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This does not violate trichotomy as long as a consistent total order is adopted: either −0 = +0 or −0 < +0 is valid. Common floating point types, however, have an exception to trichotomy: there is a special value "NaN" (Not a Number) such that x < NaN, x > NaN, and x = NaN are all false for all floating-point values x (including NaN itself).
However, supposing that floating-point comparisons are expensive, and also supposing that float is represented according to the IEEE floating-point standard, and integers are 32 bits wide, we could engage in type punning to extract the sign bit of the floating-point number using only integer operations:
The IEEE 754 specification—followed by all modern floating-point hardware—requires that the result of an elementary arithmetic operation (addition, subtraction, multiplication, division, and square root since 1985, and FMA since 2008) be correctly rounded, which implies that in rounding to nearest, the rounded result is within 0.5 ulp of ...
^e These IEEE floating-point types will be introduced in the next COBOL standard. ^f Same size as double on many implementations. ^g Swift supports 80-bit extended precision floating point type, equivalent to long double in C languages.
This is a comparison of data serialization formats, ... C++, Java, Python, PHP, Ruby, Erlang, Perl ... ^ PHP will unserialize any floating-point number correctly, ...
Arithmetic underflow can occur when the true result of a floating-point operation is smaller in magnitude (that is, closer to zero) than the smallest value representable as a normal floating-point number in the target datatype. [1] Underflow can in part be regarded as negative overflow of the exponent of the floating-point value. For example ...
Besides integers, floating-point numbers, and Booleans, other built-in types include: The void type and null pointer type nullptr_t in C++11 and C23; Characters and strings (see below) Tuple in Standard ML, Python, Scala, Swift, Elixir; List in Common Lisp, Python, Scheme, Haskell; Fixed-point number with a variety of precisions and a ...
A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-point arithmetic is often used to allow very small and very large real numbers that require fast processing times.