Disclaimer (as suggested by Toby Speight): Although IEEE 754 representations are quite common, an implementation is permitted to use any other representation that satisfies the requirements of the language. The doubles are represented in the form mantissa * 2^exponent, i.e. some of the bits are used for the non-integer part of the double number. bits … Read more
The problem is that .NET will always round a double to 15 significant decimal digits before applying your formatting, regardless of the precision requested by your format and regardless of the exact decimal value of the binary number. I’d guess that the Visual Studio debugger has its own format/display routines that directly access the internal … Read more
You’re overflowing the capacity of JavaScript’s number type, see ยง8.5 of the spec for details. Those IDs will need to be strings. IEEE-754 double-precision floating point (the kind of number JavaScript uses) can’t precisely represent all numbers (of course). Famously, 0.1 + 0.2 == 0.3 is false. That can affect whole numbers just like it … Read more
For a given IEEE-754 floating point number X, if 2^E <= abs(X) < 2^(E+1) then the distance from X to the next largest representable floating point number (epsilon) is: epsilon = 2^(E-52) % For a 64-bit float (double precision) epsilon = 2^(E-23) % For a 32-bit float (single precision) epsilon = 2^(E-10) % For a … Read more
The 1 is converted to a complex number first, 1 + 0j, which then leads to an inf * 0 multiplication, resulting in a nan. (inf + 0j) * 1 (inf + 0j) * (1 + 0j) inf * 1 + inf * 0j + 0j * 1 + 0j * 0j # ^ this … Read more
IEEE 754 basics First let’s review the basics of IEEE 754 numbers are organized. We’ll focus on single precision (32-bit), but everything can be immediately generalized to other precisions. The format is: 1 bit: sign 8 bits: exponent 23 bits: fraction Or if you like pictures: Source. The sign is simple: 0 is positive, and … Read more
PHP’s comparison operators deviate from the computer-scientific definitions in several ways: In order to constitute an equivalence relation == has to be reflexive, symmetric and transitive: PHP’s == operator is not reflexive, i.e. $a == $a is not always true: var_dump(NAN == NAN); // bool(false) Note: The fact that any comparison involving NAN is always … Read more
In Java, a – b is never equal to 0 if a != b. This is because Java mandates IEEE 754 floating point operations which support denormalized numbers. From the spec: In particular, the Java programming language requires support of IEEE 754 denormalized floating-point numbers and gradual underflow, which make it easier to prove desirable … Read more
When an operation results in a quiet NaN, there is no indication that anything is unusual until the program checks the result and sees a NaN. That is, computation continues without any signal from the floating point unit (FPU) or library if floating-point is implemented in software. A signalling NaN will produce a signal, usually … Read more
The accepted answer is 100% without question WRONG. Not halfway wrong or even slightly wrong. I fear this issue is going to confuse and mislead programmers for a long time to come when this question pops up in searches. NaN is designed to propagate through all calculations, infecting them like a virus, so if somewhere … Read more