ieee-754

Assume that t , a , b are all double (IEEE Std 754) variables, and both values of a , b are NOT NaN (but may be Inf ). After t = a - b , do I necessarily have a == b + t ? Absolutely not. One obvious case is a=DBL_MAX , b=-DBL_MAX . Then t=INFINITY , so b+t is also INFINITY . What may be more surprising is that there are cases where this happens without any overflow. Basically, they're all of the form where a-b is inexact. For example, if a is DBL_EPSILON/4 and b is -1 , a-b is 1 (assuming default rounding mode), and a-b+b is then 0. The reason I mention this second example is that this is the

Say I have two Python floats a and b , is there an easy way to find out how many representable real numbers are between the two in IEEE-754 representation (or whatever representation the machine used is using)? I don'tknow what you will be using this for - but, if both floats have the same exponent, it should be possible. As the exponent is kept on the high order bits, loading the float bytes (8 bytes in this case) as an integer and subtracting one from another should give the number you want. I use the struct model to pack the floats to a binary representation, and then unpack those as (C, 8

I am porting some program from Matlab to C++ for efficiency. It is important for the output of both programs to be exactly the same (**). I am facing different results for this operation: std::sin(0.497418836818383950) = 0.477158760259608410 (C++) sin(0.497418836818383950) = 0.47715876025960846000 (Matlab) N[Sin[0.497418836818383950], 20] = 0.477158760259608433 (Mathematica) So, as far as I know both C++ and Matlab are using IEEE754 defined double arithmetic. I think I have read somewhere that IEEE754 allows differents results in the last bit. Using mathematica to decide, seems like C++ is

If I have a IEEE float hex 424ce027, how do I convert it to decimal? unsigned char ptr[] = {0x42,0x4c,0xe0,0x27}; how do ? float tmp = 51.218899; Perhaps... float f = *reinterpret_cast<float*>(ptr); Although on my x86 machine here I had to also reverse the byte order of the character to get the value you wanted. std::reverse(ptr, ptr + 4); float f = *reinterpret_cast<float*>(ptr); You might want to use sizeof(float) instead of 4 or some other way to get the size. You might want to reverse a copy of the bytes, not the original. It's somewhat ugly however you do it. edit : As pointed out in the

I am taking in a 8 digit hexadecimal number as an IEEE 754 bit floating point number and i want to print information about that number( signbit, expbits, fractbits, normalized, denormalized, infinity, zero, NAN) floating point should be a single. I read up on bit shifting, and i think this is how i am suppose to do it?. however, i am not 100% sure. I understand that the sign bit is found in the left most position of the number. which indicates positive or negative. How much do i shift it to find each? do i just keep shifting it to find each one? Can someone explain how i am to find each one?