Is it guaranteed that the copy of a float variable will be bitwise equivalent to the original?

Question

I am working on floating point determinism and having already studied so many surprising potential causes of indeterminism, I am starting to get paranoid about copying floats:

Does anything in the C++ standard or in general guarantee me that a float lvalue, after being copied to another float variable or when used as a const-ref or by-value parameter, will always be bitwise equivalent to the original value?

Can anything cause a copied float to be bitwise inquivalent to the original value, such as changing the floating point environment or passing it into a different thread?

Here is some sample code based on what I use to check for equivalence of floating point values in my test-cases, this one will fail because it expects FE_TONEAREST:

#include <cfenv>
#include <cstdint>

// MSVC-specific pragmas for floating point control
#pragma float_control(precise, on)
#pragma float_control(except, on)
#pragma fenv_access(on)
#pragma fp_contract(off)

// May make a copy of the floats
bool compareFloats(float resultValue, float comparisonValue)
{
    // I was originally doing a bit-wise comparison here but I was made
    // aware in the comments that this might not actually be what I want
    // so I only check against the equality of the values here now
    // (NaN values etc. have to be handled extra)
    bool areEqual = (resultValue == comparisonValue);

    // Additional outputs if not equal
    // ...

    return areEqual;
}

int main()
{
    std::fesetround(FE_TOWARDZERO)
    float value = 1.f / 10;
    float expectedResult = 0x1.99999ap-4;

    compareFloats(value, expectedResult);
}

Do I have to be worried that if I pass a float by-value into the comparison function it might come out differently on the other side, even though it is an lvalue?

Answer 1

The C++ standard itself has virtually no guarantees on floating point math because it does not mandate IEEE-754 but leaves it up to the implementation (emphasis mine):

[basic.fundamental/12]

There are three floating-point types: float, double, and long double. The type double provides at least as much precision as float, and the type long double provides at least as much precision as double. The set of values of the type float is a subset of the set of values of the type double; the set of values of the type double is a subset of the set of values of the type long double. The value representation of floating-point types is implementation-defined. [ Note: This document imposes no requirements on the accuracy of floating-point operations; see also [support.limits]. — end note ]

The C++ code you write is a high-level abstract description of what you want the abstract machine to do, and it is fully in the hands of the compiler what this gets translated to. "Assignments" is an aspect of the C++ standard, and as shown above, the C++ standard does not mandate the behavior of floating point operations. To verify the statement "assignments leave floating point values unchanged" your compiler would have to specify its floating point behavior in terms of the C++ abstract machine, and I've not seen any such documentation (especially not for MSVC).

In other words: Without nailing down the exact compiler, compiler version, compilation flags etc., it is impossible to say for sure what the floating point semantics of a C++ program are (especially regarding the difficult cases like rounding, NaNs or signed zero). Most compilers differentiate between strict IEEE conformance and relaxing some of those restrictions, but even then you are not necessarily guaranteed that the program has the same outputs in non-optimized vs optimized builds due to, say, constant folding, precision of intermediate results and so on.

Point in case: For gcc, even with -O0, your program in question does not compute 1.f / 10 at run-time but at compile-time and thus your rounding mode settings are ignored: https://godbolt.org/z/U8B6bc

You should not be paranoid about copying floats in particular but paranoid of compiler optimizations for floating point in general.