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use crate::Complex;
const EPSILON: f64 = 1e-10;
const SQRT_2: f64 = 1.4142135623730951;
const INV_SQRT_2: f64 = 0.7071067811865475;
const INV_SQRT_8: f64 = 0.3535533905932738;
const INV_SQRT_32: f64 = 0.1767766952966369;
fn approx_eq(a: f64, b: f64) -> bool {
(a - b).abs() < EPSILON
}
fn format_real_symbolic(v: f64) -> Option<String> {
let abs_v = v.abs();
let sign = if v < 0.0 { "-" } else { "" };
if approx_eq(abs_v, 0.0) {
return Some("0".to_string());
}
if approx_eq(abs_v, 1.0) {
return Some(format!("{}1", sign));
}
if approx_eq(abs_v, 0.5) {
return Some(format!("{}½", sign));
}
if approx_eq(abs_v, 0.25) {
return Some(format!("{}¼", sign));
}
if approx_eq(abs_v, 0.75) {
return Some(format!("{}¾", sign));
}
if approx_eq(abs_v, 0.125) {
return Some(format!("{}⅛", sign));
}
if approx_eq(abs_v, SQRT_2) {
return Some(format!("{}√2", sign));
}
if approx_eq(abs_v, INV_SQRT_2) {
return Some(format!("{}¹⁄√2", sign));
}
if approx_eq(abs_v, INV_SQRT_8) {
return Some(format!("{}¹⁄√8", sign));
}
if approx_eq(abs_v, INV_SQRT_32) {
return Some(format!("{}¹⁄√32", sign));
}
if approx_eq(abs_v, 2.0) {
return Some(format!("{}2", sign));
}
if approx_eq(abs_v, 1.0 / 3.0) {
return Some(format!("{}⅓", sign));
}
if approx_eq(abs_v, 2.0 / 3.0) {
return Some(format!("{}⅔", sign));
}
None
}
pub fn format_amplitude(c: &Complex<f64>) -> String {
let re = c.real;
let im = c.imaginary;
let re_zero = approx_eq(re.abs(), 0.0);
let im_zero = approx_eq(im.abs(), 0.0);
if re_zero && im_zero {
return "0".to_string();
}
if im_zero {
if let Some(s) = format_real_symbolic(re) {
return s;
}
return format!("{:.4}", re);
}
if re_zero {
if approx_eq(im.abs(), 1.0) {
return if im > 0.0 {
"i".to_string()
} else {
"-i".to_string()
};
}
if let Some(s) = format_real_symbolic(im) {
return format!("{}i", s);
}
return format!("{:.4}i", im);
}
let re_str = format_real_symbolic(re).unwrap_or_else(|| format!("{:.4}", re));
let im_str = if approx_eq(im.abs(), 1.0) {
if im > 0.0 {
"+i".to_string()
} else {
"-i".to_string()
}
} else {
let im_sym = format_real_symbolic(im.abs());
let sign = if im > 0.0 { "+" } else { "-" };
match im_sym {
Some(s) => format!("{}{}i", sign, s.trim_start_matches('-')),
None => format!("{}{:.4}i", sign, im.abs()),
}
};
format!("{}{}", re_str, im_str)
}
pub fn format_probability(p: f64) -> String {
if approx_eq(p, 0.0) {
return "0".to_string();
}
if approx_eq(p, 1.0) {
return "1".to_string();
}
if approx_eq(p, 0.5) {
return "½".to_string();
}
if approx_eq(p, 0.25) {
return "¼".to_string();
}
if approx_eq(p, 0.75) {
return "¾".to_string();
}
if approx_eq(p, 0.125) {
return "⅛".to_string();
}
if approx_eq(p, 0.0625) {
return "¹⁄₁₆".to_string();
}
if approx_eq(p, 1.0 / 3.0) {
return "⅓".to_string();
}
if approx_eq(p, 2.0 / 3.0) {
return "⅔".to_string();
}
format!("{:.4}", p)
}
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