Added trace operation + test and renamed base2k to backend

backend/src/stats.rs

@@ -0,0 +1,32 @@
+use crate::znx_base::ZnxInfos;
+use crate::{Decoding, VecZnx};
+use rug::Float;
+use rug::float::Round;
+use rug::ops::{AddAssignRound, DivAssignRound, SubAssignRound};
+
+pub trait Stats {
+    /// Returns the standard devaition of the i-th polynomial.
+    fn std(&self, col_i: usize, basek: usize) -> f64;
+}
+
+impl<D: AsRef<[u8]>> Stats for VecZnx<D> {
+    fn std(&self, col_i: usize, basek: usize) -> f64 {
+        let prec: u32 = (self.size() * basek) as u32;
+        let mut data: Vec<Float> = (0..self.n()).map(|_| Float::with_val(prec, 0)).collect();
+        self.decode_vec_float(col_i, basek, &mut data);
+        // std = sqrt(sum((xi - avg)^2) / n)
+        let mut avg: Float = Float::with_val(prec, 0);
+        data.iter().for_each(|x| {
+            avg.add_assign_round(x, Round::Nearest);
+        });
+        avg.div_assign_round(Float::with_val(prec, data.len()), Round::Nearest);
+        data.iter_mut().for_each(|x| {
+            x.sub_assign_round(&avg, Round::Nearest);
+        });
+        let mut std: Float = Float::with_val(prec, 0);
+        data.iter().for_each(|x| std += x * x);
+        std.div_assign_round(Float::with_val(prec, data.len()), Round::Nearest);
+        std = std.sqrt();
+        std.to_f64()
+    }
+}