Trap representation

Question

1. What is a "trap representation" in C (some examples might help)? Does this apply to C++?

2. Given this code...

   float f=3.5;
   int *pi = (int*)&f;
   

   ... and assuming that sizeof(int) == sizeof(float), do f and *pi have the same binary representation/pattern?

Answer 1

1. A trap representation is a catch-all term used by C99 (IIRC not by C89) to describe bit patterns that fit into the space occupied by a type, but trigger undefined behavior if used as a value of that type. The definition is in section 6.2.6.1p5 (with tentacles into all of 6.2.6) and I'm not going to quote it here because it's long and confusing. A type for which such bit patterns exist is said to "have" trap representations. No type is required to have any trap representations, but the only type that the standard guarantees will not have trap representations is unsigned char (6.2.6.1p5, 6.2.6.2p1).

   The standard gives two hypothetical examples of trap representations, neither of which correspond to anything that any real CPU has done for many years, so I'm not going to confuse you with them. A good example of a trap representation (also the only thing that qualifies as a hardware-level trap representation on any CPU you are likely to encounter) is a signaling NaN in a floating-point type. C99 Annex F (section 2.1) explicitly leaves the behavior of signaling NaNs undefined, even though IEC 60559 specifies their behavior in detail.

   It's worth mentioning that, while pointer types are allowed to have trap representations, null pointers are not trap representations. Null pointers only cause undefined behavior if they are dereferenced or offset; other operations on them (most importantly, comparisons and copies) are well-defined. Trap representations cause undefined behavior if you merely read them using the type that has the trap representation. (Whether invalid but non-null pointers are, or should be, considered trap representations is a subject of debate. The CPU doesn't treat them that way, but the compiler might.)

2. The code you show has undefined behavior, but this is because of the pointer-aliasing rules, not because of trap representations. This is how to convert a float into the int with the same representation (assuming, as you say, sizeof(float) == sizeof(int))

   int extract_int(float f)
   {
       union { int i; float f; } u;
       u.f = f;
       return u.i;
   }
   

   This code has unspecified (not undefined) behavior in C99, which basically means the standard doesn't define what integer value is produced, but you do get some valid integer value, it's not a trap representation, and the compiler is not allowed to optimize on the assumption that you have not done this. (Section 6.2.6.1, para 7. My copy of C99 might include technical corrigienda — my recollection is that this was undefined in the original publication but was changed to unspecified in a TC.)

Answer 2

Undefined behaviour to alias a float with a pointer-to-int.

Answer 3

In general, any non-trap IEEE-754 floating point value can be represented as an integer on some platforms without any issue. However, there are floating point values that can result in unexpected behavior if you assume that all floating point values have a unique integer representation and you happen to force the FPU to load that value.

(The example is taken from Byte Swapping Floating Point Types.)

For instance, when working with floating point data you need to marshal between CPUs with different endianness, you might think of doing the following:

double swap(double)

Unfortunately, if the compiler loads the input into an FPU register and it's a trap representation, the FPU can write it back out with an equivalent trap representation that happens to be a different bit representation.

In other words, there are some floating point values that do not have a corresponding bit representation if you don't convert correctly (by correct I mean through a union, memcpy via char * or other standard mechanism).