1Test of Y1(X) VS Multiplication Theorem


   2000 random arguments were tested from the interval (  0.0,  4.0)


 ABS(Y1(X)) was larger   626 times
                agreed   576 times, and
           was smaller   798 times.


 There are  53 base   2 significant digits in a floating-point number.


 The maximum relative error of     0.8005E-15 =    2 ** -50.15
    occurred for X = 0.374086E+01
 The estimated loss of base   2 significant digits is   2.85


 The root mean square relative error was     0.2027E-15 =    2 ** -52.13
 The estimated loss of base   2 significant digits is   0.87


1Test of Y1(X) VS Multiplication Theorem


   2000 random arguments were tested from the interval (  4.0,  8.0)


 ABS(Y1(X)) was larger   812 times
                agreed   318 times, and
           was smaller   870 times.


 There are  53 base   2 significant digits in a floating-point number.


 The maximum relative error of     0.5055E-14 =    2 ** -47.49
    occurred for X = 0.790222E+01
 The estimated loss of base   2 significant digits is   5.51


 The root mean square relative error was     0.7062E-15 =    2 ** -50.33
 The estimated loss of base   2 significant digits is   2.67


1Test of Y1(X) VS Multiplication Theorem


    500 random arguments were tested from the interval (  8.0, 20.0)


 ABS(Y1(X)) was larger   239 times
                agreed    85 times, and
           was smaller   176 times.


 There are  53 base   2 significant digits in a floating-point number.


 The maximum relative error of     0.9214E-15 =    2 ** -49.95
    occurred for X = 0.114657E+02
 The estimated loss of base   2 significant digits is   3.05


 The root mean square relative error was     0.2447E-15 =    2 ** -51.86
 The estimated loss of base   2 significant digits is   1.14


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 -0.28611174857570285+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.
