diff --git a/src/numeric/impl_float_maths.rs b/src/numeric/impl_float_maths.rs
index 6d6ebce52..edcc03c01 100644
--- a/src/numeric/impl_float_maths.rs
+++ b/src/numeric/impl_float_maths.rs
@@ -20,12 +20,12 @@ macro_rules! boolean_ops {
         $(#[$meta2])*
         #[must_use = "method returns a new boolean value and does not mutate the original value"]
         pub fn $all(&self) -> bool {
-            $crate::Zip::from(self).all(|&elt| !elt.$func())
+            $crate::Zip::from(self).all(|&elt| elt.$func())
         }
         $(#[$meta3])*
         #[must_use = "method returns a new boolean value and does not mutate the original value"]
         pub fn $any(&self) -> bool {
-            !self.$all()
+            $crate::Zip::from(self).any(|&elt| elt.$func())
         }
     };
 }
diff --git a/tests/nan_all_repro.rs b/tests/nan_all_repro.rs
new file mode 100644
index 000000000..8cf65e6d5
--- /dev/null
+++ b/tests/nan_all_repro.rs
@@ -0,0 +1,47 @@
+// Regression test for https://github.com/rust-ndarray/ndarray/issues/1612
+//
+// `is_all_nan`, `is_any_nan`, `is_all_infinite`, and `is_any_infinite` were
+// inverted: the `$all` predicate tested `!elt.$func()` ("all NOT nan") and the
+// `$any` predicate rode on the double negation, so `is_all_nan` returned `true`
+// for an all-finite array. These tests pin the correct behavior for both the
+// NaN and infinite families.
+
+use ndarray::array;
+
+#[test]
+fn is_all_nan_and_is_any_nan()
+{
+    // All finite: neither all nor any element is NaN.
+    let all_finite = array![1.0_f64, 2.0, 3.0];
+    assert!(!all_finite.is_all_nan());
+    assert!(!all_finite.is_any_nan());
+
+    // All NaN: every element is NaN.
+    let all_nan = array![f64::NAN, f64::NAN, f64::NAN];
+    assert!(all_nan.is_all_nan());
+    assert!(all_nan.is_any_nan());
+
+    // Mixed: not all elements are NaN, but at least one is.
+    let mixed = array![1.0_f64, f64::NAN, 3.0];
+    assert!(!mixed.is_all_nan());
+    assert!(mixed.is_any_nan());
+}
+
+#[test]
+fn is_all_infinite_and_is_any_infinite()
+{
+    // All finite: neither all nor any element is infinite.
+    let all_finite = array![1.0_f64, 2.0, 3.0];
+    assert!(!all_finite.is_all_infinite());
+    assert!(!all_finite.is_any_infinite());
+
+    // All infinite: every element is infinite.
+    let all_inf = array![f64::INFINITY, f64::NEG_INFINITY, f64::INFINITY];
+    assert!(all_inf.is_all_infinite());
+    assert!(all_inf.is_any_infinite());
+
+    // Mixed: not all elements are infinite, but at least one is.
+    let mixed = array![1.0_f64, f64::INFINITY, 3.0];
+    assert!(!mixed.is_all_infinite());
+    assert!(mixed.is_any_infinite());
+}