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#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;
}
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