Floating point technical question
Author
What is the biggest error in representing a float (or double)? ie what is the biggest gap between any two consecutive representable numbers?
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I am not the Iraqi information minister.
My memory is a bit off and I''m lazy, so these mightn''t be quite right:
IEEE floats: 2105, give or take a few orders of magnitude.
IEEE doubles: 2971, give or take a few orders of magnitude.
If you want to get the numbers exactly, you can find the format here.
IEEE floats: 2105, give or take a few orders of magnitude.
IEEE doubles: 2971, give or take a few orders of magnitude.
If you want to get the numbers exactly, you can find the format here.
The values are also defined in the <float.h> header as Epsilon:
--
Simon O''Connor
ex -Creative Asylum
Programmer &
Microsoft MVP
#define DBL_EPSILON 2.2204460492503131e-016 /* smallest such that 1.0+DBL_EPSILON != 1.0 */#define FLT_EPSILON 1.192092896e-07F /* smallest such that 1.0+FLT_EPSILON != 1.0 */ --
Simon O''Connor
ex -Creative Asylum
Programmer &
Microsoft MVP
quote:Original post by walkingcarcass
What is the biggest error in representing a float (or double)? ie what is the biggest gap between any two consecutive representable numbers?
It''s not a constant number. This is because you only get a constant amount of mantessa, even though the exponent changes. So say you have 23 bits of mantessa in a float, that means that if your exponent is 0(representing numbers in the range 0-1), the space between adjacent numbers is 2^-24. However, if your exponent is 100(let''s say), then the space between adjacent numbers is 2^(-24+100).
Author
quote:#define DBL_EPSILON 2.2204460492503131e-016 /* smallest such that 1.0+DBL_EPSILON != 1.0 */#define FLT_EPSILON 1.192092896e-07F /* smallest such that 1.0+FLT_EPSILON != 1.0 */ [/code
Great, but does it hold for, say, 100000000+FLT_EPSILON!=100000000 or 0.000000001+FLT_EPSILON!=0.000000001?
********
I am not the Iraqi information minister.
Since it appears you didn''t infer it from my previous post, the distance between a floating point number and it''s successor is
2^(exponent-#of mantessa bits)
32 bit floats have 23 bits of mantessa. I don''t remember off hand how many bits doulbes have, it''s probably about 51.
2^(exponent-#of mantessa bits)
32 bit floats have 23 bits of mantessa. I don''t remember off hand how many bits doulbes have, it''s probably about 51.
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