def sh1

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64mulc.bend:64

import Base
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/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU

64def sh1(+s: Bool, +ea: Nat, +fa: WU.U64, +eb: Nat, +fb: WU.U64, +t: Bool) -> {F.mul_cls(s, ea, fa, eb, fb, t) == mimpl(s, t, X.is_zero(fa), Nat.is_eq(ea, 0n), Nat.is_eq(eb, 2047n), X.is_zero(fb), Nat.is_eq(eb, 0n), F.mul_n(s, F.norm_e(ea, fa), F.norm_f(ea, fa), F.norm_e(eb, fb), F.norm_f(eb, fb))) : F.F64}:
65  match t:
66    case True{}:
67      ion(s, Bool.or(Bool.or(Bool.not(X.is_zero(fa)), Bool.and(Nat.is_eq(eb, 2047n), Bool.not(X.is_zero(fb)))), Bool.and(Nat.is_eq(eb, 0n), X.is_zero(fb))))
68    case False{}:
69      sh2(s, ea, fa, eb, fb, Nat.is_eq(eb, 2047n))