The article that you linked to is explicit about doing something nonstandard with values near 0: Example when a value reaches zero 1.In Excel 95 or earlier, enter the following into a new workbook: A1: =1.333+1.225-1.333-1.225 2.Right-click cell A1, and then click Format Cells. On the Number tab, click Scientific under Category. Set the Decimal … Read more
Essentially, a denormalized float has the ability to represent the SMALLEST (in magnitude) number that is possible to be represented with any floating point value. That is correct. using denormalized numbers comes with a performance cost on many platforms The penalty is different on different processors, but it can be up to 2 orders of … Read more
This is what ยง2.3.2 of the JVM 7 spec has to say about it: The elements of the double value set are exactly the values that can be represented using the double floating-point format defined in the IEEE 754 standard, except that there is only one NaN value (IEEE 754 specifies 253-2 distinct NaN values). … Read more
From Wikipedia: It is claimed that the inclusion of signed zero in IEEE 754 makes it much easier to achieve numerical accuracy in some critical problems[1], in particular when computing with complex elementary functions[2]. The first reference is “Branch Cuts for Complex Elementary Functions or Much Ado About Nothing’s Sign Bit” by W. Kahan, that … Read more
You got confused by the different ways C++ and MATLAB are printing double values. MATLAB’s format long only prints 15 significant digits while C++ prints 17 significant digits. Internally both use the same numbers: IEEE 754 64 bit floating point numbers. To reproduce the C++-behaviour in MATLAB, I defined a anonymous function disp17 which prints … 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
Table of contents: C/C++ asm Creating real-life software that achieves this. In C or C++: No, a fully ISO C11 and IEEE-conforming C implementation does not guarantee bit-identical results to other C implementations, even other implementations on the same hardware. (And first of all, I’m going to assume we’re talking about normal C implementations where … Read more
The simple answer is because 3*0.1 != 0.3 due to quantization (roundoff) error (whereas 4*0.1 == 0.4 because multiplying by a power of two is usually an “exact” operation). Python tries to find the shortest string that would round to the desired value, so it can display 4*0.1 as 0.4 as these are equal, but … Read more
I believe __STDC_IEC_559__ relies on some library features and can’t be defined solely by the compiler. See this post for some information. This is not uncommon for C — the compiler and the C library must sometimes cooperate in order to implement the entire standard. What you’re asking depends on the compiler. I think you … Read more
R uses IEEE 754 double-precision floating-point numbers. Floating-point numbers are more dense near zero. This is a result of their being designed to compute accurately (the equivalent of about 16 significant decimal digits, as you have noticed) over a very wide range. Perhaps you expected a fixed-point system with uniform absolute precision. In practice fixed-point … Read more