04 April 2023 9:38:52.514 AM toms715_test(): FORTRAN90 version Test toms715(). 1Test of anorm(x) vs double series expansion 2000 Random arguments were tested from the interval ( -0.663, 0.663) ANORM(X) was larger 253 times, agreed 1595 times, and was smaller 152 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4237E-15 = 2 ** -51.07 occurred for X =-0.637105E+00 The estimated loss of base 2 significant digits is 1.93 The root mean square relative error was 0.8569E-16 = 2 ** -53.37 The estimated loss of base 2 significant digits is 0.00 Test of anorm(x) vs Taylor series about x-1/2 2000 Random arguments were tested from the interval ( -5.657, -0.663) ANORM(X) was larger 680 times, agreed 476 times, and was smaller 844 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1178E-14 = 2 ** -49.59 occurred for X =-0.506677E+01 The estimated loss of base 2 significant digits is 3.41 The root mean square relative error was 0.2661E-15 = 2 ** -51.74 The estimated loss of base 2 significant digits is 1.26 Test of anorm(x) vs Taylor series about x-1/2 2000 Random arguments were tested from the interval (-37.000, -5.657) ANORM(X) was larger 652 times, agreed 683 times, and was smaller 665 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6139E-15 = 2 ** -50.53 occurred for X =-0.318733E+02 The estimated loss of base 2 significant digits is 2.47 The root mean square relative error was 0.1769E-15 = 2 ** -52.33 The estimated loss of base 2 significant digits is 0.67 1Special Tests Check of identity anorm(X) + anorm(-X) = 1.0 X ANORM(-x) ANORM(x)+ANORM(-x)-1 0.503099E+01 0.243975E-06 0.000000E+00 0.887334E+01 0.354915E-18 0.000000E+00 0.916662E+01 0.244045E-19 0.000000E+00 0.582615E+01 0.283604E-08 0.000000E+00 0.826795E+01 0.681417E-16 0.000000E+00 0.349256E+01 0.239203E-03 0.000000E+00 0.657015E+01 0.251320E-10 0.000000E+00 0.126816E+01 0.102370E+00 0.000000E+00 0.852033E+01 0.795493E-17 0.000000E+00 0.504026E+01 0.232453E-06 0.000000E+00 Test of special arguments ANORM ( 0.179769+309) = 0.100000E+01 ANORM ( 0.000000E+00) = 0.500000E+00 ANORM (-0.179769+309) = 0.000000E+00 Test of Error Returns ANORM will be called with the argument -0.281395E+02 The result should not underflow ANORM returned the value 0.160919-173 ANORM will be called with the argument -0.375194E+02 The result may underflow ANORM returned the value 0.000000E+00 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 532 times, agreed 963 times, and was smaller 505 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4422E-15 = 2 ** -51.01 occurred for X = 0.126888E+00 The estimated loss of base 2 significant digits is 1.99 The root mean square relative error was 0.1339E-15 = 2 ** -52.73 The estimated loss of base 2 significant digits is 0.27 1Test of Dawson's Integral vs Taylor expansion 2000 Random arguments were tested from the interval ( 1.00, 2.50) F(X) was larger 663 times, agreed 794 times, and was smaller 543 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6119E-15 = 2 ** -50.54 occurred for X = 0.215456E+01 The estimated loss of base 2 significant digits is 2.46 The root mean square relative error was 0.1632E-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 513 times, agreed 1090 times, and was smaller 397 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.3846E-15 = 2 ** -51.21 occurred for X = 0.361607E+01 The estimated loss of base 2 significant digits is 1.79 The root mean square relative error was 0.1116E-15 = 2 ** -52.99 The estimated loss of base 2 significant digits is 0.01 1Test of Dawson's Integral vs Taylor expansion 2000 Random arguments were tested from the interval ( 5.00,10.00) F(X) was larger 429 times, agreed 1139 times, and was smaller 432 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.3784E-15 = 2 ** -51.23 occurred for X = 0.689120E+01 The estimated loss of base 2 significant digits is 1.77 The root mean square relative error was 0.1053E-15 = 2 ** -53.08 The estimated loss of base 2 significant digits is 0.00 1Special Tests Estimated loss of base 2 significant digits in X F(x)+F(-x) 0.057 0.00 3.145 0.00 1.086 0.00 3.761 0.00 2.133 0.00 2.656 0.00 0.009 0.00 1.078 0.00 2.692 0.00 0.447 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 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 573 times, agreed 909 times, and was smaller 518 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6589E-15 = 2 ** -50.43 occurred for X = 0.706704E+00 The estimated loss of base 2 significant digits is 2.57 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 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 738 times, agreed 534 times, and was smaller 728 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.7597E-15 = 2 ** -50.23 occurred for X = 0.162210E+01 The estimated loss of base 2 significant digits is 2.77 The root mean square relative error was 0.1786E-15 = 2 ** -52.31 The estimated loss of base 2 significant digits is 0.69 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 701 times, agreed 861 times, and was smaller 438 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5053E-15 = 2 ** -50.81 occurred for X = 0.723910E+01 The estimated loss of base 2 significant digits is 2.19 The root mean square relative error was 0.1524E-15 = 2 ** -52.54 The estimated loss of base 2 significant digits is 0.46 1Special 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 1Test 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 Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( 0.188, 0.310) EI(X) was larger 422 times, agreed 639 times, and was smaller 939 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5505E-15 = 2 ** -50.69 occurred for X = 0.300029E+00 The estimated loss of base 2 significant digits is 2.31 The root mean square relative error was 0.1817E-15 = 2 ** -52.29 The estimated loss of base 2 significant digits is 0.71 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( 0.435, 6.000) EI(X) was larger 619 times, agreed 682 times, and was smaller 699 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1593E-14 = 2 ** -49.16 occurred for X = 0.591180E+01 The estimated loss of base 2 significant digits is 3.84 The root mean square relative error was 0.2482E-15 = 2 ** -51.84 The estimated loss of base 2 significant digits is 1.16 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( 6.000, 12.000) EI(X) was larger 613 times, agreed 813 times, and was smaller 574 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1439E-14 = 2 ** -49.30 occurred for X = 0.604245E+01 The estimated loss of base 2 significant digits is 3.70 The root mean square relative error was 0.1584E-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 ( 12.000, 24.000) EI(X) was larger 567 times, agreed 848 times, and was smaller 585 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4427E-15 = 2 ** -51.00 occurred for X = 0.136210E+02 The estimated loss of base 2 significant digits is 2.00 The root mean square relative error was 0.1479E-15 = 2 ** -52.59 The estimated loss of base 2 significant digits is 0.41 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( 24.000, 48.000) EI(X) was larger 561 times, agreed 895 times, and was smaller 544 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4467E-15 = 2 ** -50.99 occurred for X = 0.286719E+02 The estimated loss of base 2 significant digits is 2.01 The root mean square relative error was 0.1388E-15 = 2 ** -52.68 The estimated loss of base 2 significant digits is 0.32 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( -0.250, -1.000) EI(X) was larger 601 times, agreed 895 times, and was smaller 504 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8323E-15 = 2 ** -50.09 occurred for X =-0.963175E+00 The estimated loss of base 2 significant digits is 2.91 The root mean square relative error was 0.1556E-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 ( -1.000, -4.000) EI(X) was larger 712 times, agreed 578 times, and was smaller 710 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8403E-15 = 2 ** -50.08 occurred for X =-0.228801E+01 The estimated loss of base 2 significant digits is 2.92 The root mean square relative error was 0.2266E-15 = 2 ** -51.97 The estimated loss of base 2 significant digits is 1.03 1Test of Ei(x) vs series expansion 2000 Random arguments were tested from the interval ( -4.000,-10.000) EI(X) was larger 559 times, agreed 891 times, and was smaller 550 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5990E-15 = 2 ** -50.57 occurred for X =-0.624667E+01 The estimated loss of base 2 significant digits is 2.43 The root mean square relative error was 0.1431E-15 = 2 ** -52.63 The estimated loss of base 2 significant digits is 0.37 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 787 times, and was smaller 1080 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.4292E-15 = 2 ** -51.05 occurred for X = 0.233398E+00 The estimated loss of base 2 significant digits is 1.95 The root mean square relative error was 0.1475E-15 = 2 ** -52.59 The estimated loss of base 2 significant digits is 0.41 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 849 times, agreed 500 times, and was smaller 651 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8449E-15 = 2 ** -50.07 occurred for X = 0.163802E+01 The estimated loss of base 2 significant digits is 2.93 The root mean square relative error was 0.2556E-15 = 2 ** -51.80 The estimated loss of base 2 significant digits is 1.20 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 817 times, agreed 618 times, and was smaller 565 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6622E-15 = 2 ** -50.42 occurred for X = 0.141916E+01 The estimated loss of base 2 significant digits is 2.58 The root mean square relative error was 0.2179E-15 = 2 ** -52.03 The estimated loss of base 2 significant digits is 0.97 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 664 times, agreed 653 times, and was smaller 683 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8781E-15 = 2 ** -50.02 occurred for X = 0.285496E+01 The estimated loss of base 2 significant digits is 2.98 The root mean square relative error was 0.1980E-15 = 2 ** -52.17 The estimated loss of base 2 significant digits is 0.83 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 474 times, agreed 1014 times, and was smaller 512 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.9356E-15 = 2 ** -49.93 occurred for X = 0.301848E+01 The estimated loss of base 2 significant digits is 3.07 The root mean square relative error was 0.1389E-15 = 2 ** -52.68 The estimated loss of base 2 significant digits is 0.32 1Special 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 570 times, agreed 826 times, and was smaller 604 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5998E-15 = 2 ** -50.57 occurred for X = 0.852084E+00 The estimated loss of base 2 significant digits is 2.43 The root mean square relative error was 0.1355E-15 = 2 ** -52.71 The estimated loss of base 2 significant digits is 0.29 1Test of GAMMA(X) vs Duplication Formula 2000 Random arguments were tested from the interval ( 2.000, 10.000) GAMMA(X) was larger 618 times, agreed 711 times, and was smaller 671 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6952E-15 = 2 ** -50.35 occurred for X = 0.944038E+01 The estimated loss of base 2 significant digits is 2.65 The root mean square relative error was 0.1800E-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 990 times, agreed 16 times, and was smaller 994 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1901E-12 = 2 ** -42.26 occurred for X = 0.141142E+03 The estimated loss of base 2 significant digits is 10.74 The root mean square relative error was 0.4591E-13 = 2 ** -44.31 The estimated loss of base 2 significant digits is 8.69 1Test of GAMMA(X) vs Duplication Formula 2000 Random arguments were tested from the interval ( -4.750, -4.250) GAMMA(X) was larger 1163 times, agreed 385 times, and was smaller 452 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1362E-14 = 2 ** -49.38 occurred for X =-0.474569E+01 The estimated loss of base 2 significant digits is 3.62 The root mean square relative error was 0.3113E-15 = 2 ** -51.51 The estimated loss of base 2 significant digits is 1.49 1Special 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 1Test 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 494 times, agreed 973 times, and was smaller 533 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5078E-15 = 2 ** -50.81 occurred for X = 0.107724E+01 The estimated loss of base 2 significant digits is 2.19 The root mean square relative error was 0.1433E-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 697 times, agreed 601 times, and was smaller 702 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8889E-15 = 2 ** -50.00 occurred for X = 0.618930E+01 The estimated loss of base 2 significant digits is 3.00 The root mean square relative error was 0.2206E-15 = 2 ** -52.01 The estimated loss of base 2 significant digits is 0.99 1Test of I0(X) vs Taylor series 2000 Random arguments were tested from the interval ( 7.50,15.00) I0(X) was larger 832 times, agreed 303 times, and was smaller 865 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1538E-14 = 2 ** -49.21 occurred for X = 0.127215E+02 The estimated loss of base 2 significant digits is 3.79 The root mean square relative error was 0.4151E-15 = 2 ** -51.10 The estimated loss of base 2 significant digits is 1.90 1Test of I0(X) vs Taylor series 2000 Random arguments were tested from the interval (15.00,30.00) I0(X) was larger 583 times, agreed 814 times, and was smaller 603 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6851E-15 = 2 ** -50.37 occurred for X = 0.150006E+02 The estimated loss of base 2 significant digits is 2.63 The root mean square relative error was 0.1576E-15 = 2 ** -52.49 The estimated loss of base 2 significant digits is 0.51 1Special Tests Test with extreme arguments I0(XMIN) = 0.10000000000000000E+01 I0(0) = 0.10000000000000000E+01 I0(-0.28449822688652987E+00 ) = 0.10203374025948893E+01 I0( 0.28449822688652987E+00 ) = 0.10203374025948893E+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 692 times, agreed 675 times, and was smaller 633 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6379E-15 = 2 ** -50.48 occurred for X = 0.130257E+00 The estimated loss of base 2 significant digits is 2.52 The root mean square relative error was 0.1813E-15 = 2 ** -52.29 The estimated loss of base 2 significant digits is 0.71 1Test of I1(X) vs Taylor series 2000 Random arguments were tested from the interval ( 1.00, 7.50) I1(X) was larger 718 times, agreed 578 times, and was smaller 704 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1016E-14 = 2 ** -49.81 occurred for X = 0.688286E+01 The estimated loss of base 2 significant digits is 3.19 The root mean square relative error was 0.2172E-15 = 2 ** -52.03 The estimated loss of base 2 significant digits is 0.97 1Test of I1(X) vs Taylor series 2000 Random arguments were tested from the interval ( 7.50,15.00) I1(X) was larger 806 times, agreed 348 times, and was smaller 846 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1219E-14 = 2 ** -49.54 occurred for X = 0.125173E+02 The estimated loss of base 2 significant digits is 3.46 The root mean square relative error was 0.3900E-15 = 2 ** -51.19 The estimated loss of base 2 significant digits is 1.81 1Test of I1(X) vs Taylor series 2000 Random arguments were tested from the interval (15.00,30.00) I1(X) was larger 633 times, agreed 759 times, and was smaller 608 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6949E-15 = 2 ** -50.35 occurred for X = 0.150215E+02 The estimated loss of base 2 significant digits is 2.65 The root mean square relative error was 0.1605E-15 = 2 ** -52.47 The estimated loss of base 2 significant digits is 0.53 1Special Tests Test with extreme arguments I1(XMIN) = 0.11125369292536007-307 I1(0) = 0.00000000000000000E+00 I1(-0.74433904881837309E+00 ) = -0.39854607729907382E+00 I1( 0.74433904881837309E+00 ) = 0.39854607729907382E+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. 1Test of J0(X) VS Taylor expansion 2000 random arguments were tested from the interval ( 0.0, 4.0) ABS(J0(X)) was larger 796 times agreed 659 times, and was smaller 545 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.9654E-15 = 2 ** -49.88 occurred for X = 0.386604E+01 The estimated loss of base 2 significant digits is 3.12 The root mean square relative error was 0.2042E-15 = 2 ** -52.12 The estimated loss of base 2 significant digits is 0.88 1Test of J0(X) VS Taylor expansion 2000 random arguments were tested from the interval ( 4.0, 8.0) ABS(J0(X)) was larger 642 times agreed 548 times, and was smaller 810 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1525E-14 = 2 ** -49.22 occurred for X = 0.394293E+01 The estimated loss of base 2 significant digits is 3.78 The root mean square relative error was 0.2553E-15 = 2 ** -51.80 The estimated loss of base 2 significant digits is 1.20 1Test of J0(X) VS Taylor expansion 2000 random arguments were tested from the interval ( 8.0, 20.0) ABS(J0(X)) was larger 655 times agreed 628 times, and was smaller 717 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.8740E-15 = 2 ** -50.02 occurred for X = 0.173463E+02 The estimated loss of base 2 significant digits is 2.98 The root mean square relative error was 0.2119E-15 = 2 ** -52.07 The estimated loss of base 2 significant digits is 0.93 1Special Tests Accuracy near zeros X BESJ0(X) Loss of base 2 digits 0.2406250000E+01 -0.739276482217002E-03 0.40 0.5519531250E+01 -0.186086517975739E-03 1.39 Test with extreme arguments J0 will be called with the argument 0.1797693135+309 This may stop execution. J0 returned the value 0.00000000000000000E+00 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 476 times agreed 793 times, and was smaller 731 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.5210E-15 = 2 ** -50.77 occurred for X = 0.677377E+00 The estimated loss of base 2 significant digits is 2.23 The root mean square relative error was 0.1563E-15 = 2 ** -52.51 The estimated loss of base 2 significant digits is 0.49 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 512 times agreed 675 times, and was smaller 813 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1254E-14 = 2 ** -49.50 occurred for X = 0.388013E+01 The estimated loss of base 2 significant digits is 3.50 The root mean square relative error was 0.2400E-15 = 2 ** -51.89 The estimated loss of base 2 significant digits is 1.11 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 802 times agreed 586 times, and was smaller 612 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.9044E-15 = 2 ** -49.97 occurred for X = 0.582776E+01 The estimated loss of base 2 significant digits is 3.03 The root mean square relative error was 0.2250E-15 = 2 ** -51.98 The estimated loss of base 2 significant digits is 1.02 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 753 times agreed 554 times, and was smaller 693 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.8585E-15 = 2 ** -50.05 occurred for X = 0.128720E+02 The estimated loss of base 2 significant digits is 2.95 The root mean square relative error was 0.2285E-15 = 2 ** -51.96 The estimated loss of base 2 significant digits is 1.04 1Special Tests Accuracy near zeros X BESJ1(X) Loss of base 2 digits 0.3832031250E+01 -0.131003930013280E-03 0.90 0.7015625000E+01 0.115034607023017E-04 0.00 Test with extreme arguments J1 will be called with the argument 0.1797693135+309 This may stop execution. J1 returned the value 0.00000000000000000E+00 This concludes the tests. 1Test of K0(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 0.0, 1.0) ABS(K0(X)) was larger 535 times, agreed 1071 times, and was smaller 394 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.5184E-15 = 2 ** -50.78 occurred for X = 0.987953E+00 The estimated loss of base 2 significant digits is 2.22 The root mean square relative error was 0.1209E-15 = 2 ** -52.88 The estimated loss of base 2 significant digits is 0.12 1Test of K0(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 1.0, 8.0) ABS(K0(X)) was larger 826 times, agreed 514 times, and was smaller 660 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.8382E-15 = 2 ** -50.08 occurred for X = 0.187771E+01 The estimated loss of base 2 significant digits is 2.92 The root mean square relative error was 0.2465E-15 = 2 ** -51.85 The estimated loss of base 2 significant digits is 1.15 1Test of K0(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 8.0, 20.0) ABS(K0(X)) was larger 646 times, agreed 609 times, and was smaller 745 times. There are 53 base 2 significant digits in a floating-point number. The maximum absolute error of 0.7285E-15 = 2 ** -50.29 occurred for X = 0.164197E+02 The estimated loss of base 2 significant digits is 2.71 The root mean square absolute error was 0.2115E-15 = 2 ** -52.07 The estimated loss of base 2 significant digits is 0.93 1Special Tests Test with extreme arguments K0(XMIN) = 0.70851235004792250E+03 K0(0) = 0.17900000000000000+309 K0(-0.61041516186224920E+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 626 times, agreed 729 times, and was smaller 645 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.8679E-15 = 2 ** -50.03 occurred for X = 0.964556E+00 The estimated loss of base 2 significant digits is 2.97 The root mean square relative error was 0.1831E-15 = 2 ** -52.28 The estimated loss of base 2 significant digits is 0.72 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 546 times, and was smaller 753 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.9703E-15 = 2 ** -49.87 occurred for X = 0.198302E+01 The estimated loss of base 2 significant digits is 3.13 The root mean square relative error was 0.2487E-15 = 2 ** -51.84 The estimated loss of base 2 significant digits is 1.16 1Test of K1(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 8.0, 20.0) ABS(K1(X)) was larger 760 times, agreed 592 times, and was smaller 648 times. There are 53 base 2 significant digits in a floating-point number. The maximum absolute error of 0.7424E-15 = 2 ** -50.26 occurred for X = 0.166829E+02 The estimated loss of base 2 significant digits is 2.74 The root mean square absolute error was 0.2160E-15 = 2 ** -52.04 The estimated loss of base 2 significant digits is 0.96 1Special Tests Test with extreme arguments K1(XLEAST) = 0.44843049327354256+308 K1(XMIN) = 0.17900000000000000+309 K1(0) = 0.17900000000000000+309 K1(-0.88999635885180317E+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 577 times agreed 690 times, and was smaller 733 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.7373E-15 = 2 ** -50.27 occurred for X = 0.984891E+00 The estimated loss of base 2 significant digits is 2.73 The root mean square relative error was 0.2174E-15 = 2 ** -52.03 The estimated loss of base 2 significant digits is 0.97 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 492 times agreed 983 times, and was smaller 525 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.7847E-15 = 2 ** -50.18 occurred for X = 0.250865E+01 The estimated loss of base 2 significant digits is 2.82 The root mean square relative error was 0.1427E-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 433 times agreed 1390 times, and was smaller 177 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.3279E-15 = 2 ** -51.44 occurred for X = 0.155047E+02 The estimated loss of base 2 significant digits is 1.56 The root mean square relative error was 0.9829E-16 = 2 ** -53.18 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 158 times agreed 211 times, and was smaller 131 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.5814E-15 = 2 ** -50.61 occurred for X =-0.175603E+02 The estimated loss of base 2 significant digits is 2.39 The root mean square relative error was 0.1732E-15 = 2 ** -52.36 The estimated loss of base 2 significant digits is 0.64 1Special 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 -0.17900000000000000+309 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 0.17900000000000000+309 PSI will be called with the argument -0.1351079888E+17 This may stop execution. PSI returned the value 0.17900000000000000+309 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 768 times, agreed 453 times, and was smaller 779 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.2156E-14 = 2 ** -48.72 occurred for X = 0.121769E+01 and NU = 0.160411E+00 The estimated loss of base 2 significant digits is 4.28 The root mean square relative error was 0.4911E-15 = 2 ** -50.85 The estimated loss of base 2 significant digits is 2.15 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 789 times, agreed 448 times, and was smaller 763 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1936E-14 = 2 ** -48.88 occurred for X = 0.264314E+01 and NU = 0.501470E-01 The estimated loss of base 2 significant digits is 4.12 The root mean square relative error was 0.5642E-15 = 2 ** -50.65 The estimated loss of base 2 significant digits is 2.35 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 764 times, agreed 408 times, and was smaller 828 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.3525E-14 = 2 ** -48.01 occurred for X = 0.995942E+01 and NU = 0.476622E-01 The estimated loss of base 2 significant digits is 4.99 The root mean square relative error was 0.4694E-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 843 times, agreed 383 times, and was smaller 774 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.3203E-14 = 2 ** -48.15 occurred for X = 0.100148E+02 and NU = 0.322212E+00 The estimated loss of base 2 significant digits is 4.85 The root mean square relative error was 0.4381E-15 = 2 ** -51.02 The estimated loss of base 2 significant digits is 1.98 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 0.1000000E+01 0.1500000E+01 5 2 0.0000000E+00 -1 0.1000000E+01 0.5000000E+00 -5 2 0.0000000E+00 -6 0.1000000E+01 0.5000000E+00 5 5 0.0000000E+00 -1 0.0000000E+00 0.1722874E-01 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 -1 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 RIBESL will be called with the argument 0.999878E+04 NCALC returned the value 2 and RIBESL returned the value NaN 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 RIBESL will be called with the argument 0.708913E+03 NCALC returned the value 2 and RIBESL returned the value 0.112931+307 RIBESL will be called with the argument 0.709087E+03 This should trigger an error message. NCALC returned the value -1 and RIBESL returned the value 0.000000E+00 This concludes the tests. 1Test of J(X,ALPHA) vs Multiplication Theorem 2000 Random arguments were tested from the interval ( 0.00, 2.00) J(X,ALPHA) was larger 670 times, agreed 643 times, and was smaller 687 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1046E-14 = 2 ** -49.76 occurred for X = 0.198702E+01 and NU = 0.115905E+00 with J(X,ALPHA) = 0.318499E+00 The estimated loss of base 2 significant digits is 3.24 The root mean square relative error was 0.2050E-15 = 2 ** -52.12 The estimated loss of base 2 significant digits is 0.88 1Test of J(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval ( 2.00,10.00) J(X,ALPHA) was larger 822 times, agreed 316 times, and was smaller 862 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1009E-13 = 2 ** -46.49 occurred for X = 0.702428E+01 and NU = 0.672654E+00 with J(X,ALPHA) = 0.140270E+00 The estimated loss of base 2 significant digits is 6.51 The root mean square relative error was 0.8908E-15 = 2 ** -50.00 The estimated loss of base 2 significant digits is 3.00 1Test of J(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval (10.00,20.00) J(X,ALPHA) was larger 964 times, agreed 158 times, and was smaller 878 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1409E-13 = 2 ** -46.01 occurred for X = 0.181389E+02 and NU = 0.107148E+00 with J(X,ALPHA) = -0.187191E-01 The estimated loss of base 2 significant digits is 6.99 The root mean square relative error was 0.1334E-14 = 2 ** -49.41 The estimated loss of base 2 significant digits is 3.59 1Test of J(X,ALPHA) vs Taylor series 2000 Random arguments were tested from the interval (30.00,40.00) J(X,ALPHA) was larger 608 times, agreed 765 times, and was smaller 627 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.3634E-14 = 2 ** -47.97 occurred for X = 0.345621E+02 and NU = 0.380305E+00 with J(X,ALPHA) = -0.257802E-01 The estimated loss of base 2 significant digits is 5.03 The root mean square relative error was 0.2201E-15 = 2 ** -52.01 The estimated loss of base 2 significant digits is 0.99 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 0.1000000E+01 0.5000000E+00 -5 0.0000000E+00 -6 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 640 times, agreed 694 times, and was smaller 666 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1248E-14 = 2 ** -49.51 occurred for X = 0.922674E+00, NU = 0.570961E+00 and IZE = 1 The estimated loss of base 2 significant digits is 3.49 The root mean square relative error was 0.2111E-15 = 2 ** -52.07 The estimated loss of base 2 significant digits is 0.93 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 686 times, agreed 676 times, and was smaller 638 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.6447E-15 = 2 ** -50.46 occurred for X = 0.370920E+01, NU = 0.595446E+00 and IZE = 1 The estimated loss of base 2 significant digits is 2.54 The root mean square relative error was 0.1949E-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 696 times, agreed 622 times, and was smaller 682 times. There are 53 base 2 significant digits in a floating-point number The maximum absolute error of 0.7945E-15 = 2 ** -50.16 occurred for X = 0.168555E+02, NU = 0.431457E+00 and IZE = 1 The estimated loss of base 2 significant digits is 2.84 The root mean square absolute error was 0.2041E-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 1983 Random arguments were tested from the interval ( 0.00, 2.00) Y(X,ALPHA) was larger 783 times, agreed 403 times, and was smaller 797 times. NOTE: first 17 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 0.2075E-14 = 2 ** -48.78 occurred for X = 0.196853E+01 and NU = 0.604741E+00 with Y(X,ALPHA) = 0.147133E+00 The estimated loss of base 2 significant digits is 4.22 The root mean square relative error was 0.3763E-15 = 2 ** -51.24 The estimated loss of base 2 significant digits is 1.76 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 710 times, agreed 486 times, and was smaller 804 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.5188E-14 = 2 ** -47.45 occurred for X = 0.831191E+01 and NU = 0.682244E+00 with Y(X,ALPHA) = 0.508201E-01 The estimated loss of base 2 significant digits is 5.55 The root mean square relative error was 0.3385E-15 = 2 ** -51.39 The estimated loss of base 2 significant digits is 1.61 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 680 times, agreed 561 times, and was smaller 759 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.3682E-14 = 2 ** -47.95 occurred for X = 0.159974E+02 and NU = 0.156113E+00 with Y(X,ALPHA) = 0.135694E+00 The estimated loss of base 2 significant digits is 5.05 The root mean square relative error was 0.2436E-15 = 2 ** -51.87 The estimated loss of base 2 significant digits is 1.13 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 613 times, agreed 768 times, and was smaller 619 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1342E-14 = 2 ** -49.40 occurred for X = 0.354141E+02 and NU = 0.269416E+00 with Y(X,ALPHA) = 0.465376E-01 The estimated loss of base 2 significant digits is 3.60 The root mean square relative error was 0.1808E-15 = 2 ** -52.30 The estimated loss of base 2 significant digits is 0.70 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 825 times agreed 617 times, and was smaller 558 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1006E-14 = 2 ** -49.82 occurred for X = 0.277849E+01 The estimated loss of base 2 significant digits is 3.18 The root mean square relative error was 0.2004E-15 = 2 ** -52.15 The estimated loss of base 2 significant digits is 0.85 1Test of Y0(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 3.0, 5.5) ABS(Y0(X)) was larger 693 times agreed 562 times, and was smaller 745 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1077E-14 = 2 ** -49.72 occurred for X = 0.380015E+01 The estimated loss of base 2 significant digits is 3.28 The root mean square relative error was 0.2046E-15 = 2 ** -52.12 The estimated loss of base 2 significant digits is 0.88 1Test of Y0(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 5.5, 8.0) ABS(Y0(X)) was larger 931 times agreed 263 times, and was smaller 806 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.2990E-14 = 2 ** -48.25 occurred for X = 0.684048E+01 The estimated loss of base 2 significant digits is 4.75 The root mean square relative error was 0.5219E-15 = 2 ** -50.77 The estimated loss of base 2 significant digits is 2.23 1Test of Y0(X) VS Multiplication Theorem 500 random arguments were tested from the interval ( 8.0, 20.0) ABS(Y0(X)) was larger 178 times agreed 92 times, and was smaller 230 times. There are 53 base 2 significant digits in a floating-point number. The maximum absolute error of 0.9764E-15 = 2 ** -49.86 occurred for X = 0.187602E+02 The estimated loss of base 2 significant digits is 3.14 The root mean square absolute error was 0.2428E-15 = 2 ** -51.87 The estimated loss of base 2 significant digits is 1.13 1Special Tests Accuracy near zeros X BESY0(X) Loss of base 2 digits 0.8906250000E+00 -0.260031427229335E-02 0.59 0.3957031250E+01 0.260534549114568E-03 0.91 0.7085937500E+01 -0.340794487147956E-04 1.84 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 -0.17900000000000000+309 Y0 will be called with the argument 0.1797693135+309 This may stop execution. Y0 returned the value 0.00000000000000000E+00 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 638 times agreed 585 times, and was smaller 777 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.6734E-15 = 2 ** -50.40 occurred for X = 0.383826E+01 The estimated loss of base 2 significant digits is 2.60 The root mean square relative error was 0.1984E-15 = 2 ** -52.16 The estimated loss of base 2 significant digits is 0.84 1Test of Y1(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 4.0, 8.0) ABS(Y1(X)) was larger 833 times agreed 338 times, and was smaller 829 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.5763E-14 = 2 ** -47.30 occurred for X = 0.799640E+01 The estimated loss of base 2 significant digits is 5.70 The root mean square relative error was 0.7343E-15 = 2 ** -50.27 The estimated loss of base 2 significant digits is 2.73 1Test of Y1(X) VS Multiplication Theorem 500 random arguments were tested from the interval ( 8.0, 20.0) ABS(Y1(X)) was larger 238 times agreed 97 times, and was smaller 165 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1105E-14 = 2 ** -49.68 occurred for X = 0.175340E+02 The estimated loss of base 2 significant digits is 3.32 The root mean square relative error was 0.2597E-15 = 2 ** -51.77 The estimated loss of base 2 significant digits is 1.23 1Special Tests Accuracy near zeros X BESY1(X) Loss of base 2 digits 0.2195312500E+01 -0.952823930977227E-03 0.04 0.5429687500E+01 -0.219818300805980E-05 0.80 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 -0.17900000000000000+309 Y1 will be called with the argument 0.1797693135+309 This may stop execution. Y1 returned the value 0.00000000000000000E+00 This concludes the tests. TOMS715_TEST Normal end of execution. 04 April 2023 9:38:52.664 AM