SSE Bilinear interpolation

Question

I'm implementing bilinear interpolation in a tight loop and trying to optimize it with SSE, but I get zero speed-up from it.

Here is the code, the non-SIMD version uses a simple vector structure which could be defined as struct Vec3f { float x, y, z; } with implemented multiplication and addition operators:

#ifdef USE_SIMD
    const Color c11 = pixelCache[y1 * size.x + x1];
    const Color c12 = pixelCache[y2 * size.x + x1];
    const Color c22 = pixelCache[y2 * size.x + x2];
    const Color c21 = pixelCache[y1 * size.x + x2];

    __declspec(align(16)) float mc11[4] = { 1.0, c11.GetB(), c11.GetG(), c11.GetR() };
    __declspec(align(16)) float mc12[4] = { 1.0, c12.GetB(), c12.GetG(), c12.GetR() };
    __declspec(align(16)) float mc22[4] = { 1.0, c22.GetB(), c22.GetG(), c22.GetR() };
    __declspec(align(16)) float mc21[4] = { 1.0, c21.GetB(), c21.GetG(), c21.GetR() };

    // scalars in vector form for SSE
    const float s11 = (x2-x)*(y2-y);
    const float s12 = (x2-x)*(y-y1);
    const float s22 = (x-x1)*(y-y1);
    const float s21 = (x-x1)*(y2-y);

    __declspec(align(16)) float ms11[4] = {1.0, s11, s11, s11};
    __declspec(align(16)) float ms12[4] = {1.0, s12, s12, s12};
    __declspec(align(16)) float ms22[4] = {1.0, s22, s22, s22};
    __declspec(align(16)) float ms21[4] = {1.0, s21, s21, s21};

    __asm {
        movaps xmm0, mc11
        movaps xmm1, mc12
        movaps xmm2, mc22
        movaps xmm3, mc21

        movaps xmm4, ms11
        movaps xmm5, ms12
        movaps xmm6, ms22
        movaps xmm7, ms21

        mulps xmm0, xmm4
        mulps xmm1, xmm5
        mulps xmm2, xmm6
        mulps xmm3, xmm7

        addps xmm0, xmm1
        addps xmm0, xmm2
        addps xmm0, xmm3

        movaps mc11, xmm0
    }
#else
    const Vec3f c11 = toFloat(pixelCache[y1 * size.x + x1]);
    const Vec3f c12 = toFloat(pixelCache[y2 * size.x + x1]);
    const Vec3f c22 = toFloat(pixelCache[y2 * size.x + x2]);
    const Vec3f c21 = toFloat(pixelCache[y1 * size.x + x2]);

    const Vec3f colour =
            c11*(x2-x)*(y2-y) +
            c21*(x-x1)*(y2-y) +
            c12*(x2-x)*(y-y1) +
            c22*(x-x1)*(y-y1);
#endif

Rearranging the asm code to reuse the registers(ended up with just three xmm registers) didn't give any effect. I've also tried using intrinsics:

// perform bilinear interpolation
const Vec3f c11 = toFloat(pixelCache[y1 * size.x + x1]);
const Vec3f c12 = toFloat(pixelCache[y2 * size.x + x1]);
const Vec3f c22 = toFloat(pixelCache[y2 * size.x + x2]);
const Vec3f c21 = toFloat(pixelCache[y1 * size.x + x2]);

// scalars in vector form for SSE
const float s11 = (x2-x)*(y2-y);
const float s12 = (x2-x)*(y-y1);
const float s22 = (x-x1)*(y-y1);
const float s21 = (x-x1)*(y2-y);

__m128 mc11 = _mm_set_ps(1.f, c11.b, c11.g, c11.r);
__m128 mc12 = _mm_set_ps(1.f, c12.b, c12.g, c12.r);
__m128 mc22 = _mm_set_ps(1.f, c22.b, c22.g, c22.r);
__m128 mc21 = _mm_set_ps(1.f, c21.b, c21.g, c21.r);

__m128 ms11 = _mm_set_ps(1.f, s11, s11, s11);
__m128 ms12 = _mm_set_ps(1.f, s12, s12, s12);
__m128 ms22 = _mm_set_ps(1.f, s22, s22, s22);
__m128 ms21 = _mm_set_ps(1.f, s21, s21, s21);

mc11 = _mm_mul_ps(mc11, ms11);
mc12 = _mm_mul_ps(mc12, ms12);
mc22 = _mm_mul_ps(mc22, ms22);
mc21 = _mm_mul_ps(mc21, ms21);

mc11 = _mm_add_ps(mc11, mc12);
mc11 = _mm_add_ps(mc11, mc22);
mc11 = _mm_add_ps(mc11, mc21);

Vec3f colour;
_mm_storeu_ps(colour.array, mc11);

And to no avail. Am I missing something, or it is impossible to gain any extra speed here?

Answer 1

Why floating point? Given packed pixel argb for a, b, c, d, and xerr, yerr in the range 0-256, a simple example is:

// =================================================================================================================
// xs_Bilerp
// =================================================================================================================
finline uint32 xs_Bilerp (uint32 a, uint32 b, uint32 c, uint32 d, uint32 xerr, uint32 yerr)
{
    #define xs_rbmask    0x00ff00ff
    #define xs_agmask    0xff00ff00

    if (a==b && c==d && a==d)   return a;

    const uint32 arb        =   a & xs_rbmask;
    const uint32 crb        =   c & xs_rbmask;
    const uint32 aag        =   a & xs_agmask;
    const uint32 cag        =   c & xs_agmask;

    const uint32 rbdx1      =  (b & xs_rbmask) - arb;
    const uint32 rbdx2      =  (d & xs_rbmask) - crb;
    const uint32 agdx1      = ((b & xs_agmask)>>8) - (aag >> 8);
    const uint32 agdx2      = ((d & xs_agmask)>>8) - (cag >> 8);

    const uint32 rb1        = (arb      + ((rbdx1 * xerr) >> 8)) & xs_rbmask;
    const uint32 ag1        = (aag      + ((agdx1 * xerr)     )) & xs_agmask;
    const uint32 rbdy       = ((crb     + ((rbdx2 * xerr) >> 8)) & xs_rbmask)       - rb1;
    const uint32 agdy       = (((cag    + ((agdx2 * xerr)     )) & xs_agmask)>>8)   - (ag1 >> 8);

    const uint32 rb         = (rb1 + ((rbdy * yerr) >> 8)) & xs_rbmask;
    const uint32 ag         = (ag1 + ((agdy * yerr)     )) & xs_agmask;

    return ag | rb;
}