def magv

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64cmp.bend:217

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/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend as FB

217def magv(+xl: U32, +xh: U32, +m31: U32, +hm31: {m31 == U32{WD.mask(32n, 31n)} : U32}) -> {SW.value(WU.U64{xl, U32.and(xh, m31)}) == Nat.add(SF.frac(F.Bits{xl, xh}), C.shift(52n, SF.efield(F.Bits{xl, xh}))) : Nat}:
218  Equal.trans(Nat, Nat.add(v(xl), C.shift(32n, v(U32.and(xh, m31)))), 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}))), Equal.cong(Nat, Nat, z => Nat.add(v(xl), C.shift(32n, z)), v(U32.and(xh, m31)), C.low(31n, v(xh)), FB.andm(xh, 31n, m31, hm31)), magQ(xl, xh))