#include <complex.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#define STRRED "\x1b[31m"
#define STRGREEN "\x1b[32m"
#define STRNORM "\x1b[m"

#define SECONDS_PER_NANOSECOND 1000000000

#define NUM_LOOPS 100000

double complex complex_turn(double turn) { return cexp(I * M_PI * turn); }

double complex approx_turn(double turn)
{
    const static double a = 8 * M_SQRT2 / 3 - 3;
    const static double b = 4 - 8 * M_SQRT2 / 3;

    double p = turn * (b * turn * turn + a);
    double q = p * p;
    double r = 1 + q;
    double c = (1 - q) / r, s = 2 * p / r;

    return (c * c - s * s) + I * (2 * c * s);
}

void print_errors(
    const double* inputs,
    const double complex* ideals,
    const double complex* approxs,
    int n
)
{
    double c_error, s_error;
    double largest_c_error, largest_s_error;
    size_t largest_c_index, largest_s_index;

    double total_c_error = 0, total_s_error = 0;

    size_t i;
    double complex ideal, approx;

    for (i = 0; i < n; i++) {
        ideal = ideals[i];
        approx = approxs[i];

        // squared error in c components
        c_error = creal(ideal) - creal(approx);
        c_error *= c_error;
        // squared error in s components
        s_error = cimag(ideal) - cimag(approx);
        s_error *= s_error;

        if (largest_c_error < c_error) {
            largest_c_error = c_error;
            largest_c_index = i;
        }

        if (largest_s_error < s_error) {
            largest_s_error = s_error;
            largest_s_index = i;
        }

        total_c_error += c_error;
        total_s_error += s_error;
    }
    // these now contain the *average* squared error
    total_c_error /= (double)n;
    total_s_error /= (double)n;

    printf(
        "Squared error in cosines: \n"
        "\tAverage: %f (%f%% error)\n"
        "\tLargest: %f (%f%% error)"
        "\n\t\tInput:\t\t%f\n\t\tValue:\t\t%f\n\t\tApproximation:\t%f\n",
        total_c_error, sqrt(total_c_error) * 100, largest_c_error,
        sqrt(largest_c_error) * 100, inputs[largest_c_index],
        creal(ideals[largest_c_index]), creal(approxs[largest_c_index])
    );
    printf(
        "Squared error in sines: \n"
        "\tAverage: %f (%f%% error)\n\tLargest: %f (%f%% error)"
        "\n\t\tInput:\t\t%f\n\t\tValue:\t\t%f\n\t\tApproximation:\t%f\n",
        total_s_error, sqrt(total_s_error) * 100, largest_s_error,
        sqrt(largest_s_error) * 100, inputs[largest_c_index],
        cimag(ideals[largest_s_index]), cimag(approxs[largest_s_index])
    );
}

// time the length of the computation `f` in nanoseconds
long time_computation(
    double complex (*f)(double),
    const double* inputs,
    double complex* results,
    int n
)
{
    size_t i;
    long tick_s;
    long tick_ns;
    struct timespec tp;

    clock_gettime(CLOCK_MONOTONIC, &tp);
    tick_ns = tp.tv_nsec;
    tick_s = tp.tv_sec;
    for (i = 0; i < n; i++) {
        results[i] = f(inputs[i]);
    }
    clock_gettime(CLOCK_MONOTONIC, &tp);

    return SECONDS_PER_NANOSECOND * (tp.tv_sec - tick_s) +
           (tp.tv_nsec - tick_ns);
}

int main(int argn, char** args)
{
    long trig_time, rat_time;

    double rands[NUM_LOOPS];
    double complex trigs[NUM_LOOPS];
    double complex rats[NUM_LOOPS];

    size_t i;
    for (i = 0; i < NUM_LOOPS; i++) {
        rands[i] = rand() / (double)RAND_MAX;
    }

    trig_time = time_computation(&complex_turn, rands, trigs, NUM_LOOPS);
    printf("Timing for %d math.h sin and cos:\t%ldns\n", NUM_LOOPS, trig_time);

    rat_time = time_computation(&approx_turn, rands, rats, NUM_LOOPS);
    printf("Timing for %d approximations:\t%ldns\n", NUM_LOOPS, rat_time);

    long diff = rat_time - trig_time;
    double frac_speed;
    if (diff > 0) {
        frac_speed = rat_time / (double)trig_time;
        printf(
            STRRED "math.h" STRNORM " faster, speedup: %ldns (%2.2fx)\n", diff,
            frac_speed
        );
    } else {
        frac_speed = trig_time / (double)rat_time;
        printf(
            STRGREEN "Approximation" STRNORM
                     " faster, speedup: %ldns (%2.2fx)\n",
            -diff, frac_speed
        );
        print_errors(rands, trigs, rats, NUM_LOOPS);
    }

    return 0;
}