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A simple BitConverter class that is capable of reading and writing Intel 80-bit long doubles. I recently found myself needing to read Intel 80-bit long doubles from a binary stream whilst integrating with another system. This is not an implementation of a long double type, but a BitConverter class that translates between long double byte arrays and regular doubles. This article describes how to read a long double byte array and create a regular double value from it.
The first step is to identify the different kinds of long doubles and their equivalent regular doubles. The internal bytes of a long double consist of four parts (or fields); a sign bit (s), a biased exponent (e), a significand bit (j) and a fraction (f). Now you're probably wondering what j is and what happens to it when translating to a double.
So, now the problem can be solved by determining the type of long double and then translating e and f (if it happens to be a normal number).
Since e is biased, to take it from 15 bits to 11 bits involves subtracting the original bias (214 - 1) and adding the new one (210 - 1). However, if e is no less than -51, it can be salvaged by translating it into a subnormal double using some careful bit manipulation.

To understand the above translation, it is important to understand the mathematical representation of a normal double. The last step in the process is to create a double byte array with our new field values and use the standard BitConverter to read it into a double. This project proved to be an interesting look into the structure and bitwise manipulation of floating point numbers. Doubles are surprisingly easy to construct and deconstruct once you understand their internals. This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves. One thing that some might find confusing is your use of the term "long double" for 80-bit IEEE 754 floating point numbers. Also I don't know anything about 80-bit IEEE 754 numbers but I know a little about 64 and 32 bit ones. Naturally, a certain amount of range and precision is lost during the process; however, for my purposes, this is acceptable. These additional bits are used to increase both the range and precision of the number and are usually used for mathematical and scientific calculations. The inverse operation is simply a matter of reversing the procedure and will not be covered here.

The rules that define each of these states can be found in the IEEE Standard 754 specification (see References).
Each of these represent adjacent (but overlapping) ranges of numbers, pseudo-denormal being the smallest, followed by subnormal, then normal. Doubles are arranged in a similar way except that they don't have a significand bit and the exponent and fraction fields are smaller.
I found it was of little significance and was only used when detecting the unsupported state, so I won't go into it here. Since the entire range of a regular double fits into the range of a normal long double, subnormal and pseudo-denormal numbers must round to zero. The following diagram illustrates these differences and shows how the fields are translated. Another way to reduce the result is to halve the f component instead, that is, bit shifting it to the right. Since the fraction field of a double is 52 bits wide, 52 becomes the maximum number of shifts we can do before we're left with zero.

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