1Test of erf(x) vs double series expansion


   2000 Random arguments were tested from the interval (  0.000,  0.469)


    ERF(X) was larger  1589 times,
               agreed   383 times, and
          was smaller    28 times.


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


 The maximum relative error of     0.2701E-06 =    2 ** -21.82
    occurred for X = 0.302275E+00
 The estimated loss of base   2 significant digits is   2.18


 The root mean square relative error was     0.1064E-06 =    2 ** -23.16
 The estimated loss of base   2 significant digits is   0.84





 Test of erfc(x) vs exp(x+1/4) SUM i^n erfc(x+1/2)


   2000 Random arguments were tested from the interval (  0.469,  2.000)


   ERFC(X) was larger   881 times,
               agreed   397 times, and
          was smaller   722 times.


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


 The maximum relative error of     0.6285E-06 =    2 ** -20.60
    occurred for X = 0.167592E+01
 The estimated loss of base   2 significant digits is   3.40


 The root mean square relative error was     0.1825E-06 =    2 ** -22.39
 The estimated loss of base   2 significant digits is   1.61


1Test of exp(x*x) erfc(x) vs SUM i^n erfc(x+1/2)


   2000 Random arguments were tested from the interval (  0.469,  2.000)


  ERFCX(X) was larger   651 times,
               agreed   624 times, and
          was smaller   725 times.


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


 The maximum relative error of     0.4512E-06 =    2 ** -21.08
    occurred for X = 0.191992E+01
 The estimated loss of base   2 significant digits is   2.92


 The root mean square relative error was     0.1206E-06 =    2 ** -22.98
 The estimated loss of base   2 significant digits is   1.02





 Test of erfc(x) vs exp(x+1/4) SUM i^n erfc(x+1/2)


   2000 Random arguments were tested from the interval (  2.000,  8.688)


   ERFC(X) was larger  1040 times,
               agreed   431 times, and
          was smaller   529 times.


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


 The maximum relative error of     0.7071E-06 =    2 ** -20.43
    occurred for X = 0.224736E+01
 The estimated loss of base   2 significant digits is   3.57


 The root mean square relative error was     0.1636E-06 =    2 ** -22.54
 The estimated loss of base   2 significant digits is   1.46


1Test of exp(x*x) erfc(x) vs SUM i^n erfc(x+1/2)


   2000 Random arguments were tested from the interval (  2.000, 20.000)


  ERFCX(X) was larger   508 times,
               agreed   997 times, and
          was smaller   495 times.


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


 The maximum relative error of     0.4161E-06 =    2 ** -21.20
    occurred for X = 0.244657E+01
 The estimated loss of base   2 significant digits is   2.80


 The root mean square relative error was     0.7756E-07 =    2 ** -23.62
 The estimated loss of base   2 significant digits is   0.38


1Special Tests


       Estimated loss of base  2significant digits in

   X     Erf(x)+Erf(-x)   Erf(x)+Erfc(x)-1   Erfcx(x)-exp(x*x)*erfc(x)

  0.000            0.00            0.00            0.00
 -0.500            0.00            0.00            0.00
 -1.000            0.00            0.00            0.68
 -1.500            0.00            0.00            0.78
 -2.000            0.00            0.00            0.00
 -2.500            0.00            0.00            0.00
 -3.000            0.00            0.00            0.00
 -3.500            0.00            0.00            0.00
 -4.000            0.00            0.00            0.00
 -4.500            0.00            0.00            0.00


 Test of special arguments


   ERF ( 0.340282E+39) =  0.100000E+01


   ERF ( 0.000000E+00) =  0.000000E+00


  ERFC ( 0.000000E+00) =  0.100000E+01


  ERFC (-0.340282E+39) =  0.200000E+01


 Test of Error Returns



 ERFC will be called with the argument 0.689591E+01
 This should not underflow


 ERFC returned the value 0.180358E-21



 ERFC will be called with the argument 0.919456E+01
 This may underflow


 ERFC returned the value 0.000000E+00



 ERFCX will be called with the argument 0.449962E+38
 This should not underflow


 ERFCX returned the value 0.125386E-37



 ERFCX will be called with the argument-0.844417E+01
 This should not overflow


 ERFCX returned the value 0.185345E+32



 ERFCX will be called with the argument-0.938243E+01
 This may overflow


 ERFCX returned the value 0.340000E+39



 This concludes the tests
