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Re: Two specific suggestions.
| From: Bradley Lucier <lucier@xxxxxxxxxxxxxxx>
| Date: Wed, 18 May 2005 22:39:14 +0200
| 1. I believe that every numerical value should have an external
Is not-a-number numerical?
SRFI-70 specifies notation for the two unique real infinities.
It also specs a single (optional) notation for 0/0, but is not as
emphatic about its uniqueness. Reading and writing 0/0 is not very
useful, because it is an error waiting to happen.
| There are many different NaNs (the only requirement is that the
| biased exponent field should be a maximum and the mantissa field be
| nonzero), so it should be possible to specify or determine this
| information about a NaN from its external representation.
The previous implementation of SCM was transparent to IEEE floats.
This lead to strange numbers like 0/0+3i which have no sensible
That period of experimentation over, SRFI-70 reins in infinities to
just three, two of which are very compatible with standard analytical
use. That the mathematical limit can be implemented as a procedure is
evidence of the power of this paradigm.
Just because more codes are available in IEEE-754 format does not mean
that using them will have more fidelity with mathematics.
| 2. If Scheme really wants to get serious about floating-point
| arithmetic, one should be able to specify the precision of
| floating- point operations. "One-precision-fits-all" doesn't cut
| it for serious code.
For i686 platforms "gcc -O3" compiles floating point calculations to
use 80-bit float representation. Reducing the precision of scalar
operands nets no speed increase from floating-point hardware.
But reducing the size of arrayed floating point numbers does increase
speed because of their smaller cache footprints. The homogeneous
arrays of SRFI-63 provide such size reductions.
Serious floating point calculations should use the vectorized
floating-point units many CPUs offer. This could be accomplished by
extending Scheme's arithmetic procedures to operate on the homogeneous
arrays of SRFI-63. Because the overhead would be amortized over many
scalar calculations, type dispatch could be done at runtime, incurring
a negligible speed penalty.