The implementation of such a library is possible outside the compiler, thanks to the ffi support of the language. The library must be split in two parts: the native ocaml source part, and the C runtime part. the OCaml source must contain the datatype declaration, as well as the declaration of all the imported functions. … Read more
According to the standard, negative zero exists but it is equal to positive zero. For almost all purposes, the two behave the same way and many consider the existence of a negative to be an implementation detail. There are, however, some functions that behave quite differently, namely division and atan2: #include <math.h> #include <stdio.h> int … Read more
These accuracy problems are due to the internal representation of floating point numbers and there’s not much you can do to avoid it. By the way, printing these values at run-time often still leads to the correct results, at least using modern C++ compilers. For most operations, this isn’t much of an issue.
The IEEE-754 standard defines a NaN as a number with all ones in the exponent, and a non-zero significand. The highest-order bit in the significand specifies whether the NaN is a signaling or quiet one. The remaining bits of the significand form what is referred to as the payload of the NaN. Whenever one of … Read more
b0lt has already explained how bias works. At a guess, perhaps you’d like to know why they use a bias representation here, even though virtually all modern computers use two’s complement essentially everywhere else (and even machines that don’t use two’s complement, use one’s complement or sign-magnitude, not bias). One of the goals of the … Read more
(Flynn’s answer is the correct answer. This one addresses the problem more generally.) You seem to be assuming, OP, that the floating-point inaccuracy in your code is deterministic and predictably wrong (in a way, your approach is the polar opposite of that of people who don’t understand floating point yet). Although (as Ben points out) … Read more
The following code should work for a lot of simple use cases with relatively small numbers and small precision inputs. However, it may not work for some uses cases because of numbers overflowing out of the range of float64 numbers, as well as IEEE-754 rounding errors (other languages have this issue as well). If you … 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
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