# Fixed-point contrasted with floating-point arithmetic

How you code arithmetic in a program (whether an arithmetic statement, an intrinsic function, an expression, or some combination of these nested within each other) determines whether the evaluation is done with floating-point or fixed-point arithmetic.

Note: Fixed-point evaluations are sometimes done with decimal floating-point instructions, which are quite different from hex floating-point instructions.

Many statements in a program could involve arithmetic. For example, each of the following types of COBOL statements requires some arithmetic evaluation:

• General arithmetic
``````
compute report-matrix-col = (emp-count ** .5) + 1
add report-matrix-min to report-matrix-max giving report-matrix-tot
``````
• Expressions and functions
``````
compute report-matrix-col = function sqrt(emp-count) + 1
compute whole-hours       = function integer-part((average-hours) + 1)
``````
• Arithmetic comparisons
``````
if report-matrix-col <     function sqrt(emp-count) + 1
if whole-hours       not = function integer-part((average-hours) + 1)
``````

## Floating-point evaluations

In general, if your arithmetic coding has either of the characteristics listed below, it is evaluated in floating-point arithmetic:

• An operand or result field is floating point.

An operand is floating point if you code it as a floating-point literal or if you code it as a data item that is defined as `USAGE COMP-1`, ```USAGE COMP-2```, or external floating point (`USAGE DISPLAY` or `USAGE NATIONAL` with a floating-point `PICTURE`).

An operand that is a nested arithmetic expression or a reference to a numeric intrinsic function results in floating-point arithmetic when any of the following conditions is true:

• An argument in an arithmetic expression results in floating point.
• The function is a floating-point function.
• The function is a mixed function with one or more floating-point arguments.
• An exponent contains decimal places.

An exponent contains decimal places if you use a literal that contains decimal places, give the item a `PICTURE` that contains decimal places, or use an arithmetic expression or function whose result has decimal places.

An arithmetic expression or numeric function yields a result that has decimal places if any operand or argument (excluding divisors and exponents) has decimal places.

## Fixed-point evaluations

In general, if an arithmetic operation contains neither of the characteristics listed above for floating point, the compiler causes it to be evaluated in fixed-point arithmetic. In other words, arithmetic evaluations are handled as fixed point only if all the operands are fixed point, the result field is defined to be fixed point, and none of the exponents represent values with decimal places. Nested arithmetic expressions and function references must also represent fixed-point values.

## Arithmetic comparisons (relation conditions)

When you compare numeric expressions using a relational operator, the numeric expressions (whether they are data items, arithmetic expressions, function references, or some combination of these) are comparands in the context of the entire evaluation. That is, the attributes of each can influence the evaluation of the other: both expressions are evaluated in fixed point, or both are evaluated in floating point. This is also true of abbreviated comparisons even though one comparand does not explicitly appear in the comparison. For example:

``````
if (a + d) = (b + e) and c
``````

This statement has two comparisons: ```(a + d) = (b + e)```, and `(a + d) = c`. Although ```(a + d)``` does not explicitly appear in the second comparison, it is a comparand in that comparison. Therefore, the attributes of `c` can influence the evaluation of `(a + d)`.

The compiler handles comparisons (and the evaluation of any arithmetic expressions nested in comparisons) in floating-point arithmetic if either comparand is a floating-point value or resolves to a floating-point value.

The compiler handles comparisons (and the evaluation of any arithmetic expressions nested in comparisons) in fixed-point arithmetic if both comparands are fixed-point values or resolve to fixed-point values.

Implicit comparisons (no relational operator used) are not handled as a unit, however; the two comparands are treated separately as to their evaluation in floating-point or fixed-point arithmetic. In the following example, five arithmetic expressions are evaluated independently of one another's attributes, and then are compared to each other.

``````
evaluate (a + d)
when (b + e) thru c
when (f / g) thru (h * i)
. . .
end-evaluate
``````