diff --git a/ff/mersenne31.hpp b/ff/mersenne31.hpp
index 83338a2..3c4ae7d 100644
--- a/ff/mersenne31.hpp
+++ b/ff/mersenne31.hpp
@@ -140,7 +140,7 @@ class mrs31_t {
     friend inline mrs31_t operator-(mrs31_t a, const mrs31_t b)
     {   return a -= b;   }
 
-    inline mrs31_t cneg(bool flag)
+    inline mrs31_t& cneg(bool flag)
     {
         if (flag && val != 0)
             val = MOD - val;
@@ -264,6 +264,20 @@ class mrs31_t {
         return mrs31_t{ret};
     }
 
+    static inline mrs31_t dot_product(mrs31_t a, mrs31_t b,
+                                      mrs31_t c, mrs31_t d)
+    {
+        uint64_t tmp = a.val*(uint64_t)b.val + c.val*(uint64_t)d.val;
+        uint32_t ret = (uint32_t)(tmp >> 31);
+        if (ret >= MOD)
+            ret -= MOD;
+        ret += (uint32_t)tmp & MOD;
+        if (ret >= MOD)
+            ret -= MOD;
+
+        return mrs31_t{ret};
+    }
+
 private:
     static inline mrs31_t sqr_n(mrs31_t s, uint32_t n)
     {
diff --git a/ff/mont32_t.cuh b/ff/mont32_t.cuh
index 2d7b96b..cd868b3 100644
--- a/ff/mont32_t.cuh
+++ b/ff/mont32_t.cuh
@@ -125,7 +125,7 @@ public:
     friend inline mont32_t operator-(mont32_t a, const mont32_t b)
     {   return a -= b;   }
 
-    inline mont32_t cneg(bool flag)
+    inline mont32_t& cneg(bool flag)
     {
         asm("{");
         asm(".reg.pred %flag;");
@@ -334,6 +334,26 @@ public:
         return final_sub(acc[1]);
     }
 
+    static inline mont32_t dot_product(mont32_t a, mont32_t b,
+                                       mont32_t c, mont32_t d)
+    {
+        uint32_t acc[2];
+
+        asm("mul.lo.u32 %0, %2, %3; mul.hi.u32 %1, %2, %3;"
+            : "=r"(acc[0]), "=r"(acc[1]) : "r"(*a), "r"(*b));
+        asm("mad.lo.cc.u32 %0, %2, %3, %0; madc.hi.u32 %1, %2, %3, %1;"
+            : "+r"(acc[0]), "+r"(acc[1]) : "r"(*c), "r"(*d));
+        if (N == 32)
+            acc[1] = final_sub(acc[1]);
+
+        uint32_t red;
+        asm("mul.lo.u32 %0, %1, %2;" : "=r"(red) : "r"(acc[0]), "r"(M0));
+        asm("mad.lo.cc.u32 %0, %2, %3, %0; madc.hi.cc.u32 %1, %2, %3, %1;"
+            : "+r"(acc[0]), "+r"(acc[1]) : "r"(red), "r"(MOD));
+
+        return final_sub(acc[1]);
+    }
+
     inline mont32_t reciprocal() const
     {   return *this ^ (MOD-2);   }
     friend inline mont32_t operator/(int one, mont32_t a)