#include "maths/format.h"

#include <math.h>
#include <stdbool.h>
#include <stdio.h>

static const double EPSILON = 1e-10;
static const double SQRT_2 = 1.4142135623730951;
static const double INV_SQRT_2 = 0.7071067811865475;
static const double INV_SQRT_8 = 0.3535533905932738;
static const double INV_SQRT_32 = 0.1767766952966369;

static bool approx_eq(double a, double b)
{
	return fabs(a - b) < EPSILON;
}

static bool real_symbolic(double v, char *out, size_t cap)
{
	double abs_v = fabs(v);
	const char *sign = v < 0.0 ? "-" : "";

	if (approx_eq(abs_v, 0.0))
	{
		snprintf(out, cap, "%s", "0");
		return true;
	}

	const char *sym = NULL;
	if (approx_eq(abs_v, 1.0))
		sym = "1";
	else if (approx_eq(abs_v, 0.5))
		sym = "½";
	else if (approx_eq(abs_v, 0.25))
		sym = "¼";
	else if (approx_eq(abs_v, 0.75))
		sym = "¾";
	else if (approx_eq(abs_v, 0.125))
		sym = "⅛";
	else if (approx_eq(abs_v, SQRT_2))
		sym = "√2";
	else if (approx_eq(abs_v, INV_SQRT_2))
		sym = "¹⁄√2";
	else if (approx_eq(abs_v, INV_SQRT_8))
		sym = "¹⁄√8";
	else if (approx_eq(abs_v, INV_SQRT_32))
		sym = "¹⁄√32";
	else if (approx_eq(abs_v, 2.0))
		sym = "2";
	else if (approx_eq(abs_v, 1.0 / 3.0))
		sym = "⅓";
	else if (approx_eq(abs_v, 2.0 / 3.0))
		sym = "⅔";
	else
		return false;

	snprintf(out, cap, "%s%s", sign, sym);
	return true;
}

char *psi_format_amplitude(struct PsiComplex c, char *out, size_t cap)
{
	double re = c.real;
	double im = c.imaginary;

	bool re_zero = approx_eq(fabs(re), 0.0);
	bool im_zero = approx_eq(fabs(im), 0.0);

	if (re_zero && im_zero)
	{
		snprintf(out, cap, "%s", "0");
		return out;
	}

	if (im_zero)
	{
		if (!real_symbolic(re, out, cap))
			snprintf(out, cap, "%.4f", re);

		return out;
	}

	if (re_zero)
	{
		if (approx_eq(fabs(im), 1.0))
		{
			snprintf(out, cap, "%s", im > 0.0 ? "i" : "-i");
			return out;
		}

		char sym[32];
		if (real_symbolic(im, sym, sizeof sym))
			snprintf(out, cap, "%si", sym);
		else
			snprintf(out, cap, "%.4fi", im);

		return out;
	}

	char re_str[32];
	if (!real_symbolic(re, re_str, sizeof re_str))
		snprintf(re_str, sizeof re_str, "%.4f", re);

	char im_str[32];
	if (approx_eq(fabs(im), 1.0))
	{
		snprintf(im_str, sizeof im_str, "%s", im > 0.0 ? "+i" : "-i");
	}
	else
	{
		const char *sign = im > 0.0 ? "+" : "-";
		char sym[32];
		if (real_symbolic(fabs(im), sym, sizeof sym))
			snprintf(im_str, sizeof im_str, "%s%si", sign, sym);
		else
			snprintf(im_str, sizeof im_str, "%s%.4fi", sign, fabs(im));
	}

	snprintf(out, cap, "%s%s", re_str, im_str);
	return out;
}

char *psi_format_probability(double p, char *out, size_t cap)
{
	if (approx_eq(p, 0.0))
		snprintf(out, cap, "%s", "0");
	else if (approx_eq(p, 1.0))
		snprintf(out, cap, "%s", "1");
	else if (approx_eq(p, 0.5))
		snprintf(out, cap, "%s", "½");
	else if (approx_eq(p, 0.25))
		snprintf(out, cap, "%s", "¼");
	else if (approx_eq(p, 0.75))
		snprintf(out, cap, "%s", "¾");
	else if (approx_eq(p, 0.125))
		snprintf(out, cap, "%s", "⅛");
	else if (approx_eq(p, 0.0625))
		snprintf(out, cap, "%s", "¹⁄₁₆");
	else if (approx_eq(p, 1.0 / 3.0))
		snprintf(out, cap, "%s", "⅓");
	else if (approx_eq(p, 2.0 / 3.0))
		snprintf(out, cap, "%s", "⅔");
	else
		snprintf(out, cap, "%.4f", p);

	return out;
}