Comparing Floating Point Numbers

FCMP $X,$Y,$Z
FEQL $X,$Y,$Z
FUN $X,$Y,$Z
FCMPE $X,$Y,$Z
FEQLE $X,$Y,$Z
FUNE $X,$Y,$Z

Specification:

FCMP:	s($X) ← - 1 if f($Y) < f($Z) 0 if f($Y) = f($Z) +1 if f($Y) > f($Z)
FEQL:	s($X) ← 1 if f ($Y) = f($Z) 0 otherwise

Let N_ε(u) = {x| |x - u|≤ ε 2^e-q}, where q is the excess and e = E + q is the sum of exponent and excess of the floating point representation of u. Then:

FCMPE:	s($X) ← - 1 if f($Y) < Nε(f($Z)) and Nε(f($Y)) < f($Z) 0 if f($Y) ∈ Nε(f($Z)) or f($Z) ∈ Nε(f ($Y)) +1 if f($Y) > Nε(f($Z)) and Nε(f($Y)) > f($Z)
FEQLE:	s($X) ← 1 if f($Y) ∈ Nε(f($Z)) and f($Z) ∈ Nε(f ($Y)) 0 otherwise

The value of ε is taken from the special register rE.

FUN:	s($X) ← 1 if either $Y or $Z is not a Number (NaN), 0 otherwise
FUNE:	s($X) ← 1 if either $Y, $Z or rE is not a Number (NaN), 0 otherwise

Description:

For a more detailed description see for example [mmix-doc].