Re: [Scheme-reports] Numerical example (real? -2.5+0.0i)

[Aubrey Jaffer <agj@x>]

 | Date: Tue, 16 Aug 2011 14:25:11 -0400
 | From: John Cowan <cowan@x>
 | 
 | Aubrey Jaffer scripsit:
 | 
 | > Algebraically, the complex numbers are the field of reals extended by
 | > a solution of x^2+1=0.  All reals are complex; there is no difference
 | > between real 2.0 and 2.0+0.0i.
 | 
 | I used the term "general complex number" in the same sense it is used
 | in R5RS, to mean a number whose imaginary part is nonzero.
 | 
 | > FreeSnell <http://people.csail.mit.edu/jaffer/FreeSnell> is a Scheme
 | > application for computing the optical properties of thin-films.  It
 | > uses complex numbers intensively in its computations.  The only
 | > effects of distinguishing real real from complex real numbers would be
 | > to increase its storage and reduce its performance.
 | 
 | I don't understand this.  How can either storage or performance depend
 | on the result returned by the real? procedure?

In SCM, inexacts are created by the C procedure:

  SCM makdbl(double x, double y).

If y is nonzero then 16.B are allocated and a tc_dblc is returned.
Otherwise only 8.B are allocated and a tc_dblr is returned.

( Actually, if x fits in a 32.bit float without loss of accuracy when
  converting back to double, then a 32.bit float is put in the CDR of
  the header cell and no malloc() is done. )

Making "complex reals" occupy 16.B would increase the storage used and
make every mathematical operation on them slower because complex
operations are more complicated than real ones.

I could play games with type bits, but with 6 internal numeric types
already (INUM, flo, dblr, dblc, bigpos, and bigneg), modifying all the
numeric dispatch code would require significant effort, all for a
distinction which I have neither wanted nor needed in years of heavy
complex-number crunching.

 | > So no, SCM won't be distinguishing "real reals" from "complex reals".

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