#define PI                          3.14159265359
#define HALF_PI                     1.570796327
#define MEDIUMP_FLT_MAX             65504.0
#define MEDIUMP_FLT_MIN             0.00006103515625
#ifdef TARGET_MOBILE
#define FLT_EPS                     MEDIUMP_FLT_MIN
#else
#define FLT_EPS                     1e-5
#endif
#define saturate(x)                 clamp(x, 0.0, 1.0)
#ifdef TARGET_MOBILE
#define PREVENT_DIV0(n, d, magic)   ((n) / max(d, magic))
#else
#define PREVENT_DIV0(n, d, magic)   ((n) / (d))
#endif
float pow5(float x) {
float x2 = x * x;
return x2 * x2 * x;
}
float sq(float x) {
return x * x;
}
float max3(const vec3 v) {
return max(v.x, max(v.y, v.z));
}
float vmax(const vec2 v) {
return max(v.x, v.y);
}
float vmax(const vec3 v) {
return max(v.x, max(v.y, v.z));
}
float vmax(const vec4 v) {
return max(max(v.x, v.y), max(v.z, v.w));
}
float min3(const vec3 v) {
return min(v.x, min(v.y, v.z));
}
float vmin(const vec2 v) {
return min(v.x, v.y);
}
float vmin(const vec3 v) {
return min(v.x, min(v.y, v.z));
}
float vmin(const vec4 v) {
return min(min(v.x, v.y), min(v.z, v.w));
}
float acosFast(float x) {
float y = abs(x);
float p = -0.1565827 * y + 1.570796;
p *= sqrt(1.0 - y);
return x >= 0.0 ? p : PI - p;
}
float acosFastPositive(float x) {
float p = -0.1565827 * x + 1.570796;
return p * sqrt(1.0 - x);
}
highp vec4 mulMat4x4Float3(const highp mat4 m, const highp vec3 v) {
return v.x * m[0] + (v.y * m[1] + (v.z * m[2] + m[3]));
}
highp vec3 mulMat3x3Float3(const highp mat4 m, const highp vec3 v) {
return v.x * m[0].xyz + (v.y * m[1].xyz + (v.z * m[2].xyz));
}
void toTangentFrame(const highp vec4 q, out highp vec3 n) {
n = vec3( 0.0,  0.0,  1.0) +
vec3( 2.0, -2.0, -2.0) * q.x * q.zwx +
vec3( 2.0,  2.0, -2.0) * q.y * q.wzy;
}
void toTangentFrame(const highp vec4 q, out highp vec3 n, out highp vec3 t) {
toTangentFrame(q, n);
t = vec3( 1.0,  0.0,  0.0) +
vec3(-2.0,  2.0, -2.0) * q.y * q.yxw +
vec3(-2.0,  2.0,  2.0) * q.z * q.zwx;
}
highp mat3 cofactor(const highp mat3 m) {
highp float a = m[0][0];
highp float b = m[1][0];
highp float c = m[2][0];
highp float d = m[0][1];
highp float e = m[1][1];
highp float f = m[2][1];
highp float g = m[0][2];
highp float h = m[1][2];
highp float i = m[2][2];
highp mat3 cof;
cof[0][0] = e * i - f * h;
cof[0][1] = c * h - b * i;
cof[0][2] = b * f - c * e;
cof[1][0] = f * g - d * i;
cof[1][1] = a * i - c * g;
cof[1][2] = c * d - a * f;
cof[2][0] = d * h - e * g;
cof[2][1] = b * g - a * h;
cof[2][2] = a * e - b * d;
return cof;
}
float interleavedGradientNoise(highp vec2 w) {
const vec3 m = vec3(0.06711056, 0.00583715, 52.9829189);
return fract(m.z * fract(dot(w, m.xy)));
}