From 77b0a9361b3ae066774bed6a3a32a4e3f1065944 Mon Sep 17 00:00:00 2001
From: hadaringonyama <hadar@ingonyama.com>
Date: Thu, 2 Jan 2025 16:30:45 +0200
Subject: [PATCH 1/5] poc

---
 icicle/include/icicle/curves/params/bn254.h |  4 +++
 icicle/include/icicle/curves/projective.h   | 36 +++++++++++++--------
 icicle/include/icicle/fields/field.h        | 32 ++++++++++++++++++
 3 files changed, 59 insertions(+), 13 deletions(-)

diff --git a/icicle/include/icicle/curves/params/bn254.h b/icicle/include/icicle/curves/params/bn254.h
index b8095b53f..6841b3429 100644
--- a/icicle/include/icicle/curves/params/bn254.h
+++ b/icicle/include/icicle/curves/params/bn254.h
@@ -24,6 +24,10 @@ namespace bn254 {
                                             0x00000000, 0x00000000, 0x00000000, 0x00000000};
     static constexpr point_field_t weierstrass_b = {0x00000003, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr point_field_t weierstrass_3b = {0x00000009, 0x00000000, 0x00000000, 0x00000000,
+                                                    0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr bool is_b_u32 = true;
+    static constexpr bool is_b_neg = false;
   }; // G1
 
   struct G2 {
diff --git a/icicle/include/icicle/curves/projective.h b/icicle/include/icicle/curves/projective.h
index 87fe0ab23..ab70ab506 100644
--- a/icicle/include/icicle/curves/projective.h
+++ b/icicle/include/icicle/curves/projective.h
@@ -64,7 +64,9 @@ class Projective
     Z3 = Z3 + Z3;                                                                      // 4. Z3 ← Z3 + Z3
     FF t1 = Y * Z;                                                                     // 5. t1 ← Y · Z
     FF t2 = FF::sqr(Z);                                                                // 6. t2 ← Z · Z
-    t2 = FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t2)); // 7. t2 ← b3 · t2
+    t2 = FF::template mul_weierstrass_3b<Gen>(t2); // 7. t2 ← b3 · t2
+    // t2 = FF::template mul_unsigned<3>(FF::template mul_weierstrass_b<Gen>(t2)); // 7. t2 ← b3 · t2
+    // t2 = FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t2)); // 7. t2 ← b3 · t2
     FF X3 = t2 * Z3;                                                                   // 8. X3 ← t2 · Z3
     FF Y3 = t0 + t2;                                                                   // 9. Y3 ← t0 + t2
     Z3 = t1 * Z3;                                                                      // 10. Z3 ← t1 · Z3
@@ -107,12 +109,16 @@ class Projective
     const FF t17 = t15 - t16; // t17 ← t15 − t16   < 2
     const FF t18 = t00 + t00; // t18 ← t00 + t00   < 2
     const FF t19 = t18 + t00; // t19 ← t18 + t00   < 2
-    const FF t20 =
-      FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t02)); // t20 ← b3 · t02    < 2
-    const FF t21 = t01 + t20;                                                        // t21 ← t01 + t20   < 2
-    const FF t22 = t01 - t20;                                                        // t22 ← t01 − t20   < 2
-    const FF t23 =
-      FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t17)); // t23 ← b3 · t17    < 2
+    const FF t20 = FF::template mul_weierstrass_3b<Gen>(t02); // t20 ← b3 · t02    < 2
+    // const FF t20 = FF::template mul_unsigned<3>(FF::template mul_weierstrass_b<Gen>(t02)); // t20 ← b3 · t02    < 2
+    // const FF t20 =
+    // FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t02)); // t20 ← b3 · t02    < 2
+    const FF t21 = t01 + t20; // t21 ← t01 + t20   < 2
+    const FF t22 = t01 - t20; // t22 ← t01 − t20   < 2
+    const FF t23 = FF::template mul_weierstrass_3b<Gen>(t17); // t23 ← b3 · t17    < 2
+    // const FF t23 = FF::template mul_unsigned<3>(FF::template mul_weierstrass_b<Gen>(t17)); // t23 ← b3 · t17    < 2
+    // const FF t23 =
+    // FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t17)); // t23 ← b3 · t17    < 2
     const auto t24 = FF::mul_wide(t12, t23);                                         // t24 ← t12 · t23   < 2
     const auto t25 = FF::mul_wide(t07, t22);                                         // t25 ← t07 · t22   < 2
     const FF X3 = FF::reduce(t25 - t24);                                             // X3 ← t25 − t24    < 2
@@ -154,12 +160,16 @@ class Projective
     const FF t17 = t15 - t16;      // t17 ← t15 − t16   < 2
     const FF t18 = t00 + t00;      // t18 ← t00 + t00   < 2
     const FF t19 = t18 + t00;      // t19 ← t18 + t00   < 2
-    const FF t20 =
-      FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t02)); // t20 ← b3 · t02    < 2
-    const FF t21 = t01 + t20;                                                        // t21 ← t01 + t20   < 2
-    const FF t22 = t01 - t20;                                                        // t22 ← t01 − t20   < 2
-    const FF t23 =
-      FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t17)); // t23 ← b3 · t17    < 2
+    const FF t20 = FF::template mul_weierstrass_3b<Gen>(t02); // t20 ← b3 · t02    < 2
+    // const FF t20 = FF::template mul_unsigned<3>(FF::template mul_weierstrass_b<Gen>(t02)); // t20 ← b3 · t02    < 2
+    // const FF t20 =
+    // FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t02)); // t20 ← b3 · t02    < 2
+    const FF t21 = t01 + t20; // t21 ← t01 + t20   < 2
+    const FF t22 = t01 - t20; // t22 ← t01 − t20   < 2
+    const FF t23 = FF::template mul_weierstrass_3b<Gen>(t17); // t23 ← b3 · t17    < 2
+    // const FF t23 = FF::template mul_unsigned<3>(FF::template mul_weierstrass_b<Gen>(t17)); // t23 ← b3 · t17    < 2
+    // const FF t23 =
+    // FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t17)); // t23 ← b3 · t17    < 2
     const auto t24 = FF::mul_wide(t12, t23);                                         // t24 ← t12 · t23   < 2
     const auto t25 = FF::mul_wide(t07, t22);                                         // t25 ← t07 · t22   < 2
     const FF X3 = FF::reduce(t25 - t24);                                             // X3 ← t25 − t24    < 2
diff --git a/icicle/include/icicle/fields/field.h b/icicle/include/icicle/fields/field.h
index 80c4b4178..47ebf3c07 100644
--- a/icicle/include/icicle/fields/field.h
+++ b/icicle/include/icicle/fields/field.h
@@ -875,6 +875,38 @@ class Field
 
   friend HOST_DEVICE bool operator!=(const Field& xs, const Field& ys) { return !(xs == ys); }
 
+template <typename Gen>
+  static HOST_DEVICE_INLINE Field mul_weierstrass_b(const Field& xs)
+  {
+    Field r = {};
+    if constexpr (Gen::is_b_u32) {
+      r = mul_unsigned<Field{Gen::weierstrass_b}.limbs_storage.limbs[0], Field>(xs);
+      if constexpr (Gen::is_b_neg)
+        return neg(r);
+      else {
+        return r;
+      }
+    } else {
+      return Field{Gen::weierstrass_b} * xs;
+    }
+  }
+
+  template <typename Gen>
+  static HOST_DEVICE_INLINE Field mul_weierstrass_3b(const Field& xs)
+  {
+    Field r = {};
+    if constexpr (Gen::is_b_u32) {
+      r = mul_unsigned<Field{Gen::weierstrass_3b}.limbs_storage.limbs[0], Field>(xs);
+      if constexpr (Gen::is_b_neg)
+        return neg(r);
+      else {
+        return r;
+      }
+    } else {
+      return Field{Gen::weierstrass_3b} * xs;
+    }
+  }
+
   template <const Field& multiplier>
   static HOST_DEVICE_INLINE Field mul_const(const Field& xs)
   {

From 9b3fbd623704f1d7a440090e63f6a5063ad4177c Mon Sep 17 00:00:00 2001
From: hadaringonyama <hadar@ingonyama.com>
Date: Thu, 2 Jan 2025 17:09:19 +0200
Subject: [PATCH 2/5] changed params

---
 .../include/icicle/curves/params/bls12_377.h  |  16 ++
 .../include/icicle/curves/params/bls12_381.h  |  16 ++
 icicle/include/icicle/curves/params/bn254.h   |  11 +-
 icicle/include/icicle/curves/params/bw6_761.h |  25 ++-
 .../include/icicle/curves/params/grumpkin.h   |  11 +-
 icicle/include/icicle/curves/projective.h     | 194 ++++++++----------
 .../include/icicle/fields/complex_extension.h |  46 +++++
 icicle/include/icicle/fields/field.h          |  16 --
 8 files changed, 209 insertions(+), 126 deletions(-)

diff --git a/icicle/include/icicle/curves/params/bls12_377.h b/icicle/include/icicle/curves/params/bls12_377.h
index da19ab2bd..71089f8f8 100644
--- a/icicle/include/icicle/curves/params/bls12_377.h
+++ b/icicle/include/icicle/curves/params/bls12_377.h
@@ -25,6 +25,11 @@ namespace bls12_377 {
     static constexpr point_field_t weierstrass_b = {0x00000001, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr point_field_t weierstrass_3b = {0x00000003, 0x00000000, 0x00000000, 0x00000000,
+                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000,
+                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr bool is_b_u32 = true;
+    static constexpr bool is_b_neg = false;
   }; // G1
 
   struct G2 {
@@ -46,6 +51,17 @@ namespace bls12_377 {
     static constexpr point_field_t weierstrass_b_g2_im = {0x9999999a, 0x1c9ed999, 0x1ccccccd, 0x0dd39e5c,
                                                           0x3c6bf800, 0x129207b6, 0xcd5fd889, 0xdc7b4f91,
                                                           0x7460c589, 0x43bd0373, 0xdb0fd6f3, 0x010222f6};
+    static constexpr point_field_t weierstrass_3b_g2_re = {0x00000000, 0x00000000, 0x00000000, 0x00000000,
+                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000,
+                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr point_field_t weierstrass_3b_g2_im = {0xcccccccd, 0xd0d3cccc, 0x26666666, 0x126f7dd0,
+                                                           0xfb3aa000, 0x18c2b4f2, 0x672a760c, 0x7b4f14c2,
+                                                           0xf0810762, 0x04fc0499, 0x796a73ef, 0x01582e9e};
+
+    static constexpr bool is_b_u32_g2_re = true;
+    static constexpr bool is_b_neg_g2_re = false;
+    static constexpr bool is_b_u32_g2_im = false;
+    static constexpr bool is_b_neg_g2_im = false;
 
     static constexpr g2_point_field_t gen_x = {g2_gen_x_re, g2_gen_x_im};
     static constexpr g2_point_field_t gen_y = {g2_gen_y_re, g2_gen_y_im};
diff --git a/icicle/include/icicle/curves/params/bls12_381.h b/icicle/include/icicle/curves/params/bls12_381.h
index 7457bd49c..116af3c14 100644
--- a/icicle/include/icicle/curves/params/bls12_381.h
+++ b/icicle/include/icicle/curves/params/bls12_381.h
@@ -25,6 +25,11 @@ namespace bls12_381 {
     static constexpr point_field_t weierstrass_b = {0x00000004, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr point_field_t weierstrass_3b = {0x0000000c, 0x00000000, 0x00000000, 0x00000000,
+                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000,
+                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr bool is_b_u32 = true;
+    static constexpr bool is_b_neg = false;
   };
 
   struct G2 {
@@ -47,6 +52,17 @@ namespace bls12_381 {
     static constexpr point_field_t weierstrass_b_g2_im = {0x00000004, 0x00000000, 0x00000000, 0x00000000,
                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000,
                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr point_field_t weierstrass_3b_g2_re = {0x0000000c, 0x00000000, 0x00000000, 0x00000000,
+                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000,
+                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr point_field_t weierstrass_3b_g2_im = {0x0000000c, 0x00000000, 0x00000000, 0x00000000,
+                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000,
+                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000};
+
+    static constexpr bool is_b_u32_g2_re = true;
+    static constexpr bool is_b_neg_g2_re = false;
+    static constexpr bool is_b_u32_g2_im = true;
+    static constexpr bool is_b_neg_g2_im = false;
 
     static constexpr g2_point_field_t gen_x = {g2_gen_x_re, g2_gen_x_im};
     static constexpr g2_point_field_t gen_y = {g2_gen_y_re, g2_gen_y_im};
diff --git a/icicle/include/icicle/curves/params/bn254.h b/icicle/include/icicle/curves/params/bn254.h
index 6841b3429..9c2b8c5fa 100644
--- a/icicle/include/icicle/curves/params/bn254.h
+++ b/icicle/include/icicle/curves/params/bn254.h
@@ -25,7 +25,7 @@ namespace bn254 {
     static constexpr point_field_t weierstrass_b = {0x00000003, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
     static constexpr point_field_t weierstrass_3b = {0x00000009, 0x00000000, 0x00000000, 0x00000000,
-                                                    0x00000000, 0x00000000, 0x00000000, 0x00000000};
+                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
     static constexpr bool is_b_u32 = true;
     static constexpr bool is_b_neg = false;
   }; // G1
@@ -43,6 +43,15 @@ namespace bn254 {
                                                           0x1be06ac3, 0x81be1899, 0xceb8aaae, 0x2b149d40};
     static constexpr point_field_t weierstrass_b_g2_im = {0x85c315d2, 0xe4a2bd06, 0xe52d1852, 0xa74fa084,
                                                           0xeed8fdf4, 0xcd2cafad, 0x3af0fed4, 0x009713b0};
+    static constexpr point_field_t weierstrass_3b_g2_re = {0xbce9b021, 0x1ef69c66, 0x3cb039cf, 0xf21b7c8d,
+                                                           0x509e8f8f, 0x1499be5e, 0xa9c6bfb8, 0x20753adc};
+    static constexpr point_field_t weierstrass_3b_g2_im = {0x91494176, 0xade83713, 0xaf8748f8, 0xf5eee18e,
+                                                           0xcc8af9dd, 0x67860f09, 0xb0d2fc7e, 0x01c53b10};
+
+    static constexpr bool is_b_u32_g2_re = false;
+    static constexpr bool is_b_neg_g2_re = false;
+    static constexpr bool is_b_u32_g2_im = false;
+    static constexpr bool is_b_neg_g2_im = false;
 
     static constexpr g2_point_field_t gen_x = {g2_gen_x_re, g2_gen_x_im};
     static constexpr g2_point_field_t gen_y = {g2_gen_y_re, g2_gen_y_im};
diff --git a/icicle/include/icicle/curves/params/bw6_761.h b/icicle/include/icicle/curves/params/bw6_761.h
index c0a1fcf5e..12d19b50f 100644
--- a/icicle/include/icicle/curves/params/bw6_761.h
+++ b/icicle/include/icicle/curves/params/bw6_761.h
@@ -25,10 +25,22 @@ namespace bw6_761 {
                                             0xb3053253, 0x9f9df141, 0x6fc2cdd4, 0xbe3fb90b, 0x717a4c55, 0xcc685d31,
                                             0x71b5b806, 0xc5b8fa17, 0xaf7e0dba, 0x265909f1, 0xa2e573a3, 0x1a7348d2,
                                             0x884c9ec6, 0x0f952589, 0x45cc2a42, 0xe6fd637b, 0x0a6fc574, 0x0058b84e};
+    // actual value:
+    // static constexpr point_field_t weierstrass_b = {
+    //   0x0000008a, 0xf49d0000, 0x70000082, 0xe6913e68, 0xeaf0a437, 0x160cf8ae, 0x5667a8f8, 0x98a116c2,
+    //   0x73ebff2e, 0x71dcd3dc, 0x12f9fd90, 0x8689c8ed, 0x25b42304, 0x03cebaff, 0xe584e919, 0x707ba638,
+    //   0x8087be41, 0x528275ef, 0x81d14688, 0xb926186a, 0x04faff3e, 0xd187c940, 0xfb83ce0a, 0x0122e824};
     static constexpr point_field_t weierstrass_b = {
-      0x0000008a, 0xf49d0000, 0x70000082, 0xe6913e68, 0xeaf0a437, 0x160cf8ae, 0x5667a8f8, 0x98a116c2,
-      0x73ebff2e, 0x71dcd3dc, 0x12f9fd90, 0x8689c8ed, 0x25b42304, 0x03cebaff, 0xe584e919, 0x707ba638,
-      0x8087be41, 0x528275ef, 0x81d14688, 0xb926186a, 0x04faff3e, 0xd187c940, 0xfb83ce0a, 0x0122e824};
+      0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
+      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
+      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr point_field_t weierstrass_3b = {
+      0x00000003, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
+      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
+      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
+
+    static constexpr bool is_b_u32 = true;
+    static constexpr bool is_b_neg = true;
   };
 
   struct G2 {
@@ -44,5 +56,12 @@ namespace bw6_761 {
       0x00000004, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
       0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
       0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr g2_point_field_t weierstrass_3b = {
+      0x0000000c, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
+      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
+      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
+
+    static constexpr bool is_b_u32 = true;
+    static constexpr bool is_b_neg = false;
   };
 } // namespace bw6_761
diff --git a/icicle/include/icicle/curves/params/grumpkin.h b/icicle/include/icicle/curves/params/grumpkin.h
index a468fd911..e968589bc 100644
--- a/icicle/include/icicle/curves/params/grumpkin.h
+++ b/icicle/include/icicle/curves/params/grumpkin.h
@@ -16,7 +16,14 @@ namespace grumpkin {
     static constexpr point_field_t gen_y = {0x823f272c, 0x833fc48d, 0xf1181294, 0x2d270d45,
                                             0x6a45d63,  0xcf135e75, 0x00000002, 0x00000000};
 
-    static constexpr point_field_t weierstrass_b = {0xeffffff0, 0x43e1f593, 0x79b97091, 0x2833e848,
-                                                    0x8181585d, 0xb85045b6, 0xe131a029, 0x30644e72};
+    // actual value:
+    // static constexpr point_field_t weierstrass_b = {0xeffffff0, 0x43e1f593, 0x79b97091, 0x2833e848,
+    // 0x8181585d, 0xb85045b6, 0xe131a029, 0x30644e72};
+    static constexpr point_field_t weierstrass_b = {0x00000011, 0x00000000, 0x00000000, 0x00000000,
+                                                    0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr point_field_t weierstrass_3b = {0x00000033, 0x00000000, 0x00000000, 0x00000000,
+                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
+    static constexpr bool is_b_u32 = true;
+    static constexpr bool is_b_neg = true;
   }; // G1
 } // namespace grumpkin
diff --git a/icicle/include/icicle/curves/projective.h b/icicle/include/icicle/curves/projective.h
index ab70ab506..0ba8eefc8 100644
--- a/icicle/include/icicle/curves/projective.h
+++ b/icicle/include/icicle/curves/projective.h
@@ -58,76 +58,68 @@ class Projective
     const FF Z = point.z;
 
     // TODO: Change to efficient dbl once implemented for field.cuh
-    FF t0 = FF::sqr(Y);                                                                // 1. t0 ← Y · Y
-    FF Z3 = t0 + t0;                                                                   // 2. Z3 ← t0 + t0
-    Z3 = Z3 + Z3;                                                                      // 3. Z3 ← Z3 + Z3
-    Z3 = Z3 + Z3;                                                                      // 4. Z3 ← Z3 + Z3
-    FF t1 = Y * Z;                                                                     // 5. t1 ← Y · Z
-    FF t2 = FF::sqr(Z);                                                                // 6. t2 ← Z · Z
+    FF t0 = FF::sqr(Y);                            // 1. t0 ← Y · Y
+    FF Z3 = t0 + t0;                               // 2. Z3 ← t0 + t0
+    Z3 = Z3 + Z3;                                  // 3. Z3 ← Z3 + Z3
+    Z3 = Z3 + Z3;                                  // 4. Z3 ← Z3 + Z3
+    FF t1 = Y * Z;                                 // 5. t1 ← Y · Z
+    FF t2 = FF::sqr(Z);                            // 6. t2 ← Z · Z
     t2 = FF::template mul_weierstrass_3b<Gen>(t2); // 7. t2 ← b3 · t2
-    // t2 = FF::template mul_unsigned<3>(FF::template mul_weierstrass_b<Gen>(t2)); // 7. t2 ← b3 · t2
-    // t2 = FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t2)); // 7. t2 ← b3 · t2
-    FF X3 = t2 * Z3;                                                                   // 8. X3 ← t2 · Z3
-    FF Y3 = t0 + t2;                                                                   // 9. Y3 ← t0 + t2
-    Z3 = t1 * Z3;                                                                      // 10. Z3 ← t1 · Z3
-    t1 = t2 + t2;                                                                      // 11. t1 ← t2 + t2
-    t2 = t1 + t2;                                                                      // 12. t2 ← t1 + t2
-    t0 = t0 - t2;                                                                      // 13. t0 ← t0 − t2
-    Y3 = t0 * Y3;                                                                      // 14. Y3 ← t0 · Y3
-    Y3 = X3 + Y3;                                                                      // 15. Y3 ← X3 + Y3
-    t1 = X * Y;                                                                        // 16. t1 ← X · Y
-    X3 = t0 * t1;                                                                      // 17. X3 ← t0 · t1
-    X3 = X3 + X3;                                                                      // 18. X3 ← X3 + X3
+    FF X3 = t2 * Z3;                               // 8. X3 ← t2 · Z3
+    FF Y3 = t0 + t2;                               // 9. Y3 ← t0 + t2
+    Z3 = t1 * Z3;                                  // 10. Z3 ← t1 · Z3
+    t1 = t2 + t2;                                  // 11. t1 ← t2 + t2
+    t2 = t1 + t2;                                  // 12. t2 ← t1 + t2
+    t0 = t0 - t2;                                  // 13. t0 ← t0 − t2
+    Y3 = t0 * Y3;                                  // 14. Y3 ← t0 · Y3
+    Y3 = X3 + Y3;                                  // 15. Y3 ← X3 + Y3
+    t1 = X * Y;                                    // 16. t1 ← X · Y
+    X3 = t0 * t1;                                  // 17. X3 ← t0 · t1
+    X3 = X3 + X3;                                  // 18. X3 ← X3 + X3
     return {X3, Y3, Z3};
   }
 
   friend HOST_DEVICE Projective operator+(Projective p1, const Projective& p2)
   {
-    const FF X1 = p1.x;       //                   < 2
-    const FF Y1 = p1.y;       //                   < 2
-    const FF Z1 = p1.z;       //                   < 2
-    const FF X2 = p2.x;       //                   < 2
-    const FF Y2 = p2.y;       //                   < 2
-    const FF Z2 = p2.z;       //                   < 2
-    const FF t00 = X1 * X2;   // t00 ← X1 · X2     < 2
-    const FF t01 = Y1 * Y2;   // t01 ← Y1 · Y2     < 2
-    const FF t02 = Z1 * Z2;   // t02 ← Z1 · Z2     < 2
-    const FF t03 = X1 + Y1;   // t03 ← X1 + Y1     < 4
-    const FF t04 = X2 + Y2;   // t04 ← X2 + Y2     < 4
-    const FF t05 = t03 * t04; // t03 ← t03 · t04   < 3
-    const FF t06 = t00 + t01; // t06 ← t00 + t01   < 4
-    const FF t07 = t05 - t06; // t05 ← t05 − t06   < 2
-    const FF t08 = Y1 + Z1;   // t08 ← Y1 + Z1     < 4
-    const FF t09 = Y2 + Z2;   // t09 ← Y2 + Z2     < 4
-    const FF t10 = t08 * t09; // t10 ← t08 · t09   < 3
-    const FF t11 = t01 + t02; // t11 ← t01 + t02   < 4
-    const FF t12 = t10 - t11; // t12 ← t10 − t11   < 2
-    const FF t13 = X1 + Z1;   // t13 ← X1 + Z1     < 4
-    const FF t14 = X2 + Z2;   // t14 ← X2 + Z2     < 4
-    const FF t15 = t13 * t14; // t15 ← t13 · t14   < 3
-    const FF t16 = t00 + t02; // t16 ← t00 + t02   < 4
-    const FF t17 = t15 - t16; // t17 ← t15 − t16   < 2
-    const FF t18 = t00 + t00; // t18 ← t00 + t00   < 2
-    const FF t19 = t18 + t00; // t19 ← t18 + t00   < 2
+    const FF X1 = p1.x;                                       //                   < 2
+    const FF Y1 = p1.y;                                       //                   < 2
+    const FF Z1 = p1.z;                                       //                   < 2
+    const FF X2 = p2.x;                                       //                   < 2
+    const FF Y2 = p2.y;                                       //                   < 2
+    const FF Z2 = p2.z;                                       //                   < 2
+    const FF t00 = X1 * X2;                                   // t00 ← X1 · X2     < 2
+    const FF t01 = Y1 * Y2;                                   // t01 ← Y1 · Y2     < 2
+    const FF t02 = Z1 * Z2;                                   // t02 ← Z1 · Z2     < 2
+    const FF t03 = X1 + Y1;                                   // t03 ← X1 + Y1     < 4
+    const FF t04 = X2 + Y2;                                   // t04 ← X2 + Y2     < 4
+    const FF t05 = t03 * t04;                                 // t03 ← t03 · t04   < 3
+    const FF t06 = t00 + t01;                                 // t06 ← t00 + t01   < 4
+    const FF t07 = t05 - t06;                                 // t05 ← t05 − t06   < 2
+    const FF t08 = Y1 + Z1;                                   // t08 ← Y1 + Z1     < 4
+    const FF t09 = Y2 + Z2;                                   // t09 ← Y2 + Z2     < 4
+    const FF t10 = t08 * t09;                                 // t10 ← t08 · t09   < 3
+    const FF t11 = t01 + t02;                                 // t11 ← t01 + t02   < 4
+    const FF t12 = t10 - t11;                                 // t12 ← t10 − t11   < 2
+    const FF t13 = X1 + Z1;                                   // t13 ← X1 + Z1     < 4
+    const FF t14 = X2 + Z2;                                   // t14 ← X2 + Z2     < 4
+    const FF t15 = t13 * t14;                                 // t15 ← t13 · t14   < 3
+    const FF t16 = t00 + t02;                                 // t16 ← t00 + t02   < 4
+    const FF t17 = t15 - t16;                                 // t17 ← t15 − t16   < 2
+    const FF t18 = t00 + t00;                                 // t18 ← t00 + t00   < 2
+    const FF t19 = t18 + t00;                                 // t19 ← t18 + t00   < 2
     const FF t20 = FF::template mul_weierstrass_3b<Gen>(t02); // t20 ← b3 · t02    < 2
-    // const FF t20 = FF::template mul_unsigned<3>(FF::template mul_weierstrass_b<Gen>(t02)); // t20 ← b3 · t02    < 2
-    // const FF t20 =
-    // FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t02)); // t20 ← b3 · t02    < 2
-    const FF t21 = t01 + t20; // t21 ← t01 + t20   < 2
-    const FF t22 = t01 - t20; // t22 ← t01 − t20   < 2
+    const FF t21 = t01 + t20;                                 // t21 ← t01 + t20   < 2
+    const FF t22 = t01 - t20;                                 // t22 ← t01 − t20   < 2
     const FF t23 = FF::template mul_weierstrass_3b<Gen>(t17); // t23 ← b3 · t17    < 2
-    // const FF t23 = FF::template mul_unsigned<3>(FF::template mul_weierstrass_b<Gen>(t17)); // t23 ← b3 · t17    < 2
-    // const FF t23 =
-    // FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t17)); // t23 ← b3 · t17    < 2
-    const auto t24 = FF::mul_wide(t12, t23);                                         // t24 ← t12 · t23   < 2
-    const auto t25 = FF::mul_wide(t07, t22);                                         // t25 ← t07 · t22   < 2
-    const FF X3 = FF::reduce(t25 - t24);                                             // X3 ← t25 − t24    < 2
-    const auto t27 = FF::mul_wide(t23, t19);                                         // t27 ← t23 · t19   < 2
-    const auto t28 = FF::mul_wide(t22, t21);                                         // t28 ← t22 · t21   < 2
-    const FF Y3 = FF::reduce(t28 + t27);                                             // Y3 ← t28 + t27    < 2
-    const auto t30 = FF::mul_wide(t19, t07);                                         // t30 ← t19 · t07   < 2
-    const auto t31 = FF::mul_wide(t21, t12);                                         // t31 ← t21 · t12   < 2
-    const FF Z3 = FF::reduce(t31 + t30);                                             // Z3 ← t31 + t30    < 2
+    const auto t24 = FF::mul_wide(t12, t23);                  // t24 ← t12 · t23   < 2
+    const auto t25 = FF::mul_wide(t07, t22);                  // t25 ← t07 · t22   < 2
+    const FF X3 = FF::reduce(t25 - t24);                      // X3 ← t25 − t24    < 2
+    const auto t27 = FF::mul_wide(t23, t19);                  // t27 ← t23 · t19   < 2
+    const auto t28 = FF::mul_wide(t22, t21);                  // t28 ← t22 · t21   < 2
+    const FF Y3 = FF::reduce(t28 + t27);                      // Y3 ← t28 + t27    < 2
+    const auto t30 = FF::mul_wide(t19, t07);                  // t30 ← t19 · t07   < 2
+    const auto t31 = FF::mul_wide(t21, t12);                  // t31 ← t21 · t12   < 2
+    const FF Z3 = FF::reduce(t31 + t30);                      // Z3 ← t31 + t30    < 2
     return {X3, Y3, Z3};
   }
 
@@ -135,50 +127,44 @@ class Projective
 
   friend HOST_DEVICE Projective operator+(Projective p1, const Affine<FF>& p2)
   {
-    const FF X1 = p1.x;            //                   < 2
-    const FF Y1 = p1.y;            //                   < 2
-    const FF Z1 = p1.z;            //                   < 2
-    const FF X2 = p2.x;            //                   < 2
-    const FF Y2 = p2.y;            //                   < 2
-    const FF t00 = X1 * X2;        // t00 ← X1 · X2     < 2
-    const FF t01 = Y1 * Y2;        // t01 ← Y1 · Y2     < 2
-    const FF t02 = Z1;             // t02 ← Z1          < 2
-    const FF t03 = X1 + Y1;        // t03 ← X1 + Y1     < 4
-    const FF t04 = X2 + Y2;        // t04 ← X2 + Y2     < 4
-    const FF t05 = t03 * t04;      // t03 ← t03 · t04   < 3
-    const FF t06 = t00 + t01;      // t06 ← t00 + t01   < 4
-    const FF t07 = t05 - t06;      // t05 ← t05 − t06   < 2
-    const FF t08 = Y1 + Z1;        // t08 ← Y1 + Z1     < 4
-    const FF t09 = Y2 + FF::one(); // t09 ← Y2 + 1      < 4
-    const FF t10 = t08 * t09;      // t10 ← t08 · t09   < 3
-    const FF t11 = t01 + t02;      // t11 ← t01 + t02   < 4
-    const FF t12 = t10 - t11;      // t12 ← t10 − t11   < 2
-    const FF t13 = X1 + Z1;        // t13 ← X1 + Z1     < 4
-    const FF t14 = X2 + FF::one(); // t14 ← X2 + 1      < 4
-    const FF t15 = t13 * t14;      // t15 ← t13 · t14   < 3
-    const FF t16 = t00 + t02;      // t16 ← t00 + t02   < 4
-    const FF t17 = t15 - t16;      // t17 ← t15 − t16   < 2
-    const FF t18 = t00 + t00;      // t18 ← t00 + t00   < 2
-    const FF t19 = t18 + t00;      // t19 ← t18 + t00   < 2
+    const FF X1 = p1.x;                                       //                   < 2
+    const FF Y1 = p1.y;                                       //                   < 2
+    const FF Z1 = p1.z;                                       //                   < 2
+    const FF X2 = p2.x;                                       //                   < 2
+    const FF Y2 = p2.y;                                       //                   < 2
+    const FF t00 = X1 * X2;                                   // t00 ← X1 · X2     < 2
+    const FF t01 = Y1 * Y2;                                   // t01 ← Y1 · Y2     < 2
+    const FF t02 = Z1;                                        // t02 ← Z1          < 2
+    const FF t03 = X1 + Y1;                                   // t03 ← X1 + Y1     < 4
+    const FF t04 = X2 + Y2;                                   // t04 ← X2 + Y2     < 4
+    const FF t05 = t03 * t04;                                 // t03 ← t03 · t04   < 3
+    const FF t06 = t00 + t01;                                 // t06 ← t00 + t01   < 4
+    const FF t07 = t05 - t06;                                 // t05 ← t05 − t06   < 2
+    const FF t08 = Y1 + Z1;                                   // t08 ← Y1 + Z1     < 4
+    const FF t09 = Y2 + FF::one();                            // t09 ← Y2 + 1      < 4
+    const FF t10 = t08 * t09;                                 // t10 ← t08 · t09   < 3
+    const FF t11 = t01 + t02;                                 // t11 ← t01 + t02   < 4
+    const FF t12 = t10 - t11;                                 // t12 ← t10 − t11   < 2
+    const FF t13 = X1 + Z1;                                   // t13 ← X1 + Z1     < 4
+    const FF t14 = X2 + FF::one();                            // t14 ← X2 + 1      < 4
+    const FF t15 = t13 * t14;                                 // t15 ← t13 · t14   < 3
+    const FF t16 = t00 + t02;                                 // t16 ← t00 + t02   < 4
+    const FF t17 = t15 - t16;                                 // t17 ← t15 − t16   < 2
+    const FF t18 = t00 + t00;                                 // t18 ← t00 + t00   < 2
+    const FF t19 = t18 + t00;                                 // t19 ← t18 + t00   < 2
     const FF t20 = FF::template mul_weierstrass_3b<Gen>(t02); // t20 ← b3 · t02    < 2
-    // const FF t20 = FF::template mul_unsigned<3>(FF::template mul_weierstrass_b<Gen>(t02)); // t20 ← b3 · t02    < 2
-    // const FF t20 =
-    // FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t02)); // t20 ← b3 · t02    < 2
-    const FF t21 = t01 + t20; // t21 ← t01 + t20   < 2
-    const FF t22 = t01 - t20; // t22 ← t01 − t20   < 2
+    const FF t21 = t01 + t20;                                 // t21 ← t01 + t20   < 2
+    const FF t22 = t01 - t20;                                 // t22 ← t01 − t20   < 2
     const FF t23 = FF::template mul_weierstrass_3b<Gen>(t17); // t23 ← b3 · t17    < 2
-    // const FF t23 = FF::template mul_unsigned<3>(FF::template mul_weierstrass_b<Gen>(t17)); // t23 ← b3 · t17    < 2
-    // const FF t23 =
-    // FF::template mul_unsigned<3>(FF::template mul_const<Gen::weierstrass_b>(t17)); // t23 ← b3 · t17    < 2
-    const auto t24 = FF::mul_wide(t12, t23);                                         // t24 ← t12 · t23   < 2
-    const auto t25 = FF::mul_wide(t07, t22);                                         // t25 ← t07 · t22   < 2
-    const FF X3 = FF::reduce(t25 - t24);                                             // X3 ← t25 − t24    < 2
-    const auto t27 = FF::mul_wide(t23, t19);                                         // t27 ← t23 · t19   < 2
-    const auto t28 = FF::mul_wide(t22, t21);                                         // t28 ← t22 · t21   < 2
-    const FF Y3 = FF::reduce(t28 + t27);                                             // Y3 ← t28 + t27    < 2
-    const auto t30 = FF::mul_wide(t19, t07);                                         // t30 ← t19 · t07   < 2
-    const auto t31 = FF::mul_wide(t21, t12);                                         // t31 ← t21 · t12   < 2
-    const FF Z3 = FF::reduce(t31 + t30);                                             // Z3 ← t31 + t30    < 2
+    const auto t24 = FF::mul_wide(t12, t23);                  // t24 ← t12 · t23   < 2
+    const auto t25 = FF::mul_wide(t07, t22);                  // t25 ← t07 · t22   < 2
+    const FF X3 = FF::reduce(t25 - t24);                      // X3 ← t25 − t24    < 2
+    const auto t27 = FF::mul_wide(t23, t19);                  // t27 ← t23 · t19   < 2
+    const auto t28 = FF::mul_wide(t22, t21);                  // t28 ← t22 · t21   < 2
+    const FF Y3 = FF::reduce(t28 + t27);                      // Y3 ← t28 + t27    < 2
+    const auto t30 = FF::mul_wide(t19, t07);                  // t30 ← t19 · t07   < 2
+    const auto t31 = FF::mul_wide(t21, t12);                  // t31 ← t21 · t12   < 2
+    const FF Z3 = FF::reduce(t31 + t30);                      // Z3 ← t31 + t30    < 2
     return {X3, Y3, Z3};
   }
 
diff --git a/icicle/include/icicle/fields/complex_extension.h b/icicle/include/icicle/fields/complex_extension.h
index 42740859f..5a451759d 100644
--- a/icicle/include/icicle/fields/complex_extension.h
+++ b/icicle/include/icicle/fields/complex_extension.h
@@ -158,6 +158,52 @@ class ComplexExtensionField
     return !(xs == ys);
   }
 
+  template <typename Gen>
+  static HOST_DEVICE_INLINE FF mul_weierstrass_3b_real(const FF& xs)
+  {
+    FF r = {};
+    if constexpr (Gen::is_b_u32_g2_re) {
+      r = FF::template mul_unsigned<FF{Gen::weierstrass_3b_g2_re}.limbs_storage.limbs[0], FF>(xs);
+      if constexpr (Gen::is_b_neg_g2_re)
+        return FF::neg(r);
+      else {
+        return r;
+      }
+    } else {
+      return FF{Gen::weierstrass_3b_g2_re} * xs;
+    }
+  }
+
+  template <typename Gen>
+  static HOST_DEVICE_INLINE FF mul_weierstrass_3b_imag(const FF& xs)
+  {
+    FF r = {};
+    if constexpr (Gen::is_b_u32_g2_im) {
+      r = FF::template mul_unsigned<FF{Gen::weierstrass_3b_g2_im}.limbs_storage.limbs[0], FF>(xs);
+      if constexpr (Gen::is_b_neg_g2_im)
+        return FF::neg(r);
+      else {
+        return r;
+      }
+    } else {
+      return FF{Gen::weierstrass_3b_g2_im} * xs;
+    }
+  }
+
+  template <typename Gen>
+  static HOST_DEVICE_INLINE ComplexExtensionField mul_weierstrass_3b(const ComplexExtensionField& xs)
+  {
+    const FF xs_real = xs.real;
+    const FF xs_imaginary = xs.imaginary;
+    FF real_prod = mul_weierstrass_3b_real<Gen>(xs_real);
+    FF imaginary_prod = mul_weierstrass_3b_imag<Gen>(xs_imaginary);
+    FF re_im = mul_weierstrass_3b_real<Gen>(xs_imaginary);
+    FF im_re = mul_weierstrass_3b_imag<Gen>(xs_real);
+    FF nonresidue_times_im = FF::template mul_unsigned<CONFIG::nonresidue>(imaginary_prod);
+    nonresidue_times_im = CONFIG::nonresidue_is_negative ? FF::neg(nonresidue_times_im) : nonresidue_times_im;
+    return ComplexExtensionField{real_prod + nonresidue_times_im, re_im + im_re};
+  }
+
   template <const ComplexExtensionField& multiplier>
   static HOST_DEVICE_INLINE ComplexExtensionField mul_const(const ComplexExtensionField& xs)
   {
diff --git a/icicle/include/icicle/fields/field.h b/icicle/include/icicle/fields/field.h
index 47ebf3c07..4fe5891c2 100644
--- a/icicle/include/icicle/fields/field.h
+++ b/icicle/include/icicle/fields/field.h
@@ -875,22 +875,6 @@ class Field
 
   friend HOST_DEVICE bool operator!=(const Field& xs, const Field& ys) { return !(xs == ys); }
 
-template <typename Gen>
-  static HOST_DEVICE_INLINE Field mul_weierstrass_b(const Field& xs)
-  {
-    Field r = {};
-    if constexpr (Gen::is_b_u32) {
-      r = mul_unsigned<Field{Gen::weierstrass_b}.limbs_storage.limbs[0], Field>(xs);
-      if constexpr (Gen::is_b_neg)
-        return neg(r);
-      else {
-        return r;
-      }
-    } else {
-      return Field{Gen::weierstrass_b} * xs;
-    }
-  }
-
   template <typename Gen>
   static HOST_DEVICE_INLINE Field mul_weierstrass_3b(const Field& xs)
   {

From cb5fe00a1d40e3a9fd864e8030cd220cd77825f7 Mon Sep 17 00:00:00 2001
From: hadaringonyama <hadar@ingonyama.com>
Date: Thu, 2 Jan 2025 17:41:22 +0200
Subject: [PATCH 3/5] fix is_on_curve func

---
 icicle/include/icicle/curves/projective.h     |  2 +-
 .../include/icicle/fields/complex_extension.h | 46 +++++++++++++++++++
 icicle/include/icicle/fields/field.h          | 16 +++++++
 3 files changed, 63 insertions(+), 1 deletion(-)

diff --git a/icicle/include/icicle/curves/projective.h b/icicle/include/icicle/curves/projective.h
index 0ba8eefc8..7974cbd16 100644
--- a/icicle/include/icicle/curves/projective.h
+++ b/icicle/include/icicle/curves/projective.h
@@ -231,7 +231,7 @@ class Projective
   {
     if (is_zero(point)) return true;
     bool eq_holds =
-      (FF::template mul_const<Gen::weierstrass_b>(FF::sqr(point.z) * point.z) + FF::sqr(point.x) * point.x ==
+      (FF::template mul_weierstrass_b<Gen>(FF::sqr(point.z) * point.z) + FF::sqr(point.x) * point.x ==
        point.z * FF::sqr(point.y));
     return point.z != FF::zero() && eq_holds;
   }
diff --git a/icicle/include/icicle/fields/complex_extension.h b/icicle/include/icicle/fields/complex_extension.h
index 5a451759d..aac882c82 100644
--- a/icicle/include/icicle/fields/complex_extension.h
+++ b/icicle/include/icicle/fields/complex_extension.h
@@ -158,6 +158,52 @@ class ComplexExtensionField
     return !(xs == ys);
   }
 
+  template <typename Gen>
+  static HOST_DEVICE_INLINE FF mul_weierstrass_b_real(const FF& xs)
+  {
+    FF r = {};
+    if constexpr (Gen::is_b_u32_g2_re) {
+      r = FF::template mul_unsigned<FF{Gen::weierstrass_b_g2_re}.limbs_storage.limbs[0], FF>(xs);
+      if constexpr (Gen::is_b_neg_g2_re)
+        return FF::neg(r);
+      else {
+        return r;
+      }
+    } else {
+      return FF{Gen::weierstrass_b_g2_re} * xs;
+    }
+  }
+
+  template <typename Gen>
+  static HOST_DEVICE_INLINE FF mul_weierstrass_b_imag(const FF& xs)
+  {
+    FF r = {};
+    if constexpr (Gen::is_b_u32_g2_im) {
+      r = FF::template mul_unsigned<FF{Gen::weierstrass_b_g2_im}.limbs_storage.limbs[0], FF>(xs);
+      if constexpr (Gen::is_b_neg_g2_im)
+        return FF::neg(r);
+      else {
+        return r;
+      }
+    } else {
+      return FF{Gen::weierstrass_b_g2_im} * xs;
+    }
+  }
+
+  template <typename Gen>
+  static HOST_DEVICE_INLINE ComplexExtensionField mul_weierstrass_b(const ComplexExtensionField& xs)
+  {
+    const FF xs_real = xs.real;
+    const FF xs_imaginary = xs.imaginary;
+    FF real_prod = mul_weierstrass_b_real<Gen>(xs_real);
+    FF imaginary_prod = mul_weierstrass_b_imag<Gen>(xs_imaginary);
+    FF re_im = mul_weierstrass_b_real<Gen>(xs_imaginary);
+    FF im_re = mul_weierstrass_b_imag<Gen>(xs_real);
+    FF nonresidue_times_im = FF::template mul_unsigned<CONFIG::nonresidue>(imaginary_prod);
+    nonresidue_times_im = CONFIG::nonresidue_is_negative ? FF::neg(nonresidue_times_im) : nonresidue_times_im;
+    return ComplexExtensionField{real_prod + nonresidue_times_im, re_im + im_re};
+  }
+
   template <typename Gen>
   static HOST_DEVICE_INLINE FF mul_weierstrass_3b_real(const FF& xs)
   {
diff --git a/icicle/include/icicle/fields/field.h b/icicle/include/icicle/fields/field.h
index 4fe5891c2..8f787ec46 100644
--- a/icicle/include/icicle/fields/field.h
+++ b/icicle/include/icicle/fields/field.h
@@ -875,6 +875,22 @@ class Field
 
   friend HOST_DEVICE bool operator!=(const Field& xs, const Field& ys) { return !(xs == ys); }
 
+  template <typename Gen>
+  static HOST_DEVICE_INLINE Field mul_weierstrass_b(const Field& xs)
+  {
+    Field r = {};
+    if constexpr (Gen::is_b_u32) {
+      r = mul_unsigned<Field{Gen::weierstrass_b}.limbs_storage.limbs[0], Field>(xs);
+      if constexpr (Gen::is_b_neg)
+        return neg(r);
+      else {
+        return r;
+      }
+    } else {
+      return Field{Gen::weierstrass_b} * xs;
+    }
+  }
+
   template <typename Gen>
   static HOST_DEVICE_INLINE Field mul_weierstrass_3b(const Field& xs)
   {

From 8e234825049dda5d76e6ca51d2b1de723dc231fa Mon Sep 17 00:00:00 2001
From: hadaringonyama <hadar@ingonyama.com>
Date: Mon, 6 Jan 2025 16:08:53 +0200
Subject: [PATCH 4/5] 3b computation

---
 .../include/icicle/curves/params/bls12_377.h  |  10 +-
 .../include/icicle/curves/params/bls12_381.h  |  10 +-
 icicle/include/icicle/curves/params/bn254.h   |   7 +-
 icicle/include/icicle/curves/params/bw6_761.h |   8 -
 .../include/icicle/curves/params/grumpkin.h   |   3 +-
 icicle/include/icicle/curves/projective.h     | 190 +++++++++---------
 .../include/icicle/fields/complex_extension.h |  60 +++++-
 icicle/include/icicle/fields/field.h          |  42 ++--
 8 files changed, 171 insertions(+), 159 deletions(-)

diff --git a/icicle/include/icicle/curves/params/bls12_377.h b/icicle/include/icicle/curves/params/bls12_377.h
index 71089f8f8..6ad767e5f 100644
--- a/icicle/include/icicle/curves/params/bls12_377.h
+++ b/icicle/include/icicle/curves/params/bls12_377.h
@@ -25,9 +25,7 @@ namespace bls12_377 {
     static constexpr point_field_t weierstrass_b = {0x00000001, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
-    static constexpr point_field_t weierstrass_3b = {0x00000003, 0x00000000, 0x00000000, 0x00000000,
-                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000,
-                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
+
     static constexpr bool is_b_u32 = true;
     static constexpr bool is_b_neg = false;
   }; // G1
@@ -51,12 +49,6 @@ namespace bls12_377 {
     static constexpr point_field_t weierstrass_b_g2_im = {0x9999999a, 0x1c9ed999, 0x1ccccccd, 0x0dd39e5c,
                                                           0x3c6bf800, 0x129207b6, 0xcd5fd889, 0xdc7b4f91,
                                                           0x7460c589, 0x43bd0373, 0xdb0fd6f3, 0x010222f6};
-    static constexpr point_field_t weierstrass_3b_g2_re = {0x00000000, 0x00000000, 0x00000000, 0x00000000,
-                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000,
-                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000};
-    static constexpr point_field_t weierstrass_3b_g2_im = {0xcccccccd, 0xd0d3cccc, 0x26666666, 0x126f7dd0,
-                                                           0xfb3aa000, 0x18c2b4f2, 0x672a760c, 0x7b4f14c2,
-                                                           0xf0810762, 0x04fc0499, 0x796a73ef, 0x01582e9e};
 
     static constexpr bool is_b_u32_g2_re = true;
     static constexpr bool is_b_neg_g2_re = false;
diff --git a/icicle/include/icicle/curves/params/bls12_381.h b/icicle/include/icicle/curves/params/bls12_381.h
index 116af3c14..18fbf9749 100644
--- a/icicle/include/icicle/curves/params/bls12_381.h
+++ b/icicle/include/icicle/curves/params/bls12_381.h
@@ -25,9 +25,7 @@ namespace bls12_381 {
     static constexpr point_field_t weierstrass_b = {0x00000004, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
-    static constexpr point_field_t weierstrass_3b = {0x0000000c, 0x00000000, 0x00000000, 0x00000000,
-                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000,
-                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
+
     static constexpr bool is_b_u32 = true;
     static constexpr bool is_b_neg = false;
   };
@@ -52,12 +50,6 @@ namespace bls12_381 {
     static constexpr point_field_t weierstrass_b_g2_im = {0x00000004, 0x00000000, 0x00000000, 0x00000000,
                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000,
                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000};
-    static constexpr point_field_t weierstrass_3b_g2_re = {0x0000000c, 0x00000000, 0x00000000, 0x00000000,
-                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000,
-                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000};
-    static constexpr point_field_t weierstrass_3b_g2_im = {0x0000000c, 0x00000000, 0x00000000, 0x00000000,
-                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000,
-                                                           0x00000000, 0x00000000, 0x00000000, 0x00000000};
 
     static constexpr bool is_b_u32_g2_re = true;
     static constexpr bool is_b_neg_g2_re = false;
diff --git a/icicle/include/icicle/curves/params/bn254.h b/icicle/include/icicle/curves/params/bn254.h
index 9c2b8c5fa..0a628afcb 100644
--- a/icicle/include/icicle/curves/params/bn254.h
+++ b/icicle/include/icicle/curves/params/bn254.h
@@ -24,8 +24,7 @@ namespace bn254 {
                                             0x00000000, 0x00000000, 0x00000000, 0x00000000};
     static constexpr point_field_t weierstrass_b = {0x00000003, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
-    static constexpr point_field_t weierstrass_3b = {0x00000009, 0x00000000, 0x00000000, 0x00000000,
-                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
+
     static constexpr bool is_b_u32 = true;
     static constexpr bool is_b_neg = false;
   }; // G1
@@ -43,10 +42,6 @@ namespace bn254 {
                                                           0x1be06ac3, 0x81be1899, 0xceb8aaae, 0x2b149d40};
     static constexpr point_field_t weierstrass_b_g2_im = {0x85c315d2, 0xe4a2bd06, 0xe52d1852, 0xa74fa084,
                                                           0xeed8fdf4, 0xcd2cafad, 0x3af0fed4, 0x009713b0};
-    static constexpr point_field_t weierstrass_3b_g2_re = {0xbce9b021, 0x1ef69c66, 0x3cb039cf, 0xf21b7c8d,
-                                                           0x509e8f8f, 0x1499be5e, 0xa9c6bfb8, 0x20753adc};
-    static constexpr point_field_t weierstrass_3b_g2_im = {0x91494176, 0xade83713, 0xaf8748f8, 0xf5eee18e,
-                                                           0xcc8af9dd, 0x67860f09, 0xb0d2fc7e, 0x01c53b10};
 
     static constexpr bool is_b_u32_g2_re = false;
     static constexpr bool is_b_neg_g2_re = false;
diff --git a/icicle/include/icicle/curves/params/bw6_761.h b/icicle/include/icicle/curves/params/bw6_761.h
index 12d19b50f..7760c2023 100644
--- a/icicle/include/icicle/curves/params/bw6_761.h
+++ b/icicle/include/icicle/curves/params/bw6_761.h
@@ -34,10 +34,6 @@ namespace bw6_761 {
       0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
       0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
       0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
-    static constexpr point_field_t weierstrass_3b = {
-      0x00000003, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
-      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
-      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
 
     static constexpr bool is_b_u32 = true;
     static constexpr bool is_b_neg = true;
@@ -56,10 +52,6 @@ namespace bw6_761 {
       0x00000004, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
       0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
       0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
-    static constexpr g2_point_field_t weierstrass_3b = {
-      0x0000000c, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
-      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
-      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
 
     static constexpr bool is_b_u32 = true;
     static constexpr bool is_b_neg = false;
diff --git a/icicle/include/icicle/curves/params/grumpkin.h b/icicle/include/icicle/curves/params/grumpkin.h
index e968589bc..d09390bcc 100644
--- a/icicle/include/icicle/curves/params/grumpkin.h
+++ b/icicle/include/icicle/curves/params/grumpkin.h
@@ -21,8 +21,7 @@ namespace grumpkin {
     // 0x8181585d, 0xb85045b6, 0xe131a029, 0x30644e72};
     static constexpr point_field_t weierstrass_b = {0x00000011, 0x00000000, 0x00000000, 0x00000000,
                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
-    static constexpr point_field_t weierstrass_3b = {0x00000033, 0x00000000, 0x00000000, 0x00000000,
-                                                     0x00000000, 0x00000000, 0x00000000, 0x00000000};
+
     static constexpr bool is_b_u32 = true;
     static constexpr bool is_b_neg = true;
   }; // G1
diff --git a/icicle/include/icicle/curves/projective.h b/icicle/include/icicle/curves/projective.h
index 7974cbd16..17cf9329c 100644
--- a/icicle/include/icicle/curves/projective.h
+++ b/icicle/include/icicle/curves/projective.h
@@ -58,68 +58,68 @@ class Projective
     const FF Z = point.z;
 
     // TODO: Change to efficient dbl once implemented for field.cuh
-    FF t0 = FF::sqr(Y);                            // 1. t0 ← Y · Y
-    FF Z3 = t0 + t0;                               // 2. Z3 ← t0 + t0
-    Z3 = Z3 + Z3;                                  // 3. Z3 ← Z3 + Z3
-    Z3 = Z3 + Z3;                                  // 4. Z3 ← Z3 + Z3
-    FF t1 = Y * Z;                                 // 5. t1 ← Y · Z
-    FF t2 = FF::sqr(Z);                            // 6. t2 ← Z · Z
-    t2 = FF::template mul_weierstrass_3b<Gen>(t2); // 7. t2 ← b3 · t2
-    FF X3 = t2 * Z3;                               // 8. X3 ← t2 · Z3
-    FF Y3 = t0 + t2;                               // 9. Y3 ← t0 + t2
-    Z3 = t1 * Z3;                                  // 10. Z3 ← t1 · Z3
-    t1 = t2 + t2;                                  // 11. t1 ← t2 + t2
-    t2 = t1 + t2;                                  // 12. t2 ← t1 + t2
-    t0 = t0 - t2;                                  // 13. t0 ← t0 − t2
-    Y3 = t0 * Y3;                                  // 14. Y3 ← t0 · Y3
-    Y3 = X3 + Y3;                                  // 15. Y3 ← X3 + Y3
-    t1 = X * Y;                                    // 16. t1 ← X · Y
-    X3 = t0 * t1;                                  // 17. X3 ← t0 · t1
-    X3 = X3 + X3;                                  // 18. X3 ← X3 + X3
+    FF t0 = FF::sqr(Y);                                 // 1. t0 ← Y · Y
+    FF Z3 = t0 + t0;                                    // 2. Z3 ← t0 + t0
+    Z3 = Z3 + Z3;                                       // 3. Z3 ← Z3 + Z3
+    Z3 = Z3 + Z3;                                       // 4. Z3 ← Z3 + Z3
+    FF t1 = Y * Z;                                      // 5. t1 ← Y · Z
+    FF t2 = FF::sqr(Z);                                 // 6. t2 ← Z · Z
+    t2 = FF::template mul_weierstrass_b<Gen, true>(t2); // 7. t2 ← b3 · t2
+    FF X3 = t2 * Z3;                                    // 8. X3 ← t2 · Z3
+    FF Y3 = t0 + t2;                                    // 9. Y3 ← t0 + t2
+    Z3 = t1 * Z3;                                       // 10. Z3 ← t1 · Z3
+    t1 = t2 + t2;                                       // 11. t1 ← t2 + t2
+    t2 = t1 + t2;                                       // 12. t2 ← t1 + t2
+    t0 = t0 - t2;                                       // 13. t0 ← t0 − t2
+    Y3 = t0 * Y3;                                       // 14. Y3 ← t0 · Y3
+    Y3 = X3 + Y3;                                       // 15. Y3 ← X3 + Y3
+    t1 = X * Y;                                         // 16. t1 ← X · Y
+    X3 = t0 * t1;                                       // 17. X3 ← t0 · t1
+    X3 = X3 + X3;                                       // 18. X3 ← X3 + X3
     return {X3, Y3, Z3};
   }
 
   friend HOST_DEVICE Projective operator+(Projective p1, const Projective& p2)
   {
-    const FF X1 = p1.x;                                       //                   < 2
-    const FF Y1 = p1.y;                                       //                   < 2
-    const FF Z1 = p1.z;                                       //                   < 2
-    const FF X2 = p2.x;                                       //                   < 2
-    const FF Y2 = p2.y;                                       //                   < 2
-    const FF Z2 = p2.z;                                       //                   < 2
-    const FF t00 = X1 * X2;                                   // t00 ← X1 · X2     < 2
-    const FF t01 = Y1 * Y2;                                   // t01 ← Y1 · Y2     < 2
-    const FF t02 = Z1 * Z2;                                   // t02 ← Z1 · Z2     < 2
-    const FF t03 = X1 + Y1;                                   // t03 ← X1 + Y1     < 4
-    const FF t04 = X2 + Y2;                                   // t04 ← X2 + Y2     < 4
-    const FF t05 = t03 * t04;                                 // t03 ← t03 · t04   < 3
-    const FF t06 = t00 + t01;                                 // t06 ← t00 + t01   < 4
-    const FF t07 = t05 - t06;                                 // t05 ← t05 − t06   < 2
-    const FF t08 = Y1 + Z1;                                   // t08 ← Y1 + Z1     < 4
-    const FF t09 = Y2 + Z2;                                   // t09 ← Y2 + Z2     < 4
-    const FF t10 = t08 * t09;                                 // t10 ← t08 · t09   < 3
-    const FF t11 = t01 + t02;                                 // t11 ← t01 + t02   < 4
-    const FF t12 = t10 - t11;                                 // t12 ← t10 − t11   < 2
-    const FF t13 = X1 + Z1;                                   // t13 ← X1 + Z1     < 4
-    const FF t14 = X2 + Z2;                                   // t14 ← X2 + Z2     < 4
-    const FF t15 = t13 * t14;                                 // t15 ← t13 · t14   < 3
-    const FF t16 = t00 + t02;                                 // t16 ← t00 + t02   < 4
-    const FF t17 = t15 - t16;                                 // t17 ← t15 − t16   < 2
-    const FF t18 = t00 + t00;                                 // t18 ← t00 + t00   < 2
-    const FF t19 = t18 + t00;                                 // t19 ← t18 + t00   < 2
-    const FF t20 = FF::template mul_weierstrass_3b<Gen>(t02); // t20 ← b3 · t02    < 2
-    const FF t21 = t01 + t20;                                 // t21 ← t01 + t20   < 2
-    const FF t22 = t01 - t20;                                 // t22 ← t01 − t20   < 2
-    const FF t23 = FF::template mul_weierstrass_3b<Gen>(t17); // t23 ← b3 · t17    < 2
-    const auto t24 = FF::mul_wide(t12, t23);                  // t24 ← t12 · t23   < 2
-    const auto t25 = FF::mul_wide(t07, t22);                  // t25 ← t07 · t22   < 2
-    const FF X3 = FF::reduce(t25 - t24);                      // X3 ← t25 − t24    < 2
-    const auto t27 = FF::mul_wide(t23, t19);                  // t27 ← t23 · t19   < 2
-    const auto t28 = FF::mul_wide(t22, t21);                  // t28 ← t22 · t21   < 2
-    const FF Y3 = FF::reduce(t28 + t27);                      // Y3 ← t28 + t27    < 2
-    const auto t30 = FF::mul_wide(t19, t07);                  // t30 ← t19 · t07   < 2
-    const auto t31 = FF::mul_wide(t21, t12);                  // t31 ← t21 · t12   < 2
-    const FF Z3 = FF::reduce(t31 + t30);                      // Z3 ← t31 + t30    < 2
+    const FF X1 = p1.x;                                            //                   < 2
+    const FF Y1 = p1.y;                                            //                   < 2
+    const FF Z1 = p1.z;                                            //                   < 2
+    const FF X2 = p2.x;                                            //                   < 2
+    const FF Y2 = p2.y;                                            //                   < 2
+    const FF Z2 = p2.z;                                            //                   < 2
+    const FF t00 = X1 * X2;                                        // t00 ← X1 · X2     < 2
+    const FF t01 = Y1 * Y2;                                        // t01 ← Y1 · Y2     < 2
+    const FF t02 = Z1 * Z2;                                        // t02 ← Z1 · Z2     < 2
+    const FF t03 = X1 + Y1;                                        // t03 ← X1 + Y1     < 4
+    const FF t04 = X2 + Y2;                                        // t04 ← X2 + Y2     < 4
+    const FF t05 = t03 * t04;                                      // t03 ← t03 · t04   < 3
+    const FF t06 = t00 + t01;                                      // t06 ← t00 + t01   < 4
+    const FF t07 = t05 - t06;                                      // t05 ← t05 − t06   < 2
+    const FF t08 = Y1 + Z1;                                        // t08 ← Y1 + Z1     < 4
+    const FF t09 = Y2 + Z2;                                        // t09 ← Y2 + Z2     < 4
+    const FF t10 = t08 * t09;                                      // t10 ← t08 · t09   < 3
+    const FF t11 = t01 + t02;                                      // t11 ← t01 + t02   < 4
+    const FF t12 = t10 - t11;                                      // t12 ← t10 − t11   < 2
+    const FF t13 = X1 + Z1;                                        // t13 ← X1 + Z1     < 4
+    const FF t14 = X2 + Z2;                                        // t14 ← X2 + Z2     < 4
+    const FF t15 = t13 * t14;                                      // t15 ← t13 · t14   < 3
+    const FF t16 = t00 + t02;                                      // t16 ← t00 + t02   < 4
+    const FF t17 = t15 - t16;                                      // t17 ← t15 − t16   < 2
+    const FF t18 = t00 + t00;                                      // t18 ← t00 + t00   < 2
+    const FF t19 = t18 + t00;                                      // t19 ← t18 + t00   < 2
+    const FF t20 = FF::template mul_weierstrass_b<Gen, true>(t02); // t20 ← b3 · t02    < 2
+    const FF t21 = t01 + t20;                                      // t21 ← t01 + t20   < 2
+    const FF t22 = t01 - t20;                                      // t22 ← t01 − t20   < 2
+    const FF t23 = FF::template mul_weierstrass_b<Gen, true>(t17); // t23 ← b3 · t17    < 2
+    const auto t24 = FF::mul_wide(t12, t23);                       // t24 ← t12 · t23   < 2
+    const auto t25 = FF::mul_wide(t07, t22);                       // t25 ← t07 · t22   < 2
+    const FF X3 = FF::reduce(t25 - t24);                           // X3 ← t25 − t24    < 2
+    const auto t27 = FF::mul_wide(t23, t19);                       // t27 ← t23 · t19   < 2
+    const auto t28 = FF::mul_wide(t22, t21);                       // t28 ← t22 · t21   < 2
+    const FF Y3 = FF::reduce(t28 + t27);                           // Y3 ← t28 + t27    < 2
+    const auto t30 = FF::mul_wide(t19, t07);                       // t30 ← t19 · t07   < 2
+    const auto t31 = FF::mul_wide(t21, t12);                       // t31 ← t21 · t12   < 2
+    const FF Z3 = FF::reduce(t31 + t30);                           // Z3 ← t31 + t30    < 2
     return {X3, Y3, Z3};
   }
 
@@ -127,44 +127,44 @@ class Projective
 
   friend HOST_DEVICE Projective operator+(Projective p1, const Affine<FF>& p2)
   {
-    const FF X1 = p1.x;                                       //                   < 2
-    const FF Y1 = p1.y;                                       //                   < 2
-    const FF Z1 = p1.z;                                       //                   < 2
-    const FF X2 = p2.x;                                       //                   < 2
-    const FF Y2 = p2.y;                                       //                   < 2
-    const FF t00 = X1 * X2;                                   // t00 ← X1 · X2     < 2
-    const FF t01 = Y1 * Y2;                                   // t01 ← Y1 · Y2     < 2
-    const FF t02 = Z1;                                        // t02 ← Z1          < 2
-    const FF t03 = X1 + Y1;                                   // t03 ← X1 + Y1     < 4
-    const FF t04 = X2 + Y2;                                   // t04 ← X2 + Y2     < 4
-    const FF t05 = t03 * t04;                                 // t03 ← t03 · t04   < 3
-    const FF t06 = t00 + t01;                                 // t06 ← t00 + t01   < 4
-    const FF t07 = t05 - t06;                                 // t05 ← t05 − t06   < 2
-    const FF t08 = Y1 + Z1;                                   // t08 ← Y1 + Z1     < 4
-    const FF t09 = Y2 + FF::one();                            // t09 ← Y2 + 1      < 4
-    const FF t10 = t08 * t09;                                 // t10 ← t08 · t09   < 3
-    const FF t11 = t01 + t02;                                 // t11 ← t01 + t02   < 4
-    const FF t12 = t10 - t11;                                 // t12 ← t10 − t11   < 2
-    const FF t13 = X1 + Z1;                                   // t13 ← X1 + Z1     < 4
-    const FF t14 = X2 + FF::one();                            // t14 ← X2 + 1      < 4
-    const FF t15 = t13 * t14;                                 // t15 ← t13 · t14   < 3
-    const FF t16 = t00 + t02;                                 // t16 ← t00 + t02   < 4
-    const FF t17 = t15 - t16;                                 // t17 ← t15 − t16   < 2
-    const FF t18 = t00 + t00;                                 // t18 ← t00 + t00   < 2
-    const FF t19 = t18 + t00;                                 // t19 ← t18 + t00   < 2
-    const FF t20 = FF::template mul_weierstrass_3b<Gen>(t02); // t20 ← b3 · t02    < 2
-    const FF t21 = t01 + t20;                                 // t21 ← t01 + t20   < 2
-    const FF t22 = t01 - t20;                                 // t22 ← t01 − t20   < 2
-    const FF t23 = FF::template mul_weierstrass_3b<Gen>(t17); // t23 ← b3 · t17    < 2
-    const auto t24 = FF::mul_wide(t12, t23);                  // t24 ← t12 · t23   < 2
-    const auto t25 = FF::mul_wide(t07, t22);                  // t25 ← t07 · t22   < 2
-    const FF X3 = FF::reduce(t25 - t24);                      // X3 ← t25 − t24    < 2
-    const auto t27 = FF::mul_wide(t23, t19);                  // t27 ← t23 · t19   < 2
-    const auto t28 = FF::mul_wide(t22, t21);                  // t28 ← t22 · t21   < 2
-    const FF Y3 = FF::reduce(t28 + t27);                      // Y3 ← t28 + t27    < 2
-    const auto t30 = FF::mul_wide(t19, t07);                  // t30 ← t19 · t07   < 2
-    const auto t31 = FF::mul_wide(t21, t12);                  // t31 ← t21 · t12   < 2
-    const FF Z3 = FF::reduce(t31 + t30);                      // Z3 ← t31 + t30    < 2
+    const FF X1 = p1.x;                                            //                   < 2
+    const FF Y1 = p1.y;                                            //                   < 2
+    const FF Z1 = p1.z;                                            //                   < 2
+    const FF X2 = p2.x;                                            //                   < 2
+    const FF Y2 = p2.y;                                            //                   < 2
+    const FF t00 = X1 * X2;                                        // t00 ← X1 · X2     < 2
+    const FF t01 = Y1 * Y2;                                        // t01 ← Y1 · Y2     < 2
+    const FF t02 = Z1;                                             // t02 ← Z1          < 2
+    const FF t03 = X1 + Y1;                                        // t03 ← X1 + Y1     < 4
+    const FF t04 = X2 + Y2;                                        // t04 ← X2 + Y2     < 4
+    const FF t05 = t03 * t04;                                      // t03 ← t03 · t04   < 3
+    const FF t06 = t00 + t01;                                      // t06 ← t00 + t01   < 4
+    const FF t07 = t05 - t06;                                      // t05 ← t05 − t06   < 2
+    const FF t08 = Y1 + Z1;                                        // t08 ← Y1 + Z1     < 4
+    const FF t09 = Y2 + FF::one();                                 // t09 ← Y2 + 1      < 4
+    const FF t10 = t08 * t09;                                      // t10 ← t08 · t09   < 3
+    const FF t11 = t01 + t02;                                      // t11 ← t01 + t02   < 4
+    const FF t12 = t10 - t11;                                      // t12 ← t10 − t11   < 2
+    const FF t13 = X1 + Z1;                                        // t13 ← X1 + Z1     < 4
+    const FF t14 = X2 + FF::one();                                 // t14 ← X2 + 1      < 4
+    const FF t15 = t13 * t14;                                      // t15 ← t13 · t14   < 3
+    const FF t16 = t00 + t02;                                      // t16 ← t00 + t02   < 4
+    const FF t17 = t15 - t16;                                      // t17 ← t15 − t16   < 2
+    const FF t18 = t00 + t00;                                      // t18 ← t00 + t00   < 2
+    const FF t19 = t18 + t00;                                      // t19 ← t18 + t00   < 2
+    const FF t20 = FF::template mul_weierstrass_b<Gen, true>(t02); // t20 ← b3 · t02    < 2
+    const FF t21 = t01 + t20;                                      // t21 ← t01 + t20   < 2
+    const FF t22 = t01 - t20;                                      // t22 ← t01 − t20   < 2
+    const FF t23 = FF::template mul_weierstrass_b<Gen, true>(t17); // t23 ← b3 · t17    < 2
+    const auto t24 = FF::mul_wide(t12, t23);                       // t24 ← t12 · t23   < 2
+    const auto t25 = FF::mul_wide(t07, t22);                       // t25 ← t07 · t22   < 2
+    const FF X3 = FF::reduce(t25 - t24);                           // X3 ← t25 − t24    < 2
+    const auto t27 = FF::mul_wide(t23, t19);                       // t27 ← t23 · t19   < 2
+    const auto t28 = FF::mul_wide(t22, t21);                       // t28 ← t22 · t21   < 2
+    const FF Y3 = FF::reduce(t28 + t27);                           // Y3 ← t28 + t27    < 2
+    const auto t30 = FF::mul_wide(t19, t07);                       // t30 ← t19 · t07   < 2
+    const auto t31 = FF::mul_wide(t21, t12);                       // t31 ← t21 · t12   < 2
+    const FF Z3 = FF::reduce(t31 + t30);                           // Z3 ← t31 + t30    < 2
     return {X3, Y3, Z3};
   }
 
diff --git a/icicle/include/icicle/fields/complex_extension.h b/icicle/include/icicle/fields/complex_extension.h
index aac882c82..6879048df 100644
--- a/icicle/include/icicle/fields/complex_extension.h
+++ b/icicle/include/icicle/fields/complex_extension.h
@@ -158,47 +158,85 @@ class ComplexExtensionField
     return !(xs == ys);
   }
 
-  template <typename Gen>
+  template <typename Gen, bool IS_3B = false>
   static HOST_DEVICE_INLINE FF mul_weierstrass_b_real(const FF& xs)
   {
     FF r = {};
+    constexpr FF b_mult = []() {
+      FF b_mult = FF{Gen::weierstrass_b_g2_re};
+      if constexpr (!IS_3B) return b_mult;
+      typename FF::ff_storage temp = {};
+      typename FF::ff_storage modulus = FF::get_modulus();
+      host_math::template add_sub_limbs<CONFIG::limbs_count, false, false, true>(
+        b_mult.limbs_storage, b_mult.limbs_storage, b_mult.limbs_storage);
+      b_mult.limbs_storage =
+        host_math::template add_sub_limbs<CONFIG::limbs_count, true, true, true>(b_mult.limbs_storage, modulus, temp)
+          ? b_mult.limbs_storage
+          : temp;
+      host_math::template add_sub_limbs<CONFIG::limbs_count, false, false, true>(
+        b_mult.limbs_storage, FF{Gen::weierstrass_b_g2_re}.limbs_storage, b_mult.limbs_storage);
+      b_mult.limbs_storage =
+        host_math::template add_sub_limbs<CONFIG::limbs_count, true, true, true>(b_mult.limbs_storage, modulus, temp)
+          ? b_mult.limbs_storage
+          : temp;
+      return b_mult;
+    }();
     if constexpr (Gen::is_b_u32_g2_re) {
-      r = FF::template mul_unsigned<FF{Gen::weierstrass_b_g2_re}.limbs_storage.limbs[0], FF>(xs);
+      r = FF::template mul_unsigned<b_mult.limbs_storage.limbs[0], FF>(xs);
       if constexpr (Gen::is_b_neg_g2_re)
         return FF::neg(r);
       else {
         return r;
       }
     } else {
-      return FF{Gen::weierstrass_b_g2_re} * xs;
+      return b_mult * xs;
     }
   }
 
-  template <typename Gen>
+  template <typename Gen, bool IS_3B = false>
   static HOST_DEVICE_INLINE FF mul_weierstrass_b_imag(const FF& xs)
   {
     FF r = {};
+    constexpr FF b_mult = []() {
+      FF b_mult = FF{Gen::weierstrass_b_g2_im};
+      if constexpr (!IS_3B) return b_mult;
+      typename FF::ff_storage temp = {};
+      typename FF::ff_storage modulus = FF::get_modulus();
+      host_math::template add_sub_limbs<CONFIG::limbs_count, false, false, true>(
+        b_mult.limbs_storage, b_mult.limbs_storage, b_mult.limbs_storage);
+      b_mult.limbs_storage =
+        host_math::template add_sub_limbs<CONFIG::limbs_count, true, true, true>(b_mult.limbs_storage, modulus, temp)
+          ? b_mult.limbs_storage
+          : temp;
+      host_math::template add_sub_limbs<CONFIG::limbs_count, false, false, true>(
+        b_mult.limbs_storage, FF{Gen::weierstrass_b_g2_im}.limbs_storage, b_mult.limbs_storage);
+      b_mult.limbs_storage =
+        host_math::template add_sub_limbs<CONFIG::limbs_count, true, true, true>(b_mult.limbs_storage, modulus, temp)
+          ? b_mult.limbs_storage
+          : temp;
+      return b_mult;
+    }();
     if constexpr (Gen::is_b_u32_g2_im) {
-      r = FF::template mul_unsigned<FF{Gen::weierstrass_b_g2_im}.limbs_storage.limbs[0], FF>(xs);
+      r = FF::template mul_unsigned<b_mult.limbs_storage.limbs[0], FF>(xs);
       if constexpr (Gen::is_b_neg_g2_im)
         return FF::neg(r);
       else {
         return r;
       }
     } else {
-      return FF{Gen::weierstrass_b_g2_im} * xs;
+      return b_mult * xs;
     }
   }
 
-  template <typename Gen>
+  template <typename Gen, bool IS_3B = false>
   static HOST_DEVICE_INLINE ComplexExtensionField mul_weierstrass_b(const ComplexExtensionField& xs)
   {
     const FF xs_real = xs.real;
     const FF xs_imaginary = xs.imaginary;
-    FF real_prod = mul_weierstrass_b_real<Gen>(xs_real);
-    FF imaginary_prod = mul_weierstrass_b_imag<Gen>(xs_imaginary);
-    FF re_im = mul_weierstrass_b_real<Gen>(xs_imaginary);
-    FF im_re = mul_weierstrass_b_imag<Gen>(xs_real);
+    FF real_prod = mul_weierstrass_b_real<Gen, IS_3B>(xs_real);
+    FF imaginary_prod = mul_weierstrass_b_imag<Gen, IS_3B>(xs_imaginary);
+    FF re_im = mul_weierstrass_b_real<Gen, IS_3B>(xs_imaginary);
+    FF im_re = mul_weierstrass_b_imag<Gen, IS_3B>(xs_real);
     FF nonresidue_times_im = FF::template mul_unsigned<CONFIG::nonresidue>(imaginary_prod);
     nonresidue_times_im = CONFIG::nonresidue_is_negative ? FF::neg(nonresidue_times_im) : nonresidue_times_im;
     return ComplexExtensionField{real_prod + nonresidue_times_im, re_im + im_re};
diff --git a/icicle/include/icicle/fields/field.h b/icicle/include/icicle/fields/field.h
index 8f787ec46..3563424c0 100644
--- a/icicle/include/icicle/fields/field.h
+++ b/icicle/include/icicle/fields/field.h
@@ -875,35 +875,39 @@ class Field
 
   friend HOST_DEVICE bool operator!=(const Field& xs, const Field& ys) { return !(xs == ys); }
 
-  template <typename Gen>
+  template <typename Gen, bool IS_3B = false>
   static HOST_DEVICE_INLINE Field mul_weierstrass_b(const Field& xs)
   {
     Field r = {};
-    if constexpr (Gen::is_b_u32) {
-      r = mul_unsigned<Field{Gen::weierstrass_b}.limbs_storage.limbs[0], Field>(xs);
-      if constexpr (Gen::is_b_neg)
-        return neg(r);
-      else {
-        return r;
-      }
-    } else {
-      return Field{Gen::weierstrass_b} * xs;
-    }
-  }
+    constexpr Field b_mult = []() {
+      Field b_mult = Field{Gen::weierstrass_b};
+      if constexpr (!IS_3B) return b_mult;
+      ff_storage temp = {};
+      ff_storage modulus = get_modulus<>();
+      host_math::template add_sub_limbs<TLC, false, false, true>(
+        b_mult.limbs_storage, b_mult.limbs_storage, b_mult.limbs_storage);
+      b_mult.limbs_storage =
+        host_math::template add_sub_limbs<TLC, true, true, true>(b_mult.limbs_storage, modulus, temp)
+          ? b_mult.limbs_storage
+          : temp;
+      host_math::template add_sub_limbs<TLC, false, false, true>(
+        b_mult.limbs_storage, Field{Gen::weierstrass_b}.limbs_storage, b_mult.limbs_storage);
+      b_mult.limbs_storage =
+        host_math::template add_sub_limbs<TLC, true, true, true>(b_mult.limbs_storage, modulus, temp)
+          ? b_mult.limbs_storage
+          : temp;
+      return b_mult;
+    }();
 
-  template <typename Gen>
-  static HOST_DEVICE_INLINE Field mul_weierstrass_3b(const Field& xs)
-  {
-    Field r = {};
-    if constexpr (Gen::is_b_u32) {
-      r = mul_unsigned<Field{Gen::weierstrass_3b}.limbs_storage.limbs[0], Field>(xs);
+    if constexpr (Gen::is_b_u32) { // assumes that 3b is also u32
+      r = mul_unsigned<b_mult.limbs_storage.limbs[0], Field>(xs);
       if constexpr (Gen::is_b_neg)
         return neg(r);
       else {
         return r;
       }
     } else {
-      return Field{Gen::weierstrass_3b} * xs;
+      return b_mult * xs;
     }
   }
 

From 46731439aee271211828db7710834792e3e8b542 Mon Sep 17 00:00:00 2001
From: hadaringonyama <hadar@ingonyama.com>
Date: Mon, 6 Jan 2025 16:13:36 +0200
Subject: [PATCH 5/5] small fix

---
 .../include/icicle/fields/complex_extension.h | 46 -------------------
 1 file changed, 46 deletions(-)

diff --git a/icicle/include/icicle/fields/complex_extension.h b/icicle/include/icicle/fields/complex_extension.h
index 6879048df..c65ad37ec 100644
--- a/icicle/include/icicle/fields/complex_extension.h
+++ b/icicle/include/icicle/fields/complex_extension.h
@@ -242,52 +242,6 @@ class ComplexExtensionField
     return ComplexExtensionField{real_prod + nonresidue_times_im, re_im + im_re};
   }
 
-  template <typename Gen>
-  static HOST_DEVICE_INLINE FF mul_weierstrass_3b_real(const FF& xs)
-  {
-    FF r = {};
-    if constexpr (Gen::is_b_u32_g2_re) {
-      r = FF::template mul_unsigned<FF{Gen::weierstrass_3b_g2_re}.limbs_storage.limbs[0], FF>(xs);
-      if constexpr (Gen::is_b_neg_g2_re)
-        return FF::neg(r);
-      else {
-        return r;
-      }
-    } else {
-      return FF{Gen::weierstrass_3b_g2_re} * xs;
-    }
-  }
-
-  template <typename Gen>
-  static HOST_DEVICE_INLINE FF mul_weierstrass_3b_imag(const FF& xs)
-  {
-    FF r = {};
-    if constexpr (Gen::is_b_u32_g2_im) {
-      r = FF::template mul_unsigned<FF{Gen::weierstrass_3b_g2_im}.limbs_storage.limbs[0], FF>(xs);
-      if constexpr (Gen::is_b_neg_g2_im)
-        return FF::neg(r);
-      else {
-        return r;
-      }
-    } else {
-      return FF{Gen::weierstrass_3b_g2_im} * xs;
-    }
-  }
-
-  template <typename Gen>
-  static HOST_DEVICE_INLINE ComplexExtensionField mul_weierstrass_3b(const ComplexExtensionField& xs)
-  {
-    const FF xs_real = xs.real;
-    const FF xs_imaginary = xs.imaginary;
-    FF real_prod = mul_weierstrass_3b_real<Gen>(xs_real);
-    FF imaginary_prod = mul_weierstrass_3b_imag<Gen>(xs_imaginary);
-    FF re_im = mul_weierstrass_3b_real<Gen>(xs_imaginary);
-    FF im_re = mul_weierstrass_3b_imag<Gen>(xs_real);
-    FF nonresidue_times_im = FF::template mul_unsigned<CONFIG::nonresidue>(imaginary_prod);
-    nonresidue_times_im = CONFIG::nonresidue_is_negative ? FF::neg(nonresidue_times_im) : nonresidue_times_im;
-    return ComplexExtensionField{real_prod + nonresidue_times_im, re_im + im_re};
-  }
-
   template <const ComplexExtensionField& multiplier>
   static HOST_DEVICE_INLINE ComplexExtensionField mul_const(const ComplexExtensionField& xs)
   {