从二进制转换为浮点

Question

I'm doing some exercises for Computer Science university and one of them is about converting an int array of 64 bit into it's double-precision floating point value.

Understanding the first bit, the sign +/-, is quite easy. Same for the exponent, as well as we know that the bias is 1023.

We are having problems with the significand . How can I calculate it?

In the end, I would like to obtain the real numbers that the bits meant.

Answer 1

You could just load the bits into an unsigned integer of the same size as a double, take the address of that and cast it to a void* which you then cast to a double* and dereference.

Of course, this might be "cheating" if you really are supposed to parse the floating point standard, but this is how I would have solved the problem given the parameters you've stated so far.

Answer 2

computing the significand of the given 64 bit is quite easy.

according to the wiki article using the IEEE 754, the significand is made up the first 53 bits (from bit 0 to bit 52). Now if you want to convert number having like 67 bits to your 64 bits value, it would be rounded by setting the trailing 64th bits of your value to 1, even if it was one before... because of the other 3 bits:

11110000 11110010 11111 becomes 11110000 11110011 after the rounding of the last byte;

therefore the there is no need to store the 53th bits because it has always a value a one. that's why you only store in 52 bits in the significand instead of 53.

now to compute it, you just need to target the bit range of the significand [bit(1) - bit(52)] -bit(0) is always 1- and use it .

int index_signf = 1; // starting at 1, not 0
int significand_length = 52;
int byteArray[53]; // array containing the bits of the significand

double significand_endValue = 0;
for( ; index_signf <= significand_length ; index_signf ++)
{
    significand_endValue += byteArray[index_signf] * (pow(2,-(index_signf)));
}

significand_endValue += 1; 

Now you just have to fill byteArray accordlingly before computing it, using function like that:

int* getSignificandBits(int* array64bits){

    //returned array

    int significandBitsArray[53];
    // indexes++
    int i_array64bits = 0; 
    int i_significandBitsArray=1;
    //set the first bit = 1

    significandBitsArray[0] = 1;



    // fill it  
    for(i_significandBitsArray=1, i_array64bits = (63 - 1); i_array64bits >= (64 - 52); i_array64bits--, i_significandBitsArray ++)
        significandBitsArray[i_significandBitsArray] = array64bits[i_array64bits];

    return significandBitsArray;
}

Answer 3

If you have a byte representation of an object you can copy the bytes into the storage of a variable of the right type to convert it.

double convert_to_double(uint64_t x) {
    double result;
    mempcy(&result, &x, sizeof(x));
    return result;
}

You will often see code like *(double *)&x to do the conversion, but whereas in practice this will always work it's undefined behavior in C.