1Test of Y1(X) VS Multiplication Theorem


   1999 random arguments were tested from the interval (  0.0,  4.0)


 ABS(Y1(X)) was larger   652 times
                agreed   586 times, and
           was smaller   761 times.


 There are  24 base   2 significant digits in a floating-point number.


 The maximum relative error of     0.4447E-06 =    2 ** -21.10
    occurred for X = 0.396162E+01
 The estimated loss of base   2 significant digits is   2.90


 The root mean square relative error was     0.1145E-06 =    2 ** -23.06
 The estimated loss of base   2 significant digits is   0.94


1Test of Y1(X) VS Multiplication Theorem


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


 ABS(Y1(X)) was larger   889 times
                agreed   294 times, and
           was smaller   817 times.


 There are  24 base   2 significant digits in a floating-point number.


 The maximum relative error of     0.2098E-05 =    2 ** -18.86
    occurred for X = 0.782328E+01
 The estimated loss of base   2 significant digits is   5.14


 The root mean square relative error was     0.3494E-06 =    2 ** -21.45
 The estimated loss of base   2 significant digits is   2.55


1Test of Y1(X) VS Multiplication Theorem


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


 ABS(Y1(X)) was larger   202 times
                agreed    96 times, and
           was smaller   202 times.


 There are  24 base   2 significant digits in a floating-point number.


 The maximum relative error of     0.4670E-06 =    2 ** -21.03
    occurred for X = 0.142488E+02
 The estimated loss of base   2 significant digits is   2.97


 The root mean square relative error was     0.1299E-06 =    2 ** -22.88
 The estimated loss of base   2 significant digits is   1.12


1Special Tests


 Accuracy near zeros

          X               BESY1(X)             Loss of base  2 digits

    0.2195312500E+01   -0.952823902480304E-03           0.00

    0.5429687500E+01   -0.219818298319296E-05           0.00



 Test with extreme arguments



 Y1 will be called with the argument  0.1175494351E-37
 This should not stop execution.


 Y1 returned the value -0.54157618557647397E+38

 Y1 will be called with the argument -0.1000000000E+01
 This may stop execution.


 Y1 returned the value -0.33999999521443640E+39

 Y1 will be called with the argument  0.3402823466E+39
 This may stop execution.


 Y1 returned the value  0.00000000000000000E+00

 This concludes the tests.
