RANPRB
 Tests for the random number routines of RANPACK.
  
  
 TEST01
 Test RANF, RANGET and RANSET routines.
  
 RANGET reports current seed is       100001
 Generate 10 random numbers with RANF:
  
   0.4703925    
   0.7990661    
   0.8832613    
   0.4076671    
   0.9583889    
   0.7986162    
   0.8270243    
   0.3780451    
   0.2556445    
   0.9555662    
  
 RANGET reports current seed is      2671957
 Now have RANSET reset the seed to       100001
  
 Now generate 20 random numbers.  The first 10
 should match the previous sequence:
   0.4703925    
   0.7990661    
   0.8832613    
   0.4076671    
   0.9583889    
   0.7986162    
   0.8270243    
   0.3780451    
   0.2556445    
   0.9555662    
   0.4457716    
   0.7214552    
   0.1818913    
   0.7364126    
   5.1569574E-02
   0.4461969    
   0.7746075    
   0.8259457    
   0.2432195    
   0.4024332    
  
 Now use RANSET to reset the seed to      2671957
 This should allow us to resume the first sequence
 where we left off.  The next 10 numbers should
 match the last 10 of the set of 20.
  
   0.4457716    
   0.7214552    
   0.1818913    
   0.7364126    
   5.1569574E-02
   0.4461969    
   0.7746075    
   0.8259457    
   0.2432195    
   0.4024332    
  
 TEST02
 Compute the average of 10000 successive random
 values, to see how far from 0.5 the answer is.
  
 ran0   average=  0.5009735     average-0.5=  9.7346306E-04
 ran1   average=  0.0000000E+00 average-0.5= -0.5000000    
 ran2   average=  0.6463727     average-0.5=  0.1463727    
 ran3   average=  0.5032091     average-0.5=  3.2091141E-03
 ran4   average=  0.5038623     average-0.5=  3.8623214E-03
 ran5   average=  0.4992100     average-0.5= -7.8999996E-04
 ran5   average=  0.4999287     average-0.5= -7.1287155E-05
 ran6   average=  0.5002977     average-0.5=  2.9772520E-04
  
 ran6   average=  0.0000000E+00 average-0.5= -0.5000000    
 ran7   average=  0.0000000E+00 average-0.5= -0.5000000    
 ran8   average=  0.4993838     average-0.5= -6.1622262E-04
 ran9   average=  0.4963118     average-0.5= -3.6881864E-03
 ran10  average=  0.4990451     average-0.5= -9.5492601E-04
 ran11  average=  0.5077505     average-0.5=  7.7505112E-03
 ran12  average=  0.4990876     average-0.5= -9.1239810E-04
 ran13  average=  0.4985010     average-0.5= -1.4989674E-03
 ran14  average=  0.4949117     average-0.5= -5.0882697E-03
 ran15  average=  0.4937658     average-0.5= -6.2341690E-03
 ran16  average=  0.5003132     average-0.5=  3.1322241E-04
 ran17  average=  0.5000409     average-0.5=  4.0888786E-05
 ran18  average=  0.5003132     average-0.5=  3.1322241E-04
 ran19  average=  0.4970459     average-0.5= -2.9540658E-03
 ran20  average=  0.5025502     average-0.5=  2.5501847E-03
 ran21  average=  0.5003132     average-0.5=  3.1322241E-04
 ran22  average=  0.5016356     average-0.5=  1.6355515E-03
 ran23  average=  0.5029995     average-0.5=  2.9995441E-03
 ran24  average=  0.5020313     average-0.5=  2.0312667E-03
 ran25  average=  0.4962493     average-0.5= -3.7507415E-03
 ran26  average=  6.6245273E-02 average-0.5= -0.4337547    
 ran27  average=  0.5004136     average-0.5=  4.1359663E-04
 ran28  average=  0.5001596     average-0.5=  1.5956163E-04
 ran29  average=  0.5050037     average-0.5=  5.0036907E-03
 halton average=  0.4295236     average-0.5= -7.0476353E-02
 sobol1 average=  0.4999257     average-0.5= -7.4326992E-05
  
 TEST03
 Test distribution of 10000 successive random values.
 Compare the ranges 0<x<0.1,... 0.9<x<1.0.
  
  
 Range         ran0    ran1    ran2    ran3    ran4  
  
  0.00 0.10     991     991    1011    1039     937
  0.10 0.20     966     966    1029     998    1015
  0.20 0.30    1014    1014     963    1009    1017
  0.30 0.40    1018    1018    1041     985     937
  0.40 0.50    1010    1010    1034     969    1096
  0.50 0.60    1008    1008     940    1013     938
  0.60 0.70     981     981     983     985    1014
  0.70 0.80    1008    1008     975    1021    1015
  0.80 0.90    1018    1018    1040     975     936
  0.90 1.00     986     986     984    1006    1095
  
 Range         ran5    ran6    ran7    ran8    ran9  
  
  0.00 0.10     995    1000    1002    1030     992
  0.10 0.20    1004     999     989    1076    1070
  0.20 0.30    1017     999     950    1035     973
  0.30 0.40     992    1003     965     998    1051
  0.40 0.50     986    1002    1026    1026    1053
  0.50 0.60    1006    1000     975     993     981
  0.60 0.70    1015     999    1070     951     981
  0.70 0.80     997    1000     975     976     968
  0.80 0.90     999    1000    1015     943     930
  0.90 1.00     989     998    1033     972    1001
  
 Range         ran10   ran11   ran12   ran13   ran14 
  
  0.00 0.10     991     936    1002    1040    1066
  0.10 0.20       0     938    1021     960     990
  0.20 0.30       0     939     953    1040     971
  0.30 0.40       0    1250    1029     960    1012
  0.40 0.50       0     938     981    1040    1039
  0.50 0.60       0     939     937     960     982
  0.60 0.70       0     938     995    1040    1006
  0.70 0.80       0     936     997     960     988
  0.80 0.90       0    1249    1008    1040     989
  0.90 1.00       0     937    1076     960     957
  
 Range         ran15   ran16   ran17   ran28   ran19 
  
  0.00 0.10    1018    1013     979    1013    1046
  0.10 0.20     920     973    1055     973     992
  0.20 0.30     953    1017     971    1017     975
  0.30 0.40     997     999    1007     999     979
  0.40 0.50     994     989     976     989     985
  0.50 0.60    1001     978     995     978     971
  0.60 0.70    1011    1017     998    1017    1017
  0.70 0.80     982    1048    1031    1048     988
  0.80 0.90    1014     971     985     971    1056
  0.90 1.00    1008     995    1003     995     991
  
 Range         ran20   ran21   ran22   ran23   ran24 
  
  0.00 0.10    1004    1013    1037    1001    1011
  0.10 0.20    1021     973    1024     939    1010
  0.20 0.30    1026    1017     961    1039     991
  0.30 0.40    1007     999     966     956     990
  0.40 0.50     973     989     971     974     979
  0.50 0.60    1006     978     987    1037     973
  0.60 0.70     990    1017    1042    1033    1008
  0.70 0.80     987    1048    1011     993     979
  0.80 0.90    1049     971     987    1046    1019
  0.90 1.00     937     995    1014     982    1040
  
 Range         ran25   ran26   ran27   ran28   ran29 
  
  0.00 0.10    1024   10000    1012     952    1061
  0.10 0.20    1022       0     973     988    1015
  0.20 0.30    1007       0    1022     997     987
  0.30 0.40     998       0    1001    1006    1002
  0.40 0.50     980       0     987    1040     987
  0.50 0.60    1016       0     978    1007    1003
  0.60 0.70     985       0    1016    1010     953
  0.70 0.80    1004       0    1048     974    1002
  0.80 0.90     988       0     969    1012     974
  0.90 1.00     976       0     994    1014    1015
  
 Range         halton  sobol1
  
  0.00 0.10    1638    1000
  0.10 0.20    1638    1000
  0.20 0.30     990    1001
  0.30 0.40     819    1000
  0.40 0.50     819     999
  0.50 0.60     820    1001
  0.60 0.70     819    1000
  0.70 0.80     819    1001
  0.80 0.90     819     999
  0.90 1.00     819     999
  
 TEST04
 Test distribution of 10000 successive normally
 distributed random values.
  
Gau1      1     4    44   157   427   902  1517  1880
       1875  1575   923   436   192    53    12     2
Gau2      2     6    45   159   454   914  1484  1920
       1946  1510   901   446   153    54     5     1
Gau3      2    15    38   171   413   880  1570  1934
       1825  1564   935   424   160    51    13     4
Gau4      1     9    55   161   475   904  1522  1893
       1929  1486   869   461   168    55    10     2
Gau5      1    13    47   170   439   886  1491  1915
       1966  1484   946   422   172    45     3     0
Gau6      0     9    54   150   425   947  1501  1933
       1907  1453   928   465   176    41    11     0
Gau7      0     0     0     0     0     0     0     0
          0  9999     1     0     0     0     0     0
Gau8      1    12    48   185   483   859  1518  1909
       1936  1483   843   466   192    52    11     2
Gau9      1    11    50   169   443   967  1525  1912
       1804  1545   923   446   151    42     8     3
Gau10     1    10    54   157   431   885  1542  1885
       1940  1486   907   460   178    49    13     0
Gau11     1    10    58   153   412   879  1551  1927
       1912  1497   948   440   156    49     3     4
Gau12   261   288   382   485   517   707   685   778
        809   747   624   580   428   399   281   220
Exact     2    11    48   165   440   918  1498  1914
       1914  1498   918   440   165    48    11     2
  
 TEST05
 Compare the speed of normal random value routines.
  
 Gau1, Gau2, Gau3, Gau4, Gau7, Gau8 are scalar codes.
 Gau5, Gau6 and Gau11 are vectorized.
  
 Gau3, Gau4, Gau5 and Gau11 return true normal
 random values, while Gau1, Gau2, Gau6, and Gau12
 return approximate normal random values,and
 Gau7 uses a sort of interpolation scheme.
  
 We time the computation of        10000 values.
  
 Gau1 required   0.1454582     seconds.
 Gau2 required   0.1415949     seconds.
 Gau3 required   3.2207489E-02 seconds.
 Gau4 required   4.8891068E-02 seconds.
 Gau5 required   5.0538063E-02 seconds.
 Gau6 required   0.1857414     seconds.
 Gau7 required   0.4216871     seconds.
 Gau8 required   6.7996979E-04 seconds.
 Gau9 required   1.1255264E-02 seconds.
 Gau10 required   2.3149490E-02 seconds.
 Gau11 required   5.1482201E-02 seconds.
 Gau12 required   2.7944565E-02 seconds.
 uniforms:       1.5400887E-02 seconds.
  
 TEST06
 Demonstrate the use of IRAN0
 random integer production.
 To run the same code on VMS and UNICOS, we pretend
 that we only have 32 bits in a word.
  
 Random integers:
  
    393100910
    440039738
   -815389082
  -1443710734
  -1260504098
   1395266090
     -2705706
    232946914
   1749962574
   1377464602
  
 TEST07
 Demonstrate the output of RNOISE
  
   -45.29000    
   -95.15700    
    354.8070    
    305.3040    
   -244.8830    
   -294.6000    
    155.1210    
    105.2340    
   -444.9690    
   -495.0190    
   -44.93800    
   -94.81000    
    354.8630    
    304.9740    
   -245.1460    
   -295.1510    
    154.5580    
    105.1690    
   -444.7640    
   -495.0520    
  
 TEST08
 Test exponential random deviate routines:
  
 Exponential distribution with 10000 points:
    Interval        Exp1        Exp2    Expected
   0.00  0.05      0.0723      0.0820      0.0771
   0.05  0.10      0.0746      0.0741      0.0734
   0.10  0.15      0.0696      0.0696      0.0698
   0.15  0.20      0.0692      0.0655      0.0664
   0.20  0.25      0.0641      0.0557      0.0632
   0.25  0.30      0.0583      0.0619      0.0601
   0.30  0.35      0.0571      0.0573      0.0572
   0.35  0.40      0.0583      0.0516      0.0544
   0.40  0.45      0.0520      0.0516      0.0517
   0.45  0.50      0.0469      0.0499      0.0492
   0.50  0.55      0.0445      0.0531      0.0468
   0.55  0.60      0.0436      0.0428      0.0445
   0.60  0.65      0.0421      0.0415      0.0423
   0.65  0.70      0.0439      0.0409      0.0403
   0.70  0.75      0.0374      0.0404      0.0383
   0.75  0.80      0.0367      0.0336      0.0364
   0.80  0.85      0.0329      0.0358      0.0347
   0.85  0.90      0.0351      0.0295      0.0330
   0.90  0.95      0.0315      0.0310      0.0314
   0.95  1.00      0.0299      0.0319      0.0298
  
 TEST09
 Compare behavior of a typical random number generator
 Ran2 with the Halton sequence generated by Halton and
 the Sobol sequence generated by Sobol1 for 
 Monte Carlo estimation of the integral of x**3
 from 0 to 1.  The correct value is 0.25.
  
 The approximation is iterative, doubling the number
 of points used until the integral does not change
 by more than a tolerance.
  
  
 Using Ran2
  
 Approximation=  1.9934380E-02
 Approximation=  0.1606981    
 Approximation=  0.2364710    
 Approximation=  0.2616688    
 Approximation=  0.3113309    
 Approximation=  0.3043447    
 Approximation=  0.2902257    
 Approximation=  0.2674368    
 Approximation=  0.2606957    
 Approximation=  0.2408769    
 Approximation=  0.2548116    
 Approximation=  0.2525187    
 Approximation=  0.2497214    
 Approximation=  0.2495250    
 tolerance achieved on step nstep=          12
 Total points required=        8192
  
 Using Halton
  
 Approximation=  0.1250000    
 Approximation=  7.0312500E-02
 Approximation=  0.1137695    
 Approximation=  0.2268372    
 Approximation=  0.2448902    
 Approximation=  0.2487651    
 Approximation=  0.2496939    
 tolerance achieved on step nstep=           5
 Total points required=          64
  
 Using Sobol1
  
 Approximation=  0.1250000    
 Approximation=  7.0312500E-02
 Approximation=  0.1264648    
 Approximation=  0.2369690    
 Approximation=  0.2468700    
 Approximation=  0.2506763    
 Approximation=  0.2477573    
 Approximation=  0.2504109    
 Approximation=  0.2501122    
 tolerance achieved on step nstep=           7
 Total points required=         256
  
 TEST10
 Demonstrate use of routines to compute the cumulative
 Normal distribution function.
  
    X        Dnorm1       Dnorm2       Dnorm3
             Dnorm4       Dnorm5       Dnorm6
  
   0.000000E+00  0.500000      0.500000      0.500000    
                 0.500000      0.500000    
                 0.500000    
   0.250000      0.598706      0.598706      0.598706    
                 0.598706      0.598706    
                 0.598740    
   0.500000      0.691462      0.691462      0.691462    
                 0.691462      0.691462    
                 0.691428    
   0.750000      0.773373      0.773373      0.773373    
                 0.773373      0.773373    
                 0.773303    
    1.00000      0.841345      0.841345      0.841345    
                 0.841345      0.841345    
                 0.841280    
    1.25000      0.894350      0.894350      0.894350    
                 0.894350      0.894350    
                 0.894308    
    1.50000      0.933193      0.933193      0.933193    
                 0.933193      0.933193    
                 0.933172    
    1.75000      0.959941      0.959941      0.959941    
                 0.959941      0.959941    
                 0.959934    
    2.00000      0.977250      0.977250      0.977250    
                 0.977250      0.977250    
                 0.977250    
    2.25000      0.987776      0.987776      0.987776    
                 0.987776      0.987776    
                 0.987777    
    2.50000      0.993790      0.993790      0.993790    
                 0.993790      0.993790    
                 0.993792    
    2.75000      0.997020      0.997020      0.997020    
                 0.997020      0.997020    
                 0.997021    
    3.00000      0.998650      0.998650      0.998650    
                 0.998650      0.998650    
                 0.998650    
    3.25000      0.999423      0.999423      0.999423    
                 0.999423      0.999423    
                 0.999423    
    3.50000      0.999767      0.999767      0.999767    
                 0.999767      0.999767    
                 0.999767    
    3.75000      0.999912      0.999912      0.999912    
                 0.999912      0.999912    
                 0.999912    
    4.00000      0.999968      0.999968      0.999968    
                 0.999968      0.999968    
                 0.999968    
  
 Now try to find X values for given probability:
  
    Dnorm1     Xnorm1      Xnorm2      Xnorm3    Xnorm4
   0.500000      0.000000E+00  0.000000E+00  0.000000E+00  0.000000E+00
   0.598706      0.250000      0.250000      0.250000      0.250000    
   0.691462      0.500000      0.500000      0.500000      0.500000    
   0.773373      0.750002      0.750000      0.750000      0.750000    
   0.841345       1.00001       1.00000       1.00000       1.00000    
   0.894350       1.25001       1.25000       1.25000       1.25000    
   0.933193       1.50004       1.50000       1.50000       1.50000    
   0.959941       1.75007       1.75000       1.75000       1.75000    
   0.977250       2.00017       2.00000       2.00000       2.00000    
   0.987776       2.25030       2.25000       2.25000       2.25000    
   0.993790       2.50060       2.50000       2.50000       2.50000    
   0.997020       2.75119       2.75000       2.75000       2.75000    
   0.998650       3.00259       2.99999       2.99999       2.99999    
   0.999423       3.25579       3.25000       3.25000       3.25000    
   0.999767       3.51386       3.49999       3.49999       3.49999    
   0.999912       3.78606       3.74990       3.74990       3.74990    
   0.999968       4.11044       3.99972       3.99971       3.99971    
  
 TEST11
 Test Xchi1, Xchi2, Pchi1 and Pchi2,
 chi-square probability routines.
  
 Given Nfree and probability, find X:
  
 Nfree down, probabilities across
  
       0.500   0.100   0.050   0.010   0.005   0.001
  
  
   1   0.455   0.016   0.004   0.000   0.000   0.000
       0.455   0.016   0.004   0.000   0.000   0.000
  
   2   1.386   0.211   0.103   0.020   0.010   0.002
       1.386   0.211   0.103   0.020   0.010   0.002
  
   3   2.366   0.584   0.352   0.115   0.072   0.024
       2.366   0.584   0.352   0.115   0.072   0.024
  
   4   3.357   1.064   0.711   0.297   0.207   0.091
       3.357   1.064   0.711   0.297   0.207   0.091
  
   5   4.351   1.610   1.145   0.554   0.412   0.210
       4.351   1.610   1.145   0.554   0.412   0.210
  
   6   5.348   2.204   1.635   0.872   0.676   0.381
       5.348   2.204   1.635   0.872   0.676   0.381
  
   7   6.346   2.833   2.167   1.239   0.989   0.598
       6.346   2.833   2.167   1.239   0.989   0.598
  
   8   7.344   3.490   2.733   1.646   1.344   0.857
       7.344   3.490   2.733   1.646   1.344   0.857
  
   9   8.343   4.168   3.325   2.088   1.735   1.152
       8.343   4.168   3.325   2.088   1.735   1.152
  
  10   9.342   4.865   3.940   2.558   2.156   1.479
       9.342   4.865   3.940   2.558   2.156   1.479
  
  11  10.341   5.578   4.575   3.053   2.603   1.834
      10.341   5.578   4.575   3.053   2.603   1.834
  
  12  11.340   6.304   5.226   3.571   3.074   2.214
      11.340   6.304   5.226   3.571   3.074   2.214
  
  13  12.340   7.042   5.892   4.107   3.565   2.617
      12.340   7.042   5.892   4.107   3.565   2.617
  
  14  13.339   7.790   6.571   4.660   4.075   3.041
      13.339   7.790   6.571   4.660   4.075   3.041
  
  15  14.339   8.547   7.261   5.229   4.601   3.483
      14.339   8.547   7.261   5.229   4.601   3.483
  
  16  15.338   9.312   7.962   5.812   5.142   3.942
      15.339   9.312   7.962   5.812   5.142   3.942
  
  17  16.338  10.085   8.672   6.408   5.697   4.416
      16.338  10.085   8.672   6.408   5.697   4.416
  
  18  17.338  10.865   9.390   7.015   6.265   4.905
      17.338  10.865   9.390   7.015   6.265   4.905
  
  19  18.338  11.651  10.117   7.633   6.844   5.407
      18.338  11.651  10.117   7.633   6.844   5.407
  
  20  19.337  12.443  10.851   8.260   7.434   5.921
      19.337  12.443  10.851   8.260   7.434   5.921
  
  21  20.337  13.240  11.591   8.897   8.034   6.447
      20.337  13.240  11.591   8.897   8.034   6.447
  
  22  21.337  14.041  12.338   9.542   8.643   6.983
      21.337  14.041  12.338   9.542   8.643   6.983
  
  23  22.337  14.848  13.091  10.196   9.260   7.529
      22.337  14.848  13.091  10.196   9.260   7.529
  
  24  23.337  15.659  13.848  10.856   9.886   8.085
      23.337  15.659  13.848  10.856   9.886   8.085
  
  25  24.337  16.473  14.611  11.524  10.520   8.649
      24.337  16.473  14.611  11.524  10.520   8.649
  
  26  25.336  17.292  15.379  12.198  11.160   9.222
      25.336  17.292  15.379  12.198  11.160   9.222
  
  27  26.336  18.114  16.151  12.879  11.808   9.803
      26.336  18.114  16.151  12.879  11.808   9.803
  
  28  27.336  18.939  16.928  13.565  12.461  10.391
      27.336  18.939  16.928  13.565  12.461  10.391
  
  29  28.336  19.768  17.708  14.256  13.121  10.986
      28.336  19.768  17.708  14.256  13.121  10.986
  
  30  29.336  20.599  18.493  14.953  13.787  11.588
      29.336  20.599  18.493  14.953  13.787  11.588
  
 Given Nfree and X, find probability:
  
 Nfree down, X values across
  
       1.000   2.000   5.000  10.000  20.000  30.000
  
  
   1   0.683   0.843   0.975   0.998   1.000   1.000
       0.683   0.843   0.975   0.998   1.000   1.000
  
   2   0.393   0.632   0.918   0.993   1.000   1.000
       0.393   0.632   0.918   0.993   1.000   1.000
  
   3   0.199   0.428   0.828   0.981   1.000   1.000
       0.199   0.428   0.828   0.981   1.000   1.000
  
   4   0.090   0.264   0.713   0.960   1.000   1.000
       0.090   0.264   0.713   0.960   1.000   1.000
  
   5   0.037   0.151   0.584   0.925   0.999   1.000
       0.037   0.151   0.584   0.925   0.999   1.000
  
   6   0.014   0.080   0.456   0.875   0.997   1.000
       0.014   0.080   0.456   0.875   0.997   1.000
  
   7   0.005   0.040   0.340   0.811   0.994   1.000
       0.005   0.040   0.340   0.811   0.994   1.000
  
   8   0.002   0.019   0.242   0.735   0.990   1.000
       0.002   0.019   0.242   0.735   0.990   1.000
  
   9   0.001   0.009   0.166   0.650   0.982   1.000
       0.001   0.009   0.166   0.650   0.982   1.000
  
  10   0.000   0.004   0.109   0.560   0.971   0.999
       0.000   0.004   0.109   0.560   0.971   0.999
  
  11   0.000   0.002   0.069   0.470   0.955   0.998
       0.000   0.002   0.069   0.470   0.955   0.998
  
  12   0.000   0.001   0.042   0.384   0.933   0.997
       0.000   0.001   0.042   0.384   0.933   0.997
  
  13   0.000   0.000   0.025   0.306   0.905   0.995
       0.000   0.000   0.025   0.306   0.905   0.995
  
  14   0.000   0.000   0.014   0.238   0.870   0.992
       0.000   0.000   0.014   0.238   0.870   0.992
  
  15   0.000   0.000   0.008   0.180   0.828   0.988
       0.000   0.000   0.008   0.180   0.828   0.988
  
  16   0.000   0.000   0.004   0.133   0.780   0.982
       0.000   0.000   0.004   0.133   0.780   0.982
  
  17   0.000   0.000   0.002   0.096   0.726   0.974
       0.000   0.000   0.002   0.096   0.726   0.974
  
  18   0.000   0.000   0.001   0.068   0.667   0.963
       0.000   0.000   0.001   0.068   0.667   0.963
  
  19   0.000   0.000   0.001   0.047   0.605   0.948
       0.000   0.000   0.001   0.047   0.605   0.948
  
  20   0.000   0.000   0.000   0.032   0.542   0.930
       0.000   0.000   0.000   0.032   0.542   0.930
  
  21   0.000   0.000   0.000   0.021   0.479   0.908
       0.000   0.000   0.000   0.021   0.479   0.908
  
  22   0.000   0.000   0.000   0.014   0.417   0.882
       0.000   0.000   0.000   0.014   0.417   0.882
  
  23   0.000   0.000   0.000   0.009   0.358   0.851
       0.000   0.000   0.000   0.009   0.358   0.851
  
  24   0.000   0.000   0.000   0.005   0.303   0.815
       0.000   0.000   0.000   0.005   0.303   0.815
  
  25   0.000   0.000   0.000   0.003   0.253   0.776
       0.000   0.000   0.000   0.003   0.253   0.776
  
  26   0.000   0.000   0.000   0.002   0.208   0.732
       0.000   0.000   0.000   0.002   0.208   0.732
  
  27   0.000   0.000   0.000   0.001   0.169   0.686
       0.000   0.000   0.000   0.001   0.169   0.686
  
  28   0.000   0.000   0.000   0.001   0.136   0.637
       0.000   0.000   0.000   0.001   0.136   0.637
  
  29   0.000   0.000   0.000   0.000   0.107   0.586
       0.000   0.000   0.000   0.000   0.107   0.586
  
  30   0.000   0.000   0.000   0.000   0.083   0.534
       0.000   0.000   0.000   0.000   0.083   0.534
  
 TEST12
 Test routines for computing Log(Gamma(X))
  
 Log of gamma function:
  
 X, Log(Gamma(X)), Gamln1, Gamln2, Gamln3
                   Gamln4
  
   0.200000       1.52406       1.52406       1.52406       1.52406    
                                1.52406    
   0.400000      0.796678      0.796678      0.796678      0.796677    
                               0.796679    
   0.600000      0.398234      0.398234      0.398234      0.398234    
                               0.398233    
   0.800000      0.152060      0.152060      0.152059      0.152059    
                               0.152059    
    1.00000      0.000000E+00  0.000000E+00  0.000000E+00  0.476837E-06
                              -0.496395E-06
    1.20000     -0.853738E-01 -0.853742E-01 -0.853739E-01 -0.853732E-01
                              -0.853744E-01
    1.40000     -0.119613     -0.119613     -0.119613     -0.119612    
                              -0.119612    
    1.60000     -0.112592     -0.112592     -0.112592     -0.112592    
                              -0.112592    
    1.80000     -0.710836E-01 -0.710839E-01 -0.710840E-01 -0.710840E-01
                              -0.710845E-01
    2.00000      0.000000E+00  0.000000E+00  0.238419E-06  0.476837E-06
                              -0.496395E-06
    10.0000       12.8018       12.8018       12.8018       12.8018    
                                12.8018    
    20.0000       39.3399       39.3399       39.3399       39.3399    
                                39.3399    
    30.0000       71.2570       71.2570       71.2570       71.2570    
                                71.2570    
  
 TEST13
 Test routines for incomplete gamma function.
  
 Y, P, Actual, Gamic1, Gamic2
               Gamic3, Gamic4
  
   0.316228E-01  0.100000      0.742026      0.742026      0.742027    
                                             0.742026      0.742026    
   0.316228      0.100000      0.911975      0.911975      0.911976    
                                             0.911975      0.911975    
    1.58114      0.100000      0.989896      0.989895      0.989896    
                                             0.989896      0.989896    
   0.707107E-01  0.500000      0.293128      0.293128      0.293128    
                                             0.293128      0.293128    
   0.707107      0.500000      0.765642      0.765642      0.765642    
                                             0.765642      0.765642    
    3.53553      0.500000      0.992166      0.992165      0.992166    
                                             0.992166      0.992166    
   0.100000       1.00000      0.951626E-01  0.951625E-01  0.951626E-01
                                             0.951626E-01  0.951626E-01
    1.00000       1.00000      0.632121      0.632120      0.632120    
                                             0.632121      0.632121    
    5.00000       1.00000      0.993262      0.993261      0.993262    
                                             0.993262      0.993262    
   0.104881       1.10000      0.757471E-01  0.757471E-01  0.757471E-01
                                             0.757471E-01  0.757471E-01
    1.04881       1.10000      0.607646      0.607646      0.607646    
                                             0.607646      0.607646    
    5.24404       1.10000      0.993343      0.993343      0.993342    
                                             0.993342      0.993342    
   0.141421       2.00000      0.910540E-02  0.910536E-02  0.910536E-02
                                             0.910537E-02  0.910537E-02
    1.41421       2.00000      0.413064      0.413064      0.413064    
                                             0.413065      0.413065    
    7.07107       2.00000      0.993145      0.993145      0.993145    
                                             0.993145      0.993145    
    2.44949       6.00000      0.387318E-01  0.387317E-01  0.387318E-01
                                             0.387319E-01  0.387319E-01
    12.2474       6.00000      0.982594      0.982590      0.982594    
                                             0.982594      0.982594    
    16.5831       11.0000      0.940427      0.940426      0.940427    
                                             0.940427      0.940427    
    25.4951       26.0000      0.486387      0.486387      0.486387    
                                             0.486389      0.486388    
    44.8219       41.0000      0.735971      0.735980      0.735970    
                                             0.735968      0.735968    
  
 TEST14
 Test CT1 and CNT1 for Student's T distribution.
  
    T, idf=1, 2, 3, 4
  
  
   0.100000      0.531726      0.535267      0.536674      0.537422    
                 0.531726      0.535267      0.536674      0.537422    
  
   0.200000      0.562833      0.570014      0.572865      0.574381    
                 0.562833      0.570014      0.572865      0.574381    
  
   0.300000      0.592774      0.603757      0.608118      0.610439    
                 0.592774      0.603757      0.608118      0.610439    
  
   0.400000      0.621119      0.636083      0.642032      0.645201    
                 0.621119      0.636083      0.642032      0.645201    
  
   0.500000      0.647584      0.666667      0.674276      0.678335    
                 0.647584      0.666667      0.674276      0.678335    
  
   0.600000      0.672021      0.695283      0.704599      0.709579    
                 0.672021      0.695283      0.704599      0.709579    
  
   0.700000      0.694400      0.721803      0.732836      0.738750    
                 0.694400      0.721803      0.732837      0.738750    
  
   0.800000      0.714777      0.746183      0.758901      0.765736    
                 0.714777      0.746183      0.758901      0.765736    
  
   0.900000      0.733262      0.768448      0.782774      0.790497    
                 0.733262      0.768448      0.782775      0.790497    
  
    1.00000      0.750000      0.788675      0.804499      0.813049    
                 0.750000      0.788675      0.804499      0.813050    
  
    1.10000      0.765146      0.806980      0.824158      0.833458    
                 0.765146      0.806980      0.824158      0.833458    
  
    1.20000      0.778858      0.823498      0.841869      0.851824    
                 0.778858      0.823498      0.841869      0.851824    
  
    1.30000      0.791286      0.838377      0.857766      0.868274    
                 0.791286      0.838377      0.857766      0.868274    
  
    1.40000      0.802568      0.851763      0.871996      0.882950    
                 0.802569      0.851763      0.871996      0.882950    
  
    1.50000      0.812833      0.863803      0.884708      0.896000    
                 0.812833      0.863803      0.884708      0.896000    
  
 TEST15
 Test routines for Owen's integral.
  
 H, A, Tha1(h,a), Tha2(h,a)
  
   0.100000      0.316228E-01  0.500615E-02  0.500615E-02
   0.100000      0.316228      0.484946E-01  0.484946E-01
   0.100000       1.58114      0.158993      0.158993    
   0.500000      0.707107E-01  0.991302E-02  0.991302E-02
   0.500000      0.707107      0.848662E-01  0.848662E-01
   0.500000       3.53553      0.152816      0.152816    
    1.00000      0.100000      0.960529E-02  0.960529E-02
    1.00000       1.00000      0.667419E-01  0.667419E-01
    1.00000       5.00000      0.793273E-01  0.793273E-01
    1.10000      0.104881      0.906200E-02  0.906200E-02
    1.10000       1.04881      0.597279E-01  0.597279E-01
    1.10000       5.24404      0.678327E-01  0.678327E-01
    2.00000      0.141421      0.298639E-02  0.298639E-02
    2.00000       1.41421      0.113565E-01  0.113565E-01
    2.00000       7.07107      0.113751E-01  0.113751E-01
    6.00000       2.44949      0.493294E-09  0.493294E-09
    6.00000       12.2474      0.493294E-09  0.493294E-09
    11.0000       16.5831      0.955332E-28  0.955332E-28
    26.0000       25.4951      0.000000E+00  0.000000E+00
    41.0000       44.8219      0.000000E+00  0.000000E+00
  
 TEST16
 Test two routines for binomial distributions.
  
 Set the probability of a head to   0.5000000    
  
 Results from Ibino1 and Ibino2:
 Number of heads in           20 tosses
 carried out         1000 times.
  
            0           0           0
            1           0           0
            2           0           1
            3           1           1
            4           3           3
            5          17          14
            6          35          42
            7          73          71
            8         118         103
            9         150         149
           10         193         187
           11         148         165
           12         120         118
           13          80          81
           14          45          42
           15          12          18
           16           3           5
           17           2           0
           18           0           0
           19           0           0
           20           0           0
  
 Results from Igeo1
 Number of heads before first tail
 Results for         1000 trials:
  
            0         511
            1         234
            2         119
            3          75
            4          29
            5          15
            6           9
            7           6
            8           1
            9           0
           10           0
           11           1
  
 TEST17
 Test UniSph
 Compute some points on an N sphere.
  
 N=           3
   0.4805577      0.7146782     -0.5082313    
 Radius=  0.9999999    
  
 N=          10
 Radius=   1.000000