How can I pack a float3 into one float - unity3d

Question

I am doing some animation jobs. I need to pack some pivots into UV and then my shader can read them.
I need to pack 4 float3 into a float4. Therefore, I need to pack each float3 into a float.
These 4 float3 are (model space position1, direction1, model space position2, direction2). I know how to handle the directions because they are normalized. I can use something like:
#define f3_f(c) (dot(round((c) * 255), float3(65536, 256, 1)))
#define f_f3(f) (frac((f) / float3(16777216, 65536, 256)))
But how can I handle positions? I am using SM3.0 and I can't use bitwise operation.

Answer 1

Do you really need to pack it into a float (4 bytes), or can you pack it into a 32-bit unsigned integer (i.e. 4 bytes)?
If, so take a look at the code in DirectXMath for converting to/from various formats as done in DirectXTex such as DXGI_FORMAT_R11G11B10_FLOAT. Since this format is positive only, you'll have to do a scale and bias to/from the format to handle the [-1,+1] range, but that's easy to do (0.5*value + 0.5 <-> 2*value - 1).
// 3D vector: 11/11/10 floating-point components
// The 3D vector is packed into 32 bits as follows: a 5-bit biased exponent
// and 6-bit mantissa for x component, a 5-bit biased exponent and
// 6-bit mantissa for y component, a 5-bit biased exponent and a 5-bit
// mantissa for z. The z component is stored in the most significant bits
// and the x component in the least significant bits. No sign bits so
// all partial-precision numbers are positive.
// (Z10Y11X11): [32] ZZZZZzzz zzzYYYYY yyyyyyXX XXXxxxxx [0]
struct XMFLOAT3PK
{
union
{
struct
{
uint32_t xm : 6; // x-mantissa
uint32_t xe : 5; // x-exponent
uint32_t ym : 6; // y-mantissa
uint32_t ye : 5; // y-exponent
uint32_t zm : 5; // z-mantissa
uint32_t ze : 5; // z-exponent
};
uint32_t v;
};
XMFLOAT3PK() = default;
XMFLOAT3PK(const XMFLOAT3PK&) = default;
XMFLOAT3PK& operator=(const XMFLOAT3PK&) = default;
XMFLOAT3PK(XMFLOAT3PK&&) = default;
XMFLOAT3PK& operator=(XMFLOAT3PK&&) = default;
explicit XM_CONSTEXPR XMFLOAT3PK(uint32_t Packed) : v(Packed) {}
XMFLOAT3PK(float _x, float _y, float _z);
explicit XMFLOAT3PK(_In_reads_(3) const float *pArray);
operator uint32_t () const { return v; }
XMFLOAT3PK& operator= (uint32_t Packed) { v = Packed; return *this; }
};
// Converts float3 to the 11/11/10 format
inline void XM_CALLCONV XMStoreFloat3PK
(
XMFLOAT3PK* pDestination,
FXMVECTOR V
)
{
assert(pDestination);
__declspec(align(16)) uint32_t IValue[4];
XMStoreFloat3A( reinterpret_cast<XMFLOAT3A*>(&IValue), V );
uint32_t Result[3];
// X & Y Channels (5-bit exponent, 6-bit mantissa)
for(uint32_t j=0; j < 2; ++j)
{
uint32_t Sign = IValue[j] & 0x80000000;
uint32_t I = IValue[j] & 0x7FFFFFFF;
if ((I & 0x7F800000) == 0x7F800000)
{
// INF or NAN
Result[j] = 0x7c0;
if (( I & 0x7FFFFF ) != 0)
{
Result[j] = 0x7c0 | (((I>>17)|(I>>11)|(I>>6)|(I))&0x3f);
}
else if ( Sign )
{
// -INF is clamped to 0 since 3PK is positive only
Result[j] = 0;
}
}
else if ( Sign )
{
// 3PK is positive only, so clamp to zero
Result[j] = 0;
}
else if (I > 0x477E0000U)
{
// The number is too large to be represented as a float11, set to max
Result[j] = 0x7BF;
}
else
{
if (I < 0x38800000U)
{
// The number is too small to be represented as a normalized float11
// Convert it to a denormalized value.
uint32_t Shift = 113U - (I >> 23U);
I = (0x800000U | (I & 0x7FFFFFU)) >> Shift;
}
else
{
// Rebias the exponent to represent the value as a normalized float11
I += 0xC8000000U;
}
Result[j] = ((I + 0xFFFFU + ((I >> 17U) & 1U)) >> 17U)&0x7ffU;
}
}
// Z Channel (5-bit exponent, 5-bit mantissa)
uint32_t Sign = IValue[2] & 0x80000000;
uint32_t I = IValue[2] & 0x7FFFFFFF;
if ((I & 0x7F800000) == 0x7F800000)
{
// INF or NAN
Result[2] = 0x3e0;
if ( I & 0x7FFFFF )
{
Result[2] = 0x3e0 | (((I>>18)|(I>>13)|(I>>3)|(I))&0x1f);
}
else if ( Sign )
{
// -INF is clamped to 0 since 3PK is positive only
Result[2] = 0;
}
}
else if ( Sign )
{
// 3PK is positive only, so clamp to zero
Result[2] = 0;
}
else if (I > 0x477C0000U)
{
// The number is too large to be represented as a float10, set to max
Result[2] = 0x3df;
}
else
{
if (I < 0x38800000U)
{
// The number is too small to be represented as a normalized float10
// Convert it to a denormalized value.
uint32_t Shift = 113U - (I >> 23U);
I = (0x800000U | (I & 0x7FFFFFU)) >> Shift;
}
else
{
// Rebias the exponent to represent the value as a normalized float10
I += 0xC8000000U;
}
Result[2] = ((I + 0x1FFFFU + ((I >> 18U) & 1U)) >> 18U)&0x3ffU;
}
// Pack Result into memory
pDestination->v = (Result[0] & 0x7ff)
| ( (Result[1] & 0x7ff) << 11 )
| ( (Result[2] & 0x3ff) << 22 );
}
// Converts the 11/11/10 format to float3
inline XMVECTOR XM_CALLCONV XMLoadFloat3PK
(
const XMFLOAT3PK* pSource
)
{
assert(pSource);
__declspec(align(16)) uint32_t Result[4];
uint32_t Mantissa;
uint32_t Exponent;
// X Channel (6-bit mantissa)
Mantissa = pSource->xm;
if ( pSource->xe == 0x1f ) // INF or NAN
{
Result[0] = static_cast<uint32_t>(0x7f800000 | (static_cast<int>(pSource->xm) << 17));
}
else
{
if ( pSource->xe != 0 ) // The value is normalized
{
Exponent = pSource->xe;
}
else if (Mantissa != 0) // The value is denormalized
{
// Normalize the value in the resulting float
Exponent = 1;
do
{
Exponent--;
Mantissa <<= 1;
} while ((Mantissa & 0x40) == 0);
Mantissa &= 0x3F;
}
else // The value is zero
{
Exponent = static_cast<uint32_t>(-112);
}
Result[0] = ((Exponent + 112) << 23) | (Mantissa << 17);
}
// Y Channel (6-bit mantissa)
Mantissa = pSource->ym;
if ( pSource->ye == 0x1f ) // INF or NAN
{
Result[1] = static_cast<uint32_t>(0x7f800000 | (static_cast<int>(pSource->ym) << 17));
}
else
{
if ( pSource->ye != 0 ) // The value is normalized
{
Exponent = pSource->ye;
}
else if (Mantissa != 0) // The value is denormalized
{
// Normalize the value in the resulting float
Exponent = 1;
do
{
Exponent--;
Mantissa <<= 1;
} while ((Mantissa & 0x40) == 0);
Mantissa &= 0x3F;
}
else // The value is zero
{
Exponent = static_cast<uint32_t>(-112);
}
Result[1] = ((Exponent + 112) << 23) | (Mantissa << 17);
}
// Z Channel (5-bit mantissa)
Mantissa = pSource->zm;
if ( pSource->ze == 0x1f ) // INF or NAN
{
Result[2] = static_cast<uint32_t>(0x7f800000 | (static_cast<int>(pSource->zm) << 17));
}
else
{
if ( pSource->ze != 0 ) // The value is normalized
{
Exponent = pSource->ze;
}
else if (Mantissa != 0) // The value is denormalized
{
// Normalize the value in the resulting float
Exponent = 1;
do
{
Exponent--;
Mantissa <<= 1;
} while ((Mantissa & 0x20) == 0);
Mantissa &= 0x1F;
}
else // The value is zero
{
Exponent = static_cast<uint32_t>(-112);
}
Result[2] = ((Exponent + 112) << 23) | (Mantissa << 18);
}
return XMLoadFloat3A( reinterpret_cast<const XMFLOAT3A*>(&Result) );
}