defocus-modules/lib/math.c

#include <defocus/base.h>
#include <defocus/intrinsic_helper.h>

#include <math.h>
#include <immintrin.h>
#include <pmmintrin.h>

df_v2 df_add_v2(df_v2 a, df_v2 b)
{
    df_v2 v = {a.x + b.x, a.y + b.y};
    return v;
}

df_v2 df_sub_v2(df_v2 a, df_v2 b)
{
    df_v2 v = {a.x - b.x, a.y - b.y};
    return v;
}

float df_dot_v2(df_v2 a, df_v2 b) { return a.x * b.x + a.y * b.y; }

df_v2 df_mul_v2(float t, df_v2 v)
{
    df_v2 r = {t * v.x, t * v.y};
    return r;
}

df_v2 df_normalize_v2(df_v2 v)
{
    float len_square = df_dot_v2(v, v);
    float len = sqrtf(len_square);
    df_v2 n = {v.x / len, v.y / len};
    return n;
}

df_v3 df_add_v3(df_v3 a, df_v3 b)
{
    df_v3 v = {a.x + b.x, a.y + b.y, a.z + b.z};
    return v;
}

df_v3 df_sub_v3(df_v3 a, df_v3 b)
{
    df_v3 v = {a.x - b.x, a.y - b.y, a.z - b.z};
    return v;
}

float df_dot_v3(df_v3 a, df_v3 b) { return a.x * b.x + a.y * b.y + a.z * b.z; }

df_v3 df_mul_v3(float t, df_v3 v)
{
    df_v3 r = {t * v.x, t * v.y, t * v.z};
    return r;
}

df_v3 df_normalize_v3(df_v3 v)
{
    float len_square = df_dot_v3(v, v);
    float len = sqrtf(len_square);
    df_v3 n = {v.x / len, v.y / len, v.z / len};
    return n;
}

df_line_plane_intersection df_calc_line_plane_intersection(df_line line, df_plane plane)
{
    /* check case */
    float dot = df_dot_v3(line.direction, plane.normal);
    df_v3 base_diff = df_sub_v3(plane.base, line.base);
    float dot2 = df_dot_v3(base_diff, plane.normal);
    if (dot != 0) {
        float t = dot2 / dot;
        df_v3 point = df_add_v3(line.base, df_mul_v3(t, line.direction));
        df_line_plane_intersection intersection = {
            .type = df_line_plane_intersection_vector,
            .vec = point,
        };
        return intersection;
    } else {
        if (dot2 == 0) {
            df_line_plane_intersection intersection = {
                .type = df_line_plane_intersection_contained,
            };
            return intersection;
        } else {
            df_line_plane_intersection intersection = {
                .type = df_line_plane_intersection_none,
            };
            return intersection;
        }
    }
}

df_m4 df_mul_m4(df_m4 a, df_m4 b)
{
    /* Super simple, we could probably do it a lot better via SIMD. */
    df_m4 p;
    for (int row = 0; row < 4; ++row) {
        for (int col = 0; col < 4; ++col) {
            DF_M4_AT(p, row, col) = 0.f;
            for (int i = 0; i < 4; ++i) {
                DF_M4_AT(p, row, col) += DF_M4_AT(a, row, i) * DF_M4_AT(b, i, col);
            }
        }
    }
    return p;
}

df_m4 df_scale(float x, float y, float z)
{
    /* clang-format off */
    df_m4 s = {{
          x, 0.f, 0.f, 0.f,
        0.f,   y, 0.f, 0.f,
        0.f, 0.f,   z, 0.f,
        0.f, 0.f, 0.f, 1.f,
    }};
    /* clang-format on */
    return s;
}

df_m4 df_translate(float x, float y, float z)
{
    /* clang-format off */
    df_m4 t = {{
        1.f, 0.f, 0.f, x,
        0.f, 1.f, 0.f, y,
        0.f, 0.f, 1.f, z,
        0.f, 0.f, 0.f, 1.f,
    }};
    /* clang-format on */
    return t;
}

/** SSE3 version of a horizontal sum:
 * computes the sum of 4 32bit floats inside v
 */
static float hsum(__m128 v)
{
    /* v = [v0, v1, v2, v3] */

    /* shuf = [v1, v1, v3, v3] */
    __m128 shuf = _mm_movehdup_ps(v);

    /* sum = [v0 + v1, 2*v1, v2 + v3, 2*v3] */
    __m128 sum = _mm_add_ps(v, shuf);

    /* shuf = [v2 + v3, 2*v3, v3, v3] */
    shuf = _mm_movehl_ps(shuf, sum);

    /* sum = [v0 + v1 + v2 + v3, ...] */
    sum = _mm_add_ss(sum, shuf);

    return _mm_cvtss_f32(sum);
}

df_v3 df_transform_v3(df_m4 T, df_v3 v)
{
    df_v3 transf;
    _Alignas(16) float tmp_v[4] = {v.x, v.y, v.z, 1.f};
    __m128 homov = _mm_load_ps(tmp_v);

    __m128 row0 = _mm_load_ps(&T.e[0]);
    __m128 row1 = _mm_load_ps(&T.e[4]);
    __m128 row2 = _mm_load_ps(&T.e[8]);

    __m128 prod = _mm_mul_ps(row0, homov);
    transf.x = hsum(prod);
    prod = _mm_mul_ps(row1, homov);
    transf.y = hsum(prod);
    prod = _mm_mul_ps(row2, homov);
    transf.z = hsum(prod);

    return transf;
}

/* Fast 4x4 matrix inverse via SIMD adapted from:
 * https://lxjk.github.io/2017/09/03/Fast-4x4-Matrix-Inverse-with-SSE-SIMD-Explained.html
 */

/* Only works if M is a transform matrix without scale:
 *
 * | R T |
 * | 0 1 |
 */
df_m4 df_inverse_transform_no_scale(df_m4 M)
{
    df_m4 I = {0.f};

    /* transpose 3x3, we know that m03 = m13 = m23 = 0 */
    __m128 t0 = DF_VEC_SHUFFLE_0101(M.vec[0], M.vec[1]); /* 00, 01, 10, 11 */
    __m128 t1 = DF_VEC_SHUFFLE_2323(M.vec[0], M.vec[1]); /* 02, 03, 12, 13 */
    I.vec[0] = DF_VEC_SHUFFLE(t0, M.vec[2], 0, 2, 0, 3); /* 00, 01, 20, 23(=0) */
    I.vec[1] = DF_VEC_SHUFFLE(t0, M.vec[2], 1, 3, 1, 3); /* 01, 11, 21, 23(=0) */
    I.vec[2] = DF_VEC_SHUFFLE(t1, M.vec[2], 0, 2, 2, 3); /* 02, 12, 22, 23(=0) */

    /* last */
    I.vec[3] = _mm_mul_ps(I.vec[0], DF_VEC_SWIZZLE1(M.vec[3], 0));
    I.vec[3] = _mm_add_ps(I.vec[3], _mm_mul_ps(I.vec[1], DF_VEC_SWIZZLE1(M.vec[3], 1)));
    I.vec[3] = _mm_add_ps(I.vec[3], _mm_mul_ps(I.vec[2], DF_VEC_SWIZZLE1(M.vec[3], 2)));
    I.vec[3] = _mm_sub_ps(_mm_setr_ps(0.f, 0.f, 0.f, 1.f), I.vec[3]);

    return I;
}

df_m4 df_inverse_transform(df_m4 M)
{
#define SMALL_NUMBER (1.e-8f)

    df_m4 I = {0.f};

    /* transpose 3x3, we know that m03 = m13 = m23 = 0 */
    __m128 t0 = DF_VEC_SHUFFLE_0101(M.vec[0], M.vec[1]); /* 00, 01, 10, 11 */
    __m128 t1 = DF_VEC_SHUFFLE_2323(M.vec[0], M.vec[1]); /* 02, 03, 12, 13 */
    I.vec[0] = DF_VEC_SHUFFLE(t0, M.vec[2], 0, 2, 0, 3); /* 00, 01, 20, 23(=0) */
    I.vec[1] = DF_VEC_SHUFFLE(t0, M.vec[2], 1, 3, 1, 3); /* 01, 11, 21, 23(=0) */
    I.vec[2] = DF_VEC_SHUFFLE(t1, M.vec[2], 0, 2, 2, 3); /* 02, 12, 22, 23(=0) */

    /* divide by the squared scale */
    __m128 size_sqr = _mm_mul_ps(I.vec[0], I.vec[0]);
    size_sqr = _mm_add_ps(size_sqr, _mm_mul_ps(I.vec[1], I.vec[1]));
    size_sqr = _mm_add_ps(size_sqr, _mm_mul_ps(I.vec[2], I.vec[2]));

    __m128 r_size_sqr = _mm_div_ps(_mm_set1_ps(1.f), size_sqr);

    I.vec[0] = _mm_mul_ps(I.vec[0], r_size_sqr);
    I.vec[1] = _mm_mul_ps(I.vec[1], r_size_sqr);
    I.vec[2] = _mm_mul_ps(I.vec[2], r_size_sqr);

    /* last */
    I.vec[3] = _mm_mul_ps(I.vec[0], DF_VEC_SWIZZLE1(M.vec[3], 0));
    I.vec[3] = _mm_add_ps(I.vec[3], _mm_mul_ps(I.vec[1], DF_VEC_SWIZZLE1(M.vec[3], 1)));
    I.vec[3] = _mm_add_ps(I.vec[3], _mm_mul_ps(I.vec[2], DF_VEC_SWIZZLE1(M.vec[3], 2)));
    I.vec[3] = _mm_sub_ps(_mm_setr_ps(0.f, 0.f, 0.f, 1.f), I.vec[3]);

    return I;
#undef SMALL_NUMBER
}