use_squares

barretenberg/cpp/src/barretenberg/polynomials/univariate.hpp

@@ -119,6 +119,13 @@ template <class Fr, size_t domain_end, size_t domain_start = 0> class Univariate
         }
         return *this;
     }
+    Univariate& self_sqr()
+    {
+        for (size_t i = 0; i < LENGTH; ++i) {
+            evaluations[i].self_sqr();
+        }
+        return *this;
+    }
     Univariate operator+(const Univariate& other) const
     {
         Univariate res(*this);
@@ -148,6 +155,13 @@ template <class Fr, size_t domain_end, size_t domain_start = 0> class Univariate
         return res;
     }
 
+    Univariate sqr() const
+    {
+        Univariate res(*this);
+        res.self_sqr();
+        return res;
+    }
+
     // Operations between Univariate and scalar
     Univariate& operator+=(const Fr& scalar)
     {
@@ -404,6 +418,12 @@ template <class Fr, size_t domain_end, size_t domain_start = 0> class Univariate
         res *= other;
         return res;
     }
+    Univariate<Fr, domain_end, domain_start> sqr() const
+    {
+        Univariate<Fr, domain_end, domain_start> res(*this);
+        res = res.sqr();
+        return res;
+    }
 
     Univariate<Fr, domain_end, domain_start> operator*(const Univariate<Fr, domain_end, domain_start>& other) const
     {

barretenberg/cpp/src/barretenberg/relations/delta_range_constraint_relation.hpp

@@ -44,6 +44,7 @@ template <typename FF_> class DeltaRangeConstraintRelationImpl {
         auto w_1_shift = View(in.w_l_shift);
         auto q_delta_range = View(in.q_delta_range);
 
+        static const FF one = FF::one();
         static const FF minus_one = FF(-1);
         static const FF minus_two = FF(-2);
         static const FF minus_three = FF(-3);
@@ -55,37 +56,29 @@ template <typename FF_> class DeltaRangeConstraintRelationImpl {
         auto delta_4 = w_1_shift - w_4;
 
         // Contribution (1)
-        auto tmp_1 = delta_1;
-        tmp_1 *= (delta_1 + minus_one);
-        tmp_1 *= (delta_1 + minus_two);
-        tmp_1 *= (delta_1 + minus_three);
+        auto tmp_1 = (delta_1 + minus_one).sqr() - one;
+        tmp_1 *= (delta_1 + minus_two).sqr() - one;
         tmp_1 *= q_delta_range;
         tmp_1 *= scaling_factor;
         std::get<0>(accumulators) += tmp_1;
 
         // Contribution (2)
-        auto tmp_2 = delta_2;
-        tmp_2 *= (delta_2 + minus_one);
-        tmp_2 *= (delta_2 + minus_two);
-        tmp_2 *= (delta_2 + minus_three);
+        auto tmp_2 = (delta_2 + minus_one).sqr() - one;
+        tmp_2 *= (delta_2 + minus_two).sqr() - one;
         tmp_2 *= q_delta_range;
         tmp_2 *= scaling_factor;
         std::get<1>(accumulators) += tmp_2;
 
         // Contribution (3)
-        auto tmp_3 = delta_3;
-        tmp_3 *= (delta_3 + minus_one);
-        tmp_3 *= (delta_3 + minus_two);
-        tmp_3 *= (delta_3 + minus_three);
+        auto tmp_3 = (delta_3 + minus_one).sqr() - one;
+        tmp_3 *= (delta_3 + minus_two).sqr() - one;
         tmp_3 *= q_delta_range;
         tmp_3 *= scaling_factor;
         std::get<2>(accumulators) += tmp_3;
 
         // Contribution (4)
-        auto tmp_4 = delta_4;
-        tmp_4 *= (delta_4 + minus_one);
-        tmp_4 *= (delta_4 + minus_two);
-        tmp_4 *= (delta_4 + minus_three);
+        auto tmp_4 = (delta_4 + minus_one).sqr() - one;
+        tmp_4 *= (delta_4 + minus_two).sqr() - one;
         tmp_4 *= q_delta_range;
         tmp_4 *= scaling_factor;
         std::get<3>(accumulators) += tmp_4;

barretenberg/cpp/src/barretenberg/relations/elliptic_relation.hpp

@@ -63,8 +63,8 @@ template <typename FF_> class EllipticRelationImpl {
         // Contribution (1) point addition, x-coordinate check
         // q_elliptic * (x3 + x2 + x1)(x2 - x1)(x2 - x1) - y2^2 - y1^2 + 2(y2y1)*q_sign = 0
         auto x_diff = (x_2 - x_1);
-        auto y2_sqr = (y_2 * y_2);
-        auto y1_sqr = (y_1 * y_1);
+        auto y2_sqr = y_2.sqr();
+        auto y1_sqr = y_1.sqr();
         auto y1y2 = y_1 * y_2 * q_sign;
         auto x_add_identity = (x_3 + x_2 + x_1) * x_diff * x_diff - y2_sqr - y1_sqr + y1y2 + y1y2;
         std::get<0>(accumulators) += x_add_identity * scaling_factor * q_elliptic * (-q_is_double + 1);
@@ -89,7 +89,8 @@ template <typename FF_> class EllipticRelationImpl {
 
         // Contribution (4) point doubling, y-coordinate check
         // (y1 + y1) (2y1) - (3 * x1 * x1)(x1 - x3) = 0
-        auto x1_sqr_mul_3 = (x_1 + x_1 + x_1) * x_1;
+        auto x1_sqr = x_1 * x_1;
+        auto x1_sqr_mul_3 = x1_sqr + x1_sqr + x1_sqr;
         auto y_double_identity = x1_sqr_mul_3 * (x_1 - x_3) - (y_1 + y_1) * (y_1 + y_3);
         std::get<1>(accumulators) += y_double_identity * scaling_factor * q_elliptic * q_is_double;
     };

barretenberg/cpp/src/barretenberg/relations/poseidon2_external_relation.hpp

@@ -66,17 +66,17 @@ template <typename FF_> class Poseidon2ExternalRelationImpl {
         auto s4 = w_4 + q_4;
 
         // apply s-box round
-        auto u1 = s1 * s1;
-        u1 *= u1;
+        auto u1 = s1.sqr();
+        u1 = u1.sqr();
         u1 *= s1;
-        auto u2 = s2 * s2;
-        u2 *= u2;
+        auto u2 = s2.sqr();
+        u2 = u2.sqr();
         u2 *= s2;
-        auto u3 = s3 * s3;
-        u3 *= u3;
+        auto u3 = s3.sqr();
+        u3 = u3.sqr();
         u3 *= s3;
-        auto u4 = s4 * s4;
-        u4 *= u4;
+        auto u4 = s4.sqr();
+        u4 = u4.sqr();
         u4 *= s4;
 
         // matrix mul v = M_E * u with 14 additions

barretenberg/cpp/src/barretenberg/relations/poseidon2_internal_relation.hpp

@@ -57,8 +57,8 @@ template <typename FF_> class Poseidon2InternalRelationImpl {
         auto s1 = w_l + q_l;
 
         // apply s-box round
-        auto u1 = s1 * s1;
-        u1 *= u1;
+        auto u1 = s1.sqr();
+        u1 = u1.sqr();
         u1 *= s1;
         auto u2 = w_r;
         auto u3 = w_o;