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Just a few small tweaks.
I think you meant to subtract the second term here:
+ #('>e', b'\x80\x01', -2.0**-25 + 2.0**-35), # Rounds to minimum subnormal
Isn't the "x < 0" part unnecessary? Maybe a comment explaining why the signbit function is used, to preserve -0, would help people who otherwise might think to replace it with "x < 0".
+ if (x < 0 || signbit(x)) {
This is creating a signaling nan. It would be better to create a quiet nan by setting the highest order bit instead of the lowest order bit.
+ else if (isnan(x)) {
+ e = 0x1f;
+ bits = 1;
+ }
Otherwise it looks great to me, good work!