/++
$(LINK2 https://research.google.com/pubs/pub40671.html, HyperLogLog++) implementation.

Authors: Ilya Yaroshenko
Copyright: Tamedia Digital
License:  Boost Software License version 1.0
+/
module hll;

version(LDC)
pragma(LDC_no_moduleinfo);

import std.uuid;
import std.traits;
import mir.ndslice.slice;
static import core.stdc.stdlib;

extern(C) @system nothrow @nogc
{
    ///
    alias HLL_Malloc = void* function(size_t size);
    ///
    alias HLL_Realloc = void* function(void* ptr, size_t size);
    ///
    alias HLL_Free = void function(void* ptr);

    /++
    Creates $(LREF HLL) instance.
    The structure constructor can be used instead.

    Params:
        hll = hll reference
        p = precision, p ∈ [4..min(pPrime, 18)]"
        pPrime = precision for sparse representation, pPrime ∈ [4..63]
        malloc = memory allocation function
        realloc = memory reallocation function
        free = memory free function

    Returns: 0 on success and a positive value if parameters are wrong.
    +/
    pragma(inline, false)
    int dlang_hll_create(
        ref HLL hll,
        uint p = 18,
        uint pPrime = 25, 
        HLL_Malloc malloc = &core.stdc.stdlib.malloc,
        HLL_Realloc realloc = &core.stdc.stdlib.realloc,
        HLL_Free free = &core.stdc.stdlib.free,
        )
    {
        if (!(4 <= p && p <= pPrime && p <= 18))
            return 1;
        if (!(pPrime <= 63))
            return 2;

        hll.p = p;
        hll.pPrime = pPrime;
        hll.malloc = malloc;
        hll.realloc = realloc;
        hll.free = free;
        hll._normal = null;
        hll._sparse = null;
        hll._sparse_count = 0;
        hll._temp = null;
        hll._temp_length = 0;

        if (hll.pPrime)
        {
            hll._temp = (cast(ulong*)hll.malloc(24 * ulong.sizeof))[0 .. 24];
        }
        else
        {
            hll._normal = cast(ulong*)malloc(normal_allocation_size(hll.p));
            foreach(ref e; hll._normal[0 .. normal_length(hll.p)])
                e = 0;
        }
        return 0;
    }

    /++
    Destroys $(LREF HLL) instance.
    The structure destructor can be used instead.
    +/
    pragma(inline, false)
    void dlang_hll_destroy(ref HLL hll)
    {
        with(hll)
        {
            deallocateSparse();
            if (_normal)
            {
                free(_normal);
            }
        }
    }

    /++
    Computes 64bit Murmurhash3 value.
    +/
    pragma(inline, false)
    ulong dlang_hll_murmurhash(const(void)* ptr, size_t size)
    {
        import std.digest.murmurhash: MurmurHash3;
        version (D_LP64)
            alias Hasher = MurmurHash3!(128, 64);
        else
            alias Hasher = MurmurHash3!(128, 32);
        Hasher d;
        d.put((cast(ubyte*)ptr)[0 .. size]);
        static union U { ubyte[16] bytes; ulong[2] longs; }
        U u = {bytes : d.finish};
        auto hashed = u.longs;
        return hashed[0] ^ hashed[1];
    }

    /++
    Puts data or hash value to the counter.
    +/
    alias put = dlang_hll_put_hash;
    ///
    alias put = dlang_hll_put_uuid;

    ///ditto
    void dlang_hll_put_uuid(ref HLL hll, ref UUID uuid)
    {
        auto ulongs = *cast(ulong[2]*)&uuid;
        enum ulong m = 0xc6a4a7935bd1e995UL;
        enum ulong n = m * 16;
        enum uint r = 47;

        ulong h = n;

        ulong k = ulongs[0];
        k *= m;
        k ^= k >> r;
        k *= m;

        h ^= k;
        h *= m;

        k = ulongs[1];
        k *= m;
        k ^= k >> r;
        k *= m;

        h ^= k;
        h *= m;
        dlang_hll_put_hash(hll, h);
    }

    ///ditto
    pragma(inline, true)
    extern(D)
    void put()(ref HLL hll, const(void)[] data)
    {
        dlang_hll_put_hash(hll, dlang_hll_murmurhash(data.ptr, data.length));
    }

    ///ditto
    pragma(inline, false)
    void dlang_hll_put_hash(ref HLL hll, ulong hash)
    {
        with(hll)
        {
            if (_temp) //temp is always allocated for sparse representation
            {
                putTemp(encodeHash(hash));
                if (temp.length >= normal_length(p) / 4)
                {
                    dlang_hll_unite_temp(hll);
                    assert(_sparse.length);
                    if (_sparse.length + _temp.length * ulong.sizeof >= normal_allocation_size(p))
                    {
                        import mir.ndslice.topology: bitpack;
                        auto from = inputSparse;
                        auto ret = cast(ulong*)malloc(normal_allocation_size(p));
                        foreach(ref e; ret[0 .. normal_length(p)])
                            e = 0;
                        auto bp = ret[0 .. normal_length(p)].sliced.bitpack!6;
                        assert(bp.length == m(p));
                        while(!from.empty)
                        {
                            auto e = from.front;
                            ulong r;
                            ulong idx = decodeHash(e, r);
                            idx >>= pPrime - p;
                            assert(idx < bp.length);
                            if (r > bp[idx])
                                bp[idx] = r;
                            from.popFront;
                        }
                        _normal = ret;
                        deallocateSparse;
                    }
                }
                return;
            }
            // normal representation
            auto bp = normal;
            auto shift = 64 - p;
            size_t idx = cast(size_t) (hash >> shift);
            assert(idx < bp.length);
            ulong r = rho(hash);
            ulong r1;
            auto idx1 = decodeHash(encodeHash(hash), r1);
            idx1 >>= pPrime - p;
            assert(idx1 == idx);
            assert(r1 == r);
            if (r > bp[idx])
                bp[idx] = r;
        }
    }

    /++
    Returns estimated cardinality number.
    +/
    alias count = dlang_hll_count;

    ///ditto
    pragma(inline, false)
    ulong dlang_hll_count(ref HLL hll)
    {
        with(hll)
        {
            if (_temp.length)
            {
                dlang_hll_unite_temp(hll);
                return cast(ulong) linearCounting(m(pPrime), m(pPrime) - _sparse_count);
            }
            import mir.math.common: pow;
            ulong overflows;
            ulong value;
            size_t v;
            foreach(e; normal)
            {
                if (e == 0)
                    v++;
                assert(e <= 63);
                e = ulong(1) << (63 - e);
                if (e > ulong.max - value)
                    overflows++;
                value += e;
            }
            double alpha = void;
            switch(p)
            {
                case 4:
                    alpha = 0.673;
                    break;
                case 5:
                    alpha =  0.697;
                    break;
                case 6:
                    alpha = 0.709;
                    break;
                default:
                    alpha = 0.7213 / (1 + 1.079 / m(p));
                    break;
            }
            enum double p2_64 = 2.0 ^^ 64;
            double e = alpha * pow(2.0, 2 * int(p) + 63) / (overflows * p2_64 + value);

            immutable double[] raw = _rawEstimateData[p - 4];
            immutable double[] data = _biasData[p - 4];
            import std.range;
            size_t lb = raw.bs_lower_bound(e);
            double bias = void;
            if (lb == 0)
                bias = data[0];
            else
            if (lb == raw.length)
                bias = data[$-1];
            else
            if (raw[lb] == e)
                bias = raw[lb];
            else
            {
                auto w1 = raw[lb] - e;
                auto w2 = e - raw[lb-1];
                bias = (data[lb] * w1 + data[lb-1] * w2) / (w1 + w2);
            }

            double ePrime = e <= 5 * m(p) ? e - bias : e;
            double h = v ? linearCounting(m(p), v) : ePrime;
            return cast(ulong)(h <= _threshold[p - 4] ? h : ePrime);
        }
    }

    ///
    void dlang_hll_unite_temp(ref HLL hll)
    {
        with(hll)
        {
            if (temp.length == 0)
                return;
            import mir.ndslice.sorting: sort;
            temp.sliced.sort!((a, b) => less(a, b));
            auto new_sparse_length = _sparse.length + temp.length * 10 + 10;
            auto new_sparse = malloc(new_sparse_length);

            auto o = OutputSparse(cast(ubyte*)new_sparse, new_sparse_length, 0, 0, 0);

            auto i1 = inputSparse;
            auto i2 = temp.sliced;
            if (!i1.empty && !i1.empty)
            for(;;)
            {
                ulong f1 = i1.front;
                ulong f2 = i2.front;
                ulong r1; 
                ulong r2;
                ulong d1 = decodeHash(f1, r1);
                ulong d2 = decodeHash(f2, r2);
                if (d1 < d2)
                {
                    o.put(f1);
                    i1.popFront;
                    if(i1.empty)
                        break;
                }
                else
                {
                    i2.popFront;
                    while(!i2.empty)
                    {
                        ulong f3 = i2.front;
                        ulong r3;
                        ulong d3 = decodeHash(f3, r3);
                        if (d3 != d2)
                        {
                            assert(d3 > d2);
                            break;
                        }
                        assert(r3 >= r2);
                        r2 = r3;
                        f2 = f3;
                        i2.popFront;
                    }
                    if (d1 > d2)
                    {
                        o.put(f2);
                        if(i2.empty)
                            break;
                    }
                    else
                    {
                        o.put(r1 > r2 ? f1 : f2);
                        i1.popFront;
                        if(i1.empty || i2.empty)
                            break;
                    }
                }
            }
            foreach (e; i1)
            {
                o.put(e);
            }
            while (!i2.empty)
            {
                ulong r2;
                ulong f2 = i2.front;
                ulong d2 = decodeHash(f2, r2);
                i2.popFront;
                while(!i2.empty)
                {
                    ulong f3 = i2.front;
                    ulong r3;
                    ulong d3 = decodeHash(f3, r3);
                    if (d3 != d2)
                    {
                        assert(d3 > d2);
                        break;
                    }
                    assert(r3 >= r2);
                    r2 = r3;
                    f2 = f3;
                    i2.popFront;
                }
                o.put(f2);
            }

            assert(o.length);
            auto r = realloc(new_sparse, o.length);
            assert(r);
            if (_sparse.length)
                free(_sparse.ptr);
            _sparse = (cast(ubyte*)r)[0 .. o.length];
            assert(_sparse.length);
            _sparse_count = o.count;
            _temp_length = 0;

        }
    }
}

private size_t bs_lower_bound()(in double[] a, double x) {
    size_t l = 0;
    size_t h = a.length;
    while (l < h) {
        size_t mid = (l + h) / 2;
        if (x <= a[mid])
            h = mid;
        else
            l = mid + 1;
    }
    return l;
}

/++
Generic $(LINK2 https://research.google.com/pubs/pub40671.html, HyperLogLog++) implementation.
Params:
    p = precision for normal representation, p ∈ [4..min(pPrime, 18)].
        The implementation uses less or equal to `2 ^^ (p - 3) * 6` bytes of memory.
    pPrime = precision for sparse representation, pPrime ∈ [4..63].

The structure is not copyable and has destructor.
+/
struct HLL
{
    ///
    @disable this();
    ///
    @disable this(this);

    extern(C) @system nothrow @nogc
    {
        HLL_Malloc malloc;
        HLL_Realloc realloc;
        HLL_Free free;
    }

    uint p; // = 18;
    uint pPrime; // = 25;

    private ulong* _normal;
    private ubyte[] _sparse;
    private size_t _sparse_count;
    private ulong[] _temp;
    size_t _temp_length;

    static nothrow @trusted size_t __xtoHash(ref const(typeof(this)))
    {
        assert(0);
    }

    static bool __xopEquals (ref const(const(typeof(this))), ref const(const(typeof(this))))
    {
        assert(0);
    }

pragma(inline, true):


    ///
    this(uint p,
        uint pPrime = 25, 
        typeof(this.malloc) malloc = &core.stdc.stdlib.malloc,
        typeof(this.realloc) realloc = &core.stdc.stdlib.realloc,
        typeof(this.free) free = &core.stdc.stdlib.free,
        )
    {
        assert(4 <= p && p <= pPrime && p <= 18, "constraint: p ∈ [4..min(pPrime, 18)]");
        assert(pPrime <= 63, "constraint: pPrime ∈ [4..63]");
        auto r = dlang_hll_create(this, p, pPrime, malloc, realloc, free);
        assert(r == 0);
    }

    ///
    ~this()
    {
        dlang_hll_destroy(this);
    }

    private:

    ulong[] temp()()
    {
        return _temp[0 .. _temp_length];
    }

    private void putTemp()(ulong x)
    {
        assert(_temp_length <= _temp.length);
        if (_temp_length == _temp.length)
        {
            auto d = (cast(void*)_temp.ptr)[0..temp.length * ulong.sizeof];
            assert(d.ptr);
            auto r = realloc(d.ptr, d.length * 2);
            assert(r);
            _temp = (cast(ulong*)r)[0 .. _temp.length * 2];
        }
        _temp[_temp_length++] = x;
    }

    void deallocateSparse()()
    {
        if (_temp.ptr)
        {
            free(_temp.ptr);
            _temp = null;
        }
        if (_sparse.ptr)
        {
            free(_sparse.ptr);
            _sparse = null;
        }
    }

    InputSparse inputSparse()()
    {
        if (_sparse.ptr)
            return InputSparse(_sparse.ptr, _sparse_count);
        return InputSparse(null, 0);
    }

    auto normal()()
    {
        import mir.ndslice.topology: bitpack;
        return _normal[0 .. normal_length(p)].sliced.bitpack!6;
    }
    pragma(inline)
    bool less()(ulong a, ulong b)
    {
        version(LDC) pragma(inline, true);
        ulong r1;
        ulong r2;
        ulong d1 = decodeHash(a, r1);
        ulong d2 = decodeHash(b, r2);
        if(long d = d1 - d2)
            return d < 0;
        return long(r1 - r2) < 0;
    }

    ulong rho()(ulong x)
    {
        x <<= p;
        x ^= 1UL << (p - 1);
        version(LDC)
        {
            import ldc.intrinsics: llvm_ctlz;
            x = llvm_ctlz(x, true) + 1;
        }
        else
        {
            import core.bitop;
            x = 64 - bsr(x);
        }
        assert(x < 64);
        assert(x <= 65 - p);
        return x;
    }

    ulong encodeHash()(ulong x)
    {
        ulong a = x >> (64 - pPrime);
        auto r = rho(x);
        assert(r <= 65 - p);
        a <<= 1;
        return (r <= pPrime - p) ? a : ((a << 6) | (r << 1) | 1);
    }

    ulong decodeHash()(ulong k, ref ulong r)
    {
        auto c = k & 1;
        k >>= 1;
        if (c == 0)
        {
            r = rho(k << (64 - pPrime));
        }
        else
        {
            auto m = (1UL << 6) - 1;
            r = k & m;
            assert(r < 64);
            k >>= 6;
        }
        assert(k < m(pPrime));
        return k;
    }
}

///
unittest
{
    import std.experimental.allocator;
    import std.experimental.allocator.mallocator;
    import mir.random;
    auto hll = HLL(18);
    enum c = 100_000;
    auto rng = Random(unpredictableSeed);        // Engines are allocated on stack or global
    foreach(_; 0 .. c)
        hll.put(rng.rand!ulong);
    puts("HLL++ test: counted ", hll.count, " unique values from ", c, " random values.");
}


pragma(inline, true)
auto linearCounting()(ulong m, ulong v)
{
    import mir.math.common: log;
    return m * log (double(m) / v);
}

struct InputSparse
{
    const(ubyte)* data;
    size_t length;
    ulong front;

pragma(inline, true):

    this()(const(ubyte)* data, size_t length)
    {
        this.data = data;
        this.length = length;
        this.front = length ? fromVarint(this.data) : 0;
    }

    bool empty()() @property
    {
        return length == 0;
    }

    void popFront()()
    {
        if (length--)
        {
            front += fromVarint(data);
        }
    }
}

struct OutputSparse 
{
    ubyte* data;
    size_t max_length;
    size_t count;
    size_t length;
    ulong lastValue;

    pragma(inline, true)
    void put()(ulong value)
    {
        assert(max_length > length + 9);
        ulong diff = value - lastValue;
        lastValue = value;
        auto d = data;
        toVarint(data, diff);
        length += data - d;
        assert(data - d <= 10);
        count++;
    }
}

unittest
{
    import mir.random;
    auto ar = new ulong[1000];
    auto rng = Random(unpredictableSeed);
    foreach(ref e; ar)
        e = rng.rand!ulong;
    auto d = new ubyte[ar.length * 10];
    import std.algorithm;
    import std.range: put;
    auto o = OutputSparse(d.ptr, d.length);
    put(o, ar);
    assert(o.count == ar.length);
    auto input = InputSparse(d.ptr, o.count);
    assert(InputSparse(d.ptr, o.count).equal(ar));
}

ulong fromVaruint()(ref const(ubyte)* d)
{
    version(LDC) pragma(inline, true);
    auto data = d;
    ulong ret;
    size_t offset;
    ulong val = *data++;
    while (val & ~ulong(byte.max))
    {
        ret ^= (val & byte.max) << offset;
        offset += 7;
        val = *data++;
    }
    assert(offset < 64);
    ret ^= (val & byte.max) << offset;
    d = data;
    return ret;
}

pragma(inline, true)
long fromVarint()(ref const(ubyte)* d)
{
    auto ux = fromVaruint(d);
    auto x = ux >> 1;
    if (ux & 1)
        x = ~x;
    return x;
}

pragma(inline, true)
size_t varintLength()(ulong n)
{
    if (n <= 127)
        return 1;
    else
    {
        import core.bitop: bsr;
        auto d = bsr(n) + 1;
        auto p = d / 7;
        auto q = d % 7;
        return p + cast(bool)(q);
    }
}

pragma(inline, true)
void toVaruint()(ref ubyte* d, ulong n)
{
    auto data = d;
    while (n > byte.max)
    {
        *data++ = cast(ubyte)((n & byte.max) ^ ~ulong(byte.max));
        n >>= 7;
    }
    *data++ = cast(ubyte) n;
    d = data;
}

pragma(inline, true)
void toVarint()(ref ubyte* d, long n)
{
    toVaruint(d, (n << 1) ^ (n >> 63));
}

unittest
{
    ulong n = 7;
    assert(varintLength(n) == 1);
    ubyte[2] variant;
    auto q = variant.ptr;
    toVaruint(q, n);
    assert(variant == [7, 0]);
    const(ubyte)* p = variant.ptr;
    assert(fromVaruint(p) == 7);
    assert(p == variant.ptr + 1);
}

unittest
{
    ulong n = 300;
    assert(varintLength(n) == 2);
    ubyte[2] variant;
    auto q = variant.ptr;
    toVaruint(q, n);
    assert(variant == [0b1010_1100, 0b0000_0010]);
    const(ubyte)* p = variant.ptr;
    assert(fromVaruint(p) == 300);
    assert(p == variant.ptr + 2);
}

pragma(inline, true)
{
    size_t m()(uint p) { return size_t(1) << p; }
    size_t normal_bit_size()(uint p) { return m(p) * 6; }
    size_t normal_size()(uint p) { return normal_bit_size(p) / 8; }
    size_t normal_length()(uint p) { return normal_size(p) / ulong.sizeof + (normal_size(p) % ulong.sizeof != 0); }
    size_t normal_allocation_size()(uint p) { return normal_length(p) * ulong.sizeof; }
}

immutable _threshold = [10, 20, 40, 80, 220, 400, 900, 1800, 3100, 6500, 11500, 20000, 50000, 120000, 350000];

immutable double[][] _rawEstimateData = [
  [11, 11.717, 12.207, 12.7896, 13.2882, 13.8204, 14.3772, 14.9342, 15.5202, 16.161, 16.7722, 17.4636, 18.0396, 18.6766, 19.3566, 20.0454, 20.7936, 21.4856, 22.2666, 22.9946, 23.766, 24.4692, 25.3638, 26.0764, 26.7864, 27.7602, 28.4814, 29.433, 30.2926, 31.0664, 31.9996, 32.7956, 33.5366, 34.5894, 35.5738, 36.2698, 37.3682, 38.0544, 39.2342, 40.0108, 40.7966, 41.9298, 42.8704, 43.6358, 44.5194, 45.773, 46.6772, 47.6174, 48.4888, 49.3304, 50.2506, 51.4996, 52.3824, 53.3078, 54.3984, 55.5838, 56.6618, 57.2174, 58.3514, 59.0802, 60.1482, 61.0376, 62.3598, 62.8078, 63.9744, 64.914, 65.781, 67.1806, 68.0594, 68.8446, 69.7928, 70.8248, 71.8324, 72.8598, 73.6246, 74.7014, 75.393, 76.6708, 77.2394, ],
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];

immutable double[][] _biasData = [
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];

unittest
{
    foreach(e; _rawEstimateData)
        foreach(i, r; e[0 .. $-1])
            assert(r <= e[i + 1]);
}

private version(unittest)
void puts(T...)(T args)
{
    import std.stdio;
    writeln(args);
    stdout.flush;
}