#include "common.h"

inline bool zero(double d)
{
	return fabs(d) < 700 * DBL_EPSILON;
	// For reference musl (64bit double) uses:
	// DBL_EPSILON  2.22044604925031308085e-16
}

/*
 * a == 0 \implies b == 0
 * and
 * d == 0 \implies c == 0
 */
void case_trivial(const double* m, Tags* t)
{
	t->scale_x = m[0];
	t->scale_y = m[3];
	t->fax = zero(m[0]) ? 0 : (m[1] / m[0]); // case condition
	t->fay = zero(m[3]) ? 0 : (m[2] / m[3]); // case condition
	if(t->scale_x < 0) {
		t->rot_y = true;
		t->scale_x = fabs(t->scale_x);
	}
	if(t->scale_y < 0) {
		t->rot_x = true;
		t->scale_y = fabs(t->scale_y);
	}
}

/**
 *  |0 b|  |0 0|  |0 b|  |0 b|    |a b|
 *  |0 0|, |c 0|, |c 0|, |c d| or |c 0|  with letters non-zero
 *  (i.e. c==0 \implies d==0  and  a==0 \implies d==0)
 *
 *  apply rot_z of 90° to get
 *  |a b|   |-scale_y*fay    -scale_y |
 *  |c d| = |  scale_x     scale_x*fax|
 */
void case_rowswap(const double* m, Tags* t)
{
	t->rot_z = 90;
	t->scale_x =  m[2];
	t->scale_y = -m[1];
	t->fax = zero(m[2]) ? 0 : (m[3] / m[2]); // case condition
	t->fay = zero(m[1]) ? 0 : (m[0] / m[1]); // case condition
	if(t->scale_x < 0) {
		t->rot_x = true;
		t->scale_x = fabs(t->scale_x);
	}
	if(t->scale_y < 0) {
		t->rot_y = true;
		t->scale_y = fabs(t->scale_y);
	}
}

/**
 *  |a 0|
 *  |c 0| with letters non-zero
 */
void case_zerocol_r(const double* m, Tags* t)
{
	t->scale_y = 0;
	t->fax = 0;
	t->fay = 0; // Arbitrary
	t->scale_x = sqrt(m[0] * m[0]  +  m[2] * m[2]);
	t->rot_z = atan(m[2] / m[0]) * 180 / C_PI;
	if (m[0] < 0) // atan always yields positive cos
		t->rot_z += 180;
}

/**
 *  |0 b|
 *  |0 d| with letters non-zero
 */
void case_zerocol_l(const double* m, Tags* t)
{
	t->scale_x = 0;
	t->fay = 0;
	t->fax = 0; // Arbitrary
	t->scale_y = sqrt(m[1] * m[1]  +  m[3] * m[3]);
	t->rot_z = atan(-m[1] / m[3]) * 180 / C_PI;
	if (m[3] < 0) // atan always yields positive cos
		t->rot_z += 180;
}

int main(int argc, char** argv)
{
	double tar[4] = {0};

	if(!parse_args(argc, argv, tar))
		exit(5);

	print_matrix("target", tar);

	Tags tags = {0};
	if(
	      !( (zero(tar[0]) && !zero(tar[1]))
	         || (zero(tar[3]) && !zero(tar[2])) )
	) {
		printf("  --trivial\n");
		case_trivial(tar, &tags);
	} else if(
	      !( (zero(tar[1]) && !zero(tar[0]))
	         || (zero(tar[2]) && !zero(tar[3])) )
	) {
		printf("  --rowswap\n");
		case_rowswap(tar, &tags);
	} else if(
	      zero(tar[0]) && zero(tar[2]) && !zero(tar[1]) && !zero(tar[3])
	) {
		printf("  --zerocol_l\n");
		case_zerocol_l(tar, &tags);
	} else if(
	      !zero(tar[0]) && !zero(tar[2]) && zero(tar[1]) && zero(tar[3])
	) {
		printf("  --zerocol_r\n");
		case_zerocol_r(tar, &tags);
	} else {
		fprintf(stderr, "Oupsie, unknown matrix-case encountered. This shouldn't happen :P\n");
		exit(6);
	}

	return evaluate_result(tar, &tags);
}