/*++
Copyright (c) 2014 Microsoft Corporation

Module Name:

    mod_interval_def.h

Abstract:

    Intervals over fixed precision modular arithmetic

Author:

    Nikolaj Bjorner (nbjorner) 2021-03-19
    Jakob Rath 2021-04-6

--*/

#pragma once

#include "fixplex_mod_interval.h"

template<typename Numeral>
bool mod_interval<Numeral>::contains(Numeral const& n) const {
    if (is_empty())
        return false;
    if (is_free())
        return true;
    if (lo < hi)
        return lo <= n && n < hi;
    else
        return lo <= n || n < hi;
}

template<typename Numeral>
bool mod_interval<Numeral>::contains(mod_interval const& other) const {
    if (is_empty())
        return other.is_empty();
    if (is_free())
        return true;
    if (hi == 0)
        return lo <= other.lo && (other.lo < other.hi || other.hi == 0);
    if (lo < hi)
        return lo <= other.lo && other.hi <= hi;
    if (other.lo < other.hi && other.hi <= hi)
        return true;
    if (other.lo < other.hi && lo <= other.lo)
        return true;
    if (other.hi == 0)
        return lo <= other.lo;
    SASSERT(other.hi < other.lo && other.hi != 0);
    SASSERT(hi < lo && hi != 0);
    return lo <= other.lo && other.hi <= hi;
}

template<typename Numeral>
mod_interval<Numeral> mod_interval<Numeral>::operator+(mod_interval<Numeral> const& other) const {
    if (is_empty())
        return *this;
    if (other.is_empty())
        return other;
    if (is_free())
        return *this;
    if (other.is_free())
        return other;
    Numeral sz = (hi - lo) + (other.hi - other.lo);
    if (sz < (hi - lo))
        return mod_interval::free();
    return mod_interval(lo + other.lo, hi + other.hi);
}

template<typename Numeral>
mod_interval<Numeral> mod_interval<Numeral>::operator-(mod_interval<Numeral> const& other) const {
    return *this + (-other);
}

template<typename Numeral>
mod_interval<Numeral> mod_interval<Numeral>::operator-() const {
    if (is_empty())
        return *this;
    if (is_free())
        return *this;
    return mod_interval(1 - hi, 1 - lo);
}

template<typename Numeral>
mod_interval<Numeral> mod_interval<Numeral>::operator*(Numeral const& n) const {
    if (is_empty())
        return *this;
    if (n == 0)
        return mod_interval(0, 1);
    if (n == 1)
        return *this;
    if (is_free())
        return *this;
    Numeral sz = hi - lo;
    if (0 - n < n) {
        Numeral mn = 0 - n;
        Numeral mz = mn * sz;            
        if (mz / mn != sz)
            return mod_interval::free();
        return mod_interval((hi - 1) * n, n * lo + 1);
    }
    else {
        Numeral mz = n * sz;
        if (mz / n != sz)
            return mod_interval::free();
        return mod_interval(n * lo, n * (hi - 1) + 1);
    }
}

template<typename Numeral>
mod_interval<Numeral> mod_interval<Numeral>::operator&(mod_interval const& other) const {
    Numeral l, h;
    if (is_free() || other.is_empty())
        return other;
    if (other.is_free() || is_empty())
        return *this;

    if (lo < hi || hi == 0) {
        if (other.lo < other.hi || other.hi == 0) {
            if (hi != 0 && hi <= other.lo)
                return mod_interval::empty();
            if (other.hi != 0 && other.hi <= lo)
                return mod_interval::empty();
            l = lo >= other.lo ? lo : other.lo;
            h = hi == 0 ? other.hi : (other.hi == 0 ? hi : (hi <= other.hi ? hi : other.hi));
            return mod_interval(l, h);
        }
        SASSERT(0 < other.hi && other.hi < other.lo);
        if (other.lo <= lo)
            return *this;
        if (other.hi <= lo && lo < hi && hi <= other.lo)
            return mod_interval::empty();
        if (lo <= other.hi && other.hi <= hi && hi <= other.lo)
            return mod_interval(lo, other.hi);
        if (hi == 0 && lo < other.hi)
            return *this;
        if (hi == 0 && other.hi <= lo)
            return mod_interval(other.lo, hi);
        if (other.hi <= lo && other.hi <= hi)
            return mod_interval(other.lo, hi);
        return *this;
    }
    SASSERT(hi < lo);
    if (other.lo < other.hi || other.hi == 0)
        return other & *this;
    SASSERT(other.hi < other.lo);
    SASSERT(hi != 0);
    SASSERT(other.hi != 0);
    if (lo <= other.hi)
        return *this;
    if (other.lo <= hi)
        return other;
    l = lo <= other.lo ? other.lo : lo;
    h = hi >= other.hi ? other.hi : hi;
    return mod_interval(l, h);

}

template<typename Numeral>
Numeral mod_interval<Numeral>::max() const {
    if (lo < hi)
        return hi - 1;
    else
        return Numeral(0) - 1;
}

template<typename Numeral>
Numeral mod_interval<Numeral>::min() const {
    if (lo < hi || hi == 0)
        return lo;
    else
        return Numeral(0);
}


template<typename Numeral>
Numeral mod_interval<Numeral>::closest_value(Numeral const& n) const {
    if (contains(n))
        return n;
    if (is_empty())
        return n;
    if ((Numeral)(lo - n) < (Numeral)(n - hi))
        return lo;
    return hi - 1;
}

template<typename Numeral>
mod_interval<Numeral>& mod_interval<Numeral>::intersect_uge(Numeral const& l) {
    if (is_empty())
        return *this;
    if (lo < hi && hi <= l)
        set_empty();
    else if (is_free())
        lo = l, hi = 0;
    else if ((lo < hi || hi == 0) && lo < l)
        lo = l;
    else if (hi < lo && hi <= l && l <= lo)
        hi = 0;
    else if (hi < lo && lo < l)
        hi = 0, lo = l;
    else if (0 < l && l < hi && hi < lo)
        lo = l, hi = 0;
    return *this;
}

template<typename Numeral>
mod_interval<Numeral>& mod_interval<Numeral>::intersect_ugt(Numeral const& l) {
    if (is_empty())
        return *this;
    if (is_max(l))
        set_empty();
    else if (is_free())
        lo = l + 1, hi = 0;
    else if (lo < hi && hi - 1 <= l)
        set_empty();
    else if (lo < hi && l < lo)
        return *this;
    else if (lo < hi)
        lo = l + 1;
    else if (hi < lo && hi <= l + 1 && l < lo)
        hi = 0;
    else if (hi < lo && lo <= l)
        hi = 0, lo = l + 1;
    else if (l <= hi && hi < lo)
        lo = l + 1, hi = 0;
    return *this;
}

template<typename Numeral>
mod_interval<Numeral>& mod_interval<Numeral>::intersect_ule(Numeral const& h) {
    if (is_empty())
        return *this;
    if (is_max(h))
        return *this;
    else if (is_free())
        lo = 0, hi = h + 1;
    else if (h < lo && (lo < hi || hi == 0))
        set_empty();
    else if (hi == 0 && h >= lo)
        hi = h + 1;
    else if (lo <= h && h + 1 < hi)
        hi = h + 1;
    else if (h < hi && hi < lo)
        hi = h + 1, lo = 0;
    else if (hi <= h && h < lo)
        lo = 0;
    else if (hi == 0 && hi == h && hi < lo)
        set_empty();
    else if (0 < hi && hi == h && hi < lo)
        lo = 0;
    else if (0 < hi && hi < h && hi < lo)
        lo = 0, hi = h + 1;
    return *this;
}

template<typename Numeral>
mod_interval<Numeral>& mod_interval<Numeral>::intersect_ult(Numeral const& h) {
    if (is_empty())
        return *this;
    if (h == 0)
        set_empty();
    else if (is_free())
        lo = 0, hi = h;
    else if (h <= lo && (lo < hi || hi == 0))
        set_empty();
    else if (h > lo && (h < hi || hi == 0))
        hi = h;
    else if (hi < lo && h <= hi)
        hi = h, lo = 0;
    else if (hi < h && h <= lo)
        lo = 0;
    else if (0 < hi && hi < lo && hi + 1 <= h)
        lo = 0, hi = h;
    return *this;
}


template<typename Numeral>
mod_interval<Numeral>& mod_interval<Numeral>::intersect_fixed(Numeral const& a) {
    if (is_empty())
        return *this;
    if (!contains(a))
        set_empty();
    else if (is_max(a))
        lo = a, hi = 0;
    else
        lo = a, hi = a + 1;
    return *this;
}

template<typename Numeral>
mod_interval<Numeral>& mod_interval<Numeral>::intersect_diff(Numeral const& a) {
    if (!contains(a) || is_empty())
        return *this;
    if (a == lo && a + 1 == hi)
        set_empty();
    else if (a == lo && hi == 0 && is_max(a))
        set_empty();
    else if (is_free())
        lo = a + 1, hi = a;
    else if (0 < hi && hi < lo && a == lo)        
        return *this;
    else if (a == lo && !is_max(a))
        lo = a + 1;
    else if (a + 1 == hi)
        hi = a;
    else if (hi == 0 && is_max(a))
        hi = a;

    return *this;
}

template<typename Numeral>
mod_interval<Numeral>& mod_interval<Numeral>::update_lo(Numeral const& new_lo) {
    SASSERT(lo <= new_lo);
    if (lo < hi && hi <= new_lo)
	    set_empty();
    else
	    lo = new_lo;
    return *this;
}

template<typename Numeral>
mod_interval<Numeral>& mod_interval<Numeral>::update_hi(Numeral const& new_hi) {
    SASSERT(new_hi <= hi);
    if (new_hi <= lo && lo < hi)
	    set_empty();
    else
	    hi = new_hi;
    return *this;
}