What is the definition of “arithmetic operation” in C99?

Question

In C99, the term arithmetic operation appears 16 times, but I don't see a definition for it.

The term arithmetic operator only appears twice in the text (again without definition) but it does appear in the Index:

arithmetic operators

additive, 6.5.6, G.5.2
bitwise, 6.5.10, 6.5.11, 6.5.12
increment and decrement, 6.5.2.4, 6.5.3.1
multiplicative 6.5.5, G.5.1
shift, 6.5.7
unary, 6.5.3.3

Then we have + - | &(binary) ++ -- *(binary) / % << >> ~ as arithmetic operators, if the Index is considered normative!

Perhaps we should identify arithmetic operation as being the use of an arithmetic operator. But F9.4.5 says that the sqrt() function is also an arithmetic operation, and refers to IEC 60559 (aka. IEEE754) for details. So there must be arithmetic operations that are not just the use of arithmetic operators.

Answer 1

Since we don't have a formal definition let's see if we can piece together a rationale interpretation of what an arithmetic operation should be. This will be speculative but I can not find any obvious defect reports or open issues that cover this.

I guess I would start with what are considered arithmetic types, which is covered in section 6.2.5 Types paragraph 18 says (emphasis mine going forward):

Integer and floating types are collectively called arithmetic types. Each arithmetic type belongs to one type domain: the real type domain comprises the real types, the complex type domain comprises the complex types.

ok, so we know that an arithmetic operation has to operate on either an integer or a floating point type. So what is an operation? It seems like we have a good go at defining that from section 5.1.2.3 Program execution paragraph 2 which says:

Accessing a volatile object, modifying an object, modifying a file, or calling a function that does any of those operations are all side effects,¹¹⁾ which are changes in the state of the execution environment. [...]

So modifying an object or call a function that does that, it is an operation. What is an object? Section 3.14 says:

region of data storage in the execution environment, the contents of which can represent values

Although the standard seems to use the term operation more loosely to mean an evaluation, for example in section 7.12.1 Treatment of error conditions it says:

The behavior of each of the functions in is specified for all representable values of its input arguments, except where stated otherwise. Each function shall execute as if it were a single operation without generating any externally visible exceptional conditions.

and in section 6.5 Expressions paragraph 8 which says:

A floating expression may be contracted, that is, evaluated as though it were an atomic operation [...]

So this would seem to imply that an evaluation is an operation.

So it would seem from these sections that pretty much all the arithmetic operators and any math function would fall under a common sense definition of arithmetic operation.

Answer 2

The most convincing bit I could find to be an implicit definition lies in 7.14 Signal Handling, paragraph 3, in the definition of the SIGFPE signal:

SIGFPE - an erroneous arithmetic operation, such as a zero divide or an operation resulting in overflow

One might then draw a conclusion that any operation that may cause SIGFPE to be raised can be considered an arithmetic operation; only arithmetic operations can result in the SIGFPE signal being raised.

That covers pretty much anything in <math.h> and the arithmetic operators, and <complex.h> if implemented. While a signal may not be raised for integral types, signed overflow and other "exceptional" conditions are allowed to generate trap representations, which means no other operations may be carried out reliably until a valid value is obtained — something that can only be done via assignment. In other words, the definition can apply equally to operations on an integral value.

As a result, pretty much any operation other than getting the size of an object/type, dereferencing a pointer, and taking the address of an object may be considered an arithmetic operation. Note that a[n] is *((a) + (n)), so even using an array can be considered an arithmetic operation.

Answer 3

An arithmetic operation involve manipulation of numbers. sqrt also manipulate numbers and that could be the reason that standard says it an arithmetic operation.