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Re: How Computers Represent Floats [message #22751 is a reply to message #22640]

Fri, 01 December 2000 00:00

Karl Schultz
Messages: 341
Registered: October 1999

Senior Member

Here's another useful table if anyone is interested in pondering the
limits of floating point representations:

32-bit(single) 64-bit(double)
Mantissa 24 bits 53 bits
Exponent 8 bits 11 bits
EPS 1.19209e-007 2.22045e-016
Min 1.17549e-038 2.22507e-308
Max 3.40282e+038 1.79769e+308
Decimal Places 6 15

80-bit 128-bit(quad)
Mantissa 65 bits 113 bits
Exponent 15 bits 15 bits
EPS 1.08420e-019 1.92593e-034
Min 3.36210e-4932 3.36210e-4932
Max 1.18973e+4932 1.18973e+4932
Decimal Places 18 33

The mantissa bit counts include the sign bit.

I find it a little interesting that the number of bits in the exponent
remains the same between 80-bit and 128-bit.

I also think that the EPS (machine epsilon or machine precision) is
probably one of the most important values. It is the smallest value
that you can add to 1.0 and still have the result be something other
than 1.0. This can give you an idea of how closely you can resolve
(differentiate) floating point values at a given magnitude.

For example, see what this does in IDL 5.3:
PLOT,FINDGEN(100),FINDGEN(100)+2d8,YSTYLE=3

IDL 5.4 gives different results because PLOT works in double
precision. You can "simulate" the old 5.3 behavior with:

PLOT,FINDGEN(100),FLOAT(FINDGEN(100)+2d8), YSTYLE=3

Karl

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[Message index]

		How Computers Represent Floats By: davidf on Wed, 29 November 2000 00:00
		Re: How Computers Represent Floats By: Karl Schultz on Fri, 01 December 2000 00:00
		Re: How Computers Represent Floats By: colinr on Fri, 01 December 2000 00:00

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