Is it safe to assume floating point is represented using IEEE754 floats in C?

问题

Floating point is implementation defined in the C. So there isn't any guarantees.

Our code needs to be portable, we are discussing whether or not acceptable to use IEEE754 floats in our protocol. For performance reasons it would be nice if we don't have to convert back and forth between a fixed point format when sending or receiving data.

While I know that there can be differences between platforms and architectures regarding the size of long or wchar_t. But I can't seem to find any specific about the float and double.

What I found so far that the byte order maybe reversed on big endian platforms. While there are platforms without floating point support where a code containing float and double wouldn't even link. Otherwise platforms seem to stick to IEEE754 single and double precision.

So is it safe to assume that floating point is in IEEE754 when available?

EDIT: In response to a comment:

What is your definition of "safe"?

By safe I mean, the bit pattern on one system means the same on the another (after the byte rotation to deal with endianness).

回答1:

Essentially all architectures in current non-punch-card use, including embedded architectures and exotic signal processing architectures, offer one of two floating point systems:

• IEEE-754.
• IEEE-754 except for blah. That is, they mostly implement 754, but cheap out on some of the more expensive and/or fiddly bits.

The most common cheap-outs:

• Flushing denormals to zero. This invalidates certain sometimes-useful theorems (in particular, the theorem that a-b can be exactly represented if a and b are within a factor of 2), but in practice it's generally not going to be an issue.
• Failure to recognize inf and NaN as special. These architectures will fail to follow the rules regarding inf and NaN as operands, and may not saturate to inf, instead producing numbers that are larger than FLT_MAX, which will generally be recognized by other architectures as NaN.
• Proper rounding of division and square root. It's a whole lot easier to guarantee that the result is within 1-3 ulps of the exact result than within 1/2 ulp. A particularly common case is for division to be implemented as reciprocal+multiplication, which loses you one bit of precision.
• Fewer or no guard digits. This is an unusual cheap-out, but means that other operations can be 1-2 ulps off.

BUUUUT... even those except for blah architectures still use IEEE-754's representation of numbers. Other than byte ordering issues, the bits describing a float or double on architecture A are essentially guaranteed to have the same meaning on architecture B.

So as long as all you care about is the representation of values, you're totally fine. If you care about cross-platform consistency of operations, you may need to do some extra work.

EDIT: As Chux mentions in the comments, a common extra source of inconsistency between platforms is the use of extended precision, such as the x87's 80-bit internal representation. That's the opposite of a cheap-out, and (with proper treatment) fully conforms to both IEEE-754 and the C standard, but it will likewise cause results to differ between architectures, and even between compiler versions and following apparently minor and unrelated code changes. However: a particular x86/x64 executable will NOT produce different results on different processors due to extended precision.

回答2:

There is a macro to check (since C99):

C11 §6.10.8.3 Conditional feature macros

__STDC_IEC_559__ The integer constant 1, intended to indicate conformance to the specifications in annex F (IEC 60559 floating-point arithmetic).

IEC 60559 (short for ISO/IEC/IEEE 60559) is another name for IEEE-754.

Annex F then establishes the mapping between C floating types and IEEE-754 types:

The C floating types match the IEC 60559 formats as follows:

• The float type matches the IEC 60559 single format.
• The double type matches the IEC 60559 double format.
• The long double type matches an IEC 60559 extended format, 357) else a non-IEC 60559 extended format, else the IEC 60559 double format.

回答3:

I suggest you need to look more carefully at your definition of portable.

I would also suggest your definition of "safe" is insufficient. Even if the binary representation (allowing for endianness) is okay, the operations on variables may behave differently. After all, there are few applications of floating point that don't involve operations on variables.

If you want to support all host architectures that have ever been created then assuming IEEE floating point format is inherently unsafe. You will have to deal with systems that support different formats, systems that don't support floating point at all, systems for which compilers have switches to select floating point behaviours (with some behaviours being associated with non-IEEE formats), CPUs that have an optional co-processor (so floating point support depends on whether an additional chip is installed, but otherwise variants of the CPU are identical), systems that emulate floating point operations in software (some such software emulators are configurable at run time), and systems with buggy or incomplete implementation of floating point (which may or may not be IEEE based).

If you are willing to limit yourself to hardware of post 2000 vintage, then your risk is lower but non-zero. Virtually all CPUs of that vintage support IEEE in some form. However you still (as with older CPUs too) need to consider what floating point operations you wish to have supported, and the trade-offs you are willing to accept to have them. Different CPUs (or software emulation) have less complete implementation of floating point than others, and some are configured by default to not support some features - so it is necessary to change settings to enable some features, which can impact on performance or correctness of your code.

If you need to share floating point values between applications (which may be on different hosts with different features, built with different compilers, etc) then you will need to define a protocol. That protocol might involve IEEE format, but all your applications will need to be able to handle conversion between the protocol and their native representations.

回答4:

Almost all common architectures now use IEEE-754, this is not required by the standard. There used to be old non IEE-754 architectures, and some could still be around.

If the only requirement is for exchange of network data, my advice is:

• if __STDC_IEC_559__ is defined, only use network order for the bytes and assume you do have standard IEE-754 for float and double.
• if __STDC_IEC_559__ is not defined, use a special interchange format, that could be IEE-754 - one single protocol - or anything else - need a protocol indication.

回答5:

Like others have mentioned, there's the __STDC_IEC_559__ macro, but it isn't very useful because it's only set by compilers that completely implement the respective annex in the C standard. There are compilers that implement only a subset but still have (mostly) usable IEEE floating point support.

If you're only concerned with the binary representation, you should write a feature test that checks the bit patterns of certain floating numbers. Something like:

#include <stdint.h>
#include <stdio.h>

typedef union {
    double   d;
    uint64_t i;
} double_bits;

int main() {
    double_bits b;
    b.d = 2.5;
    if (b.i != UINT64_C(0x4004000000000000)) {
        fprintf(stderr, "Not an IEEE-754 double\n");
        return 1;
    }
    return 0;
}

Check a couple of numbers with different exponents, mantissae, and signs, and you should be on the safe side. Since these tests aren't expensive, you could even run them once at runtime.

回答6:

Strictly speaking, it's not safe to assume floating-point support; generally speaking, the vast majority of platforms will support it. Notable exceptions include (now deprecated) VMS systems running on Alpha chips

If you have the luxury of runtime checking, consider paranoia, a floating-point vetting tool written by William Kahan.

Edit: sounds like your application is more concerned with binary formats as they pertain to storage and/or serialization. I would suggest narrowing your scope to choosing a third-party library that supports this. You could do worse than Google Protocol Buffers.

来源：https://stackoverflow.com/questions/31967040/is-it-safe-to-assume-floating-point-is-represented-using-ieee754-floats-in-c