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From: Dennis Lee Bieber <wlfraed@ix.netcom.com>
Subject: Re: Exact integer-valued floats
Date: Fri, 21 Sep 2012 16:26:26 -0400
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Xref: csiph.com comp.lang.python:29676

On 21 Sep 2012 17:29:13 GMT, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> declaimed the following in
gmane.comp.python.general:

> 
> The question is, what is the largest integer number N such that every 
> whole number between -N and N inclusive can be represented as a float?
>
	Single precision commonly has 7 significant (decimal) digits. Double
precision runs somewhere between 13 and 15 (decimal) significant digits 

> If my tests are correct, that value is 9007199254740992.0 = 2**53.
>

	For an encoding of a double precision using one sign bit and an
8-bit exponent, you have 53 bits available for the mantissa. This
ignores the possibility of an implied msb in the mantissa (encodings
which normalize to put the leading 1-bit at the msb can on some machines
remove that 1-bit and shift the mantissa one more place; effectively
giving a 54-bit mantissa). Something like an old XDS Sigma-6 used
non-binary exponents (exponent was in power of 16 <> 2^4) and used
"non-normalized" mantissa -- the mantissa could have up to three leading
0-bits); this affected the decimal significance...


-- 
	Wulfraed                 Dennis Lee Bieber         AF6VN
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