Basically, to determine what the smallest delta for a given floating-point, decompose that value's ieee representation into sign, fraction, and exponent. My perl's NV is double-precision (53bit precision): from MSB to LSB, sign bit, 11 exponent bits, and 52 fractional bits (plus an implied 1), for sign*(1+fract_bits/2^52)*(2**exp), where (which my perl's NV is), the smallest change would be 2**(-52+exp). So you should just need to know your exp for the current representation (not forgetting to subtract 1023 from the 11bit exponent number). If your NV is more precise (lucky you), just adjust it appropriately.

That's a nice insight. Thankyou. If I need to go this route, that is almost certainly the way to do it.

However, I'm not certain of this yet, but I think my OP question may not actually be required. The problem appears to be -- I'm still struggling with x64 assembler to try and confirm this -- that I'm encountering a lot of denormal numbers; and if I can avoid them, the underlying problem that my OP was an attempt to solve, goes away.

And the problem with avoiding denormal numbers is that the purpose of the code that is generating them is a Newton-Raphson iteration to converge on zero. The exact place where denormals raise their ugly heads. The solution may be (maybe?) to add a constant (say 1 or 2) to both sides of the equations and converge to that number instead. (Not sure about that; but it might work :)

I started work on a module that will expand an ieee754 double-precision float into sign*(1+fract)*2^exp, based on the internal representation.

You might find Exploring IEEE754 floating point bit patterns. (and as you're working with 5.6 , the version at Re^2: Exploring IEEE754 floating point bit patterns.) interesting or even useful.