17 September 2021 9:31:09.081 AM FASTGL_TEST: FORTRAN90 version. Test the FASTGL library. BESSELJZERO_TEST: BESSELJZERO returns the K-th zero of J0(X). K X(K) J0(X(K)) 1 2.404825557695773 -0.5553876295239997E-16 2 5.520078110286311 -0.2666015572788445E-16 3 8.653727912911013 -0.7918276418867505E-16 4 11.79153443901428 -0.6555381838919634E-16 5 14.93091770848779 -0.1461463191627680E-15 6 18.07106396791092 0.1814218851436404E-15 7 21.21163662987926 0.8563933302065787E-16 8 24.35247153074930 -0.1482500997739738E-15 9 27.49347913204025 0.2464784048700305E-15 10 30.63460646843198 0.7771557167225001E-16 11 33.77582021357357 0.1995587237009700E-15 12 36.91709835366404 0.1216959173717813E-15 13 40.05842576462824 -0.3371047515291648E-16 14 43.19979171317673 -0.1038624839785532E-15 15 46.34118837166181 -0.1063547056574846E-15 16 49.48260989739781 -0.2701955835992770E-15 17 52.62405184111500 -0.1931321298301444E-15 18 55.76551075501998 0.2401031991630749E-15 19 58.90698392608094 0.1957403252890847E-15 20 62.04846919022717 -0.3592012798817341E-15 21 65.18996480020687 -0.5397507550382613E-15 22 68.33146932985679 -0.1044094141724201E-14 23 71.47298160359372 0.8969618703197079E-15 24 74.61450064370183 -0.6362846801653335E-15 25 77.75602563038805 0.2612731316835445E-15 26 80.89755587113763 -0.1136841709423886E-15 27 84.03909077693818 0.7803197674310891E-15 28 87.18062984364116 0.2553684088322987E-15 29 90.32217263721049 -0.4479426639094836E-15 30 93.46371878194476 -0.9024658571874119E-15 BESSELJ1SQUARED_TEST: BESSELJ1SQUARED returns the square of the Bessel J1(X) function at the K-th zero of J0(X). K X(K) J1(X(K))^2 BESSELJ1SQUARED 1 2.404825557695773 0.2695141239419168 0.2695141239419169 2 5.520078110286311 0.1157801385822037 0.1157801385822037 3 8.653727912911013 0.7368635113640823E-01 0.7368635113640822E-01 4 11.79153443901428 0.5403757319811629E-01 0.5403757319811628E-01 5 14.93091770848779 0.4266142901724309E-01 0.4266142901724309E-01 6 18.07106396791092 0.3524210349099610E-01 0.3524210349099610E-01 7 21.21163662987926 0.3002107010305466E-01 0.3002107010305467E-01 8 24.35247153074930 0.2614739149530809E-01 0.2614739149530809E-01 9 27.49347913204025 0.2315912182469139E-01 0.2315912182469139E-01 10 30.63460646843198 0.2078382912226786E-01 0.2078382912226786E-01 11 33.77582021357357 0.1885045066931767E-01 0.1885045066931767E-01 12 36.91709835366404 0.1724615756966501E-01 0.1724615756966501E-01 13 40.05842576462824 0.1589351810592360E-01 0.1589351810592360E-01 14 43.19979171317673 0.1473762609647219E-01 0.1473762609647219E-01 15 46.34118837166181 0.1373846514538712E-01 0.1373846514538712E-01 16 49.48260989739781 0.1286618173761513E-01 0.1286618173761513E-01 17 52.62405184111500 0.1209805154862680E-01 0.1209805154862680E-01 18 55.76551075501998 0.1141647122449160E-01 0.1141647122449161E-01 19 58.90698392608094 0.1080759279118020E-01 0.1080759279118020E-01 20 62.04846919022717 0.1026037292628077E-01 0.1026037292628076E-01 21 65.18996480020687 0.9765897139791053E-02 0.9765897139791051E-02 22 68.33146932985679 0.9316890387627164E-02 0.9316890387627166E-02 23 71.47298160359372 0.8907356754001993E-02 0.8907356754001991E-02 24 74.61450064370183 0.8532310161358081E-02 0.8532310161358083E-02 25 77.75602563038805 0.8187570362708153E-02 0.8187570362708157E-02 26 80.89755587113763 0.7869606469720767E-02 0.7869606469720769E-02 27 84.03909077693818 0.7575415577297654E-02 0.7575415577297647E-02 28 87.18062984364116 0.7302427631477638E-02 0.7302427631477641E-02 29 90.32217263721049 0.7048430150990360E-02 0.7048430150990362E-02 30 93.46371878194476 0.6811508131014088E-02 0.6811508131014086E-02 GLPAIR_TEST Estimate integral ( 0 <= x <= 1 ) ln(x) dx. Nodes Estimate 1 -0.6931471805599453 10 -0.9942637022162133 100 -0.9999374873224512 1000 -0.9999993692484898 10000 -0.9999999936868078 100000 -0.9999999999368618 1000000 -0.9999999999993812 Exact -1.0 GLPAIRS_TEST: integral ( -1 <= x <= 1 ) cos(1000 x) dx Nodes Estimate 500 -0.2538816332422891 520 0.1592120992016624E-02 540 0.1653759028178648E-02 560 0.1653759081049292E-02 580 0.1653759081048851E-02 600 0.1653759081066034E-02 Exact 0.1653759081064005E-02 GLPAIRTABULATED_TEST: integral ( -1 <= x <= 1 ) exp(x) dx Nodes Estimate 1 2.000000000000000 2 2.342696087909731 3 2.350336928680012 4 2.350402092156377 5 2.350402386462826 6 2.350402387286035 7 2.350402387287601 8 2.350402387287603 9 2.350402387287603 Exact 2.350402387287603 LEGENDRE_THETA_TEST: LEGENDRE_THETA returns the K-th theta value for a Gauss Legendre rule of order L. Gauss Legendre rule of order 1 K Theta Cos(Theta) 1 1.57080 0.612323E-16 Gauss Legendre rule of order 2 K Theta Cos(Theta) 1 2.18628 -0.577350 2 0.955317 0.577350 Gauss Legendre rule of order 3 K Theta Cos(Theta) 1 2.45687 -0.774597 2 1.57080 0.612323E-16 3 0.684719 0.774597 Gauss Legendre rule of order 4 K Theta Cos(Theta) 1 2.60830 -0.861136 2 1.91769 -0.339981 3 1.22390 0.339981 4 0.533296 0.861136 Gauss Legendre rule of order 5 K Theta Cos(Theta) 1 2.70496 -0.906180 2 2.13942 -0.538469 3 1.57080 0.612323E-16 4 1.00218 0.538469 5 0.436635 0.906180 Gauss Legendre rule of order 6 K Theta Cos(Theta) 1 2.77199 -0.932470 2 2.29323 -0.661209 3 1.81174 -0.238619 4 1.32985 0.238619 5 0.848367 0.661209 6 0.369607 0.932470 Gauss Legendre rule of order 7 K Theta Cos(Theta) 1 2.82119 -0.949108 2 2.40615 -0.741531 3 1.98870 -0.405845 4 1.57080 0.612323E-16 5 1.15289 0.405845 6 0.735447 0.741531 7 0.320405 0.949108 Gauss Legendre rule of order 8 K Theta Cos(Theta) 1 2.85884 -0.960290 2 2.49256 -0.796666 3 2.12414 -0.525532 4 1.75528 -0.183435 5 1.38632 0.183435 6 1.01746 0.525532 7 0.649037 0.796666 8 0.282757 0.960290 Gauss Legendre rule of order 9 K Theta Cos(Theta) 1 2.88857 -0.968160 2 2.56081 -0.836031 3 2.23112 -0.613371 4 1.90102 -0.324253 5 1.57080 0.612323E-16 6 1.24057 0.324253 7 0.910474 0.613371 8 0.580787 0.836031 9 0.253022 0.968160 Gauss Legendre rule of order 10 K Theta Cos(Theta) 1 2.91265 -0.973907 2 2.61607 -0.865063 3 2.31775 -0.679410 4 2.01905 -0.433395 5 1.72023 -0.148874 6 1.42137 0.148874 7 1.12254 0.433395 8 0.823839 0.679410 9 0.525520 0.865063 10 0.228944 0.973907 LEGENDRE_WEIGHT_TEST: LEGENDRE_WEIGHT returns the K-th weight for a Gauss Legendre rule of order L. Gauss Legendre rule of order 1 K Weight 1 2.00000 Gauss Legendre rule of order 2 K Weight 1 1.00000 2 1.00000 Gauss Legendre rule of order 3 K Weight 1 0.555556 2 0.888889 3 0.555556 Gauss Legendre rule of order 4 K Weight 1 0.347855 2 0.652145 3 0.652145 4 0.347855 Gauss Legendre rule of order 5 K Weight 1 0.236927 2 0.478629 3 0.568889 4 0.478629 5 0.236927 Gauss Legendre rule of order 6 K Weight 1 0.171324 2 0.360762 3 0.467914 4 0.467914 5 0.360762 6 0.171324 Gauss Legendre rule of order 7 K Weight 1 0.129485 2 0.279705 3 0.381830 4 0.417959 5 0.381830 6 0.279705 7 0.129485 Gauss Legendre rule of order 8 K Weight 1 0.101229 2 0.222381 3 0.313707 4 0.362684 5 0.362684 6 0.313707 7 0.222381 8 0.101229 Gauss Legendre rule of order 9 K Weight 1 0.812744E-01 2 0.180648 3 0.260611 4 0.312347 5 0.330239 6 0.312347 7 0.260611 8 0.180648 9 0.812744E-01 Gauss Legendre rule of order 10 K Weight 1 0.666713E-01 2 0.149451 3 0.219086 4 0.269267 5 0.295524 6 0.295524 7 0.269267 8 0.219086 9 0.149451 10 0.666713E-01 FASTGL_TEST: Normal end of execution. 17 September 2021 9:31:09.258 AM