diff --git a/src/librustc/middle/check_match.rs b/src/librustc/middle/check_match.rs
index 36edb567a507b..793cd374718df 100644
--- a/src/librustc/middle/check_match.rs
+++ b/src/librustc/middle/check_match.rs
@@ -10,7 +10,7 @@
 
 
 use middle::const_eval::{compare_const_vals, lookup_const_by_id};
-use middle::const_eval::{eval_const_expr, const_val, const_bool};
+use middle::const_eval::{eval_const_expr, const_val, const_bool, const_float};
 use middle::pat_util::*;
 use middle::ty::*;
 use middle::ty;
@@ -102,6 +102,27 @@ pub fn check_arms(cx: &MatchCheckCtxt, arms: &[arm]) {
     let mut seen = ~[];
     for arms.iter().advance |arm| {
         for arm.pats.iter().advance |pat| {
+
+            // Check that we do not match against a static NaN (#6804)
+            let pat_matches_nan: &fn(@pat) -> bool = |p| {
+                match cx.tcx.def_map.find(&p.id) {
+                    Some(&def_static(did, false)) => {
+                        let const_expr = lookup_const_by_id(cx.tcx, did).get();
+                        match eval_const_expr(cx.tcx, const_expr) {
+                            const_float(f) if f.is_NaN() => true,
+                            _ => false
+                        }
+                    }
+                    _ => false
+                }
+            };
+            for walk_pat(*pat) |p| {
+                if pat_matches_nan(p) {
+                    cx.tcx.sess.span_warn(p.span, "unmatchable NaN in pattern, \
+                                                   use the is_NaN method in a guard instead");
+                }
+            }
+
             let v = ~[*pat];
             match is_useful(cx, &seen, v) {
               not_useful => {
diff --git a/src/test/compile-fail/issue-6804.rs b/src/test/compile-fail/issue-6804.rs
new file mode 100644
index 0000000000000..0a62e889d091a
--- /dev/null
+++ b/src/test/compile-fail/issue-6804.rs
@@ -0,0 +1,21 @@
+// Matching against NaN should result in a warning
+
+use std::float::NaN;
+
+fn main() {
+    let x = NaN;
+    match x {
+        NaN => {},
+        _ => {},
+    };
+    //~^^^ WARNING unmatchable NaN in pattern, use the is_NaN method in a guard instead
+    match [x, 1.0] {
+        [NaN, _] => {},
+        _ => {},
+    };
+    //~^^^ WARNING unmatchable NaN in pattern, use the is_NaN method in a guard instead
+}
+
+// At least one error is needed so that compilation fails
+#[static_assert]
+static b: bool = false; //~ ERROR static assertion failed