diff --git a/README.md b/README.md
index a0c6d6aef2..a8837c0aff 100644
--- a/README.md
+++ b/README.md
@@ -165,88 +165,88 @@ Now obviously I'm not advocating for replacing FireFox's optimising compiler wit
 
 ## Specification compliance
 
-It's hard to judge, since each test in the spec testsuite covers a wide range of features (to check their interactions), but currently 40 out of 76 of the spec suite tests pass when run in Wasmtime with Lightbeam as a backend. Here's the full test output:
+It's hard to judge, since each test in the spec testsuite covers a wide range of features (to check their interactions), but currently 42 out of 76 of the spec suite tests pass when run in Wasmtime with Lightbeam as a backend. Here's the full test output:
 
 ```
 running 76 tests
-test misc_testsuite::stack_overflow         ... ok
-test spec_testsuite::binary                 ... ok
-test misc_testsuite::misc_traps             ... ok
-test spec_testsuite::align                  ... FAILED
-test spec_testsuite::address                ... FAILED
-test spec_testsuite::block                  ... ok
-test spec_testsuite::break_drop             ... ok
-test spec_testsuite::call                   ... FAILED
-test spec_testsuite::br                     ... ok
-test spec_testsuite::call_indirect          ... FAILED
-test spec_testsuite::comments               ... ok
-test spec_testsuite::const_                 ... ok
-test spec_testsuite::custom                 ... ok
-test spec_testsuite::custom_section         ... ok
-test spec_testsuite::data                   ... ok
-test spec_testsuite::conversions            ... FAILED
-test spec_testsuite::endianness             ... FAILED
-test spec_testsuite::elem                   ... FAILED
-test spec_testsuite::br_if                  ... ok
-test spec_testsuite::exports                ... ok
-test spec_testsuite::f32_bitwise            ... FAILED
-test spec_testsuite::br_table               ... FAILED
-test spec_testsuite::f64_bitwise            ... FAILED
-test spec_testsuite::f32                    ... FAILED
-test spec_testsuite::f32_cmp                ... FAILED
-test spec_testsuite::fac                    ... ok
-test spec_testsuite::f64                    ... FAILED
-test spec_testsuite::f64_cmp                ... FAILED
-test spec_testsuite::float_memory           ... ok
-test spec_testsuite::forward                ... ok
-test spec_testsuite::float_misc             ... FAILED
-test spec_testsuite::func_ptrs              ... FAILED
-test spec_testsuite::get_local              ... FAILED
-test spec_testsuite::float_exprs            ... FAILED
-test spec_testsuite::float_literals         ... ok
-test spec_testsuite::globals                ... ok
-test spec_testsuite::if_                    ... FAILED
-test spec_testsuite::func                   ... ok
-test spec_testsuite::inline_module          ... ok
-test spec_testsuite::imports                ... FAILED
-test spec_testsuite::i32                    ... ok
-test spec_testsuite::i64                    ... ok
-test spec_testsuite::int_literals           ... ok
-test spec_testsuite::labels                 ... ok
-test spec_testsuite::linking                ... FAILED
-test spec_testsuite::left_to_right          ... FAILED
-test spec_testsuite::loop_                  ... FAILED
-test spec_testsuite::memory                 ... FAILED
-test spec_testsuite::memory_grow            ... FAILED
-test spec_testsuite::memory_redundancy      ... ok
-test spec_testsuite::memory_trap            ... FAILED
-test spec_testsuite::resizing               ... FAILED
-test spec_testsuite::nop                    ... FAILED
-test spec_testsuite::return_minimal         ... ok
-test spec_testsuite::int_exprs              ... ok
-test spec_testsuite::set_local              ... FAILED
-test spec_testsuite::select                 ... FAILED
-test spec_testsuite::skip_stack_guard_page  ... FAILED
-test spec_testsuite::stack                  ... ok
-test spec_testsuite::store_retval           ... ok
-test spec_testsuite::start                  ... FAILED
-test spec_testsuite::tee_local              ... FAILED
-test spec_testsuite::token                  ... ok
-test spec_testsuite::switch                 ... ok
-test spec_testsuite::type_                  ... ok
-test spec_testsuite::return_                ... ok
-test spec_testsuite::typecheck              ... ok
-test spec_testsuite::traps                  ... FAILED
-test spec_testsuite::unwind                 ... FAILED
-test spec_testsuite::unreached_invalid      ... ok
+test misc_testsuite::stack_overflow ... ok
+test misc_testsuite::misc_traps ... ok
+test spec_testsuite::binary ... ok
+test spec_testsuite::align ... FAILED
+test spec_testsuite::address ... FAILED
+test spec_testsuite::block ... ok
+test spec_testsuite::break_drop ... ok
+test spec_testsuite::br ... ok
+test spec_testsuite::call ... FAILED
+test spec_testsuite::comments ... ok
+test spec_testsuite::call_indirect ... FAILED
+test spec_testsuite::const_ ... ok
+test spec_testsuite::custom ... ok
+test spec_testsuite::custom_section ... ok
+test spec_testsuite::br_if ... ok
+test spec_testsuite::data ... ok
+test spec_testsuite::conversions ... FAILED
+test spec_testsuite::endianness ... FAILED
+test spec_testsuite::exports ... ok
+test spec_testsuite::elem ... FAILED
+test spec_testsuite::f32_bitwise ... FAILED
+test spec_testsuite::br_table ... FAILED
+test spec_testsuite::f64_bitwise ... FAILED
+test spec_testsuite::f32 ... FAILED
+test spec_testsuite::fac ... ok
+test spec_testsuite::f64 ... FAILED
+test spec_testsuite::f32_cmp ... ok
+test spec_testsuite::float_memory ... ok
+test spec_testsuite::f64_cmp ... ok
+test spec_testsuite::forward ... ok
+test spec_testsuite::float_misc ... FAILED
+test spec_testsuite::func_ptrs ... FAILED
+test spec_testsuite::get_local ... FAILED
+test spec_testsuite::float_literals ... ok
+test spec_testsuite::float_exprs ... FAILED
+test spec_testsuite::globals ... ok
+test spec_testsuite::func ... ok
+test spec_testsuite::if_ ... FAILED
+test spec_testsuite::inline_module ... ok
+test spec_testsuite::imports ... FAILED
+test spec_testsuite::i32 ... ok
+test spec_testsuite::int_literals ... ok
+test spec_testsuite::labels ... ok
+test spec_testsuite::linking ... FAILED
+test spec_testsuite::i64 ... ok
+test spec_testsuite::left_to_right ... FAILED
+test spec_testsuite::loop_ ... FAILED
+test spec_testsuite::memory ... FAILED
+test spec_testsuite::memory_grow ... FAILED
+test spec_testsuite::memory_redundancy ... ok
+test spec_testsuite::memory_trap ... FAILED
+test spec_testsuite::resizing ... FAILED
+test spec_testsuite::nop ... FAILED
+test spec_testsuite::return_minimal ... ok
+test spec_testsuite::int_exprs ... ok
+test spec_testsuite::set_local ... FAILED
+test spec_testsuite::select ... FAILED
+test spec_testsuite::skip_stack_guard_page ... FAILED
+test spec_testsuite::stack ... ok
+test spec_testsuite::store_retval ... ok
+test spec_testsuite::start ... FAILED
+test spec_testsuite::tee_local ... FAILED
+test spec_testsuite::token ... ok
+test spec_testsuite::switch ... ok
+test spec_testsuite::type_ ... ok
+test spec_testsuite::typecheck ... ok
+test spec_testsuite::traps ... FAILED
+test spec_testsuite::return_ ... ok
+test spec_testsuite::unreached_invalid ... ok
+test spec_testsuite::unwind ... FAILED
 test spec_testsuite::utf8_custom_section_id ... ok
-test spec_testsuite::utf8_import_field      ... ok
-test spec_testsuite::utf8_import_module     ... ok
-test spec_testsuite::utf8_invalid_encoding  ... ok
-test spec_testsuite::unreachable            ... ok
-test spec_testsuite::names                  ... FAILED
+test spec_testsuite::utf8_import_field ... ok
+test spec_testsuite::utf8_import_module ... ok
+test spec_testsuite::utf8_invalid_encoding ... ok
+test spec_testsuite::unreachable ... ok
+test spec_testsuite::names ... FAILED
 
-test result: FAILED. 40 passed; 36 failed; 0 ignored; 0 measured; 0 filtered out
+test result: FAILED. 42 passed; 34 failed; 0 ignored; 0 measured; 0 filtered out
 ```
 
 ## Getting involved
diff --git a/src/backend.rs b/src/backend.rs
index 59c67dd354..7e725a35a2 100644
--- a/src/backend.rs
+++ b/src/backend.rs
@@ -1245,6 +1245,48 @@ macro_rules! cmp_f32 {
     };
 }
 
+macro_rules! eq_float {
+    ($name:ident, $instr:ident, $imm_fn:ident, $const_fallback:expr) => {
+        pub fn $name(&mut self) {
+            let right = self.pop();
+            let left = self.pop();
+
+            if let Some(right) = right.immediate() {
+                if let Some(left) = left.immediate() {
+                    self.push(ValueLocation::Immediate(
+                        if $const_fallback(left.$imm_fn().unwrap(), right.$imm_fn().unwrap()) {
+                            1u32
+                        } else {
+                            0
+                        }.into()
+                    ));
+                    return;
+                }
+            }
+
+            let (left, right) = match left {
+                ValueLocation::Reg(r) if self.block_state.regs.num_usages(r) <= 1 => (left, right),
+                _ =>  (right, left)
+            };
+
+            let left = self.into_temp_reg(GPRType::Rx, left);
+            let right = self.into_reg(GPRType::Rx, right);
+            let out = self.block_state.regs.take(I32);
+
+            dynasm!(self.asm
+                ; $instr Rx(left.rx().unwrap()), Rx(right.rx().unwrap())
+                ; movd Rd(out.rq().unwrap()), Rx(left.rx().unwrap())
+                ; and Rd(out.rq().unwrap()), 1
+            );
+
+            self.push(ValueLocation::Reg(out));
+            self.free_value(ValueLocation::Reg(left));
+            self.free_value(ValueLocation::Reg(right));
+        }
+
+    }
+}
+
 macro_rules! cmp_f64 {
     ($name:ident, $reverse_name:ident, $instr:ident, $const_fallback:expr) => {
         cmp_float!(
@@ -1855,9 +1897,33 @@ impl<'module, M: ModuleContext> Context<'module, M> {
 
     cmp_f32!(f32_gt, f32_lt, seta, |a, b| a > b);
     cmp_f32!(f32_ge, f32_le, setnc, |a, b| a >= b);
+    eq_float!(
+        f32_eq,
+        cmpeqss,
+        as_f32,
+        |a: wasmparser::Ieee32, b: wasmparser::Ieee32| f32::from_bits(a.0) == f32::from_bits(b.0)
+    );
+    eq_float!(
+        f32_ne,
+        cmpneqss,
+        as_f32,
+        |a: wasmparser::Ieee32, b: wasmparser::Ieee32| f32::from_bits(a.0) != f32::from_bits(b.0)
+    );
 
     cmp_f64!(f64_gt, f64_lt, seta, |a, b| a > b);
     cmp_f64!(f64_ge, f64_le, setnc, |a, b| a >= b);
+    eq_float!(
+        f64_eq,
+        cmpeqsd,
+        as_f64,
+        |a: wasmparser::Ieee64, b: wasmparser::Ieee64| f64::from_bits(a.0) == f64::from_bits(b.0)
+    );
+    eq_float!(
+        f64_ne,
+        cmpneqsd,
+        as_f64,
+        |a: wasmparser::Ieee64, b: wasmparser::Ieee64| f64::from_bits(a.0) != f64::from_bits(b.0)
+    );
 
     // TODO: Should we do this logic in `eq` and just have this delegate to `eq`?
     //       That would mean that `eqz` and `eq` with a const 0 argument don't
diff --git a/src/function_body.rs b/src/function_body.rs
index 78088c5692..4608fabbea 100644
--- a/src/function_body.rs
+++ b/src/function_body.rs
@@ -459,6 +459,8 @@ where
             Operator::Div(SF32) => ctx.f32_div(),
             Operator::Neg(Size::_32) => ctx.f32_neg(),
             Operator::Abs(Size::_32) => ctx.f32_abs(),
+            Operator::Eq(F32) => ctx.f32_eq(),
+            Operator::Ne(F32) => ctx.f32_ne(),
             Operator::Gt(SF32) => ctx.f32_gt(),
             Operator::Ge(SF32) => ctx.f32_ge(),
             Operator::Lt(SF32) => ctx.f32_lt(),
@@ -469,6 +471,8 @@ where
             Operator::Div(SF64) => ctx.f64_div(),
             Operator::Neg(Size::_64) => ctx.f64_neg(),
             Operator::Abs(Size::_64) => ctx.f64_abs(),
+            Operator::Eq(F64) => ctx.f64_eq(),
+            Operator::Ne(F64) => ctx.f64_ne(),
             Operator::Gt(SF64) => ctx.f64_gt(),
             Operator::Ge(SF64) => ctx.f64_ge(),
             Operator::Lt(SF64) => ctx.f64_lt(),