gistfile1.txt

#include <cmath>
#include <cstdint>
#include <cstdio>

// uncomment the one to use:
//
#define bhaskar
//#define taylor
//#define stdf
//#define stdd

#ifdef stdf
#warning "using sinf/cosf"
#define coarse_sin sinf
#define coarse_cos cosf
#endif

#ifdef stdd
#warning "using sin/cos"
#define coarse_sin sin
#define coarse_cos cos
#endif

#ifdef bhaskar
#warning "bhaskar"
// extremely fast sine and cosine approximations good to roughly four digits
// of accuracy (suitable for 16-bit audio calculations).
// Credit: Bhaskara I (c. 600 – c. 680) sine approximation formula
constexpr float coarse_sin(float rad)
{
	constexpr auto pi_f = static_cast<float>(M_PI);
	rad /= 2 * pi_f;
	rad -= static_cast<int>(rad);

	if (rad <= 0.5f) {
		const float t = 2 * rad * (2 * rad - 1);
		return (pi_f * t) / ((pi_f - 4) * t - 1);
	} else {
		const float t = 2 * (1 - rad) * (1 - 2 * rad);
		return -(pi_f * t) / ((pi_f - 4) * t - 1);
	}
}

constexpr float coarse_cos(float rad)
{
	constexpr auto pi_f = static_cast<float>(M_PI);
	return coarse_sin(rad + 0.5f * pi_f);
}
#endif

#ifdef taylor
#warning "taylor"
constexpr float coarse_sin(float x)
{
	constexpr int fact_3 = 1 * 2 * 3;
	constexpr int fact_5 = fact_3 * 4 * 5;
	constexpr int fact_7 = fact_5 * 6 * 7;

	const float x_pow_2 = x * x;
	const float x_pow_3 = x_pow_2 * x;
	const float x_pow_5 = x_pow_3 * x_pow_2;
	const float x_pow_7 = x_pow_5 * x_pow_2;

	const float taylor_1 = x - (x_pow_3 / fact_3);
	const float taylor_2 = taylor_1 + (x_pow_5 / fact_5);
	const float taylor_3 = taylor_2 - (x_pow_7 / fact_7);

	return taylor_3;
}

constexpr float coarse_cos(float x)
{
	constexpr auto pi_f = static_cast<float>(M_PI);
	return coarse_sin(x + 0.5f * pi_f);
}

#endif

#define ROUNDS 100000000
int main(int argc, char**argv)
{
	uint32_t round = ROUNDS + argc;
	const float step = 1.0 / ROUNDS;
	float angle = 0;
	double sum = 0;
	while (round--) {
		sum += coarse_cos(angle) + coarse_sin(angle);
		angle += step;
	}
	printf("sum over %d round is %f\n", ROUNDS, sum);
	return 0;
}

sin_speed.cpp

#include <cmath>
#include <cstdint>
#include <cstdio>

// uncomment the one to use:
//
#define bhaskar
//#define taylor
//#define stdf
//#define stdd

#ifdef stdf
#warning "using sinf/cosf"
#define coarse_sin sinf
#define coarse_cos cosf
#endif

#ifdef stdd
#warning "using sin/cos"
#define coarse_sin sin
#define coarse_cos cos
#endif

#ifdef bhaskar
#warning "bhaskar"
// extremely fast sine and cosine approximations good to roughly four digits
// of accuracy (suitable for 16-bit audio calculations).
// Credit: Bhaskara I (c. 600 – c. 680) sine approximation formula
constexpr float coarse_sin(float rad)
{
	constexpr auto pi_f = static_cast<float>(M_PI);
	rad /= 2 * pi_f;
	rad -= static_cast<int>(rad);

	if (rad <= 0.5f) {
		const float t = 2 * rad * (2 * rad - 1);
		return (pi_f * t) / ((pi_f - 4) * t - 1);
	} else {
		const float t = 2 * (1 - rad) * (1 - 2 * rad);
		return -(pi_f * t) / ((pi_f - 4) * t - 1);
	}
}

constexpr float coarse_cos(float rad)
{
	constexpr auto pi_f = static_cast<float>(M_PI);
	return coarse_sin(rad + 0.5f * pi_f);
}
#endif

#ifdef taylor
#warning "taylor"
constexpr float coarse_sin(float x)
{
	constexpr int fact_3 = 1 * 2 * 3;
	constexpr int fact_5 = fact_3 * 4 * 5;
	constexpr int fact_7 = fact_5 * 6 * 7;

	const float x_pow_2 = x * x;
	const float x_pow_3 = x_pow_2 * x;
	const float x_pow_5 = x_pow_3 * x_pow_2;
	const float x_pow_7 = x_pow_5 * x_pow_2;

	const float taylor_1 = x - (x_pow_3 / fact_3);
	const float taylor_2 = taylor_1 + (x_pow_5 / fact_5);
	const float taylor_3 = taylor_2 - (x_pow_7 / fact_7);

	return taylor_3;
}

constexpr float coarse_cos(float x)
{
	constexpr auto pi_f = static_cast<float>(M_PI);
	return coarse_sin(x + 0.5f * pi_f);
}

#endif

#define ROUNDS 100000000
int main(int argc, char**argv)
{
	uint32_t round = ROUNDS + argc;
	const float step = 1.0 / ROUNDS;
	float angle = 0;
	double sum = 0;
	while (round--) {
		sum += coarse_cos(angle) + coarse_sin(angle);
		angle += step;
	}
	printf("sum over %d round is %f\n", ROUNDS, sum);
	return 0;
}