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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;
}
void psi_print_matrix(struct PsiMatrix m, FILE* out)
{
int re_width = 0;
int im_width = 0;
for (size_t k = 0; k < m.rows * m.cols; k++)
{
int rl = snprintf(NULL, 0, "%.2f", m.data[k].real);
int il = snprintf(NULL, 0, "%.2f", fabs(m.data[k].imaginary));
if (rl > re_width)
re_width = rl;
if (il > im_width)
im_width = il;
}
for (size_t i = 0; i < m.rows; i++)
{
fputs(i == 0 ? "┌" : (i == m.rows - 1 ? "└" : "│"), out);
for (size_t j = 0; j < m.cols; j++)
{
struct PsiComplex e = m.data[i * m.cols + j];
const char* sign = e.imaginary > 0.0 ? "+" : "-";
fprintf(out, "%*.2f %s %*.2fi", re_width, e.real, sign, im_width, fabs(e.imaginary));
if (j != m.cols - 1)
fputs(", ", out);
}
fputs(i == 0 ? "┐" : (i == m.rows - 1 ? "┘" : "│"), out);
if (i != m.rows - 1)
fputc('\n', out);
}
}
void psi_print_vector(struct PsiVector v, FILE* out)
{
if (v.kind == PSI_COLUMN_VECTOR)
{
struct PsiMatrix m = psi_matrix_from_vector(v);
psi_print_matrix(m, out);
psi_free_matrix(&m);
return;
}
fputc('[', out);
for (size_t i = 0; i < v.size; i++)
{
fprintf(out, "%g + %gi", v.data[i].real, v.data[i].imaginary);
if (i != v.size - 1)
fputs(", ", out);
}
fputc(']', out);
}
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