Fortran中的浮点运算

Question

I've inherited some Fortran code that I'm trying to make sense of. It uses REAL variables in many places that, I think, it shouldn't - but maybe I'm misunderstanding how this works in Fortran (as compared to C++ which I'm much more familiar with), hence this question.

So the variables in question are essentially 'categorical values', 'factors' or 'enums' depending on how you look at it/want to call it. They are of data type REAL and can only take on a finite number of pre-determined, integer values. So say variable a can only be of value 1, 2 or 3. These values are read in from external files; in these external files, they are represented as integers, so it's not a case of 'rounding issues in external data sources' or something.

However in the code, it never does a straight comparison, always a greater than/lower than check. So, instead of doing

if (a == 1) then

it does

if (a > 0.9 .and. a < 1.1) then

You can imagine that this gets very confusing/tiresome to read, especially when it needs to check if a value is one of multiple categories.

So I think this is a case where someone at some point heard 'never compare REAL values' (because of the nature of the finite precision of storing floating point values, this same problem exists in every programming language), but then didn't really understand when that applies (I guess the first error is that categorical values should have been represented as integer values but that situation is what it is for now).

OTOH maybe I'm just misunderstanding how REAL and INTEGER values are represented and work in Fortran? Could there ever be a case where

b = 1.5
a = REAL(INT(b))

if (a > 0.9 .and. a < 1.1) then

would make sense?

Answer 1

ONLY in the case you're not performing any operation with the real values (just assigning a value and comparing equality with the same literal you assigned, with same kind parameter), you won't need tolerance.

The thing is, for a real variable a such as:

Real a
a = 2

You can be sure that

a == 2

Will be always .true. . But eg, for another real value represented by b:

a  / b * b == 2

(Or any other operation) is not guaranteed to be .true.

Answer 2

If for some reason the variable has to stay REAL then you may use the intrinsic Fortran function NINT (nearest integer) in the comparisons:

if( nint(a) == 1 ) then 
....