ggml : Enable MMA for BF16 in llamafile_sgemm (llama/13148)

This patch upstreams llamafile's cpu matrix multiplication kernels for ppc64le using MMA builtins for BF16 data type.

This change results in 9x - 40x gains
in total speed S t/s (ie all tokens/total time), across various batch sizes tested using llama-batched-bench benchmark.

The patch is tested with Meta-Lllama-3-8B,
and Mistral-7B models (BF16 models generated by using llama-quantize from corresponding FP32 models) on an IBM POWER10 machine.

Signed-off-by: Shalini Salomi Bodapati <[email protected]>

ggml/src/ggml-cpu/llamafile/sgemm.cpp

@@ -1054,6 +1054,493 @@ class tinyBLAS_Q0_AVX {
       } \
    } \
 
+template <typename TA, typename TB, typename TC>
+class tinyBLAS_BF16_PPC {
+  public:
+    tinyBLAS_BF16_PPC(int64_t k,
+                const TA *A, int64_t lda,
+                const TB *B, int64_t ldb,
+                TC *C, int64_t ldc,
+                int ith, int nth)
+        : A(A), B(B), C(C), k(k), lda(lda), ldb(ldb), ldc(ldc), ith(ith), nth(nth) {
+    }
+
+    void matmul(int64_t m, int64_t n) {
+        mnpack(0, m, 0, n);
+    }
+
+  private:
+    void vector_permute_store(vec_t *c, int numVec, unsigned char *vecOffset) {
+        vec_t t[8], s[8];
+        vec_t swiz1 = {0, 1, 2, 3, 16, 17, 18, 19, 4, 5, 6, 7, 20, 21, 22, 23};
+        vec_t swiz2 = {8, 9, 10, 11, 24, 25, 26, 27, 12, 13, 14, 15, 28, 29, 30, 31};
+        vec_t swiz3 = {0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23};
+        vec_t swiz4 = {8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31};
+
+        if (numVec == 2) {
+            t[0] = vec_perm(c[0], c[1], swiz1);
+            t[1] = vec_perm(c[2], c[3], swiz1);
+            s[0] = vec_perm(t[0], t[1], swiz3);
+            s[1] = vec_perm(t[0], t[1], swiz4);
+            vec_xst(s[0], 0, (vec_t*)vecOffset);
+            vec_xst(s[1], 0, (vec_t*)(vecOffset + 16));
+        } else if (numVec == 4) {
+            t[0] = vec_perm(c[0], c[1], swiz1);
+            t[1] = vec_perm(c[0], c[1], swiz2);
+            t[2] = vec_perm(c[2], c[3], swiz1);
+            t[3] = vec_perm(c[2], c[3], swiz2);
+            s[0] = vec_perm(t[0], t[2], swiz3);
+            s[1] = vec_perm(t[0], t[2], swiz4);
+            s[2] = vec_perm(t[1], t[3], swiz3);
+            s[3] = vec_perm(t[1], t[3], swiz4);
+            for (int i = 0; i < 4; ++i)
+                vec_xst(s[i], 0, (vec_t*)(vecOffset + i * 16));
+        } else if (numVec == 8) {
+            for (int i = 0; i < 4; i += 2) {
+                t[i+0] = vec_perm(c[i+0], c[i+1], swiz1);
+                t[i+1] = vec_perm(c[i+0], c[i+1], swiz2);
+            }
+            for (int i = 4; i < 8; i += 2) {
+                t[i+0] = vec_perm(c[i+0], c[i+1], swiz1);
+                t[i+1] = vec_perm(c[i+0], c[i+1], swiz2);
+            }
+            s[0] = vec_perm(t[0], t[2], swiz3);
+            s[1] = vec_perm(t[0], t[2], swiz4);
+            s[2] = vec_perm(t[1], t[3], swiz3);
+            s[3] = vec_perm(t[1], t[3], swiz4);
+            s[4] = vec_perm(t[4], t[6], swiz3);
+            s[5] = vec_perm(t[4], t[6], swiz4);
+            s[6] = vec_perm(t[5], t[7], swiz3);
+            s[7] = vec_perm(t[5], t[7], swiz4);
+            for (int i = 0; i < 8; ++i)
+                vec_xst(s[i], 0, (vec_t*)(vecOffset + i * 16));
+        }
+    }
+
+    void packNormal(const TA* a, int64_t lda, int rows, int cols, unsigned char* vec) {
+        int64_t i, j;
+        TA *aoffset = NULL;
+        unsigned char *vecOffset = NULL;
+        TA * aoffsets[8];
+        vector unsigned char c_arr[8];
+        aoffset = const_cast<TA*>(a);
+        vecOffset = vec;
+        j = (rows >> 3);
+        if (j > 0) {
+            do {
+                if (cols == 4) {
+                    aoffsets[0] = aoffset;
+                    for (int it = 1; it < 4; ++it)
+                        aoffsets[it] = aoffsets[it-1] + lda;
+                    aoffset += 4 * lda;
+                    for (int i = 0; i < 4; ++i)
+                        c_arr[i] = vec_xl(0, (vector unsigned char*)aoffsets[i]);
+                    vector_permute_store(c_arr, 4, vecOffset);
+                    for (int i = 0; i<4; i++)
+                        aoffsets[i] = aoffsets[i]+lda;
+                    vecOffset +=64;
+                }
+                i = (cols >> 3);
+                if (i > 0) {
+                    aoffsets[0] = aoffset;
+                    for (int it = 1; it < 8; ++it) {
+                        aoffsets[it] = aoffsets[it-1] + lda;
+                    }
+                    aoffset += 8 * lda;
+                    do {
+                        for (int it = 0; it < 8; ++it)
+                            c_arr[it] = vec_xl(0, (vector unsigned char*)aoffsets[it]);
+                        vector_permute_store(c_arr, 8, vecOffset);
+                        for (int it = 0; it < 8; ++it)
+                            aoffsets[it] = aoffsets[it] + 8*lda;
+                        vecOffset += 128;
+                        i--;
+                    } while(i > 0);
+                }
+                j--;
+            } while(j > 0);
+        }
+        if (rows & 4) {
+            aoffsets[0] = aoffset;
+            for (int it = 1; it < 4; ++it)
+                aoffsets[it] = aoffsets[it-1] + lda;
+            aoffset += 4 * lda;
+            if (cols == 4) {
+                for (int it = 0; it < 4; ++it)
+                    c_arr[it] = vec_xl(0, (vector unsigned char*)aoffsets[it]);
+                vector_permute_store(c_arr, 2, vecOffset);
+                for (int it = 0; it< 4; it++)
+                    aoffsets[it] = aoffsets[it] + lda;
+                vecOffset += 32;
+            }
+            i = (cols >> 3);
+            if (i > 0) {
+                do {
+                    for (int it = 0; it < 4; ++it)
+                        c_arr[it] = vec_xl(0, (vector unsigned char*)aoffsets[it]);
+                    vector_permute_store(c_arr, 4, vecOffset);
+                    for (int it = 0; it< 4; it++)
+                        aoffsets[it] = aoffsets[it] + 8*lda;
+                    vecOffset += 64;
+                    i--;
+                } while(i > 0);
+            }
+        }
+        if (rows & 3) {
+            aoffsets[0] = aoffset;
+            for (int it = 1; it < 4; ++it)
+                aoffsets[it] = aoffsets[it-1] + lda;
+            if (cols == 4) {
+                switch(rows) {
+                    case 3: c_arr[2] = vec_xl(0, (vector unsigned char*)aoffsets[2]);
+                    case 2: c_arr[1] = vec_xl(0, (vector unsigned char*)aoffsets[1]);
+                    case 1: c_arr[0] = vec_xl(0, (vector unsigned char*)aoffsets[0]);
+                        break;
+                }
+                vector_permute_store(c_arr, 2, vecOffset);
+                for (int it = 0; it< 4; it++)
+                     aoffsets[it] = aoffsets[it] + lda;
+                vecOffset += 32;
+            }
+            i = (cols >> 3);
+            if (i > 0) {
+                do {
+                    switch(rows) {
+                        case 3: c_arr[2] = vec_xl(0, (vector unsigned char*)aoffsets[2]);
+                        case 2: c_arr[1] = vec_xl(0, (vector unsigned char*)aoffsets[1]);
+                        case 1: c_arr[0] = vec_xl(0, (vector unsigned char*)aoffsets[0]);
+                            break;
+                    }
+                    vector_permute_store(c_arr, 4, vecOffset);
+                    for (int it = 0; it <4; it++)
+                         aoffsets[it] = aoffsets[it] + 8* lda;
+                    vecOffset += 64;
+                    i--;
+                } while(i > 0);
+            }
+        }
+    }
+
+    void mnpack(int64_t m0, int64_t m, int64_t n0, int64_t n) {
+        int64_t mc, nc, mp, np;
+        int m_rem = MIN(m - m0, 8);
+        int n_rem = MIN(n - n0, 8);
+
+        if (m_rem >= 8 && n_rem >= 8) {
+            mc = 8;
+            nc = 8;
+            gemm<8,8>(m0, m, n0, n);
+        } else if (m_rem >= 4 && n_rem >= 8) {
+            mc = 4;
+            nc = 8;
+            gemm<4,8>(m0, m, n0, n);
+        } else if (m_rem >=8 && n_rem >=4){
+                mc = 8;
+                nc = 4;
+                gemm<8,4>(m0, m, n0, n);
+        } else if ((m_rem < 4) && (n_rem >= 8)) {
+            nc = 8;
+            switch(m_rem) {
+                case 1:
+                    mc = 1;
+                    gemm_Mx8<1>(m0, m, n0, n);
+                    break;
+                case 2:
+                    mc = 2;
+                    gemm_Mx8<2>(m0, m, n0, n);
+                    break;
+                case 3:
+                    mc = 3;
+                    gemm_Mx8<3>(m0, m, n0, n);
+                    break;
+                default:
+                    return;
+            }
+        } else if (m_rem >= 4 && n_rem >= 4) {
+            mc = 4;
+            nc = 4;
+            gemm_small<4, 4>(m0, m, n0, n);
+        } else if ((m_rem > 4) && (n_rem < 4)) {
+            mc = 4;
+            switch(n_rem) {
+                case 1:
+                    nc = 1;
+                    gemm_small<4, 1>(m0, m, n0, n);
+                    break;
+                case 2:
+                    nc = 2;
+                    gemm_small<4, 2>(m0, m, n0, n);
+                    break;
+                case 3:
+                    nc = 3;
+                    gemm_small<4, 3>(m0, m, n0, n);
+                    break;
+
+                default:
+                    return;
+            }
+        } else {
+            switch((m_rem << 4) | n_rem) {
+                case 0x43:
+                    mc = 4;
+                    nc = 3;
+                    gemm_small<4, 3>(m0, m, n0, n);
+                    break;
+                case 0x42:
+                    mc = 4;
+                    nc = 2;
+                    gemm_small<4, 2>(m0, m, n0, n);
+                    break;
+                case 0x41:
+                    mc = 4;
+                    nc = 1;
+                    gemm_small<4, 1>(m0, m, n0, n);
+                    break;
+                case 0x34:
+                    mc = 3;
+                    nc = 4;
+                    gemm_small<3, 4>(m0, m, n0, n);
+                    break;
+                case 0x33:
+                    mc = 3;
+                    nc = 3;
+                    gemm_small<3, 3>(m0, m, n0, n);
+                    break;
+                case 0x32:
+                    mc = 3;
+                    nc = 2;
+                    gemm_small<3, 2>(m0, m, n0, n);
+                    break;
+                case 0x31:
+                    mc = 3;
+                    nc = 1;
+                    gemm_small<3, 1>(m0, m, n0, n);
+                    break;
+                case 0x24:
+                    mc = 2;
+                    nc = 4;
+                    gemm_small<2,4>(m0, m, n0, n);
+                    break;
+                case 0x23:
+                    mc = 2;
+                    nc = 3;
+                    gemm_small<2, 3>(m0, m, n0, n);
+                    break;
+                case 0x22:
+                    mc = 2;
+                    nc = 2;
+                    gemm_small<2, 2>(m0, m, n0, n);
+                    break;
+                case 0x21:
+                    mc = 2;
+                    nc = 1;
+                    gemm_small<2, 1>(m0, m, n0, n);
+                    break;
+                case 0x14:
+                    mc = 1;
+                    nc = 4;
+                    gemm_small<1, 4>(m0, m, n0, n);
+                    break;
+                case 0x13:
+                    mc = 1;
+                    nc = 3;
+                    gemm_small<1, 3>(m0, m, n0, n);
+                    break;
+                case 0x12:
+                    mc = 1;
+                    nc = 2;
+                    gemm_small<1, 2>(m0, m, n0, n);
+                    break;
+                case 0x11:
+                    mc = 1;
+                    nc = 1;
+                    gemm_small<1, 1>(m0, m, n0, n);
+                    break;
+                default:
+                    return;
+            }
+        }
+        mp = m0 + (m - m0) / mc * mc;
+        np = n0 + (n - n0) / nc * nc;
+        mnpack(mp, m, n0, np);
+        mnpack(m0, m, np, n);
+    }
+
+    void KERNEL_4x8(int64_t ii, int64_t jj) {
+        vec_t vec_A[4], vec_B[8] , vec_C[4];
+        acc_t acc_0, acc_1;
+        __builtin_mma_xxsetaccz(&acc_0);
+        __builtin_mma_xxsetaccz(&acc_1);
+        for (int l = 0; l < k; l+=8) {
+            packNormal((A+(ii*lda)+l), lda, 4, 8, (uint8_t*)vec_A);
+            packNormal((B+(jj*ldb)+l), ldb, 8, 8, (uint8_t*)vec_B);
+            for (int x = 0; x < 4; x++) {
+                __builtin_mma_xvbf16ger2pp(&acc_0, vec_A[x], vec_B[x]);
+                __builtin_mma_xvbf16ger2pp(&acc_1, vec_A[x], vec_B[x+4]);
+            }
+        }
+        SAVE_ACC(&acc_0, ii, jj);
+        SAVE_ACC(&acc_1, ii, jj+4);
+    }
+
+    void KERNEL_8x4(int64_t ii, int64_t jj) {
+        vec_t vec_A[8], vec_B[4] , vec_C[4];
+        acc_t acc_0, acc_1;
+        __builtin_mma_xxsetaccz(&acc_0);
+        __builtin_mma_xxsetaccz(&acc_1);
+        for (int l = 0; l < k; l+=8) {
+            packNormal((A+(ii*lda)+l), lda, 8, 8, (uint8_t*)vec_A);
+            packNormal((B+(jj*ldb)+l), ldb, 8, 4, (uint8_t*)vec_B);
+            for (int x = 0; x < 4; x++) {
+                __builtin_mma_xvbf16ger2pp(&acc_0, vec_A[x], vec_B[x]);
+                __builtin_mma_xvbf16ger2pp(&acc_1, vec_A[x+4], vec_B[x]);
+            }
+        }
+        SAVE_ACC(&acc_0, ii, jj);
+        SAVE_ACC(&acc_1, ii+4, jj);
+    }
+
+
+    void KERNEL_8x8(int64_t ii, int64_t jj) {
+        vec_t vec_A[8], vec_B[8], vec_C[4];
+        acc_t acc_0, acc_1, acc_2, acc_3;
+        __builtin_mma_xxsetaccz(&acc_0);
+        __builtin_mma_xxsetaccz(&acc_1);
+        __builtin_mma_xxsetaccz(&acc_2);
+        __builtin_mma_xxsetaccz(&acc_3);
+        for (int l = 0; l < k; l+=8) {
+            packNormal(A+(ii*lda)+l, lda, 8, 8, (uint8_t*)vec_A);
+            packNormal(B+(jj*ldb)+l, ldb, 8, 8, (uint8_t*)vec_B);
+            for (int x = 0; x < 4; x++) {
+                __builtin_mma_xvbf16ger2pp(&acc_0, vec_A[x], vec_B[x]);
+                __builtin_mma_xvbf16ger2pp(&acc_1, (vec_t)vec_A[x], (vec_t)vec_B[x+4]);
+                __builtin_mma_xvbf16ger2pp(&acc_2, (vec_t)vec_A[x+4], (vec_t)vec_B[x]);
+                __builtin_mma_xvbf16ger2pp(&acc_3, (vec_t)vec_A[x+4], (vec_t)vec_B[x+4]);
+            }
+        }
+
+        SAVE_ACC(&acc_0, ii, jj);
+        SAVE_ACC(&acc_1, ii, jj+4);
+        SAVE_ACC(&acc_2, ii+4, jj);
+        SAVE_ACC(&acc_3, ii+4, jj+4);
+    }
+
+    template<int RM, int RN>
+    void gemm_small(int64_t m0, int64_t m, int64_t n0, int64_t n) {
+        int64_t ytiles = (m - m0) / RM;
+        int64_t xtiles = (n - n0) / RN;
+        int64_t tiles = xtiles * ytiles;
+        int64_t duty = (tiles + nth - 1) / nth;
+        int64_t start = duty * ith;
+        int64_t end = start + duty;
+        if (end > tiles)
+            end = tiles;
+        for (int64_t job = start; job < end; ++job) {
+            int64_t ii = m0 + job / xtiles * RM;
+            int64_t jj = n0 + job % xtiles * RN;
+            vec_t vec_C[4];
+            acc_t acc_0;
+            __builtin_mma_xxsetaccz(&acc_0);
+            vec_t vec_A[2], vec_B[2];
+            for (int l=0; l<k; l+=4) {
+                packNormal(A+(ii*lda)+l, lda, RM, 4, (uint8_t*)vec_A);
+                packNormal(B+(jj*ldb)+l, ldb, RN, 4, (uint8_t*)vec_B);
+                for (int x = 0; x<2; x++) {
+                    __builtin_mma_xvbf16ger2pp(&acc_0, vec_A[x], vec_B[x]);
+                }
+            }
+            __builtin_mma_disassemble_acc(vec_C, &acc_0);
+            for (int I = 0; I < RM; I++) {
+                for (int J = 0; J < RN; J++) {
+                    *((TC*)(C+ii+((jj+J)*ldc)+I)) = *((TC*)&vec_C[I]+J);
+                }
+            }
+        }
+    }
+
+    template<int RM>
+    void gemm_Mx8(int64_t m0, int64_t m, int64_t n0, int64_t n) {
+        int RN = 8;
+        int64_t ytiles = (m - m0) / RM;
+        int64_t xtiles = (n - n0) / RN;
+        int64_t tiles = xtiles * ytiles;
+        int64_t duty = (tiles + nth - 1) / nth;
+        int64_t start = duty * ith;
+        int64_t end = start + duty;
+        if (end > tiles)
+            end = tiles;
+        for (int64_t job = start; job < end; ++job) {
+            int64_t ii = m0 + job / xtiles * RM;
+            int64_t jj = n0 + job % xtiles * RN;
+            vec_t vec_C[4];
+            acc_t acc_0, acc_1;
+            __builtin_mma_xxsetaccz(&acc_0);
+            __builtin_mma_xxsetaccz(&acc_1);
+            vec_t vec_A[4], vec_B[8];
+            for (int l=0; l<k; l+=8) {
+                packNormal(A+(ii*lda)+l, lda, RM, 8, (uint8_t*)vec_A);
+                packNormal(B+(jj*ldb)+l, ldb, RN, 8, (uint8_t*)vec_B);
+                for (int x = 0; x<4; x++) {
+                    __builtin_mma_xvbf16ger2pp(&acc_0, vec_A[x], vec_B[x]);
+                    __builtin_mma_xvbf16ger2pp(&acc_1, vec_A[x], vec_B[x+4]);
+                }
+            }
+            __builtin_mma_disassemble_acc(vec_C, &acc_0);
+            for (int I = 0; I < RM; I++) {
+                for (int J = 0; J < 4; J++) {
+                    *((TC*)(C+ii+((jj+J)*ldc)+I)) = *((TC*)&vec_C[I]+J);
+                }
+            }
+            __builtin_mma_disassemble_acc(vec_C, &acc_1);
+            for (int I = 0; I < RM; I++) {
+                for (int J = 0; J < 4; J++) {
+                    *((TC*)(C+ii+((jj+4+J)*ldc)+I)) = *((TC*)&vec_C[I]+J);
+                }
+            }
+        }
+    }
+
+    template<int RM, int RN>
+    inline void kernel(int64_t ii, int64_t jj) {
+       if constexpr(RM == 4 && RN == 8) {
+          KERNEL_4x8(ii,jj);
+       } else if constexpr(RM == 8 && RN == 8) {
+          KERNEL_8x8(ii,jj);
+       } else if constexpr(RM == 8 && RN == 4) {
+          KERNEL_8x4(ii,jj);
+       } else {
+          static_assert(false, "RN/RM values not supported");
+       }
+    }
+
+    template <int RM, int RN>
+    NOINLINE void gemm(int64_t m0, int64_t m, int64_t n0, int64_t n) {
+        int64_t ytiles = (m - m0) / RM;
+        int64_t xtiles = (n - n0) / RN;
+        int64_t tiles = xtiles * ytiles;
+        int64_t duty = (tiles + nth - 1) / nth;
+        int64_t start = duty * ith;
+        int64_t end = start + duty;
+        if (end > tiles)
+            end = tiles;
+        for (int64_t job = start; job < end; ++job) {
+            int64_t ii = m0 + job / xtiles * RM;
+            int64_t jj = n0 + job % xtiles * RN;
+            kernel<RM, RN>(ii, jj);
+        }
+    }
+
+    const TA *const A;
+    const TB *const B;
+    TC *C;
+    const int64_t k;
+    const int64_t lda;
+    const int64_t ldb;
+    const int64_t ldc;
+    const int ith;
+    const int nth;
+};
+
 template <typename TA, typename TB, typename TC>
 class tinyBLAS_Q0_PPC {
   public:
@@ -2202,6 +2689,7 @@ class tinyBLAS_PPC {
         boffset = vec;
         j = (rows >> 3);
         if (j > 0) {
+
             do {
                 aoffset1 = aoffset;
                 aoffset2 = aoffset1 + lda;
@@ -2875,9 +3363,22 @@ bool llamafile_sgemm(const struct ggml_compute_params * params, int64_t m, int64
                 (float *)C, ldc};
             return tb.matmul(m, n);
         }
+#elif defined(__MMA__)
+        if ((k % 8))
+                return false;
+        if(Btype == GGML_TYPE_BF16) {
+           tinyBLAS_BF16_PPC<ggml_bf16_t, ggml_bf16_t, float> tb{ k,
+            (const ggml_bf16_t *)A, lda,
+            (const ggml_bf16_t *)B, ldb,
+            (float *)C, ldc,
+            params->ith, params->nth};
+        tb.matmul(m, n);
+        return true;
+        }
 #endif
         return false;
     }
+
     case GGML_TYPE_F16: {
 #if defined(__AVX512F__)
         if (Btype == GGML_TYPE_F16) {