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*To*: srfi-70@xxxxxxxxxxxxxxxxx*Subject*: Re: infinities reformulated*From*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Date*: Thu, 26 May 2005 17:50:55 -0400 (EDT)*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <20050526031948.53ECE1B77B4@xxxxxxxxxxxxxxxx> (message from Aubrey Jaffer on Wed, 25 May 2005 23:19:48 -0400 (EDT))*References*: <20050525014828.708C41332@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> <20050526031948.53ECE1B77B4@xxxxxxxxxxxxxxxx>

| 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.

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