Question

I am trying to convert an 80-bit extended precision floating point number (in a buffer) to double.
The buffer basically contains the content of an x87 register.

This question helped me get started as I wasn’t all that familiar with the IEEE standard.
Anyway, I am struggling to find useful info on subnormal (or denormalized) numbers in the 80-bit format.
What I know is that unlike float32 or float64 it doesn’t have a hidden bit in the mantissa (no implied addition of 1.0), so one way to know if a number is normalized is to check if the highest bit in the mantissa is set. That leaves me with the following question:

From what wikipedia tells me, float32 and float64 indicate a subnormal number with a (biased) exponent of 0 and a non-zero mantissa.

• What does that tell me in an 80-bit float?
• Can 80-bit floats with a mantissa < 1.0 even have a non-zero exponent?
• Alternatively, can 80-bit floats with an exponent of 0 even have a mantissa >= 1.0?

EDIT: I guess the question boils down to:

Can I expect the FPU to sanitize exponent and highest mantissa bit in x87 registers?

If not, what kind of number should the conversion result in? Should I ignore the exponent altogether in that case? Or is it qNaN?

EDIT:

I read the FPU section in the Intel manual (Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 1: Basic Architecture) which was less scary than I had feared. As it turns out the following values are not defined:

• exponent == 0 + mantissa with the highest bit set
• exponent != 0 + mantissa without the highest bit set

It doesn’t mention if these values can appear in the wild, nor if they are internally converted.
So I actually dusted off Ollydbg and manually set bits in the x87 registers.
I crafted ST(0) to contain all bits set in the exponent and a mantissa of 0. Then I made it execute

FSTP QWORD [ESP]
FLD QWORD [ESP]

The value stored at [ESP] was converted to a signaling NaN.
After the FLD, ST(0) contained a quiet NaN.

I guess that answers my question. I accepted J-16 SDiZ‘s solution because it’s the most straight forward solution (although it doesn’t explicitly explain some of the finer details).

Anyway, case solved. Thanks, everybody.

Answer 1

Try SoftFloat library, it have floatx80_to_float32, floatx80_to_float64 and floatx80_to_float128. Detect the native format, act accordingly.