01 -0.80930107 -8 0.52496793E-01 -0.76159416 -7 0.63064613E-01 -0.70390560 -6 0.74573226E-01 -0.63514895 -5 0.86552393E-01 -0.55459972 -4 0.98305967E-01 -0.46211716 -3 0.10894750 -0.35835740 -2 0.11750186 -0.24491866 -1 0.12306704 -0.12435300 0 0.12500000 0.0000000 1 0.12306704 0.12435300 2 0.11750186 0.24491866 3 0.10894750 0.35835740 4 0.98305967E-01 0.46211716 5 0.86552393E-01 0.55459972 6 0.74573226E-01 0.63514895 7 0.63064613E-01 0.70390560 8 0.52496793E-01 0.76159416 9 0.43128972E-01 0.80930107 10 0.35051858E-01 0.84828364 11 0.28238122E-01 0.87982670 12 0.22588330E-01 0.90514825 13 0.17966795E-01 0.92534623 14 0.14226512E-01 0.94137554 15 0.11224705E-01 0.95404526 16 0.88313531E-02 0.96402758 17 0.69329207E-02 0.97187275 18 0.54331149E-02 0.97802611 19 0.42519561E-02 0.98284503 20 0.33240283E-02 0.98661430 21 0.25964380E-02 0.98955975 22 0.20267858E-02 0.99185972 23 0.15813085E-02 0.99365463 24 0.12332546E-02 0.99505475 25 0.96151118E-03 0.99614653 26 0.74946435E-03 0.99699764 27 0.58407126E-03 0.99766098 28 0.45511059E-03 0.99817790 29 0.35458338E-03 0.99858066 30 0.27623654E-03 0.99889444 31 0.21518585E-03 0.99913889 32 0.16761884E-03 0.99932930 33 0.13056105E-03 0.99947762 34 0.10169280E-03 0.99959315 35 0.79205559E-04 0.99968313 36 0.61689675E-04 0.99975321 37 0.48046590E-04 0.99980780 38 0.37420313E-04 0.99985031 39 0.29143934E-04 0.99988342 40 0.22697904E-04 0.99990920 41 0.17677500E-04 0.99992929 42 0.13767466E-04 0.99994493 43 0.10722244E-04 0.99995711 44 0.83505715E-05 0.99996660 45 0.65034796E-05 0.99997399 46 0.50649442E-05 0.99997974 47 0.39446002E-05 0.99998422 48 0.30720684E-05 0.99998771 49 0.23925358E-05 0.99999043 50 0.18633127E-05 0.99999255 51 0.14511518E-05 0.99999420 52 0.11301596E-05 0.99999548 53 0.88017006E-06 0.99999648 54 0.68547766E-06 0.99999726 55 0.53385087E-06 0.99999786 56 0.41576367E-06 0.99999834 57 0.32379719E-06 0.99999870 58 0.25217358E-06 0.99999899 59 0.19639302E-06 0.99999921 60 0.15295107E-06 0.99999939 61 0.11911843E-06 0.99999952 62 0.92769534E-07 0.99999963 63 0.72248991E-07 0.99999971 64 0.56267575E-07 0.99999977 65 0.43821233E-07 0.99999982 66 0.34128012E-07 0.99999986 67 0.26578923E-07 0.99999989 68 0.20699687E-07 0.99999992 69 0.16120933E-07 0.99999994 70 0.12554995E-07 0.99999995 71 0.97778402E-08 0.99999996 72 0.76149896E-08 0.99999997 73 0.59305599E-08 0.99999998 74 0.46187247E-08 0.99999998 75 0.35970665E-08 0.99999999 76 0.28013982E-08 0.99999999 77 0.21817311E-08 0.99999999 78 0.16991339E-08 0.99999999 79 0.13232868E-08 0.99999999 80 0.10305768E-08 1.0000000 81 0.80261403E-09 1.0000000 82 0.62507643E-09 1.0000000 83 0.48681001E-09 1.0000000 84 0.37912802E-09 1.0000000 85 0.29526520E-09 1.0000000 86 0.22995277E-09 1.0000000 87 0.17908740E-09 1.0000000 88 0.13947340E-09 1.0000000 89 0.10862200E-09 1.0000000 90 0.84594896E-10 1.0000000 91 0.65882571E-10 1.0000000 92 0.51309398E-10 1.0000000 93 0.39959799E-10 1.0000000 94 0.31120723E-10 1.0000000 95 0.24236844E-10 1.0000000 96 0.18875673E-10 1.0000000 97 0.14700389E-10 1.0000000 98 0.11448674E-10 1.0000000 99 0.89162365E-11 1.0000000 100 0.69439719E-11 1.0000000 101 0.54079708E-11 1.0000000 102 0.42117319E-11 1.0000000 103 0.32801001E-11 1.0000000 104 0.25545445E-11 1.0000000 105 0.19894813E-11 1.0000000 106 0.15494096E-11 1.0000000 107 0.12066814E-11 1.0000000 108 0.93976441E-12 1.0000000 109 0.73188926E-12 1.0000000 110 0.56999593E-12 1.0000000 111 0.44391327E-12 1.0000000 112 0.34572001E-12 1.0000000 113 0.26924701E-12 1.0000000 114 0.20968978E-12 1.0000000 115 0.16330657E-12 1.0000000 116 0.12718328E-12 1.0000000 117 0.99050440E-13 1.0000000 118 0.77140560E-13 1.0000000 119 0.60077129E-13 1.0000000 120 0.46788115E-13 1.0000000 121 0.36438620E-13 1.0000000 122 0.28378426E-13 1.0000000 123 0.22101141E-13 1.0000000 124 0.17212386E-13 1.0000000 125 0.13405019E-13 1.0000000 126 0.10439840E-13 1.0000000 127 0.81305552E-14 1.0000000 128 0.63320828E-14 1.0000000 129 0.49314310E-14 1.0000000 130 0.38406023E-14 1.0000000 131 0.29910641E-14 1.0000000 132 0.23294431E-14 1.0000000 133 0.18141721E-14 1.0000000 134 0.14128786E-14 1.0000000 135 0.11003510E-14 1.0000000 136 0.85695422E-15 1.0000000 137 0.66739661E-15 1.0000000 138 0.51976901E-15 1.0000000 139 0.40479651E-15 1.0000000 140 0.31525584E-15 1.0000000 141 0.24552149E-15 1.0000000 142 0.19121233E-15 1.0000000 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 1 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 1.0000000 1.0000000 0.22204460E-14 2 0.69930070E-02 142 1.0000000 1.0000000 0.62172489E-14 3 0.35842294E-02 278 1.0000000 1.0000000 0.89928065E-14 4 0.18348624E-02 544 1.0000000 1.0000000 0.22648550E-13 5 0.93808630E-03 1065 1.0000000 1.0000000 0.34638958E-13 6 0.47938639E-03 2085 1.0000000 1.0000000 0.13544721E-13 7 0.24491795E-03 4082 1.0000000 1.0000000 0.59729999E-13 8 0.12520346E-03 7986 1.0000000 1.0000000 0.14899193E-12 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 2 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 1.0000000 1.0000000 0.0000000 2 0.69930070E-02 142 1.0000000 1.0000000 0.22204460E-15 3 0.35842294E-02 278 1.0000000 1.0000000 0.0000000 4 0.18348624E-02 544 1.0000000 1.0000000 0.11102230E-15 5 0.93808630E-03 1065 1.0000000 1.0000000 0.55511151E-15 6 0.47938639E-03 2085 1.0000000 1.0000000 0.22204460E-15 7 0.24491795E-03 4082 1.0000000 1.0000000 0.11102230E-15 8 0.12520346E-03 7986 1.0000000 1.0000000 0.11102230E-15 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 3 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 1.0000000 0.99988679 0.11320899E-03 2 0.69930070E-02 142 1.0000000 0.99996956 0.30435602E-04 3 0.35842294E-02 278 1.0000000 0.99999199 0.80119206E-05 4 0.18348624E-02 544 1.0000000 0.99999790 0.21018834E-05 5 0.93808630E-03 1065 1.0000000 0.99999945 0.54969413E-06 6 0.47938639E-03 2085 1.0000000 0.99999986 0.14359075E-06 7 0.24491795E-03 4082 1.0000000 0.99999996 0.37484993E-07 8 0.12520346E-03 7986 1.0000000 0.99999999 0.97967030E-08 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 4 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 -0.31671420 -0.31234187 0.43723257E-02 2 0.69930070E-02 142 -0.31671420 -0.31441229 0.23019053E-02 3 0.35842294E-02 278 -0.31671420 -0.31552144 0.11927599E-02 4 0.18348624E-02 544 -0.31671420 -0.31609955 0.61464739E-03 5 0.93808630E-03 1065 -0.31671420 -0.31639872 0.31547286E-03 6 0.47938639E-03 2085 -0.31671420 -0.31655262 0.16158125E-03 7 0.24491795E-03 4082 -0.31671420 -0.31663154 0.82659146E-04 8 0.12520346E-03 7986 -0.31671420 -0.31667191 0.42286956E-04 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 5 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 0.25000000 0.24997752 0.22484889E-04 2 0.69930070E-02 142 0.25000000 0.24999395 0.60485035E-05 3 0.35842294E-02 278 0.25000000 0.24999841 0.15927123E-05 4 0.18348624E-02 544 0.25000000 0.24999958 0.41790599E-06 5 0.93808630E-03 1065 0.25000000 0.24999989 0.10930163E-06 6 0.47938639E-03 2085 0.25000000 0.24999997 0.28552899E-07 7 0.24491795E-03 4082 0.25000000 0.24999999 0.74540183E-08 8 0.12520346E-03 7986 0.25000000 0.25000000 0.19481291E-08 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 6 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 0.21065725 0.21061810 0.39153734E-04 2 0.69930070E-02 142 0.21065725 0.21064674 0.10515696E-04 3 0.35842294E-02 278 0.21065725 0.21065448 0.27667120E-05 4 0.18348624E-02 544 0.21065725 0.21065653 0.72563513E-06 5 0.93808630E-03 1065 0.21065725 0.21065706 0.18974503E-06 6 0.47938639E-03 2085 0.21065725 0.21065720 0.49561552E-07 7 0.24491795E-03 4082 0.21065725 0.21065724 0.12937789E-07 8 0.12520346E-03 7986 0.21065725 0.21065725 0.33812292E-08 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 7 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 1.9052387 1.9055085 0.26985250E-03 2 0.69930070E-02 142 1.9052387 1.9053113 0.72633265E-04 3 0.35842294E-02 278 1.9052387 1.9052578 0.19131832E-04 4 0.18348624E-02 544 1.9052387 1.9052437 0.50207124E-05 5 0.93808630E-03 1065 1.9052387 1.9052400 0.13132517E-05 6 0.47938639E-03 2085 1.9052387 1.9052390 0.34307515E-06 7 0.24491795E-03 4082 1.9052387 1.9052388 0.89565038E-07 8 0.12520346E-03 7986 1.9052387 1.9052387 0.23408338E-07 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 8 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 0.51404190 0.51404868 0.67881449E-05 2 0.69930070E-02 142 0.51404190 0.51404372 0.18289669E-05 3 0.35842294E-02 278 0.51404190 0.51404238 0.48200948E-06 4 0.18348624E-02 544 0.51404190 0.51404202 0.12652625E-06 5 0.93808630E-03 1065 0.51404190 0.51404193 0.33099586E-07 6 0.47938639E-03 2085 0.51404190 0.51404190 0.86475711E-08 7 0.24491795E-03 4082 0.51404190 0.51404190 0.22576617E-08 8 0.12520346E-03 7986 0.51404190 0.51404190 0.59005700E-09 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 9 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 -0.44444444 -0.44507380 0.62935371E-03 2 0.69930070E-02 142 -0.44444444 -0.44471653 0.27208160E-03 3 0.35842294E-02 278 -0.44444444 -0.44455856 0.11411932E-03 4 0.18348624E-02 544 -0.44444444 -0.44449154 0.47095154E-04 5 0.93808630E-03 1065 -0.44444444 -0.44446361 0.19170336E-04 6 0.47938639E-03 2085 -0.44444444 -0.44445217 0.77213497E-05 7 0.24491795E-03 4082 -0.44444444 -0.44444753 0.30830101E-05 8 0.12520346E-03 7986 -0.44444444 -0.44444567 0.12232883E-05 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 10 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 0.78539816 0.78562690 0.22873555E-03 2 0.69930070E-02 142 0.78539816 0.78548344 0.85279798E-04 3 0.35842294E-02 278 0.78539816 0.78542948 0.31316954E-04 4 0.18348624E-02 544 0.78539816 0.78540964 0.11475144E-04 5 0.93808630E-03 1065 0.78539816 0.78540236 0.41956652E-05 6 0.47938639E-03 2085 0.78539816 0.78539970 0.15328771E-05 7 0.24491795E-03 4082 0.78539816 0.78539872 0.55979758E-06 8 0.12520346E-03 7986 0.78539816 0.78539837 0.20461400E-06 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 11 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 1.1981402 1.1424541 0.55686103E-01 2 0.69930070E-02 142 1.1981402 1.1580355 0.40104758E-01 3 0.35842294E-02 278 1.1981402 1.1694110 0.28729223E-01 4 0.18348624E-02 544 1.1981402 1.1775784 0.20561853E-01 5 0.93808630E-03 1065 1.1981402 1.1834357 0.14704520E-01 6 0.47938639E-03 2085 1.1981402 1.1876277 0.10512538E-01 7 0.24491795E-03 4082 1.1981402 1.1906259 0.75143784E-02 8 0.12520346E-03 7986 1.1981402 1.1927674 0.53727931E-02 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 12 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 2.0000000 1.9243879 0.75612130E-01 2 0.69930070E-02 142 2.0000000 1.9566386 0.43361426E-01 3 0.35842294E-02 278 2.0000000 1.9755739 0.24426074E-01 4 0.18348624E-02 544 2.0000000 1.9863667 0.13633344E-01 5 0.93808630E-03 1065 2.0000000 1.9924515 0.75484735E-02 6 0.47938639E-03 2085 2.0000000 1.9958468 0.41532063E-02 7 0.24491795E-03 4082 2.0000000 1.9977270 0.22730180E-02 8 0.12520346E-03 7986 2.0000000 1.9987608 0.12391793E-02 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 13 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 -1.0887930 -1.0790403 0.97527452E-02 2 0.69930070E-02 142 -1.0887930 -1.0837460 0.50470261E-02 3 0.35842294E-02 278 -1.0887930 -1.0862062 0.25868479E-02 4 0.18348624E-02 544 -1.0887930 -1.0874688 0.13242791E-02 5 0.93808630E-03 1065 -1.0887930 -1.0881160 0.67704737E-03 6 0.47938639E-03 2085 -1.0887930 -1.0884471 0.34598878E-03 7 0.24491795E-03 4082 -1.0887930 -1.0886163 0.17676528E-03 8 0.12520346E-03 7986 -1.0887930 -1.0887027 0.90363420E-04 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 14 Tolerance TOL = 0.22204460E-15 M H_MIDPOINT N Exact Quad Error 1 0.13513514E-01 73 2.2214415 2.1228225 0.98618942E-01 2 0.69930070E-02 142 2.2214415 2.1503883 0.71053166E-01 3 0.35842294E-02 278 2.2214415 2.1705315 0.50909950E-01 4 0.18348624E-02 544 2.2214415 2.1850007 0.36440802E-01 5 0.93808630E-03 1065 2.2214415 2.1953799 0.26061571E-01 6 0.47938639E-03 2085 2.2214415 2.2028090 0.18632436E-01 7 0.24491795E-03 4082 2.2214415 2.2081228 0.13318687E-01 8 0.12520346E-03 7986 2.2214415 2.2119185 0.95229540E-02 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 1 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 1.0000000 1.0000000 0.28865799E-14 2 0.25000000 142 1.0000000 1.0000000 0.11102230E-14 3 0.12500000 278 1.0000000 1.0000000 0.53290705E-14 4 0.62500000E-01 544 1.0000000 1.0000000 0.26645353E-13 5 0.31250000E-01 1065 1.0000000 1.0000000 0.32751579E-13 6 0.15625000E-01 2085 1.0000000 1.0000000 0.62838623E-13 7 0.78125000E-02 4082 1.0000000 1.0000000 0.16742163E-12 8 0.39062500E-02 7986 1.0000000 1.0000000 0.25934810E-12 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 2 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 1.0000000 1.0000000 0.0000000 2 0.25000000 142 1.0000000 1.0000000 0.22204460E-15 3 0.12500000 278 1.0000000 1.0000000 0.0000000 4 0.62500000E-01 544 1.0000000 1.0000000 0.0000000 5 0.31250000E-01 1065 1.0000000 1.0000000 0.0000000 6 0.15625000E-01 2085 1.0000000 1.0000000 0.0000000 7 0.78125000E-02 4082 1.0000000 1.0000000 0.11102230E-15 8 0.39062500E-02 7986 1.0000000 1.0000000 0.33306691E-15 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 3 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 1.0000000 1.0000235 0.23456558E-04 2 0.25000000 142 1.0000000 1.0000062 0.61991668E-05 3 0.12500000 278 1.0000000 1.0000016 0.16174111E-05 4 0.62500000E-01 544 1.0000000 1.0000004 0.42238862E-06 5 0.31250000E-01 1065 1.0000000 1.0000001 0.11020741E-06 6 0.15625000E-01 2085 1.0000000 1.0000000 0.28753975E-07 7 0.78125000E-02 4082 1.0000000 1.0000000 0.75017734E-08 8 0.39062500E-02 7986 1.0000000 1.0000000 0.19599773E-08 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 4 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 -0.31671420 -Infinity Infinity 2 0.25000000 142 -0.31671420 -Infinity Infinity 3 0.12500000 278 -0.31671420 -Infinity Infinity 4 0.62500000E-01 544 -0.31671420 -Infinity Infinity 5 0.31250000E-01 1065 -0.31671420 -Infinity Infinity 6 0.15625000E-01 2085 -0.31671420 -Infinity Infinity 7 0.78125000E-02 4082 -0.31671420 -Infinity Infinity 8 0.39062500E-02 7986 -0.31671420 -Infinity Infinity TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 5 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 0.25000000 0.25000466 0.46645135E-05 2 0.25000000 142 0.25000000 0.25000123 0.12327525E-05 3 0.12500000 278 0.25000000 0.25000032 0.32163488E-06 4 0.62500000E-01 544 0.25000000 0.25000008 0.83995297E-07 5 0.31250000E-01 1065 0.25000000 0.25000002 0.21915610E-07 6 0.15625000E-01 2085 0.25000000 0.25000001 0.57179544E-08 7 0.78125000E-02 4082 0.25000000 0.25000000 0.14917872E-08 8 0.39062500E-02 7986 0.25000000 0.25000000 0.38975689E-09 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 6 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 0.21065725 0.21066535 0.80956427E-05 2 0.25000000 142 0.21065725 0.21065939 0.21395365E-05 3 0.12500000 278 0.21065725 0.21065781 0.55822158E-06 4 0.62500000E-01 544 0.21065725 0.21065740 0.14578014E-06 5 0.31250000E-01 1065 0.21065725 0.21065729 0.38036184E-07 6 0.15625000E-01 2085 0.21065725 0.21065726 0.99239374E-08 7 0.78125000E-02 4082 0.21065725 0.21065725 0.25891084E-08 8 0.39062500E-02 7986 0.21065725 0.21065725 0.67645292E-09 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 7 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 1.9052387 1.9051826 0.56048438E-04 2 0.25000000 142 1.9052387 1.9052239 0.14812670E-04 3 0.12500000 278 1.9052387 1.9052348 0.38647434E-05 4 0.62500000E-01 544 1.9052387 1.9052377 0.10092820E-05 5 0.31250000E-01 1065 1.9052387 1.9052384 0.26333653E-06 6 0.15625000E-01 2085 1.9052387 1.9052386 0.68706567E-07 7 0.78125000E-02 4082 1.9052387 1.9052387 0.17925219E-07 8 0.39062500E-02 7986 1.9052387 1.9052387 0.46833017E-08 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 8 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 0.51404190 0.51404048 0.14128660E-05 2 0.25000000 142 0.51404190 0.51404152 0.37339633E-06 3 0.12500000 278 0.51404190 0.51404180 0.97422024E-07 4 0.62500000E-01 544 0.51404190 0.51404187 0.25441866E-07 5 0.31250000E-01 1065 0.51404190 0.51404189 0.66381569E-08 6 0.15625000E-01 2085 0.51404190 0.51404189 0.17319476E-08 7 0.78125000E-02 4082 0.51404190 0.51404190 0.45185589E-09 8 0.39062500E-02 7986 0.51404190 0.51404190 0.11805279E-09 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 9 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 -0.44444444 NaN NaN 2 0.25000000 142 -0.44444444 NaN NaN 3 0.12500000 278 -0.44444444 NaN NaN 4 0.62500000E-01 544 -0.44444444 NaN NaN 5 0.31250000E-01 1065 -0.44444444 NaN NaN 6 0.15625000E-01 2085 -0.44444444 NaN NaN 7 0.78125000E-02 4082 -0.44444444 NaN NaN 8 0.39062500E-02 7986 -0.44444444 NaN NaN TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 10 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 0.78539816 0.78523155 0.16661737E-03 2 0.25000000 142 0.78539816 0.78533674 0.61420923E-04 3 0.12500000 278 0.78539816 0.78537574 0.22423561E-04 4 0.62500000E-01 544 0.78539816 0.78538997 0.81919093E-05 5 0.31250000E-01 1065 0.78539816 0.78539517 0.29906463E-05 6 0.15625000E-01 2085 0.78539816 0.78539707 0.10917757E-05 7 0.78125000E-02 4082 0.78539816 0.78539776 0.39855163E-06 8 0.39062500E-02 7986 0.78539816 0.78539802 0.14564680E-06 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 11 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 1.1981402 Infinity Infinity 2 0.25000000 142 1.1981402 Infinity Infinity 3 0.12500000 278 1.1981402 Infinity Infinity 4 0.62500000E-01 544 1.1981402 Infinity Infinity 5 0.31250000E-01 1065 1.1981402 Infinity Infinity 6 0.15625000E-01 2085 1.1981402 Infinity Infinity 7 0.78125000E-02 4082 1.1981402 Infinity Infinity 8 0.39062500E-02 7986 1.1981402 Infinity Infinity TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 12 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 2.0000000 Infinity Infinity 2 0.25000000 142 2.0000000 Infinity Infinity 3 0.12500000 278 2.0000000 Infinity Infinity 4 0.62500000E-01 544 2.0000000 Infinity Infinity 5 0.31250000E-01 1065 2.0000000 Infinity Infinity 6 0.15625000E-01 2085 2.0000000 Infinity Infinity 7 0.78125000E-02 4082 2.0000000 Infinity Infinity 8 0.39062500E-02 7986 2.0000000 Infinity Infinity TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 13 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 -1.0887930 -1.2553510 0.16655796 2 0.25000000 142 -1.0887930 -1.1725778 0.83784804E-01 3 0.12500000 278 -1.0887930 -1.1306406 0.41847587E-01 4 0.62500000E-01 544 -1.0887930 -1.1096938 0.20900734E-01 5 0.31250000E-01 1065 -1.0887930 -1.0992214 0.10428349E-01 6 0.15625000E-01 2085 -1.0887930 -1.0939932 0.52001816E-02 7 0.78125000E-02 4082 -1.0887930 -1.0913846 0.25915130E-02 8 0.39062500E-02 7986 -1.0887930 -1.0900847 0.12916372E-02 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 14 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error 1 0.50000000 73 2.2214415 687460.75 687458.52 2 0.25000000 142 2.2214415 353413.97 353411.75 3 0.12500000 278 2.2214415 180521.87 180519.65 4 0.62500000E-01 544 2.2214415 92253.055 92250.833 5 0.31250000E-01 1065 2.2214415 47123.762 47121.541 6 0.15625000E-01 2085 2.2214415 24071.490 24069.268 7 0.78125000E-02 4082 2.2214415 12296.293 12294.072 8 0.39062500E-02 7986 2.2214415 6286.2645 6284.0430 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 1 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 1.0000000 1.1440336 0.14403362 -1 2.0000000 19 1.0000000 1.0020422 0.20421608E-02 0 1.0000000 37 1.0000000 1.0000002 0.21123227E-06 1 0.50000000 73 1.0000000 1.0000000 0.11102230E-14 2 0.25000000 142 1.0000000 1.0000000 0.12212453E-14 3 0.12500000 278 1.0000000 1.0000000 0.12212453E-14 4 0.62500000E-01 544 1.0000000 1.0000000 0.34416914E-14 5 0.31250000E-01 1065 1.0000000 1.0000000 0.71054274E-14 6 0.15625000E-01 2085 1.0000000 1.0000000 0.14432899E-13 7 0.78125000E-02 4082 1.0000000 1.0000000 0.29531932E-13 8 0.39062500E-02 7986 1.0000000 1.0000000 0.57620575E-13 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 2 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 1.0000000 1.1440336 0.14403362 -1 2.0000000 19 1.0000000 1.0020422 0.20421608E-02 0 1.0000000 37 1.0000000 1.0000002 0.21123227E-06 1 0.50000000 73 1.0000000 1.0000000 0.11102230E-14 2 0.25000000 142 1.0000000 1.0000000 0.55511151E-15 3 0.12500000 278 1.0000000 1.0000000 0.77715612E-15 4 0.62500000E-01 544 1.0000000 1.0000000 0.48849813E-14 5 0.31250000E-01 1065 1.0000000 1.0000000 0.77715612E-14 6 0.15625000E-01 2085 1.0000000 1.0000000 0.15321078E-13 7 0.78125000E-02 4082 1.0000000 1.0000000 0.26312286E-13 8 0.39062500E-02 7986 1.0000000 1.0000000 0.57731597E-13 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 3 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 1.0000000 0.95856043 0.41439575E-01 -1 2.0000000 19 1.0000000 0.99196137 0.80386266E-02 0 1.0000000 37 1.0000000 0.99999604 0.39583258E-05 1 0.50000000 73 1.0000000 1.0000000 0.88595797E-13 2 0.25000000 142 1.0000000 1.0000000 0.99920072E-15 3 0.12500000 278 1.0000000 1.0000000 0.22204460E-14 4 0.62500000E-01 544 1.0000000 1.0000000 0.56621374E-14 5 0.31250000E-01 1065 1.0000000 1.0000000 0.10325074E-13 6 0.15625000E-01 2085 1.0000000 1.0000000 0.20872193E-13 7 0.78125000E-02 4082 1.0000000 1.0000000 0.41300297E-13 8 0.39062500E-02 7986 1.0000000 1.0000000 0.85043084E-13 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 4 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 -0.31671420 -Infinity Infinity -1 2.0000000 19 -0.31671420 -Infinity Infinity 0 1.0000000 37 -0.31671420 -0.31665833 0.55861890E-04 1 0.50000000 73 -0.31671420 -0.31671420 0.77242546E-10 2 0.25000000 142 -0.31671420 -0.31671420 0.89928065E-14 3 0.12500000 278 -0.31671420 -0.31671420 0.19595436E-13 4 0.62500000E-01 544 -0.31671420 -0.31671420 0.41022741E-13 5 0.31250000E-01 1065 -0.31671420 -0.31671420 0.84598994E-13 6 0.15625000E-01 2085 -0.31671420 -0.31671420 0.16653345E-12 7 0.78125000E-02 4082 -0.31671420 -0.31671420 0.32562841E-12 8 0.39062500E-02 7986 -0.31671420 -0.31671420 0.64137584E-12 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 5 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 0.25000000 0.25116534 0.11653443E-02 -1 2.0000000 19 0.25000000 0.24870645 0.12935531E-02 0 1.0000000 37 0.25000000 0.24999943 0.56910377E-06 1 0.50000000 73 0.25000000 0.25000000 0.82711615E-14 2 0.25000000 142 0.25000000 0.25000000 0.33306691E-15 3 0.12500000 278 0.25000000 0.25000000 0.49960036E-15 4 0.62500000E-01 544 0.25000000 0.25000000 0.11934898E-14 5 0.31250000E-01 1065 0.25000000 0.25000000 0.21649349E-14 6 0.15625000E-01 2085 0.25000000 0.25000000 0.54400928E-14 7 0.78125000E-02 4082 0.25000000 0.25000000 0.94091401E-14 8 0.39062500E-02 7986 0.25000000 0.25000000 0.19428903E-13 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 6 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 0.21065725 0.16987687 0.40780385E-01 -1 2.0000000 19 0.21065725 0.20685130 0.38059495E-02 0 1.0000000 37 0.21065725 0.21065478 0.24760434E-05 1 0.50000000 73 0.21065725 0.21065725 0.43687276E-13 2 0.25000000 142 0.21065725 0.21065725 0.22204460E-15 3 0.12500000 278 0.21065725 0.21065725 0.49960036E-15 4 0.62500000E-01 544 0.21065725 0.21065725 0.11657342E-14 5 0.31250000E-01 1065 0.21065725 0.21065725 0.28588243E-14 6 0.15625000E-01 2085 0.21065725 0.21065725 0.57731597E-14 7 0.78125000E-02 4082 0.21065725 0.21065725 0.11074475E-13 8 0.39062500E-02 7986 0.21065725 0.21065725 0.22121194E-13 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 7 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 1.9052387 2.5670472 0.66180849 -1 2.0000000 19 1.9052387 1.9273423 0.22103649E-01 0 1.0000000 37 1.9052387 1.9052409 0.22263384E-05 1 0.50000000 73 1.9052387 1.9052387 0.64703798E-12 2 0.25000000 142 1.9052387 1.9052387 0.11102230E-14 3 0.12500000 278 1.9052387 1.9052387 0.66613381E-15 4 0.62500000E-01 544 1.9052387 1.9052387 0.39968029E-14 5 0.31250000E-01 1065 1.9052387 1.9052387 0.62172489E-14 6 0.15625000E-01 2085 1.9052387 1.9052387 0.73274720E-14 7 0.78125000E-02 4082 1.9052387 1.9052387 0.28421709E-13 8 0.39062500E-02 7986 1.9052387 1.9052387 0.55289107E-13 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 8 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 0.51404190 0.59502205 0.80980157E-01 -1 2.0000000 19 0.51404190 0.51515932 0.11174242E-02 0 1.0000000 37 0.51404190 0.51404080 0.10946586E-05 1 0.50000000 73 0.51404190 0.51404190 0.23969715E-12 2 0.25000000 142 0.51404190 0.51404190 0.33306691E-15 3 0.12500000 278 0.51404190 0.51404190 0.99920072E-15 4 0.62500000E-01 544 0.51404190 0.51404190 0.11102230E-14 5 0.31250000E-01 1065 0.51404190 0.51404190 0.32196468E-14 6 0.15625000E-01 2085 0.51404190 0.51404190 0.48849813E-14 7 0.78125000E-02 4082 0.51404190 0.51404190 0.17541524E-13 8 0.39062500E-02 7986 0.51404190 0.51404190 0.27866598E-13 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 9 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 -0.44444444 NaN NaN -1 2.0000000 19 -0.44444444 -0.44554171 0.10972641E-02 0 1.0000000 37 -0.44444444 -0.44444448 0.32145405E-07 1 0.50000000 73 -0.44444444 -0.44444444 0.88817842E-15 2 0.25000000 142 -0.44444444 -0.44444444 0.16653345E-15 3 0.12500000 278 -0.44444444 -0.44444444 0.16653345E-15 4 0.62500000E-01 544 -0.44444444 -0.44444444 0.0000000 5 0.31250000E-01 1065 -0.44444444 -0.44444444 0.38857806E-15 6 0.15625000E-01 2085 -0.44444444 -0.44444444 0.55511151E-16 7 0.78125000E-02 4082 -0.44444444 -0.44444444 0.49960036E-15 8 0.39062500E-02 7986 -0.44444444 -0.44444444 0.30531133E-14 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 10 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 0.78539816 0.95140512 0.16600696 -1 2.0000000 19 0.78539816 0.78899320 0.35950379E-02 0 1.0000000 37 0.78539816 0.78539884 0.67876683E-06 1 0.50000000 73 0.78539816 0.78539816 0.74384943E-14 2 0.25000000 142 0.78539816 0.78539816 0.22204460E-15 3 0.12500000 278 0.78539816 0.78539816 0.17763568E-14 4 0.62500000E-01 544 0.78539816 0.78539816 0.29976022E-14 5 0.31250000E-01 1065 0.78539816 0.78539816 0.39968029E-14 6 0.15625000E-01 2085 0.78539816 0.78539816 0.85487173E-14 7 0.78125000E-02 4082 0.78539816 0.78539816 0.19539925E-13 8 0.39062500E-02 7986 0.78539816 0.78539816 0.34194869E-13 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 11 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 1.1981402 Infinity Infinity -1 2.0000000 19 1.1981402 Infinity Infinity 0 1.0000000 37 1.1981402 1.1981403 0.61443248E-07 1 0.50000000 73 1.1981402 1.1981402 0.17042102E-07 2 0.25000000 142 1.1981402 1.1981402 0.26667974E-07 3 0.12500000 278 1.1981402 1.1981402 0.39229554E-07 4 0.62500000E-01 544 1.1981402 1.1981402 0.57620126E-07 5 0.31250000E-01 1065 1.1981402 1.1981402 0.83248862E-07 6 0.15625000E-01 2085 1.1981402 1.1981401 0.11877995E-06 7 0.78125000E-02 4082 1.1981402 1.1981401 0.16778378E-06 8 0.39062500E-02 7986 1.1981402 1.1981400 0.23775051E-06 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 12 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 2.0000000 Infinity Infinity -1 2.0000000 19 2.0000000 1.9958069 0.41931285E-02 0 1.0000000 37 2.0000000 1.9999998 0.17902391E-06 1 0.50000000 73 2.0000000 2.0000000 0.15609736E-12 2 0.25000000 142 2.0000000 2.0000000 0.45630166E-12 3 0.12500000 278 2.0000000 2.0000000 0.97677422E-12 4 0.62500000E-01 544 2.0000000 2.0000000 0.20410340E-11 5 0.31250000E-01 1065 2.0000000 2.0000000 0.40727421E-11 6 0.15625000E-01 2085 2.0000000 2.0000000 0.79618534E-11 7 0.78125000E-02 4082 2.0000000 2.0000000 0.15243806E-10 8 0.39062500E-02 7986 2.0000000 2.0000000 0.29337865E-10 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 13 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 -1.0887930 -0.95662375 0.13216929 -1 2.0000000 19 -1.0887930 -1.0830763 0.57167337E-02 0 1.0000000 37 -1.0887930 -1.0887916 0.14061636E-05 1 0.50000000 73 -1.0887930 -1.0887930 0.24868996E-13 2 0.25000000 142 -1.0887930 -1.0887930 0.21760371E-13 3 0.12500000 278 -1.0887930 -1.0887930 0.44408921E-13 4 0.62500000E-01 544 -1.0887930 -1.0887930 0.94146912E-13 5 0.31250000E-01 1065 -1.0887930 -1.0887930 0.18474111E-12 6 0.15625000E-01 2085 -1.0887930 -1.0887930 0.36659564E-12 7 0.78125000E-02 4082 -1.0887930 -1.0887930 0.71631590E-12 8 0.39062500E-02 7986 -1.0887930 -1.0887930 0.14097612E-11 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 14 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 10 2.2214415 2.3558079 0.13436640 -1 2.0000000 19 2.2214415 2.2236213 0.21798150E-02 0 1.0000000 37 2.2214415 2.2214417 0.21763475E-06 1 0.50000000 73 2.2214415 2.2214414 0.35770218E-07 2 0.25000000 142 2.2214415 2.2214414 0.49449313E-07 3 0.12500000 278 2.2214415 2.2214414 0.71012935E-07 4 0.62500000E-01 544 2.2214415 2.2214414 0.10329735E-06 5 0.31250000E-01 1065 2.2214415 2.2214413 0.14836975E-06 6 0.15625000E-01 2085 2.2214415 2.2214413 0.21114039E-06 7 0.78125000E-02 4082 2.2214415 2.2214412 0.29782465E-06 8 0.39062500E-02 7986 2.2214415 2.2214410 0.42169109E-06 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 1 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 1.0000000 3.1415927 2.1415927 -1 2.0000000 2 1.0000000 1.5713287 0.57132873 0 1.0000000 4 1.0000000 1.0156868 0.15686758E-01 1 0.50000000 7 1.0000000 1.0000034 0.33595708E-05 2 0.25000000 13 1.0000000 1.0000000 0.36637360E-13 3 0.12500000 26 1.0000000 1.0000000 0.0000000 4 0.62500000E-01 51 1.0000000 1.0000000 0.22204460E-15 5 0.31250000E-01 102 1.0000000 1.0000000 0.22204460E-15 6 0.15625000E-01 201 1.0000000 1.0000000 0.55511151E-15 7 0.78125000E-02 400 1.0000000 1.0000000 0.11102230E-14 8 0.39062500E-02 794 1.0000000 1.0000000 0.0000000 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 2 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 1.0000000 3.1415927 2.1415927 -1 2.0000000 2 1.0000000 1.5713287 0.57132873 0 1.0000000 4 1.0000000 1.0156868 0.15686758E-01 1 0.50000000 7 1.0000000 1.0000034 0.33595708E-05 2 0.25000000 13 1.0000000 1.0000000 0.36637360E-13 3 0.12500000 26 1.0000000 1.0000000 0.22204460E-15 4 0.62500000E-01 51 1.0000000 1.0000000 0.33306691E-15 5 0.31250000E-01 102 1.0000000 1.0000000 0.44408921E-15 6 0.15625000E-01 201 1.0000000 1.0000000 0.0000000 7 0.78125000E-02 400 1.0000000 1.0000000 0.17763568E-14 8 0.39062500E-02 794 1.0000000 1.0000000 0.55511151E-15 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 3 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 1.0000000 2.3561945 1.3561945 -1 2.0000000 2 1.0000000 1.1788958 0.17889583 0 1.0000000 4 1.0000000 0.91810984 0.81890165E-01 1 0.50000000 7 1.0000000 0.99970961 0.29038780E-03 2 0.25000000 13 1.0000000 1.0000000 0.49084292E-10 3 0.12500000 26 1.0000000 1.0000000 0.22204460E-15 4 0.62500000E-01 51 1.0000000 1.0000000 0.33306691E-15 5 0.31250000E-01 102 1.0000000 1.0000000 0.44408921E-15 6 0.15625000E-01 201 1.0000000 1.0000000 0.0000000 7 0.78125000E-02 400 1.0000000 1.0000000 0.19984014E-14 8 0.39062500E-02 794 1.0000000 1.0000000 0.22204460E-14 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 4 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 -0.31671420 -Infinity Infinity -1 2.0000000 2 -0.31671420 -Infinity Infinity 0 1.0000000 4 -0.31671420 -Infinity Infinity 1 0.50000000 7 -0.31671420 -Infinity Infinity 2 0.25000000 13 -0.31671420 -Infinity Infinity 3 0.12500000 26 -0.31671420 -Infinity Infinity 4 0.62500000E-01 51 -0.31671420 -Infinity Infinity 5 0.31250000E-01 102 -0.31671420 -Infinity Infinity 6 0.15625000E-01 201 -0.31671420 -0.31671420 0.34416914E-14 7 0.78125000E-02 400 -0.31671420 -0.31671420 0.72719608E-14 8 0.39062500E-02 794 -0.31671420 -0.31671420 0.17430501E-13 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 5 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 0.25000000 0.63690310 0.38690310 -1 2.0000000 2 0.25000000 0.31863606 0.68636064E-01 0 1.0000000 4 0.25000000 0.23579378 0.14206225E-01 1 0.50000000 7 0.25000000 0.24996056 0.39443437E-04 2 0.25000000 13 0.25000000 0.25000000 0.37137793E-11 3 0.12500000 26 0.25000000 0.25000000 0.0000000 4 0.62500000E-01 51 0.25000000 0.25000000 0.55511151E-16 5 0.31250000E-01 102 0.25000000 0.25000000 0.55511151E-16 6 0.15625000E-01 201 0.25000000 0.25000000 0.11102230E-15 7 0.78125000E-02 400 0.25000000 0.25000000 0.52735594E-15 8 0.39062500E-02 794 0.25000000 0.25000000 0.66613381E-15 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 6 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 0.21065725 0.36414798 0.15349073 -1 2.0000000 2 0.21065725 0.18228306 0.28374194E-01 0 1.0000000 4 0.21065725 0.17578582 0.34871435E-01 1 0.50000000 7 0.21065725 0.21047231 0.18493877E-03 2 0.25000000 13 0.21065725 0.21065725 0.12020301E-10 3 0.12500000 26 0.21065725 0.21065725 0.27755576E-16 4 0.62500000E-01 51 0.21065725 0.21065725 0.27755576E-16 5 0.31250000E-01 102 0.21065725 0.21065725 0.55511151E-16 6 0.15625000E-01 201 0.21065725 0.21065725 0.27755576E-16 7 0.78125000E-02 400 0.21065725 0.21065725 0.27755576E-15 8 0.39062500E-02 794 0.21065725 0.21065725 0.33306691E-15 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 7 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 1.9052387 7.6533018 5.7480631 -1 2.0000000 2 1.9052387 3.8270691 1.9218304 0 1.0000000 4 1.9052387 2.1330330 0.22779432 1 0.50000000 7 1.9052387 1.9053095 0.70798216E-04 2 0.25000000 13 1.9052387 1.9052387 0.24850138E-08 3 0.12500000 26 1.9052387 1.9052387 0.22204460E-15 4 0.62500000E-01 51 1.9052387 1.9052387 0.66613381E-15 5 0.31250000E-01 102 1.9052387 1.9052387 0.44408921E-15 6 0.15625000E-01 201 1.9052387 1.9052387 0.66613381E-15 7 0.78125000E-02 400 1.9052387 1.9052387 0.88817842E-15 8 0.39062500E-02 794 1.9052387 1.9052387 0.22204460E-14 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 8 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 0.51404190 1.6466867 1.1326448 -1 2.0000000 2 0.51404190 0.82360364 0.30956174 0 1.0000000 4 0.51404190 0.52523358 0.11191680E-01 1 0.50000000 7 0.51404190 0.51397488 0.67017459E-04 2 0.25000000 13 0.51404190 0.51404189 0.22633614E-08 3 0.12500000 26 0.51404190 0.51404190 0.11102230E-15 4 0.62500000E-01 51 0.51404190 0.51404190 0.22204460E-15 5 0.31250000E-01 102 0.51404190 0.51404190 0.22204460E-15 6 0.15625000E-01 201 0.51404190 0.51404190 0.0000000 7 0.78125000E-02 400 0.51404190 0.51404190 0.22204460E-15 8 0.39062500E-02 794 0.51404190 0.51404190 0.0000000 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 9 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 -0.44444444 NaN NaN -1 2.0000000 2 -0.44444444 NaN NaN 0 1.0000000 4 -0.44444444 NaN NaN 1 0.50000000 7 -0.44444444 NaN NaN 2 0.25000000 13 -0.44444444 NaN NaN 3 0.12500000 26 -0.44444444 NaN NaN 4 0.62500000E-01 51 -0.44444444 -0.44444444 0.27755576E-15 5 0.31250000E-01 102 -0.44444444 -0.44444444 0.11102230E-15 6 0.15625000E-01 201 -0.44444444 -0.44444444 0.16653345E-15 7 0.78125000E-02 400 -0.44444444 -0.44444444 0.66613381E-15 8 0.39062500E-02 794 -0.44444444 -0.44444444 0.33306691E-15 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 10 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 0.78539816 2.7206990 1.9353009 -1 2.0000000 2 0.78539816 1.3606170 0.57521882 0 1.0000000 4 0.78539816 0.82049407 0.35095910E-01 1 0.50000000 7 0.78539816 0.78542738 0.29220447E-04 2 0.25000000 13 0.78539816 0.78539816 0.14799273E-11 3 0.12500000 26 0.78539816 0.78539816 0.0000000 4 0.62500000E-01 51 0.78539816 0.78539816 0.0000000 5 0.31250000E-01 102 0.78539816 0.78539816 0.11102230E-15 6 0.15625000E-01 201 0.78539816 0.78539816 0.22204460E-15 7 0.78125000E-02 400 0.78539816 0.78539816 0.99920072E-15 8 0.39062500E-02 794 0.78539816 0.78539816 0.55511151E-15 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 11 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 1.1981402 Infinity Infinity -1 2.0000000 2 1.1981402 Infinity Infinity 0 1.0000000 4 1.1981402 Infinity Infinity 1 0.50000000 7 1.1981402 Infinity Infinity 2 0.25000000 13 1.1981402 Infinity Infinity 3 0.12500000 26 1.1981402 Infinity Infinity 4 0.62500000E-01 51 1.1981402 Infinity Infinity 5 0.31250000E-01 102 1.1981402 Infinity Infinity 6 0.15625000E-01 201 1.1981402 1.1981402 0.16811027E-07 7 0.78125000E-02 400 1.1981402 1.1981402 0.23649506E-07 8 0.39062500E-02 794 1.1981402 1.1981402 0.36902382E-07 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 12 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 2.0000000 Infinity Infinity -1 2.0000000 2 2.0000000 Infinity Infinity 0 1.0000000 4 2.0000000 Infinity Infinity 1 0.50000000 7 2.0000000 Infinity Infinity 2 0.25000000 13 2.0000000 Infinity Infinity 3 0.12500000 26 2.0000000 Infinity Infinity 4 0.62500000E-01 51 2.0000000 2.0000000 0.15099033E-13 5 0.31250000E-01 102 2.0000000 2.0000000 0.31530334E-13 6 0.15625000E-01 201 2.0000000 2.0000000 0.19340085E-12 7 0.78125000E-02 400 2.0000000 2.0000000 0.38058445E-12 8 0.39062500E-02 794 2.0000000 2.0000000 0.88817842E-12 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 13 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 -1.0887930 -1.7102721 0.62147907 -1 2.0000000 2 -1.0887930 -0.85971165 0.22908140 0 1.0000000 4 -1.0887930 -1.0198905 0.68902568E-01 1 0.50000000 7 -1.0887930 -1.0887212 0.71889913E-04 2 0.25000000 13 -1.0887930 -1.0887930 0.54323213E-11 3 0.12500000 26 -1.0887930 -1.0887930 0.19984014E-14 4 0.62500000E-01 51 -1.0887930 -1.0887930 0.31086245E-14 5 0.31250000E-01 102 -1.0887930 -1.0887930 0.31086245E-14 6 0.15625000E-01 201 -1.0887930 -1.0887930 0.11102230E-13 7 0.78125000E-02 400 -1.0887930 -1.0887930 0.19317881E-13 8 0.39062500E-02 794 -1.0887930 -1.0887930 0.40634163E-13 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 14 Tolerance TOL = 0.22204460E-15 M H N Exact Quad Error -2 4.0000000 1 2.2214415 4.9348022 2.7133607 -1 2.0000000 2 2.2214415 2.5668226 0.34538112 0 1.0000000 4 2.2214415 2.2428953 0.21453848E-01 1 0.50000000 7 2.2214415 2.2214419 0.44708657E-06 2 0.25000000 13 2.2214415 2.2214415 0.17441378E-07 3 0.12500000 26 2.2214415 2.2214415 0.10058408E-07 4 0.62500000E-01 51 2.2214415 2.2214415 0.11408853E-07 5 0.31250000E-01 102 2.2214415 2.2214415 0.15150013E-07 6 0.15625000E-01 201 2.2214415 2.2214414 0.33755441E-07 7 0.78125000E-02 400 2.2214415 2.2214414 0.44457355E-07 8 0.39062500E-02 794 2.2214415 2.2214414 0.67182761E-07 TANH_QUAD_TEST Normal end of execution. 21 March 2018 1:23:08.827 PM