BigInt1.swift

BigInt.swift

struct BigInt {
    private let overflows: UInt64
    private var remainder: UInt64
  
    func add(_ x: BigInt) -> BigInt {
        let totalOverflows = self.overflows + x.overflows
        let result = self.remainder.addingReportingOverflow(x.remainder)

        return BigInt(
            overflows: totalOverflows + (result.overflow ? 1 : 0),
            remainder: result.partialValue)
    }

    //((a * n) + c1) * ((b * n) + c2) = (a * n) * (b * n) + (a * n) * c2 + c1 * (b * n) + c1 * c2
    func multiply(by x: BigInt) -> BigInt {
        let totalOverflows = self.overflows.multipliedReportingOverflow(by: x.overflows)
        let xRemainderOverflows = self.overflows.multipliedReportingOverflow(by: x.remainder)
        let selfRemainderOverflow = self.remainder.multipliedReportingOverflow(by: x.overflows)
        let remainder = self.remainder.multipliedReportingOverflow(by: x.remainder)

        return BigInt(
            overflows: totalOverflows.partialValue
            + xRemainderOverflows.partialValue
            + selfRemainderOverflow.partialValue
            + (remainder.overflow ? 1 : 0),
            remainder: remainder.partialValue
        )
    }
}