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This odd behavior is caused by an implicit conversion of i_value to float when it is compared with f_value. The conversion causes loss of precision, which makes the values equal before the comparison. Important takeaways: float to int causes truncation, i.e., removal of the fractional part. double to float causes rounding of digit.
The type-generic macros that correspond to a function that is defined for only real numbers encapsulates a total of 3 different functions: float, double and long double variants of the function. The C++ language includes native support for function overloading and thus does not provide the <tgmath.h> header even as a compatibility feature.
Information about the actual properties, such as size, of the basic arithmetic types, is provided via macro constants in two headers: <limits.h> header (climits header in C++) defines macros for integer types and <float.h> header (cfloat header in C++) defines macros for floating-point types. The actual values depend on the implementation.
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.
On x86 and x86-64, the most common C/C++ compilers implement long double as either 80-bit extended precision (e.g. the GNU C Compiler gcc [13] and the Intel C++ Compiler with a /Qlong‑double switch [14]) or simply as being synonymous with double precision (e.g. Microsoft Visual C++ [15]), rather than as quadruple precision.
A simple method to add floating-point numbers is to first represent them with the same exponent. In the example below, the second number (with the smaller exponent) is shifted right by three digits, and one then proceeds with the usual addition method: 123456.7 = 1.234567 × 10^5 101.7654 = 1.017654 × 10^2 = 0.001017654 × 10^5
C++14 allows the creation of variables that are templated. An example given in the proposal is a variable pi that can be read to get the value of pi for various types (e.g., 3 when read as an integral type; the closest value possible with float, double or long double precision when read as float, double or long double, respectively; etc.).
Therefore the use of type punning with floating point data is a questionable method with unpredictable results. This kind of type punning is more dangerous than most. Whereas the former example relied only on guarantees made by the C programming language about structure layout and pointer convertibility, the latter example relies on assumptions ...