19 December 2023 8:37:28.223 AM specfun_test1(): Fortran77 version Test specfun(). Test of LGAMA(X) vs LN(2*SQRT(PI))-2X*LN(2)+LGAMA(2X)-LGAMA(X+1/2) 2000 Random arguments were tested from the interval ( 0.0, 0.9) LGAMA(X) was larger 577 times, agreed 897 times, and was smaller 526 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6164E-15 = 2 ** -50.53 occurred for X = 0.869815E+00 The estimated loss of base 2 significant digits is 2.47 The root mean square relative error was 0.1457E-15 = 2 ** -52.61 The estimated loss of base 2 significant digits is 0.39 1Test of LGAMA(X) vs LN(2*SQRT(PI))-(2X-1)*LN(2)+LGAMA(X-1/2)-LGAMA(2X-1) 2000 Random arguments were tested from the interval ( 1.3, 1.6) LGAMA(X) was larger 808 times, agreed 522 times, and was smaller 670 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.7593E-15 = 2 ** -50.23 occurred for X = 0.162161E+01 The estimated loss of base 2 significant digits is 2.77 The root mean square relative error was 0.1735E-15 = 2 ** -52.36 The estimated loss of base 2 significant digits is 0.64 1Test of LGAMA(X) vs -LN(2*SQRT(PI))+X*LN(2)+LGAMA(X/2)+LGAMA(X/2+1/2) 2000 Random arguments were tested from the interval ( 4.0, 20.0) LGAMA(X) was larger 683 times, agreed 882 times, and was smaller 435 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4735E-15 = 2 ** -50.91 occurred for X = 0.748383E+01 The estimated loss of base 2 significant digits is 2.09 The root mean square relative error was 0.1514E-15 = 2 ** -52.55 The estimated loss of base 2 significant digits is 0.45 Special Tests: Test of special arguments LGAMA ( 0.222045E-15) = 0.360437E+02 LGAMA ( 0.500000E+00) = 0.572365E+00 LGAMA ( 0.100000E+01) = 0.000000E+00 LGAMA ( 0.200000E+01) = 0.000000E+00 Test of Error Returns: LGAMA will be called with the argument 0.222507-307 This should not trigger an error message LGAMA returned the value 0.708396E+03 LGAMA will be called with the argument 0.253442+306 This should not trigger an error message LGAMA returned the value 0.177972+309 LGAMA will be called with the argument-0.100000E+01 This should trigger an error message LGAMA returned the value 0.179000+309 LGAMA will be called with the argument 0.000000E+00 This should trigger an error message LGAMA returned the value 0.179000+309 LGAMA will be called with the argument 0.177972+309 This should trigger an error message LGAMA returned the value 0.179000+309 This concludes the tests. 1Test of Dawson's Integral vs Taylor expansion 2000 Random arguments were tested from the interval ( 0.06, 1.00) F(X) was larger 513 times, agreed 964 times, and was smaller 523 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4421E-15 = 2 ** -51.01 occurred for X = 0.672985E+00 The estimated loss of base 2 significant digits is 1.99 The root mean square relative error was 0.1350E-15 = 2 ** -52.72 The estimated loss of base 2 significant digits is 0.28 1Test of Dawson's Integral vs Taylor expansion 2000 Random arguments were tested from the interval ( 1.00, 2.50) F(X) was larger 631 times, agreed 777 times, and was smaller 592 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5913E-15 = 2 ** -50.59 occurred for X = 0.210132E+01 The estimated loss of base 2 significant digits is 2.41 The root mean square relative error was 0.1642E-15 = 2 ** -52.44 The estimated loss of base 2 significant digits is 0.56 1Test of Dawson's Integral vs Taylor expansion 2000 Random arguments were tested from the interval ( 2.50, 5.00) F(X) was larger 534 times, agreed 1024 times, and was smaller 442 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5133E-15 = 2 ** -50.79 occurred for X = 0.256100E+01 The estimated loss of base 2 significant digits is 2.21 The root mean square relative error was 0.1172E-15 = 2 ** -52.92 The estimated loss of base 2 significant digits is 0.08 1Test of Dawson's Integral vs Taylor expansion 2000 Random arguments were tested from the interval ( 5.00,10.00) F(X) was larger 404 times, agreed 1147 times, and was smaller 449 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.3350E-15 = 2 ** -51.41 occurred for X = 0.611902E+01 The estimated loss of base 2 significant digits is 1.59 The root mean square relative error was 0.1060E-15 = 2 ** -53.07 The estimated loss of base 2 significant digits is 0.00 Special Tests: Estimated loss of base 2 significant digits in X F(x)+F(-x) 2.404 0.00 0.465 0.00 2.074 0.00 3.286 0.00 2.759 0.00 0.918 0.00 2.694 0.00 0.785 0.00 2.182 0.00 0.736 0.00 Test of special arguments F(XMIN) = 0.22250738585072014-307 Test of Error Returns: DAW will be called with the argument 0.223834+308 This should not underflow DAW returned the value 0.223380-307 DAW will be called with the argument 0.224712+308 This may underflow DAW returned the value 0.000000E+00 DAW will be called with the argument 0.225589+308 This may underflow DAW returned the value 0.000000E+00 This concludes the tests. 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( 0.188, 0.310) EI(X) was larger 402 times, agreed 710 times, and was smaller 888 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6294E-15 = 2 ** -50.50 occurred for X = 0.289009E+00 The estimated loss of base 2 significant digits is 2.50 The root mean square relative error was 0.1767E-15 = 2 ** -52.33 The estimated loss of base 2 significant digits is 0.67 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( 0.435, 6.000) EI(X) was larger 605 times, agreed 706 times, and was smaller 689 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1465E-14 = 2 ** -49.28 occurred for X = 0.586824E+01 The estimated loss of base 2 significant digits is 3.72 The root mean square relative error was 0.2573E-15 = 2 ** -51.79 The estimated loss of base 2 significant digits is 1.21 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( 6.000, 12.000) EI(X) was larger 583 times, agreed 806 times, and was smaller 611 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.9811E-15 = 2 ** -49.86 occurred for X = 0.601352E+01 The estimated loss of base 2 significant digits is 3.14 The root mean square relative error was 0.1561E-15 = 2 ** -52.51 The estimated loss of base 2 significant digits is 0.49 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( 12.000, 24.000) EI(X) was larger 566 times, agreed 871 times, and was smaller 563 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4685E-15 = 2 ** -50.92 occurred for X = 0.147501E+02 The estimated loss of base 2 significant digits is 2.08 The root mean square relative error was 0.1455E-15 = 2 ** -52.61 The estimated loss of base 2 significant digits is 0.39 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( 24.000, 48.000) EI(X) was larger 553 times, agreed 921 times, and was smaller 526 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5192E-15 = 2 ** -50.77 occurred for X = 0.270756E+02 The estimated loss of base 2 significant digits is 2.23 The root mean square relative error was 0.1374E-15 = 2 ** -52.69 The estimated loss of base 2 significant digits is 0.31 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( -0.250, -1.000) EI(X) was larger 597 times, agreed 911 times, and was smaller 492 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.7004E-15 = 2 ** -50.34 occurred for X =-0.952377E+00 The estimated loss of base 2 significant digits is 2.66 The root mean square relative error was 0.1580E-15 = 2 ** -52.49 The estimated loss of base 2 significant digits is 0.51 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( -1.000, -4.000) EI(X) was larger 672 times, agreed 590 times, and was smaller 738 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8639E-15 = 2 ** -50.04 occurred for X =-0.230866E+01 The estimated loss of base 2 significant digits is 2.96 The root mean square relative error was 0.2349E-15 = 2 ** -51.92 The estimated loss of base 2 significant digits is 1.08 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( -4.000,-10.000) EI(X) was larger 584 times, agreed 856 times, and was smaller 560 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4556E-15 = 2 ** -50.96 occurred for X =-0.540703E+01 The estimated loss of base 2 significant digits is 2.04 The root mean square relative error was 0.1462E-15 = 2 ** -52.60 The estimated loss of base 2 significant digits is 0.40 Test of special arguments EI ( 0.375000E+00) = 0.969138E-02 The relative error is 0.1398E-16 = 2 ** -55.99 The estimated loss of base 2 significant digits is 0.00 Test of Error Returns: EONE will be called with the argument 0.701800E+03 This should not underflow EONE returned the value 0.231901-307 EONE will be called with the argument 0.701844E+03 This should underflow EONE returned the value-0.000000E+00 EI will be called with the argument 0.716300E+03 This should not overflow EI returned the value 0.170079+309 EI will be called with the argument 0.716356E+03 This should overflow EI returned the value 0.179000+309 EXPEI will be called with the argument 0.449423+308 This should not underflow EXPEI returned the value 0.222507-307 EI will be called with the argument 0.000000E+00 This should overflow EI returned the value-0.179000+309 This concludes the tests. 1Test of erf(x) vs double series expansion 2000 Random arguments were tested from the interval ( 0.000, 0.469) ERF(X) was larger 133 times, agreed 825 times, and was smaller 1042 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4426E-15 = 2 ** -51.00 occurred for X = 0.226101E+00 The estimated loss of base 2 significant digits is 2.00 The root mean square relative error was 0.1452E-15 = 2 ** -52.61 The estimated loss of base 2 significant digits is 0.39 Test of erfc(x) vs exp(x+1/4) SUM i^n erfc(x+1/2) 2000 Random arguments were tested from the interval ( 0.469, 2.000) ERFC(X) was larger 823 times, agreed 491 times, and was smaller 686 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8235E-15 = 2 ** -50.11 occurred for X = 0.186287E+01 The estimated loss of base 2 significant digits is 2.89 The root mean square relative error was 0.2601E-15 = 2 ** -51.77 The estimated loss of base 2 significant digits is 1.23 1Test of exp(x*x) erfc(x) vs SUM i^n erfc(x+1/2) 2000 Random arguments were tested from the interval ( 0.469, 2.000) ERFCX(X) was larger 826 times, agreed 632 times, and was smaller 542 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6555E-15 = 2 ** -50.44 occurred for X = 0.746815E+00 The estimated loss of base 2 significant digits is 2.56 The root mean square relative error was 0.2121E-15 = 2 ** -52.07 The estimated loss of base 2 significant digits is 0.93 Test of erfc(x) vs exp(x+1/4) SUM i^n erfc(x+1/2) 2000 Random arguments were tested from the interval ( 2.000, 26.000) ERFC(X) was larger 660 times, agreed 656 times, and was smaller 684 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.9963E-15 = 2 ** -49.83 occurred for X = 0.307603E+01 The estimated loss of base 2 significant digits is 3.17 The root mean square relative error was 0.1956E-15 = 2 ** -52.18 The estimated loss of base 2 significant digits is 0.82 1Test of exp(x*x) erfc(x) vs SUM i^n erfc(x+1/2) 2000 Random arguments were tested from the interval ( 2.000, 20.000) ERFCX(X) was larger 494 times, agreed 1019 times, and was smaller 487 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.9395E-15 = 2 ** -49.92 occurred for X = 0.303251E+01 The estimated loss of base 2 significant digits is 3.08 The root mean square relative error was 0.1446E-15 = 2 ** -52.62 The estimated loss of base 2 significant digits is 0.38 Special Tests: Estimated loss of base 2significant digits in X Erf(x)+Erf(-x) Erf(x)+Erfc(x)-1 Erfcx(x)-exp(x*x)*erfc(x) 0.000 0.00 0.00 0.00 -0.500 0.00 0.00 0.03 -1.000 0.00 0.00 0.00 -1.500 0.00 0.00 0.00 -2.000 0.00 0.00 0.00 -2.500 0.00 0.00 0.00 -3.000 0.00 0.00 0.02 -3.500 0.00 0.00 0.33 -4.000 0.00 0.00 0.00 -4.500 0.00 0.00 0.00 Test of special arguments ERF ( 0.179769+309) = 0.100000E+01 ERF ( 0.000000E+00) = 0.000000E+00 ERFC ( 0.000000E+00) = 0.100000E+01 ERFC (-0.179769+309) = 0.200000E+01 Test of Error Returns: ERFC will be called with the argument 0.199074E+02 This should not underflow ERFC returned the value 0.217879-173 ERFC will be called with the argument 0.265433E+02 This may underflow ERFC returned the value 0.000000E+00 ERFCX will be called with the argument 0.237712+308 This should not underflow ERFCX returned the value 0.237341-307 ERFCX will be called with the argument-0.239659E+02 This should not overflow ERFCX returned the value 0.554007+250 ERFCX will be called with the argument-0.266287E+02 This may overflow ERFCX returned the value 0.179000+309 This concludes the tests. 1Test of GAMMA(X) vs Duplication Formula 2000 Random arguments were tested from the interval ( 0.000, 2.000) GAMMA(X) was larger 549 times, agreed 835 times, and was smaller 616 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4431E-15 = 2 ** -51.00 occurred for X = 0.996006E+00 The estimated loss of base 2 significant digits is 2.00 The root mean square relative error was 0.1327E-15 = 2 ** -52.74 The estimated loss of base 2 significant digits is 0.26 1Test of GAMMA(X) vs Duplication Formula 2000 Random arguments were tested from the interval ( 2.000, 10.000) GAMMA(X) was larger 614 times, agreed 760 times, and was smaller 626 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.7671E-15 = 2 ** -50.21 occurred for X = 0.817005E+01 The estimated loss of base 2 significant digits is 2.79 The root mean square relative error was 0.1802E-15 = 2 ** -52.30 The estimated loss of base 2 significant digits is 0.70 1Test of GAMMA(X) vs Duplication Formula 2000 Random arguments were tested from the interval ( 10.000,171.124) GAMMA(X) was larger 998 times, agreed 8 times, and was smaller 994 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.2174E-12 = 2 ** -42.06 occurred for X = 0.145859E+03 The estimated loss of base 2 significant digits is 10.94 The root mean square relative error was 0.4490E-13 = 2 ** -44.34 The estimated loss of base 2 significant digits is 8.66 1Test of GAMMA(X) vs Duplication Formula 2000 Random arguments were tested from the interval ( -4.750, -4.250) GAMMA(X) was larger 1191 times, agreed 363 times, and was smaller 446 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1031E-14 = 2 ** -49.78 occurred for X =-0.470808E+01 The estimated loss of base 2 significant digits is 3.22 The root mean square relative error was 0.3162E-15 = 2 ** -51.49 The estimated loss of base 2 significant digits is 1.51 Special Tests: Test of special arguments GAMMA (-0.500000E+00) = -0.354491E+01 GAMMA ( 0.224755-307) = 0.444929+308 GAMMA ( 0.100000E+01) = 0.100000E+01 GAMMA ( 0.200000E+01) = 0.100000E+01 GAMMA ( 0.169908E+03) = 0.266542+305 Test of Error Returns: GAMMA will be called with the argument-0.100000E+01 This should trigger an error message GAMMA returned the value 0.179000+309 GAMMA will be called with the argument 0.000000E+00 This should trigger an error message GAMMA returned the value 0.179000+309 GAMMA will be called with the argument 0.222507-307 This should trigger an error message GAMMA returned the value 0.179000+309 GAMMA will be called with the argument 0.171624E+03 This should trigger an error message GAMMA returned the value 0.179000+309 This concludes the tests. 1Test of I0(X) vs Multiplication Theorem 2000 Random arguments were tested from the interval ( 0.00, 2.00) I0(X) was larger 522 times, agreed 971 times, and was smaller 507 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5579E-15 = 2 ** -50.67 occurred for X = 0.860807E+00 The estimated loss of base 2 significant digits is 2.33 The root mean square relative error was 0.1435E-15 = 2 ** -52.63 The estimated loss of base 2 significant digits is 0.37 1Test of I0(X) vs Taylor series 2000 Random arguments were tested from the interval ( 2.00, 7.50) I0(X) was larger 719 times, agreed 598 times, and was smaller 683 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8953E-15 = 2 ** -49.99 occurred for X = 0.593718E+01 The estimated loss of base 2 significant digits is 3.01 The root mean square relative error was 0.2215E-15 = 2 ** -52.00 The estimated loss of base 2 significant digits is 1.00 1Test of I0(X) vs Taylor series 2000 Random arguments were tested from the interval ( 7.50,15.00) I0(X) was larger 850 times, agreed 307 times, and was smaller 843 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1459E-14 = 2 ** -49.28 occurred for X = 0.126371E+02 The estimated loss of base 2 significant digits is 3.72 The root mean square relative error was 0.4162E-15 = 2 ** -51.09 The estimated loss of base 2 significant digits is 1.91 1Test of I0(X) vs Taylor series 2000 Random arguments were tested from the interval (15.00,30.00) I0(X) was larger 612 times, agreed 784 times, and was smaller 604 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5399E-15 = 2 ** -50.72 occurred for X = 0.284450E+02 The estimated loss of base 2 significant digits is 2.28 The root mean square relative error was 0.1592E-15 = 2 ** -52.48 The estimated loss of base 2 significant digits is 0.52 Special Tests: Test with extreme arguments I0(XMIN) = 0.10000000000000000E+01 I0(0) = 0.10000000000000000E+01 I0(-0.15095557157417472E+00 ) = 0.10057050149414297E+01 I0( 0.15095557157417472E+00 ) = 0.10057050149414297E+01 E**-X * I0(XMAX) = 0.29754474593158999-154 Tests near the largest argument for unscaled functions I0( 0.69235094188622168E+03 ) = 0.73285657728857090+299 I0( 0.73629899972079636E+03 ) = 0.17900000000000000+309 This concludes the tests. 1Test of I1(X) vs Multiplication Theorem 2000 Random arguments were tested from the interval ( 0.00, 1.00) I1(X) was larger 636 times, agreed 697 times, and was smaller 667 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6405E-15 = 2 ** -50.47 occurred for X = 0.800796E+00 The estimated loss of base 2 significant digits is 2.53 The root mean square relative error was 0.1795E-15 = 2 ** -52.31 The estimated loss of base 2 significant digits is 0.69 1Test of I1(X) vs Taylor series 2000 Random arguments were tested from the interval ( 1.00, 7.50) I1(X) was larger 709 times, agreed 607 times, and was smaller 684 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8265E-15 = 2 ** -50.10 occurred for X = 0.612303E+01 The estimated loss of base 2 significant digits is 2.90 The root mean square relative error was 0.2133E-15 = 2 ** -52.06 The estimated loss of base 2 significant digits is 0.94 1Test of I1(X) vs Taylor series 2000 Random arguments were tested from the interval ( 7.50,15.00) I1(X) was larger 845 times, agreed 346 times, and was smaller 809 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1264E-14 = 2 ** -49.49 occurred for X = 0.138079E+02 The estimated loss of base 2 significant digits is 3.51 The root mean square relative error was 0.3839E-15 = 2 ** -51.21 The estimated loss of base 2 significant digits is 1.79 1Test of I1(X) vs Taylor series 2000 Random arguments were tested from the interval (15.00,30.00) I1(X) was larger 604 times, agreed 747 times, and was smaller 649 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6935E-15 = 2 ** -50.36 occurred for X = 0.150237E+02 The estimated loss of base 2 significant digits is 2.64 The root mean square relative error was 0.1630E-15 = 2 ** -52.45 The estimated loss of base 2 significant digits is 0.55 Special Tests: Test with extreme arguments I1(XMIN) = 0.11125369292536007-307 I1(0) = 0.00000000000000000E+00 I1(-0.35161287759900950E+00 ) = -0.17853737479898507E+00 I1( 0.35161287759900950E+00 ) = 0.17853737479898507E+00 E**-X * I1(XMAX) = 0.29754474593158999-154 Tests near the largest argument for unscaled functions I1( 0.69235162141875753E+03 ) = 0.73282458365806542+299 I1( 0.73629972238772166E+03 ) = 0.17900000000000000+309 This concludes the tests. Test of J0(X) vs Taylor expansion 2000 random arguments were tested from the interval ( 0.0, 4.0) ABS(J0(X)) was larger 483 times agreed 1044 times, and was smaller 473 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.8058E-15 = 2 ** -50.14 occurred for X = 0.244667E+01 The estimated loss of base 2 significant digits is 2.86 The root mean square relative error was 0.1474E-15 = 2 ** -52.59 The estimated loss of base 2 significant digits is 0.41 Test of J0(X) vs Taylor expansion 2000 random arguments were tested from the interval ( 4.0, 8.0) ABS(J0(X)) was larger 636 times agreed 701 times, and was smaller 663 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.6823E-15 = 2 ** -50.38 occurred for X = 0.555757E+01 The estimated loss of base 2 significant digits is 2.62 The root mean square relative error was 0.1865E-15 = 2 ** -52.25 The estimated loss of base 2 significant digits is 0.75 Test of J0(X) vs Taylor expansion 2000 random arguments were tested from the interval ( 8.0, 20.0) ABS(J0(X)) was larger 680 times agreed 635 times, and was smaller 685 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.6844E-15 = 2 ** -50.38 occurred for X = 0.148819E+02 The estimated loss of base 2 significant digits is 2.62 The root mean square relative error was 0.1896E-15 = 2 ** -52.23 The estimated loss of base 2 significant digits is 0.77 Special Tests: Accuracy near zeros X BESJ0(X) Loss of base 2 digits 0.2406250000E+01 -0.739276482217003E-03 2.72 0.5519531250E+01 -0.186086517975737E-03 6.12 Test with extreme arguments J0 will be called with the argument 0.1797693135+309 This may stop execution. J0 returned the value -0.41869868495853734-154 This concludes the tests. 1Test of J1(X) VS Maclaurin expansion 2000 random arguments were tested from the interval ( 0.0, 1.0) ABS(J1(X)) was larger 204 times agreed 1586 times, and was smaller 210 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.2193E-15 = 2 ** -52.02 occurred for X = 0.524010E+00 The estimated loss of base 2 significant digits is 0.98 The root mean square relative error was 0.7052E-16 = 2 ** -53.65 The estimated loss of base 2 significant digits is 0.00 1Test of J1(X) VS local Taylor expansion 2000 random arguments were tested from the interval ( 1.0, 4.0) ABS(J1(X)) was larger 600 times agreed 802 times, and was smaller 598 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1474E-14 = 2 ** -49.27 occurred for X = 0.378523E+01 The estimated loss of base 2 significant digits is 3.73 The root mean square relative error was 0.2072E-15 = 2 ** -52.10 The estimated loss of base 2 significant digits is 0.90 1Test of J1(X) VS local Taylor expansion 2000 random arguments were tested from the interval ( 4.0, 8.0) ABS(J1(X)) was larger 685 times agreed 635 times, and was smaller 680 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1076E-14 = 2 ** -49.72 occurred for X = 0.688752E+01 The estimated loss of base 2 significant digits is 3.28 The root mean square relative error was 0.2086E-15 = 2 ** -52.09 The estimated loss of base 2 significant digits is 0.91 1Test of J1(X) VS local Taylor expansion 2000 random arguments were tested from the interval ( 8.0, 20.0) ABS(J1(X)) was larger 652 times agreed 601 times, and was smaller 747 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1033E-14 = 2 ** -49.78 occurred for X = 0.102072E+02 The estimated loss of base 2 significant digits is 3.22 The root mean square relative error was 0.2093E-15 = 2 ** -52.09 The estimated loss of base 2 significant digits is 0.91 Special Tests: Accuracy near zeros X BESJ1(X) Loss of base 2 digits 0.3832031250E+01 -0.131003930013275E-03 8.37 0.7015625000E+01 0.115034607023044E-04 11.02 Test with extreme arguments J1 will be called with the argument 0.1797693135+309 This may stop execution. J1 returned the value 0.42287458488299958-154 This concludes the tests. Test of K0(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 0.0, 1.0) ABS(K0(X)) was larger 514 times, agreed 1082 times, and was smaller 404 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.6105E-15 = 2 ** -50.54 occurred for X = 0.946643E+00 The estimated loss of base 2 significant digits is 2.46 The root mean square relative error was 0.1221E-15 = 2 ** -52.86 The estimated loss of base 2 significant digits is 0.14 Test of K0(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 1.0, 8.0) ABS(K0(X)) was larger 782 times, agreed 545 times, and was smaller 673 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.7860E-15 = 2 ** -50.18 occurred for X = 0.112501E+01 The estimated loss of base 2 significant digits is 2.82 The root mean square relative error was 0.2424E-15 = 2 ** -51.87 The estimated loss of base 2 significant digits is 1.13 Test of K0(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 8.0, 20.0) ABS(K0(X)) was larger 658 times, agreed 564 times, and was smaller 778 times. There are 53 base 2 significant digits in a floating-point number. The maximum absolute error of 0.6524E-15 = 2 ** -50.45 occurred for X = 0.815222E+01 The estimated loss of base 2 significant digits is 2.55 The root mean square absolute error was 0.2149E-15 = 2 ** -52.05 The estimated loss of base 2 significant digits is 0.95 Special Tests: Test with extreme arguments K0(XMIN) = 0.70851235004792250E+03 K0(0) = 0.17900000000000000+309 K0(-0.76518805666868239E+00 ) = 0.17900000000000000+309 E**X * K0(XMAX) = 0.93476438793292451-154 K0( 0.66125877272454943E+03 ) = 0.32118560786711748-288 K0( 0.79351052726945932E+03 ) = 0.00000000000000000E+00 1Test of K1(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 0.0, 1.0) ABS(K1(X)) was larger 657 times, agreed 690 times, and was smaller 653 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.6807E-15 = 2 ** -50.38 occurred for X = 0.953168E+00 The estimated loss of base 2 significant digits is 2.62 The root mean square relative error was 0.1848E-15 = 2 ** -52.26 The estimated loss of base 2 significant digits is 0.74 1Test of K1(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 1.0, 8.0) ABS(K1(X)) was larger 701 times, agreed 525 times, and was smaller 774 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1075E-14 = 2 ** -49.72 occurred for X = 0.500247E+01 The estimated loss of base 2 significant digits is 3.28 The root mean square relative error was 0.2499E-15 = 2 ** -51.83 The estimated loss of base 2 significant digits is 1.17 1Test of K1(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 8.0, 20.0) ABS(K1(X)) was larger 761 times, agreed 599 times, and was smaller 640 times. There are 53 base 2 significant digits in a floating-point number. The maximum absolute error of 0.7137E-15 = 2 ** -50.32 occurred for X = 0.106420E+02 The estimated loss of base 2 significant digits is 2.68 The root mean square absolute error was 0.2103E-15 = 2 ** -52.08 The estimated loss of base 2 significant digits is 0.92 Special Tests: Test with extreme arguments K1(XLEAST) = 0.44843049327354256+308 K1(XMIN) = 0.17900000000000000+309 K1(0) = 0.17900000000000000+309 K1(-0.94144617986413459E+00 ) = 0.17900000000000000+309 E**X * K1(XMAX) = 0.93476438793292451-154 K1( 0.66125943635324325E+03 ) = 0.32121497573487907-288 K1( 0.79351132362389194E+03 ) = 0.00000000000000000E+00 1 Test of PSI(X) vs (PSI(X/2)+PSI(X/2+1/2))/2 + ln(2) 2000 random arguments were tested from the interval ( 0.0, 1.0) ABS(PSI(X)) was larger 580 times agreed 671 times, and was smaller 749 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.8993E-15 = 2 ** -49.98 occurred for X = 0.845756E+00 The estimated loss of base 2 significant digits is 3.02 The root mean square relative error was 0.2207E-15 = 2 ** -52.01 The estimated loss of base 2 significant digits is 0.99 Test of PSI(X) vs (PSI(X/2)+PSI(X/2+1/2))/2 + ln(2) 2000 random arguments were tested from the interval ( 2.0, 8.0) ABS(PSI(X)) was larger 474 times agreed 947 times, and was smaller 579 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.7343E-15 = 2 ** -50.27 occurred for X = 0.261050E+01 The estimated loss of base 2 significant digits is 2.73 The root mean square relative error was 0.1429E-15 = 2 ** -52.64 The estimated loss of base 2 significant digits is 0.36 1 Test of PSI(X) vs (PSI(X/2)+PSI(X/2+1/2))/2 + ln(2) 2000 random arguments were tested from the interval ( 8.0, 20.0) ABS(PSI(X)) was larger 429 times agreed 1374 times, and was smaller 197 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.3252E-15 = 2 ** -51.45 occurred for X = 0.158456E+02 The estimated loss of base 2 significant digits is 1.55 The root mean square relative error was 0.9999E-16 = 2 ** -53.15 The estimated loss of base 2 significant digits is 0.00 Test of PSI(X) vs (PSI(X/2)+PSI(X/2+1/2))/2 + ln(2) 500 random arguments were tested from the interval (-17.6,-16.9) ABS(PSI(X)) was larger 164 times agreed 204 times, and was smaller 132 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.6413E-15 = 2 ** -50.47 occurred for X =-0.176131E+02 The estimated loss of base 2 significant digits is 2.53 The root mean square relative error was 0.1763E-15 = 2 ** -52.33 The estimated loss of base 2 significant digits is 0.67 Special Tests: Accuracy near positive zero PSI( 0.1460938E+01) = -0.67240239024288055E-03 Loss of base 2 digits = 0.54 Test with extreme arguments PSI will be called with the argument 0.2225073859-307 This should not stop execution. PSI returned the value -0.17000000000000000E+39 PSI will be called with the argument 0.1797693135+309 This should not stop execution. PSI returned the value 0.70978271289338397E+03 Test of error returns PSI will be called with the argument 0.0000000000E+00 This may stop execution. PSI returned the value 0.17000000000000000E+39 PSI will be called with the argument -0.1351079888E+17 This may stop execution. PSI returned the value 0.17000000000000000E+39 This concludes the tests. 1Test of I(X,ALPHA) vs Multiplication Theorem 2000 Random arguments were tested from the interval ( 0.00, 2.00) I(X,ALPHA) was larger 765 times, agreed 487 times, and was smaller 748 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.2118E-14 = 2 ** -48.75 occurred for X = 0.121085E+01 and NU = 0.100442E+00 The estimated loss of base 2 significant digits is 4.25 The root mean square relative error was 0.4792E-15 = 2 ** -50.89 The estimated loss of base 2 significant digits is 2.11 1Test of I(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval ( 2.00, 4.00) I(X,ALPHA) was larger 819 times, agreed 462 times, and was smaller 719 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1928E-14 = 2 ** -48.88 occurred for X = 0.287600E+01 and NU = 0.514761E+00 The estimated loss of base 2 significant digits is 4.12 The root mean square relative error was 0.5505E-15 = 2 ** -50.69 The estimated loss of base 2 significant digits is 2.31 1Test of I(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval ( 4.00,10.00) I(X,ALPHA) was larger 839 times, agreed 420 times, and was smaller 741 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.2795E-14 = 2 ** -48.35 occurred for X = 0.933065E+01 and NU = 0.595020E+00 The estimated loss of base 2 significant digits is 4.65 The root mean square relative error was 0.4695E-15 = 2 ** -50.92 The estimated loss of base 2 significant digits is 2.08 1Test of I(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval (10.00,20.00) I(X,ALPHA) was larger 770 times, agreed 434 times, and was smaller 796 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.3164E-14 = 2 ** -48.17 occurred for X = 0.100237E+02 and NU = 0.184445E+00 The estimated loss of base 2 significant digits is 4.83 The root mean square relative error was 0.4465E-15 = 2 ** -50.99 The estimated loss of base 2 significant digits is 2.01 1Check of Error Returns The following summarizes calls with indicated parameters NCALC different from MB indicates some form of error See documentation for RIBESL for details ARG ALPHA MB IZ RES NCALC RIBESL - Fatal error! 1 < ALPHA. 0.1000000E+01 0.1500000E+01 5 2 0.0000000E+00 -1 RIBESL - Fatal error! NB <= 0. 0.1000000E+01 0.5000000E+00 -5 2 0.0000000E+00 -1 0.1000000E+01 0.5000000E+00 5 5 0.0000000E+00 -1 0.0000000E+00 0.3571937E+00 2 1 0.0000000E+00 2 0.0000000E+00 0.0000000E+00 2 1 0.1000000E+01 2 0.0000000E+00 0.1000000E+01 2 1 0.0000000E+00 2 RIBESL - Fatal error! X < 0.0. RIBESL will be called with the argument-0.100000E+01 This should trigger an error message. NCALC returned the value -1 and RIBESL returned the value 0.000000E+00 Tests near the largest argument for scaled functions This RIBESL test will be skipped. It causes a floating exception. RIBESL will be called with the argument-0.100000E+01 NCALC returned the value -1 and RIBESL returned the value 0.000000E+00 RIBESL will be called with the argument 0.100012E+05 This should trigger an error message. NCALC returned the value -1 and RIBESL returned the value 0.000000E+00 Tests near the largest argument for unscaled functions This RIBESL test will be skipped. It causes a floating exception. RIBESL will be called with the argument 0.100012E+05 NCALC returned the value -1 and RIBESL returned the value 0.000000E+00 RIBESL will be called with the argument 0.432985E+08 This should trigger an error message. NCALC returned the value -1 and RIBESL returned the value 0.000000E+00 This concludes the tests. Test of J(X,ALPHA) vs Multiplication Theorem 2000 Random arguments were tested from the interval ( 0.00, 2.00) J(X,ALPHA) was larger 664 times, agreed 666 times, and was smaller 670 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8744E-15 = 2 ** -50.02 occurred for X = 0.184316E+01 and NU = 0.919337E-01 with J(X,ALPHA) = 0.380888E+00 The estimated loss of base 2 significant digits is 2.98 The root mean square relative error was 0.2028E-15 = 2 ** -52.13 The estimated loss of base 2 significant digits is 0.87 Test of J(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval ( 2.00,10.00) J(X,ALPHA) was larger 856 times, agreed 293 times, and was smaller 851 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6416E-13 = 2 ** -43.83 occurred for X = 0.702432E+01 and NU = 0.903654E+00 with J(X,ALPHA) = 0.442339E-01 The estimated loss of base 2 significant digits is 9.17 The root mean square relative error was 0.1893E-14 = 2 ** -48.91 The estimated loss of base 2 significant digits is 4.09 Test of J(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval (10.00,20.00) J(X,ALPHA) was larger 910 times, agreed 171 times, and was smaller 919 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1340E-13 = 2 ** -46.09 occurred for X = 0.122851E+02 and NU = 0.419382E+00 with J(X,ALPHA) = -0.357362E-01 The estimated loss of base 2 significant digits is 6.91 The root mean square relative error was 0.1389E-14 = 2 ** -49.35 The estimated loss of base 2 significant digits is 3.65 Test of J(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval (30.00,40.00) J(X,ALPHA) was larger 661 times, agreed 674 times, and was smaller 665 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1568E-14 = 2 ** -49.18 occurred for X = 0.345748E+02 and NU = 0.253296E+00 with J(X,ALPHA) = -0.531053E-01 The estimated loss of base 2 significant digits is 3.82 The root mean square relative error was 0.1972E-15 = 2 ** -52.17 The estimated loss of base 2 significant digits is 0.83 1Check of Error Returns The following summarizes calls with indicated parameters NCALC different from MB indicates some form of error See documentation for RJBESL for details ARG ALPHA MB B(1) NCALC 0.1000000E+01 0.1500000E+01 5 0.0000000E+00 -1 0.0000000E+00 0.1000000E+01 2 0.0000000E+00 -1 -0.1000000E+01 0.5000000E+00 5 0.0000000E+00 -1 Tests near the largest acceptable argument for RJBESL RJBESL will be called with the argument 0.999878E+04 NCALC returned the value 2 and RJBESL returned U(1) = 0.630030E-02 RJBESL will be called with the argument 0.100012E+05 This should trigger an error message. NCALC returned the value -1 and RJBESL returned U(1) = 0.000000E+00 This concludes the tests. 1Test of K(X,ALPHA) vs Multiplication Theorem 2000 Random arguments were tested from the interval ( 0.00, 1.00) K(X,ALPHA) was larger 679 times, agreed 663 times, and was smaller 658 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.3334E-14 = 2 ** -48.09 occurred for X = 0.947922E+00, NU = 0.503249E+00 and IZE = 1 The estimated loss of base 2 significant digits is 4.91 The root mean square relative error was 0.2310E-15 = 2 ** -51.94 The estimated loss of base 2 significant digits is 1.06 1Test of K(X,ALPHA) vs Multiplication Theorem 2000 Random arguments were tested from the interval ( 1.00,10.00) K(X,ALPHA) was larger 685 times, agreed 614 times, and was smaller 701 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6493E-15 = 2 ** -50.45 occurred for X = 0.749606E+01, NU = 0.121625E+00 and IZE = 1 The estimated loss of base 2 significant digits is 2.55 The root mean square relative error was 0.1948E-15 = 2 ** -52.19 The estimated loss of base 2 significant digits is 0.81 1Test of K(X,ALPHA) vs Multiplication Theorem 2000 Random arguments were tested from the interval (10.00,20.00) K(X,ALPHA) was larger 663 times, agreed 629 times, and was smaller 708 times. There are 53 base 2 significant digits in a floating-point number The maximum absolute error of 0.7673E-15 = 2 ** -50.21 occurred for X = 0.191680E+02, NU = 0.104347E+00 and IZE = 1 The estimated loss of base 2 significant digits is 2.79 The root mean square absolute error was 0.2050E-15 = 2 ** -52.12 The estimated loss of base 2 significant digits is 0.88 1Check of Error Returns The following summarizes calls with indicated parameters NCALC different from MB indicates some form of error See documentation for RKBESL for details ARG ALPHA MB IZ RES NCALC -0.1000000E+01 0.5000000E+00 5 2 0.0000000E+00 -2 0.1000000E+01 0.1500000E+01 5 2 0.0000000E+00 -2 0.1000000E+01 0.5000000E+00 -5 2 0.0000000E+00 -7 0.1000000E+01 0.5000000E+00 5 5 0.0000000E+00 -2 0.2225074-307 0.0000000E+00 2 2 0.7085124E+03 2 0.1000000E-09 0.0000000E+00 20 2 0.2314178E+02 20 0.1000000E-09 0.0000000E+00 20 2 0.2314178E+02 20 0.6612588E+03 0.0000000E+00 2 1 0.3211860-288 2 0.7053427E+03 0.0000000E+00 2 1 0.0000000E+00 -2 0.4503600E+17 0.0000000E+00 2 2 0.5905818E-08 2 0.1797693+309 0.0000000E+00 2 2 0.9347644-154 2 1Test of Y(X,ALPHA) vs Multiplication Theorem 1980 Random arguments were tested from the interval ( 0.00, 2.00) Y(X,ALPHA) was larger 738 times, agreed 436 times, and was smaller 806 times. NOTE: first 20 arguments in test interval skipped because multiplication theorem did not converge There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1731E-14 = 2 ** -49.04 occurred for X = 0.160250E+01 and NU = 0.329926E+00 with Y(X,ALPHA) = 0.160340E+00 The estimated loss of base 2 significant digits is 3.96 The root mean square relative error was 0.3607E-15 = 2 ** -51.30 The estimated loss of base 2 significant digits is 1.70 1Test of Y(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval ( 2.00,10.00) Y(X,ALPHA) was larger 734 times, agreed 491 times, and was smaller 775 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4880E-14 = 2 ** -47.54 occurred for X = 0.818633E+01 and NU = 0.601736E+00 with Y(X,ALPHA) = 0.497635E-01 The estimated loss of base 2 significant digits is 5.46 The root mean square relative error was 0.3242E-15 = 2 ** -51.45 The estimated loss of base 2 significant digits is 1.55 1Test of Y(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval (10.00,20.00) Y(X,ALPHA) was larger 688 times, agreed 563 times, and was smaller 749 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1875E-14 = 2 ** -48.92 occurred for X = 0.177067E+02 and NU = 0.862278E+00 with Y(X,ALPHA) = 0.240567E-01 The estimated loss of base 2 significant digits is 4.08 The root mean square relative error was 0.2415E-15 = 2 ** -51.88 The estimated loss of base 2 significant digits is 1.12 1Test of Y(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval (30.00,40.00) Y(X,ALPHA) was larger 625 times, agreed 748 times, and was smaller 627 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1397E-14 = 2 ** -49.35 occurred for X = 0.314358E+02 and NU = 0.962444E+00 with Y(X,ALPHA) = -0.109248E+00 The estimated loss of base 2 significant digits is 3.65 The root mean square relative error was 0.1755E-15 = 2 ** -52.34 The estimated loss of base 2 significant digits is 0.66 1Check of Error Returns The following summarizes calls with indicated parameters NCALC different from MB indicates some form of error See documentation for RYBESL for details ARG ALPHA MB B(1) NCALC 0.1000000E+01 0.1500000E+01 5 0.0000000E+00 -1 0.1000000E+01 0.5000000E+00 -5 0.0000000E+00 -6 0.2225074-307 0.0000000E+00 2 0.0000000E+00 -1 0.6675222-307 0.0000000E+00 2 -0.4503536E+03 2 0.6675222-307 0.1000000E+01 2 -0.9537058+307 1 Tests near the largest acceptable argument for RYBESL RYBESL will be called with the arguments 0.335544E+08 0.500000E+00 NCALC returned the value 2 and RYBESL returned U(1) = 0.296749E-04 RYBESL will be called with the arguments 0.536871E+09 0.500000E+00 This should trigger an error message. NCALC returned the value -1 and RYBESL returned U(1) = 0.000000E+00 This concludes the tests. 1Test of Y0(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 0.0, 3.0) ABS(Y0(X)) was larger 670 times agreed 665 times, and was smaller 665 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1338E-14 = 2 ** -49.41 occurred for X = 0.847598E+00 The estimated loss of base 2 significant digits is 3.59 The root mean square relative error was 0.1883E-15 = 2 ** -52.24 The estimated loss of base 2 significant digits is 0.76 1Test of Y0(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 3.0, 5.5) ABS(Y0(X)) was larger 721 times agreed 584 times, and was smaller 695 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.8029E-15 = 2 ** -50.15 occurred for X = 0.380968E+01 The estimated loss of base 2 significant digits is 2.85 The root mean square relative error was 0.1932E-15 = 2 ** -52.20 The estimated loss of base 2 significant digits is 0.80 1Test of Y0(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 5.5, 8.0) ABS(Y0(X)) was larger 738 times agreed 551 times, and was smaller 711 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1013E-14 = 2 ** -49.81 occurred for X = 0.672220E+01 The estimated loss of base 2 significant digits is 3.19 The root mean square relative error was 0.2014E-15 = 2 ** -52.14 The estimated loss of base 2 significant digits is 0.86 1Test of Y0(X) VS Multiplication Theorem 500 random arguments were tested from the interval ( 8.0, 20.0) ABS(Y0(X)) was larger 188 times agreed 120 times, and was smaller 192 times. There are 53 base 2 significant digits in a floating-point number. The maximum absolute error of 0.7409E-15 = 2 ** -50.26 occurred for X = 0.162406E+02 The estimated loss of base 2 significant digits is 2.74 The root mean square absolute error was 0.1855E-15 = 2 ** -52.26 The estimated loss of base 2 significant digits is 0.74 Special Tests: Accuracy near zeros X BESY0(X) Loss of base 2 digits 0.8906250000E+00 -0.260031427229336E-02 5.39 0.3957031250E+01 0.260534549114568E-03 1.91 0.7085937500E+01 -0.340794487147973E-04 8.81 Test with extreme arguments Y0 will be called with the argument 0.2225073859-307 This should not stop execution. Y0 returned the value -0.45105297100712858E+03 Y0 will be called with the argument 0.0000000000E+00 This may stop execution. Y0 returned the value -Infinity Y0 will be called with the argument 0.1797693135+309 This may stop execution. Y0 returned the value 0.42287458488299958-154 This concludes the tests. 1Test of Y1(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 0.0, 4.0) ABS(Y1(X)) was larger 682 times agreed 648 times, and was smaller 670 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1283E-14 = 2 ** -49.47 occurred for X = 0.212916E+01 The estimated loss of base 2 significant digits is 3.53 The root mean square relative error was 0.2077E-15 = 2 ** -52.10 The estimated loss of base 2 significant digits is 0.90 1Test of Y1(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 4.0, 8.0) ABS(Y1(X)) was larger 731 times agreed 543 times, and was smaller 726 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.8024E-15 = 2 ** -50.15 occurred for X = 0.517897E+01 The estimated loss of base 2 significant digits is 2.85 The root mean square relative error was 0.2065E-15 = 2 ** -52.10 The estimated loss of base 2 significant digits is 0.90 1Test of Y1(X) VS Multiplication Theorem 500 random arguments were tested from the interval ( 8.0, 20.0) ABS(Y1(X)) was larger 188 times agreed 125 times, and was smaller 187 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.6235E-15 = 2 ** -50.51 occurred for X = 0.112615E+02 The estimated loss of base 2 significant digits is 2.49 The root mean square relative error was 0.1821E-15 = 2 ** -52.29 The estimated loss of base 2 significant digits is 0.71 Special Tests: Accuracy near zeros X BESY1(X) Loss of base 2 digits 0.2195312500E+01 -0.952823930977230E-03 4.68 0.5429687500E+01 -0.219818300806240E-05 13.38 Test with extreme arguments Y1 will be called with the argument 0.2225073859-307 This should not stop execution. Y1 returned the value -0.28611174857570283+308 Y1 will be called with the argument -0.1000000000E+01 This may stop execution. Y1 returned the value NaN Y1 will be called with the argument 0.1797693135+309 This may stop execution. Y1 returned the value 0.41869868495853734-154 This concludes the tests. specfun_test1(): Normal end of execution. 19 December 2023 8:37:28.367 AM