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    Re: Barrie Hudson Challenge
    From: Dan Allen
    Date: 2002 Nov 9, 10:46 -0800

    On Saturday, November 9, 2002, at 01:38 AM, Peter Fogg wrote:
    
    > I have no idea why the course is different.
    
    It is due to trig rounding problems.  Cos(n) as n approaches zero, or
    Sin(n) as n approaches 90 degrees are interesting to watch converge to
    1.
    
    Using high accuracy 80-bit trig functions (accurate to 1 ulp at 18
    decimal digits):
    
    Cos(0.1)    = 0.999998476913287699
    Cos(0.01)   = 0.999999984769129049
    Cos(0.001)  = 0.999999999847691290
    Cos(0.0001) = 0.999999999998476913
    
    Note that with each factor of ten in the argument (.1 to .01, .01 to
    .001, etc.) the result is 100 times closer to unity!
    
    If you have arguments in your equations which approach zero as an
    argument to cosine or approach 90 degrees as an argument to sine, it is
    often best to use the complement functions to maintain accuracy.
    
    Dan
    
    
    

       
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