/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*

 * This file is part of the LibreOffice project.

 *

 * This Source Code Form is subject to the terms of the Mozilla Public

 * License, v. 2.0. If a copy of the MPL was not distributed with this

 * file, You can obtain one at http://mozilla.org/MPL/2.0/.

 *

 * This file incorporates work covered by the following license notice:

 *

 *   Licensed to the Apache Software Foundation (ASF) under one or more

 *   contributor license agreements. See the NOTICE file distributed

 *   with this work for additional information regarding copyright

 *   ownership. The ASF licenses this file to you under the Apache

 *   License, Version 2.0 (the "License"); you may not use this file

 *   except in compliance with the License. You may obtain a copy of

 *   the License at http://www.apache.org/licenses/LICENSE-2.0 .

 */

#include <sal/config.h>

#include <osl/diagnose.h>

#include <tools/bigint.hxx>

#include <algorithm>

#include <cmath>

#include <cstring>

#include <limits>

#include <span>

/**

 * The range in which we can perform add/sub without fear of overflow

 */

const sal_Int32 MY_MAXLONG  = 0x3fffffff;

const sal_Int32 MY_MINLONG  = -MY_MAXLONG;

/*

 * The algorithms for Addition, Subtraction, Multiplication and Division

 * of large numbers originate from SEMINUMERICAL ALGORITHMS by

 * DONALD E. KNUTH in the series The Art of Computer Programming:

 * chapter 4.3.1. The Classical Algorithms.

 */

BigInt BigInt::MakeBig() const

{

    if (IsBig())

    {

        BigInt ret(*this);

        while ( ret.nLen > 1 && ret.nNum[ret.nLen-1] == 0 )

            ret.nLen--;

        return ret;

    }

    BigInt ret;

    if (nVal < 0)

    {

        ret.bIsNeg = true;

        ret.nNum[0] = -static_cast<sal_Int64>(nVal);

    }

    else

    {

        ret.bIsNeg = false;

        ret.nNum[0] = nVal;

    }

    ret.nLen = 1;

    return ret;

}

void BigInt::Normalize()

{

    if (IsBig())

    {

        while ( nLen > 1 && nNum[nLen-1] == 0 )

            nLen--;

        if (nLen < 2)

        {

            static constexpr sal_uInt32 maxForPosInt32 = std::numeric_limits<sal_Int32>::max();

            static constexpr sal_uInt32 maxForNegInt32 = -sal_Int64(std::numeric_limits<sal_Int32>::min());

            sal_uInt32 nNum0 = nNum[0];

            if (bIsNeg && nNum0 <= maxForNegInt32)

            {

                nVal = -sal_Int64(nNum0);

                nLen = 0;

            }

            else if (!bIsNeg && nNum0 <= maxForPosInt32)

            {

                nVal = nNum0;

                nLen = 0;

            }

        }

    }

}

// Normalization in DivLong requires that dividend is multiplied by a number, and the resulting

// value has 1 more 32-bit "digits". 'ret' provides enough room for that. Use of std::span gives

// run-time index checking in debug builds.

static std::span<sal_uInt32> Mult(std::span<const sal_uInt32> aNum, sal_uInt32 nMul, std::span<sal_uInt32> retBuf)

{

    assert(retBuf.size() >= aNum.size());

    sal_uInt64 nK = 0;

    for (size_t i = 0; i < aNum.size(); i++)

    {

        sal_uInt64 nTmp = static_cast<sal_uInt64>(aNum[i]) * nMul + nK;

        nK = nTmp >> 32;

        retBuf[i] = static_cast<sal_uInt32>(nTmp);

    }

    if ( nK )

    {

        assert(retBuf.size() > aNum.size());

        retBuf[aNum.size()] = nK;

        return retBuf.subspan(0, aNum.size() + 1);

    }

    return retBuf.subspan(0, aNum.size());

}

static size_t DivInPlace(std::span<sal_uInt32> aNum, sal_uInt32 nDiv, sal_uInt32& rRem)

{

    assert(aNum.size() > 0);

    sal_uInt64 nK = 0;

    for (int i = aNum.size() - 1; i >= 0; i--)

    {

        sal_uInt64 nTmp = aNum[i] + (nK << 32);

        aNum[i] = nTmp / nDiv;

        nK            = nTmp % nDiv;

    }

    rRem = nK;

    if (aNum[aNum.size() - 1] == 0)

        return aNum.size() - 1;

    return aNum.size();

}

bool BigInt::ABS_IsLessBig(const BigInt& rVal) const

{

    assert(IsBig() && rVal.IsBig());

    if ( rVal.nLen < nLen)

        return false;

    if ( rVal.nLen > nLen )

        return true;

    int i = nLen - 1;

    while (i > 0 && nNum[i] == rVal.nNum[i])

        --i;

    return nNum[i] < rVal.nNum[i];

}

void BigInt::AddBig(BigInt& rB, BigInt& rRes)

{

    assert(IsBig() && rB.IsBig());

    if ( bIsNeg == rB.bIsNeg )

    {

        int  i;

        char len;

        // if length of the two values differ, fill remaining positions

        // of the smaller value with zeros.

        if (nLen >= rB.nLen)

        {

            len = nLen;

            for (i = rB.nLen; i < len; i++)

                rB.nNum[i] = 0;

        }

        else

        {

            len = rB.nLen;

            for (i = nLen; i < len; i++)

                nNum[i] = 0;

        }

        // Add numerals, starting from the back

        sal_Int64 k = 0;

        for (i = 0; i < len; i++) {

            sal_Int64 nZ = static_cast<sal_Int64>(nNum[i]) + static_cast<sal_Int64>(rB.nNum[i]) + k;

            if (nZ > sal_Int64(std::numeric_limits<sal_uInt32>::max()))

                k = 1;

            else

                k = 0;

            rRes.nNum[i] = static_cast<sal_uInt32>(nZ);

        }

        // If an overflow occurred, add to solution

        if (k)

        {

            assert(i < MAX_DIGITS);

            rRes.nNum[i] = 1;

            len++;

        }

        // Set length and sign

        rRes.nLen = len;

        rRes.bIsNeg = bIsNeg;

    }

    // If one of the values is negative, perform subtraction instead

    else

    {

        bIsNeg = !bIsNeg;

        rB.SubBig(*this, rRes);

        bIsNeg = !bIsNeg;

    }

}

void BigInt::SubBig(BigInt& rB, BigInt& rRes)

{

    assert(IsBig() && rB.IsBig());

    if ( bIsNeg == rB.bIsNeg )

    {

        char len;

        // if length of the two values differ, fill remaining positions

        // of the smaller value with zeros.

        if (nLen >= rB.nLen)

        {

            len = nLen;

            for (int i = rB.nLen; i < len; i++)

                rB.nNum[i] = 0;

        }

        else

        {

            len = rB.nLen;

            for (int i = nLen; i < len; i++)

                nNum[i] = 0;

        }

        const bool bThisIsLess = ABS_IsLessBig(rB);

        BigInt& rGreater = bThisIsLess ? rB : *this;

        BigInt& rSmaller = bThisIsLess ? *this : rB;

        sal_Int64 k = 0;

        for (int i = 0; i < len; i++)

        {

            sal_Int64 nZ = static_cast<sal_Int64>(rGreater.nNum[i]) - static_cast<sal_Int64>(rSmaller.nNum[i]) + k;

            if (nZ < 0)

                k = -1;

            else

                k = 0;

            rRes.nNum[i] = static_cast<sal_uInt32>(nZ);

        }

        // if a < b, revert sign

        rRes.bIsNeg = bThisIsLess ? !bIsNeg : bIsNeg;

        rRes.nLen   = len;

    }

    // If one of the values is negative, perform addition instead

    else

    {

        bIsNeg = !bIsNeg;

        AddBig(rB, rRes);

        bIsNeg = !bIsNeg;

        rRes.bIsNeg = bIsNeg;

    }

}

void BigInt::MultBig(const BigInt& rB, BigInt& rRes) const

{

    assert(IsBig() && rB.IsBig());

    rRes.bIsNeg = bIsNeg != rB.bIsNeg;

    rRes.nLen = nLen + rB.nLen;

    assert(rRes.nLen <= MAX_DIGITS);

    for (int i = 0; i < rRes.nLen; i++)

        rRes.nNum[i] = 0;

    for (int j = 0; j < rB.nLen; j++)

    {

        sal_uInt64 k = 0;

        int i;

        for (i = 0; i < nLen; i++)

        {

            sal_uInt64 nZ = static_cast<sal_uInt64>(nNum[i]) * static_cast<sal_uInt64>(rB.nNum[j]) +

                 static_cast<sal_uInt64>(rRes.nNum[i + j]) + k;

            rRes.nNum[i + j] = static_cast<sal_uInt32>(nZ);

            k = nZ >> 32;

        }

        rRes.nNum[i + j] = k;

    }

}

void BigInt::DivModBig(const BigInt& rB, BigInt* pDiv, BigInt* pMod) const

{

    assert(IsBig() && rB.IsBig());

    assert(nLen >= rB.nLen);

    assert(rB.nNum[rB.nLen - 1] != 0);

    sal_uInt32 nMult = static_cast<sal_uInt32>(0x100000000 / (static_cast<sal_Int64>(rB.nNum[rB.nLen - 1]) + 1));

    sal_uInt32 numBuf[MAX_DIGITS + 1]; // normalized dividend

    auto num = Mult({ nNum, nLen }, nMult, numBuf);

    if (num.size() == nLen)

    {

        num = std::span(numBuf, nLen + 1);

        num[nLen] = 0;

    }

    sal_uInt32 denBuf[MAX_DIGITS + 1]; // normalized divisor

    const auto den = Mult({ rB.nNum, rB.nLen }, nMult, denBuf);

    assert(den.size() == rB.nLen);

    const sal_uInt64 nDenMostSig = den[rB.nLen - 1];

    assert(nDenMostSig >= 0x100000000 / 2);

    const sal_uInt64 nDen2ndSig = rB.nLen > 1 ? den[rB.nLen - 2] : 0;

    BigInt aTmp;

    BigInt& rRes = pDiv ? *pDiv : aTmp;

    for (size_t j = num.size() - 1; j >= den.size(); j--)

    { // guess divisor

        assert(num[j] < nDenMostSig || (num[j] == nDenMostSig && num[j - 1] == 0));

        sal_uInt64 nTmp = ( static_cast<sal_uInt64>(num[j]) << 32 ) + num[j - 1];

        sal_uInt32 nQ;

        if (num[j] == nDenMostSig)

            nQ = 0xFFFFFFFF;

        else

            nQ = static_cast<sal_uInt32>(nTmp / nDenMostSig);

        if (nDen2ndSig && (nDen2ndSig * nQ) > ((nTmp - nDenMostSig * nQ) << 32) + num[j - 2])

            nQ--;

        // Start division

        sal_uInt32 nK = 0;

        size_t i;

        for (i = 0; i < den.size(); i++)

        {

            nTmp = static_cast<sal_uInt64>(num[j - den.size() + i])

                   - (static_cast<sal_uInt64>(den[i]) * nQ)

                   - nK;

            num[j - den.size() + i] = static_cast<sal_uInt32>(nTmp);

            nK = static_cast<sal_uInt32>(nTmp >> 32);

            if ( nK )

                nK = static_cast<sal_uInt32>(0x100000000 - nK);

        }

        sal_uInt32& rNum(num[j - den.size() + i]);

        rNum -= nK;

        if (num[j - den.size() + i] == 0)

            rRes.nNum[j - den.size()] = nQ;

        else

        {

            rRes.nNum[j - den.size()] = nQ - 1;

            nK = 0;

            for (i = 0; i < den.size(); i++)

            {

                nTmp = num[j - den.size() + i] + den[i] + nK;

                num[j - den.size() + i] = static_cast<sal_uInt32>(nTmp & 0xFFFFFFFF);

                if (nTmp > std::numeric_limits<sal_uInt32>::max())

                    nK = 1;

                else

                    nK = 0;

            }

        }

    }

    if (pMod)

    {

        pMod->nLen = DivInPlace(num, nMult, nMult);

        assert(pMod->nLen <= MAX_DIGITS);

        pMod->bIsNeg = bIsNeg;

        std::copy_n(num.begin(), pMod->nLen, pMod->nNum);

        pMod->Normalize();

    }

    if (pDiv) // rRes references pDiv

    {

        pDiv->bIsNeg = bIsNeg != rB.bIsNeg;

        pDiv->nLen = nLen - rB.nLen + 1;

        pDiv->Normalize();

    }

}

BigInt::BigInt( std::u16string_view rString )

    : nLen(0)

{

    bIsNeg = false;

    nVal   = 0;

    bool bNeg = false;

    auto p = rString.begin();

    auto pEnd = rString.end();

    if (p == pEnd)

        return;

    if ( *p == '-' )

    {

        bNeg = true;

        p++;

    }

    if (p == pEnd)

        return;

    while( p != pEnd && *p >= '0' && *p <= '9' )

    {

        *this *= 10;

        *this += *p - '0';

        p++;

    }

    if (IsBig())

        bIsNeg = bNeg;

    else if( bNeg )

        nVal = -nVal;

}

BigInt::BigInt( double nValue )

    : nVal(0)

{

    if ( nValue < 0 )

    {

        nValue *= -1;

        bIsNeg  = true;

    }

    else

    {

        bIsNeg  = false;

    }

    if ( nValue < 1 )

    {

        nVal   = 0;

        nLen   = 0;

    }

    else

    {

        int i=0;

        while ( ( nValue > 0x100000000 ) && ( i < MAX_DIGITS ) )

        {

            nNum[i] = static_cast<sal_uInt32>(fmod( nValue, 0x100000000 ));

            nValue -= nNum[i];

            nValue /= 0x100000000;

            i++;

        }

        if ( i < MAX_DIGITS )

            nNum[i++] = static_cast<sal_uInt32>(nValue);

        nLen = i;

        if ( i < 2 )

            Normalize();

    }

}

BigInt::BigInt( sal_uInt32 nValue )

    : nVal(0)

    , bIsNeg(false)

{

    if ( nValue & 0x80000000U )

    {

        nNum[0] = nValue;

        nLen = 1;

    }

    else

    {

        nVal   = nValue;

        nLen   = 0;

    }

}

BigInt::BigInt( sal_Int64 nValue )

    : nVal(0)

{

    bIsNeg = nValue < 0;

    nLen = 0;

    if ((nValue >= SAL_MIN_INT32) && (nValue <= SAL_MAX_INT32))

    {

        nVal = static_cast<sal_Int32>(nValue);

    }

    else

    {

        for (sal_uInt64 n = static_cast<sal_uInt64>(

                 (bIsNeg && nValue != std::numeric_limits<sal_Int64>::min()) ? -nValue : nValue);

             n != 0; n >>= 32)

            nNum[nLen++] = static_cast<sal_uInt32>(n);

    }

}

BigInt::operator double() const

{

    if (!IsBig())

        return static_cast<double>(nVal);

    else

    {

        int     i = nLen-1;

        double  nRet = static_cast<double>(nNum[i]);

        while ( i )

        {

            nRet *= 0x100000000;

            i--;

            nRet += static_cast<double>(nNum[i]);

        }

        if ( bIsNeg )

            nRet *= -1;

        return nRet;

    }

}

BigInt& BigInt::operator=( const BigInt& rBigInt )

{

    if (this == &rBigInt)

        return *this;

    if (rBigInt.IsBig())

        memcpy( static_cast<void*>(this), static_cast<const void*>(&rBigInt), sizeof( BigInt ) );

    else

    {

        nLen = 0;

        nVal = rBigInt.nVal;

    }

    return *this;

}

BigInt& BigInt::operator+=( const BigInt& rVal )

{

    if (!IsBig() && !rVal.IsBig())

    {

        if( nVal <= MY_MAXLONG && rVal.nVal <= MY_MAXLONG

            && nVal >= MY_MINLONG && rVal.nVal >= MY_MINLONG )

        { // No overflows may occur here

            nVal += rVal.nVal;

            return *this;

        }

        if( (nVal < 0) != (rVal.nVal < 0) )

        { // No overflows may occur here

            nVal += rVal.nVal;

            return *this;

        }

    }

    BigInt aTmp2 = rVal.MakeBig();

    MakeBig().AddBig(aTmp2, *this);

    Normalize();

    return *this;

}

BigInt& BigInt::operator-=( const BigInt& rVal )

{

    if (!IsBig() && !rVal.IsBig())

    {

        if ( nVal <= MY_MAXLONG && rVal.nVal <= MY_MAXLONG &&

             nVal >= MY_MINLONG && rVal.nVal >= MY_MINLONG )

        { // No overflows may occur here

            nVal -= rVal.nVal;

            return *this;

        }

        if ( (nVal < 0) == (rVal.nVal < 0) )

        { // No overflows may occur here

            nVal -= rVal.nVal;

            return *this;

        }

    }

    BigInt aTmp2 = rVal.MakeBig();

    MakeBig().SubBig(aTmp2, *this);

    Normalize();

    return *this;

}

BigInt& BigInt::operator*=( const BigInt& rVal )

{

    static const sal_Int32 MY_MAXSHORT = 0x00007fff;

    static const sal_Int32 MY_MINSHORT = -MY_MAXSHORT;

    if (!IsBig() && !rVal.IsBig()

         && nVal <= MY_MAXSHORT && rVal.nVal <= MY_MAXSHORT

         && nVal >= MY_MINSHORT && rVal.nVal >= MY_MINSHORT )

         // TODO: not optimal !!! W.P.

    { // No overflows may occur here

        nVal *= rVal.nVal;

    }

    else

    {

        rVal.MakeBig().MultBig(MakeBig(), *this);

        Normalize();

    }

    return *this;

}

void BigInt::DivMod(const BigInt& rVal, BigInt* pDiv, BigInt* pMod) const

{

    assert(pDiv || pMod); // Avoid useless calls

    if (!rVal.IsBig())

    {

        if ( rVal.nVal == 0 )

        {

            OSL_FAIL( "BigInt::operator/ --> divide by zero" );

            return;

        }

        if (rVal.nVal == 1)

        {

            if (pDiv)

            {

                *pDiv = *this;

                pDiv->Normalize();

            }

            if (pMod)

                *pMod = 0;

            return;

        }

        if (!IsBig())

        {

            // No overflows may occur here

            const sal_Int32 nDiv = nVal / rVal.nVal; // Compilers usually optimize adjacent

            const sal_Int32 nMod = nVal % rVal.nVal; // / and % into a single instruction

            if (pDiv)

                *pDiv = nDiv;

            if (pMod)

                *pMod = nMod;

            return;

        }

        if ( rVal.nVal == -1 )

        {

            if (pDiv)

            {

                *pDiv = *this;

                pDiv->bIsNeg = !bIsNeg;

                pDiv->Normalize();

            }

            if (pMod)

                *pMod = 0;

            return;

        }

        // Divide BigInt with an sal_uInt32

        sal_uInt32 nTmp;

        bool bNegate;

        if ( rVal.nVal < 0 )

        {

            nTmp = static_cast<sal_uInt32>(-rVal.nVal);

            bNegate = true;

        }

        else

        {

            nTmp = static_cast<sal_uInt32>(rVal.nVal);

            bNegate = false;

        }

        BigInt aTmp;

        BigInt& rDiv = pDiv ? *pDiv : aTmp;

        rDiv = *this;

        rDiv.nLen = DivInPlace({ rDiv.nNum, rDiv.nLen }, nTmp, nTmp);

        if (pDiv)

        {

            if (bNegate)

                pDiv->bIsNeg = !pDiv->bIsNeg;

            pDiv->Normalize();

        }

        if (pMod)

        {

            *pMod = BigInt(nTmp);

        }

        return;

    }

    BigInt tmpA = MakeBig(), tmpB = rVal.MakeBig();

    if (tmpA.ABS_IsLessBig(tmpB))

    {

        // First store *this to *pMod, then nullify *pDiv, to handle 'pDiv == this' case

        if (pMod)

        {

            *pMod = *this;

            pMod->Normalize();

        }

        if (pDiv)

            *pDiv = 0;

        return;

    }

    // Divide BigInt with BigInt

    tmpA.DivModBig(tmpB, pDiv, pMod);

}

BigInt& BigInt::operator/=( const BigInt& rVal )

{

    DivMod(rVal, this, nullptr);

    return *this;

}

BigInt& BigInt::operator%=( const BigInt& rVal )

{

    DivMod(rVal, nullptr, this);

    return *this;

}

bool operator==( const BigInt& rVal1, const BigInt& rVal2 )

{

    if (!rVal1.IsBig() && !rVal2.IsBig())

        return rVal1.nVal == rVal2.nVal;

    BigInt nA = rVal1.MakeBig(), nB = rVal2.MakeBig();

    return nA.bIsNeg == nB.bIsNeg && nA.nLen == nB.nLen

           && std::equal(nA.nNum, nA.nNum + nA.nLen, nB.nNum);

}

std::strong_ordering operator<=>(const BigInt& rVal1, const BigInt& rVal2)

{

    if (!rVal1.IsBig() && !rVal2.IsBig())

        return rVal1.nVal <=> rVal2.nVal;

    BigInt nA = rVal1.MakeBig(), nB = rVal2.MakeBig();

    if (nA.bIsNeg != nB.bIsNeg)

        return nB.bIsNeg ? std::strong_ordering::less : std::strong_ordering::greater;

    if (nA.nLen < nB.nLen)

        return nB.bIsNeg ? std::strong_ordering::greater : std::strong_ordering::less;

    if (nA.nLen > nB.nLen)

        return nB.bIsNeg ? std::strong_ordering::less : std::strong_ordering::greater;

    int i = nA.nLen - 1;

    while (i > 0 && nA.nNum[i] == nB.nNum[i])

        --i;

    return nB.bIsNeg ? (nB.nNum[i] <=> nA.nNum[i]) : (nA.nNum[i] <=> nB.nNum[i]);

}

tools::Long BigInt::Scale( tools::Long nVal, tools::Long nMul, tools::Long nDiv )

{

    BigInt aVal( nVal );

    aVal *= nMul;

    if ( aVal.IsNeg() != ( nDiv < 0 ) )

        aVal -= nDiv / 2; // for correct rounding

    else

        aVal += nDiv / 2; // for correct rounding

    aVal /= nDiv;

    return tools::Long( aVal );

}

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