9 May 2025   9:47:13.928 PM

toms597_test():
  FORTRAN90 version
  Test toms597():

ren_test():
  FORTRAN90 version
  ren() returns a random value in [0,1].

   1    0.470393    
   2    0.799067    
   3    0.883262    
   4    0.407668    
   5    0.958390    
   6    0.798617    
   7    0.827025    
   8    0.378046    
   9    0.255645    
  10    0.955567    

test of i(x,alpha) vs series expansion

   2000 random arguments were tested from the interval (  0.0,  2.0)


 i(x,alpha) was larger   734 times,
                agreed   557 times, and
           was smaller   709 times.


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


 the maximum relative error of     0.2170E-14 =    2 ** -48.71
    occurred for x = 0.113794E+01  and nu = 0.540015E-01
 the estimated loss of base   2 significant digits is   4.29


 the root mean square relative error was     0.5196E-15 =    2 ** -50.77
 the estimated loss of base   2 significant digits is   2.23



test of i(x,alpha) vs series expansion

   2000 random arguments were tested from the interval (  2.0,  4.0)


 i(x,alpha) was larger   825 times,
                agreed   357 times, and
           was smaller   818 times.


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


 the maximum relative error of     0.2358E-14 =    2 ** -48.59
    occurred for x = 0.352654E+01  and nu = 0.887898E-01
 the estimated loss of base   2 significant digits is   4.41


 the root mean square relative error was     0.8155E-15 =    2 ** -50.12
 the estimated loss of base   2 significant digits is   2.88



test of i(x,alpha) vs series expansion

   2000 random arguments were tested from the interval (  4.0, 10.0)


 i(x,alpha) was larger   890 times,
                agreed   249 times, and
           was smaller   861 times.


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


 the maximum relative error of     0.4056E-14 =    2 ** -47.81
    occurred for x = 0.879057E+01  and nu = 0.122677E+00
 the estimated loss of base   2 significant digits is   5.19


 the root mean square relative error was     0.1372E-14 =    2 ** -49.37
 the estimated loss of base   2 significant digits is   3.63



test of exp(-x)*i(x,0.5) vs 1/sqrt(2*x*pi)

   2000 random arguments were tested from the interval ( 20.0, 30.0)


 i(x,alpha) was larger   278 times,
                agreed   637 times, and
           was smaller  1085 times.


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


 the maximum relative error of     0.7461E-15 =    2 ** -50.25
    occurred for x = 0.287546E+02  and nu = 0.500000E+00
 the estimated loss of base   2 significant digits is   2.75


 the root mean square relative error was     0.2150E-15 =    2 ** -52.05
 the estimated loss of base   2 significant digits is   0.95


1check of error returns 


 the following summarizes calls with indicated parameters

 ncalc different from nb indicates some form of error

 see documentation for ribesl for details 

       arg            alpha      nb   iz       res      ncalc


  0.1000000E+01  0.5000000E+00    5    1  0.9376749E+00    5
 -0.1000000E+01  0.5000000E+00    5    1  0.0000000E+00   -1
  0.1000000E+01  0.1500000E+01    5    1  0.0000000E+00   -1
  0.1000000E+01  0.5000000E+00   -5    1  0.0000000E+00   -6
  0.1000000E+01  0.5000000E+00    5    5  0.3449513E+00    5
  0.4940656-323  0.0000000E+00  150    1  0.1000000E+01    1
  0.3000000E+02  0.0000000E+00  150    1  0.7816723E+12   78
       Infinity  0.0000000E+00  150    1  0.0000000E+00   -1

toms597_test():
  Normal end of execution.

 9 May 2025   9:47:13.935 PM