#include <math.h>
#include <stdint.h>

template<int32_t period, int32_t max_val>
int32_t sine(int32_t t) {
    // 0 <= t < period is 0 <= t_2pi < 2 pi
    t %= period;
    float t_2pi =  2 * M_PI / static_cast<float>(period) * t;
    return static_cast<int32_t>(sinf(t_2pi) * max_val);
}

template<int32_t period, int32_t max_val>
int32_t square(int32_t t) {
    t %= period;
    if (t <= period / 2) {
        return -max_val;
    } else {
        return max_val;
    }
}

template<int32_t period, int32_t max_val>
int32_t sawtooth(int32_t t) {
    // f(t) = a t + y
    // f(0) = -max_val = y
    // f(period) = a * period - max_val = max_val
    // a = 2 * max_val / period
    t %= period;
    return 2 * max_val * t / period - max_val;
}