diff --git a/tessellate_ipu/core/vertex/tile_jacobi_vertex.cpp b/tessellate_ipu/core/vertex/tile_jacobi_vertex.cpp
index 0cb74c0..e30de5f 100644
--- a/tessellate_ipu/core/vertex/tile_jacobi_vertex.cpp
+++ b/tessellate_ipu/core/vertex/tile_jacobi_vertex.cpp
@@ -3,6 +3,7 @@
 #include <poplar/Vertex.hpp>
 
 #include "intrinsics_utils.hpp"
+#include "tile_small_dot.hpp"
 
 using namespace poplar;
 
@@ -78,7 +79,7 @@ class JacobiSymSchur2 : public Vertex {
   }
 };
 
-template <typename T>
+template <class IpuTag, typename T>
 void jacob_update_first_step(const T* pcol, const T* qcol, T* pcol_updated,
                              T* qcol_updated, T* cs, unsigned p, unsigned q,
                              unsigned short wstart,
@@ -89,16 +90,13 @@ void jacob_update_first_step(const T* pcol, const T* qcol, T* pcol_updated,
   const T Apq = pcol[q];
   const T App = pcol[p];
   const T Aqq = qcol[q];
-
   // Schur2 decomposition.
   const T2 cs_vec = sym_schur2(App, Aqq, Apq);
   const T& c = cs_vec[0];
   const T& s = cs_vec[1];
   cs[0] = c;
   cs[1] = s;
-
   // Worker load: start + end vectorized indexes.
-  constexpr unsigned ptr_step = 1;
   const IndexType wsize = wend - wstart;
 
   // pcol, qcol and results pointers.
@@ -106,23 +104,9 @@ void jacob_update_first_step(const T* pcol, const T* qcol, T* pcol_updated,
   const float2* ptr_qcol = reinterpret_cast<const float2*>(qcol) + wstart;
   float2* ptr_pcol_updated = reinterpret_cast<float2*>(pcol_updated) + wstart;
   float2* ptr_qcol_updated = reinterpret_cast<float2*>(qcol_updated) + wstart;
-
-  const T2 cvec = T2{c, c};
-  const T2 svec = T2{s, s};
-
-  // Easier to vectorized + parallelize if start with normal update first.
-  for (IndexType idx = 0; idx != wsize; ++idx) {
-    // TODO: investigate assembly?
-    const T2 pvec = ipu::load_postinc(&ptr_pcol, 1);
-    const T2 qvec = ipu::load_postinc(&ptr_qcol, 1);
-
-    const T2 pvec_updated = cvec * pvec - svec * qvec;
-    const T2 qvec_updated = svec * pvec + cvec * qvec;
-
-    ipu::store_postinc(&ptr_pcol_updated, pvec_updated, 1);
-    ipu::store_postinc(&ptr_qcol_updated, qvec_updated, 1);
-  }
-
+  // Apply Schur2 cs rotation to p/q columns (optimized kernel).
+  rotation2d_f32<IpuTag>(cs_vec, ptr_pcol, ptr_qcol, ptr_pcol_updated,
+                                ptr_qcol_updated, wsize);
   // Update main values App, Apq, Aqq
   pcol_updated[p] = c * c * App - 2 * s * c * Apq + s * s * Aqq;
   qcol_updated[q] = s * s * App + 2 * s * c * Apq + c * c * Aqq;
@@ -137,7 +121,9 @@ void jacob_update_first_step(const T* pcol, const T* qcol, T* pcol_updated,
  * See:  Gene H. Golub, Charles F. Van Loan, MATRIX COMPUTATIONS, 3rd edition,
  * Johns Hopkins Chapter 8.
  */
-class [[poplar::constraint("elem(*pcol) != elem(*qcol)")]] JacobiUpdateFirstStep
+class [[poplar::constraint(
+    "elem(*pcol) != elem(*pcol_updated)",
+    "elem(*qcol) != elem(*qcol_updated)")]] JacobiUpdateFirstStep
     : public MultiVertex {
  public:
   using T = float;
@@ -179,7 +165,7 @@ class [[poplar::constraint("elem(*pcol) != elem(*qcol)")]] JacobiUpdateFirstStep
 
     if (p <= q) {
       // Proper ordering of p and q already.
-      jacob_update_first_step(
+      jacob_update_first_step<IPU_TAG_TYPE>(
           pcol.data() + INDEX_PREFIX, qcol.data() + INDEX_PREFIX,
           pcol_updated.data() + INDEX_PREFIX,
           qcol_updated.data() + INDEX_PREFIX, cs.data(), p, q, wstart, wend);
@@ -187,7 +173,7 @@ class [[poplar::constraint("elem(*pcol) != elem(*qcol)")]] JacobiUpdateFirstStep
       rotset_sorted[1] = q;
     } else {
       // Swap p and q columns as q < p
-      jacob_update_first_step(
+      jacob_update_first_step<IPU_TAG_TYPE>(
           qcol.data() + INDEX_PREFIX, pcol.data() + INDEX_PREFIX,
           qcol_updated.data() + INDEX_PREFIX,
           pcol_updated.data() + INDEX_PREFIX, cs.data(), q, p, wstart, wend);
@@ -229,7 +215,6 @@ class JacobiUpdateSecondStep : public MultiVertex {
     // Size of the index prefix in pcol and qcol.
     constexpr int INDEX_PREFIX = 2;
     // Worker load: start + end vectorized indexes.
-    constexpr unsigned ptr_step = 1;
     const IndexType wstart = worker_offsets[wid];
     const IndexType wend = worker_offsets[wid + 1];
     const IndexType wsize = wend - wstart;
diff --git a/tessellate_ipu/core/vertex/tile_small_dot.cpp b/tessellate_ipu/core/vertex/tile_small_dot.cpp
index 2391ca1..531bbe7 100644
--- a/tessellate_ipu/core/vertex/tile_small_dot.cpp
+++ b/tessellate_ipu/core/vertex/tile_small_dot.cpp
@@ -48,6 +48,7 @@ class [[poplar::constraint("elem(*inrow0) != elem(*outrow0)",
     T2* outrow0_ptr = reinterpret_cast<T2*>(outrow0.data()) + wstart;
     T2* outrow1_ptr = reinterpret_cast<T2*>(outrow1.data()) + wstart;
 
+    // Passing IPU model/hardware tag type.
     rotation2d_f32<IPU_TAG_TYPE>(cs_ptr[0], inrow0_ptr, inrow1_ptr, outrow0_ptr,
                                  outrow1_ptr, wsize);
     return true;
diff --git a/tests/linalg/test_tile_linalg_jacobi.py b/tests/linalg/test_tile_linalg_jacobi.py
index 01f43b1..e54dd6c 100644
--- a/tests/linalg/test_tile_linalg_jacobi.py
+++ b/tests/linalg/test_tile_linalg_jacobi.py
@@ -100,7 +100,7 @@ def jacobi_sym_schur2_fn(pq, pcol, qcol):
         # assert False
 
     def test__jacobi_update_first_step_vertex__benchmark_performance(self):
-        N = 128
+        N = 256
         tiles = (0,)
         pq = np.array([3, N // 2], dtype=np.uint32)
         pcol = np.random.randn(1, N).astype(np.float32)
@@ -123,7 +123,7 @@ def jacobi_update_first_step_fn(pq, pcol, qcol):
 
         start, end = np.asarray(start)[0], np.asarray(end)[0]
         qr_correction_cycle_count = end[0] - start[0]
-        assert qr_correction_cycle_count <= 1700
+        assert qr_correction_cycle_count <= 1550
         # print("CYCLE count:", qr_correction_cycle_count)
         # assert False