Fortran - want to round to one decimal point - fortran

Question

In fortran I have to round latitude and longitude to one digit after decimal point.
I am using gfortran compiler and the nint function but the following does not work:
print *, nint( 1.40 * 10. ) / 10. ! prints 1.39999998
print *, nint( 1.49 * 10. ) / 10. ! prints 1.50000000
Looking for both general and specific solutions here. For example:
How can we display numbers rounded to one decimal place?
How can we store such rounded numbers in fortran. It's not possible in a float variable, but are there other ways?
How can we write such numbers to NetCDF?
How can we write such numbers to a CSV or text file?

Answer 1

As others have said, the issue is the use of floating point representation in the NetCDF file. Using nco utilities, you can change the latitude/longitude to short integers with scale_factor and add_offset. Like this:
ncap2 -s 'latitude=pack(latitude, 0.1, 0); longitude=pack(longitude, 0.1, 0);' old.nc new.nc

Answer 2

There is no way to do what you are asking. The underlying problem is that the rounded values you desire are not necessarily able to be represented using floating point.
For example, if you had a value 10.58, this is represented exactly as 1.3225000 x 2^3 = 10.580000 in IEEE754 float32.
When you round this to value to one decimal point (however you choose to do so), the result would be 10.6, however 10.6 does not have an exact representation. The nearest representation is 1.3249999 x 2^3 = 10.599999 in float32. So no matter how you deal with the rounding, there is no way to store 10.6 exactly in a float32 value, and no way to write it as a floating point value into a netCDF file.

Answer 3

YES, IT CAN BE DONE! The "accepted" answer above is correct in its limited range, but is wrong about what you can actually accomplish in Fortran (or various other HGL's).
The only question is what price are you willing to pay, if the something like a Write with F(6.1) fails?
From one perspective, your problem is a particularly trivial variation on the subject of "Arbitrary Precision" computing. How do you imagine cryptography is handled when you need to store, manipulate, and perform "math" with, say, 1024 bit numbers, with exact precision?
A simple strategy in this case would be to separate each number into its constituent "LHSofD" (Left Hand Side of Decimal), and "RHSofD" values. For example, you might have an RLon(i,j) = 105.591, and would like to print 105.6 (or any manner of rounding) to your netCDF (or any normal) file. Split this into RLonLHS(i,j) = 105, and RLonRHS(i,j) = 591.
... at this point you have choices that increase generality, but at some expense. To save "money" the RHS might be retained as 0.591 (but loose generality if you need to do fancier things).
For simplicity, assume the "cheap and cheerful" second strategy.
The LHS is easy (Int()).
Now, for the RHS, multiply by 10 (if, you wish to round to 1 DEC), e.g. to arrive at RLonRHS(i,j) = 5.91, and then apply Fortran "round to nearest Int" NInt() intrinsic ... leaving you with RLonRHS(i,j) = 6.0.
... and Bob's your uncle:
Now you print the LHS and RHS to your netCDF using a suitable Write statement concatenating the "duals", and will created an EXACT representation as per the required objectives in the OP.
... of course later reading-in those values returns to the same issues as illustrated above, unless the read-in also is ArbPrec aware.
... we wrote our own ArbPrec lib, but there are several about, also in VBA and other HGL's ... but be warned a full ArbPrec bit of machinery is a non-trivial matter ... lucky you problem is so simple.

Answer 4

There are several aspects one can consider in relation to "rounding to one decimal place". These relate to: internal storage and manipulation; display and interchange.
Display and interchange
The simplest aspects cover how we report stored value, regardless of the internal representation used. As covered in depth in other answers and elsewhere we can use a numeric edit descriptor with a single fractional digit:
print '(F0.1,2X,F0.1)', 10.3, 10.17
end
How the output is rounded is a changeable mode:
print '(RU,F0.1,2X,RD,F0.1)', 10.17, 10.17
end
In this example we've chosen to round up and then down, but we could also round to zero or round to nearest (or let the compiler choose for us).
For any formatted output, whether to screen or file, such edit descriptors are available. A G edit descriptor, such as one may use to write CSV files, will also do this rounding.
For unformatted output this concept of rounding is not applicable as the internal representation is referenced. Equally for an interchange format such as NetCDF and HDF5 we do not have this rounding.
For NetCDF your attribute convention may specify something like FORTRAN_format which gives an appropriate format for ultimate display of the (default) real, non-rounded, variable .
Internal storage
Other answers and the question itself mention the impossibility of accurately representing (and working with) decimal digits. However, nothing in the Fortran language requires this to be impossible:
integer, parameter :: rk = SELECTED_REAL_KIND(radix=10)
real(rk) x
x = 0.1_rk
print *, x
end
is a Fortran program which has a radix-10 variable and literal constant. See also IEEE_SELECTED_REAL_KIND(radix=10).
Now, you are exceptionally likely to see that selected_real_kind(radix=10) gives you the value -5, but if you want something positive that can be used as a type parameter you just need to find someone offering you such a system.
If you aren't able to find such a thing then you will need to work accounting for errors. There are two parts to consider here.
The intrinsic real numerical types in Fortran are floating point ones. To use a fixed point numeric type, or a system like binary-coded decimal, you will need to resort to non-intrinsic types. Such a topic is beyond the scope of this answer, but pointers are made in that direction by DrOli.
These efforts will not be computationally/programmer-time cheap. You will also need to take care of managing these types in your output and interchange.
Depending on the requirements of your work, you may find simply scaling by (powers of) ten and working on integers suits. In such cases, you will also want to find the corresponding NetCDF attribute in your convention, such as scale_factor.
Relating to our internal representation concerns we have similar rounding issues to output. For example, if my input data has a longitude of 10.17... but I want to round it in my internal representation to (the nearest representable value to) a single decimal digit (say 10.2/10.1999998) and then work through with that, how do I manage that?
We've seen how nint(10.17*10)/10. gives us this, but we've also learned something about how numeric edit descriptors do this nicely for output, including controlling the rounding mode:
character(10) :: intermediate
real :: rounded
write(intermediate, '(RN,F0.1)') 10.17
read(intermediate, *) rounded
print *, rounded ! This may look not "exact"
end
We can track the accumulation of errors here if this is desired.

Answer 5

The `round_x = nint(x*10d0)/10d0' operator rounds x (for abs(x) < 2**31/10, for large numbers use dnint()) and assigns the rounded value to the round_x variable for further calculations.
As mentioned in the answers above, not all numbers with one significant digit after the decimal point have an exact representation, for example, 0.3 does not.
print *, 0.3d0
Output:
0.29999999999999999
To output a rounded value to a file, to the screen, or to convert it to a string with a single significant digit after the decimal point, use edit descriptor 'Fw.1' (w - width w characters, 0 - variable width). For example:
print '(5(1x, f0.1))', 1.30, 1.31, 1.35, 1.39, 345.46
Output:
1.3 1.3 1.4 1.4 345.5
#JohnE, using 'G10.2' is incorrect, it rounds the result to two significant digits, not to one digit after the decimal point. Eg:
print '(g10.2)', 345.46
Output:
0.35E+03
P.S.
For NetCDF, rounding should be handled by NetCDF viewer, however, you can output variables as NC_STRING type:
write(NetCDF_out_string, '(F0.1)') 1.49
Or, alternatively, get "beautiful" NC_FLOAT/NC_DOUBLE numbers:
beautiful_float_x = nint(x*10.)/10. + epsilon(1.)*nint(x*10.)/10./2.
beautiful_double_x = dnint(x*10d0)/10d0 + epsilon(1d0)*dnint(x*10d0)/10d0/2d0
P.P.S. #JohnE
The preferred solution is not to round intermediate results in memory or in files. Rounding is performed only when the final output of human-readable data is issued;
Use print with edit descriptor ‘Fw.1’, see above;
There are no simple and reliable ways to accurately store rounded numbers (numbers with a decimal fixed point):
2.1. Theoretically, some Fortran implementations can support decimal arithmetic, but I am not aware of implementations that in which ‘selected_real_kind(4, 4, 10)’ returns a value other than -5;
2.2. It is possible to store rounded numbers as strings;
2.3. You can use the Fortran binding of GIMP library. Functions with the mpq_ prefix are designed to work with rational numbers;
There are no simple and reliable ways to write rounded numbers in a netCDF file while preserving their properties for the reader of this file:
3.1. netCDF supports 'Packed Data Values‘, i.e. you can set an integer type with the attributes’ scale_factor‘,’ add_offset' and save arrays of integers. But, in the file ‘scale_factor’ will be stored as a floating number of single or double precision, i.e. the value will differ from 0.1. Accordingly, when reading, when calculating by the netCDF library unpacked_data_value = packed_data_value*scale_factor + add_offset, there will be a rounding error. (You can set scale_factor=0.1*(1.+epsilon(1.)) or scale_factor=0.1d0*(1d0+epsilon(1d0)) to exclude a large number of digits '9'.);
3.2. There are C_format and FORTRAN_format attributes. But it is quite difficult to predict which reader will use which attribute and whether they will use them at all;
3.3. You can store rounded numbers as strings or user-defined types;
Use write() with edit descriptor ‘Fw.1’, see above.