View frustum culling optimization: Representation matters

vfc5.cpp

#include <stdbool.h>
#include <spu_intrinsics.h>
 
// shuffle helpers
#define L0 0x00010203
#define L1 0x04050607
#define L2 0x08090a0b
#define L3 0x0c0d0e0f
 
#define R0 0x10111213
#define R1 0x14151617
#define R2 0x18191a1b
#define R3 0x1c1d1e1f
 
#define ZERO 0x80808080
 
#define SHUFFLE(l, r, x, y, z, w) si_shufb(l, r, ((qword)(vec_uint4){x, y, z, w}))
 
// splat helper
#define SPLAT(v, idx) si_shufb(v, v, (qword)(vec_uint4)(L ## idx))
 
struct matrix_t
{
    vec_float4 row0;
    vec_float4 row1;
    vec_float4 row2;
    vec_float4 row3;
};
 
struct aabb_t
{
    vec_float4 min;
    vec_float4 max;
};
 
static inline void transform_points_4(qword* dest, qword x, qword y, qword z, const struct matrix_t* mat)
{
#define COMP(c) \
    qword res_ ## c = SPLAT((qword)mat->row3, c); \
    res_ ## c = si_fma(z, SPLAT((qword)mat->row2, c), res_ ## c); \
    res_ ## c = si_fma(y, SPLAT((qword)mat->row1, c), res_ ## c); \
    res_ ## c = si_fma(x, SPLAT((qword)mat->row0, c), res_ ## c); \
    dest[c] = res_ ## c;
 
    COMP(0);
    COMP(1);
    COMP(2);
    COMP(3);
   
#undef COMP
}
 
static inline void transform_matrix(struct matrix_t* dest, const struct matrix_t* lhs, const struct matrix_t* rhs)
{
#define COMP_0(c) \
    qword res_ ## c = si_fm((qword)lhs->row2, SPLAT((qword)rhs->row ## c, 2)); \
    res_ ## c = si_fma((qword)lhs->row1, SPLAT((qword)rhs->row ## c, 1), res_ ## c); \
    res_ ## c = si_fma((qword)lhs->row0, SPLAT((qword)rhs->row ## c, 0), res_ ## c); \
    dest->row ## c = (vec_float4)res_ ## c;
 
#define COMP_1(c) \
    qword res_ ## c = si_fma((qword)lhs->row2, SPLAT((qword)rhs->row ## c, 2), (qword)lhs->row3); \
    res_ ## c = si_fma((qword)lhs->row1, SPLAT((qword)rhs->row ## c, 1), res_ ## c); \
    res_ ## c = si_fma((qword)lhs->row0, SPLAT((qword)rhs->row ## c, 0), res_ ## c); \
    dest->row ## c = (vec_float4)res_ ## c;
 
    COMP_0(0);
    COMP_0(1);
    COMP_0(2);
    COMP_1(3);
 
#undef COMP_0
#undef COMP_1
}
 
__attribute__((noinline)) unsigned int is_visible(const struct matrix_t* transform, const struct aabb_t* aabb, const struct matrix_t* frustum)
{
    qword min = (qword)aabb->min;
    qword max = (qword)aabb->max;
 
    // get aabb points (SoA)
    qword minmax_x = SHUFFLE(min, max, L0, R0, L0, R0); // x X x X
    qword minmax_y = SHUFFLE(min, max, L1, L1, R1, R1); // y y Y Y
    qword minmax_z_0 = SPLAT(min, 2); // z z z z
    qword minmax_z_1 = SPLAT(max, 2); // Z Z Z Z
 
    // get clipping matrix
    struct matrix_t clip;
 
    transform_matrix(&clip, frustum, transform);
 
    // transform points to clip space
    qword points_cs_0[4];
    qword points_cs_1[4];
 
    transform_points_4(points_cs_0, minmax_x, minmax_y, minmax_z_0, &clip);
    transform_points_4(points_cs_1, minmax_x, minmax_y, minmax_z_1, &clip);
 
    // calculate -w
    qword points_cs_0_negw = si_xor(points_cs_0[3], (qword)(vec_uint4)(0x80000000));
    qword points_cs_1_negw = si_xor(points_cs_1[3], (qword)(vec_uint4)(0x80000000));
 
    // for each plane...
    #define NOUT(a, b, c, d) si_orx(si_or(si_fcgt(a, b), si_fcgt(c, d)))
 
    qword nout0 = NOUT(points_cs_0[0], points_cs_0_negw, points_cs_1[0], points_cs_1_negw);
    qword nout1 = NOUT(points_cs_0[3], points_cs_0[0], points_cs_1[3], points_cs_1[0]);
    qword nout2 = NOUT(points_cs_0[1], points_cs_0_negw, points_cs_1[1], points_cs_1_negw);
    qword nout3 = NOUT(points_cs_0[3], points_cs_0[1], points_cs_1[3], points_cs_1[1]);
    qword nout4 = NOUT(points_cs_0[2], (qword)(0), points_cs_1[2], (qword)(0));
    qword nout5 = NOUT(points_cs_0[3], points_cs_0[2], points_cs_1[3], points_cs_1[2]);
 
    #undef NOUT
 
    // merge "not outside" flags
    qword nout01 = si_and(nout0, nout1);
    qword nout012 = si_and(nout01, nout2);
 
    qword nout34 = si_and(nout3, nout4);
    qword nout345 = si_and(nout34, nout5);
 
    qword nout = si_and(nout012, nout345);
 
    return si_to_uint(nout);
}
 
// simple ortho frustum
struct matrix_t frustum =
{
    { 0.1f, 0, 0, 0 },
    { 0, 0.1f, 0, 0 },
    { 0, 0, 0.1f, 0 },
    { 0, 0, 0, 1 }
};
 
// small box
struct aabb_t aabb =
{
    { -1, -2, -3 },
    { 1, 2, 3 }
};
 
// and some weird matrix
struct matrix_t transform =
{
    { 0.123f, 0.456f, 0.789f },
    { 0.456f, 0.123f, 0.789f },
    { 0.789f, 0.123f, 0.456f },
    { 1.f, -1.f, 1.f }
};
 
int main()
{
    is_visible(&transform, &aabb, &frustum);
    si_stop(0);
}