How to check that IEEE 754 single-precision (32-bit) floating-point representation is used?

Question

I want to test the following things on my target board:

• Is \'float\' implemented with IEEE 754 single-precision (32-bit) floating-point variable?

Answer 1

No simple test exists.

The overwhelming majority of systems today use IEEE-754 formats for floating-point. However, most C implementations do not fully conform to IEEE 754 (which is identical to IEC 60559) and do not set the preprocessor identifier __STDC_IEC_559__. In the absence of this identifier, the only way to determine whether a C implementation conforms to IEEE 754 is one or a combination of:

• Read its documentation.
• Examine its source code.
• Test it (which is, of course, difficult when only exhaustive testing can be conclusive).

In many C implementations and software applications, the deviations from IEEE 754 can be ignored or worked around: You may write code as if IEEE 754 were in use, and much code will largely work. However, there are a variety of things that can trip up an unsuspecting programmer; writing completely correct floating-point code is difficult even when the full specification is obeyed.

Common deviations include:

• Intermediate arithmetic is performed with more precision than the nominal type. E.g., expressions that use double values may be calculated with long double precision.
• sqrt does not return a correctly rounded value in every case.
• Other math library routines return values that may be slightly off (a few ULP) from the correctly rounded results. (In fact, nobody has implemented all the math routines recommended in IEEE 754-2008 with both guaranteed correct rounding and guaranteed bound run time.)
• Subnormal numbers (tiny numbers near the edge of the floating-point format) may be converted to zero instead of handled as specified by IEEE 754.
• Conversions between decimal numerals (e.g., 3.1415926535897932384626433 in the source code) and binary floating-point formats (e.g., the common double format, IEEE-754 64-bit binary) do not always round correctly, in either conversion direction.
• Only round-to-nearest mode is supported; the other rounding modes specified in IEEE 754 are not supported. Or they may be available for simple arithmetic but require using machine-specific assembly language to access. Standard math libraries (cos, log, et cetera) rarely support other rounding modes.