feat: symbolic amplitude and probability formatting

1 files changed, 147 insertions, 0 deletions

diff --git a/src/maths/format.c b/src/maths/format.c
new file mode 100644
index 0000000..ad80ff0
--- /dev/null
+++ b/src/maths/format.c
@@ -0,0 +1,147 @@
+#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;
+}