SSE is fully specified*. Muller is an expert in floating point arithmetic; who are you going to trust, him or some guy on a gamedev forum? (*) there are actually a few exceptions for non-IEEE-754 operations like rsqrtss, where Intel never fully specified the behavior, but that doesn’t effect the IEEE-754 basic operations, and more … 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
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
As for php, output is related to ini settings of precision: ini_set(‘precision’, 15); print 0.3 – 0.2; // 0.1 ini_set(‘precision’, 17); print 0.3 – 0.2; //0.099999999999999978 This may be also cause for other languages
It’s a nonsense from the mathematical perspective. Yes. No. Sort of. The thing is: Floating-point numbers are approximations. You want to use a wide range of exponents and a limited number of digits and get results which are not completely wrong. 🙂 The idea behind IEEE-754 is that every operation could trigger “traps” which indicate … 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
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
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
str(0.47000000000000003) give ‘0.47’ and float(‘0.47’) can be 0.46999999999999997. This is due to the way floating point number are represented (see this wikipedia article) Note: float(repr(0.47000000000000003)) or eval(repr(0.47000000000000003)) will give you the expected result, but you should use Decimal if you need precision.