Fortran's numeric environment is flexible, which helps make Fortran a strong language for intensive numerical calculations. The Fortran standard purposely leaves the precision of numeric quantities and the method of rounding numeric results unspecified. This allows Fortran to operate efficiently for diverse applications on diverse systems.
The effect of math computations on integers is straightforward:
Operations on integers result in other integers within this range. The only arithmetic rule to remember is that integer division results in truncation (for example, 8/3 evaluates to 2).
Computations on real numbers, however, may not yield what you expect. This happens because the hardware must represent numbers in a finite number of bits.
There are several effects of using finite floating-point numbers. The hardware is not able to represent every real number exactly, but must approximate exact representations by rounding or truncating to finite length. In addition, some numbers lie outside the range of representation of the maximum and minimum exponents and can result in calculations that underflow and overflow. As an example of one consequence, finite precision produces many numbers that, although non-zero, behave in addition as zero.
You can minimize the effects of finite representation with programming techniques; for example, by not using floating-point numbers in LOGICAL comparisons or by giving them a tolerance (for example, IF (x <= 10.001)), and by not attempting to combine or compare numbers that differ by more than the number of significant bits. (For more information on programming methods to reduce the effects of imprecision, see Rounding Errors.)
For further discussion of how floating-point numbers are represented, see: