def abs_g

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64bits.bend:381

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/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

381def abs_g(+l: U32, +h: U32, +m31: U32, +hm31: {m31 == U32{WD.mask(32n, 31n)} : U32}) -> {F.Bits{l, U32.and(h, m31)} == SF.encode(False{}, SF.efield(F.Bits{l, h}), SF.frac(F.Bits{l, h})) : F.F64}:
382  +H = v(h)
383  +f = C.low(20n, H)
384  +E = C.low(11n, C.high(20n, H))
385  +e1 = Equal.trans(Nat, v(U32.and(h, m31)), C.low(31n, H), Nat.add(f, C.shift(20n, E)), andm(h, 31n, m31, hm31), low_split(20n, 11n, H))
386  +e2 = Equal.cong(Nat, Nat, z => Nat.add(f, C.shift(20n, z)), E, Nat.add(E, C.shift(11n, SF.b2n(False{}))), Equal.sym(Nat, Nat.add(E, 0n), E, N.add_zero(E)))
387  enc_g(l, h, False{}, U32.and(h, m31), Equal.trans(Nat, v(U32.and(h, m31)), Nat.add(f, C.shift(20n, E)), Nat.add(f, C.shift(20n, Nat.add(E, C.shift(11n, SF.b2n(False{}))))), e1, e2))