Require Import ZArith Floats.

Definition two := Eval compute in (one + one)%float.
Definition half := Eval compute in (one / two)%float.
Definition huge := Eval compute in ldexp one (1023)%Z.
Definition tiny := Eval compute in ldexp one (-1023)%Z.
Definition denorm := Eval compute in ldexp one (-1074)%Z.

Check (eq_refl : SF2Prim (Prim2SF zero) = zero).
Check (eq_refl : SF2Prim (Prim2SF neg_zero) = neg_zero).
Check (eq_refl : SF2Prim (Prim2SF one) = one).
Check (eq_refl : SF2Prim (Prim2SF (-one)) = (-one)%float).
Check (eq_refl : SF2Prim (Prim2SF infinity) = infinity).
Check (eq_refl : SF2Prim (Prim2SF neg_infinity) = neg_infinity).
Check (eq_refl : SF2Prim (Prim2SF huge) = huge).
Check (eq_refl : SF2Prim (Prim2SF tiny) = tiny).
Check (eq_refl : SF2Prim (Prim2SF denorm) = denorm).
Check (eq_refl : SF2Prim (Prim2SF nan) = nan).
Check (eq_refl : SF2Prim (Prim2SF two) = two).
Check (eq_refl : SF2Prim (Prim2SF half) = half).

Check (eq_refl zero <: SF2Prim (Prim2SF zero) = zero).
Check (eq_refl neg_zero <: SF2Prim (Prim2SF neg_zero) = neg_zero).
Check (eq_refl one <: SF2Prim (Prim2SF one) = one).
Check (eq_refl (-one)%float <: SF2Prim (Prim2SF (-one)) = (-one)%float).
Check (eq_refl infinity <: SF2Prim (Prim2SF infinity) = infinity).
Check (eq_refl neg_infinity <: SF2Prim (Prim2SF neg_infinity) = neg_infinity).
Check (eq_refl huge <: SF2Prim (Prim2SF huge) = huge).
Check (eq_refl tiny <: SF2Prim (Prim2SF tiny) = tiny).
Check (eq_refl denorm <: SF2Prim (Prim2SF denorm) = denorm).
Check (eq_refl nan <: SF2Prim (Prim2SF nan) = nan).
Check (eq_refl two <: SF2Prim (Prim2SF two) = two).
Check (eq_refl half <: SF2Prim (Prim2SF half) = half).

Check (eq_refl zero <<: SF2Prim (Prim2SF zero) = zero).
Check (eq_refl neg_zero <<: SF2Prim (Prim2SF neg_zero) = neg_zero).
Check (eq_refl one <<: SF2Prim (Prim2SF one) = one).
Check (eq_refl (-one)%float <<: SF2Prim (Prim2SF (-one)) = (-one)%float).
Check (eq_refl infinity <<: SF2Prim (Prim2SF infinity) = infinity).
Check (eq_refl neg_infinity <<: SF2Prim (Prim2SF neg_infinity) = neg_infinity).
Check (eq_refl huge <<: SF2Prim (Prim2SF huge) = huge).
Check (eq_refl tiny <<: SF2Prim (Prim2SF tiny) = tiny).
Check (eq_refl denorm <<: SF2Prim (Prim2SF denorm) = denorm).
Check (eq_refl nan <<: SF2Prim (Prim2SF nan) = nan).
Check (eq_refl two <<: SF2Prim (Prim2SF two) = two).
Check (eq_refl half <<: SF2Prim (Prim2SF half) = half).