bigint.cxx

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/* -*- 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 <math.h>
 
#include <osl/diagnose.h>
#include <tools/bigint.hxx>
 
#include <algorithm>
#include <string.h>
 
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.
 */
 
// TODO: Needs conversion to sal_uInt16/INT16/sal_uInt32/sal_Int32
void BigInt::MakeBigInt( const BigInt& rVal )
{
    if ( rVal.nLen != 0 )
    {
        memcpy( static_cast<void*>(this), static_cast<const void*>(&rVal), sizeof( BigInt ) );
        while ( nLen > 1 && nNum[nLen-1] == 0 )
            nLen--;
    }
    else
    {
        nVal = rVal.nVal;
        sal_uInt32 nTmp;
        if (nVal < 0)
        {
            bIsNeg = true;
            nTmp = -static_cast<sal_Int64>(nVal);
        }
        else
        {
            bIsNeg = false;
            nTmp = nVal;
        }
 
        nNum[0] = static_cast<sal_uInt16>(nTmp & 0xffffL);
        nNum[1] = static_cast<sal_uInt16>(nTmp >> 16);
        if ( nTmp & 0xffff0000L )
            nLen = 2;
        else
            nLen = 1;
    }
}
 
void BigInt::Normalize()
{
    if ( nLen != 0 )
    {
        while ( nLen > 1 && nNum[nLen-1] == 0 )
            nLen--;
 
        if ( nLen < 3 )
        {
            sal_Int32 newVal;
            if ( nLen < 2 )
                newVal = nNum[0];
            else if ( nNum[1] & 0x8000 )
                return;
            else
                newVal = (static_cast<sal_Int32>(nNum[1]) << 16) + nNum[0];
 
            nLen = 0;
            nVal = newVal;
 
            if ( bIsNeg )
                nVal = -nVal;
        }
        // else nVal is undefined !!! W.P.
    }
    // why? nVal is undefined ??? W.P.
    else if ( nVal & 0xFFFF0000L )
        nLen = 2;
    else
        nLen = 1;
}
 
void BigInt::Mult( const BigInt &rVal, sal_uInt16 nMul )
{
    sal_uInt16 nK = 0;
    for ( int i = 0; i < rVal.nLen; i++ )
    {
        sal_uInt32 nTmp = static_cast<sal_uInt32>(rVal.nNum[i]) * static_cast<sal_uInt32>(nMul) + nK;
        nK            = static_cast<sal_uInt16>(nTmp >> 16);
        nNum[i] = static_cast<sal_uInt16>(nTmp);
    }
 
    if ( nK )
    {
        nNum[rVal.nLen] = nK;
        nLen = rVal.nLen + 1;
    }
    else
        nLen = rVal.nLen;
 
    bIsNeg = rVal.bIsNeg;
}
 
void BigInt::Div( sal_uInt16 nDiv, sal_uInt16& rRem )
{
    sal_uInt32 nK = 0;
    for ( int i = nLen - 1; i >= 0; i-- )
    {
        sal_uInt32 nTmp = static_cast<sal_uInt32>(nNum[i]) + (nK << 16);
        nNum[i] = static_cast<sal_uInt16>(nTmp / nDiv);
        nK            = nTmp % nDiv;
    }
    rRem = static_cast<sal_uInt16>(nK);
 
    if ( nNum[nLen-1] == 0 )
        nLen -= 1;
}
 
bool BigInt::IsLess( const BigInt& rVal ) const
{
    if ( rVal.nLen < nLen)
        return true;
    if ( rVal.nLen > nLen )
        return false;
 
    int i;
    for ( i = nLen - 1; i > 0 && nNum[i] == rVal.nNum[i]; i-- )
    {
    }
    return rVal.nNum[i] < nNum[i];
}
 
void BigInt::AddLong( BigInt& rB, BigInt& rErg )
{
    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_Int32 k;
        sal_Int32 nZ = 0;
        for (i = 0, k = 0; i < len; i++) {
            nZ = static_cast<sal_Int32>(nNum[i]) + static_cast<sal_Int32>(rB.nNum[i]) + k;
            if (nZ & 0xff0000L)
                k = 1;
            else
                k = 0;
            rErg.nNum[i] = static_cast<sal_uInt16>(nZ & 0xffffL);
        }
        // If an overflow occurred, add to solution
        if (nZ & 0xff0000L) // or if(k)
        {
            rErg.nNum[i] = 1;
            len++;
        }
        // Set length and sign
        rErg.nLen   = len;
        rErg.bIsNeg = bIsNeg && rB.bIsNeg;
    }
    // If one of the values is negative, perform subtraction instead
    else if (bIsNeg)
    {
        bIsNeg = false;
        rB.SubLong(*this, rErg);
        bIsNeg = true;
    }
    else
    {
        rB.bIsNeg = false;
        SubLong(rB, rErg);
        rB.bIsNeg = true;
    }
}
 
void BigInt::SubLong( BigInt& rB, BigInt& rErg )
{
    if ( bIsNeg == rB.bIsNeg )
    {
        int  i;
        char len;
        sal_Int32 nZ, k;
 
        // 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;
        }
 
        if ( IsLess(rB) )
        {
            for (i = 0, k = 0; i < len; i++)
            {
                nZ = static_cast<sal_Int32>(nNum[i]) - static_cast<sal_Int32>(rB.nNum[i]) + k;
                if (nZ < 0)
                    k = -1;
                else
                    k = 0;
                rErg.nNum[i] = static_cast<sal_uInt16>(nZ & 0xffffL);
            }
            rErg.bIsNeg = bIsNeg;
        }
        else
        {
            for (i = 0, k = 0; i < len; i++)
            {
                nZ = static_cast<sal_Int32>(rB.nNum[i]) - static_cast<sal_Int32>(nNum[i]) + k;
                if (nZ < 0)
                    k = -1;
                else
                    k = 0;
                rErg.nNum[i] = static_cast<sal_uInt16>(nZ & 0xffffL);
            }
            // if a < b, revert sign
            rErg.bIsNeg = !bIsNeg;
        }
        rErg.nLen   = len;
    }
    // If one of the values is negative, perform addition instead
    else if (bIsNeg)
    {
        bIsNeg = false;
        AddLong(rB, rErg);
        bIsNeg = true;
        rErg.bIsNeg = true;
    }
    else
    {
        rB.bIsNeg = false;
        AddLong(rB, rErg);
        rB.bIsNeg = true;
        rErg.bIsNeg = false;
    }
}
 
void BigInt::MultLong( const BigInt& rB, BigInt& rErg ) const
{
    int        i, j;
    sal_uInt32 nZ, k;
 
    rErg.bIsNeg = bIsNeg != rB.bIsNeg;
    rErg.nLen   = nLen + rB.nLen;
 
    for (i = 0; i < rErg.nLen; i++)
        rErg.nNum[i] = 0;
 
    for (j = 0; j < rB.nLen; j++)
    {
        for (i = 0, k = 0; i < nLen; i++)
        {
            nZ = static_cast<sal_uInt32>(nNum[i]) * static_cast<sal_uInt32>(rB.nNum[j]) +
                 static_cast<sal_uInt32>(rErg.nNum[i + j]) + k;
            rErg.nNum[i + j] = static_cast<sal_uInt16>(nZ & 0xffffU);
            k = nZ >> 16;
        }
        rErg.nNum[i + j] = static_cast<sal_uInt16>(k);
    }
}
 
void BigInt::DivLong( const BigInt& rB, BigInt& rErg ) const
{
    int    i, j;
    sal_uInt16 nK, nQ, nMult;
    sal_uInt16  nLenB  = rB.nLen;
    sal_uInt16  nLenB1 = rB.nLen - 1;
    BigInt aTmpA, aTmpB;
 
    nMult = static_cast<sal_uInt16>(0x10000L / (static_cast<sal_Int32>(rB.nNum[nLenB1]) + 1));
 
    aTmpA.Mult( *this, nMult );
    if ( aTmpA.nLen == nLen )
    {
        aTmpA.nNum[aTmpA.nLen] = 0;
        aTmpA.nLen++;
    }
 
    aTmpB.Mult( rB, nMult );
 
    for (j = aTmpA.nLen - 1; j >= nLenB; j--)
    { // guess divisor
        sal_uInt32 nTmp = ( static_cast<sal_uInt32>(aTmpA.nNum[j]) << 16 ) + aTmpA.nNum[j - 1];
        if (aTmpA.nNum[j] == aTmpB.nNum[nLenB1])
            nQ = 0xFFFF;
        else
            nQ = static_cast<sal_uInt16>(nTmp / aTmpB.nNum[nLenB1]);
 
        if ( (static_cast<sal_uInt32>(aTmpB.nNum[nLenB1 - 1]) * nQ) >
            ((nTmp - static_cast<sal_uInt32>(aTmpB.nNum[nLenB1]) * nQ) << 16) + aTmpA.nNum[j - 2])
            nQ--;
        // Start division
        nK = 0;
        for (i = 0; i < nLenB; i++)
        {
            nTmp = static_cast<sal_uInt32>(aTmpA.nNum[j - nLenB + i])
                   - (static_cast<sal_uInt32>(aTmpB.nNum[i]) * nQ)
                   - nK;
            aTmpA.nNum[j - nLenB + i] = static_cast<sal_uInt16>(nTmp);
            nK = static_cast<sal_uInt16>(nTmp >> 16);
            if ( nK )
                nK = static_cast<sal_uInt16>(0x10000U - nK);
        }
        sal_uInt16& rNum( aTmpA.nNum[j - nLenB + i] );
        rNum -= nK;
        if (aTmpA.nNum[j - nLenB + i] == 0)
            rErg.nNum[j - nLenB] = nQ;
        else
        {
            rErg.nNum[j - nLenB] = nQ - 1;
            nK = 0;
            for (i = 0; i < nLenB; i++)
            {
                nTmp = aTmpA.nNum[j - nLenB + i] + aTmpB.nNum[i] + nK;
                aTmpA.nNum[j - nLenB + i] = static_cast<sal_uInt16>(nTmp & 0xFFFFL);
                if (nTmp & 0xFFFF0000L)
                    nK = 1;
                else
                    nK = 0;
            }
        }
    }
 
    rErg.bIsNeg = bIsNeg != rB.bIsNeg;
    rErg.nLen   = nLen - rB.nLen + 1;
}
 
void BigInt::ModLong( const BigInt& rB, BigInt& rErg ) const
{
    sal_uInt16 i, j;
    sal_uInt16 nK, nQ, nMult;
    sal_Int16  nLenB  = rB.nLen;
    sal_Int16  nLenB1 = rB.nLen - 1;
    BigInt aTmpA, aTmpB;
 
    nMult = static_cast<sal_uInt16>(0x10000L / (static_cast<sal_Int32>(rB.nNum[nLenB1]) + 1));
 
    aTmpA.Mult( *this, nMult);
    if ( aTmpA.nLen == nLen )
    {
        aTmpA.nNum[aTmpA.nLen] = 0;
        aTmpA.nLen++;
    }
 
    aTmpB.Mult( rB, nMult);
 
    for (j = aTmpA.nLen - 1; j >= nLenB; j--)
    { // Guess divisor
        sal_uInt32 nTmp = ( static_cast<sal_uInt32>(aTmpA.nNum[j]) << 16 ) + aTmpA.nNum[j - 1];
        if (aTmpA.nNum[j] == aTmpB.nNum[nLenB1])
            nQ = 0xFFFF;
        else
            nQ = static_cast<sal_uInt16>(nTmp / aTmpB.nNum[nLenB1]);
 
        if ( (static_cast<sal_uInt32>(aTmpB.nNum[nLenB1 - 1]) * nQ) >
            ((nTmp - aTmpB.nNum[nLenB1] * nQ) << 16) + aTmpA.nNum[j - 2])
            nQ--;
        // Start division
        nK = 0;
        for (i = 0; i < nLenB; i++)
        {
            nTmp = static_cast<sal_uInt32>(aTmpA.nNum[j - nLenB + i])
                   - (static_cast<sal_uInt32>(aTmpB.nNum[i]) * nQ)
                   - nK;
            aTmpA.nNum[j - nLenB + i] = static_cast<sal_uInt16>(nTmp);
            nK = static_cast<sal_uInt16>(nTmp >> 16);
            if ( nK )
                nK = static_cast<sal_uInt16>(0x10000U - nK);
        }
        sal_uInt16& rNum( aTmpA.nNum[j - nLenB + i] );
        rNum = rNum - nK;
        if (aTmpA.nNum[j - nLenB + i] == 0)
            rErg.nNum[j - nLenB] = nQ;
        else
        {
            rErg.nNum[j - nLenB] = nQ - 1;
            nK = 0;
            for (i = 0; i < nLenB; i++) {
                nTmp = aTmpA.nNum[j - nLenB + i] + aTmpB.nNum[i] + nK;
                aTmpA.nNum[j - nLenB + i] = static_cast<sal_uInt16>(nTmp & 0xFFFFL);
                if (nTmp & 0xFFFF0000L)
                    nK = 1;
                else
                    nK = 0;
            }
        }
    }
 
    rErg = aTmpA;
    rErg.Div( nMult, nQ );
}
 
bool BigInt::ABS_IsLess( const BigInt& rB ) const
{
    if (nLen != 0 || rB.nLen != 0)
    {
        BigInt nA, nB;
        nA.MakeBigInt( *this );
        nB.MakeBigInt( rB );
        if (nA.nLen == nB.nLen)
        {
            int i;
            for (i = nA.nLen - 1; i > 0 && nA.nNum[i] == nB.nNum[i]; i--)
            {
            }
            return nA.nNum[i] < nB.nNum[i];
        }
        else
            return nA.nLen < nB.nLen;
    }
    if ( nVal < 0 )
        if ( rB.nVal < 0 )
            return nVal > rB.nVal;
        else
            return nVal > -rB.nVal;
    else
        if ( rB.nVal < 0 )
            return nVal < -rB.nVal;
        else
            return nVal < rB.nVal;
}
 
BigInt::BigInt( const BigInt& rBigInt )
    : nLen(0)
    , bIsNeg(false)
{
    if ( rBigInt.nLen != 0 )
        memcpy( static_cast<void*>(this), static_cast<const void*>(&rBigInt), sizeof( BigInt ) );
    else
        nVal = rBigInt.nVal;
}
 
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 ( nLen != 0 )
        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 > 65536.0 ) && ( i < MAX_DIGITS ) )
        {
            nNum[i] = static_cast<sal_uInt16>(fmod( nValue, 65536.0 ));
            nValue -= nNum[i];
            nValue /= 65536.0;
            i++;
        }
        if ( i < MAX_DIGITS )
            nNum[i++] = static_cast<sal_uInt16>(nValue);
 
        nLen = i;
 
        if ( i < 3 )
            Normalize();
    }
}
 
BigInt::BigInt( sal_uInt32 nValue )
    : nVal(0)
{
    if ( nValue & 0x80000000U )
    {
        bIsNeg  = false;
        nNum[0] = static_cast<sal_uInt16>(nValue & 0xffffU);
        nNum[1] = static_cast<sal_uInt16>(nValue >> 16);
        nLen    = 2;
    }
    else
    {
        bIsNeg = false;
        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
    {
        sal_uInt64 nUValue = static_cast<sal_uInt64>(bIsNeg ? -nValue : nValue);
        for (int i = 0; (i != sizeof(sal_uInt64) / 2) && (nUValue != 0); ++i)
        {
            nNum[i] = static_cast<sal_uInt16>(nUValue & 0xffffUL);
            nUValue = nUValue >> 16;
            ++nLen;
        }
    }
}
 
BigInt::operator double() const
{
    if ( nLen == 0 )
        return static_cast<double>(nVal);
    else
    {
        int     i = nLen-1;
        double  nRet = static_cast<double>(static_cast<sal_uInt32>(nNum[i]));
 
        while ( i )
        {
            nRet *= 65536.0;
            i--;
            nRet += static_cast<double>(static_cast<sal_uInt32>(nNum[i]));
        }
 
        if ( bIsNeg )
            nRet *= -1;
 
        return nRet;
    }
}
 
BigInt& BigInt::operator=( const BigInt& rBigInt )
{
    if (this == &rBigInt)
        return *this;
 
    if ( rBigInt.nLen != 0 )
        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 ( nLen == 0 && rVal.nLen == 0 )
    {
        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 aTmp1, aTmp2;
    aTmp1.MakeBigInt( *this );
    aTmp2.MakeBigInt( rVal );
    aTmp1.AddLong( aTmp2, *this );
    Normalize();
    return *this;
}
 
BigInt& BigInt::operator-=( const BigInt& rVal )
{
    if ( nLen == 0 && rVal.nLen == 0 )
    {
        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 aTmp1, aTmp2;
    aTmp1.MakeBigInt( *this );
    aTmp2.MakeBigInt( rVal );
    aTmp1.SubLong( 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 ( nLen == 0 && rVal.nLen == 0
         && 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
    {
        BigInt aTmp1, aTmp2;
        aTmp1.MakeBigInt( rVal );
        aTmp2.MakeBigInt( *this );
        aTmp1.MultLong(aTmp2, *this);
        Normalize();
    }
    return *this;
}
 
BigInt& BigInt::operator/=( const BigInt& rVal )
{
    if ( rVal.nLen == 0 )
    {
        if ( rVal.nVal == 0 )
        {
            OSL_FAIL( "BigInt::operator/ --> divide by zero" );
            return *this;
        }
 
        if ( nLen == 0 )
        {
            // No overflows may occur here
            nVal /= rVal.nVal;
            return *this;
        }
 
        if ( rVal.nVal == 1 )
            return *this;
 
        if ( rVal.nVal == -1 )
        {
            bIsNeg = !bIsNeg;
            return *this;
        }
 
        if ( rVal.nVal <= 0xFFFF && rVal.nVal >= -0xFFFF )
        {
            // Divide BigInt with an sal_uInt16
            sal_uInt16 nTmp;
            if ( rVal.nVal < 0 )
            {
                nTmp = static_cast<sal_uInt16>(-rVal.nVal);
                bIsNeg = !bIsNeg;
            }
            else
                nTmp = static_cast<sal_uInt16>(rVal.nVal);
 
            Div( nTmp, nTmp );
            Normalize();
            return *this;
        }
    }
 
    if ( ABS_IsLess( rVal ) )
    {
        *this = BigInt( 0 );
        return *this;
    }
 
    // Divide BigInt with BigInt
    BigInt aTmp1, aTmp2;
    aTmp1.MakeBigInt( *this );
    aTmp2.MakeBigInt( rVal );
    aTmp1.DivLong(aTmp2, *this);
    Normalize();
    return *this;
}
 
BigInt& BigInt::operator%=( const BigInt& rVal )
{
    if ( rVal.nLen == 0 )
    {
        if ( rVal.nVal == 0 )
        {
            OSL_FAIL( "BigInt::operator/ --> divide by zero" );
            return *this;
        }
 
        if ( nLen == 0 )
        {
            // No overflows may occur here
            nVal %= rVal.nVal;
            return *this;
        }
 
        if ( rVal.nVal <= 0xFFFF && rVal.nVal >= -0xFFFF )
        {
            // Divide Bigint by int16
            sal_uInt16 nTmp;
            if ( rVal.nVal < 0 )
            {
                nTmp = static_cast<sal_uInt16>(-rVal.nVal);
                bIsNeg = !bIsNeg;
            }
            else
                nTmp = static_cast<sal_uInt16>(rVal.nVal);
 
            Div( nTmp, nTmp );
            *this = BigInt( nTmp );
            return *this;
        }
    }
 
    if ( ABS_IsLess( rVal ) )
        return *this;
 
    // Divide BigInt with BigInt
    BigInt aTmp1, aTmp2;
    aTmp1.MakeBigInt( *this );
    aTmp2.MakeBigInt( rVal );
    aTmp1.ModLong(aTmp2, *this);
    Normalize();
    return *this;
}
 
bool operator==( const BigInt& rVal1, const BigInt& rVal2 )
{
    if (rVal1.nLen == 0 && rVal2.nLen == 0)
        return rVal1.nVal == rVal2.nVal;
 
    BigInt nA, nB;
    nA.MakeBigInt(rVal1);
    nB.MakeBigInt(rVal2);
    return nA.bIsNeg == nB.bIsNeg && nA.nLen == nB.nLen
           && std::equal(nA.nNum, nA.nNum + nA.nLen, nB.nNum);
}
 
bool operator<( const BigInt& rVal1, const BigInt& rVal2 )
{
    if (rVal1.nLen == 0 && rVal2.nLen == 0)
        return rVal1.nVal < rVal2.nVal;
 
    BigInt nA, nB;
    nA.MakeBigInt(rVal1);
    nB.MakeBigInt(rVal2);
    if (nA.bIsNeg != nB.bIsNeg)
        return !nB.bIsNeg;
    if (nA.nLen != nB.nLen)
        return nA.bIsNeg ? (nA.nLen > nB.nLen) : (nA.nLen < nB.nLen);
    int i = nA.nLen - 1;
    while (i > 0 && nA.nNum[i] == nB.nNum[i])
        --i;
    return nA.bIsNeg ? (nA.nNum[i] > nB.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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