FLT_EPSILON > 5.42101e-20
Dariusz Linda
Can anyone tell me please, why FLT_EPSILON, wchich is 1.19209290e-07
in MSVC and GCC, is actually NOT the smallest value such that 1.0 +
FLT_EPSILON != 1.0. A simple computation:
float eps = 1.0;
while (eps + 1.0 != 1.0) eps *= 0.5;
shows that it's value should be 5.42101e-20.
thanks
D.L.
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Jean-Marc Bourguet
> Hi!
> Can anyone tell me please, why FLT_EPSILON, wchich is 1.19209290e-07
> in MSVC and GCC, is actually NOT the smallest value such that 1.0 +
> FLT_EPSILON != 1.0. A simple computation:
> float eps = 1.0;
> while (eps + 1.0 != 1.0) eps *= 0.5;
> shows that it's value should be 5.42101e-20.
Three reasons:
1/ there is a promotion to double in the expressions you are giving,
2/ C standard allows for intermediate computations to be done in a more
precise type than their static type
3/ rounding can also account for a factor 2 (the true definition is "the
difference between 1 and the next representable floating point number",
which doesn't depend on rounding).
Yours,
--
Jean-Marc
Keith Thompson
> Can anyone tell me please, why FLT_EPSILON, wchich is 1.19209290e-07
> in MSVC and GCC, is actually NOT the smallest value such that 1.0 +
> FLT_EPSILON != 1.0. A simple computation:
> float eps = 1.0;
> while (eps + 1.0 != 1.0) eps *= 0.5;
> shows that it's value should be 5.42101e-20.
For one thing, that's not how FLT_EPSILON is defined. See C99
5.2.4.2.2p10. It's "the difference between 1 and the least value
greater than 1 that is representable in the given floating point
type". (K&R2 gets this wrong, or at least disagrees with the
standard.)
For another, the expressions ``eps + 1.0'' and ``1.0'' are of type
double, not float. And even if you replace 1.0 by 1.0f, the
implementation is permitted to evaluate intermediate expressions in
greater precision.
You can avoid this by storing the result of ``eps + 1.0'' in an object
before comparing it, but when I tried this I still got a result that
was off by a factor of 2 due to rounding issues.
--
Keith Thompson (The_Other_Keith) ks...@mib.org <http://www.ghoti.net/~kst>
Nokia
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Hans-Bernhard Bröker
> Can anyone tell me please, why FLT_EPSILON, wchich is 1.19209290e-07
> in MSVC and GCC, is actually NOT the smallest value such that 1.0 +
> FLT_EPSILON != 1.0.
Ultimately because that's the definition of DBL_EPSILON, not FLT_EPSILON
you're quoting. The definition of FLT_EPSILON would have a formula like
(float)(1.0f + FLT_EPSILON) != 1.0f
in it.
> float eps = 1.0;
> while (eps + 1.0 != 1.0) eps *= 0.5;
> shows that it's value should be 5.42101e-20.
No. That computes DBL_EPSILON if you're lucky. The result suggests
you're not.
Barry Schwarz
<darius...@gmail.com> wrote:
>Hi!
>Can anyone tell me please, why FLT_EPSILON, wchich is 1.19209290e-07
>in MSVC and GCC, is actually NOT the smallest value such that 1.0 +
>FLT_EPSILON != 1.0. A simple computation:
>float eps = 1.0;
>while (eps + 1.0 != 1.0) eps *= 0.5;
Everything is converted to doubles. If you want to perform float
arithmetic, use 1.0f etc.
>shows that it's value should be 5.42101e-20.
>
>thanks
>D.L.
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Alan Curry
Dariusz Linda <darius...@gmail.com> wrote:
>Hi!
>Can anyone tell me please, why FLT_EPSILON, wchich is 1.19209290e-07
>in MSVC and GCC, is actually NOT the smallest value such that 1.0 +
>FLT_EPSILON != 1.0. A simple computation:
>float eps = 1.0;
>while (eps + 1.0 != 1.0) eps *= 0.5;
1.0 is a double, so your addition and comparison are done as doubles. Change
both instances of 1.0 to 1.0f and try again. eps will end up being half of
FLT_EPSILON, since the value you want is actually the one that was present on
the next-to-last pass through the loop (which passed the "add to 1" test)
rather than the final pass through the loop (which failed the "add to 1"
test).
--
Alan Curry
Jasen Betts
> Hi!
> Can anyone tell me please, why FLT_EPSILON, wchich is 1.19209290e-07
> in MSVC and GCC, is actually NOT the smallest value such that 1.0 +
> FLT_EPSILON != 1.0. A simple computation:
> float eps = 1.0;
> while (eps + 1.0 != 1.0) eps *= 0.5;
> shows that it's value should be 5.42101e-20.
you're using doubles (or worse) for the computation.
#include <stdio.h>
int main()
{
float a=1;
float b=1;
a+=(1.19209290e-07/2);
printf("a=%f b=%f a-b=%f a=b:%d\n",a,b,a-b,a=b);
return 0;
Thomas Richter
> Hi!
> Can anyone tell me please, why FLT_EPSILON, wchich is 1.19209290e-07
> in MSVC and GCC, is actually NOT the smallest value such that 1.0 +
> FLT_EPSILON != 1.0. A simple computation:
> float eps = 1.0;
> while (eps + 1.0 != 1.0) eps *= 0.5;
> shows that it's value should be 5.42101e-20.
Note that 1.0 is a double, not a float, so the expression eps + 1.0 is
evaluated by first converting eps to a double. Instead, you should use:
while (eps + 1.0f != 1.0f) eps *= 0.5;
Greetings,
Thomas