fix: PI format for rust Circuit display (#15917)

* fix: added a intermediate function format_float_pi to find closet pi ratio up to a certain limit. also added relative tests named as test_pi_float_format. files modified :crates/circuit/src/circuit_drawer.rs .This concerns the issue #15849

* fix: changed the code according to the comments left. Added more parameters to the function to copy the use of pi_check. Added the possibility of choosing a specific format. Next step is to add the features to support other format.

* fix: moved the function format_float_pi to its own file 'py_check.rs' for better reading. Added support of formats according to the original py_check.py. Added tests for the rust function. Modified the lib.rs to be able to use the function accross files.

* fixe: moved the function to circuit_drawer.rs as asked. Added test to the same file. Removed function parameters as asked and modified output to only have text format

* fix: forgot to remove py_check.rs

* fix: added the fix needed. Merged checks 5 and 6. Rewrite test part into an array for better reading.

* fix: forgot a '}'. Ran all tests

* Apply minor touch-ups to comments and tests

---------

Co-authored-by: OnyxBrumeSky <cowbeez@MacBook-Pro-de-CowBeez.local>
Co-authored-by: OnyxBrumeSky <cowbeez@f6r14s10.clusters.42paris.fr>
Co-authored-by: OnyxBrumeSky <cowbeez@f6r14s14.clusters.42paris.fr>
Co-authored-by: Eli Arbel <arbel@il.ibm.com>

Author: 5 people

crates/circuit/src/circuit_drawer.rs

@@ -20,6 +20,7 @@ use crossterm::terminal;
 use hashbrown::HashSet;
 use itertools::{Itertools, MinMaxResult};
 use pyo3::prelude::*;
+use std::f64::consts::PI;
 use std::fmt::Debug;
 use std::ops::Index;
 use unicode_segmentation::UnicodeSegmentation;
@@ -60,7 +61,10 @@ pub fn draw_circuit(
             if approx::abs_diff_eq!(*f, 0.) {
                 String::new()
             } else {
-                format!("global phase: {}\n", f)
+                format!(
+                    "global phase: {}\n",
+                    format_float_pi(*f).unwrap_or_else(|| f.to_string())
+                )
             }
         }
         Param::ParameterExpression(expr) => {
@@ -763,7 +767,7 @@ impl TextDrawer {
                         .params_view()
                         .iter()
                         .map(|param| match param {
-                            Param::Float(f) => f.to_string(),
+                            Param::Float(f) => format_float_pi(*f).unwrap_or_else(|| f.to_string()),
                             Param::ParameterExpression(expr) => expr.to_string(),
                             _ => format!("{:?}", param),
                         })
@@ -1202,6 +1206,93 @@ impl TextDrawer {
     }
 }
 
+/// Computes if a number is close to an integer
+/// fraction or multiple of PI and returns the
+/// corresponding string.
+///
+/// Args:
+///     f : Number to check.
+///
+/// Returns:
+///     The string representation of output. None if no Pi formatting is found.  
+pub fn format_float_pi(f: f64) -> Option<String> {
+    const DENOMINATOR: i64 = 16;
+    // epsilon value defines the threshold to detect pi.
+    const EPS: f64 = 1e-9;
+
+    // pi_str is needed to match the output expected according to the format needed
+    let pi_str = "π";
+
+    // f_abs and sign help us working through each steps
+    let f_abs = f.abs();
+    let sign = if f < 0.0 { "-" } else { "" };
+
+    // Detecting 0 before moving on
+    if f_abs < EPS {
+        return Some("0".to_string());
+    }
+
+    // First check is for whole multiples of pi
+    let val = f_abs / PI;
+    let round = val.round();
+    if val >= 1.0 - EPS && (val - round).abs() < EPS {
+        let round = round as usize;
+        return Some(if round == 1 {
+            format!("{}{}", sign, pi_str)
+        } else {
+            format!("{}{}{}", sign, round, pi_str)
+        });
+    }
+
+    // Second is a check for powers of pi
+    if f_abs > PI {
+        if let Some(k) = (2..=4).find(|k| (f_abs - PI.powi(*k)).abs() < EPS) {
+            return Some(format!("{}{}^{}", sign, pi_str, k));
+        }
+    }
+
+    // Third is a check for a number larger than DENOMINATOR * pi, not a
+    // multiple or power of pi, since no fractions will exceed DENOMINATOR * pi
+    if f_abs > (DENOMINATOR as f64 * PI) {
+        return None;
+    }
+
+    // Fourth check is for fractions for 1*pi in the numer and any
+    // number in the denom.
+    let val = PI / f_abs;
+    let round = val.round();
+    if round >= 1.0 && (val - round).abs() < EPS {
+        let d = round as usize;
+        let str_out = format!("{}{}/{}", sign, pi_str, d);
+        return Some(str_out);
+    }
+
+    // Fifth check is for fractions of the form (numer/denom) * pi or (numer/denom) / pi
+    // where 1 <= numer,denom <= DENOMINATOR, which are not covered in the previous checks.
+    // Ex. 15pi/16, 2pi/5, 15pi/2, 16pi/9 or 15/16pi, 2/5pi, 15/2pi, 16/9pi
+    for denom in 1..=DENOMINATOR {
+        for numer in 1..=DENOMINATOR {
+            let up = numer as f64 / denom as f64;
+            let val = up * PI;
+            if (f_abs - val).abs() < EPS {
+                let str_out = format!("{}{}{}/{}", sign, numer, pi_str, denom);
+                return Some(str_out);
+            }
+            let val = up / PI;
+            if (f_abs - val).abs() < EPS {
+                let str_out = match denom {
+                    1 => format!("{}{}/{}", sign, numer, pi_str),
+                    d => format!("{}{}/{}{}", sign, numer, d, pi_str),
+                };
+                return Some(str_out);
+            }
+        }
+    }
+
+    // fall back when no conversion is possible
+    None
+}
+
 #[cfg(test)]
 mod tests {
     use ndarray::Array2;
@@ -2000,4 +2091,59 @@ q_1: ┤ Ry(🎩) ├┤1          ├┤ 💶🔉(🎩) ├┤1           ├
 ";
         assert_eq!(result, expected.trim_start_matches("\n"));
     }
+
+    #[test]
+    fn test_format_float_pi() {
+        let test_points = [
+            (0.0, Some("0")),
+            (-0.0, Some("0")),
+            (1e-12, Some("0")),
+            (PI, Some("π")),
+            (-PI, Some("-π")),
+            (2.0 * PI, Some("2π")),
+            (3.0 * PI, Some("3π")),
+            (10.0 * PI, Some("10π")),
+            (16.0 * PI, Some("16π")),
+            (-2.0 * PI, Some("-2π")),
+            (-5.0 * PI, Some("-5π")),
+            (PI.powi(2), Some("π^2")),
+            (-PI.powi(2), Some("-π^2")),
+            (PI.powi(3), Some("π^3")),
+            (PI.powi(4), Some("π^4")),
+            (PI / 2.0, Some("π/2")),
+            (PI / 3.0, Some("π/3")),
+            (PI / 4.0, Some("π/4")),
+            (PI / 6.0, Some("π/6")),
+            (-PI / 2.0, Some("-π/2")),
+            (2.0 * PI / 3.0, Some("2π/3")),
+            (3.0 * PI / 4.0, Some("3π/4")),
+            (5.0 * PI / 6.0, Some("5π/6")),
+            (7.0 * PI / 4.0, Some("7π/4")),
+            (15.0 * PI / 16.0, Some("15π/16")),
+            (-2.0 * PI / 3.0, Some("-2π/3")),
+            (1.0 / PI, Some("1/π")),
+            (2.0 / PI, Some("2/π")),
+            (1.0 / (2.0 * PI), Some("1/2π")),
+            (3.0 / (4.0 * PI), Some("3/4π")),
+            (-1.0 / PI, Some("-1/π")),
+            (-1.0 / (2.0 * PI), Some("-1/2π")),
+            (-18.0 / 16.0 * PI, Some("-9π/8")),
+            (60.0 / 44.0 / PI, Some("15/11π")),
+            (17.0 * PI + 1.0, None),
+            (100.0, None),
+            (1.0, None),
+            (2.0, None),
+            (1.5, None),
+            (-7.3, None),
+            (PI + 1e-6, None),
+            (PI - 1e-6, None),
+            (PI / 2.0 + 1e-6, None),
+            (17.0 * PI / 2.0, None),
+            (9.0 / (17.0 * PI), None),
+        ];
+
+        for test in test_points {
+            assert_eq!(format_float_pi(test.0), test.1.map(|s| s.to_string()));
+        }
+    }
 }