#include <stdio.h>

#define HALFPI 1.5707963268

// Compute factorial iteratively
double factorial(int n) {
    double result = 1.0;
    for (int i = 2; i <= n; ++i) {
        result *= i;
    }
    return result;
}

double abs_double(double x) { return x < 0 ? -x : x; }

// SICP-style iterative approximation for sin(x)
double sin_iter(double x) {
    double term = x;   // First term of the series
    double sum = term; // Initial sum
    // double prev_sum;
    int n = 1; // Starting from x^3/3!

    do {
        // prev_sum = sum;
        term *= -x * x / ((2 * n) * (2 * n + 1)); // Next term in series
        sum += term;
        ++n;
    } while (abs_double(term) > 1e-10); // Stop when term is sufficiently small

    return sum;
}

int main() {
    printf("Approximated sin(pi/2) = %.10f\n", sin_iter(HALFPI));
    return 0;
}