// uint256: Fixed size 256-bit math library
// Copyright 2020 uint256 Authors
// SPDX-License-Identifier: BSD-3-Clause

package uint256

import "math/bits"

// reciprocal2by1 computes <^d, ^0> / d.
func reciprocal2by1(d uint64) uint64 {
	reciprocal, _ := bits.Div64(^d, ^uint64(0), d)
	return reciprocal
}

// udivrem2by1 divides <uh, ul> / d and produces both quotient and remainder.
// It uses the provided d's reciprocal.
// Implementation ported from https://github.com/chfast/intx and is based on
// "Improved division by invariant integers", Algorithm 4.
func udivrem2by1(uh, ul, d, reciprocal uint64) (quot, rem uint64) {
	qh, ql := bits.Mul64(reciprocal, uh)
	ql, carry := bits.Add64(ql, ul, 0)
	qh, _ = bits.Add64(qh, uh, carry)
	qh++

	r := ul - qh*d

	if r > ql {
		qh--
		r += d
	}

	if r >= d {
		qh++
		r -= d
	}

	return qh, r
}