``Computer Literacy'' Assignment}

1. Write a Fortran subroutine to implement a linear 
   congruential generator with a modulus of $2^{31}-1$ and 
   a multiplier of 397204094.  For a test, generate ten 
   numbers starting with a seed of 1. 

2. Write a Fortran subroutine to implement a linear 
   congruential generator with a modulus of $2^{31}-1$ and 
   a multiplier of 16807, that will generate two separate 
   streams 10,000 numbers apart.  For a test, generate ten 
   numbers in each stream, starting with a seed of 1. 

3. Write a program to determine the smallest and largest relative 
   spacings.  Use it to determine them on the Silicon Graphics  
   machines. 

4. Write a program to determine the bit pattern of $+\infty$,  
   $-\infty$, and NaN on a computer that implements the IEEE 
   binary standard.  (This may be harder than it seems.) 

5. Find a Fortran routine somewhere on the net to compute the 
   incomplete gamma integral:  

       \int_0^x t^{\alpha -1} e^{-t/\beta} \, dt 

   (Hint: the {\sl Applied Statistics} routines in {\tt apstat} 
   at {\tt statlib} just might have one.  There are actually 2 
   such routines there; use the better one -- it's the later one.)  
   Obtain the subroutine and any necessary additional subroutines.  
   Evaluate the incomplete gamma for $\alpha = 5$ and $\beta = 2$  
   at the point 3.  (The routine your get may not have a $\beta$ 
   parameter; if it doesn't have that parameter, the value is 1; 
   so that's OK, a little calculus will allow you to use any value 
   of $\beta$ (it's just a scale parameter). 

Add an entry to your Web page for ``Assignment 2'', in which you give 
the computed results from each question above.