def magQ

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64cmp.bend:210

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/f64.bend as SF
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend as FB

210# the magnitude word is K
211def magQ(+xl: U32, +xh: U32) -> {Nat.add(v(xl), C.shift(32n, C.low(31n, v(xh)))) == Nat.add(SF.frac(F.Bits{xl, xh}), C.shift(52n, SF.efield(F.Bits{xl, xh}))) : Nat}:
212  +H = v(xh)
213  +f = C.low(20n, H)
214  +Ee = C.low(11n, C.high(20n, H))
215  Equal.trans(Nat, Nat.add(v(xl), C.shift(32n, C.low(31n, H))), Nat.add(v(xl), C.shift(32n, Nat.add(f, C.shift(20n, Ee)))), Nat.add(Nat.add(v(xl), C.shift(32n, f)), C.shift(52n, Ee)), Equal.cong(Nat, Nat, z => Nat.add(v(xl), C.shift(32n, z)), C.low(31n, H), Nat.add(f, C.shift(20n, Ee)), FB.low_split(20n, 11n, H)), Equal.trans(Nat, Nat.add(v(xl), C.shift(32n, Nat.add(f, C.shift(20n, Ee)))), Nat.add(v(xl), Nat.add(C.shift(32n, f), C.shift(32n, C.shift(20n, Ee)))), Nat.add(Nat.add(v(xl), C.shift(32n, f)), C.shift(52n, Ee)), Equal.cong(Nat, Nat, z => Nat.add(v(xl), z), C.shift(32n, Nat.add(f, C.shift(20n, Ee))), Nat.add(C.shift(32n, f), C.shift(32n, C.shift(20n, Ee))), WW.shift_add(32n, f, C.shift(20n, Ee))), Equal.trans(Nat, Nat.add(v(xl), Nat.add(C.shift(32n, f), C.shift(32n, C.shift(20n, Ee)))), Nat.add(v(xl), Nat.add(C.shift(32n, f), C.shift(52n, Ee))), Nat.add(Nat.add(v(xl), C.shift(32n, f)), C.shift(52n, Ee)), Equal.cong(Nat, Nat, z => Nat.add(v(xl), Nat.add(C.shift(32n, f), z)), C.shift(32n, C.shift(20n, Ee)), C.shift(52n, Ee), Equal.sym(Nat, C.shift(52n, Ee), C.shift(32n, C.shift(20n, Ee)), WW.shift_comp(32n, 20n, Ee))), Equal.sym(Nat, Nat.add(Nat.add(v(xl), C.shift(32n, f)), C.shift(52n, Ee)), Nat.add(v(xl), Nat.add(C.shift(32n, f), C.shift(52n, Ee))), NA.add_assoc(v(xl), C.shift(32n, f), C.shift(52n, Ee))))))