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Re: About the bits reserved for float variable [message #39505 is a reply to message #39504]

Fri, 21 May 2004 08:00

James Kuyper
Messages: 425
Registered: March 2000

Senior Member

Nuno Oliveira wrote:
> I looking at the Chapter 5 of the Bulding Aplication.
>
> It says, for float variables that it's a 32 bits number in the range of
> +/-10^38 withe approximately six or seven decimal places of significance.
> What I'm missing here? How can a number 32 bit number range between -10^38
> and +10^38?

It can do that by not representing every integer value in that range. A
32-bit type can represent a maximum of 2^32 different values. An
ordinary 32 bit integer type represents 2^32 consecutive integer values.
A 32-bit IEEE format floating point number represents a slightly smaller
set of values (because some of the bit patters represent +infinity,
-infinity, denormalized numbers, and NaNs), but those values are very
closely spaced near 0, and more widely spaced out the larger the values
are, which allows them to cover a much larger dynamic range.

To be specific, an IEEE format number contains a sign bit, a mantissa,
an exponent, and has an implicit offset which is used to interpret the
value. The value represented by such a number is

(-1)^sign *(1 + mantissa/2^n)*2^(exponent+offset)

where 'n' is the number of bits in the mantissa, and offset is negative.
Note that this formula provides no way to represent 0 (the mantissa is
never negative). As a special exception, a mantissa and exponent that
are both zero are treated as representing 0, rather than 2^offset, which
is what the general formula would call for.

Thus, for any given value of 'k' within a certain range, this format can
represent exactly 2^n different value x in the range 2^k <= x < 2^k+1,
evenly spaced within that interval.

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[Message index]

		Re: About the bits reserved for float variable By: George N. White III on Sat, 22 May 2004 05:01
		Re: About the bits reserved for float variable By: Kenneth P. Bowman on Fri, 21 May 2004 15:22
		Re: About the bits reserved for float variable By: David Fanning on Fri, 21 May 2004 08:07
		Re: About the bits reserved for float variable By: James Kuyper on Fri, 21 May 2004 08:00
		Re: About the bits reserved for float variable By: Paul Van Delst[1] on Fri, 21 May 2004 07:44
		Re: About the bits reserved for float variable By: Chris Lee on Fri, 21 May 2004 07:36
		Re: About the bits reserved for float variable By: Nuno Oliveira on Tue, 25 May 2004 10:08

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