diff --git a/src/maybe_nan/impl_not_none.rs b/src/maybe_nan/impl_not_none.rs
index 2ab4f07..e437de4 100644
--- a/src/maybe_nan/impl_not_none.rs
+++ b/src/maybe_nan/impl_not_none.rs
@@ -1,5 +1,5 @@
 use super::NotNone;
-use num_traits::{FromPrimitive, ToPrimitive};
+use num_traits::{Euclid, FromPrimitive, ToPrimitive};
 use std::cmp;
 use std::fmt;
 use std::ops::{Add, Deref, DerefMut, Div, Mul, Rem, Sub};
@@ -101,6 +101,19 @@ impl<T: Rem> Rem for NotNone<T> {
     }
 }
 
+impl<T: Euclid> Euclid for NotNone<T> {
+    #[inline]
+    fn div_euclid(&self, rhs: &Self) -> Self {
+        let result = self.deref().div_euclid(rhs.deref());
+        NotNone(Some(result))
+    }
+    #[inline]
+    fn rem_euclid(&self, rhs: &Self) -> Self {
+        let result = self.deref().rem_euclid(rhs.deref());
+        NotNone(Some(result))
+    }
+}
+
 impl<T: ToPrimitive> ToPrimitive for NotNone<T> {
     #[inline]
     fn to_isize(&self) -> Option<isize> {
diff --git a/src/quantile/interpolate.rs b/src/quantile/interpolate.rs
index 0b7871d..f006994 100644
--- a/src/quantile/interpolate.rs
+++ b/src/quantile/interpolate.rs
@@ -1,6 +1,8 @@
 //! Interpolation strategies.
 use noisy_float::types::N64;
-use num_traits::{Float, FromPrimitive, NumOps, ToPrimitive};
+use num_traits::{Euclid, Float, FromPrimitive, NumOps, ToPrimitive};
+
+use crate::maybe_nan::NotNone;
 
 fn float_quantile_index(q: N64, len: usize) -> N64 {
     q * ((len - 1) as f64)
@@ -104,25 +106,69 @@ impl<T> Interpolate<T> for Nearest {
     private_impl! {}
 }
 
-impl<T> Interpolate<T> for Midpoint
-where
-    T: NumOps + Clone + FromPrimitive,
-{
-    fn needs_lower(_q: N64, _len: usize) -> bool {
-        true
-    }
-    fn needs_higher(_q: N64, _len: usize) -> bool {
-        true
+macro_rules! impl_midpoint_interpolate_for_float {
+    ($($t:ty),*) => {
+        $(
+            impl Interpolate<$t> for Midpoint {
+                fn needs_lower(_q: N64, _len: usize) -> bool {
+                    true
+                }
+                fn needs_higher(_q: N64, _len: usize) -> bool {
+                    true
+                }
+                fn interpolate(lower: Option<$t>, higher: Option<$t>, _q: N64, _len: usize) -> $t {
+                    let lower = lower.unwrap();
+                    let higher = higher.unwrap();
+                    lower + (higher - lower) / 2.0
+                }
+                private_impl! {}
+            }
+        )*
     }
-    fn interpolate(lower: Option<T>, higher: Option<T>, _q: N64, _len: usize) -> T {
-        let denom = T::from_u8(2).unwrap();
-        let lower = lower.unwrap();
-        let higher = higher.unwrap();
-        lower.clone() + (higher.clone() - lower.clone()) / denom.clone()
+}
+
+impl_midpoint_interpolate_for_float!(f32, f64);
+
+macro_rules! impl_midpoint_interpolate_for_integer {
+    ($($t:ty),*) => {
+        $(
+            impl Interpolate<$t> for Midpoint {
+                fn needs_lower(_q: N64, _len: usize) -> bool {
+                    true
+                }
+                fn needs_higher(_q: N64, _len: usize) -> bool {
+                    true
+                }
+                fn interpolate(lower: Option<$t>, higher: Option<$t>, _q: N64, _len: usize) -> $t {
+                    let two = <$t>::from_u8(2).unwrap();
+                    let (lower_half, lower_rem) = lower.unwrap().div_rem_euclid(&two);
+                    let (higher_half, higher_rem) = higher.unwrap().div_rem_euclid(&two);
+                    lower_half + higher_half + (lower_rem * higher_rem)
+                }
+                private_impl! {}
+            }
+        )*
     }
-    private_impl! {}
 }
 
+impl_midpoint_interpolate_for_integer!(
+    i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, usize
+);
+impl_midpoint_interpolate_for_integer!(
+    NotNone<i8>,
+    NotNone<i16>,
+    NotNone<i32>,
+    NotNone<i64>,
+    NotNone<i128>,
+    NotNone<isize>,
+    NotNone<u8>,
+    NotNone<u16>,
+    NotNone<u32>,
+    NotNone<u64>,
+    NotNone<u128>,
+    NotNone<usize>
+);
+
 impl<T> Interpolate<T> for Linear
 where
     T: NumOps + Clone + FromPrimitive + ToPrimitive,
@@ -143,3 +189,46 @@ where
     }
     private_impl! {}
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use noisy_float::types::n64;
+    use quickcheck::TestResult;
+    use quickcheck_macros::quickcheck;
+
+    #[derive(Clone, Copy, Debug)]
+    struct LowerHigherPair<T>(T, T);
+
+    impl quickcheck::Arbitrary for LowerHigherPair<i64> {
+        fn arbitrary<G: quickcheck::Gen>(g: &mut G) -> Self {
+            let (l, h) = loop {
+                let (l, h) = (i64::arbitrary(g), i64::arbitrary(g));
+                if l > h || h.checked_sub(l).is_none() {
+                    continue;
+                }
+                break (l, h);
+            };
+            LowerHigherPair(l, h)
+        }
+    }
+
+    impl From<LowerHigherPair<i64>> for (i64, i64) {
+        fn from(value: LowerHigherPair<i64>) -> Self {
+            (value.0, value.1)
+        }
+    }
+
+    fn naive_midpoint_i64(lower: i64, higher: i64) -> i64 {
+        // Overflows when higher is very big and lower is very small
+        lower + (higher - lower) / 2
+    }
+
+    #[quickcheck]
+    fn test_midpoint_algo_eq_naive_algo_i64(lh: LowerHigherPair<i64>) -> TestResult {
+        let (lower, higher) = lh.into();
+        let naive = naive_midpoint_i64(lower, higher);
+        let midpoint = Midpoint::interpolate(Some(lower), Some(higher), n64(0.0), 0);
+        TestResult::from_bool(naive == midpoint)
+    }
+}
diff --git a/tests/quantile.rs b/tests/quantile.rs
index 9d58071..5aa3e68 100644
--- a/tests/quantile.rs
+++ b/tests/quantile.rs
@@ -268,7 +268,7 @@ fn test_quantile_axis_skipnan_mut_linear_opt_i32() {
 }
 
 #[test]
-fn test_midpoint_overflow() {
+fn test_midpoint_overflow_unsigned() {
     // Regression test
     // This triggered an overflow panic with a naive Midpoint implementation: (a+b)/2
     let mut a: Array1<u8> = array![129, 130, 130, 131];
@@ -277,6 +277,16 @@ fn test_midpoint_overflow() {
     assert_eq!(median, expected_median);
 }
 
+#[test]
+fn test_midpoint_overflow_signed() {
+    // Regression test
+    // This triggered an overflow panic with a naive Midpoint implementation: b+(a-b)/2
+    let mut a: Array1<i64> = array![i64::MIN, i64::MAX];
+    let median = a.quantile_mut(n64(0.5), &Midpoint).unwrap();
+    let expected_median = -1;
+    assert_eq!(median, expected_median);
+}
+
 #[quickcheck]
 fn test_quantiles_mut(xs: Vec<i64>) -> bool {
     let v = Array::from(xs.clone());