Complex bakeoff - example 4

[Harry H. Cheng]

> Complex bakeoff - example 4                              10/13/95     10:02 AM
> 
> In "Augmenting a Programming Language with Complex Arithmetic" (NCEG/91-039), 
> W. Kahan and I presented two examples illustrating how the sign of zero 
> can be used to distinguish the two sides of a branch cut to simplify the 
> conceptualization and coding for problems involving branch cuts.  Bakeoff 
> example 3 covered the first of these examples.  This bakeoff example 4 covers 
> the second one.  In both examples, a simple, straightforward program solves
> the 
> problem, but the program depends on consistent treatment of the sign of zero. 
> 
> For both examples, the paper contains a plot showing the bad affects on the 
> program of treating -0 like +0.  This example better suggests the potential
> challenge of debugging and fixing such a program failure.
> 
> For comparison purposes, how might one code this example for a system 
> which does not support the sign of zero? 
> Does the code become more
> complicated 
> or less efficient?  What is the effort to devise the workaround?  See Harry H.
> Cheng's 
> "Handling of Complex Numbers in the C^H Programming Language" (X3J11.1/93-020)
> 
> for a detailed analysis of this example.


Your program can run in an implementation of complex system
with the sign of zero being ignored without any problem. 
The round-off error from pi will eat your sign of zero.

Jim, I am just wondering what will be your next example. :-)

> 
> Example 4


...
> const double    pi      = 4 * atan(1.0);
> const double    dtheta  = pi / (2 * M); // Angle between radial lines   
...
>                         z = g(n * drho * exp(I * m * dtheta));


Harry Cheng
UC Davis

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