Why doesn’t 1.0 = 2.0 work? Isn’t real an equality type? No. The type variable ”Z indicates that the operands of = must have equality types. Why won’t reals in patterns work […]? Pattern matching relies implicitly on testing for equality. The cryptic error message syntax error: inserting EQUALOP indicates that the SML/NJ parser does … Read more
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
The biggest problem with x87 is basically that all register operations are done in 80 bits, whereas most of the time people only use 64 bit floats (i.e. double-precision floats). What happens is, you load a 64 bit float into the x87 stack, and it gets converted to 80 bits. You do some operations on … Read more
The specific reason in your case is that the real number 0.94 cannot be represented exactly in a double precision floating point. When you type 0.94, the actual number stored is 0.939999999999999946709294817992486059665679931640625.
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
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
As mentioned, the Wikipedia article on IEEE 754 does a good job of showing how floating point numbers are stored on most systems. Now, here are some common gotchas: The biggest is that you almost never want to compare two floating point numbers for equality (or inequality). You’ll want to use greater than/less than comparisons … 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
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.