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Re: infinities reformulated

This page is part of the web mail archives of SRFI 70 from before July 7th, 2015. The new archives for SRFI 70 contain all messages, not just those from before July 7th, 2015.

 | From: Aubrey Jaffer <agj@xxxxxxxxxxxx>
 | Date: Wed, 25 May 2005 23:19:48 -0400 (EDT)
 | Transcendental functions can return irrational numbers which cannot
 | be distinguished from each other when represented by finite length
 | decimal strings.  Thus the precision of an inexact (or exact)
 | number representation cannot be unlimited.
 | But exponent size does not suffer from the same limitation.  An
 | inexact number representation with big exponents will never
 | overflow into an infinity.  Infinities will result only from
 | operations on infinities or limit points.  Thus there would be no
 | continuity between the rational flonums and infinities; which bodes
 | poorly for LIMIT.

Increasing exponent sizes without increasing precision has some
problems.  With IEEE-754 flonums it is already the case that:

(atan 1 0)                      ==> 1.5707963267948965
(tan 1.5707963267948965)        ==> 16.331778728383844e15
(tan 1.5707963267948966)        ==> 16.331778728383844e15
(tan 1.5707963267948967)        ==> -6.218352966023783e15

The mantissa does not have enough precision so that there would exist
a number which makes TAN return 1/0.  This sort of problem gets worse
if exponents alone are expanded.