CWE-ou-minkata/Sources/Plasma/CoreLib/hsWide.cpp

/*==LICENSE==*

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*==LICENSE==*/
#include "hsWide.h"

/////////////////////////////////////////////////////////////////////////

inline bool OverflowAdd(uint32_t* sum, uint32_t a, uint32_t b)
{
    *sum = a + b;

    return (a | b) > *sum;  // true if overflow
}

/*
    Return the overflow from adding the three longs into a signed-wide
    
    wide = (high << 32) + (middle << 16) + low
*/
inline bool SetWide3(hsWide* target, int32_t high, uint32_t middle, uint32_t low)
{
    hsAssert(high >= 0, "high is neg");

    target->fLo = low + (middle << 16);
    target->fHi = high + (middle >> 16) + (((low >> 16) + (uint16_t)middle) >> 16);

    return target->fHi < 0; // true if overflow
}

/////////////////////////////////////////////////////////////////////////

hsWide* hsWide::Mul(int32_t src1, int32_t src2)
{
    int neg = 0;
    
    if (src1 < 0)
    {   src1 = -src1;
        neg = ~0;
    }
    if (src2 < 0)
    {   src2 = -src2;
        neg = ~neg;
    }
    
    uint32_t  a = src1 >> 16;
    uint32_t  b = (uint16_t)src1;
    uint32_t  c = src2 >> 16;
    uint32_t  d = (uint16_t)src2;
    
    (void)SetWide3(this, a * c, a * d + c * b, b * d);

    if (neg)
        this->Negate();
    return this;
}

hsWide* hsWide::Mul(int32_t A)
{
    int     neg = 0;
    uint32_t  B = fLo;
    int32_t   C = fHi;
    int32_t   tmp;
    uint32_t  clo,blo,bhi,alo;

    if (A < 0)
    {   A = -A;
        neg = ~0;
    }
    if (WIDE_ISNEG(C, B))
    {   WIDE_NEGATE(C, B);
        neg = ~neg;
    }

    uint32_t  ahi = A >> 16;
    uint32_t  chi = C >> 16;
    if (ahi != 0 && chi != 0)
        goto OVER_FLOW;

    alo = (uint16_t)A;
    bhi = B >> 16;
    blo = (uint16_t)B;
    clo = (uint16_t)C;

    tmp = alo * clo;
    if (tmp < 0 || SetWide3(this, tmp, alo * bhi, alo * blo))
        goto OVER_FLOW;

    if (chi != 0)
    {   uint32_t  Vh = alo * chi;
        if (Vh >> 15)
            goto OVER_FLOW;
        if (((this->fHi >> 16) + (uint16_t)Vh) >> 15)
            goto OVER_FLOW;
        this->fHi += Vh << 16;
    }
    else                            // ahi != 0 && chi == 0
    {   hsWide  w;
        uint32_t  Vh = ahi * clo;
        if (Vh >> 16)
            goto OVER_FLOW;
        tmp = ahi * bhi;
        if (tmp < 0 || SetWide3(&w, tmp, ahi * blo, 0))
            goto OVER_FLOW;
        if (((w.fHi >> 16) + (uint16_t)Vh) >> 15)
            goto OVER_FLOW;
        w.fHi += Vh << 16;
        this->Add(&w);
    }
    
    if (neg)
        this->Negate();
    return this;

OVER_FLOW:
    *this = neg ? kNegInfinity64 : kPosInfinity64;
    return this;
}

hsWide* hsWide::Div(int32_t denom)
{
    if (denom == 0)
    {   if (this->IsNeg())
        {   hsSignalMathUnderflow();
            *this = kNegInfinity64;
        }
        else
        {   hsSignalMathOverflow();
            *this = kPosInfinity64;
        }
        return this;
    }

    int     neg = 0;
    int32_t   resultH = 0;
    uint32_t  resultL = 0;
    int32_t   numerH = this->fHi;
    uint32_t  numerL = this->fLo;

    if (denom < 0)
    {   denom = -denom;
        neg = ~0;
    }
    if (WIDE_ISNEG(numerH, numerL))
    {   WIDE_NEGATE(numerH, numerL);
        neg = ~neg;
    }
    
    WIDE_ADDPOS(numerH, numerL, denom >> 1);    // add denom/2 to get a round result

    uint32_t  curr = (uint32_t)numerH >> 31;

    for (int i = 0; i < 64; i++)
    {
        WIDE_SHIFTLEFT(resultH, resultL, resultH, resultL, 1);
        if (uint32_t(denom) <= curr)
        {
            resultL |= 1;
            curr -= denom;
        }
        WIDE_SHIFTLEFT(numerH, numerL, numerH, numerL, 1);
        curr = (curr << 1) | ((uint32_t)numerH >> 31);
    }

    if (neg)
        WIDE_NEGATE(resultH, resultL);
    return this->Set(resultH, resultL);
}

hsWide* hsWide::Div(const hsWide* denom)
{
    hsWide  d = *denom;
    int     shift = 0;
    
    while (d.IsWide())
    {   (void)d.ShiftRight(1);
        shift += 1;
    }
    if (shift)
    {   d = *denom;
        (void)this->RoundRight(shift);
        (void)d.RoundRight(shift);
    }
    return this->Div(d.AsLong());
}

inline int MaxLeftShift(const hsWide* w)
{
    int32_t hi = w->fHi;

    if (hi == 0)
        return 31;
    else
    {   int shift = -1;

        if (hi < 0) hi = -hi;

        do {
            hi <<= 1;
            shift += 1;
        } while (hi > 0);
        return shift;
    }
}

int32_t hsWide::FixDiv(const hsWide* denom) const
{
    hsWide  num = *this;
    hsWide  den = *denom;
    int     maxShift = MaxLeftShift(this);

    if (maxShift >= 16) // easy case
        (void)num.ShiftLeft(16);
    else
    {   (void)num.ShiftLeft(maxShift);
        (void)den.RoundRight(16 - maxShift);
    }
    
    return num.Div(&den)->AsLong();
}

int32_t hsWide::FracDiv(const hsWide* denom) const
{
    hsWide  num = *this;
    hsWide  den = *denom;
    int     maxShift = MaxLeftShift(this);

    if (maxShift >= 30) // easy case
        (void)num.ShiftLeft(30);
    else
    {   (void)num.ShiftLeft(maxShift);
        (void)den.RoundRight(30 - maxShift);
    }
    
    return num.Div(&den)->AsLong();
}

////////////////////////////////////////////////////////////////////////////////////

int32_t hsWide::Sqrt() const
{
    int     bits = 32;
    uint32_t  root = 0;
    uint32_t  valueH = (uint32_t)fHi;
    uint32_t  valueL = fLo;
    uint32_t  currH = 0;
    uint32_t  currL = 0;
    uint32_t  guessH, guessL;
    
    do {
        WIDE_SHIFTLEFT(currH, currL, currH, currL, 2);
        currL |= TOP2BITS(valueH);
        WIDE_SHIFTLEFT(valueH, valueL, valueH, valueL, 2);      
        WIDE_SHIFTLEFT(guessH, guessL, 0, root, 2);
        root <<= 1;
        if (WIDE_LESSTHAN(guessH, guessL, currH, currL))
        {   WIDE_ADDPOS(guessH, guessL, 1);
            WIDE_SUBWIDE(currH, currL, guessH, guessL);
            root |= 1;
        }
    } while (--bits);

    return (int32_t)root;
}

int32_t hsWide::CubeRoot() const
{
    int     bits = 21;
    uint32_t  root = 0;
    uint32_t  valueH = (uint32_t)fHi;
    uint32_t  valueL = fLo;
    uint32_t  currH, currL;
    uint32_t  guessH, guessL;
    bool  neg = false;

    if (WIDE_ISNEG(valueH, valueL))
    {   neg = true;
        WIDE_NEGATE(valueH, valueL);
    }

    currH = currL = 0;
    WIDE_SHIFTLEFT(valueH, valueL, valueH, valueL, 1);  
    do {
        WIDE_SHIFTLEFT(currH, currL, currH, currL, 3);
        currL |= TOP3BITS(valueH);
        WIDE_SHIFTLEFT(valueH, valueL, valueH, valueL, 3);      

        root <<= 1;

        hsWide w;
        w.Mul(root, root)->Add(root);
    #if 0
        w.Mul(3);
    #else
        hsWide w2 = w;
        w.ShiftLeft(1)->Add(&w2);
    #endif
        guessH = (uint32_t)w.fHi;
        guessL = w.fLo;

        if (WIDE_LESSTHAN(guessH, guessL, currH, currL))
        {   WIDE_ADDPOS(guessH, guessL, 1);
            WIDE_SUBWIDE(currH, currL, guessH, guessL);
            root |= 1;
        }
    } while (--bits);

    if (neg)
        root = -int32_t(root);
    return (int32_t)root;
}