9 January 2016 10:16:12.869 PM TOMS715_PRB FORTRAN77 version Test the TOMS715 library. 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 477 times, and was smaller 843 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 647 times, agreed 685 times, and was smaller 668 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 0.1764E-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 700 times, agreed 859 times, and was smaller 441 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 0.1525E-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 Infinity LGAMA will be called with the argument 0.000000E+00 This should trigger an error message LGAMA returned the value Infinity LGAMA will be called with the argument 0.177972+309 This should trigger an error message LGAMA returned the value Infinity 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 642 times, and was smaller 936 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 812 times, and was smaller 575 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 0.1585E-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 846 times, and was smaller 587 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 0.1480E-15 = 2 ** -52.58 The estimated loss of base 2 significant digits is 0.42 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 894 times, and was smaller 545 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 600 times, agreed 896 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 713 times, agreed 577 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 0.2263E-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 560 times, agreed 893 times, and was smaller 547 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 0.1430E-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 499 times, and was smaller 652 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.8198E-15 = 2 ** -50.12 occurred for X = 0.176224E+01 The estimated loss of base 2 significant digits is 2.88 The root mean square relative error was 0.2550E-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 666 times, agreed 649 times, and was smaller 685 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 0.1977E-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 0.222508-307 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 0.1356E-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 619 times, agreed 711 times, and was smaller 670 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 989 times, agreed 16 times, and was smaller 995 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 1161 times, agreed 371 times, and was smaller 468 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.1114E-14 = 2 ** -49.67 occurred for X =-0.474569E+01 The estimated loss of base 2 significant digits is 3.33 The root mean square relative error was 0.3147E-15 = 2 ** -51.50 The estimated loss of base 2 significant digits is 1.50 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 NaN GAMMA will be called with the argument 0.000000E+00 This should trigger an error message GAMMA returned the value Infinity GAMMA will be called with the argument 0.222507-307 This should trigger an error message GAMMA returned the value 0.449423+308 GAMMA will be called with the argument 0.171624E+03 This should trigger an error message GAMMA returned the value Infinity 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 586 times, agreed 814 times, and was smaller 600 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 0.1574E-15 = 2 ** -52.50 The estimated loss of base 2 significant digits is 0.50 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 634 times, agreed 758 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 0.1607E-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 479 times agreed 1037 times, and was smaller 484 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1122E-14 = 2 ** -49.66 occurred for X = 0.244691E+01 The estimated loss of base 2 significant digits is 3.34 The root mean square relative error was 0.1532E-15 = 2 ** -52.54 The estimated loss of base 2 significant digits is 0.46 1Test of J0(X) VS Taylor expansion 2000 random arguments were tested from the interval ( 4.0, 8.0) ABS(J0(X)) was larger 680 times agreed 651 times, and was smaller 669 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 = 0.547580E+01 The estimated loss of base 2 significant digits is 2.85 The root mean square relative error was 0.1972E-15 = 2 ** -52.17 The estimated loss of base 2 significant digits is 0.83 1Test of J0(X) VS Taylor expansion 2000 random arguments were tested from the interval ( 8.0, 20.0) ABS(J0(X)) was larger 713 times agreed 645 times, and was smaller 642 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.7715E-15 = 2 ** -50.20 occurred for X = 0.184689E+02 The estimated loss of base 2 significant digits is 2.80 The root mean square relative error was 0.1930E-15 = 2 ** -52.20 The estimated loss of base 2 significant digits is 0.80 1Special Tests Accuracy near zeros X BESJ0(X) Loss of base 2 digits 0.2406250000E+01 -0.739276482217003E-03 2.72 0.5519531250E+01 -0.186086517975740E-03 5.71 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 226 times agreed 1567 times, and was smaller 207 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.2220E-15 = 2 ** -52.00 occurred for X = 0.517111E+00 The estimated loss of base 2 significant digits is 1.00 The root mean square relative error was 0.7144E-16 = 2 ** -53.64 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 804 times, and was smaller 596 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.2165E-14 = 2 ** -48.71 occurred for X = 0.379211E+01 The estimated loss of base 2 significant digits is 4.29 The root mean square relative error was 0.2243E-15 = 2 ** -51.99 The estimated loss of base 2 significant digits is 1.01 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 702 times agreed 622 times, and was smaller 676 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.8900E-15 = 2 ** -50.00 occurred for X = 0.697672E+01 The estimated loss of base 2 significant digits is 3.00 The root mean square relative error was 0.2110E-15 = 2 ** -52.07 The estimated loss of base 2 significant digits is 0.93 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 674 times agreed 595 times, and was smaller 731 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.9803E-15 = 2 ** -49.86 occurred for X = 0.164391E+02 The estimated loss of base 2 significant digits is 3.14 The root mean square relative error was 0.2035E-15 = 2 ** -52.13 The estimated loss of base 2 significant digits is 0.87 1Special 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. 1Test of K0(X) vs Multiplication Theorem 2000 random arguments were tested from the interval ( 0.0, 1.0) ABS(K0(X)) was larger 534 times, agreed 1072 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 0.1208E-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 516 times, and was smaller 658 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 0.2463E-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 643 times, agreed 611 times, and was smaller 746 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 0.2116E-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 0.2486E-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 764 times, agreed 588 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 0.2163E-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 597 times agreed 629 times, and was smaller 774 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.8652E-15 = 2 ** -50.04 occurred for X = 0.829865E+00 The estimated loss of base 2 significant digits is 2.96 The root mean square relative error was 0.2276E-15 = 2 ** -51.96 The estimated loss of base 2 significant digits is 1.04 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 489 times agreed 985 times, and was smaller 526 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 0.1426E-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 170 times agreed 181 times, and was smaller 149 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.6061E-15 = 2 ** -50.55 occurred for X =-0.176040E+02 The estimated loss of base 2 significant digits is 2.45 The root mean square relative error was 0.1899E-15 = 2 ** -52.23 The estimated loss of base 2 significant digits is 0.77 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 762 times, agreed 459 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 0.4887E-15 = 2 ** -50.86 The estimated loss of base 2 significant digits is 2.14 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 775 times, agreed 461 times, and was smaller 764 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 0.5648E-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 763 times, agreed 406 times, and was smaller 831 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 0.4682E-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 839 times, agreed 399 times, and was smaller 762 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 0.4403E-15 = 2 ** -51.01 The estimated loss of base 2 significant digits is 1.99 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 672 times, agreed 630 times, and was smaller 698 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 0.2051E-15 = 2 ** -52.11 The estimated loss of base 2 significant digits is 0.89 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 832 times, agreed 309 times, and was smaller 859 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 0.8911E-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 965 times, agreed 155 times, and was smaller 880 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 0.1336E-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 621 times, agreed 739 times, and was smaller 640 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 0.2250E-15 = 2 ** -51.98 The estimated loss of base 2 significant digits is 1.02 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 646 times, agreed 684 times, and was smaller 670 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 0.2098E-15 = 2 ** -52.08 The estimated loss of base 2 significant digits is 0.92 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 675 times, and was smaller 639 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 697 times, agreed 620 times, and was smaller 683 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 0.2043E-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 781 times, agreed 410 times, and was smaller 792 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 0.3747E-15 = 2 ** -51.25 The estimated loss of base 2 significant digits is 1.75 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 713 times, agreed 498 times, and was smaller 789 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 0.3386E-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 690 times, agreed 565 times, and was smaller 745 times. There are 53 base 2 significant digits in a floating-point number The maximum relative error of 0.3886E-14 = 2 ** -47.87 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 5.13 The root mean square relative error was 0.2475E-15 = 2 ** -51.84 The estimated loss of base 2 significant digits is 1.16 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 617 times, agreed 752 times, and was smaller 631 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 0.1825E-15 = 2 ** -52.28 The estimated loss of base 2 significant digits is 0.72 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 660 times agreed 692 times, and was smaller 648 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1756E-14 = 2 ** -49.02 occurred for X = 0.862659E+00 The estimated loss of base 2 significant digits is 3.98 The root mean square relative error was 0.1915E-15 = 2 ** -52.21 The estimated loss of base 2 significant digits is 0.79 1Test of Y0(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 3.0, 5.5) ABS(Y0(X)) was larger 685 times agreed 576 times, and was smaller 739 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1177E-14 = 2 ** -49.59 occurred for X = 0.383639E+01 The estimated loss of base 2 significant digits is 3.41 The root mean square relative error was 0.1982E-15 = 2 ** -52.16 The estimated loss of base 2 significant digits is 0.84 1Test of Y0(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 5.5, 8.0) ABS(Y0(X)) was larger 720 times agreed 546 times, and was smaller 734 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1019E-14 = 2 ** -49.80 occurred for X = 0.686142E+01 The estimated loss of base 2 significant digits is 3.20 The root mean square relative error was 0.1970E-15 = 2 ** -52.17 The estimated loss of base 2 significant digits is 0.83 1Test of Y0(X) VS Multiplication Theorem 500 random arguments were tested from the interval ( 8.0, 20.0) ABS(Y0(X)) was larger 192 times agreed 118 times, and was smaller 190 times. There are 53 base 2 significant digits in a floating-point number. The maximum absolute error of 0.8042E-15 = 2 ** -50.14 occurred for X = 0.129987E+02 The estimated loss of base 2 significant digits is 2.86 The root mean square absolute error was 0.1904E-15 = 2 ** -52.22 The estimated loss of base 2 significant digits is 0.78 1Special Tests Accuracy near zeros X BESY0(X) Loss of base 2 digits 0.8906250000E+00 -0.260031427229334E-02 4.91 0.3957031250E+01 0.260534549114568E-03 1.91 0.7085937500E+01 -0.340794487147958E-04 5.93 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 710 times agreed 635 times, and was smaller 655 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.1407E-14 = 2 ** -49.34 occurred for X = 0.212260E+01 The estimated loss of base 2 significant digits is 3.66 The root mean square relative error was 0.2160E-15 = 2 ** -52.04 The estimated loss of base 2 significant digits is 0.96 1Test of Y1(X) VS Multiplication Theorem 2000 random arguments were tested from the interval ( 4.0, 8.0) ABS(Y1(X)) was larger 749 times agreed 523 times, and was smaller 728 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 = 0.520585E+01 The estimated loss of base 2 significant digits is 3.02 The root mean square relative error was 0.2193E-15 = 2 ** -52.02 The estimated loss of base 2 significant digits is 0.98 1Test of Y1(X) VS Multiplication Theorem 500 random arguments were tested from the interval ( 8.0, 20.0) ABS(Y1(X)) was larger 198 times agreed 112 times, and was smaller 190 times. There are 53 base 2 significant digits in a floating-point number. The maximum relative error of 0.7203E-15 = 2 ** -50.30 occurred for X = 0.171171E+02 The estimated loss of base 2 significant digits is 2.70 The root mean square relative error was 0.1968E-15 = 2 ** -52.17 The estimated loss of base 2 significant digits is 0.83 1Special Tests Accuracy near zeros X BESY1(X) Loss of base 2 digits 0.2195312500E+01 -0.952823930977219E-03 6.21 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. TOMS715_PRB Normal end of execution. 9 January 2016 10:16:13.083 PM