# checking for close enough floating point values.

Discussion in 'C Programming' started by pereges, May 29, 2008.

1. ### peregesGuest

Let's say I have two doubles:

double a, b;

a = 9.35678910034592
b = 9.35678925602334

Obviously, a < b but lets say I just want to check up to 6 places
after the decimal. I want to check if the condition a >= b is
satisfied. I have a tolerance value:

#define EPSILON 0.000001

Is this a good way to check for a >= b

if( fabs(a-b) <= EPSILON)
....

pereges, May 29, 2008

2. ### Guest

On May 29, 8:30 pm, pereges <> wrote:
> Let's say I have two doubles:
>
> double a, b;
>
> a = 9.35678910034592
> b = 9.35678925602334
>
> Obviously, a < b but lets say I just want to check up to 6 places
> after the decimal. I want to check if the condition a >= b is
> satisfied. I have a tolerance value:
>
> #define EPSILON 0.000001
>
> Is this a good way to check for a >= b
>
> if( fabs(a-b) <= EPSILON)
> ...

Question 14.5 of the C-FAQ.
<http://c-faq.com/>

, May 29, 2008

3. ### Walter RobersonGuest

In article <>,
pereges <> wrote:
>Let's say I have two doubles:

>double a, b;

>a = 9.35678910034592
>b = 9.35678925602334

>Obviously, a < b but lets say I just want to check up to 6 places
>after the decimal. I want to check if the condition a >= b is
>satisfied. I have a tolerance value:

>#define EPSILON 0.000001

>Is this a good way to check for a >= b

>if( fabs(a-b) <= EPSILON)
>...

That is a typical way to check whether values are "close enough"
to being equal.

However, you should be aware that this is -not- a test for
equality up to the 6th decimal place. There is no exact representation
for 0.000001 in binary floating point arithmetic, so chances
are that instead if you use that EPSILON, what you will end up doing is
checking whether they are equal to within
9.99999999999999954748111825886258685613938723690807819366455078125e-07

That's a number slightly less than 0.000001. This could make a difference
if your a and b values were (for example) on the order of .00009 themselves.

--
"Beauty, like all other qualities presented to human experience,
is relative; and the definition of it becomes unmeaning and
useless in proportion to its abstractness." -- Walter Pater

Walter Roberson, May 29, 2008
4. ### Barry SchwarzGuest

On Thu, 29 May 2008 10:30:49 -0700 (PDT), pereges <>
wrote:

>Let's say I have two doubles:
>
>double a, b;
>
>a = 9.35678910034592
>b = 9.35678925602334
>
>Obviously, a < b but lets say I just want to check up to 6 places
>after the decimal. I want to check if the condition a >= b is
>satisfied. I have a tolerance value:
>
>#define EPSILON 0.000001
>
>Is this a good way to check for a >= b
>
>if( fabs(a-b) <= EPSILON)
>...

This checks for a == b, not a >= b.

if (a + EPSILON >= b) would be the corresponding check for >=.

However, you should read 14.5 in the c-faq (www.c-faq.com) to see why
an unscaled EPSILON is a bad idea.

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Barry Schwarz, May 30, 2008
5. ### peregesGuest

On May 30, 9:52 am, Barry Schwarz <> wrote:

> This checks for a == b, not a >= b.
>
> if (a + EPSILON >= b) would be the corresponding check for >=.
>
> However, you should read 14.5 in the c-faq (www.c-faq.com) to see why
> an unscaled EPSILON is a bad idea.

So do you think it will be better to use the relative difference
method as suggested in the C faq 14.5 ?

#define Abs(x) ((x) < 0 ? -(x) : (x))
#define Max(a, b) ((a) > (b) ? (a) : (b))

double RelDif(double a, double b)
{
double c = Abs(a);
double d = Abs(b);

d = Max(c, d);

return d == 0.0 ? 0.0 : Abs(a - b) / d;
}

....
to check for a >= b,

if(RelDif(a, b) <= TOLERANCE || a > b)
...

Btw the floating point data that I'm reading has 6 places after the
decimal point so I though I would take a tolerance value of 0.000001.

pereges, May 30, 2008
6. ### peregesGuest

I don't know why a seperate macro has been written for finding
absolute value. Was it not possible to use fabs() ?

#define Abs(x) ((x) < 0 ? -(x) : (x))

pereges, May 30, 2008
7. ### BartcGuest

"Barry Schwarz" <> wrote in message
news:...
> On Thu, 29 May 2008 10:30:49 -0700 (PDT), pereges <>
> wrote:
>
>>Let's say I have two doubles:
>>
>>double a, b;
>>
>>a = 9.35678910034592
>>b = 9.35678925602334
>>
>>Obviously, a < b but lets say I just want to check up to 6 places
>>after the decimal. I want to check if the condition a >= b is
>>satisfied. I have a tolerance value:
>>
>>#define EPSILON 0.000001
>>
>>Is this a good way to check for a >= b
>>
>>if( fabs(a-b) <= EPSILON)
>>...

>
> This checks for a == b, not a >= b.
>
> if (a + EPSILON >= b) would be the corresponding check for >=.

if ( a>b || (fabs(a-b)<=EPSILON) )

for a>=b ? This would be faster when a is normally expected to be greater
than b.

--
Bartc

Bartc, May 30, 2008
8. ### Barry SchwarzGuest

On Fri, 30 May 2008 02:07:53 -0700 (PDT), pereges <>
wrote:

>On May 30, 9:52 am, Barry Schwarz <> wrote:
>
>> This checks for a == b, not a >= b.
>>
>> if (a + EPSILON >= b) would be the corresponding check for >=.
>>
>> However, you should read 14.5 in the c-faq (www.c-faq.com) to see why
>> an unscaled EPSILON is a bad idea.

>
>So do you think it will be better to use the relative difference
>method as suggested in the C faq 14.5 ?
>

snip

>Btw the floating point data that I'm reading has 6 places after the
>decimal point so I though I would take a tolerance value of 0.000001.

If you can guarantee that all the data will be within a certain range
then you don't need to scale based on the current value. But what
happens when one set of values is near 1e-6 and another is near 1e10?
That is the point I thought the faq was trying to make.

Remove del for email

Barry Schwarz, May 31, 2008