def hid

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64norm.bend:39

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/w64.bend as SW
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
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
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/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sh.bend as SH
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend as FB

39# the hidden bit: f + 2^52 for a fraction below 2^52
40def hid(+one: Nat, +h1: {one == 1n : Nat}, +fa: WU.U64, +hF: {C.fits(52n, SW.value(fa)) == True{} : Bool}, +c: U32, +hc: {c == U32{WD.pw(32n, 20n)} : U32}) -> {SW.value(X.add(fa, WU.U64{0, c})) == Nat.add(SW.value(fa), C.shift(52n, one)) : Nat}:
41  a1 = WA.add_value(fa, WU.U64{0, c})
42  +ec = Equal.trans(Nat, C.shift(32n, v(c)), C.shift(32n, C.shift(20n, one)), C.shift(52n, one), Equal.cong(Nat, Nat, z => C.shift(32n, z), v(c), C.shift(20n, one), FB.pwv(20n, {==}, one, h1, c, hc)), Equal.sym(Nat, C.shift(52n, one), C.shift(32n, C.shift(20n, one)), WW.shift_comp(32n, 20n, one)))
43  +f53 = WW.limbs_fit(52n, 1n, SW.value(fa), one, hF, L.subst(Nat, z => {C.fits(1n, z) == True{} : Bool}, 1n, one, Equal.sym(Nat, one, 1n, h1), {==}))
44  +f64 = SH.fits_mono(53n, 64n, Nat.add(SW.value(fa), C.shift(52n, one)), {==}, f53)
45  Equal.trans(Nat, SW.value(X.add(fa, WU.U64{0, c})), C.low(64n, Nat.add(SW.value(fa), C.shift(32n, v(c)))), Nat.add(SW.value(fa), C.shift(52n, one)), a1, Equal.trans(Nat, C.low(64n, Nat.add(SW.value(fa), C.shift(32n, v(c)))), C.low(64n, Nat.add(SW.value(fa), C.shift(52n, one))), Nat.add(SW.value(fa), C.shift(52n, one)), Equal.cong(Nat, Nat, z => C.low(64n, Nat.add(SW.value(fa), z)), C.shift(32n, v(c)), C.shift(52n, one), ec), WW.low_fit(64n, Nat.add(SW.value(fa), C.shift(52n, one)), f64)))