“Almost Equals” Is Not a Good Function 4 is not an appropriate value: The answer you point to states “Therefore, 4 should be enough for ordinary use” but contains no basis for that claim. In fact, there are ordinary situations in which numbers calculated in floating-point by different means may differ by many ULP even … Read more
An IEEE754 64-bit double can represent any 32-bit integer, simply because it has 53-odd(a) bits available for precision and the 32-bit integer only needs, well, 32 🙂 It would be plausible for a (non IEEE754 double precision) 64-bit floating point number to have less than 32 bits of precision. That would allow truly huge numbers … Read more
Brian “Beej Jorgensen” Hall gives in his Guide to Network Programming some code to pack float (resp. double) to uint32_t (resp. uint64_t) to be able to safely transmit it over the network between two machine that may not both agree to their representation. It has some limitation, mainly it does not support NaN and infinity. … Read more
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
Actually you have an easier way to achieve this in C++. From the C++ standard 18.2.1.1 the class numeric_limits exists within std. In order to access said static member you simply do this: std::numeric_limits<double>::is_iec559; Or: std::numeric_limits<float>::is_iec559; Which should return true if IEEE 754 is in use, false otherwise. As an alternative method, the second part … Read more
The value of a float does not change when converted to a double. There is a difference in the displayed numerals because more digits are required to distinguish a double value from its neighbors, which is required by the Java documentation. That is the documentation for toString, which is referred (through several links) from the … Read more
You can do it with typed arrays: var buffer = new ArrayBuffer(4); var intView = new Int32Array(buffer); var floatView = new Float32Array(buffer); floatView[0] = Math.PI console.log(intView[0].toString(2)); //bits of the 32 bit float Or another way: var view = new DataView(new ArrayBuffer(4)); view.setFloat32(0, Math.PI); console.log(view.getInt32(0).toString(2)); //bits of the 32 bit float Not sure what browser support … Read more
The code used by various software environments to convert floating-point numbers to string representations is typically based on the following publications (the work by Steele and White is particularly frequently cited): Jerome T. Coonen: “An Implementation Guide to a Proposed Standard for Floating-Point Arithmetic.” Computer, Vol. 13, No. 1, January 1980, pp. 68-79 Guy. L. … Read more
Complete conversion from single precision to half precision. This is a direct copy from my SSE version, so it’s branch-less. It makes use of the fact that -true == ~0 to preform branchless selections (GCC converts if statements into an unholy mess of conditional jumps, while Clang just converts them to conditional moves.) Update (2019-11-04): … 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