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   714 times
                      agreed   626 times, and
                 was smaller   660 times.


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


 The maximum relative error of     0.4723E-06 =    2 ** -21.01
    occurred for X = 0.898855E+00
 The estimated loss of base   2 significant digits is   2.99


 The root mean square relative error was     0.1166E-06 =    2 ** -23.03
 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   434 times
                      agreed  1102 times, and
                 was smaller   464 times.


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


 The maximum relative error of     0.2874E-06 =    2 ** -21.73
    occurred for X = 0.277423E+01
 The estimated loss of base   2 significant digits is   2.27


 The root mean square relative error was     0.6468E-07 =    2 ** -23.88
 The estimated loss of base   2 significant digits is   0.12


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   280 times
                      agreed  1440 times, and
                 was smaller   280 times.


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


 The maximum relative error of     0.1183E-06 =    2 ** -23.01
    occurred for X = 0.800229E+01
 The estimated loss of base   2 significant digits is   0.99


 The root mean square relative error was     0.5026E-07 =    2 ** -24.25
 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   166 times
                      agreed   167 times, and
                 was smaller   167 times.


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


 The maximum relative error of     0.4805E-06 =    2 ** -20.99
    occurred for X =-0.176126E+02
 The estimated loss of base   2 significant digits is   3.01


 The root mean square relative error was     0.1140E-06 =    2 ** -23.06
 The estimated loss of base   2 significant digits is   0.94


1Special Tests


 Accuracy near positive zero

 PSI( 0.1460938E+01) = -0.67240244243294000E-03
             Loss of base  2 digits =    0.54



 Test with extreme arguments

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

 PSI returned the value -0.33999999521443640E+39


 PSI will be called with the argument  0.3402823466E+39
 This should not stop execution.

 PSI returned the value  0.88722839355468750E+02




 Test of error returns


 PSI will be called with the argument  0.0000000000E+00
 This may stop execution.

 PSI returned the value  0.33999999521443640E+39


 PSI will be called with the argument -0.2516582400E+08
 This may stop execution.

 PSI returned the value  0.33999999521443640E+39


 This concludes the tests.
