diff --git a/ggml/src/ggml-cpu/llamafile/sgemm.cpp b/ggml/src/ggml-cpu/llamafile/sgemm.cpp
index 9b6a2eda0..00f7f1170 100644
--- a/ggml/src/ggml-cpu/llamafile/sgemm.cpp
+++ b/ggml/src/ggml-cpu/llamafile/sgemm.cpp
@@ -291,10 +291,13 @@ static const __m128i iq4nlt = _mm_loadu_si128((const __m128i *) kvalues_iq4nl);
 // FLOATING POINT MATRIX MULTIPLICATION
 
 template <int M>
-static int64_t BLOCK_SIZE(size_t m) {
+static inline int64_t BLOCK_SIZE(size_t m) {
     const int64_t NB_BLOC_M = (m + M - 1) / M;
-    int64_t res = (m % NB_BLOC_M == 0) ? m / NB_BLOC_M : (m / NB_BLOC_M) + 1;
-    return res;
+    return (m % NB_BLOC_M == 0) ? m / NB_BLOC_M : (m / NB_BLOC_M) + 1;
+}
+
+static constexpr inline int64_t BLOC_POS(int64_t ib, int64_t ibN, int64_t bloc_size) {
+    return ib < ibN ? ib * bloc_size : ibN * bloc_size + (ib - ibN) * (bloc_size - 1);
 }
 
 template <int KN, typename D, typename V, typename TA, typename TB, typename TC>
@@ -310,32 +313,37 @@ class tinyBLAS {
     bool matmul(int64_t m, int64_t n) {
         if (k % KN != 0)
             return false;
-        // compute RN/RM for only tile with size RN&RN-1/RM&RM-1
+        // compute RM for only need tile with size RM&RM-1
 #if VECTOR_REGISTERS == 32
-        if (m % 16 == 0) {
+        if (m % 16 == 0 && (m/16 >= params->nth)) {
             const int64_t SIZE_N = BLOCK_SIZE<6>(n);
-            mnpack<4, 6, 4>(m, n, SIZE_N);
+            mnpack<4, 6, 4>(m, n, SIZE_N, 12);
             return true;
         }
-        if (m % 8 == 0) {
+        if (m % 8 == 0 ) {
             const int64_t SIZE_N = BLOCK_SIZE<6>(n);
-            mnpack<4, 6, 2>(m, n, SIZE_N);
+            mnpack<4, 6, 2>(m, n, SIZE_N, 12);
             return true;
         }
         if (m % 4 == 0) {
             const int64_t SIZE_N = BLOCK_SIZE<6>(n);
-            mnpack<4, 6, 1>(m, n, SIZE_N);
+            mnpack<4, 6, 1>(m, n, SIZE_N, 12);
             return true;
         }
 #else  // VECTOR_REGISTERS == 16
-        if (m % 8 == 0) {
+        if (m % 16 == 0 && (m/16 >= params->nth)) {
             const int64_t SIZE_N = BLOCK_SIZE<3>(n);
-            mnpack<4, 3, 2>(m, n, SIZE_N);
+            mnpack<4, 3, 4>(m, n, SIZE_N, 24);
+            return true;
+        }
+        if (m % 8 == 0 ) {
+            const int64_t SIZE_N = BLOCK_SIZE<3>(n);
+            mnpack<4, 3, 2>(m, n, SIZE_N, 24);
             return true;
         }
         if (m % 4 == 0) {
             const int64_t SIZE_N = BLOCK_SIZE<3>(n);
-            mnpack<4, 3, 1>(m, n, SIZE_N);
+            mnpack<4, 3, 1>(m, n, SIZE_N, 24);
             return true;
         }
 #endif
@@ -344,12 +352,12 @@ class tinyBLAS {
 
   private:
     template <int RM, int RN, int BM>
-    inline void mnpack(int64_t m, int64_t n, int64_t SIZE_N) {
+    inline void mnpack(int64_t m, int64_t n, int64_t SIZE_N, int64_t BN) {
         if (SIZE_N == RN) {
-            return gemm<RM, RN, BM>(m, n);
+            return gemm<RM, RN, BM>(m, n, BN);
         }
         if constexpr (RN > 1) {
-            return mnpack<RM, RN-1, BM>(m, n, SIZE_N);
+            return mnpack<RM, RN-1, BM>(m, n, SIZE_N, BN);
         } else {
             GGML_LOG_ERROR("mnpack<%d, %d> bloc size not supported\n", RM, (int)SIZE_N);
             GGML_ASSERT(false); // we have miss something.
@@ -391,39 +399,58 @@ class tinyBLAS {
     }
 
     template <int RM, int RN, int BM>
-    NOINLINE void gemm(int64_t m, int64_t n) {
-        GGML_ASSERT(m % (RM * BM) == 0);
-        // const int64_t ytiles = m / (RM * BM);
-        const int64_t xtiles = (n + RN -1) / RN;
-        const int64_t jj_RN = (xtiles - (xtiles * RN - n)) * RN;
-
+    NOINLINE void gemm(int64_t m, int64_t n, int64_t BN) {
         static std::atomic<int64_t> current_chunk;
-        if (params->ith == 0) {
-            GGML_ASSERT((xtiles * RN - n) >= 0);
-            GGML_ASSERT((xtiles * RN - n) < RN);
 
+        GGML_ASSERT(m % (RM * BM) == 0);
+        const int64_t ytiles = m / (RM * BM);
+        const int64_t xtiles = (n + RN -1) / RN;
+        const int64_t jj_RN = (xtiles - (xtiles * RN - n));
+
+        // "round" bloc_size to "nearest" BN
+        const int64_t NB_BN = xtiles < BN ? 1 : (xtiles + BN / 2) / BN;
+        const int64_t SIZE_BN = xtiles % NB_BN == 0 ? xtiles / NB_BN : xtiles / NB_BN + 1;
+        const int64_t jj_BN = (NB_BN - (NB_BN * SIZE_BN - xtiles));
+        const int64_t nb_job = ytiles * NB_BN;
+
+        if (params->ith == 0) {
+            GGML_ASSERT( jj_BN * SIZE_BN + (NB_BN - jj_BN) * (SIZE_BN - 1) == xtiles);
             // Every thread starts at ith, so the first unprocessed chunk is nth.  This save a bit of coordination right at the start.
             std::atomic_store_explicit(&current_chunk, (int64_t)params->nth, std::memory_order_relaxed);
         }
-        ggml_barrier(params->threadpool);
-        int64_t ii = params->ith * RM * BM;
 
-        while (ii < m) {
-            for (int64_t bi = 0; bi < BM * RM; bi+=RM) {
-                int64_t jj = 0;
-                for (; jj<jj_RN; jj+=RN) {
+        ggml_barrier(params->threadpool);
+
+        int64_t job = params->ith;
+        while (job < nb_job) {
+            const int64_t ii = (job % ytiles) * RM * BM;
+            const int64_t jb =  job / ytiles;
+            const int64_t jr0 = BLOC_POS(jb  , jj_BN, SIZE_BN);
+            const int64_t jrN = BLOC_POS(jb+1, jj_BN, SIZE_BN);
+
+            const int64_t jj0 = BLOC_POS(jr0, jj_RN, RN);
+            const int64_t jj2 = BLOC_POS(jrN, jj_RN, RN);
+            const int64_t jj1 = jj2 < jj_RN * RN ? jj2 : jj_RN * RN;
+
+            for (int64_t bi = 0; bi < BM * RM; bi += RM) {
+                int64_t jj = jj0;
+                for (; jj < jj1; jj += RN) {
                     gemm_bloc<RM, RN>(ii + bi, jj);
                 }
                 if constexpr (RN > 1) {
-                    for (; jj<n; jj+=RN-1) {
+                    for (; jj < jj2; jj += RN - 1) {
                         gemm_bloc<RM, RN-1>(ii + bi, jj);
                     }
                 }
-                GGML_ASSERT(jj == n);
+                GGML_ASSERT(jj == jj2);
             }
-            ii = std::atomic_fetch_add_explicit(&current_chunk, (int64_t)1, std::memory_order_relaxed) * RM * BM;
+
+            // next step.
+            job = std::atomic_fetch_add_explicit(&current_chunk, (int64_t)1, std::memory_order_relaxed);
         }
+
         ggml_barrier(params->threadpool);
+        return;
     }
 
     const ggml_compute_params * params;
@@ -1650,7 +1677,6 @@ bool llamafile_sgemm(const struct ggml_compute_params * params, int64_t m, int64
     assert(params->nth > 0);
     assert(params->ith < params->nth);
 
-    // OK avec moins de thread 4 max en zen3 / 16 coeurs?
     // only enable sgemm for prompt processing
     if (n < 2)
         return false;