[fix]: rounding errors and fancy printing

5 files changed, 169 insertions, 17 deletions

diff --git a/libpsi-core/src/core/circuit.rs b/libpsi-core/src/core/circuit.rs
index 293d509..eb64aaf 100644
--- a/libpsi-core/src/core/circuit.rs
+++ b/libpsi-core/src/core/circuit.rs
@@ -1,5 +1,5 @@
 use super::{QuantumGate, QuantumRegister, QuantumState};
-use crate::Vector;
+use crate::{format_amplitude, format_probability, Vector};
 use core::fmt;
 
 #[derive(Clone)]
@@ -211,9 +211,23 @@ impl<'a> fmt::Display for QuantumCircuit<'a> {
             let amp = state.get(i);
             if amp.real.abs() > 1e-10 || amp.imaginary.abs() > 1e-10 {
                 let basis: String = format!("{:0width$b}", i, width = self.num_qubits());
-                writeln!(f, "  |{}⟩: {:.4}", basis, amp)?;
+                writeln!(f, "  |{}⟩: {}", basis, format_amplitude(&amp))?;
             }
         }
         Ok(())
     }
 }
+
+impl<'a> QuantumCircuit<'a> {
+    pub fn print_probabilities(&self) {
+        let probs = self.probabilities();
+        let n = self.num_qubits();
+        println!("Probabilities:");
+        for (i, p) in probs.iter().enumerate() {
+            if *p > 1e-10 {
+                let basis: String = format!("{:0width$b}", i, width = n);
+                println!("  |{}⟩: {}", basis, format_probability(*p));
+            }
+        }
+    }
+}
diff --git a/libpsi-core/src/lib.rs b/libpsi-core/src/lib.rs
index 81c9fe2..23da477 100644
--- a/libpsi-core/src/lib.rs
+++ b/libpsi-core/src/lib.rs
@@ -2,6 +2,7 @@ pub mod core;
 pub mod maths;
 
 pub use maths::complex::*;
+pub use maths::format::*;
 pub use maths::matrix::*;
 pub use maths::numeric::*;
 pub use maths::vector::*;
diff --git a/libpsi-core/src/maths/format.rs b/libpsi-core/src/maths/format.rs
new file mode 100644
index 0000000..957f1b6
--- /dev/null
+++ b/libpsi-core/src/maths/format.rs
@@ -0,0 +1,141 @@
+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)
+}
diff --git a/libpsi-core/src/maths/mod.rs b/libpsi-core/src/maths/mod.rs
index 5bc7f6d..e716181 100644
--- a/libpsi-core/src/maths/mod.rs
+++ b/libpsi-core/src/maths/mod.rs
@@ -1,10 +1,12 @@
 pub mod complex;
+pub mod format;
 pub mod matrix;
 pub mod numeric;
 pub mod vector;
 pub mod vector_ops;
 
 pub use complex::*;
+pub use format::*;
 pub use matrix::*;
 pub use numeric::*;
 pub use vector::*;
diff --git a/tester/src/main.rs b/tester/src/main.rs
index 96fc86f..4bab72d 100644
--- a/tester/src/main.rs
+++ b/tester/src/main.rs
@@ -7,7 +7,7 @@ fn main() {
     bell.h(0).cnot(0, 1);
     println!("{}", bell);
 
-    print!("\n------\n\n");
+    print!("------\n\n");
 
     println!("GHZ State (3-qubit entanglement): |GHZ> = (|000⟩ + |111⟩)/√2");
     println!("   Circuit: H(q0) → CNOT(q0, q1) → CNOT(q0, q2)");
@@ -15,7 +15,7 @@ fn main() {
     ghz.h(0).cnot(0, 1).cnot(0, 2);
     println!("{}", ghz);
 
-    print!("\n------\n\n");
+    print!("------\n\n");
 
     println!("SWAP via 3 CNOTs");
     println!("   Start with |10>, apply CNOT chain");
@@ -27,7 +27,7 @@ fn main() {
         .cnot(0, 1);
     println!("{}", swap_circuit);
 
-    print!("\n------\n\n");
+    print!("------\n\n");
 
     println!("Toffoli Gate (Reversible AND)");
     println!("   CCNOT flips q2 only when q0=1 AND q1=1");
@@ -38,7 +38,7 @@ fn main() {
         .toffoli(0, 1, 2);
     println!("{}", toffoli_circuit);
 
-    print!("\n------\n\n");
+    print!("------\n\n");
 
     println!("Fredkin Gate (Controlled SWAP)");
     println!("   CSWAP swaps q1 and q2 only when q0=1");
@@ -49,7 +49,7 @@ fn main() {
         .fredkin(0, 1, 2);
     println!("{}", fredkin_circuit);
 
-    print!("\n------\n\n");
+    print!("------\n\n");
 
     println!("6. Non-contiguous CNOT (q0 controls q2, skipping q1)");
     let mut nc_circuit = QuantumCircuit::new(3);
@@ -58,28 +58,22 @@ fn main() {
         .cnot(0, 2); // CNOT with control=q0, target=q2
     println!("{}", nc_circuit);
 
-    print!("\n------\n\n");
+    print!("------\n\n");
 
     println!("Full Superposition (H on all qubits)");
     let mut super_circuit = QuantumCircuit::new(3);
     super_circuit.h(0).h(1).h(2);
     println!("{}", super_circuit);
 
-    print!("\n------\n\n");
+    print!("------\n\n");
 
     println!("Probability Test");
     let mut prob_circuit = QuantumCircuit::new(2);
     prob_circuit.h(0).cnot(0, 1);
-    println!("   Bell state probabilities:");
-    let probs = prob_circuit.probabilities();
-    for (i, p) in probs.iter().enumerate() {
-        if *p > 1e-10 {
-            println!("     |{:02b}⟩: {:.4}", i, p);
-        }
-    }
+    prob_circuit.print_probabilities();
     println!();
 
-    print!("\n------\n\n");
+    print!("------\n\n");
 
     println!("Complex Circuit with Method Chaining");
     let mut complex = QuantumCircuit::new(4);