Contents
Why are floats so inaccurate?
Because often-times, they are approximating rationals that cannot be represented finitely in base 2 (the digits repeat), and in general they are approximating real (possibly irrational) numbers which may not be representable in finitely many digits in any base.
Are Floating point comparisons reliable?
The floating point comparison is not similar to the integer comparison. To compare two floating point values, we have to consider the precision in to the comparison. For example, if two numbers are 3.1428 and 3.1415, then they are same up to the precision 0.01, but after that, like 0.001 they are not same.
What’s the problem with using = = to compare floats?
Using == to compare two floats/doubles/any decimal type number can potentially cause problems because of the way they are stored. A single-precision float (as per IEEE standard 754) has 32 bits, distributed as follows: 23 bits – Mantisa. The actuall number that is stored. The mantisa is what causes the problem.
How can I compare two floating point numbers?
In the above example, we can see the inaccuracy in comparing two floating-point numbers using “==” operator. The two numbers ‘a’ and ‘b’ are equal ( as (0.3 * 3) + 0.1 = 1 ) but the program results in an incorrect output. Let’s take a closer look at the numbers in the next snippet.
Is it OK to compare two floats for equality?
You should be aware that if you are comparing two floats for equality, you are intrinsically doing the wrong thing. Adding a slop factor to the comparison is not good enough. You should use the standard define in float.h: [EDIT: Made it just a little bit more readable.]
Can a ULP be used to compare floating point numbers?
ULPs are the wrong tool to compare values near or across zero, as we’ll see below. Almost all modern CPUs use two’s complement arithmetic, while floats use signed magnitude . Converting one format to the other in order to meaningfully add or subtract differently-signed values requires some extra work.