def neg_g

bend-collections-laws-crypto@1.0.0.0 · proofs/math/typed/f64bits.bend:365

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/spec/math/f64.bend as SF
import bend-collections-laws-crypto@1.0.0.0/src/math/f64.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD

365def neg_g(+l: U32, +h: U32, +c: U32, +hc: {c == U32{WD.pw(32n, 31n)} : U32}) -> {F.Bits{l, U32.xor(h, c)} == SF.neg(F.Bits{l, h}) : F.F64}:
366  +H = v(h)
367  +f = C.low(20n, H)
368  +E = C.low(11n, C.high(20n, H))
369  +t = Nat.sub(1n, C.high(31n, H))
370  +tb = SF.b2n(Bool.not(SF.sign(F.Bits{l, h})))
371  +e1 = Equal.trans(Nat, v(U32.xor(h, c)), Nat.add(C.low(31n, H), C.shift(31n, t)), Nat.add(Nat.add(f, C.shift(20n, E)), C.shift(31n, t)), xorv(h, c, hc), Equal.cong(Nat, Nat, z => Nat.add(z, C.shift(31n, t)), C.low(31n, H), Nat.add(f, C.shift(20n, E)), low_split(20n, 11n, H)))
372  +e2 = Equal.trans(Nat, v(U32.xor(h, c)), Nat.add(Nat.add(f, C.shift(20n, E)), C.shift(31n, t)), Nat.add(f, C.shift(20n, Nat.add(E, C.shift(11n, t)))), e1, fold(f, E, t))
373  +e3 = Equal.cong(Nat, Nat, z => Nat.add(f, C.shift(20n, Nat.add(E, C.shift(11n, z)))), t, tb, nbit_c(C.high(31n, H), half0(h)))
374  enc_g(l, h, Bool.not(SF.sign(F.Bits{l, h})), U32.xor(h, c), Equal.trans(Nat, v(U32.xor(h, c)), Nat.add(f, C.shift(20n, Nat.add(E, C.shift(11n, t)))), Nat.add(f, C.shift(20n, Nat.add(E, C.shift(11n, tb)))), e2, e3))