def saturating_mul

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix64.bend:91

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/generic.bend as SG
import bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend as SF
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/src/math/fixed.bend as F
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/fixgen.bend as G

91def saturating_mul(+a: WU.U64, +b: WU.U64) -> SF.SaturatingMul.value(~WU.U64, ~SG.u64_val, ~F.u64_saturating_mul, 64n, a, b):
92  G.sat_fit(~WU.U64, ~SG.u64_val, 64n, Nat.mul(SG.u64_val(a), SG.u64_val(b)), X.mul(a, b), F.u64_max(), X.mul_over(a, b), WA.mul_over_value(a, b), WA.mul_value(a, b), top(1n, {==}), C.fits(64n, Nat.mul(SG.u64_val(a), SG.u64_val(b))), {==})