#pragma once

#include <math.hfa>

trait fromint(otype T) {
    void ?{}(T&, int);
};
trait zeroinit(otype T) {
    void ?{}(T&, zero_t);
};
trait zero_assign(otype T) {
    T ?=?(T&, zero_t);
};
trait subtract(otype T) {
    T ?-?(T, T);
};
trait negate(otype T) {
    T -?(T);
};
trait add(otype T) {
    T ?+?(T, T);
};
trait multiply(otype T) {
    T ?*?(T, T);
};
trait divide(otype T) {
    T ?/?(T, T);
};
trait lessthan(otype T) {
    int ?<?(T, T);
};
trait equality(otype T) {
    int ?==?(T, T);
};
trait sqrt(otype T) {
    T sqrt(T);
};

static inline {
// int
int ?=?(int& n, zero_t) { return n = 0.f; }
// unsigned int
int ?=?(unsigned int& n, zero_t) { return n = 0.f; }
/* float */
void ?{}(float& a, int b) { a = b; }
float ?=?(float& n, zero_t) { return n = 0.f; }
/* double */
void ?{}(double& a, int b) { a = b; }
double ?=?(double& n, zero_t) { return n = 0L; }
// long double
void ?{}(long double& a, int b) { a = b; }
long double ?=?(long double& n, zero_t) { return n = 0L; }
}

trait dottable(otype V, otype T) {
    T dot(V, V);
};

static inline {

forall(otype T | sqrt(T), otype V | dottable(V, T))
T length(V v) {
   return sqrt(dot(v, v));
}

forall(otype T, otype V | dottable(V, T))
T length_squared(V v) {
   return dot(v, v);
}

forall(otype T, otype V | { T length(V); } | subtract(V))
T distance(V v1, V v2) {
    return length(v1 - v2);
}

forall(otype T, otype V | { T length(V); V ?/?(V, T); })
V normalize(V v) {
    return v / length(v);
}

// Project vector u onto vector v
forall(otype T, otype V | dottable(V, T) | { V normalize(V); V ?*?(V, T); })
V project(V u, V v) {
    V v_norm = normalize(v);
    return v_norm * dot(u, v_norm);
}

// Reflect incident vector v with respect to surface with normal n
forall(otype T | fromint(T), otype V | { V project(V, V); V ?*?(T, V); V ?-?(V,V); })
V reflect(V v, V n) {
    return v - (T){2} * project(v, n);
}

// Refract incident vector v with respect to surface with normal n
// eta is the ratio of indices of refraction between starting material and
// entering material (i.e., from air to water, eta = 1/1.33)
// v and n must already be normalized
forall(otype T | fromint(T) | subtract(T) | multiply(T) | add(T) | lessthan(T) | sqrt(T),
       otype V | dottable(V, T) | { V ?*?(T, V); V ?-?(V,V); void ?{}(V&, zero_t); })
V refract(V v, V n, T eta) {
    T dotValue = dot(n, v);
    T k = (T){1} - eta * eta * ((T){1} - dotValue * dotValue);
    if (k < (T){0}) {
        return 0;
    }
    return eta * v - (eta * dotValue + sqrt(k)) * n;
}

// Given a perturbed normal and a geometric normal,
// flip the perturbed normal if the geometric normal is pointing away
// from the observer.
// n is the perturbed vector that we want to align
// i is the incident vector
// ng is the geometric normal of the surface
forall(otype T | lessthan(T) | zeroinit(T), otype V | dottable(V, T) | negate(V))
V faceforward(V n, V i, V ng) {
    return dot(ng, i) < (T){0} ? n : -n;
}

} // inline