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   624 times
                      agreed   648 times, and
                 was smaller   728 times.


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


 The maximum relative error of     0.8515E-15 =    2 ** -50.06
    occurred for X = 0.956052E+00
 The estimated loss of base   2 significant digits is   2.94


 The root mean square relative error was     0.2256E-15 =    2 ** -51.98
 The estimated loss of base   2 significant digits is   1.02


 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   822 times
                      agreed   833 times, and
                 was smaller   345 times.


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


 The maximum relative error of     0.6464E-15 =    2 ** -50.46
    occurred for X = 0.214999E+01
 The estimated loss of base   2 significant digits is   2.54


 The root mean square relative error was     0.1498E-15 =    2 ** -52.57
 The estimated loss of base   2 significant digits is   0.43


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   379 times
                      agreed  1378 times, and
                 was smaller   243 times.


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


 The maximum relative error of     0.2203E-15 =    2 ** -52.01
    occurred for X = 0.800229E+01
 The estimated loss of base   2 significant digits is   0.99


 The root mean square relative error was     0.9971E-16 =    2 ** -53.15
 The estimated loss of base   2 significant digits is   0.00


 Test of PSI(X) vs (PSI(X/2)+PSI(X/2+1/2))/2 + ln(2)


    500 random arguments were tested from the interval (-17.6,-16.9)


 ABS(PSI(X)) was larger   164 times
                      agreed   189 times, and
                 was smaller   147 times.


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


 The maximum relative error of     0.1010E-14 =    2 ** -49.82
    occurred for X =-0.176106E+02
 The estimated loss of base   2 significant digits is   3.18


 The root mean square relative error was     0.1940E-15 =    2 ** -52.20
 The estimated loss of base   2 significant digits is   0.80


1Special Tests


 Accuracy near positive zero

 PSI( 0.1460938E+01) = -0.67240239024288062E-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  0.70978271289338401E+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.
