diff --git a/include/caffe/util/math_functions.hpp b/include/caffe/util/math_functions.hpp
index a78eb5bc978..12823f8da0c 100644
--- a/include/caffe/util/math_functions.hpp
+++ b/include/caffe/util/math_functions.hpp
@@ -108,7 +108,7 @@ Dtype caffe_cpu_asum(const int n, const Dtype* x);
 // the branchless, type-safe version from
 // http://stackoverflow.com/questions/1903954/is-there-a-standard-sign-function-signum-sgn-in-c-c
 template<typename Dtype>
-inline char caffe_sign(Dtype val) {
+inline int8_t caffe_sign(Dtype val) {
   return (Dtype(0) < val) - (val < Dtype(0));
 }
 
@@ -127,12 +127,6 @@ inline char caffe_sign(Dtype val) {
     } \
   }
 
-#define INSTANTIATE_CAFFE_CPU_UNARY_FUNC(name) \
-  template <> \
-  void caffe_cpu_##name<float>(const int n, const float* x, float* y); \
-  template <> \
-  void caffe_cpu_##name<double>(const int n, const double* x, double* y)
-
 // output is 1 for the positives, 0 for zero, and -1 for the negatives
 DEFINE_CAFFE_CPU_UNARY_FUNC(sign, y[i] = caffe_sign<Dtype>(x[i]));
 
@@ -140,7 +134,8 @@ DEFINE_CAFFE_CPU_UNARY_FUNC(sign, y[i] = caffe_sign<Dtype>(x[i]));
 // The name sngbit is meant to avoid conflicts with std::signbit in the macro.
 // The extra parens are needed because CUDA < 6.5 defines signbit as a macro,
 // and we don't want that to expand here when CUDA headers are also included.
-DEFINE_CAFFE_CPU_UNARY_FUNC(sgnbit, y[i] = (std::signbit)(x[i]));
+DEFINE_CAFFE_CPU_UNARY_FUNC(sgnbit, \
+    y[i] = static_cast<bool>((std::signbit)(x[i])));
 
 DEFINE_CAFFE_CPU_UNARY_FUNC(fabs, y[i] = std::fabs(x[i]));
 
diff --git a/src/caffe/test/test_net.cpp b/src/caffe/test/test_net.cpp
index 930486dd6c5..611d11bd832 100644
--- a/src/caffe/test/test_net.cpp
+++ b/src/caffe/test/test_net.cpp
@@ -1155,7 +1155,7 @@ TYPED_TEST(NetTest, TestParamPropagateDown) {
   for (int i = 0; i < num_params; ++i) {
     const Dtype param_asum =
        caffe_cpu_asum(params2[i]->count(), params2[i]->cpu_diff());
-    EXPECT_EQ(param_asum, param_asums[i]);
+    EXPECT_FLOAT_EQ(param_asum, param_asums[i]);
   }
 
   // Change a subset of the learning rates to zero; check that we see zero
@@ -1172,9 +1172,9 @@ TYPED_TEST(NetTest, TestParamPropagateDown) {
     const Dtype param_asum =
        caffe_cpu_asum(params3[i]->count(), params3[i]->cpu_diff());
     if (i == 1 || i == 2) {
-      EXPECT_EQ(0, param_asum);
+      EXPECT_FLOAT_EQ(0, param_asum);
     } else {
-      EXPECT_EQ(param_asum, param_asums[i]);
+      EXPECT_FLOAT_EQ(param_asum, param_asums[i]);
     }
   }
 
@@ -1191,9 +1191,9 @@ TYPED_TEST(NetTest, TestParamPropagateDown) {
     const Dtype param_asum =
        caffe_cpu_asum(params4[i]->count(), params4[i]->cpu_diff());
     if (i == 0 || i == 3) {
-      EXPECT_EQ(0, param_asum);
+      EXPECT_FLOAT_EQ(0, param_asum);
     } else {
-      EXPECT_EQ(param_asum, param_asums[i]);
+      EXPECT_FLOAT_EQ(param_asum, param_asums[i]);
     }
   }
 }
diff --git a/src/caffe/util/math_functions.cpp b/src/caffe/util/math_functions.cpp
index c3afd2ffbc5..13e17be582b 100644
--- a/src/caffe/util/math_functions.cpp
+++ b/src/caffe/util/math_functions.cpp
@@ -370,9 +370,6 @@ double caffe_cpu_asum<double>(const int n, const double* x) {
   return cblas_dasum(n, x, 1);
 }
 
-INSTANTIATE_CAFFE_CPU_UNARY_FUNC(sign);
-INSTANTIATE_CAFFE_CPU_UNARY_FUNC(sgnbit);
-
 template <>
 void caffe_cpu_scale<float>(const int n, const float alpha, const float *x,
                             float* y) {