/**
 * Returns the result of compressing the given floating point expansion.
 * 
 * * primarily for internal library use
 * 
 * * see [Shewchuk](https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf)
 * 
 * Theorem 23 (Shewchuck): Let e = sum_(i=1)^m(e_i) be a nonoverlapping 
 * expansion of m p-bit components, where m >= 3. Suppose that the components of
 * e are sorted in order of increasing magnitude, except that any of the e_i may
 * be zero. Then the following algorithm will produce a nonoverlapping expansion 	
 * (nonadjacent if round-to even tiebreaking is used) such that 
 * h = sum_(i=1)^n(h_i) = e, where the components h_i are in order of increasing
 * magnitude. If h != 0, none of the h_i will be zero. Furthermore, the largest 
 * component h_n approximates h with an error smaller than ulp(h_n).
 */
function eCompress(e: number[]) {
    //return e;
    const e_ = e.slice();
    const m = e_.length;

    if (m === 1) { 
        return e_; 
    }

    let Q = e_[m-1];
    let bottom = m;
    for (let i=m-2; i>=0; --i) {
        const a = Q;
        const b = e_[i];
        Q = a + b;
        const bv = Q - a;
        const q = b - bv;
        if (q) {
            e_[--bottom] = Q;
            Q = q;
        }
    }

    let top = 0;
    for (let i=bottom; i<m; ++i) {
        const a = e_[i];
        const b = Q;
        Q = a + b;
        const bv = Q - a;
        const q = b - bv;
        if (q) {
            e_[top++] = q;
        }
    }

    e_[top++] = Q;
    e_.length = top;

    return e_;
}


export { eCompress }