kmath.h

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#pragma once
 
#include "core/kmemory.h"
#include "defines.h"
#include "math_types.h"
 
#define K_PI 3.14159265358979323846f
 
#define K_2PI (2.0f * K_PI)
 
#define K_4PI (4.0f * K_PI)
 
#define K_HALF_PI (0.5f * K_PI)
 
#define K_QUARTER_PI (0.25f * K_PI)
 
#define K_ONE_OVER_PI (1.0f / K_PI)
 
#define K_ONE_OVER_TWO_PI (1.0f / K_2PI)
 
#define K_SQRT_TWO 1.41421356237309504880f
 
#define K_SQRT_THREE 1.73205080756887729352f
 
#define K_SQRT_ONE_OVER_TWO 0.70710678118654752440f
 
#define K_SQRT_ONE_OVER_THREE 0.57735026918962576450f
 
#define K_DEG2RAD_MULTIPLIER (K_PI / 180.0f)
 
#define K_RAD2DEG_MULTIPLIER (180.0f / K_PI)
 
#define K_SEC_TO_US_MULTIPLIER (1000.0f * 1000.0f)
 
#define K_SEC_TO_MS_MULTIPLIER 1000.0f
 
#define K_MS_TO_SEC_MULTIPLIER 0.001f
 
#define K_INFINITY (1e30f * 1e30f)
 
#define K_FLOAT_EPSILON 1.192092896e-07f
 
// ------------------------------------------
// General math functions
// ------------------------------------------
 
KINLINE void kswapf(f32 *a, f32 *b) {
    f32 temp = *a;
    *a = *b;
    *b = temp;
}
 
#define KSWAP(type, a, b) \
    {                     \
        type temp = a;    \
        a = b;            \
        b = temp;         \
    }
 
KINLINE f32 ksign(f32 x) {
    return x == 0.0f ? 0.0f : x < 0.0f ? -1.0f
                                       : 1.0f;
}
 
KINLINE f32 kstep(f32 edge, f32 x) {
    return x < edge ? 0.0f : 1.0f;
}
 
KAPI f32 ksin(f32 x);
 
KAPI f32 kcos(f32 x);
 
KAPI f32 ktan(f32 x);
 
KAPI f32 kacos(f32 x);
 
KAPI f32 ksqrt(f32 x);
 
KAPI f32 kabs(f32 x);
 
KAPI f32 kfloor(f32 x);
 
KAPI f32 klog2(f32 x);
 
KINLINE b8 is_power_of_2(u64 value) {
    return (value != 0) && ((value & (value - 1)) == 0);
}
 
KAPI i32 krandom(void);
 
KAPI i32 krandom_in_range(i32 min, i32 max);
 
KAPI f32 kfrandom(void);
 
KAPI f32 kfrandom_in_range(f32 min, f32 max);
 
KINLINE f32 ksmoothstep(f32 edge_0, f32 edge_1, f32 x) {
    f32 t = KCLAMP((x - edge_0) / (edge_1 - edge_0), 0.0f, 1.0f);
    return t * t * (3.0 - 2.0 * t);
}
 
KINLINE b8 kfloat_compare(f32 f_0, f32 f_1) {
    return kabs(f_0 - f_1) < K_FLOAT_EPSILON;
}
 
// ------------------------------------------
// Vector 2
// ------------------------------------------
 
KINLINE vec2 vec2_create(f32 x, f32 y) {
    vec2 out_vector;
    out_vector.x = x;
    out_vector.y = y;
    return out_vector;
}
 
KINLINE vec2 vec2_zero(void) { return (vec2){0.0f, 0.0f}; }
 
KINLINE vec2 vec2_one(void) { return (vec2){1.0f, 1.0f}; }
 
KINLINE vec2 vec2_up(void) { return (vec2){0.0f, 1.0f}; }
 
KINLINE vec2 vec2_down(void) { return (vec2){0.0f, -1.0f}; }
 
KINLINE vec2 vec2_left(void) { return (vec2){-1.0f, 0.0f}; }
 
KINLINE vec2 vec2_right(void) { return (vec2){1.0f, 0.0f}; }
 
KINLINE vec2 vec2_add(vec2 vector_0, vec2 vector_1) {
    return (vec2){vector_0.x + vector_1.x, vector_0.y + vector_1.y};
}
 
KINLINE vec2 vec2_sub(vec2 vector_0, vec2 vector_1) {
    return (vec2){vector_0.x - vector_1.x, vector_0.y - vector_1.y};
}
 
KINLINE vec2 vec2_mul(vec2 vector_0, vec2 vector_1) {
    return (vec2){vector_0.x * vector_1.x, vector_0.y * vector_1.y};
}
 
KINLINE vec2 vec2_mul_scalar(vec2 vector_0, f32 scalar) {
    return (vec2){vector_0.x * scalar, vector_0.y * scalar};
}
 
KINLINE vec2 vec2_mul_add(vec2 vector_0, vec2 vector_1, vec2 vector_2) {
    return (vec2){
        vector_0.x * vector_1.x + vector_2.x,
        vector_0.y * vector_1.y + vector_2.y};
}
 
KINLINE vec2 vec2_div(vec2 vector_0, vec2 vector_1) {
    return (vec2){vector_0.x / vector_1.x, vector_0.y / vector_1.y};
}
 
KINLINE f32 vec2_length_squared(vec2 vector) {
    return vector.x * vector.x + vector.y * vector.y;
}
 
KINLINE f32 vec2_length(vec2 vector) {
    return ksqrt(vec2_length_squared(vector));
}
 
KINLINE void vec2_normalize(vec2 *vector) {
    const f32 length = vec2_length(*vector);
    vector->x /= length;
    vector->y /= length;
}
 
KINLINE vec2 vec2_normalized(vec2 vector) {
    vec2_normalize(&vector);
    return vector;
}
 
KINLINE b8 vec2_compare(vec2 vector_0, vec2 vector_1, f32 tolerance) {
    if (kabs(vector_0.x - vector_1.x) > tolerance) {
        return false;
    }
 
    if (kabs(vector_0.y - vector_1.y) > tolerance) {
        return false;
    }
 
    return true;
}
 
KINLINE f32 vec2_distance(vec2 vector_0, vec2 vector_1) {
    vec2 d = (vec2){vector_0.x - vector_1.x, vector_0.y - vector_1.y};
    return vec2_length(d);
}
 
KINLINE f32 vec2_distance_squared(vec2 vector_0, vec2 vector_1) {
    vec2 d = (vec2){vector_0.x - vector_1.x, vector_0.y - vector_1.y};
    return vec2_length_squared(d);
}
 
// ------------------------------------------
// Vector 3
// ------------------------------------------
 
KINLINE vec3 vec3_create(f32 x, f32 y, f32 z) { return (vec3){x, y, z}; }
 
KINLINE vec3 vec3_from_vec4(vec4 vector) {
    return (vec3){vector.x, vector.y, vector.z};
}
 
KINLINE vec4 vec3_to_vec4(vec3 vector, f32 w) {
    return (vec4){vector.x, vector.y, vector.z, w};
}
 
KINLINE vec3 vec3_zero(void) { return (vec3){0.0f, 0.0f, 0.0f}; }
 
KINLINE vec3 vec3_one(void) { return (vec3){1.0f, 1.0f, 1.0f}; }
 
KINLINE vec3 vec3_up(void) { return (vec3){0.0f, 1.0f, 0.0f}; }
 
KINLINE vec3 vec3_down(void) { return (vec3){0.0f, -1.0f, 0.0f}; }
 
KINLINE vec3 vec3_left(void) { return (vec3){-1.0f, 0.0f, 0.0f}; }
 
KINLINE vec3 vec3_right(void) { return (vec3){1.0f, 0.0f, 0.0f}; }
 
KINLINE vec3 vec3_forward(void) { return (vec3){0.0f, 0.0f, -1.0f}; }
 
KINLINE vec3 vec3_back(void) { return (vec3){0.0f, 0.0f, 1.0f}; }
 
KINLINE vec3 vec3_add(vec3 vector_0, vec3 vector_1) {
    return (vec3){vector_0.x + vector_1.x, vector_0.y + vector_1.y,
                  vector_0.z + vector_1.z};
}
 
KINLINE vec3 vec3_sub(vec3 vector_0, vec3 vector_1) {
    return (vec3){vector_0.x - vector_1.x, vector_0.y - vector_1.y,
                  vector_0.z - vector_1.z};
}
 
KINLINE vec3 vec3_mul(vec3 vector_0, vec3 vector_1) {
    return (vec3){vector_0.x * vector_1.x, vector_0.y * vector_1.y,
                  vector_0.z * vector_1.z};
}
 
KINLINE vec3 vec3_mul_scalar(vec3 vector_0, f32 scalar) {
    return (vec3){vector_0.x * scalar, vector_0.y * scalar, vector_0.z * scalar};
}
 
KINLINE vec3 vec3_mul_add(vec3 vector_0, vec3 vector_1, vec3 vector_2) {
    return (vec3){
        vector_0.x * vector_1.x + vector_2.x,
        vector_0.y * vector_1.y + vector_2.y,
        vector_0.z * vector_1.z + vector_2.z};
}
 
KINLINE vec3 vec3_div(vec3 vector_0, vec3 vector_1) {
    return (vec3){vector_0.x / vector_1.x, vector_0.y / vector_1.y,
                  vector_0.z / vector_1.z};
}
 
KINLINE f32 vec3_length_squared(vec3 vector) {
    return vector.x * vector.x + vector.y * vector.y + vector.z * vector.z;
}
 
KINLINE f32 vec3_length(vec3 vector) {
    return ksqrt(vec3_length_squared(vector));
}
 
KINLINE void vec3_normalize(vec3 *vector) {
    const f32 length = vec3_length(*vector);
    vector->x /= length;
    vector->y /= length;
    vector->z /= length;
}
 
KINLINE vec3 vec3_normalized(vec3 vector) {
    vec3_normalize(&vector);
    return vector;
}
 
KINLINE f32 vec3_dot(vec3 vector_0, vec3 vector_1) {
    f32 p = 0;
    p += vector_0.x * vector_1.x;
    p += vector_0.y * vector_1.y;
    p += vector_0.z * vector_1.z;
    return p;
}
 
KINLINE vec3 vec3_cross(vec3 vector_0, vec3 vector_1) {
    return (vec3){vector_0.y * vector_1.z - vector_0.z * vector_1.y,
                  vector_0.z * vector_1.x - vector_0.x * vector_1.z,
                  vector_0.x * vector_1.y - vector_0.y * vector_1.x};
}
 
KINLINE b8 vec3_compare(vec3 vector_0, vec3 vector_1, f32 tolerance) {
    if (kabs(vector_0.x - vector_1.x) > tolerance) {
        return false;
    }
 
    if (kabs(vector_0.y - vector_1.y) > tolerance) {
        return false;
    }
 
    if (kabs(vector_0.z - vector_1.z) > tolerance) {
        return false;
    }
 
    return true;
}
 
KINLINE f32 vec3_distance(vec3 vector_0, vec3 vector_1) {
    vec3 d = (vec3){vector_0.x - vector_1.x, vector_0.y - vector_1.y,
                    vector_0.z - vector_1.z};
    return vec3_length(d);
}
 
KINLINE f32 vec3_distance_squared(vec3 vector_0, vec3 vector_1) {
    vec3 d = (vec3){vector_0.x - vector_1.x, vector_0.y - vector_1.y,
                    vector_0.z - vector_1.z};
    return vec3_length_squared(d);
}
 
KINLINE vec3 vec3_transform(vec3 v, f32 w, mat4 m) {
    vec3 out;
    out.x = v.x * m.data[0 + 0] + v.y * m.data[4 + 0] + v.z * m.data[8 + 0] + w * m.data[12 + 0];
    out.y = v.x * m.data[0 + 1] + v.y * m.data[4 + 1] + v.z * m.data[8 + 1] + w * m.data[12 + 1];
    out.z = v.x * m.data[0 + 2] + v.y * m.data[4 + 2] + v.z * m.data[8 + 2] + w * m.data[12 + 2];
    return out;
}
 
// ------------------------------------------
// Vector 4
// ------------------------------------------
 
KINLINE vec4 vec4_create(f32 x, f32 y, f32 z, f32 w) {
    vec4 out_vector;
#if defined(KUSE_SIMD)
    out_vector.data = _mm_setr_ps(x, y, z, w);
#else
    out_vector.x = x;
    out_vector.y = y;
    out_vector.z = z;
    out_vector.w = w;
#endif
    return out_vector;
}
 
KINLINE vec3 vec4_to_vec3(vec4 vector) {
    return (vec3){vector.x, vector.y, vector.z};
}
 
KINLINE vec4 vec4_from_vec3(vec3 vector, f32 w) {
#if defined(KUSE_SIMD)
    vec4 out_vector;
    out_vector.data = _mm_setr_ps(x, y, z, w);
    return out_vector;
#else
    return (vec4){vector.x, vector.y, vector.z, w};
#endif
}
 
KINLINE vec4 vec4_zero(void) { return (vec4){0.0f, 0.0f, 0.0f, 0.0f}; }
 
KINLINE vec4 vec4_one(void) { return (vec4){1.0f, 1.0f, 1.0f, 1.0f}; }
 
KINLINE vec4 vec4_add(vec4 vector_0, vec4 vector_1) {
    vec4 result;
    for (u64 i = 0; i < 4; ++i) {
        result.elements[i] = vector_0.elements[i] + vector_1.elements[i];
    }
    return result;
}
 
KINLINE vec4 vec4_sub(vec4 vector_0, vec4 vector_1) {
    vec4 result;
    for (u64 i = 0; i < 4; ++i) {
        result.elements[i] = vector_0.elements[i] - vector_1.elements[i];
    }
    return result;
}
 
KINLINE vec4 vec4_mul(vec4 vector_0, vec4 vector_1) {
    vec4 result;
    for (u64 i = 0; i < 4; ++i) {
        result.elements[i] = vector_0.elements[i] * vector_1.elements[i];
    }
    return result;
}
 
KINLINE vec4 vec4_mul_scalar(vec4 vector_0, f32 scalar) {
    return (vec4){vector_0.x * scalar, vector_0.y * scalar, vector_0.z * scalar, vector_0.w * scalar};
}
 
KINLINE vec4 vec4_mul_add(vec4 vector_0, vec4 vector_1, vec4 vector_2) {
    return (vec4){
        vector_0.x * vector_1.x + vector_2.x,
        vector_0.y * vector_1.y + vector_2.y,
        vector_0.z * vector_1.z + vector_2.z,
        vector_0.w * vector_1.w + vector_2.w,
    };
}
 
KINLINE vec4 vec4_div(vec4 vector_0, vec4 vector_1) {
    vec4 result;
    for (u64 i = 0; i < 4; ++i) {
        result.elements[i] = vector_0.elements[i] / vector_1.elements[i];
    }
    return result;
}
 
KINLINE f32 vec4_length_squared(vec4 vector) {
    return vector.x * vector.x + vector.y * vector.y + vector.z * vector.z +
           vector.w * vector.w;
}
 
KINLINE f32 vec4_length(vec4 vector) {
    return ksqrt(vec4_length_squared(vector));
}
 
KINLINE void vec4_normalize(vec4 *vector) {
    const f32 length = vec4_length(*vector);
    vector->x /= length;
    vector->y /= length;
    vector->z /= length;
    vector->w /= length;
}
 
KINLINE vec4 vec4_normalized(vec4 vector) {
    vec4_normalize(&vector);
    return vector;
}
 
KINLINE f32 vec4_dot_f32(f32 a0, f32 a1, f32 a2, f32 a3, f32 b0, f32 b1, f32 b2,
                         f32 b3) {
    f32 p;
    p = a0 * b0 + a1 * b1 + a2 * b2 + a3 * b3;
    return p;
}
 
KINLINE b8 vec4_compare(vec4 vector_0, vec4 vector_1, f32 tolerance) {
    if (kabs(vector_0.x - vector_1.x) > tolerance) {
        return false;
    }
 
    if (kabs(vector_0.y - vector_1.y) > tolerance) {
        return false;
    }
 
    if (kabs(vector_0.z - vector_1.z) > tolerance) {
        return false;
    }
 
    if (kabs(vector_0.w - vector_1.w) > tolerance) {
        return false;
    }
 
    return true;
}
 
KINLINE mat4 mat4_identity(void) {
    mat4 out_matrix;
    kzero_memory(out_matrix.data, sizeof(f32) * 16);
    out_matrix.data[0] = 1.0f;
    out_matrix.data[5] = 1.0f;
    out_matrix.data[10] = 1.0f;
    out_matrix.data[15] = 1.0f;
    return out_matrix;
}
 
KINLINE mat4 mat4_mul(mat4 matrix_0, mat4 matrix_1) {
    mat4 out_matrix = mat4_identity();
 
    const f32 *m1_ptr = matrix_0.data;
    const f32 *m2_ptr = matrix_1.data;
    f32 *dst_ptr = out_matrix.data;
 
    for (i32 i = 0; i < 4; ++i) {
        for (i32 j = 0; j < 4; ++j) {
            *dst_ptr = m1_ptr[0] * m2_ptr[0 + j] + m1_ptr[1] * m2_ptr[4 + j] +
                       m1_ptr[2] * m2_ptr[8 + j] + m1_ptr[3] * m2_ptr[12 + j];
            dst_ptr++;
        }
        m1_ptr += 4;
    }
    return out_matrix;
}
 
KINLINE mat4 mat4_orthographic(f32 left, f32 right, f32 bottom, f32 top,
                               f32 near_clip, f32 far_clip) {
    mat4 out_matrix = mat4_identity();
 
    f32 lr = 1.0f / (left - right);
    f32 bt = 1.0f / (bottom - top);
    f32 nf = 1.0f / (near_clip - far_clip);
 
    out_matrix.data[0] = -2.0f * lr;
    out_matrix.data[5] = -2.0f * bt;
    out_matrix.data[10] = 2.0f * nf;
 
    out_matrix.data[12] = (left + right) * lr;
    out_matrix.data[13] = (top + bottom) * bt;
    out_matrix.data[14] = (far_clip + near_clip) * nf;
    return out_matrix;
}
 
KINLINE mat4 mat4_perspective(f32 fov_radians, f32 aspect_ratio, f32 near_clip,
                              f32 far_clip) {
    f32 half_tan_fov = ktan(fov_radians * 0.5f);
    mat4 out_matrix;
    kzero_memory(out_matrix.data, sizeof(f32) * 16);
    out_matrix.data[0] = 1.0f / (aspect_ratio * half_tan_fov);
    out_matrix.data[5] = 1.0f / half_tan_fov;
    out_matrix.data[10] = -((far_clip + near_clip) / (far_clip - near_clip));
    out_matrix.data[11] = -1.0f;
    out_matrix.data[14] =
        -((2.0f * far_clip * near_clip) / (far_clip - near_clip));
    return out_matrix;
}
 
KINLINE mat4 mat4_look_at(vec3 position, vec3 target, vec3 up) {
    mat4 out_matrix;
    vec3 z_axis;
    z_axis.x = target.x - position.x;
    z_axis.y = target.y - position.y;
    z_axis.z = target.z - position.z;
 
    z_axis = vec3_normalized(z_axis);
    vec3 x_axis = vec3_normalized(vec3_cross(z_axis, up));
    vec3 y_axis = vec3_cross(x_axis, z_axis);
 
    out_matrix.data[0] = x_axis.x;
    out_matrix.data[1] = y_axis.x;
    out_matrix.data[2] = -z_axis.x;
    out_matrix.data[3] = 0;
    out_matrix.data[4] = x_axis.y;
    out_matrix.data[5] = y_axis.y;
    out_matrix.data[6] = -z_axis.y;
    out_matrix.data[7] = 0;
    out_matrix.data[8] = x_axis.z;
    out_matrix.data[9] = y_axis.z;
    out_matrix.data[10] = -z_axis.z;
    out_matrix.data[11] = 0;
    out_matrix.data[12] = -vec3_dot(x_axis, position);
    out_matrix.data[13] = -vec3_dot(y_axis, position);
    out_matrix.data[14] = vec3_dot(z_axis, position);
    out_matrix.data[15] = 1.0f;
 
    return out_matrix;
}
 
KINLINE mat4 mat4_transposed(mat4 matrix) {
    mat4 out_matrix = mat4_identity();
    out_matrix.data[0] = matrix.data[0];
    out_matrix.data[1] = matrix.data[4];
    out_matrix.data[2] = matrix.data[8];
    out_matrix.data[3] = matrix.data[12];
    out_matrix.data[4] = matrix.data[1];
    out_matrix.data[5] = matrix.data[5];
    out_matrix.data[6] = matrix.data[9];
    out_matrix.data[7] = matrix.data[13];
    out_matrix.data[8] = matrix.data[2];
    out_matrix.data[9] = matrix.data[6];
    out_matrix.data[10] = matrix.data[10];
    out_matrix.data[11] = matrix.data[14];
    out_matrix.data[12] = matrix.data[3];
    out_matrix.data[13] = matrix.data[7];
    out_matrix.data[14] = matrix.data[11];
    out_matrix.data[15] = matrix.data[15];
    return out_matrix;
}
 
KINLINE f32 mat4_determinant(mat4 matrix) {
    const f32 *m = matrix.data;
 
    f32 t0 = m[10] * m[15];
    f32 t1 = m[14] * m[11];
    f32 t2 = m[6] * m[15];
    f32 t3 = m[14] * m[7];
    f32 t4 = m[6] * m[11];
    f32 t5 = m[10] * m[7];
    f32 t6 = m[2] * m[15];
    f32 t7 = m[14] * m[3];
    f32 t8 = m[2] * m[11];
    f32 t9 = m[10] * m[3];
    f32 t10 = m[2] * m[7];
    f32 t11 = m[6] * m[3];
 
    mat3 temp_mat;
    f32 *o = temp_mat.data;
 
    o[0] = (t0 * m[5] + t3 * m[9] + t4 * m[13]) -
           (t1 * m[5] + t2 * m[9] + t5 * m[13]);
    o[1] = (t1 * m[1] + t6 * m[9] + t9 * m[13]) -
           (t0 * m[1] + t7 * m[9] + t8 * m[13]);
    o[2] = (t2 * m[1] + t7 * m[5] + t10 * m[13]) -
           (t3 * m[1] + t6 * m[5] + t11 * m[13]);
    o[3] = (t5 * m[1] + t8 * m[5] + t11 * m[9]) -
           (t4 * m[1] + t9 * m[5] + t10 * m[9]);
 
    f32 determinant = 1.0f / (m[0] * o[0] + m[4] * o[1] + m[8] * o[2] + m[12] * o[3]);
    return determinant;
}
 
KINLINE mat4 mat4_inverse(mat4 matrix) {
    const f32 *m = matrix.data;
 
    f32 t0 = m[10] * m[15];
    f32 t1 = m[14] * m[11];
    f32 t2 = m[6] * m[15];
    f32 t3 = m[14] * m[7];
    f32 t4 = m[6] * m[11];
    f32 t5 = m[10] * m[7];
    f32 t6 = m[2] * m[15];
    f32 t7 = m[14] * m[3];
    f32 t8 = m[2] * m[11];
    f32 t9 = m[10] * m[3];
    f32 t10 = m[2] * m[7];
    f32 t11 = m[6] * m[3];
    f32 t12 = m[8] * m[13];
    f32 t13 = m[12] * m[9];
    f32 t14 = m[4] * m[13];
    f32 t15 = m[12] * m[5];
    f32 t16 = m[4] * m[9];
    f32 t17 = m[8] * m[5];
    f32 t18 = m[0] * m[13];
    f32 t19 = m[12] * m[1];
    f32 t20 = m[0] * m[9];
    f32 t21 = m[8] * m[1];
    f32 t22 = m[0] * m[5];
    f32 t23 = m[4] * m[1];
 
    mat4 out_matrix;
    f32 *o = out_matrix.data;
 
    o[0] = (t0 * m[5] + t3 * m[9] + t4 * m[13]) -
           (t1 * m[5] + t2 * m[9] + t5 * m[13]);
    o[1] = (t1 * m[1] + t6 * m[9] + t9 * m[13]) -
           (t0 * m[1] + t7 * m[9] + t8 * m[13]);
    o[2] = (t2 * m[1] + t7 * m[5] + t10 * m[13]) -
           (t3 * m[1] + t6 * m[5] + t11 * m[13]);
    o[3] = (t5 * m[1] + t8 * m[5] + t11 * m[9]) -
           (t4 * m[1] + t9 * m[5] + t10 * m[9]);
 
    f32 d = 1.0f / (m[0] * o[0] + m[4] * o[1] + m[8] * o[2] + m[12] * o[3]);
 
    o[0] = d * o[0];
    o[1] = d * o[1];
    o[2] = d * o[2];
    o[3] = d * o[3];
    o[4] = d * ((t1 * m[4] + t2 * m[8] + t5 * m[12]) -
                (t0 * m[4] + t3 * m[8] + t4 * m[12]));
    o[5] = d * ((t0 * m[0] + t7 * m[8] + t8 * m[12]) -
                (t1 * m[0] + t6 * m[8] + t9 * m[12]));
    o[6] = d * ((t3 * m[0] + t6 * m[4] + t11 * m[12]) -
                (t2 * m[0] + t7 * m[4] + t10 * m[12]));
    o[7] = d * ((t4 * m[0] + t9 * m[4] + t10 * m[8]) -
                (t5 * m[0] + t8 * m[4] + t11 * m[8]));
    o[8] = d * ((t12 * m[7] + t15 * m[11] + t16 * m[15]) -
                (t13 * m[7] + t14 * m[11] + t17 * m[15]));
    o[9] = d * ((t13 * m[3] + t18 * m[11] + t21 * m[15]) -
                (t12 * m[3] + t19 * m[11] + t20 * m[15]));
    o[10] = d * ((t14 * m[3] + t19 * m[7] + t22 * m[15]) -
                 (t15 * m[3] + t18 * m[7] + t23 * m[15]));
    o[11] = d * ((t17 * m[3] + t20 * m[7] + t23 * m[11]) -
                 (t16 * m[3] + t21 * m[7] + t22 * m[11]));
    o[12] = d * ((t14 * m[10] + t17 * m[14] + t13 * m[6]) -
                 (t16 * m[14] + t12 * m[6] + t15 * m[10]));
    o[13] = d * ((t20 * m[14] + t12 * m[2] + t19 * m[10]) -
                 (t18 * m[10] + t21 * m[14] + t13 * m[2]));
    o[14] = d * ((t18 * m[6] + t23 * m[14] + t15 * m[2]) -
                 (t22 * m[14] + t14 * m[2] + t19 * m[6]));
    o[15] = d * ((t22 * m[10] + t16 * m[2] + t21 * m[6]) -
                 (t20 * m[6] + t23 * m[10] + t17 * m[2]));
 
    return out_matrix;
}
 
KINLINE mat4 mat4_translation(vec3 position) {
    mat4 out_matrix = mat4_identity();
    out_matrix.data[12] = position.x;
    out_matrix.data[13] = position.y;
    out_matrix.data[14] = position.z;
    return out_matrix;
}
 
KINLINE mat4 mat4_scale(vec3 scale) {
    mat4 out_matrix = mat4_identity();
    out_matrix.data[0] = scale.x;
    out_matrix.data[5] = scale.y;
    out_matrix.data[10] = scale.z;
    return out_matrix;
}
 
KINLINE mat4 mat4_euler_x(f32 angle_radians) {
    mat4 out_matrix = mat4_identity();
    f32 c = kcos(angle_radians);
    f32 s = ksin(angle_radians);
 
    out_matrix.data[5] = c;
    out_matrix.data[6] = s;
    out_matrix.data[9] = -s;
    out_matrix.data[10] = c;
    return out_matrix;
}
 
KINLINE mat4 mat4_euler_y(f32 angle_radians) {
    mat4 out_matrix = mat4_identity();
    f32 c = kcos(angle_radians);
    f32 s = ksin(angle_radians);
 
    out_matrix.data[0] = c;
    out_matrix.data[2] = -s;
    out_matrix.data[8] = s;
    out_matrix.data[10] = c;
    return out_matrix;
}
 
KINLINE mat4 mat4_euler_z(f32 angle_radians) {
    mat4 out_matrix = mat4_identity();
 
    f32 c = kcos(angle_radians);
    f32 s = ksin(angle_radians);
 
    out_matrix.data[0] = c;
    out_matrix.data[1] = s;
    out_matrix.data[4] = -s;
    out_matrix.data[5] = c;
    return out_matrix;
}
 
KINLINE mat4 mat4_euler_xyz(f32 x_radians, f32 y_radians, f32 z_radians) {
    mat4 rx = mat4_euler_x(x_radians);
    mat4 ry = mat4_euler_y(y_radians);
    mat4 rz = mat4_euler_z(z_radians);
    mat4 out_matrix = mat4_mul(rx, ry);
    out_matrix = mat4_mul(out_matrix, rz);
    return out_matrix;
}
 
KINLINE vec3 mat4_forward(mat4 matrix) {
    vec3 forward;
    forward.x = -matrix.data[2];
    forward.y = -matrix.data[6];
    forward.z = -matrix.data[10];
    vec3_normalize(&forward);
    return forward;
}
 
KINLINE vec3 mat4_backward(mat4 matrix) {
    vec3 backward;
    backward.x = matrix.data[2];
    backward.y = matrix.data[6];
    backward.z = matrix.data[10];
    vec3_normalize(&backward);
    return backward;
}
 
KINLINE vec3 mat4_up(mat4 matrix) {
    vec3 up;
    up.x = matrix.data[1];
    up.y = matrix.data[5];
    up.z = matrix.data[9];
    vec3_normalize(&up);
    return up;
}
 
KINLINE vec3 mat4_down(mat4 matrix) {
    vec3 down;
    down.x = -matrix.data[1];
    down.y = -matrix.data[5];
    down.z = -matrix.data[9];
    vec3_normalize(&down);
    return down;
}
 
KINLINE vec3 mat4_left(mat4 matrix) {
    vec3 left;
    left.x = -matrix.data[0];
    left.y = -matrix.data[4];
    left.z = -matrix.data[8];
    vec3_normalize(&left);
    return left;
}
 
KINLINE vec3 mat4_right(mat4 matrix) {
    vec3 right;
    right.x = matrix.data[0];
    right.y = matrix.data[4];
    right.z = matrix.data[8];
    vec3_normalize(&right);
    return right;
}
 
KINLINE vec3 mat4_mul_vec3(mat4 m, vec3 v) {
    return (vec3){v.x * m.data[0] + v.y * m.data[1] + v.z * m.data[2] + m.data[3],
                  v.x * m.data[4] + v.y * m.data[5] + v.z * m.data[6] + m.data[7],
                  v.x * m.data[8] + v.y * m.data[9] + v.z * m.data[10] +
                      m.data[11]};
}
 
KINLINE vec3 vec3_mul_mat4(vec3 v, mat4 m) {
    return (vec3){
        v.x * m.data[0] + v.y * m.data[4] + v.z * m.data[8] + m.data[12],
        v.x * m.data[1] + v.y * m.data[5] + v.z * m.data[9] + m.data[13],
        v.x * m.data[2] + v.y * m.data[6] + v.z * m.data[10] + m.data[14]};
}
 
KINLINE vec4 mat4_mul_vec4(mat4 m, vec4 v) {
    return (vec4){
        v.x * m.data[0] + v.y * m.data[1] + v.z * m.data[2] + v.w * m.data[3],
        v.x * m.data[4] + v.y * m.data[5] + v.z * m.data[6] + v.w * m.data[7],
        v.x * m.data[8] + v.y * m.data[9] + v.z * m.data[10] + v.w * m.data[11],
        v.x * m.data[12] + v.y * m.data[13] + v.z * m.data[14] +
            v.w * m.data[15]};
}
 
KINLINE vec4 vec4_mul_mat4(vec4 v, mat4 m) {
    return (vec4){
        v.x * m.data[0] + v.y * m.data[4] + v.z * m.data[8] + v.w * m.data[12],
        v.x * m.data[1] + v.y * m.data[5] + v.z * m.data[9] + v.w * m.data[13],
        v.x * m.data[2] + v.y * m.data[6] + v.z * m.data[10] + v.w * m.data[14],
        v.x * m.data[3] + v.y * m.data[7] + v.z * m.data[11] + v.w * m.data[15]};
}
 
// ------------------------------------------
// Quaternion
// ------------------------------------------
 
KINLINE quat quat_identity(void) { return (quat){0, 0, 0, 1.0f}; }
 
KINLINE f32 quat_normal(quat q) {
    return ksqrt(q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w);
}
 
KINLINE quat quat_normalize(quat q) {
    f32 normal = quat_normal(q);
    return (quat){q.x / normal, q.y / normal, q.z / normal, q.w / normal};
}
 
KINLINE quat quat_conjugate(quat q) { return (quat){-q.x, -q.y, -q.z, q.w}; }
 
KINLINE quat quat_inverse(quat q) { return quat_normalize(quat_conjugate(q)); }
 
KINLINE quat quat_mul(quat q_0, quat q_1) {
    quat out_quaternion;
 
    out_quaternion.x =
        q_0.x * q_1.w + q_0.y * q_1.z - q_0.z * q_1.y + q_0.w * q_1.x;
 
    out_quaternion.y =
        -q_0.x * q_1.z + q_0.y * q_1.w + q_0.z * q_1.x + q_0.w * q_1.y;
 
    out_quaternion.z =
        q_0.x * q_1.y - q_0.y * q_1.x + q_0.z * q_1.w + q_0.w * q_1.z;
 
    out_quaternion.w =
        -q_0.x * q_1.x - q_0.y * q_1.y - q_0.z * q_1.z + q_0.w * q_1.w;
 
    return out_quaternion;
}
 
KINLINE f32 quat_dot(quat q_0, quat q_1) {
    return q_0.x * q_1.x + q_0.y * q_1.y + q_0.z * q_1.z + q_0.w * q_1.w;
}
 
KINLINE vec3 vec3_min(vec3 vector_0, vec3 vector_1) {
    return vec3_create(
        KMIN(vector_0.x, vector_1.y),
        KMIN(vector_0.y, vector_1.y),
        KMIN(vector_0.z, vector_1.z));
}
 
KINLINE vec3 vec3_max(vec3 vector_0, vec3 vector_1) {
    return vec3_create(
        KMAX(vector_0.x, vector_1.y),
        KMAX(vector_0.y, vector_1.y),
        KMAX(vector_0.z, vector_1.z));
}
 
KINLINE vec3 vec3_sign(vec3 v) {
    return vec3_create(ksign(v.x), ksign(v.y), ksign(v.z));
}
 
KINLINE vec3 vec3_rotate(vec3 v, quat q) {
    vec3 u = vec3_create(q.x, q.y, q.z);
    f32 s = q.w;
 
    return vec3_add(
        vec3_add(
            vec3_mul_scalar(u, 2.0f * vec3_dot(u, v)),
            vec3_mul_scalar(v, (s * s - vec3_dot(u, u)))),
        vec3_mul_scalar(vec3_cross(u, v), 2.0f * s));
}
 
KINLINE mat4 quat_to_mat4(quat q) {
    mat4 out_matrix = mat4_identity();
 
    // https://stackoverflow.com/questions/1556260/convert-quaternion-rotation-to-rotation-matrix
 
    quat n = quat_normalize(q);
 
    out_matrix.data[0] = 1.0f - 2.0f * n.y * n.y - 2.0f * n.z * n.z;
    out_matrix.data[1] = 2.0f * n.x * n.y - 2.0f * n.z * n.w;
    out_matrix.data[2] = 2.0f * n.x * n.z + 2.0f * n.y * n.w;
 
    out_matrix.data[4] = 2.0f * n.x * n.y + 2.0f * n.z * n.w;
    out_matrix.data[5] = 1.0f - 2.0f * n.x * n.x - 2.0f * n.z * n.z;
    out_matrix.data[6] = 2.0f * n.y * n.z - 2.0f * n.x * n.w;
 
    out_matrix.data[8] = 2.0f * n.x * n.z - 2.0f * n.y * n.w;
    out_matrix.data[9] = 2.0f * n.y * n.z + 2.0f * n.x * n.w;
    out_matrix.data[10] = 1.0f - 2.0f * n.x * n.x - 2.0f * n.y * n.y;
 
    return out_matrix;
}
 
KINLINE mat4 quat_to_rotation_matrix(quat q, vec3 center) {
    mat4 out_matrix;
 
    f32 *o = out_matrix.data;
    o[0] = (q.x * q.x) - (q.y * q.y) - (q.z * q.z) + (q.w * q.w);
    o[1] = 2.0f * ((q.x * q.y) + (q.z * q.w));
    o[2] = 2.0f * ((q.x * q.z) - (q.y * q.w));
    o[3] = center.x - center.x * o[0] - center.y * o[1] - center.z * o[2];
 
    o[4] = 2.0f * ((q.x * q.y) - (q.z * q.w));
    o[5] = -(q.x * q.x) + (q.y * q.y) - (q.z * q.z) + (q.w * q.w);
    o[6] = 2.0f * ((q.y * q.z) + (q.x * q.w));
    o[7] = center.y - center.x * o[4] - center.y * o[5] - center.z * o[6];
 
    o[8] = 2.0f * ((q.x * q.z) + (q.y * q.w));
    o[9] = 2.0f * ((q.y * q.z) - (q.x * q.w));
    o[10] = -(q.x * q.x) - (q.y * q.y) + (q.z * q.z) + (q.w * q.w);
    o[11] = center.z - center.x * o[8] - center.y * o[9] - center.z * o[10];
 
    o[12] = 0.0f;
    o[13] = 0.0f;
    o[14] = 0.0f;
    o[15] = 1.0f;
    return out_matrix;
}
 
KINLINE quat quat_from_axis_angle(vec3 axis, f32 angle, b8 normalize) {
    const f32 half_angle = 0.5f * angle;
    f32 s = ksin(half_angle);
    f32 c = kcos(half_angle);
 
    quat q = (quat){s * axis.x, s * axis.y, s * axis.z, c};
    if (normalize) {
        return quat_normalize(q);
    }
    return q;
}
 
KINLINE quat quat_slerp(quat q_0, quat q_1, f32 percentage) {
    quat out_quaternion;
    // Source: https://en.wikipedia.org/wiki/Slerp
    // Only unit quaternions are valid rotations.
    // Normalize to avoid undefined behavior.
    quat v0 = quat_normalize(q_0);
    quat v1 = quat_normalize(q_1);
 
    // Compute the cosine of the angle between the two vectors.
    f32 dot = quat_dot(v0, v1);
 
    // If the dot product is negative, slerp won't take
    // the shorter path. Note that v1 and -v1 are equivalent when
    // the negation is applied to all four components. Fix by
    // reversing one quaternion.
    if (dot < 0.0f) {
        v1.x = -v1.x;
        v1.y = -v1.y;
        v1.z = -v1.z;
        v1.w = -v1.w;
        dot = -dot;
    }
 
    const f32 DOT_THRESHOLD = 0.9995f;
    if (dot > DOT_THRESHOLD) {
        // If the inputs are too close for comfort, linearly interpolate
        // and normalize the result.
        out_quaternion = (quat){v0.x + ((v1.x - v0.x) * percentage),
                                v0.y + ((v1.y - v0.y) * percentage),
                                v0.z + ((v1.z - v0.z) * percentage),
                                v0.w + ((v1.w - v0.w) * percentage)};
 
        return quat_normalize(out_quaternion);
    }
 
    // Since dot is in range [0, DOT_THRESHOLD], acos is safe
    f32 theta_0 = kacos(dot);          // theta_0 = angle between input vectors
    f32 theta = theta_0 * percentage;  // theta = angle between v0 and result
    f32 sin_theta = ksin(theta);       // compute this value only once
    f32 sin_theta_0 = ksin(theta_0);   // compute this value only once
 
    f32 s0 =
        kcos(theta) -
        dot * sin_theta / sin_theta_0;  // == sin(theta_0 - theta) / sin(theta_0)
    f32 s1 = sin_theta / sin_theta_0;
 
    return (quat){(v0.x * s0) + (v1.x * s1), (v0.y * s0) + (v1.y * s1),
                  (v0.z * s0) + (v1.z * s1), (v0.w * s0) + (v1.w * s1)};
}
 
KINLINE f32 deg_to_rad(f32 degrees) { return degrees * K_DEG2RAD_MULTIPLIER; }
 
KINLINE f32 rad_to_deg(f32 radians) { return radians * K_RAD2DEG_MULTIPLIER; }
 
KINLINE f32 range_convert_f32(f32 value, f32 old_min, f32 old_max, f32 new_min,
                              f32 new_max) {
    return (((value - old_min) * (new_max - new_min)) / (old_max - old_min)) +
           new_min;
}
 
KINLINE void rgbu_to_u32(u32 r, u32 g, u32 b, u32 *out_u32) {
    *out_u32 = (((r & 0x0FF) << 16) | ((g & 0x0FF) << 8) | (b & 0x0FF));
}
 
KINLINE void u32_to_rgb(u32 rgbu, u32 *out_r, u32 *out_g, u32 *out_b) {
    *out_r = (rgbu >> 16) & 0x0FF;
    *out_g = (rgbu >> 8) & 0x0FF;
    *out_b = (rgbu)&0x0FF;
}
 
KINLINE void rgb_u32_to_vec3(u32 r, u32 g, u32 b, vec3 *out_v) {
    out_v->r = r / 255.0f;
    out_v->g = g / 255.0f;
    out_v->b = b / 255.0f;
}
 
KINLINE void vec3_to_rgb_u32(vec3 v, u32 *out_r, u32 *out_g, u32 *out_b) {
    *out_r = v.r * 255;
    *out_g = v.g * 255;
    *out_b = v.b * 255;
}
 
KAPI plane_3d plane_3d_create(vec3 p1, vec3 norm);
 
KAPI frustum frustum_create(const vec3 *position, const vec3 *forward,
                            const vec3 *right, const vec3 *up, f32 aspect,
                            f32 fov, f32 near, f32 far);
 
KAPI f32 plane_signed_distance(const plane_3d *p, const vec3 *position);
 
KAPI b8 plane_intersects_sphere(const plane_3d *p, const vec3 *center,
                                f32 radius);
 
KAPI b8 frustum_intersects_sphere(const frustum *f, const vec3 *center,
                                  f32 radius);
 
KAPI b8 plane_intersects_aabb(const plane_3d *p, const vec3 *center,
                              const vec3 *extents);
 
KAPI b8 frustum_intersects_aabb(const frustum *f, const vec3 *center,
                                const vec3 *extents);