From a5ab648ad813524b31855e16701beb5853820867 Mon Sep 17 00:00:00 2001
From: Yida <jakebomber@live.cn>
Date: Fri, 13 Dec 2024 23:35:52 +0800
Subject: [PATCH] v4.2.0

---
 PanguLU_Users_s_Guide.pdf                     |  Bin 0 -> 215457 bytes
 README.md                                     |   34 +-
 examples/mmio_highlevel.h                     |    1 +
 examples/run.sh                               |    4 +-
 make.inc                                      |   14 +-
 src/languages/pangulu_en.h                    |   62 +
 src/pangulu.c                                 |   65 +-
 src/pangulu_common.h                          |  127 +-
 src/pangulu_destroy.c                         |   10 +-
 src/pangulu_gessm_fp64_cuda.c                 |    4 +-
 src/pangulu_kernel_interface.c                |   15 +-
 src/pangulu_malloc.c                          |  101 +-
 src/pangulu_numeric.c                         |    2 +-
 src/pangulu_preprocessing.c                   |  717 +++-------
 src/pangulu_reorder.c                         |  275 ++--
 src/pangulu_symbolic.c                        |    5 +
 src/pangulu_time.c                            |    2 +-
 src/pangulu_tstrf_fp64.c                      |    8 +-
 src/pangulu_tstrf_fp64_cuda.c                 |    8 +-
 src/pangulu_utils.c                           | 1160 ++++++++++++++++-
 .../02_GPU/01_CUDA/000_CUDA/pangulu_cuda.cu   |    4 +-
 .../02_GPU/01_CUDA/000_CUDA/pangulu_cuda.h    |    4 +-
 22 files changed, 1801 insertions(+), 821 deletions(-)
 create mode 100644 PanguLU_Users_s_Guide.pdf
 create mode 100644 src/languages/pangulu_en.h

diff --git a/PanguLU_Users_s_Guide.pdf b/PanguLU_Users_s_Guide.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..f58e5fdbd5ef19a6017475f0195cc55800eb801a
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literal 0
HcmV?d00001

diff --git a/README.md b/README.md
index 2064778..367d4e0 100644
--- a/README.md
+++ b/README.md
@@ -154,32 +154,36 @@ In this example, 6 processes are used to test, the block_size is 4, matrix name
 
 ## Release versions
 
-#### <p align='left'>Version 4.1.0 (Sep. 01, 2024) </p>
+#### <p align='left'>Version 4.2.0 (Dec. 13, 2024) </p>
 
-* Optimized memory usage of numeric factorisation and solving.
+* Updated preprocessing phase to distributed data structure.
+
+#### <p align='left'>Version 4.1.0 (Sep. 1, 2024) </p>
+
+* Optimized memory usage of numeric factorisation and solving;
 * Added parallel building support.
 
 #### <p align='left'>Version 4.0.0 (Jul. 24, 2024) </p>
 
-* Optimized user interfaces of solver routines.
-* Optimized performance of numeric factorisation phase on CPU platforms.
-* Added support on complex matrix solving.
-* Optimized pre-processing performance.
+* Optimized user interfaces of solver routines;
+* Optimized performamce of numeric factorisation phase on CPU platform;
+* Added support on complex matrix solving;
+* Optimized preprocessing performance;
 
 #### <p align='left'>Version 3.5.0 (Aug. 06, 2023) </p>
 
 * Updated the pre-processing phase with OpenMP.
-* Updated the compilation method, compilling libpangulu.so and libpangulu.a at the same time.
-* Updated timing for the reordering phase, the symbolic factorisation phase, and the pre-processing phase.
-* Computed GFLOPS for the numeric factorisation phase.
+* Updated the compilation method of PanguLU, compile libpangulu.so and libpangulu.a at the same time.
+* Updated timing for the reorder phase, the symbolic factorisation phase, the pre-processing phase.
+* Added GFLOPS for the numeric factorisation phase.
  
 #### <p align='left'>Version 3.0.0 (Apr. 02, 2023) </p>
 
-* Used an adaptive method for selecting sparse BLAS in the numeric factorisation phase.
-* Added the reordering phase.
-* Added the symbolic factorisation phase.
-* Added the MC64 algorithm in the reordering phase.
-* Added an interface for 64-bit METIS package in the reordering phase.
+* Used adaptive selection sparse BLAS in the numeric factorisation phase.
+* Added the reorder phase.
+* Added the symbolic factorisation phase. 
+* Added mc64 sorting algorithm in the reorder phase.
+* Added interface for 64-bit metis package in the reorder phase.
 
 
 #### <p align='left'> Version 2.0.0 (Jul. &thinsp;22, 2022) </p>
@@ -191,7 +195,7 @@ In this example, 6 processes are used to test, the block_size is 4, matrix name
 #### <p align='left'>Version 1.0.0 (Oct. 19, 2021) </p>
 
 * Used a rule-based 2D LU factorisation scheduling strategy.
-* Used sparse BLAS for floating point calculations on GPUs.
+* Used Sparse BLAS for floating point calculations on GPUs.
 * Added the pre-processing phase.
 * Added the numeric factorisation phase.
 * Added the triangular solve phase.
diff --git a/examples/mmio_highlevel.h b/examples/mmio_highlevel.h
index 841a414..6fdee49 100644
--- a/examples/mmio_highlevel.h
+++ b/examples/mmio_highlevel.h
@@ -136,6 +136,7 @@ int mmio_info(sparse_index_t *m, sparse_index_t *n, sparse_pointer_t *nnz, spars
     // free tmp space
     free(csr_colIdx_tmp);
     free(csr_rowIdx_tmp);
+    free(csr_row_ptr_counter);
 
     return 0;
 }
diff --git a/examples/run.sh b/examples/run.sh
index 8d55958..817e439 100755
--- a/examples/run.sh
+++ b/examples/run.sh
@@ -7,6 +7,6 @@ if [ ! -f $1 ];then
   exit
 fi
 
-echo mpirun -np $[$NP] ./$numeric_file -nb $nb -f $Smatrix_name
+echo mpirun -np $NP ./$numeric_file -nb $nb -f $Smatrix_name
 
-mpirun -np $[$NP] ./$numeric_file -nb $nb -f $Smatrix_name
+mpirun -np $NP ./$numeric_file -nb $nb -f $Smatrix_name
diff --git a/make.inc b/make.inc
index 98ef885..0fcaa3a 100644
--- a/make.inc
+++ b/make.inc
@@ -1,18 +1,18 @@
 COMPILE_LEVEL = -O3
 
 #0201000,GPU_CUDA
-CUDA_PATH = /path/to/cuda
+CUDA_PATH = /usr/local/cuda
 CUDA_INC = -I$(CUDA_PATH)/include
 CUDA_LIB = -L$(CUDA_PATH)/lib64 -lcudart -lcusparse
 NVCC = nvcc $(COMPILE_LEVEL)
 NVCCFLAGS = $(PANGULU_FLAGS) -w -Xptxas -dlcm=cg -gencode=arch=compute_61,code=sm_61 -gencode=arch=compute_61,code=compute_61 $(CUDA_INC) $(CUDA_LIB)
 
 #general
-CC = gcc $(COMPILE_LEVEL)
-MPICC = mpicc $(COMPILE_LEVEL)
-OPENBLAS_INC = -I/path/to/OpenBLAS/include
-OPENBLAS_LIB = -L/path/to/OpenBLAS/lib -lopenblas
+CC = gcc $(COMPILE_LEVEL) #-fsanitize=address
+MPICC = mpicc $(COMPILE_LEVEL) #-fsanitize=address
+OPENBLAS_INC = -I$(PATH_TO_OPENBLAS_INC)
+OPENBLAS_LIB = -L$(PATH_TO_OPENBLAS_LIB) -lopenblas
 MPICCFLAGS = $(OPENBLAS_INC) $(CUDA_INC) $(OPENBLAS_LIB) -fopenmp -lpthread -lm
 MPICCLINK = $(OPENBLAS_LIB)
-METISFLAGS = -I/path/to/GKlib/include -I/path/to/METIS/include
-PANGULU_FLAGS = -DPANGULU_LOG_INFO -DCALCULATE_TYPE_R64 -DPANGULU_MC64 -DMETIS #-DGPU_OPEN -DHT_IS_OPEN
+METISFLAGS = -I$(PATH_TO_GKLIB_INC) -I$(PATH_TO_METIS_I64_INC)
+PANGULU_FLAGS = -DPANGULU_LOG_INFO -DCALCULATE_TYPE_R64 -DMETIS -DPANGULU_MC64 #-DGPU_OPEN -DHT_IS_OPEN
diff --git a/src/languages/pangulu_en.h b/src/languages/pangulu_en.h
new file mode 100644
index 0000000..46b7bb7
--- /dev/null
+++ b/src/languages/pangulu_en.h
@@ -0,0 +1,62 @@
+#ifdef PANGULU_EN
+
+#ifdef PANGULU_LOG_ERROR
+#define PANGULU_E_NB_IS_ZERO "[PanguLU Error] nb is zero.\n"
+#define PANGULU_E_INVALID_HEAP_SELECT "[PanguLU Error] Invalid heap comparing strategy.\n"
+#define PANGULU_E_HEAP_FULL "[PanguLU Error] The heap is full on rank " FMT_PANGULU_INT32_T ".\n", rank
+#define PANGULU_E_HEAP_EMPTY "[PanguLU Error] The heap is empty on rank " FMT_PANGULU_INT32_T ".\n", rank
+#define PANGULU_E_CPU_MEM "[PanguLU Error] Failed to allocate " FMT_PANGULU_INT64_T " byte(s). CPU memory is not enough. %s:" FMT_PANGULU_INT64_T "\n", size, file, line
+#define PANGULU_E_ISEND_CSR "[PanguLU Error] pangulu_isend_whole_pangulu_smatrix_csr error. value != s->value.\n"
+#define PANGULU_E_ISEND_CSC "[PanguLU Error] pangulu_isend_whole_pangulu_smatrix_csc error. value != s->value_csc.\n"
+#define PANGULU_E_ROW_IS_NULL "[PanguLU Error] The matrix has zero row(s).\n"
+#define PANGULU_E_ROW_DONT_HAVE_DIA "[PanguLU Error] Row[" FMT_PANGULU_EXBLOCK_IDX "] don't have diagonal element.\n", i
+#define PANGULU_E_ERR_IN_RRCL "[PanguLU Error] Invalid numeric factorization task on rank " FMT_PANGULU_INT32_T ". row=" FMT_PANGULU_INT64_T " col=" FMT_PANGULU_INT64_T " level=" FMT_PANGULU_INT64_T "\n", rank, row, col, level
+#define PANGULU_E_K_ID "[PanguLU Error] Invalid kernel id " FMT_PANGULU_INT64_T " for numeric factorization.\n", kernel_id
+#define PANGULU_E_ASYM "[PanguLU Error] MPI_Barrier_asym error.\n"
+#define PANGULU_E_ADD_DIA "[PanguLU Error] pangulu_add_diagonal_element error\n"
+#define PANGULU_E_CUDA_MALLOC "[PanguLU Error] Failed to cudaMalloc %lu byte(s). GPU memory is not enough.\n", size
+#define PANGULU_E_ROW_IS_ZERO "[PanguLU Error] Invalid input matrix.\n"
+#define PANGULU_E_MAX_NULL "[PanguLU Error] pangulu_mc64 internal error. (now_row_max==0)\n"
+#define PANGULU_E_WORK_ERR "[PanguLU Error]  Invalid kernel id " FMT_PANGULU_INT64_T " for sptrsv.\n", kernel_id
+#define PANGULU_E_BIP_PTR_INVALID "[PanguLU Error] Invalid pangulu_block_info pointer.\n"
+#define PANGULU_E_BIP_INVALID "[PanguLU Error] Invalid pangulu_block_info.\n"
+#define PANGULU_E_BIP_NOT_EMPTY "[PanguLU Error] Block info pool is not empty.\n"
+#define PANGULU_E_BIP_OUT_OF_RANGE "[PanguLU Error] PANGULU_BIP index out of range.\n"
+#define PANGULU_E_OPTION_IS_NULLPTR "[PanguLU Error] Option struct pointer is NULL. (pangulu_init)\n"
+#define PANGULU_E_GSTRF_OPTION_IS_NULLPTR "[PanguLU Error] Option struct pointer is NULL. (pangulu_gstrf)\n"
+#define PANGULU_E_GSTRS_OPTION_IS_NULLPTR "[PanguLU Error] Option struct pointer is NULL. (pangulu_gstrs)\n"
+#endif // PANGULU_LOG_ERROR
+
+#ifdef PANGULU_LOG_WARNING
+#define PANGULU_W_RANK_HEAP_DONT_NULL "[PanguLU Warning] " FMT_PANGULU_INT64_T " task remaining on rank " FMT_PANGULU_INT32_T ".\n", heap->length, rank
+#define PANGULU_W_ERR_RANK "[PanguLU Warning] Receiving message error on rank " FMT_PANGULU_INT32_T ".\n", rank
+#define PANGULU_W_BIP_INCREASE_SPEED_TOO_SMALL "[PanguLU Warning] PANGULU_BIP_INCREASE_SPEED too small.\n"
+#define PANGULU_W_GPU_BIG_BLOCK "[PanguLU Warning] When GPU is open, init_options->nb > 256 and pangulu_inblock_idx isn't pangulu_uint32_t, performance will be limited.\n"
+#define PANGULU_W_COMPLEX_FALLBACK "[PanguLU Warning] Calculating complex value on GPU is not supported. Fallback to CPU.\n"
+#endif // PANGULU_LOG_WARNING
+
+#ifdef PANGULU_LOG_INFO
+#define PANGULU_I_VECT2NORM_ERR "[PanguLU Info] || Ax - B || / || Ax || = %12.4le.\n", error
+#define PANGULU_I_CHECK_PASS  "[PanguLU Info] Check ------------------------------------- pass\n"
+#define PANGULU_I_CHECK_ERROR "[PanguLU Info] Check ------------------------------------ error\n"
+#define PANGULU_I_DEV_IS "[PanguLU Info] Device is %s.\n", prop.name
+#define PANGULU_I_TASK_INFO "[PanguLU Info] Info of inserting task is: row=" FMT_PANGULU_INT64_T " col=" FMT_PANGULU_INT64_T " level=" FMT_PANGULU_INT64_T " kernel=" FMT_PANGULU_INT64_T ".\n", row, col, task_level, kernel_id
+#define PANGULU_I_HEAP_LEN "[PanguLU Info] heap.length=" FMT_PANGULU_INT64_T " heap.capacity=" FMT_PANGULU_INT64_T "\n", heap->length, heap->max_length
+#define PANGULU_I_ADAPTIVE_KERNEL_SELECTION_ON  "[PanguLU Info] ADAPTIVE_KERNEL_SELECTION ------------- ON\n"
+#define PANGULU_I_ADAPTIVE_KERNEL_SELECTION_OFF "[PanguLU Info] ADAPTIVE_KERNEL_SELECTION ------------- OFF\n"
+#define PANGULU_I_SYNCHRONIZE_FREE_ON           "[PanguLU Info] SYNCHRONIZE_FREE ---------------------- ON\n"
+#define PANGULU_I_SYNCHRONIZE_FREE_OFF          "[PanguLU Info] SYNCHRONIZE_FREE ---------------------- OFF\n"
+#ifdef METIS
+#define PANGULU_I_BASIC_INFO "[PanguLU Info] n=" FMT_PANGULU_INT64_T " nnz=" FMT_PANGULU_EXBLOCK_PTR " nb=" FMT_PANGULU_INT32_T " mpi_process=" FMT_PANGULU_INT32_T " preprocessing_thread=%d METIS:%s\n", n, origin_smatrix->rowpointer[n], nb, size, init_options->nthread, (sizeof(idx_t) == 4) ? ("i32") : ((sizeof(idx_t) == 8) ? ("i64") : ("?"))
+#else
+#define PANGULU_I_BASIC_INFO "[PanguLU Info] n=" FMT_PANGULU_INT64_T " nnz=" FMT_PANGULU_EXBLOCK_PTR " nb=" FMT_PANGULU_INT32_T " mpi_process=" FMT_PANGULU_INT32_T " preprocessing_thread=%d\n", n, origin_smatrix->rowpointer[n], nb, size, init_options->nthread
+#endif
+#define PANGULU_I_TIME_REORDER "[PanguLU Info] Reordering time is %lf s.\n", elapsed_time
+#define PANGULU_I_TIME_SYMBOLIC "[PanguLU Info] Symbolic factorization time is %lf s.\n", elapsed_time
+#define PANGULU_I_TIME_PRE "[PanguLU Info] Preprocessing time is %lf s.\n", elapsed_time
+#define PANGULU_I_TIME_NUMERICAL "[PanguLU Info] Numeric factorization time is %lf s.\n", elapsed_time //, flop / pangulu_get_spend_time(common) / 1000000000.0
+#define PANGULU_I_TIME_SPTRSV "[PanguLU Info] Solving time is %lf s.\n", elapsed_time
+#define PANGULU_I_SYMBOLIC_NONZERO "[PanguLU Info] Symbolic nonzero count is " FMT_PANGULU_EXBLOCK_PTR ".\n",*symbolic_nnz
+#endif // PANGULU_LOG_INFO
+
+#endif // #ifdef PANGULU_EN
\ No newline at end of file
diff --git a/src/pangulu.c b/src/pangulu.c
index 82a054f..2b76b9e 100644
--- a/src/pangulu.c
+++ b/src/pangulu.c
@@ -17,7 +17,7 @@ pangulu_int64_t INDEX_NUM = 0;
 pangulu_int32_t pangu_omp_num_threads = 1;
 
 pangulu_int64_t flop = 0;
-double time_transport = 0.0;
+double time_transpose = 0.0;
 double time_isend = 0.0;
 double time_receive = 0.0;
 double time_getrf = 0.0;
@@ -46,6 +46,9 @@ void pangulu_init(pangulu_exblock_idx pangulu_n, pangulu_exblock_ptr pangulu_nnz
 {
     MPI_Comm_rank(MPI_COMM_WORLD, &rank);
 
+    struct timeval time_start;
+    double elapsed_time;
+
     pangulu_int32_t size;
     MPI_Comm_size(MPI_COMM_WORLD, &size);
     pangulu_common *common = (pangulu_common *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_common));
@@ -111,7 +114,6 @@ void pangulu_init(pangulu_exblock_idx pangulu_n, pangulu_exblock_ptr pangulu_nnz
     pangulu_int32_t q = common->q;
     pangulu_int32_t nb = common->nb;
     MPI_Barrier(MPI_COMM_WORLD);
-    pangulu_time_start(common);
     common->n = pangulu_bcast_n(origin_smatrix->row, 0);
     pangulu_int64_t n = common->n;
     omp_set_num_threads(init_options->nthread);
@@ -120,16 +122,16 @@ void pangulu_init(pangulu_exblock_idx pangulu_n, pangulu_exblock_ptr pangulu_nnz
 #endif
     if (rank == 0)
     {
-#ifdef ADAPTIVE_KERNEL_SELECTION
-        printf(PANGULU_I_ADAPTIVE_KERNEL_SELECTION_ON);
-#else
-        printf(PANGULU_I_ADAPTIVE_KERNEL_SELECTION_OFF);
-#endif
-#ifdef SYNCHRONIZE_FREE
-        printf(PANGULU_I_SYNCHRONIZE_FREE_ON);
-#else
-        printf(PANGULU_I_SYNCHRONIZE_FREE_OFF);
-#endif
+// #ifdef ADAPTIVE_KERNEL_SELECTION
+//         printf(PANGULU_I_ADAPTIVE_KERNEL_SELECTION_ON);
+// #else
+//         printf(PANGULU_I_ADAPTIVE_KERNEL_SELECTION_OFF);
+// #endif
+// #ifdef SYNCHRONIZE_FREE
+//         printf(PANGULU_I_SYNCHRONIZE_FREE_ON);
+// #else
+//         printf(PANGULU_I_SYNCHRONIZE_FREE_OFF);
+// #endif
 #ifdef PANGULU_GPU_COMPLEX_FALLBACK_FLAG
         printf(PANGULU_W_COMPLEX_FALLBACK);
 #endif
@@ -168,14 +170,14 @@ void pangulu_init(pangulu_exblock_idx pangulu_n, pangulu_exblock_ptr pangulu_nnz
     block_common->rank_col_length = (block_common->block_length / q + (((block_common->block_length % q) > (rank % q)) ? 1 : 0));
     block_common->every_level_length = PANGULU_MIN(block_common->every_level_length, block_common->block_length);
     MPI_Barrier(MPI_COMM_WORLD);
-    pangulu_time_start(common);
+    pangulu_time_start(&time_start);
 
     pangulu_reorder(block_smatrix,
                     origin_smatrix,
                     reorder_matrix);
 
     MPI_Barrier(MPI_COMM_WORLD);
-    pangulu_time_stop(common);
+    elapsed_time = pangulu_time_stop(&time_start);
     if (rank == 0)
     {
         printf(PANGULU_I_TIME_REORDER);
@@ -184,8 +186,7 @@ void pangulu_init(pangulu_exblock_idx pangulu_n, pangulu_exblock_ptr pangulu_nnz
     calculate_time = 0;
 
     MPI_Barrier(MPI_COMM_WORLD);
-    pangulu_time_start(common);
-
+    pangulu_time_start(&time_start);
     if (rank == 0)
     {
         pangulu_symbolic(block_common,
@@ -194,7 +195,7 @@ void pangulu_init(pangulu_exblock_idx pangulu_n, pangulu_exblock_ptr pangulu_nnz
     }
 
     MPI_Barrier(MPI_COMM_WORLD);
-    pangulu_time_stop(common);
+    elapsed_time = pangulu_time_stop(&time_start);
     if (rank == 0)
     {
         printf(PANGULU_I_TIME_SYMBOLIC);
@@ -203,30 +204,26 @@ void pangulu_init(pangulu_exblock_idx pangulu_n, pangulu_exblock_ptr pangulu_nnz
     pangulu_init_heap_select(0);
 
     MPI_Barrier(MPI_COMM_WORLD);
-    pangulu_time_start(common);
-
+    pangulu_time_start(&time_start);
     pangulu_preprocessing(
         block_common,
         block_smatrix,
         reorder_matrix,
         init_options->nthread);
 
-#ifdef PANGULU_SPTRSV
-
-#endif
     MPI_Barrier(MPI_COMM_WORLD);
 
-    pangulu_time_stop(common);
+    elapsed_time = pangulu_time_stop(&time_start);
     if (rank == 0)
     {
         printf(PANGULU_I_TIME_PRE);
     }
 
-    pangulu_free(__FILE__, __LINE__, block_smatrix->symbolic_rowpointer);
-    block_smatrix->symbolic_rowpointer = NULL;
+    // pangulu_free(__FILE__, __LINE__, block_smatrix->symbolic_rowpointer);
+    // block_smatrix->symbolic_rowpointer = NULL;
 
-    pangulu_free(__FILE__, __LINE__, block_smatrix->symbolic_columnindex);
-    block_smatrix->symbolic_columnindex = NULL;
+    // pangulu_free(__FILE__, __LINE__, block_smatrix->symbolic_columnindex);
+    // block_smatrix->symbolic_columnindex = NULL;
 
     pangulu_free(__FILE__, __LINE__, origin_smatrix);
     origin_smatrix = NULL;
@@ -249,6 +246,9 @@ void pangulu_gstrf(pangulu_gstrf_options *gstrf_options, void **pangulu_handle)
     pangulu_block_smatrix *block_smatrix = (*(pangulu_handle_t **)pangulu_handle)->block_smatrix;
     pangulu_common *common = (*(pangulu_handle_t **)pangulu_handle)->commmon;
 
+    struct timeval time_start;
+    double elapsed_time;
+
     if (rank == 0)
     {
         if (gstrf_options == NULL)
@@ -270,13 +270,13 @@ void pangulu_gstrf(pangulu_gstrf_options *gstrf_options, void **pangulu_handle)
 
     pangulu_time_init();
     MPI_Barrier(MPI_COMM_WORLD);
-    pangulu_time_start(common);
+    pangulu_time_start(&time_start);
 
     pangulu_numeric(block_common,
                     block_smatrix);
 
     MPI_Barrier(MPI_COMM_WORLD);
-    pangulu_time_stop(common);
+    elapsed_time = pangulu_time_stop(&time_start);
 
     if (rank == 0)
     {
@@ -306,6 +306,9 @@ void pangulu_gstrs(calculate_type *rhs, pangulu_gstrs_options *gstrs_options, vo
     pangulu_block_smatrix *block_smatrix = (*(pangulu_handle_t **)pangulu_handle)->block_smatrix;
     pangulu_common *common = (*(pangulu_handle_t **)pangulu_handle)->commmon;
 
+    struct timeval time_start;
+    double elapsed_time;
+
     if (rank == 0)
     {
         if (gstrs_options == NULL)
@@ -340,14 +343,14 @@ void pangulu_gstrs(calculate_type *rhs, pangulu_gstrs_options *gstrs_options, vo
 #ifdef PANGULU_SPTRSV
 
     MPI_Barrier(MPI_COMM_WORLD);
-    pangulu_time_start(common);
+    pangulu_time_start(&time_start);
 
     pangulu_sptrsv_L(block_common, block_smatrix);
     pangulu_init_heap_select(4);
     pangulu_sptrsv_U(block_common, block_smatrix);
 
     MPI_Barrier(MPI_COMM_WORLD);
-    pangulu_time_stop(common);
+    elapsed_time = pangulu_time_stop(&time_start);
 
     if (rank == 0)
     {
diff --git a/src/pangulu_common.h b/src/pangulu_common.h
index 796fc7e..dbd7157 100644
--- a/src/pangulu_common.h
+++ b/src/pangulu_common.h
@@ -101,7 +101,7 @@ extern pangulu_int64_t cpu_peak_memory;
 extern pangulu_int64_t gpu_memory;
 
 extern pangulu_int64_t flop;
-extern double time_transport;
+extern double time_transpose;
 extern double time_isend;
 extern double time_receive;
 extern double time_getrf;
@@ -174,8 +174,8 @@ typedef int idx_t;
 #include "./platforms/02_GPU/01_CUDA/000_CUDA/pangulu_cuda.h"
 #endif
 
-// #if !defined(PANGULU_EN_US)
-#define PANGULU_EN_US
+// #if !defined(PANGULU_EN)
+#define PANGULU_EN
 // #endif
 
 #if defined(PANGULU_LOG_INFO) && !defined(PANGULU_LOG_WARNING)
@@ -185,7 +185,7 @@ typedef int idx_t;
 #define PANGULU_LOG_ERROR
 #endif
 
-#include "./languages/pangulu_en_us.h"
+#include "./languages/pangulu_en.h"
 
 #if !defined(PANGULU_LOG_ERROR)
 #define PANGULU_E_NB_IS_ZERO ""
@@ -251,6 +251,7 @@ typedef int idx_t;
 #define PANGULU_BIP_SIBLING_LEN 8
 #define PANGULU_BIP_MAP_LENGTH(index_upper_bound) ((index_upper_bound + PANGULU_BIP_SIBLING_LEN - 1) / PANGULU_BIP_SIBLING_LEN)
 
+#define PANGULU_ICEIL(a, b) (((a) + (b) - 1) / (b))
 #define setbit(x, y) x |= (1 << y)    // set the yth bit of x is 1
 #define getbit(x, y) ((x) >> (y) & 1) // get the yth bit of x
 
@@ -476,7 +477,6 @@ typedef struct pangulu_block_smatrix
     pangulu_inblock_ptr *block_smatrix_nnza_num;
     pangulu_inblock_ptr *block_smatrix_non_zero_vector_l;
     pangulu_inblock_ptr *block_smatrix_non_zero_vector_u;
-    char *blocks_current_rank;
     pangulu_smatrix *big_pangulu_smatrix_value;
     pangulu_inblock_ptr *l_pangulu_smatrix_columnpointer;
     pangulu_inblock_idx *l_pangulu_smatrix_rowindex;
@@ -1020,8 +1020,6 @@ void pangulu_mc64(pangulu_origin_smatrix *s, pangulu_exblock_idx **perm, pangulu
                   calculate_type **row_scale, calculate_type **col_scale);
 #endif
 
-void pangulu_origin_smatrix_transport_transport_iperm(pangulu_origin_smatrix *s, pangulu_origin_smatrix *new_S, pangulu_exblock_idx *metis_perm);
-
 #ifdef METIS
 
 void pangulu_get_graph_struct(pangulu_origin_smatrix *s, idx_t **xadj_adress, idx_t **adjincy_adress);
@@ -1414,9 +1412,13 @@ void pangulu_init_pangulu_origin_smatrix(pangulu_origin_smatrix *s);
 
 void pangulu_read_pangulu_origin_smatrix(pangulu_origin_smatrix *s, int wcs_n, long long wcs_nnz, pangulu_exblock_ptr *csr_rowptr, pangulu_exblock_idx *csr_colidx, calculate_type *csr_value);
 
-void pangulu_time_start(pangulu_common *common);
+// void pangulu_time_start(pangulu_common *common);
+
+// void pangulu_time_stop(pangulu_common *common);
 
-void pangulu_time_stop(pangulu_common *common);
+void pangulu_time_start(struct timeval* start);
+
+double pangulu_time_stop(struct timeval* start);
 
 void pangulu_memcpy_zero_pangulu_smatrix_csc_value(pangulu_smatrix *s);
 
@@ -1426,9 +1428,9 @@ void pangulu_display_pangulu_smatrix_csc(pangulu_smatrix *s);
 
 double pangulu_get_spend_time(pangulu_common *common);
 
-void pangulu_transport_pangulu_smatrix_csc_to_csr(pangulu_smatrix *s);
+void pangulu_transpose_pangulu_smatrix_csc_to_csr(pangulu_smatrix *s);
 
-void pangulu_transport_pangulu_smatrix_csr_to_csc(pangulu_smatrix *s);
+void pangulu_transpose_pangulu_smatrix_csr_to_csc(pangulu_smatrix *s);
 
 void pangulu_pangulu_smatrix_memcpy_rowpointer_csr(pangulu_smatrix *s, pangulu_smatrix *copy_S);
 
@@ -1551,5 +1553,108 @@ const pangulu_block_info *pangulu_bip_get(pangulu_int64_t index, pangulu_block_i
 
 pangulu_block_info *pangulu_bip_set(pangulu_int64_t index, pangulu_block_info_pool *BIP);
 
+void pangulu_convert_csr_to_csc(
+    int free_csrmatrix,
+    pangulu_exblock_idx n,
+    pangulu_exblock_ptr** csr_pointer,
+    pangulu_exblock_idx** csr_index,
+    calculate_type** csr_value,
+    pangulu_exblock_ptr** csc_pointer,
+    pangulu_exblock_idx** csc_index,
+    calculate_type** csc_value
+);
+
+void pangulu_cm_distribute_csc_to_distcsc(
+    pangulu_int32_t root_rank,
+    int rootproc_free_originmatrix,
+    pangulu_exblock_idx* n,
+    pangulu_inblock_idx rowchunk_align,
+    pangulu_int32_t* distcsc_nproc,
+    pangulu_exblock_idx* n_loc,
+    
+    pangulu_exblock_ptr** distcsc_proc_nnzptr,
+    pangulu_exblock_ptr** distcsc_pointer,
+    pangulu_exblock_idx** distcsc_index,
+    calculate_type** distcsc_value
+);
+
+void pangulu_cm_distribute_distcsc_to_distbcsc(
+    int rootproc_free_originmatrix,
+    int malloc_distbcsc_value,
+    pangulu_exblock_idx n_glo,
+    pangulu_exblock_idx n_loc,
+    pangulu_inblock_idx block_order,
+    
+    pangulu_exblock_ptr* distcsc_proc_nnzptr,
+    pangulu_exblock_ptr* distcsc_pointer,
+    pangulu_exblock_idx* distcsc_index,
+    calculate_type* distcsc_value,
+
+    pangulu_exblock_ptr** bcsc_struct_pointer,
+    pangulu_exblock_idx** bcsc_struct_index,
+    pangulu_exblock_ptr** bcsc_struct_nnzptr,
+    pangulu_inblock_ptr*** bcsc_inblock_pointers,
+    pangulu_inblock_idx*** bcsc_inblock_indeces,
+    calculate_type*** bcsc_values
+);
+
+void pangulu_convert_ordered_halfsymcsc_to_csc_struct(
+    int free_halfmatrix,
+    int if_colsort,
+    pangulu_exblock_idx n,
+    pangulu_exblock_ptr** half_csc_pointer,
+    pangulu_exblock_idx** half_csc_index,
+    pangulu_exblock_ptr** csc_pointer,
+    pangulu_exblock_idx** csc_index
+);
+
+void pangulu_convert_bcsc_fill_value_to_struct(
+    int free_valuebcsc,
+    pangulu_exblock_idx n,
+    pangulu_inblock_idx nb,
+
+    pangulu_exblock_ptr* value_bcsc_struct_pointer,
+    pangulu_exblock_idx* value_bcsc_struct_index,
+    pangulu_exblock_ptr* value_bcsc_struct_nnzptr,
+    pangulu_inblock_ptr** value_bcsc_inblock_pointers,
+    pangulu_inblock_idx** value_bcsc_inblock_indeces,
+    calculate_type** value_bcsc_values,
+
+    pangulu_exblock_ptr* struct_bcsc_struct_pointer,
+    pangulu_exblock_idx* struct_bcsc_struct_index,
+    pangulu_exblock_ptr* struct_bcsc_struct_nnzptr,
+    pangulu_inblock_ptr** struct_bcsc_inblock_pointers,
+    pangulu_inblock_idx** struct_bcsc_inblock_indeces,
+    calculate_type** struct_bcsc_values
+);
+
+void pangulu_cm_rank(pangulu_int32_t* rank);
+
+void pangulu_cm_size(pangulu_int32_t* size);
+
+void pangulu_cm_sync();
+
+void pangulu_cm_bcast(void *buffer, int count, MPI_Datatype datatype, int root);
+
+void pangulu_cm_isend(char* buf, pangulu_int64_t count, pangulu_int32_t remote_rank, pangulu_int32_t tag, pangulu_int32_t tag_ub);
+
+void pangulu_cm_send(char* buf, pangulu_int64_t count, pangulu_int32_t remote_rank, pangulu_int32_t tag, pangulu_int32_t tag_ub);
+
+void pangulu_cm_recv(char* buf, pangulu_int64_t count, pangulu_int32_t fetch_rank, pangulu_int32_t tag, pangulu_int32_t tag_ub);
+
+void pangulu_sort_exblock_struct(
+    pangulu_exblock_idx n,
+    pangulu_exblock_ptr* pointer,
+    pangulu_exblock_idx* index,
+    pangulu_int32_t nthread
+);
+
+int cmp_exidx_asc(const void* a, const void* b);
+
+void pangulu_kvsort(pangulu_exblock_idx *key, calculate_type *val, pangulu_int64_t start, pangulu_int64_t end);
+
+
+void pangulu_cm_sync_asym(int wake_rank);
+
 #endif // PANGULU_PLATFORM_ENV
 #endif // PANGULU_COMMON_H
\ No newline at end of file
diff --git a/src/pangulu_destroy.c b/src/pangulu_destroy.c
index 0045564..54c9479 100644
--- a/src/pangulu_destroy.c
+++ b/src/pangulu_destroy.c
@@ -220,10 +220,16 @@ void pangulu_destroy(pangulu_block_common *block_common,
     pangulu_block_info_pool* BIP = block_smatrix->BIP;
 
     for(pangulu_exblock_ptr i=0;i<block_smatrix->current_rank_block_count;i++){
-        pangulu_free(__FILE__, __LINE__, block_smatrix->big_pangulu_smatrix_value[i].columnpointer);
         pangulu_free(__FILE__, __LINE__, block_smatrix->big_pangulu_smatrix_value[i].csc_to_csr_index);
         pangulu_free(__FILE__, __LINE__, block_smatrix->big_pangulu_smatrix_value[i].bin_rowpointer);
         pangulu_free(__FILE__, __LINE__, block_smatrix->big_pangulu_smatrix_value[i].bin_rowindex);
+        pangulu_free(__FILE__, __LINE__, block_smatrix->big_pangulu_smatrix_value[i].rowpointer);
+        pangulu_free(__FILE__, __LINE__, block_smatrix->big_pangulu_smatrix_value[i].columnindex);
+        pangulu_free(__FILE__, __LINE__, block_smatrix->big_pangulu_smatrix_value[i].value);
+    }
+
+    if(block_smatrix->current_rank_block_count){
+        pangulu_free(__FILE__, __LINE__, block_smatrix->big_pangulu_smatrix_value[0].columnpointer);
     }
 
     for(pangulu_exblock_ptr i=0;i<block_common->rank_col_length;i++){
@@ -257,7 +263,7 @@ void pangulu_destroy(pangulu_block_common *block_common,
 #endif
         }
     }
-    pangulu_free(__FILE__, __LINE__, block_smatrix->blocks_current_rank);
+    // pangulu_free(__FILE__, __LINE__, block_smatrix->blocks_current_rank);
 
     for (pangulu_int64_t i = 0; i < L_smatrix_nzz * every_level_length; i++)
     {
diff --git a/src/pangulu_gessm_fp64_cuda.c b/src/pangulu_gessm_fp64_cuda.c
index 8883f5c..7459f4e 100644
--- a/src/pangulu_gessm_fp64_cuda.c
+++ b/src/pangulu_gessm_fp64_cuda.c
@@ -191,13 +191,13 @@ void pangulu_gessm_interface_g_v2(pangulu_smatrix *a,
                                   pangulu_smatrix *x)
 {
     pangulu_smatrix_cuda_memcpy_value_csc(a, a);
-    pangulu_transport_pangulu_smatrix_csc_to_csr(a);
+    pangulu_transpose_pangulu_smatrix_csc_to_csr(a);
     pangulu_smatrix_cuda_memcpy_complete_csr(a, a);
 
     pangulu_gessm_fp64_cuda_v8(a, l, x);
 
     pangulu_smatrix_cuda_memcpy_value_csr(a, x);
-    pangulu_transport_pangulu_smatrix_csr_to_csc(a);
+    pangulu_transpose_pangulu_smatrix_csr_to_csc(a);
 }
 void pangulu_gessm_interface_g_v3(pangulu_smatrix *a,
                                   pangulu_smatrix *l,
diff --git a/src/pangulu_kernel_interface.c b/src/pangulu_kernel_interface.c
index 3512725..7e16dc8 100644
--- a/src/pangulu_kernel_interface.c
+++ b/src/pangulu_kernel_interface.c
@@ -45,6 +45,7 @@ void pangulu_getrf_interface(pangulu_smatrix *a, pangulu_smatrix *l, pangulu_sma
 
 #endif // ADD_GPU_MEMORY
 #else // GPU_OPEN
+
     pangulu_getrf_fp64(a, l, u);
 
 #endif // GPU_OPEN
@@ -135,10 +136,10 @@ void pangulu_tstrf_interface(pangulu_smatrix *a, pangulu_smatrix *save_X, pangul
     pangulu_pangulu_smatrix_memcpy_columnpointer_csc(save_X, a);
 
     // // csr
-    // pangulu_transport_pangulu_smatrix_csc_to_csr(a);
+    // pangulu_transpose_pangulu_smatrix_csc_to_csr(a);
     // pangulu_pangulu_smatrix_memcpy_value_csc_copy_length(calculate_X, a);
     // pangulu_tstrf_fp64_CPU_6(a, calculate_X, u);
-    // pangulu_transport_pangulu_smatrix_csr_to_csc(a);
+    // pangulu_transpose_pangulu_smatrix_csr_to_csc(a);
     // pangulu_pangulu_smatrix_memcpy_columnpointer_csc(save_X, a);
 
 #endif // GPU_OPEN
@@ -166,11 +167,11 @@ void pangulu_gessm_interface(pangulu_smatrix *a, pangulu_smatrix *save_X, pangul
 
 #ifndef CPU_OPTION
     pangulu_smatrix_cuda_memcpy_value_csc(a, a);
-    pangulu_transport_pangulu_smatrix_csc_to_csr(a);
+    pangulu_transpose_pangulu_smatrix_csc_to_csr(a);
     pangulu_pangulu_smatrix_memcpy_value_csr_copy_length(calculate_X, a);
-    pangulu_transport_pangulu_smatrix_csc_to_csr(l);
+    pangulu_transpose_pangulu_smatrix_csc_to_csr(l);
     pangulu_gessm_interface_cpu(a, l, calculate_X);
-    pangulu_transport_pangulu_smatrix_csr_to_csc(a);
+    pangulu_transpose_pangulu_smatrix_csr_to_csc(a);
 #else
 
     /*******************Choose the best performance（性能择优）*************************/
@@ -229,10 +230,10 @@ void pangulu_gessm_interface(pangulu_smatrix *a, pangulu_smatrix *save_X, pangul
     pangulu_pangulu_smatrix_memcpy_value_csr_copy_length(calculate_X, a);
     pangulu_gessm_fp64_cpu_6(a, l, calculate_X);
     pangulu_pangulu_smatrix_memcpy_columnpointer_csc(save_X, a);
-    // pangulu_transport_pangulu_smatrix_csc_to_csr(a);
+    // pangulu_transpose_pangulu_smatrix_csc_to_csr(a);
     // pangulu_pangulu_smatrix_memcpy_value_csr_copy_length(calculate_X, a);
     // pangulu_gessm_interface_CPU_csr(a, l, calculate_X);
-    // pangulu_transport_pangulu_smatrix_csr_to_csc(a);
+    // pangulu_transpose_pangulu_smatrix_csr_to_csc(a);
     // pangulu_pangulu_smatrix_memcpy_columnpointer_csc(save_X, a);
 #endif
 
diff --git a/src/pangulu_malloc.c b/src/pangulu_malloc.c
index 74591d4..4c79893 100644
--- a/src/pangulu_malloc.c
+++ b/src/pangulu_malloc.c
@@ -2,6 +2,9 @@
 
 void *pangulu_malloc(const char* file, pangulu_int64_t line, pangulu_int64_t size)
 {
+    if(size == 0){
+        return NULL;
+    }
     cpu_memory += size;
     if (cpu_memory > cpu_peak_memory)
     {
@@ -20,6 +23,10 @@ void *pangulu_malloc(const char* file, pangulu_int64_t line, pangulu_int64_t siz
 
 void *pangulu_realloc(const char* file, pangulu_int64_t line, void* oldptr, pangulu_int64_t size)
 {
+    if(size == 0){
+        pangulu_free(__FILE__, __LINE__, oldptr);
+        return NULL;
+    }
     cpu_memory += size;
     if (cpu_memory > cpu_peak_memory)
     {
@@ -189,7 +196,7 @@ void pangulu_get_pangulu_smatrix_to_l(pangulu_smatrix *s,
 
 void pangulu_smatrix_add_more_memory(pangulu_smatrix *a)
 {
-    // add CPU moemory
+    // add CPU memory
     pangulu_int64_t nnzA = a->rowpointer[a->row];
     pangulu_int64_t n = a->row;
     char *now_malloc_space = (char *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_inblock_ptr) * (n + 1) + sizeof(pangulu_inblock_idx) * nnzA + sizeof(calculate_type) * nnzA);
@@ -274,7 +281,7 @@ void pangulu_smatrix_add_more_memory(pangulu_smatrix *a)
 
 void pangulu_smatrix_add_more_memory_csr(pangulu_smatrix *a)
 {
-    // add CPU moemory
+    // add CPU memory
 
     pangulu_int64_t nnzA = a->nnz;
     pangulu_int64_t n = a->row;
@@ -360,7 +367,7 @@ void pangulu_smatrix_add_more_memory_csr(pangulu_smatrix *a)
 
 void pangulu_smatrix_add_csc(pangulu_smatrix *a)
 {
-    // add csc moemory
+    // add csc memory
     pangulu_int64_t nnzA = a->rowpointer[a->row];
     pangulu_int64_t n = a->row;
     char *now_malloc_space = (char *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_inblock_ptr) * (n + 1) + sizeof(pangulu_inblock_idx) * nnzA + sizeof(calculate_type) * nnzA);
@@ -411,57 +418,105 @@ void pangulu_smatrix_add_csc(pangulu_smatrix *a)
     pangulu_free(__FILE__, __LINE__, index_rowpointer);
 }
 
+// void pangulu_origin_smatrix_add_csc(pangulu_origin_smatrix *a)
+// {
+//     // add csc memory
+//     pangulu_exblock_ptr nnzA = a->rowpointer[a->row];
+//     pangulu_exblock_idx n = a->row;
+//     char *now_malloc_space = (char *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1) + sizeof(pangulu_exblock_idx) * nnzA + sizeof(calculate_type) * nnzA);
+
+//     pangulu_exblock_ptr *rowpointer = (pangulu_exblock_ptr *)now_malloc_space;
+//     pangulu_exblock_idx *columnindex = (pangulu_exblock_idx *)(now_malloc_space + sizeof(pangulu_exblock_ptr) * (n + 1));
+//     calculate_type *value = (calculate_type *)(now_malloc_space + sizeof(pangulu_exblock_ptr) * (n + 1) + sizeof(pangulu_exblock_idx) * nnzA);
+//     pangulu_exblock_ptr *csc_to_csr_index = (pangulu_exblock_ptr *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * nnzA);
+//     for (pangulu_exblock_ptr i = 0; i < nnzA; i++)
+//     {
+//         value[i] = 0.0;
+//     }
+
+//     for (pangulu_exblock_idx i = 0; i < (n + 1); i++)
+//     {
+//         rowpointer[i] = 0;
+//     }
+//     for (pangulu_exblock_ptr i = 0; i < nnzA; i++)
+//     {
+//         rowpointer[a->columnindex[i] + 1]++;
+//     }
+//     for (pangulu_exblock_idx i = 0; i < n; i++)
+//     {
+//         rowpointer[i + 1] += rowpointer[i];
+//     }
+//     pangulu_exblock_ptr *index_rowpointer = (pangulu_exblock_ptr *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
+//     for (pangulu_exblock_idx i = 0; i < n; i++)
+//     {
+//         index_rowpointer[i] = rowpointer[i];
+//     }
+//     for (pangulu_exblock_idx i = 0; i < n; i++)
+//     {
+//         for (pangulu_exblock_ptr j = a->rowpointer[i]; j < a->rowpointer[i + 1]; j++)
+//         {
+
+//             pangulu_exblock_idx col = a->columnindex[j];
+//             pangulu_exblock_ptr index = index_rowpointer[col];
+//             columnindex[index] = i;
+//             value[index] = a->value[j];
+//             csc_to_csr_index[index] = j;
+//             index_rowpointer[col]++;
+//         }
+//     }
+//     a->columnpointer = rowpointer;
+//     a->rowindex = columnindex;
+//     a->value_csc = value;
+//     a->csc_to_csr_index = csc_to_csr_index;
+//     pangulu_free(__FILE__, __LINE__, index_rowpointer);
+// }
+
 void pangulu_origin_smatrix_add_csc(pangulu_origin_smatrix *a)
 {
-    // add csc moemory
     pangulu_exblock_ptr nnzA = a->rowpointer[a->row];
     pangulu_exblock_idx n = a->row;
     char *now_malloc_space = (char *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1) + sizeof(pangulu_exblock_idx) * nnzA + sizeof(calculate_type) * nnzA);
-
-    pangulu_exblock_ptr *rowpointer = (pangulu_exblock_ptr *)now_malloc_space;
-    pangulu_exblock_idx *columnindex = (pangulu_exblock_idx *)(now_malloc_space + sizeof(pangulu_exblock_ptr) * (n + 1));
+    pangulu_exblock_ptr *columnpointer = (pangulu_exblock_ptr *)now_malloc_space;
+    pangulu_exblock_idx *rowindex = (pangulu_exblock_idx *)(now_malloc_space + sizeof(pangulu_exblock_ptr) * (n + 1));
     calculate_type *value = (calculate_type *)(now_malloc_space + sizeof(pangulu_exblock_ptr) * (n + 1) + sizeof(pangulu_exblock_idx) * nnzA);
     pangulu_exblock_ptr *csc_to_csr_index = (pangulu_exblock_ptr *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * nnzA);
-    for (pangulu_exblock_ptr i = 0; i < nnzA; i++)
-    {
-        value[i] = 0.0;
-    }
+    pangulu_exblock_ptr *index_columnpointer = (pangulu_exblock_ptr *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
 
+    #pragma omp parallel for
     for (pangulu_exblock_idx i = 0; i < (n + 1); i++)
     {
-        rowpointer[i] = 0;
+        columnpointer[i] = 0;
     }
     for (pangulu_exblock_ptr i = 0; i < nnzA; i++)
     {
-        rowpointer[a->columnindex[i] + 1]++;
+        columnpointer[a->columnindex[i] + 1]++;
     }
     for (pangulu_exblock_idx i = 0; i < n; i++)
     {
-        rowpointer[i + 1] += rowpointer[i];
+        columnpointer[i + 1] += columnpointer[i];
     }
-    pangulu_exblock_ptr *index_rowpointer = (pangulu_exblock_ptr *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
+    #pragma omp parallel for
     for (pangulu_exblock_idx i = 0; i < n; i++)
     {
-        index_rowpointer[i] = rowpointer[i];
+        index_columnpointer[i] = columnpointer[i];
     }
     for (pangulu_exblock_idx i = 0; i < n; i++)
     {
         for (pangulu_exblock_ptr j = a->rowpointer[i]; j < a->rowpointer[i + 1]; j++)
         {
-
             pangulu_exblock_idx col = a->columnindex[j];
-            pangulu_exblock_ptr index = index_rowpointer[col];
-            columnindex[index] = i;
+            pangulu_exblock_ptr index = index_columnpointer[col];
+            rowindex[index] = i;
             value[index] = a->value[j];
             csc_to_csr_index[index] = j;
-            index_rowpointer[col]++;
+            index_columnpointer[col]++;
         }
     }
-    a->columnpointer = rowpointer;
-    a->rowindex = columnindex;
+    a->columnpointer = columnpointer;
+    a->rowindex = rowindex;
     a->value_csc = value;
     a->csc_to_csr_index = csc_to_csr_index;
-    pangulu_free(__FILE__, __LINE__, index_rowpointer);
+    pangulu_free(__FILE__, __LINE__, index_columnpointer);
 }
 
 void pangulu_malloc_pangulu_smatrix_csc(pangulu_smatrix *s,
diff --git a/src/pangulu_numeric.c b/src/pangulu_numeric.c
index af4c32e..5a9a941 100644
--- a/src/pangulu_numeric.c
+++ b/src/pangulu_numeric.c
@@ -23,7 +23,7 @@ void pangulu_solve_a_to_lu(pangulu_int64_t level, pangulu_int64_t row, pangulu_i
     pangulu_getrf_interface(a, l, u, calculate_L, calculate_U);
 
     #ifdef GPU_TSTRF
-    pangulu_transport_pangulu_smatrix_csc_to_csr(u);
+    pangulu_transpose_pangulu_smatrix_csc_to_csr(u);
     #endif
 
 #ifdef OVERLAP
diff --git a/src/pangulu_preprocessing.c b/src/pangulu_preprocessing.c
index b6ded41..5113d6d 100644
--- a/src/pangulu_preprocessing.c
+++ b/src/pangulu_preprocessing.c
@@ -10,6 +10,36 @@ void pangulu_preprocessing(pangulu_block_common *block_common,
                            pangulu_origin_smatrix *reorder_matrix,
                            pangulu_int64_t nthread)
 {
+    struct timeval start_time;
+    pangulu_exblock_idx n = block_common->n;
+    pangulu_exblock_idx n_loc = 0;
+    pangulu_exblock_idx nb = block_common->nb;
+    pangulu_exblock_idx block_length = block_common->block_length;
+    pangulu_int32_t rank = block_common->rank;
+    pangulu_int32_t nproc = block_common->sum_rank_size;
+
+    pangulu_exblock_ptr* distcsc_proc_nnzptr;
+    pangulu_exblock_ptr* distcsc_symbolic_proc_nnzptr;
+    pangulu_exblock_ptr* distcsc_pointer;
+    pangulu_exblock_idx* distcsc_index;
+    calculate_type* distcsc_value;
+    pangulu_exblock_ptr* bcsc_nofill_pointer;
+    pangulu_exblock_idx* bcsc_nofill_index;
+    pangulu_exblock_ptr* bcsc_nofill_blknnzptr;
+    pangulu_inblock_ptr** bcsc_nofill_inblk_pointers;
+    pangulu_inblock_idx** bcsc_nofill_inblk_indeces;
+    calculate_type** bcsc_nofill_inblk_values;
+    pangulu_exblock_ptr* bcsc_pointer;
+    pangulu_exblock_idx* bcsc_index;
+    pangulu_exblock_ptr* bcsc_blknnzptr;
+    pangulu_inblock_ptr** bcsc_inblk_pointers;
+    pangulu_inblock_idx** bcsc_inblk_indeces;
+    calculate_type** bcsc_inblk_values;
+
+    pangulu_exblock_ptr* bcsc_related_pointer;
+    pangulu_exblock_idx* bcsc_related_index;
+    pangulu_uint64_t* bcsc_related_draft_info;
+
     const pangulu_int64_t preprocess_ompnum = nthread;
     pangulu_int64_t preprocess_ompnum_sort = preprocess_ompnum;
     pangulu_int64_t preprocess_ompnum_fill_columnindex = preprocess_ompnum;
@@ -17,16 +47,14 @@ void pangulu_preprocessing(pangulu_block_common *block_common,
     pangulu_int64_t preprocess_ompnum_separate_block = preprocess_ompnum;
     pangulu_int64_t preprocess_ompnum_send_block = preprocess_ompnum;
 
-    pangulu_int64_t n = block_common->n;
     pangulu_int32_t p = block_common->p;
     pangulu_int32_t q = block_common->q;
-    pangulu_int32_t nb = block_common->nb;
     pangulu_block_info_pool *BIP = block_smatrix->BIP;
 
     pangulu_exblock_ptr *symbolic_rowpointer = NULL;
     pangulu_exblock_idx *symbolic_columnindex = NULL;
 
-    pangulu_int32_t block_length = block_common->block_length;
+    bind_to_core((rank) % sysconf(_SC_NPROCESSORS_ONLN));
 
     // rank 0 only
     pangulu_int64_t block_num;
@@ -114,72 +142,145 @@ void pangulu_preprocessing(pangulu_block_common *block_common,
     MPI_Bcast((char *)(BIP->data), sizeof(pangulu_block_info) * BIP->length, MPI_CHAR, 0, MPI_COMM_WORLD);             // containing block_smatrix_nnzA_num
     MPI_Bcast(BIP->block_map, PANGULU_BIP_MAP_LENGTH(BIP->index_upper_bound), MPI_PANGULU_INT64_T, 0, MPI_COMM_WORLD); // containing block_smatrix_nnzA_num
 
-    if (rank == 0)
-    {
-
-        for (pangulu_exblock_idx i = 0; i < n; i++)
-        {
-            for (pangulu_exblock_ptr j = reorder_matrix->rowpointer[i]; j < reorder_matrix->rowpointer[i + 1]; j++)
-            {
-                pangulu_exblock_idx block_row = i / nb;
-                pangulu_exblock_idx block_col = (reorder_matrix->columnindex[j]) / nb;
-            }
-        }
 
-        A_nnz_rowpointer_num = 0;
-
-        for (pangulu_int32_t offset_block_row = 0; offset_block_row < p; offset_block_row++)
-        {
-            for (pangulu_int32_t offset_block_col = 0; offset_block_col < q; offset_block_col++)
-            {
-                for (pangulu_exblock_idx i = offset_block_row; i < block_length; i += p)
-                {
-                    for (pangulu_exblock_idx j = offset_block_col; j < block_length; j += q)
-                    {
-                        if (pangulu_bip_get(i * block_length + j, BIP)->block_smatrix_nnza_num != 0)
-                        {
-                            A_nnz_rowpointer_num++;
-                        }
-                    }
-                }
-            }
-        }
-    }
+    if(rank == 0){
+        pangulu_time_start(&start_time);
+        pangulu_convert_csr_to_csc(
+            1, n,
+            &reorder_matrix->rowpointer,
+            &reorder_matrix->columnindex,
+            &reorder_matrix->value,
+            &reorder_matrix->columnpointer,
+            &reorder_matrix->rowindex,
+            &reorder_matrix->value_csc
+        );
+        printf("[PanguLU Info] 6 PanguLU transpose reordered matrix time is %lf s.\n", pangulu_time_stop(&start_time));
+        distcsc_pointer = reorder_matrix->columnpointer;
+        distcsc_index = reorder_matrix->rowindex;
+        distcsc_value = reorder_matrix->value_csc;
+        reorder_matrix->columnpointer = NULL;
+        reorder_matrix->rowindex = NULL;
+        reorder_matrix->value_csc = NULL;
+    }
+
+    pangulu_cm_sync();
+
+    double time_dist_prep = 0;
+
+    if(rank == 0){
+        pangulu_time_start(&start_time);
+    }
+    //  distribute to processes
+    pangulu_cm_distribute_csc_to_distcsc(
+        0, 1, &n, nb, &nproc, &n_loc,
+        &distcsc_proc_nnzptr,
+        &distcsc_pointer,
+        &distcsc_index,
+        &distcsc_value
+    );
+
+    pangulu_cm_sync();
+    
+    pangulu_cm_distribute_distcsc_to_distbcsc(
+        1, 1, n, n_loc, nb,
+        distcsc_proc_nnzptr,
+        distcsc_pointer,
+        distcsc_index,
+        distcsc_value,
+        &bcsc_nofill_pointer,
+        &bcsc_nofill_index,
+        &bcsc_nofill_blknnzptr,
+        &bcsc_nofill_inblk_pointers,
+        &bcsc_nofill_inblk_indeces,
+        &bcsc_nofill_inblk_values
+    );
+
+    pangulu_cm_sync();
+
+    if(rank == 0){
+        time_dist_prep += pangulu_time_stop(&start_time);
+    }
+
+    if(rank == 0){
+        //  generate full symbolic struct
+        pangulu_sort_exblock_struct(n, block_smatrix->symbolic_rowpointer, block_smatrix->symbolic_columnindex, 0);
+        pangulu_time_start(&start_time);
+        pangulu_convert_ordered_halfsymcsc_to_csc_struct(
+            1, 0, n,
+            &block_smatrix->symbolic_rowpointer,
+            &block_smatrix->symbolic_columnindex,
+            &block_smatrix->symbolic_rowpointer,
+            &block_smatrix->symbolic_columnindex
+        );
+        printf("[PanguLU Info] 7 PanguLU generate full symbolic matrix time is %lf s.\n", pangulu_time_stop(&start_time));
+    }
+
+    pangulu_cm_sync_asym(0);
+    pangulu_cm_sync();
+
+    if(rank == 0){
+        pangulu_time_start(&start_time);
+    }
+
+    //  distribute to processes
+    pangulu_cm_distribute_csc_to_distcsc(
+        0, 1, &n, nb, &nproc, &n_loc,
+        &distcsc_symbolic_proc_nnzptr,
+        &block_smatrix->symbolic_rowpointer,
+        &block_smatrix->symbolic_columnindex,
+        NULL
+    );
+    
+    pangulu_cm_sync();
+    
+    // pangulu_sort_exblock_struct(n_loc, block_smatrix->symbolic_rowpointer, block_smatrix->symbolic_columnindex, 0);
+
+    // pangulu_cm_sync_asym(nproc - 1);
+
+    pangulu_cm_distribute_distcsc_to_distbcsc(
+        1, 1, n, n_loc, nb,
+        distcsc_symbolic_proc_nnzptr,
+        block_smatrix->symbolic_rowpointer,
+        block_smatrix->symbolic_columnindex,
+        NULL,
+        &bcsc_pointer,
+        &bcsc_index,
+        &bcsc_blknnzptr,
+        &bcsc_inblk_pointers,
+        &bcsc_inblk_indeces,
+        &bcsc_inblk_values
+    );
+
+    pangulu_cm_sync();
+
+    pangulu_convert_bcsc_fill_value_to_struct(
+        1, n, nb,
+        bcsc_nofill_pointer,
+        bcsc_nofill_index,
+        bcsc_nofill_blknnzptr,
+        bcsc_nofill_inblk_pointers,
+        bcsc_nofill_inblk_indeces,
+        bcsc_nofill_inblk_values,
+        bcsc_pointer,
+        bcsc_index,
+        bcsc_blknnzptr,
+        bcsc_inblk_pointers,
+        bcsc_inblk_indeces,
+        bcsc_inblk_values
+    );
+    bcsc_nofill_pointer = NULL;
+    bcsc_nofill_index = NULL;
+    bcsc_nofill_blknnzptr = NULL;
+    bcsc_nofill_inblk_pointers = NULL;
+    bcsc_nofill_inblk_indeces = NULL;
+    bcsc_nofill_inblk_values = NULL;
 
     pangulu_bcast_vector(block_smatrix_non_zero_vector_L, block_length, 0);
     pangulu_bcast_vector(block_smatrix_non_zero_vector_U, block_length, 0);
 
-    every_rank_block_num[rank] = 0;
-    for (pangulu_exblock_idx row = 0; row < block_length; row++)
-    {
-        for (pangulu_exblock_idx col = 0; col < block_length; col++)
-        {
-            if (pangulu_bip_get(row * block_length + col, BIP)->block_smatrix_nnza_num != 0)
-            {
-                int32_t now_rank = (row % p) * q + (col % q);
-                if (now_rank == rank)
-                {
-                    every_rank_block_num[rank]++;
-                }
-            }
-        }
-    }
-
-    every_rank_block_nnz[rank] = 0;
-    for (pangulu_exblock_idx row = 0; row < block_length; row++)
-    {
-        for (pangulu_exblock_idx col = 0; col < block_length; col++)
-        {
-            if (pangulu_bip_get(row * block_length + col, BIP)->block_smatrix_nnza_num != 0)
-            {
-                int32_t now_rank = (row % p) * q + (col % q);
-                if (now_rank == rank)
-                {
-                    every_rank_block_nnz[rank] += pangulu_bip_get(row * block_length + col, BIP)->block_smatrix_nnza_num;
-                }
-            }
-        }
-    }
+    every_rank_block_num[rank] = bcsc_pointer[block_length];
+    every_rank_block_nnz[rank] = bcsc_blknnzptr[bcsc_pointer[block_length]];
+    pangulu_free(__FILE__, __LINE__, bcsc_blknnzptr);
 
     if (rank == 0)
     {
@@ -215,11 +316,8 @@ void pangulu_preprocessing(pangulu_block_common *block_common,
         }
     }
 
-    if (rank != 0)
-    {
-        pangulu_free(__FILE__, __LINE__, every_rank_block_num);
-        pangulu_free(__FILE__, __LINE__, every_rank_block_nnz);
-    }
+    pangulu_free(__FILE__, __LINE__, every_rank_block_num);
+    pangulu_free(__FILE__, __LINE__, every_rank_block_nnz);
 
     pangulu_smatrix *Big_smatrix_value = (pangulu_smatrix *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_smatrix) * current_rank_block_count);
     for (pangulu_int64_t i = 0; i < current_rank_block_count; i++)
@@ -229,472 +327,32 @@ void pangulu_preprocessing(pangulu_block_common *block_common,
 
     current_rank_block_count = 0;
     current_rank_nnz_count = 0;
-    pangulu_int64_t max_nnz = 0;
 
     pangulu_exblock_ptr nzblk_current_rank = 0;
     pangulu_exblock_ptr nnz_current_rank = 0;
-    char *blkcsr_current_rank = NULL;
-    char *blocks_current_rank = NULL;
 
-    if (rank == 0)
+    for (pangulu_exblock_idx bcol = 0; bcol < block_length; bcol++)
     {
-        struct timeval fill_start, fill_end;
-        struct timeval fill_all_start, fill_all_end;
-
-        gettimeofday(&fill_all_start, NULL);
-        gettimeofday(&fill_start, NULL);
-        pangulu_exblock_ptr *symbolic_full_rowpointer = (pangulu_exblock_ptr *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
-        pangulu_exblock_idx *symbolic_full_columnindex = (pangulu_exblock_idx *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * block_smatrix->symbolic_nnz);
-        pangulu_int64_t *symbolic_aid_array = (pangulu_int64_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int64_t) * n * (preprocess_ompnum_fill_columnindex + 1));
-        memset(symbolic_aid_array, 0, sizeof(pangulu_int64_t) * n * (preprocess_ompnum_fill_columnindex + 1));
-        memset(symbolic_full_rowpointer, 0, sizeof(pangulu_int64_t) * (n + 1));
-        gettimeofday(&fill_end, NULL);
-
-        gettimeofday(&fill_start, NULL);
-        for (int32_t row = 0; row < n; row++)
+        for (pangulu_exblock_ptr bidx = bcsc_pointer[bcol]; bidx < bcsc_pointer[bcol + 1]; bidx++)
         {
-            for (pangulu_int64_t j = symbolic_rowpointer[row]; j < symbolic_rowpointer[row + 1]; j++)
-            {
-                int32_t column = symbolic_columnindex[j];
-                symbolic_aid_array[((row % preprocess_ompnum_fill_columnindex) + 1) * n + column]++;
-                if (row != column)
-                {
-                    symbolic_full_rowpointer[column + 1]++;
-                }
-            }
-        }
-        gettimeofday(&fill_end, NULL);
-
-        gettimeofday(&fill_start, NULL);
-        for (int j = 0; j < n; j++)
-        {
-            for (int i = 1; i < preprocess_ompnum_fill_columnindex + 1; i++)
-            {
-                symbolic_aid_array[i * n + j] += symbolic_aid_array[(i - 1) * n + j];
-            }
-        }
-        for (pangulu_int32_t row = 1; row < n + 1; row++)
-        {
-            for (int i = 0; i < preprocess_ompnum_fill_columnindex + 1; i++)
-            {
-                symbolic_aid_array[i * n + (row - 1)] += symbolic_full_rowpointer[row - 1];
-            }
-            symbolic_full_rowpointer[row] = symbolic_full_rowpointer[row] + symbolic_full_rowpointer[row - 1] + (symbolic_rowpointer[row] - symbolic_rowpointer[row - 1]);
+            pangulu_exblock_idx brow = bcsc_index[bidx];
+            pangulu_smatrix *current = &Big_smatrix_value[current_rank_block_count];
+            current->row = nb;
+            current->column = nb;
+            current->nnz = bcsc_inblk_pointers[bidx][nb];
+            current->columnpointer = bcsc_inblk_pointers[bidx];
+            current->rowindex = bcsc_inblk_indeces[bidx];
+            current->value_csc = bcsc_inblk_values[bidx];
+            pangulu_bip_set(brow * block_length + bcol, BIP)->mapper_a = current_rank_block_count;
+            current_rank_block_count++;
         }
-        gettimeofday(&fill_end, NULL);
-
-        gettimeofday(&fill_start, NULL);
-        for (pangulu_int32_t row = 0; row < n; row++)
-        {
-            memcpy(&symbolic_full_columnindex[symbolic_full_rowpointer[row + 1] - (symbolic_rowpointer[row + 1] - symbolic_rowpointer[row])], &symbolic_columnindex[symbolic_rowpointer[row]], sizeof(pangulu_int32_t) * (symbolic_rowpointer[row + 1] - symbolic_rowpointer[row]));
-        }
-        gettimeofday(&fill_end, NULL);
-
-        gettimeofday(&fill_start, NULL);
-#pragma omp parallel num_threads(preprocess_ompnum_fill_columnindex)
-        {
-            int tid = omp_get_thread_num();
-            for (pangulu_int32_t row = tid; row < n; row += preprocess_ompnum_fill_columnindex)
-            {
-                for (pangulu_int64_t j = symbolic_rowpointer[row]; j < symbolic_rowpointer[row + 1]; j++)
-                {
-                    int32_t column = symbolic_columnindex[j];
-                    symbolic_full_columnindex[symbolic_aid_array[tid * n + column]++] = row;
-                }
-            }
-        }
-        gettimeofday(&fill_end, NULL);
-
-        gettimeofday(&fill_start, NULL);
-        const int row_count_of_one_chunk = 500;
-        int total_chunk_count = (n + row_count_of_one_chunk + 1) / row_count_of_one_chunk;
-        pangulu_int32_t *chunks_of_omp_rank = (pangulu_int32_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int32_t) * total_chunk_count * preprocess_ompnum_sort);
-        pangulu_int32_t *chunk_count_of_omp_rank = (pangulu_int32_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int32_t) * preprocess_ompnum_sort);
-        pangulu_int64_t *omp_rank_total_nnz = (pangulu_int64_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int64_t) * preprocess_ompnum_sort);
-        memset(chunk_count_of_omp_rank, 0, sizeof(pangulu_int32_t) * preprocess_ompnum_sort);
-        memset(omp_rank_total_nnz, 0, sizeof(pangulu_int64_t) * preprocess_ompnum_sort);
-        for (pangulu_int32_t chunk_id = 0; chunk_id < total_chunk_count; chunk_id++)
-        {
-            pangulu_int64_t chunk_nnz = symbolic_full_rowpointer[PANGULU_MIN((chunk_id + 1) * row_count_of_one_chunk, n)] - symbolic_full_rowpointer[chunk_id * row_count_of_one_chunk];
-            pangulu_int64_t min_nnz = 0x7FFFFFFFFFFFFFFF;
-            int min_nnz_rank = 0;
-            for (int i = 0; i < preprocess_ompnum_sort; i++)
-            {
-                if (omp_rank_total_nnz[i] < min_nnz)
-                {
-                    min_nnz = omp_rank_total_nnz[i];
-                    min_nnz_rank = i;
-                }
-            }
-            omp_rank_total_nnz[min_nnz_rank] += chunk_nnz;
-            chunks_of_omp_rank[min_nnz_rank * total_chunk_count + chunk_count_of_omp_rank[min_nnz_rank]] = chunk_id;
-            chunk_count_of_omp_rank[min_nnz_rank]++;
-        }
-        gettimeofday(&fill_end, NULL);
-
-        gettimeofday(&fill_start, NULL);
-#pragma omp parallel num_threads(preprocess_ompnum_sort)
-        {
-            int omp_size = omp_get_num_threads();
-            int omp_tid = omp_get_thread_num();
-            for (pangulu_int32_t i = 0; i < chunk_count_of_omp_rank[omp_tid]; i++)
-            {
-                for (pangulu_int32_t row = chunks_of_omp_rank[omp_tid * total_chunk_count + i] * row_count_of_one_chunk; row < PANGULU_MIN((chunks_of_omp_rank[omp_tid * total_chunk_count + i] + 1) * row_count_of_one_chunk, n); row++)
-                {
-                    qsort(&symbolic_full_columnindex[symbolic_full_rowpointer[row]], symbolic_full_rowpointer[row + 1] - symbolic_full_rowpointer[row], sizeof(pangulu_int32_t), cmp_int32t_asc);
-                }
-            }
-        }
-        gettimeofday(&fill_end, NULL);
-        gettimeofday(&fill_start, NULL);
-        pangulu_free(__FILE__, __LINE__, chunks_of_omp_rank);
-        pangulu_free(__FILE__, __LINE__, chunk_count_of_omp_rank);
-        pangulu_free(__FILE__, __LINE__, omp_rank_total_nnz);
-        pangulu_free(__FILE__, __LINE__, symbolic_aid_array);
-        gettimeofday(&fill_end, NULL);
-
-        gettimeofday(&fill_start, NULL);
-        pangulu_int64_t nnz = symbolic_full_rowpointer[n];
-        int bit_length = (block_length + 31) / 32;
-
-        pangulu_int64_t avg_nnz = (nnz + preprocess_ompnum_separate_block - 1) / preprocess_ompnum_separate_block;
-        pangulu_int64_t *block_row_nnz_pt = (pangulu_int64_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int64_t) * (block_length + 1));
-        for (int i = 0; i < block_length; i++)
-        {
-            block_row_nnz_pt[i] = symbolic_full_rowpointer[i * nb];
-        }
-        block_row_nnz_pt[block_length] = symbolic_full_rowpointer[n];
-        int *pt = (int *)pangulu_malloc(__FILE__, __LINE__, sizeof(int) * (preprocess_ompnum_separate_block + 1));
-        pt[0] = 0;
-        for (int i = 1; i < preprocess_ompnum_separate_block + 1; i++)
-        {
-            pt[i] = binarylowerbound(block_row_nnz_pt, block_length, avg_nnz * i);
-        }
-
-        pangulu_int64_t *block_row_pt = (pangulu_int64_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int64_t) * (block_length + 1));
-        memset(block_row_pt, 0, sizeof(pangulu_int64_t) * (block_length + 1));
-
-        unsigned int *bit_array = (unsigned int *)pangulu_malloc(__FILE__, __LINE__, sizeof(unsigned int) * bit_length * preprocess_ompnum_separate_block);
-
-#pragma omp parallel num_threads(preprocess_ompnum_separate_block)
-        {
-            int tid = omp_get_thread_num();
-            unsigned int *tmp_bit = bit_array + bit_length * tid;
-
-            for (int level = pt[tid]; level < pt[tid + 1]; level++)
-            {
-                memset(tmp_bit, 0, sizeof(unsigned int) * bit_length);
-
-                int start_row = level * nb;
-                int end_row = ((level + 1) * nb) < n ? ((level + 1) * nb) : n;
-
-                for (int rid = start_row; rid < end_row; rid++)
-                {
-                    for (pangulu_int64_t idx = symbolic_full_rowpointer[rid]; idx < symbolic_full_rowpointer[rid + 1]; idx++)
-                    {
-                        pangulu_int32_t colidx = symbolic_full_columnindex[idx];
-                        pangulu_int32_t block_cid = colidx / nb;
-                        setbit(tmp_bit[block_cid / 32], block_cid % 32);
-                    }
-                }
-
-                pangulu_int64_t tmp_blocknum = 0;
-                for (int i = 0; i < bit_length; i++)
-                {
-                    tmp_blocknum += __builtin_popcount(tmp_bit[i]);
-                }
-
-                block_row_pt[level] = tmp_blocknum;
-            }
-        }
-        exclusive_scan_1(block_row_pt, block_length + 1);
-        block_num = block_row_pt[block_length];
-
-        block_nnz_pt = (pangulu_int64_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int64_t) * (block_num + 1));
-        memset(block_nnz_pt, 0, sizeof(pangulu_int64_t) * (block_num + 1));
-        pangulu_int32_t *block_col_idx = (pangulu_int32_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int32_t) * block_num);
-
-        int *count_array = (int *)pangulu_malloc(__FILE__, __LINE__, sizeof(int) * block_length * preprocess_ompnum_separate_block);
-
-#pragma omp parallel num_threads(preprocess_ompnum_separate_block)
-        {
-            int tid = omp_get_thread_num();
-            unsigned int *tmp_bit = bit_array + bit_length * tid;
-            int *tmp_count = count_array + block_length * tid;
-
-            for (int level = pt[tid]; level < pt[tid + 1]; level++)
-            {
-                memset(tmp_bit, 0, sizeof(unsigned int) * bit_length);
-                memset(tmp_count, 0, sizeof(int) * block_length);
-
-                pangulu_int64_t *cur_block_nnz_pt = block_nnz_pt + block_row_pt[level];
-                pangulu_int32_t *cur_block_col_idx = block_col_idx + block_row_pt[level];
-
-                int start_row = level * nb;
-                int end_row = ((level + 1) * nb) < n ? ((level + 1) * nb) : n;
-
-                for (int rid = start_row; rid < end_row; rid++)
-                {
-                    for (pangulu_int64_t idx = symbolic_full_rowpointer[rid]; idx < symbolic_full_rowpointer[rid + 1]; idx++)
-                    {
-                        pangulu_int32_t colidx = symbolic_full_columnindex[idx];
-                        pangulu_int32_t block_cid = colidx / nb;
-                        setbit(tmp_bit[block_cid / 32], block_cid % 32);
-                        tmp_count[block_cid]++;
-                    }
-                }
-
-                pangulu_int64_t cnt = 0;
-                for (int i = 0; i < block_length; i++)
-                {
-                    if (getbit(tmp_bit[i / 32], i % 32))
-                    {
-                        cur_block_nnz_pt[cnt] = tmp_count[i];
-                        cur_block_col_idx[cnt] = i;
-                        cnt++;
-                    }
-                }
-            }
-        }
-        exclusive_scan_1(block_nnz_pt, block_num + 1);
-        block_csr = (char *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_inblock_ptr) * (nb + 1) * block_num + sizeof(pangulu_inblock_idx) * nnz + sizeof(calculate_type) * nnz);
-
-#pragma omp parallel num_threads(preprocess_ompnum_separate_block)
-        {
-            int tid = omp_get_thread_num();
-            int *tmp_count = count_array + block_length * tid;
-
-            for (int level = pt[tid]; level < pt[tid + 1]; level++)
-            {
-
-                memset(tmp_count, 0, sizeof(int) * block_length);
-
-                for (pangulu_int64_t blc = block_row_pt[level]; blc < block_row_pt[level + 1]; blc++)
-                {
-                    pangulu_int64_t tmp_stride = blc * (nb + 1) * sizeof(pangulu_inblock_ptr) + block_nnz_pt[blc] * (sizeof(pangulu_inblock_idx) + sizeof(calculate_type));
-                    pangulu_inblock_ptr *cur_csr_rpt = (pangulu_inblock_ptr *)(block_csr + tmp_stride);
-
-                    memset(cur_csr_rpt, 0, sizeof(pangulu_inblock_ptr) * (nb + 1));
-                }
-
-                int start_row = level * nb;
-                int end_row = ((level + 1) * nb) < n ? ((level + 1) * nb) : n;
-
-                for (int rid = start_row, r_in_blc = 0; rid < end_row; rid++, r_in_blc++)
-                {
-                    pangulu_int64_t cur_block_idx = block_row_pt[level];
-
-                    pangulu_int64_t arr_len = cur_block_idx * (nb + 1) * sizeof(pangulu_inblock_ptr) + block_nnz_pt[cur_block_idx] * (sizeof(pangulu_inblock_idx) + sizeof(calculate_type));
-                    pangulu_inblock_ptr *cur_block_rowptr = (pangulu_inblock_ptr *)(block_csr + arr_len);
-                    pangulu_inblock_idx *cur_block_colidx = (pangulu_inblock_idx *)(block_csr + arr_len + (nb + 1) * sizeof(pangulu_inblock_ptr));
-                    calculate_type *cur_block_value = (calculate_type *)(block_csr + arr_len + (nb + 1) * sizeof(pangulu_inblock_ptr) + (block_nnz_pt[cur_block_idx + 1] - block_nnz_pt[cur_block_idx]) * sizeof(pangulu_inblock_idx));
-
-                    pangulu_exblock_ptr reorder_matrix_idx = reorder_matrix->rowpointer[rid];
-                    pangulu_exblock_ptr reorder_matrix_idx_ub = reorder_matrix->rowpointer[rid + 1];
-                    for (pangulu_exblock_ptr idx = symbolic_full_rowpointer[rid]; idx < symbolic_full_rowpointer[rid + 1]; idx++)
-                    {
-                        pangulu_exblock_idx colidx = symbolic_full_columnindex[idx];
-                        pangulu_exblock_idx block_cid = colidx / nb;
-                        if (block_col_idx[cur_block_idx] != block_cid)
-                        {
-                            cur_block_idx = binarysearch(block_col_idx, cur_block_idx, block_row_pt[level + 1], block_cid);
-
-                            arr_len = cur_block_idx * (nb + 1) * sizeof(pangulu_inblock_ptr) + block_nnz_pt[cur_block_idx] * (sizeof(pangulu_inblock_idx) + sizeof(calculate_type));
-                            cur_block_rowptr = (pangulu_inblock_ptr *)(block_csr + arr_len);
-                            cur_block_colidx = (pangulu_inblock_idx *)(block_csr + arr_len + (nb + 1) * sizeof(pangulu_inblock_ptr));
-                            cur_block_value = (calculate_type *)(block_csr + arr_len + (nb + 1) * sizeof(pangulu_inblock_ptr) + (block_nnz_pt[cur_block_idx + 1] - block_nnz_pt[cur_block_idx]) * sizeof(pangulu_inblock_idx));
-                        }
-                        if ((reorder_matrix->columnindex[reorder_matrix_idx] == colidx) && (reorder_matrix_idx < reorder_matrix_idx_ub))
-                        {
-                            cur_block_value[tmp_count[block_cid]] = reorder_matrix->value[reorder_matrix_idx];
-                            reorder_matrix_idx++;
-                        }
-                        else
-                        {
-                            cur_block_value[tmp_count[block_cid]] = 0.0;
-                        }
-                        cur_block_colidx[tmp_count[block_cid]++] = colidx % nb;
-                        cur_block_rowptr[r_in_blc]++;
-                    }
-                }
-
-                for (pangulu_int64_t blc = block_row_pt[level]; blc < block_row_pt[level + 1]; blc++)
-                {
-                    pangulu_int64_t tmp_stride = blc * (nb + 1) * sizeof(pangulu_inblock_ptr) + block_nnz_pt[blc] * (sizeof(pangulu_inblock_idx) + sizeof(calculate_type));
-                    pangulu_inblock_ptr *cur_csr_rpt = (pangulu_inblock_ptr *)(block_csr + tmp_stride);
-                    exclusive_scan_3(cur_csr_rpt, nb + 1);
-                }
-            }
-        }
-
-        gettimeofday(&fill_end, NULL);
-        pangulu_free(__FILE__, __LINE__, symbolic_full_rowpointer);
-        pangulu_free(__FILE__, __LINE__, symbolic_full_columnindex);
-
-        mpi_barrier_asym(MPI_COMM_WORLD, 0, 1e5);
-
-        gettimeofday(&fill_start, NULL);
-        pangulu_exblock_ptr *calculated_nzblk_count_each_rank = (pangulu_exblock_ptr *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * sum_rank_size);
-        memset(calculated_nzblk_count_each_rank, 0, sizeof(pangulu_exblock_ptr) * sum_rank_size);
-        char *blkcsr_all_rank = (char *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (block_length + 1) * sum_rank_size + (sizeof(pangulu_exblock_idx) /*blk_colidx*/ + sizeof(pangulu_inblock_ptr) /*blk_value(nnz_in_block)*/) * block_num);
-        char **blkcsr_each_rank = (char **)pangulu_malloc(__FILE__, __LINE__, sizeof(char *) * sum_rank_size);
-        pangulu_int64_t counted_block = 0;
-        for (int i = 0; i < sum_rank_size; i++)
-        {
-            blkcsr_each_rank[i] = blkcsr_all_rank + sizeof(pangulu_exblock_ptr) * (block_length + 1) * i + (sizeof(pangulu_exblock_idx) /*blk_colidx*/ + sizeof(pangulu_inblock_ptr) /*blk_value(nnz_in_block)*/) * counted_block;
-            counted_block += every_rank_block_num[i];
-        }
-
-        for (int target_rank = 0; target_rank < sum_rank_size; target_rank++)
-        {
-            pangulu_exblock_ptr *blkcsr_rowptr = (pangulu_exblock_ptr *)blkcsr_each_rank[target_rank];
-            blkcsr_rowptr[0] = 0;
-        }
-        for (int brow = 0; brow < block_length; brow++)
-        {
-            for (pangulu_int64_t bidx = block_row_pt[brow]; bidx < block_row_pt[brow + 1]; bidx++)
-            {
-                int bcol = block_col_idx[bidx];
-                int target_rank = (brow % p) * q + (bcol % q);
-
-                pangulu_exblock_idx *blkcsr_colidx = (pangulu_exblock_idx *)(blkcsr_each_rank[target_rank] + sizeof(pangulu_exblock_ptr) * (block_length + 1));
-                pangulu_inblock_ptr *blkcsr_value_blknnz = (pangulu_inblock_ptr *)(blkcsr_each_rank[target_rank] + sizeof(pangulu_exblock_ptr) * (block_length + 1) + sizeof(pangulu_exblock_idx) * every_rank_block_num[target_rank]);
-
-                pangulu_exblock_ptr bidx_in_target_rank = calculated_nzblk_count_each_rank[target_rank];
-                blkcsr_colidx[bidx_in_target_rank] = bcol;
-                blkcsr_value_blknnz[bidx_in_target_rank] = block_nnz_pt[bidx + 1] - block_nnz_pt[bidx];
-
-                calculated_nzblk_count_each_rank[target_rank]++;
-            }
-            for (int target_rank = 0; target_rank < sum_rank_size; target_rank++)
-            {
-                pangulu_exblock_ptr *blkcsr_rowptr = (pangulu_exblock_ptr *)blkcsr_each_rank[target_rank];
-                blkcsr_rowptr[brow + 1] = calculated_nzblk_count_each_rank[target_rank];
-            }
-        }
-        pangulu_free(__FILE__, __LINE__, every_rank_block_num);
-
-        pangulu_exblock_idx *sent_block_count_each_rank = (pangulu_exblock_idx *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * sum_rank_size);
-        memset(sent_block_count_each_rank, 0, sizeof(pangulu_exblock_idx) * sum_rank_size);
-#pragma omp parallel num_threads(preprocess_ompnum_send_block)
-        {
-            int tid = omp_get_thread_num();
-            int nthread = omp_get_num_threads();
-            for (int target_rank = tid; target_rank < sum_rank_size; target_rank += nthread)
-            {
-                if (target_rank != 0)
-                {
-                    MPI_Send(calculated_nzblk_count_each_rank + target_rank, 1, MPI_PANGULU_EXBLOCK_PTR, target_rank, 0xCAFE + 1, MPI_COMM_WORLD);
-                    MPI_Send(every_rank_block_nnz + target_rank, 1, MPI_PANGULU_INT64_T, target_rank, 0xCAFE + 2, MPI_COMM_WORLD);
-                    MPI_Send(blkcsr_each_rank[target_rank], sizeof(pangulu_exblock_ptr) * (block_length + 1) + (sizeof(pangulu_exblock_idx) + sizeof(pangulu_inblock_ptr)) * calculated_nzblk_count_each_rank[target_rank], MPI_CHAR, target_rank, 0xCAFE + 3, MPI_COMM_WORLD);
-                }
-                else
-                {
-                    nzblk_current_rank = calculated_nzblk_count_each_rank[target_rank];
-                    nnz_current_rank = every_rank_block_nnz[target_rank];
-                    blkcsr_current_rank = blkcsr_each_rank[0];
-                    blocks_current_rank = (char *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_inblock_ptr) * (nb + 1) * nzblk_current_rank + (sizeof(pangulu_inblock_idx) + sizeof(calculate_type)) * nnz_current_rank);
-                }
-                pangulu_int64_t blocks_current_rank_receive_offset = 0;
-                for (pangulu_exblock_idx brow = 0; brow < block_length; brow++)
-                {
-                    if (brow % p != target_rank / q)
-                    {
-                        continue;
-                    }
-                    for (pangulu_exblock_ptr bidx = block_row_pt[brow]; bidx < block_row_pt[brow + 1]; bidx++)
-                    {
-                        pangulu_exblock_idx bcol = block_col_idx[bidx];
-                        if (bcol % q != target_rank % q)
-                        {
-                            continue;
-                        }
-                        pangulu_int64_t block_byte_offset = sizeof(pangulu_inblock_ptr) * (bidx * (nb + 1)) + (sizeof(pangulu_inblock_idx) + sizeof(calculate_type)) * block_nnz_pt[bidx];
-                        if (target_rank != 0)
-                        {
-                            MPI_Send(block_csr + block_byte_offset, sizeof(pangulu_inblock_ptr) * (nb + 1) + (sizeof(pangulu_inblock_idx) + sizeof(calculate_type)) * (block_nnz_pt[bidx + 1] - block_nnz_pt[bidx]), MPI_CHAR, target_rank, sent_block_count_each_rank[target_rank], MPI_COMM_WORLD);
-                            sent_block_count_each_rank[target_rank]++;
-                        }
-                        else
-                        {
-                            memcpy(blocks_current_rank + blocks_current_rank_receive_offset, block_csr + block_byte_offset, sizeof(pangulu_inblock_ptr) * (nb + 1) + (sizeof(pangulu_inblock_idx) + sizeof(calculate_type)) * (block_nnz_pt[bidx + 1] - block_nnz_pt[bidx]));
-
-                            pangulu_smatrix *current = &Big_smatrix_value[current_rank_block_count];
-                            current->row = nb;
-                            current->column = nb;
-                            current->rowpointer = (pangulu_inblock_ptr *)(blocks_current_rank + blocks_current_rank_receive_offset);
-                            current->nnz = current->rowpointer[nb];
-                            current->columnindex = (pangulu_inblock_idx *)(blocks_current_rank + blocks_current_rank_receive_offset + sizeof(pangulu_inblock_ptr) * (nb + 1));
-                            current->value = (calculate_type *)(blocks_current_rank + blocks_current_rank_receive_offset + sizeof(pangulu_inblock_ptr) * (nb + 1) + sizeof(pangulu_inblock_idx) * current->nnz);
-
-                            pangulu_bip_set(brow * block_length + bcol, BIP)->mapper_a = current_rank_block_count;
-
-                            blocks_current_rank_receive_offset += sizeof(pangulu_inblock_ptr) * (nb + 1) + (sizeof(pangulu_inblock_idx) + sizeof(calculate_type)) * (block_nnz_pt[bidx + 1] - block_nnz_pt[bidx]);
-                            current_rank_block_count++;
-                        }
-                    }
-                }
-            }
-        }
-        gettimeofday(&fill_end, NULL);
-        gettimeofday(&fill_start, NULL);
-        pangulu_free(__FILE__, __LINE__, pt);
-        pangulu_free(__FILE__, __LINE__, block_nnz_pt);
-        pangulu_free(__FILE__, __LINE__, block_row_nnz_pt);
-        pangulu_free(__FILE__, __LINE__, block_row_pt);
-        pangulu_free(__FILE__, __LINE__, block_col_idx);
-        pangulu_free(__FILE__, __LINE__, bit_array);
-        pangulu_free(__FILE__, __LINE__, count_array);
-        pangulu_free(__FILE__, __LINE__, block_csr);
-        pangulu_free(__FILE__, __LINE__, every_rank_block_nnz);
-        pangulu_free(__FILE__, __LINE__, calculated_nzblk_count_each_rank);
-        pangulu_free(__FILE__, __LINE__, blkcsr_each_rank);
-        pangulu_free(__FILE__, __LINE__, sent_block_count_each_rank);
-        blkcsr_current_rank = (char *)pangulu_realloc(__FILE__, __LINE__, blkcsr_current_rank, sizeof(pangulu_exblock_ptr) * (block_length + 1) + (sizeof(pangulu_exblock_idx) + sizeof(pangulu_inblock_ptr)) * nzblk_current_rank);
-
-        gettimeofday(&fill_end, NULL);
-
-        gettimeofday(&fill_all_end, NULL);
     }
-    else
-    {
-        MPI_Status mpi_stat;
-        mpi_barrier_asym(MPI_COMM_WORLD, 0, 1e5);
-        MPI_Recv(&nzblk_current_rank, 1, MPI_PANGULU_EXBLOCK_PTR, 0, 0xCAFE + 1, MPI_COMM_WORLD, &mpi_stat);
-        MPI_Recv(&nnz_current_rank, 1, MPI_PANGULU_EXBLOCK_PTR, 0, 0xCAFE + 2, MPI_COMM_WORLD, &mpi_stat);
-
-        blkcsr_current_rank = (char *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (block_length + 1) + (sizeof(pangulu_exblock_idx) + sizeof(pangulu_inblock_ptr)) * nzblk_current_rank);
-        MPI_Recv(blkcsr_current_rank, sizeof(pangulu_exblock_ptr) * (block_length + 1) + (sizeof(pangulu_exblock_idx) + sizeof(pangulu_inblock_ptr)) * nzblk_current_rank, MPI_CHAR, 0, 0xCAFE + 3, MPI_COMM_WORLD, &mpi_stat);
-        blocks_current_rank = (char *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_inblock_ptr) * (nb + 1) * nzblk_current_rank + (sizeof(pangulu_inblock_idx) + sizeof(calculate_type)) * nnz_current_rank);
+    pangulu_free(__FILE__, __LINE__, bcsc_pointer);
+    pangulu_free(__FILE__, __LINE__, bcsc_index);
+    pangulu_free(__FILE__, __LINE__, bcsc_inblk_pointers);
+    pangulu_free(__FILE__, __LINE__, bcsc_inblk_indeces);
+    pangulu_free(__FILE__, __LINE__, bcsc_inblk_values);
 
-        pangulu_exblock_ptr *blkcsr_rowptr = (pangulu_exblock_ptr *)blkcsr_current_rank;
-        pangulu_exblock_idx *blkcsr_colidx = (pangulu_exblock_idx *)(blkcsr_current_rank + sizeof(pangulu_exblock_ptr) * (block_length + 1));
-        pangulu_inblock_ptr *blkcsr_value_blknnz = (pangulu_inblock_ptr *)(blkcsr_current_rank + sizeof(pangulu_exblock_ptr) * (block_length + 1) + sizeof(pangulu_exblock_idx) * nzblk_current_rank);
-
-        pangulu_int64_t blocks_current_rank_receive_offset = 0;
-        for (pangulu_exblock_idx brow = 0; brow < block_length; brow++)
-        {
-            for (pangulu_exblock_ptr bidx = blkcsr_rowptr[brow]; bidx < blkcsr_rowptr[brow + 1]; bidx++)
-            {
-                pangulu_exblock_idx bcol = blkcsr_colidx[bidx];
-                MPI_Recv(blocks_current_rank + blocks_current_rank_receive_offset, sizeof(pangulu_inblock_ptr) * (nb + 1) + (sizeof(pangulu_inblock_idx) + sizeof(calculate_type)) * blkcsr_value_blknnz[bidx], MPI_CHAR, 0, bidx, MPI_COMM_WORLD, &mpi_stat);
-
-                pangulu_smatrix *current = &Big_smatrix_value[current_rank_block_count];
-                current->row = nb;
-                current->column = nb;
-                current->rowpointer = (pangulu_inblock_ptr *)(blocks_current_rank + blocks_current_rank_receive_offset);
-                current->nnz = current->rowpointer[nb];
-                current->columnindex = (pangulu_inblock_idx *)(blocks_current_rank + blocks_current_rank_receive_offset + sizeof(pangulu_inblock_ptr) * (nb + 1));
-                current->value = (calculate_type *)(blocks_current_rank + blocks_current_rank_receive_offset + sizeof(pangulu_inblock_ptr) * (nb + 1) + sizeof(pangulu_inblock_idx) * current->nnz);
-
-                pangulu_bip_set(brow * block_length + bcol, BIP)->mapper_a = current_rank_block_count;
-
-                blocks_current_rank_receive_offset += sizeof(pangulu_inblock_ptr) * (nb + 1) + (sizeof(pangulu_inblock_idx) + sizeof(calculate_type)) * blkcsr_value_blknnz[bidx];
-                current_rank_block_count++;
-            }
-        }
-    }
-    pangulu_free(__FILE__, __LINE__, blkcsr_current_rank);
 
     for (pangulu_int64_t offset_block_index = 0; offset_block_index < p * q; offset_block_index++)
     {
@@ -1020,7 +678,7 @@ void pangulu_preprocessing(pangulu_block_common *block_common,
 
     for (pangulu_int64_t i = 0; i < current_rank_block_count; i++)
     {
-        pangulu_smatrix_add_more_memory(&Big_smatrix_value[i]);
+        pangulu_smatrix_add_more_memory_csr(&Big_smatrix_value[i]);
 
 #ifdef GPU_OPEN
         pangulu_smatrix_add_cuda_memory(&Big_smatrix_value[i]);
@@ -1530,8 +1188,11 @@ void pangulu_preprocessing(pangulu_block_common *block_common,
     }
 
     temp_a_value = (calculate_type *)pangulu_malloc(__FILE__, __LINE__, sizeof(calculate_type) * nb * nb);
+    memset(temp_a_value, 0, sizeof(calculate_type) * nb * nb);
     ssssm_l_value = (calculate_type *)pangulu_malloc(__FILE__, __LINE__, sizeof(calculate_type) * nb * nb);
+    memset(ssssm_l_value, 0, sizeof(calculate_type) * nb * nb);
     ssssm_u_value = (calculate_type *)pangulu_malloc(__FILE__, __LINE__, sizeof(calculate_type) * nb * nb);
+    memset(ssssm_u_value, 0, sizeof(calculate_type) * nb * nb);
     ssssm_hash_l_row = (pangulu_int32_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int32_t) * (nb));
     ssssm_hash_u_col = (pangulu_int32_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int32_t) * (nb));
     ssssm_hash_lu = (pangulu_int32_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int32_t) * (nb));
@@ -1585,7 +1246,7 @@ void pangulu_preprocessing(pangulu_block_common *block_common,
     block_smatrix->save_send_rank_flag = save_send_rank_flag;
 
     block_smatrix->receive_level_num = receive_level_num;
-    block_smatrix->blocks_current_rank = blocks_current_rank;
+    // block_smatrix->blocks_current_rank = blocks_current_rank;
     block_smatrix->save_tmp = NULL;
 
     block_smatrix->level_index = level_index;
diff --git a/src/pangulu_reorder.c b/src/pangulu_reorder.c
index dd95bab..469f3ff 100644
--- a/src/pangulu_reorder.c
+++ b/src/pangulu_reorder.c
@@ -652,24 +652,24 @@ void pangulu_mc64(pangulu_origin_smatrix *s, pangulu_exblock_idx **perm, pangulu
 }
 #endif
 
-void pangulu_origin_smatrix_transport_transport_iperm(pangulu_origin_smatrix *s, pangulu_origin_smatrix *new_S, pangulu_exblock_idx *metis_perm)
+void pangulu_metis_reorder(pangulu_origin_smatrix *s, pangulu_origin_smatrix *new_S, pangulu_exblock_idx *metis_perm)
 {
     pangulu_exblock_idx n = s->row;
     pangulu_exblock_ptr nnz = s->nnz;
     pangulu_exblock_ptr *rowpointer = (pangulu_exblock_ptr *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
     pangulu_exblock_idx *columnindex = (pangulu_exblock_idx *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * nnz);
     calculate_type *value = (calculate_type *)pangulu_malloc(__FILE__, __LINE__, sizeof(calculate_type) * nnz);
+    #pragma omp parallel for
     for (pangulu_exblock_idx i = 0; i < n; i++)
     {
-        pangulu_exblock_idx row_num = s->rowpointer[i + 1] - s->rowpointer[i];
-        pangulu_exblock_idx index = metis_perm[i];
-        rowpointer[index + 1] = row_num;
+        rowpointer[metis_perm[i] + 1] = s->rowpointer[i + 1] - s->rowpointer[i];
     }
     rowpointer[0] = 0;
     for (pangulu_exblock_idx i = 0; i < n; i++)
     {
         rowpointer[i + 1] += rowpointer[i];
     }
+    #pragma omp parallel for
     for (pangulu_exblock_idx i = 0; i < n; i++)
     {
         pangulu_exblock_idx index = metis_perm[i];
@@ -689,185 +689,105 @@ void pangulu_origin_smatrix_transport_transport_iperm(pangulu_origin_smatrix *s,
 }
 
 #ifdef METIS
-void pangulu_get_graph_struct(pangulu_origin_smatrix *s, idx_t **xadj_adress, idx_t **adjincy_adress)
-{
+
+void pangulu_get_graph_struct(pangulu_origin_smatrix *s, idx_t **xadj_address, idx_t **adjincy_address){
+    struct timeval start_time;
+    
+    pangulu_time_start(&start_time);
     pangulu_add_diagonal_element(s);
+    printf("[PanguLU Info] 2.1 PanguLU METIS add_diagonal_element time is %lf s.\n", pangulu_time_stop(&start_time));
+
+    pangulu_time_start(&start_time);
     pangulu_origin_smatrix_add_csc(s);
+    printf("[PanguLU Info] 2.2 PanguLU METIS transpose time is %lf s.\n", pangulu_time_stop(&start_time));
+
+    pangulu_time_start(&start_time);
     idx_t *xadj = (idx_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(idx_t) * (s->row + 1));
-    xadj[0] = 0;
+    idx_t *adjincy = pangulu_malloc(__FILE__, __LINE__, sizeof(idx_t) * s->nnz * 2);
 
-    for (pangulu_exblock_idx i = 0; i < s->row; i++)
-    {
-        pangulu_exblock_ptr index1 = s->rowpointer[i];
-        pangulu_exblock_ptr index2 = s->columnpointer[i];
-        pangulu_exblock_ptr end1 = s->rowpointer[i + 1];
-        pangulu_exblock_ptr end2 = s->columnpointer[i + 1];
-        char diagonal_flag = 0;
-        pangulu_int64_t sum_num = 0;
-        pangulu_exblock_idx col1 = s->columnindex[index1];
-        pangulu_exblock_idx col2 = s->rowindex[index2];
-        while ((index1 < end1) && (index2 < end2))
-        {
-            if (col1 == col2)
-            {
-                if ((diagonal_flag == 0) && (col1 == i))
-                {
-                    diagonal_flag = 1;
+    xadj[0] = 0;
+    for(pangulu_exblock_idx rc = 0; rc < s->row; rc++){
+        pangulu_exblock_idx nnz_count = 0;
+        pangulu_exblock_ptr start1 = s->rowpointer[rc];
+        pangulu_exblock_ptr end1 = s->rowpointer[rc+1];
+        pangulu_exblock_ptr start2 = s->columnpointer[rc];
+        pangulu_exblock_ptr end2 = s->columnpointer[rc+1];
+        pangulu_exblock_ptr idx1 = start1;
+        pangulu_exblock_ptr idx2 = start2;
+
+        while((idx1 < end1) && (idx2 < end2)){
+            if(s->columnindex[idx1] < s->rowindex[idx2]){
+                idx1++;
+            }else if(s->columnindex[idx1] > s->rowindex[idx2]){
+                idx2++;
+            }else{
+                idx1++;
+                idx2++;
+            }
+            nnz_count++;
+        }
+        while(idx1 < end1){
+            idx1++;
+            nnz_count++;
+        }
+        while(idx2 < end2){
+            idx2++;
+            nnz_count++;
+        }
+        nnz_count--;
+        xadj[rc + 1] = xadj[rc] + nnz_count;
+
+        nnz_count = 0;
+        idx1 = start1;
+        idx2 = start2;
+        while((idx1 < end1) && (idx2 < end2)){
+            if(s->columnindex[idx1] < s->rowindex[idx2]){
+                if(s->columnindex[idx1] != rc){
+                    adjincy[xadj[rc] + nnz_count] = s->columnindex[idx1];
+                    nnz_count++;
                 }
-                index1++;
-                index2++;
-                col1 = s->columnindex[index1];
-                col2 = s->rowindex[index2];
-            }
-            else if (col1 < col2)
-            {
-                if ((diagonal_flag == 0) && (col1 == i))
-                {
-                    diagonal_flag = 1;
+                idx1++;
+            }else if(s->columnindex[idx1] > s->rowindex[idx2]){
+                if(s->rowindex[idx2] != rc){
+                    adjincy[xadj[rc] + nnz_count] = s->rowindex[idx2];
+                    nnz_count++;
                 }
-                index1++;
-                col1 = s->columnindex[index1];
-            }
-            else
-            {
-                if ((diagonal_flag == 0) && (col2 == i))
-                {
-                    diagonal_flag = 1;
+                idx2++;
+            }else{
+                if(s->columnindex[idx1] != rc){
+                    adjincy[xadj[rc] + nnz_count] = s->columnindex[idx1];
+                    nnz_count++;
                 }
-                index2++;
-                col2 = s->rowindex[index2];
+                idx1++;
+                idx2++;
             }
-            sum_num++;
         }
-        while (index1 < end1)
-        {
-            sum_num++;
-            if ((diagonal_flag == 0) && (col1 == i))
-            {
-                diagonal_flag = 1;
+        while(idx1 < end1){
+            if(s->columnindex[idx1] != rc){
+                adjincy[xadj[rc] + nnz_count] = s->columnindex[idx1];
+                nnz_count++;
             }
-            index1++;
-            col1 = s->columnindex[index1];
+            idx1++;
         }
-
-        while (index2 < end2)
-        {
-            sum_num++;
-            if ((diagonal_flag == 0) && (col2 == i))
-            {
-                diagonal_flag = 1;
+        while(idx2 < end2){
+            if(s->rowindex[idx2] != rc){
+                adjincy[xadj[rc] + nnz_count] = s->rowindex[idx2];
+                nnz_count++;
             }
-            index2++;
-            col2 = s->rowindex[index2];
+            idx2++;
         }
-        if (diagonal_flag == 0)
-        {
-            printf(PANGULU_E_ROW_DONT_HAVE_DIA);
-            pangulu_exit(1);
-        }
-        xadj[i + 1] = sum_num - diagonal_flag;
-    }
-    for (pangulu_exblock_idx i = 0; i < s->row; i++)
-    {
-        xadj[i + 1] += xadj[i];
     }
 
-    idx_t *adjincy = (idx_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(idx_t) * (xadj[s->row]));
-
-    for (pangulu_exblock_ptr i = 0; i < s->row; i++)
-    {
-        idx_t now_adjincy_index = xadj[i];
-        pangulu_exblock_ptr index1 = s->rowpointer[i];
-        pangulu_exblock_ptr index2 = s->columnpointer[i];
-        pangulu_exblock_ptr end1 = s->rowpointer[i + 1];
-        pangulu_exblock_ptr end2 = s->columnpointer[i + 1];
-        char diagonal_flag = 0;
-        pangulu_exblock_idx col1 = s->columnindex[index1];
-        pangulu_exblock_idx col2 = s->rowindex[index2];
-        while ((index1 < end1) && (index2 < end2))
-        {
-            if (col1 == col2)
-            {
-                if ((diagonal_flag == 0) && (col1 == i))
-                {
-                    diagonal_flag = 1;
-                }
-                else
-                {
-                    adjincy[now_adjincy_index] = col1;
-                    now_adjincy_index++;
-                }
-                index1++;
-                index2++;
-                col1 = s->columnindex[index1];
-                col2 = s->rowindex[index2];
-            }
-            else if (col1 < col2)
-            {
-                if ((diagonal_flag == 0) && (col1 == i))
-                {
-                    diagonal_flag = 1;
-                }
-                else
-                {
-                    adjincy[now_adjincy_index] = col1;
-                    now_adjincy_index++;
-                }
-                index1++;
-                col1 = s->columnindex[index1];
-            }
-            else
-            {
-                if ((diagonal_flag == 0) && (col2 == i))
-                {
-                    diagonal_flag = 1;
-                }
-                else
-                {
-                    adjincy[now_adjincy_index] = col2;
-                    now_adjincy_index++;
-                }
-                index2++;
-                col2 = s->rowindex[index2];
-            }
-        }
-        while (index1 < end1)
-        {
-            if ((diagonal_flag == 0) && (col1 == i))
-            {
-                diagonal_flag = 1;
-            }
-            else
-            {
-                adjincy[now_adjincy_index] = col1;
-                now_adjincy_index++;
-            }
-            index1++;
-            col1 = s->columnindex[index1];
-        }
-
-        while (index2 < end2)
-        {
-            if ((diagonal_flag == 0) && (col2 == i))
-            {
-                diagonal_flag = 1;
-            }
-            else
-            {
-                adjincy[now_adjincy_index] = col2;
-                now_adjincy_index++;
-            }
-            index2++;
-            col2 = s->rowindex[index2];
-        }
-    }
-    *xadj_adress = xadj;
-    *adjincy_adress = adjincy;
+    adjincy = pangulu_realloc(__FILE__, __LINE__, adjincy, sizeof(idx_t) * xadj[s->row]);
+    *xadj_address = xadj;
+    *adjincy_address = adjincy;
+    printf("[PanguLU Info] 2.3 PanguLU METIS get_graph_struct.other_code time is %lf s.\n", pangulu_time_stop(&start_time));
 }
 
 void pangulu_metis(pangulu_origin_smatrix *a, idx_t **metis_perm)
 {
 
+    struct timeval start_time;
     idx_t n = a->row;
 
     idx_t *iperm = (idx_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(idx_t) * n);
@@ -876,8 +796,13 @@ void pangulu_metis(pangulu_origin_smatrix *a, idx_t **metis_perm)
     idx_t *xadj = NULL;
     idx_t *adjincy = NULL;
 
+    pangulu_time_start(&start_time);
     pangulu_get_graph_struct(a, &xadj, &adjincy);
+    printf("[PanguLU Info] 2 PanguLU METIS get_graph_struct time is %lf s.\n", pangulu_time_stop(&start_time));
+    
+    pangulu_time_start(&start_time);
     METIS_NodeND(&n, xadj, adjincy, NULL, NULL, perm, iperm);
+    printf("[PanguLU Info] 3.1 PanguLU METIS generate the perm time is %lf s.\n", pangulu_time_stop(&start_time));
 
     pangulu_free(__FILE__, __LINE__, perm);
     pangulu_free(__FILE__, __LINE__, xadj);
@@ -930,6 +855,7 @@ void pangulu_reorder(pangulu_block_smatrix *block_smatrix,
                      pangulu_origin_smatrix *origin_matrix,
                      pangulu_origin_smatrix *reorder_matrix)
 {
+    struct timeval start_time;
     pangulu_exblock_idx n = origin_matrix->row;
     pangulu_exblock_ptr nnz = origin_matrix->nnz;
     pangulu_exblock_idx *perm = NULL;
@@ -942,7 +868,9 @@ void pangulu_reorder(pangulu_block_smatrix *block_smatrix,
     if (rank == 0)
     {
 #if defined(PANGULU_MC64)
+        pangulu_time_start(&start_time);
         pangulu_mc64(origin_matrix, &perm, &iperm, &row_scale, &col_scale);
+        printf("[PanguLU Info] 1.1 PanguLU MC64 generate the perm time is %lf s.\n", pangulu_time_stop(&start_time));
 #else
         perm = (pangulu_exblock_idx *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * n);
         iperm = (pangulu_exblock_idx *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * n);
@@ -970,6 +898,7 @@ void pangulu_reorder(pangulu_block_smatrix *block_smatrix,
             col_scale[i] = 1.0;
         }
 #endif
+        pangulu_time_start(&start_time);
         tmp = (pangulu_origin_smatrix *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_origin_smatrix));
         pangulu_init_pangulu_origin_smatrix(tmp);
         tmp->row = n;
@@ -981,6 +910,7 @@ void pangulu_reorder(pangulu_block_smatrix *block_smatrix,
 
         tmp->rowpointer[0] = 0;
 
+        #pragma omp parallel for
         for (pangulu_int64_t i = 0; i < n; i++)
         {
             pangulu_int64_t row = perm[i];
@@ -992,6 +922,7 @@ void pangulu_reorder(pangulu_block_smatrix *block_smatrix,
             tmp->rowpointer[i + 1] += tmp->rowpointer[i];
         }
 
+        #pragma omp parallel for
         for (pangulu_int64_t i = 0; i < n; i++)
         {
             pangulu_exblock_idx row = perm[i];
@@ -1002,15 +933,10 @@ void pangulu_reorder(pangulu_block_smatrix *block_smatrix,
                 pangulu_exblock_idx col = origin_matrix->columnindex[j];
                 tmp->columnindex[tmp_index] = col;
                 tmp->value[tmp_index] = (origin_matrix->value[j] * rs * col_scale[col]);
-                // if (col == row)
-                // {
-                //     if (fabs(fabs(tmp->value[tmp_index]) - 1.0) > 1e-10)
-                //     {
-                //     }
-                // }
                 tmp_index++;
             }
         }
+        printf("[PanguLU Info] 1.2 PanguLU MC64 reordering time is %lf s.\n", pangulu_time_stop(&start_time));
     }
 
 #ifdef METIS
@@ -1037,8 +963,17 @@ void pangulu_reorder(pangulu_block_smatrix *block_smatrix,
 #endif
     if (rank == 0)
     {
-        pangulu_origin_smatrix_transport_transport_iperm(tmp, reorder_matrix, metis_perm);
+        pangulu_time_start(&start_time);
+        pangulu_metis_reorder(tmp, reorder_matrix, metis_perm);
         pangulu_sort_pangulu_origin_smatrix(reorder_matrix);
+        for(pangulu_exblock_idx row = 0; row < n; row++){
+            for(pangulu_exblock_ptr idx = reorder_matrix->rowpointer[row]; idx < reorder_matrix->rowpointer[row+1]; idx++){
+                if((row == reorder_matrix->columnindex[idx]) && (fabs(reorder_matrix->value[idx]) < ZERO_ELEMENT)){
+                    reorder_matrix->value[idx] = ZERO_ELEMENT;
+                }
+            }
+        }
+        printf("[PanguLU Info] 3.2 PanguLU METIS reordering time is %lf s.\n", pangulu_time_stop(&start_time));
 
         block_smatrix->row_perm = perm;
         block_smatrix->col_perm = iperm;
diff --git a/src/pangulu_symbolic.c b/src/pangulu_symbolic.c
index a789a59..5e3cb33 100644
--- a/src/pangulu_symbolic.c
+++ b/src/pangulu_symbolic.c
@@ -507,9 +507,12 @@ void pangulu_symbolic(pangulu_block_common *block_common,
     pangulu_exblock_ptr *new_rowpointer=NULL;
     pangulu_exblock_idx *new_columnindex=NULL;
     pangulu_exblock_ptr new_nnz;
+    struct timeval start_time;
+    pangulu_time_start(&start_time);
     at_plus_a_dist(reorder_matrix->row,reorder_matrix->nnz,
                    reorder_matrix->rowpointer,reorder_matrix->columnindex,
                    &new_nnz,&new_rowpointer,&new_columnindex);
+    printf("[PanguLU Info] 4 PanguLU A+AT (before symbolic) time is %lf s.\n", pangulu_time_stop(&start_time));
     pangulu_exblock_ptr *symbolic_rowpointer = NULL;
     pangulu_exblock_idx *symbolic_columnindex = NULL;
     pangulu_inblock_idx nb = block_common->nb;
@@ -532,6 +535,7 @@ void pangulu_symbolic(pangulu_block_common *block_common,
         block_smatrix_nnzA_num[i] = 0;
     }
 
+    pangulu_time_start(&start_time);
     fill_in_sym_prune(reorder_matrix->row,new_nnz,new_columnindex,new_rowpointer,
                     &symbolic_rowpointer,&symbolic_columnindex,
                     nb,block_length,
@@ -540,6 +544,7 @@ void pangulu_symbolic(pangulu_block_common *block_common,
                     block_smatrix_nnzA_num,
                     &block_smatrix->symbolic_nnz
                     );
+    printf("[PanguLU Info] 5 PanguLU symbolic time is %lf s.\n", pangulu_time_stop(&start_time));
     
     pangulu_free(__FILE__, __LINE__, new_rowpointer);
     pangulu_free(__FILE__, __LINE__, new_columnindex);
diff --git a/src/pangulu_time.c b/src/pangulu_time.c
index 700c4d3..3404d20 100644
--- a/src/pangulu_time.c
+++ b/src/pangulu_time.c
@@ -15,7 +15,7 @@ double pangulu_time_check_end(struct timeval *GET_TIME_START)
 
 void pangulu_time_init()
 {
-    time_transport = 0.0;
+    time_transpose = 0.0;
     time_isend = 0.0;
     time_receive = 0.0;
     time_getrf = 0.0;
diff --git a/src/pangulu_tstrf_fp64.c b/src/pangulu_tstrf_fp64.c
index 3f0e11d..8c3fd75 100644
--- a/src/pangulu_tstrf_fp64.c
+++ b/src/pangulu_tstrf_fp64.c
@@ -351,10 +351,10 @@ void pangulu_tstrf_interface_c_v1(pangulu_smatrix *a,
 #ifdef GPU_OPEN
     pangulu_smatrix_cuda_memcpy_value_csc(a, a);
 #endif
-    pangulu_transport_pangulu_smatrix_csc_to_csr(a);
+    pangulu_transpose_pangulu_smatrix_csc_to_csr(a);
     pangulu_pangulu_smatrix_memcpy_value_csc_copy_length(x, a);
     pangulu_tstrf_fp64_cpu_4(a, x, u);
-    pangulu_transport_pangulu_smatrix_csr_to_csc(a);
+    pangulu_transpose_pangulu_smatrix_csr_to_csc(a);
 #ifdef GPU_OPEN
     pangulu_smatrix_cuda_memcpy_to_device_value_csc(a, a);
 #endif
@@ -366,10 +366,10 @@ void pangulu_tstrf_interface_c_v2(pangulu_smatrix *a,
 #ifdef GPU_OPEN
     pangulu_smatrix_cuda_memcpy_value_csc(a, a);
 #endif
-    pangulu_transport_pangulu_smatrix_csc_to_csr(a);
+    pangulu_transpose_pangulu_smatrix_csc_to_csr(a);
     pangulu_pangulu_smatrix_memcpy_value_csc_copy_length(x, a);
     pangulu_tstrf_fp64_cpu_6(a, x, u);
-    pangulu_transport_pangulu_smatrix_csr_to_csc(a);
+    pangulu_transpose_pangulu_smatrix_csr_to_csc(a);
 #ifdef GPU_OPEN
     pangulu_smatrix_cuda_memcpy_to_device_value_csc(a, a);
 #endif
diff --git a/src/pangulu_tstrf_fp64_cuda.c b/src/pangulu_tstrf_fp64_cuda.c
index 01145a5..01d3546 100644
--- a/src/pangulu_tstrf_fp64_cuda.c
+++ b/src/pangulu_tstrf_fp64_cuda.c
@@ -178,11 +178,11 @@ void pangulu_tstrf_interface_G_V1(pangulu_smatrix *a,
                                   pangulu_smatrix *u)
 {
     pangulu_smatrix_cuda_memcpy_value_csc(a, a);
-    pangulu_transport_pangulu_smatrix_csc_to_csr(a);
+    pangulu_transpose_pangulu_smatrix_csc_to_csr(a);
     pangulu_smatrix_cuda_memcpy_complete_csr(a, a);
     pangulu_tstrf_fp64_cuda_v7(a, x, u);
     pangulu_smatrix_cuda_memcpy_value_csr(a, x);
-    pangulu_transport_pangulu_smatrix_csr_to_csc(a);
+    pangulu_transpose_pangulu_smatrix_csr_to_csc(a);
 }
 void pangulu_tstrf_interface_G_V2(pangulu_smatrix *a,
                                   pangulu_smatrix *x,
@@ -196,10 +196,10 @@ void pangulu_tstrf_interface_G_V3(pangulu_smatrix *a,
                                   pangulu_smatrix *u)
 {
     pangulu_smatrix_cuda_memcpy_value_csc(a, a);
-    pangulu_transport_pangulu_smatrix_csc_to_csr(a);
+    pangulu_transpose_pangulu_smatrix_csc_to_csr(a);
     pangulu_smatrix_cuda_memcpy_complete_csr(a, a);
     pangulu_tstrf_fp64_cuda_v10(a, x, u);
     pangulu_smatrix_cuda_memcpy_value_csr(a, x);
-    pangulu_transport_pangulu_smatrix_csr_to_csc(a);
+    pangulu_transpose_pangulu_smatrix_csr_to_csc(a);
 }
 #endif
\ No newline at end of file
diff --git a/src/pangulu_utils.c b/src/pangulu_utils.c
index f66e74d..e199a64 100644
--- a/src/pangulu_utils.c
+++ b/src/pangulu_utils.c
@@ -1,5 +1,1136 @@
 #include "pangulu_common.h"
 
+void pangulu_sort_exblock_struct(
+    pangulu_exblock_idx n,
+    pangulu_exblock_ptr* pointer,
+    pangulu_exblock_idx* index,
+    pangulu_int32_t nthread
+){
+    if(nthread <= 0){
+        nthread = sysconf(_SC_NPROCESSORS_ONLN);
+    }
+    
+    #pragma omp parallel num_threads(nthread)
+    {
+        bind_to_core(omp_get_thread_num() % sysconf(_SC_NPROCESSORS_ONLN));
+    }
+
+    #pragma omp parallel for num_threads(nthread) schedule(guided)
+    for (pangulu_exblock_idx i = 0; i < n; i++)
+    {
+        pangulu_kvsort(index, NULL, pointer[i], pointer[i + 1] - 1);
+    }
+}
+
+int cmp_exidx_asc(const void* a, const void* b){
+    if((*(pangulu_exblock_idx*)a) > (*(pangulu_exblock_idx*)b)){
+        return 1;
+    }else if((*(pangulu_exblock_idx*)a) < (*(pangulu_exblock_idx*)b)){
+        return -1;
+    }else{
+        return 0;
+    }
+}
+
+
+void pangulu_kvsort(pangulu_exblock_idx *key, calculate_type *val, pangulu_int64_t start, pangulu_int64_t end)
+{
+    if(val){
+        if (start < end)
+        {
+            pangulu_int64_t pivot;
+            pangulu_int64_t i, j, k;
+
+            // k = choose_pivot(start, end);
+            k = (start + end) / 2;
+            swap_index_1(&key[start], &key[k]);
+            swap_value(&val[start], &val[k]);
+            pivot = key[start];
+
+            i = start + 1;
+            j = end;
+            while (i <= j)
+            {
+                while ((i <= end) && (key[i] <= pivot))
+                    i++;
+                while ((j >= start) && (key[j] > pivot))
+                    j--;
+                if (i < j)
+                {
+                    swap_index_1(&key[i], &key[j]);
+                    swap_value(&val[i], &val[j]);
+                }
+            }
+
+            // swap two elements
+            swap_index_1(&key[start], &key[j]);
+            swap_value(&val[start], &val[j]);
+
+            // recursively sort the lesser key
+            pangulu_kvsort(key, val, start, j - 1);
+            pangulu_kvsort(key, val, j + 1, end);
+        }
+    }else{
+        qsort(key + start, end + 1 - start , sizeof(pangulu_exblock_idx), cmp_exidx_asc);
+    }
+}
+
+void pangulu_cm_distribute_distcsc_to_distbcsc(
+    int rootproc_free_originmatrix,
+    int malloc_distbcsc_value,
+    pangulu_exblock_idx n_glo,
+    pangulu_exblock_idx n_loc,
+    pangulu_inblock_idx block_order,
+    
+    pangulu_exblock_ptr* distcsc_proc_nnzptr,
+    pangulu_exblock_ptr* distcsc_pointer,
+    pangulu_exblock_idx* distcsc_index,
+    calculate_type* distcsc_value,
+
+    pangulu_exblock_ptr** bcsc_struct_pointer,
+    pangulu_exblock_idx** bcsc_struct_index,
+    pangulu_exblock_ptr** bcsc_struct_nnzptr,
+    pangulu_inblock_ptr*** bcsc_inblock_pointers,
+    pangulu_inblock_idx*** bcsc_inblock_indeces,
+    calculate_type*** bcsc_values
+){
+#define _PANGULU_SET_VALUE_SIZE(size) ((distcsc_value)?(size):(0))
+#define _PANGULU_SET_BVALUE_SIZE(size) ((malloc_distbcsc_value)?(size):(0))
+
+    if(distcsc_value){
+        malloc_distbcsc_value = 1;
+    }
+    // printf("malloc_distbcsc_value = %d\n", malloc_distbcsc_value);
+
+    struct timeval start_time;
+    pangulu_time_start(&start_time);
+
+    pangulu_int32_t rank, nproc;
+    pangulu_cm_rank(&rank);
+    pangulu_cm_size(&nproc);
+
+    if(distcsc_proc_nnzptr){
+        pangulu_free(__FILE__, __LINE__, distcsc_proc_nnzptr);
+    }
+    // printf("1.1\n");
+
+    int preprocess_ompnum_separate_block = 2;
+
+    bind_to_core((rank * preprocess_ompnum_separate_block) % sysconf(_SC_NPROCESSORS_ONLN));
+
+    #pragma omp parallel num_threads(preprocess_ompnum_separate_block)
+    {
+        bind_to_core((rank * preprocess_ompnum_separate_block + omp_get_thread_num()) % sysconf(_SC_NPROCESSORS_ONLN));
+    }
+
+    pangulu_int64_t p = sqrt(nproc);
+    while ((nproc % p) != 0)
+    {
+        p--;
+    }
+    pangulu_int64_t q = nproc / p;
+    pangulu_exblock_idx col_per_rank = PANGULU_ICEIL(PANGULU_ICEIL(n_glo, block_order * q), nproc) * (block_order * q);
+    pangulu_int64_t block_length = PANGULU_ICEIL(col_per_rank, block_order);
+    pangulu_int64_t block_length_col = PANGULU_ICEIL(n_glo, block_order);
+    pangulu_exblock_ptr nnz = distcsc_pointer[n_loc];
+    pangulu_int64_t bit_length = (block_length_col + 31) / 32;
+    pangulu_int64_t block_num = 0;
+    pangulu_int64_t *block_nnz_pt;
+    // printf("1.2\n");
+
+    pangulu_int64_t avg_nnz = PANGULU_ICEIL(nnz, preprocess_ompnum_separate_block);
+    pangulu_int64_t *block_row_nnz_pt = (pangulu_int64_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int64_t) * (block_length + 1));
+    for (int i = 0; i < block_length; i++)
+    {
+        block_row_nnz_pt[i] = distcsc_pointer[PANGULU_MIN(i * block_order, n_loc)];
+    }
+    block_row_nnz_pt[block_length] = distcsc_pointer[n_loc];
+
+    int *thread_pt = (int *)pangulu_malloc(__FILE__, __LINE__, sizeof(int) * (preprocess_ompnum_separate_block + 1));
+    thread_pt[0] = 0;
+    for (int i = 1; i < preprocess_ompnum_separate_block + 1; i++)
+    {
+        thread_pt[i] = binarylowerbound(block_row_nnz_pt, block_length, avg_nnz * i);
+    }
+    pangulu_free(__FILE__, __LINE__, block_row_nnz_pt);
+    block_row_nnz_pt = NULL;
+
+    pangulu_int64_t *block_row_pt = (pangulu_int64_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int64_t) * (block_length + 1));
+    memset(block_row_pt, 0, sizeof(pangulu_int64_t) * (block_length + 1));
+
+    unsigned int *bit_array = (unsigned int *)pangulu_malloc(__FILE__, __LINE__, sizeof(unsigned int) * bit_length * preprocess_ompnum_separate_block);
+
+#pragma omp parallel num_threads(preprocess_ompnum_separate_block)
+    {
+        int tid = omp_get_thread_num();
+        unsigned int *tmp_bit = bit_array + bit_length * tid;
+
+        for (int level = thread_pt[tid]; level < thread_pt[tid + 1]; level++)
+        {
+            memset(tmp_bit, 0, sizeof(unsigned int) * bit_length);
+
+            int start_row = level * block_order;
+            int end_row = ((level + 1) * block_order) < n_loc ? ((level + 1) * block_order) : n_loc;
+
+            for (int rid = start_row; rid < end_row; rid++)
+            {
+                for (pangulu_int64_t idx = distcsc_pointer[rid]; idx < distcsc_pointer[rid + 1]; idx++)
+                {
+                    pangulu_int32_t colidx = distcsc_index[idx];
+                    pangulu_int32_t block_cid = colidx / block_order;
+                    setbit(tmp_bit[block_cid / 32], block_cid % 32);
+                }
+            }
+
+            pangulu_int64_t tmp_blocknum = 0;
+            for (int i = 0; i < bit_length; i++)
+            {
+                tmp_blocknum += __builtin_popcount(tmp_bit[i]);
+            }
+
+            block_row_pt[level] = tmp_blocknum;
+        }
+    }
+    exclusive_scan_1(block_row_pt, block_length + 1);
+    block_num = block_row_pt[block_length];
+
+    block_nnz_pt = (pangulu_int64_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int64_t) * (block_num + 1));
+    memset(block_nnz_pt, 0, sizeof(pangulu_int64_t) * (block_num + 1));
+    pangulu_int32_t *block_col_idx = (pangulu_int32_t *)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_int32_t) * block_num);
+
+    int *count_array = (int *)pangulu_malloc(__FILE__, __LINE__, sizeof(int) * block_length_col * preprocess_ompnum_separate_block);
+#pragma omp parallel num_threads(preprocess_ompnum_separate_block)
+    {
+        int tid = omp_get_thread_num();
+        unsigned int *tmp_bit = bit_array + bit_length * tid;
+        int *tmp_count = count_array + block_length_col * tid;
+
+        for (int level = thread_pt[tid]; level < thread_pt[tid + 1]; level++)
+        {
+            memset(tmp_bit, 0, sizeof(unsigned int) * bit_length);
+            memset(tmp_count, 0, sizeof(int) * block_length_col);
+
+            pangulu_int64_t *cur_block_nnz_pt = block_nnz_pt + block_row_pt[level];
+            pangulu_int32_t *cur_block_col_idx = block_col_idx + block_row_pt[level];
+
+            int start_row = level * block_order;
+            int end_row = ((level + 1) * block_order) < n_loc ? ((level + 1) * block_order) : n_loc;
+
+            for (int rid = start_row; rid < end_row; rid++)
+            {
+                for (pangulu_int64_t idx = distcsc_pointer[rid]; idx < distcsc_pointer[rid + 1]; idx++)
+                {
+                    pangulu_int32_t colidx = distcsc_index[idx];
+                    pangulu_int32_t block_cid = colidx / block_order;
+                    setbit(tmp_bit[block_cid / 32], block_cid % 32);
+                    tmp_count[block_cid]++;
+                }
+            }
+
+            pangulu_int64_t cnt = 0;
+            for (int i = 0; i < block_length_col; i++)
+            {
+                if (getbit(tmp_bit[i / 32], i % 32))
+                {
+                    cur_block_nnz_pt[cnt] = tmp_count[i];
+                    cur_block_col_idx[cnt] = i;
+                    cnt++;
+                }
+            }
+        }
+    }
+    pangulu_free(__FILE__, __LINE__, bit_array);
+    bit_array = NULL;
+    pangulu_free(__FILE__, __LINE__, count_array);
+    count_array = NULL;
+    exclusive_scan_1(block_nnz_pt, block_num + 1);
+    
+    // printf("1.3\n");
+    
+    pangulu_exblock_ptr* nzblk_each_rank_ptr = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (nproc + 1));
+    pangulu_exblock_ptr* nnz_each_rank_ptr = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (nproc + 1));
+    memset(nzblk_each_rank_ptr, 0, sizeof(pangulu_exblock_ptr) * (nproc + 1));
+    memset(nnz_each_rank_ptr, 0, sizeof(pangulu_exblock_ptr) * (nproc + 1));
+    for(pangulu_exblock_idx bcol = 0; bcol < block_length; bcol++){
+        for(pangulu_exblock_ptr bidx = block_row_pt[bcol]; bidx < block_row_pt[bcol+1]; bidx++){
+            pangulu_exblock_idx brow = block_col_idx[bidx];
+            nzblk_each_rank_ptr[(brow % p) * q + (bcol % q) + 1]++;
+            nnz_each_rank_ptr[(brow % p) * q + (bcol % q) + 1] += (block_nnz_pt[bidx + 1] - block_nnz_pt[bidx]);
+        }
+    }
+    for(pangulu_int32_t remote_rank = 0; remote_rank < nproc; remote_rank++){
+        nzblk_each_rank_ptr[remote_rank + 1] += nzblk_each_rank_ptr[remote_rank];
+        nnz_each_rank_ptr[remote_rank + 1] += nnz_each_rank_ptr[remote_rank];
+    }
+    char** csc_draft_remote = pangulu_malloc(__FILE__, __LINE__, sizeof(char*) * nproc);
+    for(pangulu_int32_t remote_rank = 0; remote_rank < nproc; remote_rank++){
+        csc_draft_remote[remote_rank] = pangulu_malloc(
+            __FILE__, __LINE__, 
+            sizeof(pangulu_exblock_ptr) * (block_length + 1) + 
+            sizeof(pangulu_exblock_idx) * (nzblk_each_rank_ptr[remote_rank + 1] - nzblk_each_rank_ptr[remote_rank]) +
+            sizeof(pangulu_exblock_ptr) * (nzblk_each_rank_ptr[remote_rank + 1] - nzblk_each_rank_ptr[remote_rank] + 1)
+        );
+        memset(csc_draft_remote[remote_rank], 0, 
+            sizeof(pangulu_exblock_ptr) * (block_length + 1) + 
+            sizeof(pangulu_exblock_idx) * (nzblk_each_rank_ptr[remote_rank + 1] - nzblk_each_rank_ptr[remote_rank]) +
+            sizeof(pangulu_exblock_ptr) * (nzblk_each_rank_ptr[remote_rank + 1] - nzblk_each_rank_ptr[remote_rank] + 1)
+        );
+    }
+    
+    for(pangulu_exblock_idx bcol = 0; bcol < block_length; bcol++){
+        for(pangulu_exblock_ptr bidx = block_row_pt[bcol]; bidx < block_row_pt[bcol+1]; bidx++){
+            pangulu_exblock_idx brow = block_col_idx[bidx];
+            pangulu_inblock_ptr nnz_in_blk = block_nnz_pt[bidx + 1] - block_nnz_pt[bidx];
+            pangulu_int32_t remote_rank = (brow % p) * q + (bcol % q);
+            pangulu_exblock_ptr* remote_bcolptr = (pangulu_exblock_ptr*)csc_draft_remote[remote_rank];
+            remote_bcolptr[bcol + 1]++;
+        }
+    }
+    // printf("1.4\n");
+
+    pangulu_exblock_ptr* aid_arr_colptr_remote = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (block_length + 1) * nproc);
+    for(pangulu_int32_t remote_rank = 0; remote_rank < nproc; remote_rank++){
+        pangulu_exblock_ptr* remote_bcolptr = (pangulu_exblock_ptr*)csc_draft_remote[remote_rank];
+        for(pangulu_exblock_idx bcol = 0; bcol < block_length; bcol++){
+            remote_bcolptr[bcol + 1] += remote_bcolptr[bcol];
+        }
+        memcpy(&aid_arr_colptr_remote[(block_length + 1) * remote_rank], remote_bcolptr, sizeof(pangulu_exblock_ptr) * (block_length + 1));
+    }
+
+    for(pangulu_exblock_idx bcol = 0; bcol < block_length; bcol++){
+        for(pangulu_exblock_ptr bidx = block_row_pt[bcol]; bidx < block_row_pt[bcol+1]; bidx++){
+            pangulu_exblock_idx brow = block_col_idx[bidx];
+            pangulu_inblock_ptr nnz_in_blk = block_nnz_pt[bidx + 1] - block_nnz_pt[bidx];
+            pangulu_int32_t remote_rank = (brow % p) * q + (bcol % q);
+            
+            pangulu_exblock_idx* remote_browidx = (pangulu_exblock_idx*)
+                (csc_draft_remote[remote_rank] + 
+                sizeof(pangulu_exblock_ptr) * (block_length + 1));
+            pangulu_exblock_ptr* remote_blknnzptr = (pangulu_exblock_ptr*)
+                (csc_draft_remote[remote_rank] + 
+                sizeof(pangulu_exblock_ptr) * (block_length + 1) + 
+                sizeof(pangulu_exblock_idx) * (nzblk_each_rank_ptr[remote_rank + 1] - nzblk_each_rank_ptr[remote_rank]));
+            
+            remote_browidx[aid_arr_colptr_remote[(block_length + 1) * remote_rank + bcol]] = brow;
+            remote_blknnzptr[aid_arr_colptr_remote[(block_length + 1) * remote_rank + bcol] + 1] = nnz_in_blk;
+            aid_arr_colptr_remote[(block_length + 1) * remote_rank + bcol]++;
+        }
+    }
+    pangulu_free(__FILE__, __LINE__, aid_arr_colptr_remote);
+    aid_arr_colptr_remote = NULL;
+    pangulu_free(__FILE__, __LINE__, block_nnz_pt);
+    block_nnz_pt = NULL;
+    
+    for(pangulu_int32_t remote_rank = 0; remote_rank < nproc; remote_rank++){
+        pangulu_exblock_ptr* remote_bcolptr = csc_draft_remote[remote_rank];
+        pangulu_exblock_ptr* remote_blknnzptr = 
+                csc_draft_remote[remote_rank] + 
+                sizeof(pangulu_exblock_ptr) * (block_length + 1) + 
+                sizeof(pangulu_exblock_idx) * (nzblk_each_rank_ptr[remote_rank + 1] - nzblk_each_rank_ptr[remote_rank]);
+        for(pangulu_inblock_ptr bidx = 0; bidx < remote_bcolptr[block_length]; bidx++){
+            remote_blknnzptr[bidx + 1] += remote_blknnzptr[bidx];
+        }
+    }
+
+    char** block_csc_remote = pangulu_malloc(__FILE__, __LINE__, sizeof(char*) * nproc);
+    for(pangulu_int32_t target_rank = 0; target_rank < nproc; target_rank++){
+        block_csc_remote[target_rank] = pangulu_malloc(
+            __FILE__, __LINE__, 
+            sizeof(pangulu_inblock_ptr) * (block_order + 1) * (nzblk_each_rank_ptr[target_rank + 1] - nzblk_each_rank_ptr[target_rank]) +
+            sizeof(pangulu_inblock_idx) * (nnz_each_rank_ptr[target_rank + 1] - nnz_each_rank_ptr[target_rank]) + 
+            _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type)) * (nnz_each_rank_ptr[target_rank + 1] - nnz_each_rank_ptr[target_rank])
+        );
+        memset(
+            block_csc_remote[target_rank], 0, 
+            sizeof(pangulu_inblock_ptr) * (block_order + 1) * (nzblk_each_rank_ptr[target_rank + 1] - nzblk_each_rank_ptr[target_rank]) +
+            sizeof(pangulu_inblock_idx) * (nnz_each_rank_ptr[target_rank + 1] - nnz_each_rank_ptr[target_rank]) + 
+            _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type)) * (nnz_each_rank_ptr[target_rank + 1] - nnz_each_rank_ptr[target_rank])
+        );
+    }
+
+
+#pragma omp parallel num_threads(preprocess_ompnum_separate_block)
+    {
+        int tid = omp_get_thread_num();
+        int* tmp_count = pangulu_malloc(__FILE__, __LINE__, sizeof(int) * block_length_col * q);
+
+        for (int level = thread_pt[tid]; level < thread_pt[tid + 1]; level++)
+        {
+
+            memset(tmp_count, 0, sizeof(int) * block_length_col * q);
+        
+            pangulu_exblock_idx start_col = level * block_order;
+            pangulu_exblock_idx end_col = ((level + 1) * block_order) < n_loc ? ((level + 1) * block_order) : n_loc;
+            
+            for (pangulu_exblock_idx col = start_col, col_in_blc = 0; col < end_col; col++, col_in_blc++)
+            {
+                pangulu_int64_t bidx_glo = block_row_pt[level];
+                pangulu_exblock_idx brow = block_col_idx[bidx_glo];
+                pangulu_int32_t target_rank = (brow % p) * q + (level % q);
+                pangulu_exblock_ptr* remote_bcolptr = csc_draft_remote[target_rank];
+                pangulu_exblock_idx* remote_browidx = csc_draft_remote[target_rank] + sizeof(pangulu_exblock_ptr) * (block_length + 1);
+                pangulu_exblock_ptr* remote_bnnzptr = 
+                    csc_draft_remote[target_rank] + 
+                    sizeof(pangulu_exblock_ptr) * (block_length + 1) + 
+                    sizeof(pangulu_exblock_idx) * (nzblk_each_rank_ptr[target_rank + 1] - nzblk_each_rank_ptr[target_rank]);
+                pangulu_int64_t bidx = remote_bcolptr[level];
+
+                pangulu_int64_t arr_len = 
+                    sizeof(pangulu_inblock_ptr) * bidx * (block_order + 1) + 
+                    (sizeof(pangulu_inblock_idx) + _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type))) * remote_bnnzptr[bidx];
+                pangulu_inblock_ptr *cur_block_rowptr = (pangulu_inblock_ptr *)(block_csc_remote[target_rank] + arr_len);
+                pangulu_inblock_idx *cur_block_colidx = (pangulu_inblock_idx *)(block_csc_remote[target_rank] + arr_len + sizeof(pangulu_inblock_ptr) * (block_order + 1));
+                calculate_type *cur_block_value = NULL;
+                if(malloc_distbcsc_value){
+                    cur_block_value = (calculate_type *)(
+                        block_csc_remote[target_rank] + arr_len + 
+                        sizeof(pangulu_inblock_ptr) * (block_order + 1) + 
+                        sizeof(pangulu_inblock_idx) * (remote_bnnzptr[bidx + 1] - remote_bnnzptr[bidx])
+                    );
+                }
+
+                pangulu_exblock_ptr reorder_matrix_idx = distcsc_pointer[col];
+                pangulu_exblock_ptr reorder_matrix_idx_ub = distcsc_pointer[col + 1];
+                for (pangulu_exblock_ptr idx = distcsc_pointer[col]; idx < distcsc_pointer[col + 1]; idx++)
+                {
+                    pangulu_exblock_idx row = distcsc_index[idx];
+                    brow = row / block_order;
+                    if (block_col_idx[bidx_glo] != brow)
+                    {
+                        bidx_glo = binarysearch(block_col_idx, bidx_glo, block_row_pt[level + 1], brow);
+                        target_rank = (brow % p) * q + (level % q);
+                        remote_bcolptr = csc_draft_remote[target_rank];
+                        remote_browidx = csc_draft_remote[target_rank] + sizeof(pangulu_exblock_ptr) * (block_length + 1);
+                        remote_bnnzptr = 
+                            csc_draft_remote[target_rank] + 
+                            sizeof(pangulu_exblock_ptr) * (block_length + 1) + 
+                            sizeof(pangulu_exblock_idx) * (nzblk_each_rank_ptr[target_rank + 1] - nzblk_each_rank_ptr[target_rank]);
+                        bidx = binarysearch(remote_browidx, remote_bcolptr[level], remote_bcolptr[level + 1], brow);
+                        arr_len = 
+                            sizeof(pangulu_inblock_ptr) * bidx * (block_order + 1) + 
+                            (sizeof(pangulu_inblock_idx) + _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type))) * remote_bnnzptr[bidx];
+                        cur_block_rowptr = (pangulu_inblock_ptr *)(block_csc_remote[target_rank] + arr_len);
+                        cur_block_colidx = (pangulu_inblock_idx *)(block_csc_remote[target_rank] + arr_len + sizeof(pangulu_inblock_ptr) * (block_order + 1));
+                        if(malloc_distbcsc_value){
+                            cur_block_value = (calculate_type *)(
+                                block_csc_remote[target_rank] + arr_len + 
+                                sizeof(pangulu_inblock_ptr) * (block_order + 1) + 
+                                sizeof(pangulu_inblock_idx) * (remote_bnnzptr[bidx + 1] - remote_bnnzptr[bidx])
+                            );
+                        }
+                    }
+                    if(distcsc_value){
+                        cur_block_value[tmp_count[(level % q) * block_length_col + brow]] = distcsc_value[reorder_matrix_idx];
+                    }else if(malloc_distbcsc_value){
+                        cur_block_value[tmp_count[(level % q) * block_length_col + brow]] = 0;
+                    }
+                    reorder_matrix_idx++;
+                    cur_block_colidx[tmp_count[(level % q) * block_length_col + brow]++] = row % block_order;
+                    cur_block_rowptr[col_in_blc]++;
+                }
+            }
+
+            for(pangulu_int32_t target_rank = 0; target_rank < nproc; target_rank++){
+                pangulu_exblock_ptr* remote_bcolptr = csc_draft_remote[target_rank];
+                pangulu_exblock_ptr* remote_bnnzptr = 
+                    csc_draft_remote[target_rank] + 
+                    sizeof(pangulu_exblock_ptr) * (block_length + 1) + 
+                    sizeof(pangulu_exblock_idx) * (nzblk_each_rank_ptr[target_rank + 1] - nzblk_each_rank_ptr[target_rank]);
+                for (pangulu_int64_t bidx = remote_bcolptr[level]; bidx < remote_bcolptr[level + 1]; bidx++)
+                {
+                    pangulu_int64_t tmp_stride = bidx * (block_order + 1) * sizeof(pangulu_inblock_ptr) + remote_bnnzptr[bidx] * (sizeof(pangulu_inblock_idx) + _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type)));
+                    pangulu_inblock_ptr *cur_csr_rpt = (pangulu_inblock_ptr *)(block_csc_remote[target_rank] + tmp_stride);
+                    exclusive_scan_3(cur_csr_rpt, block_order + 1);
+                }
+            }
+        }
+        pangulu_free(__FILE__, __LINE__, tmp_count);
+        tmp_count = NULL;
+    }
+    pangulu_free(__FILE__, __LINE__, thread_pt);
+    thread_pt = NULL;
+    pangulu_free(__FILE__, __LINE__, block_row_pt);
+    block_row_pt = NULL;
+    pangulu_free(__FILE__, __LINE__, block_col_idx);
+    block_col_idx = NULL;
+
+    if(rootproc_free_originmatrix){
+        pangulu_free(__FILE__, __LINE__, distcsc_pointer);
+        pangulu_free(__FILE__, __LINE__, distcsc_index);
+        if(distcsc_value){
+            pangulu_free(__FILE__, __LINE__, distcsc_value); // Don't set distcsc_value to NULL.
+        }
+    }
+
+    // comm TAG=0
+    pangulu_cm_sync();
+    pangulu_exblock_ptr* nzblk_remote = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * nproc);
+    for(pangulu_int32_t remote_rank = 0; remote_rank < nproc; remote_rank++){
+        MPI_Request req;
+        nzblk_remote[remote_rank] = nzblk_each_rank_ptr[remote_rank + 1] - nzblk_each_rank_ptr[remote_rank];
+        MPI_Isend(&nzblk_remote[remote_rank], 1, MPI_PANGULU_EXBLOCK_PTR, remote_rank, 0, MPI_COMM_WORLD, &req);
+    }
+    pangulu_exblock_ptr* nzblk_fetch = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * nproc);
+    for(pangulu_int32_t fetch_rank = 0; fetch_rank < nproc; fetch_rank++){
+        MPI_Status stat;
+        MPI_Recv(&nzblk_fetch[fetch_rank], 1, MPI_PANGULU_EXBLOCK_PTR, fetch_rank, 0, MPI_COMM_WORLD, &stat);
+    }
+    pangulu_cm_sync();
+    pangulu_free(__FILE__, __LINE__, nzblk_remote);
+    // printf("#%d 1.7\n", rank);
+
+    // comm TAG=1 send csc_draft_remote
+    pangulu_cm_sync();
+    for(pangulu_int32_t remote_rank = 0; remote_rank < nproc; remote_rank++){
+        pangulu_cm_isend(
+            csc_draft_remote[remote_rank], 
+            sizeof(pangulu_exblock_ptr) * (block_length + 1) + 
+                sizeof(pangulu_exblock_idx) * (nzblk_each_rank_ptr[remote_rank + 1] - nzblk_each_rank_ptr[remote_rank]) +
+                sizeof(pangulu_exblock_ptr) * (nzblk_each_rank_ptr[remote_rank + 1] - nzblk_each_rank_ptr[remote_rank] + 1),
+            remote_rank, 1, 10
+        );
+    }
+    char** bstruct_csc_fetch = pangulu_malloc(__FILE__, __LINE__, sizeof(char*) * nproc);
+    for(pangulu_int32_t fetch_rank = 0; fetch_rank < nproc; fetch_rank++){
+        bstruct_csc_fetch[fetch_rank] = pangulu_malloc(
+            __FILE__, __LINE__, 
+            sizeof(pangulu_exblock_ptr) * (block_length+1) + 
+            sizeof(pangulu_exblock_idx) * nzblk_fetch[fetch_rank] + 
+            sizeof(pangulu_exblock_ptr) * (nzblk_fetch[fetch_rank] + 1)
+        );
+        pangulu_cm_recv(
+            bstruct_csc_fetch[fetch_rank],
+            sizeof(pangulu_exblock_ptr) * (block_length+1) + sizeof(pangulu_exblock_idx) * nzblk_fetch[fetch_rank] + sizeof(pangulu_exblock_ptr) * (nzblk_fetch[fetch_rank] + 1),
+            fetch_rank, 1, 10
+        );
+    }
+    pangulu_cm_sync();
+    for(pangulu_int32_t remote_rank = 0; remote_rank < nproc; remote_rank++){
+        pangulu_free(__FILE__, __LINE__, csc_draft_remote[remote_rank]);
+    }
+    pangulu_free(__FILE__, __LINE__, csc_draft_remote);
+    csc_draft_remote = NULL;
+    
+    // comm TAG=2 send block_csc_remote
+    for(pangulu_int32_t remote_rank = 0; remote_rank < nproc; remote_rank++){
+        // MPI_Request req;
+        pangulu_int64_t send_size = sizeof(pangulu_inblock_ptr) * (block_order + 1) * (nzblk_each_rank_ptr[remote_rank + 1] - nzblk_each_rank_ptr[remote_rank]) +
+            sizeof(pangulu_inblock_idx) * (nnz_each_rank_ptr[remote_rank + 1] - nnz_each_rank_ptr[remote_rank]) + 
+            _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type)) * (nnz_each_rank_ptr[remote_rank + 1] - nnz_each_rank_ptr[remote_rank]);
+        pangulu_cm_isend(block_csc_remote[remote_rank], send_size, remote_rank, 2, 10);
+    }
+    pangulu_free(__FILE__, __LINE__, nzblk_each_rank_ptr);
+    nzblk_each_rank_ptr = NULL;
+    pangulu_free(__FILE__, __LINE__, nnz_each_rank_ptr);
+    nnz_each_rank_ptr = NULL;
+    char** block_csc_fetch = pangulu_malloc(__FILE__, __LINE__, sizeof(char*) * nproc);
+    for(pangulu_int32_t fetch_rank = 0; fetch_rank < nproc; fetch_rank++){
+        MPI_Status stat;
+        pangulu_exblock_ptr* remote_bcolptr = bstruct_csc_fetch[fetch_rank];
+        pangulu_exblock_idx* remote_browidx = bstruct_csc_fetch[fetch_rank] + sizeof(pangulu_exblock_ptr) * (block_length + 1);
+        pangulu_exblock_ptr* remote_bnnzptr = 
+            bstruct_csc_fetch[fetch_rank] + 
+            sizeof(pangulu_exblock_ptr) * (block_length + 1) + 
+            sizeof(pangulu_exblock_idx) * (remote_bcolptr[block_length]);
+        
+        pangulu_int64_t recv_size = 
+            sizeof(pangulu_inblock_ptr) * (block_order + 1) * remote_bcolptr[block_length] + 
+            sizeof(pangulu_inblock_idx) * remote_bnnzptr[remote_bcolptr[block_length]] + 
+            _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type)) * remote_bnnzptr[remote_bcolptr[block_length]];
+        block_csc_fetch[fetch_rank] = pangulu_malloc(__FILE__, __LINE__, recv_size);
+        // MPI_Recv(block_csc_fetch[fetch_rank], recv_size, MPI_CHAR, fetch_rank, 2, MPI_COMM_WORLD, &stat);
+        pangulu_cm_recv(block_csc_fetch[fetch_rank], recv_size, fetch_rank, 2, 10);
+    }
+    pangulu_cm_sync();
+    for(pangulu_int32_t remote_rank = 0; remote_rank < nproc; remote_rank++){
+        pangulu_free(__FILE__, __LINE__, block_csc_remote[remote_rank]);
+    }
+    pangulu_free(__FILE__, __LINE__, block_csc_remote);
+    block_csc_remote = NULL;
+    
+    pangulu_exblock_ptr* struct_bcolptr = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (block_length_col + 1));
+    memset(struct_bcolptr, 0, sizeof(pangulu_exblock_ptr) * (block_length_col + 1));
+    pangulu_exblock_ptr last_fetch_rank_ptr = 0;
+    for(pangulu_int32_t fetch_rank = 0; fetch_rank < nproc; fetch_rank++){
+        pangulu_exblock_ptr* bstruct_fetch_pointer = bstruct_csc_fetch[fetch_rank];
+        for(pangulu_exblock_idx brow_offset = 0; brow_offset < block_length; brow_offset++){
+            if(fetch_rank * block_length + brow_offset > block_length_col){
+                break;
+            }
+            struct_bcolptr[fetch_rank * block_length + brow_offset] = bstruct_fetch_pointer[brow_offset] + last_fetch_rank_ptr;
+        }
+        last_fetch_rank_ptr += bstruct_fetch_pointer[block_length];
+    }
+    struct_bcolptr[block_length_col] = last_fetch_rank_ptr;
+    
+    pangulu_exblock_idx* struct_browidx = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * struct_bcolptr[block_length_col]);
+    pangulu_exblock_ptr* struct_bnnzptr = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (struct_bcolptr[block_length_col] + 1));
+    pangulu_exblock_ptr last_fetch_bnnz_ptr = 0;
+    for(pangulu_int32_t fetch_rank = 0; fetch_rank < nproc; fetch_rank++){
+        pangulu_exblock_ptr* bstruct_fetch_pointer = bstruct_csc_fetch[fetch_rank];
+        pangulu_exblock_idx* bstruct_fetch_index = bstruct_csc_fetch[fetch_rank] + sizeof(pangulu_exblock_ptr) * (block_length+1);
+        pangulu_exblock_ptr* bstruct_fetch_nnzptr = bstruct_csc_fetch[fetch_rank] + sizeof(pangulu_exblock_ptr) * (block_length+1) + sizeof(pangulu_exblock_idx) * nzblk_fetch[fetch_rank];
+        for(pangulu_exblock_ptr bidx_offset = 0; bidx_offset < nzblk_fetch[fetch_rank]; bidx_offset++){
+            struct_browidx[struct_bcolptr[fetch_rank * block_length] + bidx_offset] = bstruct_fetch_index[bidx_offset];
+        }
+        for(pangulu_exblock_ptr bidx_offset = 0; bidx_offset < nzblk_fetch[fetch_rank]; bidx_offset++){
+            struct_bnnzptr[struct_bcolptr[fetch_rank * block_length] + bidx_offset] = bstruct_fetch_nnzptr[bidx_offset] + last_fetch_bnnz_ptr;
+        }
+        last_fetch_bnnz_ptr += bstruct_fetch_nnzptr[nzblk_fetch[fetch_rank]];
+    }
+    struct_bnnzptr[struct_bcolptr[block_length_col]] = last_fetch_bnnz_ptr;
+    for(pangulu_int32_t fetch_rank = 0; fetch_rank < nproc; fetch_rank++){
+        pangulu_free(__FILE__, __LINE__, bstruct_csc_fetch[fetch_rank]);
+    }
+    pangulu_free(__FILE__, __LINE__, bstruct_csc_fetch);
+    bstruct_csc_fetch = NULL;
+    pangulu_free(__FILE__, __LINE__, nzblk_fetch);
+    nzblk_fetch = NULL;
+
+    char* block_csc = pangulu_malloc(
+        __FILE__, __LINE__,
+        sizeof(pangulu_inblock_ptr) * (block_order + 1) * struct_bcolptr[block_length_col] + 
+        sizeof(pangulu_inblock_idx) * struct_bnnzptr[struct_bcolptr[block_length_col]] + 
+        _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type)) * struct_bnnzptr[struct_bcolptr[block_length_col]]
+    );
+    for(pangulu_int32_t fetch_rank = 0; fetch_rank < nproc; fetch_rank++){
+        pangulu_exblock_idx bidx_ub = struct_bcolptr[PANGULU_MIN((fetch_rank + 1) * block_length, block_length_col)];
+        pangulu_exblock_idx bidx_lb = struct_bcolptr[PANGULU_MIN(fetch_rank * block_length, block_length_col)];
+        pangulu_int64_t offset = 
+            sizeof(pangulu_inblock_ptr) * (block_order + 1) * bidx_lb + 
+            sizeof(pangulu_inblock_idx) * struct_bnnzptr[bidx_lb] + 
+            _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type)) * struct_bnnzptr[bidx_lb];
+        pangulu_int64_t copy_size = 
+            sizeof(pangulu_inblock_ptr) * (block_order + 1) * (bidx_ub - bidx_lb) +
+            sizeof(pangulu_inblock_idx) * (struct_bnnzptr[bidx_ub] - struct_bnnzptr[bidx_lb]) + 
+            _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type)) * (struct_bnnzptr[bidx_ub] - struct_bnnzptr[bidx_lb]);
+        memcpy(block_csc + offset, block_csc_fetch[fetch_rank], copy_size);
+        pangulu_free(__FILE__, __LINE__, block_csc_fetch[fetch_rank]);
+    }
+    pangulu_free(__FILE__, __LINE__, block_csc_fetch);
+    block_csc_fetch = NULL;
+
+    pangulu_inblock_ptr** inblock_pointers = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_inblock_ptr*) * struct_bcolptr[block_length_col]);
+    pangulu_inblock_idx** inblock_indeces = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_inblock_idx*) * struct_bcolptr[block_length_col]);
+    calculate_type** inblock_values = NULL;
+    if(malloc_distbcsc_value){
+        inblock_values = pangulu_malloc(__FILE__, __LINE__, sizeof(calculate_type*) * struct_bcolptr[block_length_col]);
+    }
+
+    for(pangulu_exblock_ptr bidx = 0; bidx < struct_bcolptr[block_length_col]; bidx++){
+        pangulu_int64_t offset = 
+            sizeof(pangulu_inblock_ptr) * (block_order + 1) * bidx + 
+            sizeof(pangulu_inblock_idx) * struct_bnnzptr[bidx] + 
+            _PANGULU_SET_BVALUE_SIZE(sizeof(calculate_type)) * struct_bnnzptr[bidx];
+        inblock_pointers[bidx] = block_csc + offset;
+        inblock_indeces[bidx] = block_csc + offset + 
+            sizeof(pangulu_inblock_ptr) * (block_order + 1);
+        if(malloc_distbcsc_value){
+            inblock_values[bidx] = block_csc + offset + 
+                sizeof(pangulu_inblock_ptr) * (block_order + 1) + 
+                sizeof(pangulu_inblock_idx) * (struct_bnnzptr[bidx + 1] - struct_bnnzptr[bidx]);
+        }
+    }
+
+    *bcsc_struct_pointer = struct_bcolptr;
+    *bcsc_struct_index = struct_browidx;
+    *bcsc_struct_nnzptr = struct_bnnzptr;
+    *bcsc_inblock_pointers = inblock_pointers;
+    *bcsc_inblock_indeces = inblock_indeces;
+    if(malloc_distbcsc_value){
+        *bcsc_values = inblock_values;
+    }
+
+    bind_to_core(rank % sysconf(_SC_NPROCESSORS_ONLN));
+
+#undef _PANGULU_SET_BVALUE_SIZE
+#undef _PANGULU_SET_VALUE_SIZE
+}
+
+void pangulu_cm_rank(pangulu_int32_t* rank){MPI_Comm_rank(MPI_COMM_WORLD, rank);}
+void pangulu_cm_size(pangulu_int32_t* size){MPI_Comm_size(MPI_COMM_WORLD, size);}
+void pangulu_cm_sync(){MPI_Barrier(MPI_COMM_WORLD);}
+void pangulu_cm_bcast(void *buffer, int count, MPI_Datatype datatype, int root){MPI_Bcast(buffer, count, datatype, root, MPI_COMM_WORLD);}
+void pangulu_cm_isend(char* buf, pangulu_int64_t count, pangulu_int32_t remote_rank, pangulu_int32_t tag, pangulu_int32_t tag_ub){
+    MPI_Request req;
+    const pangulu_int64_t send_maxlen = 0x7FFFFFFF;
+    pangulu_int64_t send_times = PANGULU_ICEIL(count, send_maxlen);
+    for(pangulu_int64_t iter = 0; iter < send_times; iter++){
+        int count_current = PANGULU_MIN((iter + 1) * send_maxlen, count) - iter * send_maxlen;
+        MPI_Isend(buf + iter * send_maxlen, count_current, MPI_CHAR, remote_rank, iter * tag_ub + tag, MPI_COMM_WORLD, &req);
+    }
+    if(send_times == 0){
+        MPI_Isend(buf, 0, MPI_CHAR, remote_rank, tag, MPI_COMM_WORLD, &req);
+    }
+}
+void pangulu_cm_send(char* buf, pangulu_int64_t count, pangulu_int32_t remote_rank, pangulu_int32_t tag, pangulu_int32_t tag_ub){
+    const pangulu_int64_t send_maxlen = 0x7FFFFFFF;
+    pangulu_int64_t send_times = PANGULU_ICEIL(count, send_maxlen);
+    for(pangulu_int64_t iter = 0; iter < send_times; iter++){
+        int count_current = PANGULU_MIN((iter + 1) * send_maxlen, count) - iter * send_maxlen;
+        MPI_Send(buf + iter * send_maxlen, count_current, MPI_CHAR, remote_rank, iter * tag_ub + tag, MPI_COMM_WORLD);
+    }
+    if(send_times == 0){
+        MPI_Send(buf, 0, MPI_CHAR, remote_rank, tag, MPI_COMM_WORLD);
+    }
+}
+void pangulu_cm_recv(char* buf, pangulu_int64_t count, pangulu_int32_t fetch_rank, pangulu_int32_t tag, pangulu_int32_t tag_ub){
+    MPI_Status stat;
+    const pangulu_int64_t send_maxlen = 0x7FFFFFFF;
+    pangulu_int64_t recv_times = PANGULU_ICEIL(count, send_maxlen);
+    for(pangulu_int64_t iter = 0; iter < recv_times; iter++){
+        int count_current = PANGULU_MIN((iter + 1) * send_maxlen, count) - iter * send_maxlen;
+        MPI_Recv(buf + iter * send_maxlen, count_current, MPI_CHAR, fetch_rank, iter * tag_ub + tag, MPI_COMM_WORLD, &stat);
+    }
+    if(recv_times == 0){
+        MPI_Recv(buf, 0, MPI_CHAR, fetch_rank, tag, MPI_COMM_WORLD, &stat);
+    }
+}
+void pangulu_cm_sync_asym(int wake_rank)
+{
+    pangulu_int32_t sum_rank_size, rank;
+    pangulu_cm_rank(&rank);
+    pangulu_cm_size(&sum_rank_size);
+    if (rank == wake_rank)
+    {
+        for (int i = 0; i < sum_rank_size; i++)
+        {
+            if (i != wake_rank)
+            {
+                MPI_Send(&sum_rank_size, 1, MPI_INT, i, 0xCAFE, MPI_COMM_WORLD);
+            }
+        }
+    }
+    else
+    {
+        int mpi_buf_int;
+        int mpi_flag;
+        MPI_Status mpi_stat;
+        while (1)
+        {
+            mpi_flag = 0;
+            MPI_Iprobe(wake_rank, 0xCAFE, MPI_COMM_WORLD, &mpi_flag, &mpi_stat);
+            if (mpi_flag != 0 && mpi_stat.MPI_TAG == 0xCAFE)
+            {
+                MPI_Recv(&mpi_buf_int, 1, MPI_INT, wake_rank, 0xCAFE, MPI_COMM_WORLD, &mpi_stat);
+                if (mpi_buf_int == sum_rank_size)
+                {
+                    break;
+                }
+                else
+                {
+                    printf(PANGULU_E_ASYM);
+                    exit(1);
+                }
+            }
+            usleep(50);
+        }
+    }
+    pangulu_cm_sync();
+}
+void pangulu_cm_probe(MPI_Status *status)
+{
+    int have_msg=0;
+    do{
+        MPI_Iprobe(MPI_ANY_SOURCE, MPI_ANY_TAG, MPI_COMM_WORLD, &have_msg, status);
+        if(have_msg){
+            return;
+        }
+        usleep(10);
+    }while(!have_msg);
+}
+
+// void pangulu_cm_distribute_bcsc_to_distbcsc(
+//     pangulu_int32_t root_rank,
+//     int rootproc_free_originmatrix,
+//     pangulu_exblock_idx* n,
+
+//     pangulu_exblock_ptr** bcsc_struct_pointer,
+//     pangulu_exblock_idx** bcsc_struct_index,
+//     pangulu_inblock_ptr** bcsc_struct_nnz,
+//     pangulu_inblock_ptr*** bcsc_inblock_pointers,
+//     pangulu_inblock_idx*** bcsc_inblock_indeces,
+//     calculate_type*** bcsc_values
+// ){
+    
+
+// }
+
+void pangulu_cm_distribute_csc_to_distcsc(
+    pangulu_int32_t root_rank,
+    int rootproc_free_originmatrix,
+    pangulu_exblock_idx* n,
+    pangulu_inblock_idx rowchunk_align,
+    pangulu_int32_t* distcsc_nproc,
+    pangulu_exblock_idx* n_loc,
+    
+    pangulu_exblock_ptr** distcsc_proc_nnzptr,
+    pangulu_exblock_ptr** distcsc_pointer,
+    pangulu_exblock_idx** distcsc_index,
+    calculate_type** distcsc_value
+){
+    struct timeval start_time;
+    pangulu_time_start(&start_time);
+    // printf("1.1\n");
+
+
+    pangulu_int32_t nproc = 0;
+    pangulu_int32_t rank;
+    pangulu_cm_size(&nproc);
+    pangulu_cm_rank(&rank);
+    *distcsc_nproc = nproc;
+    pangulu_int64_t p = sqrt(nproc);
+    while ((nproc % p) != 0)
+    {
+        p--;
+    }
+    pangulu_int64_t q = nproc / p;
+    pangulu_cm_bcast(n, 1, MPI_PANGULU_EXBLOCK_IDX, root_rank);
+    // printf("#%d 1.2\n", rank);
+
+    rowchunk_align *= q;
+    pangulu_exblock_idx col_per_rank = PANGULU_ICEIL(PANGULU_ICEIL(*n, rowchunk_align), nproc) * rowchunk_align;
+
+    *distcsc_proc_nnzptr = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (nproc + 1));
+    if(rank == root_rank){
+        pangulu_exblock_ptr* columnpointer = *distcsc_pointer;
+        pangulu_exblock_idx* rowindex = *distcsc_index;
+        calculate_type* value_csc = NULL;
+        if(distcsc_value){
+            value_csc = *distcsc_value;
+        }
+        (*distcsc_proc_nnzptr)[0] = 0;
+    // printf("#%d 1.3.1\n", rank);
+        for(pangulu_int32_t target_rank = 0; target_rank < nproc; target_rank++){
+    // printf("#%d 1.3.2\n", rank);
+            pangulu_exblock_idx n_loc_remote = PANGULU_MIN(col_per_rank * (target_rank + 1), *n) - PANGULU_MIN(col_per_rank * target_rank, *n);
+            (*distcsc_proc_nnzptr)[target_rank + 1] = columnpointer[PANGULU_MIN(col_per_rank * (target_rank + 1), *n)];
+            if(rank == target_rank){
+                *n_loc = n_loc_remote;
+    // printf("#%d n_loc = %d\n", rank, *n_loc);
+
+                *distcsc_pointer = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (*n_loc + 1));
+                memcpy(*distcsc_pointer, &columnpointer[PANGULU_MIN(col_per_rank * target_rank, *n)], sizeof(pangulu_exblock_ptr) * (*n_loc + 1));
+                pangulu_exblock_idx col_offset = (*distcsc_pointer)[0];
+                for(pangulu_exblock_idx col = 0; col < *n_loc + 1; col++){
+                    (*distcsc_pointer)[col] -= col_offset;
+                }
+                pangulu_exblock_ptr nnz_loc = (*distcsc_pointer)[*n_loc];
+                *distcsc_index = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * nnz_loc);
+                memcpy(*distcsc_index, &rowindex[(*distcsc_proc_nnzptr)[target_rank]], sizeof(pangulu_exblock_idx) * nnz_loc);
+
+                if(distcsc_value){
+                    *distcsc_value = pangulu_malloc(__FILE__, __LINE__, sizeof(calculate_type) * nnz_loc);
+                    memcpy(*distcsc_value, &value_csc[(*distcsc_proc_nnzptr)[target_rank]], sizeof(calculate_type) * nnz_loc);
+                }
+            }else{
+                MPI_Send(&n_loc_remote, 1, MPI_PANGULU_EXBLOCK_IDX, target_rank, 0, MPI_COMM_WORLD);
+                MPI_Send(&columnpointer[PANGULU_MIN(col_per_rank * target_rank, *n)], n_loc_remote + 1, MPI_PANGULU_EXBLOCK_PTR, target_rank, 1, MPI_COMM_WORLD);
+                // MPI_Send(
+                //     &rowindex[(*distcsc_proc_nnzptr)[target_rank]], 
+                //     (*distcsc_proc_nnzptr)[target_rank+1] - (*distcsc_proc_nnzptr)[target_rank], 
+                //     MPI_PANGULU_EXBLOCK_IDX, target_rank, 2, MPI_COMM_WORLD
+                // );
+                pangulu_cm_send(&rowindex[(*distcsc_proc_nnzptr)[target_rank]], sizeof(pangulu_exblock_idx) * ((*distcsc_proc_nnzptr)[target_rank+1] - (*distcsc_proc_nnzptr)[target_rank]), target_rank, 2, 10);
+                if(distcsc_value){
+                    // MPI_Send(
+                    //     &value_csc[(*distcsc_proc_nnzptr)[target_rank]],
+                    //     (*distcsc_proc_nnzptr)[target_rank+1] - (*distcsc_proc_nnzptr)[target_rank],
+                    //     MPI_VAL_TYPE, target_rank, 3, MPI_COMM_WORLD
+                    // );
+                    pangulu_cm_send(&value_csc[(*distcsc_proc_nnzptr)[target_rank]], sizeof(calculate_type) * ((*distcsc_proc_nnzptr)[target_rank+1] - (*distcsc_proc_nnzptr)[target_rank]), target_rank, 3, 10);
+                    // printf("Sent %d->%d\n", rank, target_rank);
+                }else{
+                    int nouse = 0;
+                    MPI_Send(&nouse, 1, MPI_INT, target_rank, 4, MPI_COMM_WORLD);
+                }
+            }
+    // printf("#%d 1.3.3\n", rank);
+        }
+        MPI_Bcast(*distcsc_proc_nnzptr, nproc+1, MPI_PANGULU_EXBLOCK_PTR, root_rank, MPI_COMM_WORLD);
+        if(rootproc_free_originmatrix){
+            pangulu_free(__FILE__, __LINE__, columnpointer);
+            pangulu_free(__FILE__, __LINE__, rowindex);
+            if(distcsc_value){
+                pangulu_free(__FILE__, __LINE__, value_csc);
+            }
+        }
+    // printf("#%d 1.3.4\n", rank);
+    }else{
+    // printf("#%d 1.4.1\n", rank);
+        MPI_Status mpi_stat;
+        MPI_Recv(n_loc, 1, MPI_PANGULU_EXBLOCK_IDX, root_rank, 0, MPI_COMM_WORLD, &mpi_stat);
+    // printf("#%d n_loc = %d\n", rank, *n_loc);
+        
+        *distcsc_pointer = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (*n_loc + 1));
+        MPI_Recv(*distcsc_pointer, *n_loc+1, MPI_PANGULU_EXBLOCK_PTR, root_rank, 1, MPI_COMM_WORLD, &mpi_stat);
+        pangulu_exblock_idx col_offset = (*distcsc_pointer)[0];
+        for(pangulu_exblock_idx col = 0; col < *n_loc + 1; col++){
+            (*distcsc_pointer)[col] -= col_offset;
+        }
+        pangulu_exblock_ptr nnz_loc = (*distcsc_pointer)[*n_loc];
+        *distcsc_index = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * nnz_loc);
+        // MPI_Recv(*distcsc_index, nnz_loc, MPI_PANGULU_EXBLOCK_IDX, root_rank, 2, MPI_COMM_WORLD, &mpi_stat);
+        pangulu_cm_recv(*distcsc_index, sizeof(pangulu_exblock_idx) * nnz_loc, root_rank, 2, 10);
+    // printf("#%d 1.4.2\n", rank);
+
+        MPI_Probe(root_rank, MPI_ANY_TAG, MPI_COMM_WORLD, &mpi_stat);
+        // printf("Probe\n");
+        if((mpi_stat.MPI_TAG%10) == 3){
+            *distcsc_value = pangulu_malloc(__FILE__, __LINE__, sizeof(calculate_type) * nnz_loc);
+            // MPI_Recv(*distcsc_value, nnz_loc, MPI_VAL_TYPE, root_rank, 3, MPI_COMM_WORLD, &mpi_stat);
+            pangulu_cm_recv(*distcsc_value, sizeof(calculate_type) * nnz_loc, root_rank, 3, 10);
+        }else if(mpi_stat.MPI_TAG == 4){
+            int nouse = 0;
+            MPI_Recv(&nouse, 1, MPI_INT, root_rank, 4, MPI_COMM_WORLD, &mpi_stat);
+        }
+    // printf("#%d 1.4.25\n", rank);
+
+        MPI_Bcast(*distcsc_proc_nnzptr, nproc+1, MPI_PANGULU_EXBLOCK_PTR, root_rank, MPI_COMM_WORLD);
+    // printf("#%d 1.4.3\n", rank);
+    }
+    // printf("#%d 1.5\n", rank);
+
+    // printf("[PanguLU LOG] pangulu_cm_distribute_csc_to_distcsc time : %.2lf ms\n", pangulu_time_stop(&start_time) * 1e3);
+}
+
+void pangulu_convert_csr_to_csc(
+    int free_csrmatrix,
+    pangulu_exblock_idx n,
+    pangulu_exblock_ptr** csr_pointer,
+    pangulu_exblock_idx** csr_index,
+    calculate_type** csr_value,
+    pangulu_exblock_ptr** csc_pointer,
+    pangulu_exblock_idx** csc_index,
+    calculate_type** csc_value
+){
+    struct timeval start_time;
+    pangulu_time_start(&start_time);
+
+    pangulu_exblock_ptr* rowpointer = *csr_pointer;
+    pangulu_exblock_idx* columnindex = *csr_index;
+    calculate_type* value = NULL;
+    if(csr_value){
+        value = *csr_value;
+    }
+
+    pangulu_exblock_ptr nnz = rowpointer[n];
+    
+    pangulu_exblock_ptr* columnpointer = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
+    pangulu_exblock_ptr* aid_ptr_arr = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
+    pangulu_exblock_idx* rowindex = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * nnz);
+    calculate_type* value_csc = NULL;
+    if(value){
+        value_csc = pangulu_malloc(__FILE__, __LINE__, sizeof(calculate_type) * nnz);
+    }
+
+    memset(columnpointer, 0, sizeof(pangulu_exblock_ptr) * (n + 1));
+    for(pangulu_exblock_idx row = 0; row < n; row++){
+        for(pangulu_exblock_ptr idx = rowpointer[row]; idx < rowpointer[row+1]; idx++){
+            pangulu_exblock_idx col = columnindex[idx];
+            columnpointer[col+1]++;
+        }
+    }
+    for(pangulu_exblock_idx col = 0; col < n; col++){
+        columnpointer[col+1] += columnpointer[col];
+    }
+    memcpy(aid_ptr_arr, columnpointer, sizeof(pangulu_exblock_ptr) * (n + 1));
+
+    if(value){
+        for(pangulu_exblock_idx row = 0; row < n; row++){
+            for(pangulu_exblock_ptr idx = rowpointer[row]; idx < rowpointer[row+1]; idx++){
+                pangulu_exblock_idx col = columnindex[idx];
+                rowindex[aid_ptr_arr[col]] = row;
+                value_csc[aid_ptr_arr[col]] = value[idx];
+                aid_ptr_arr[col]++;
+            }
+        }
+    }else{
+        for(pangulu_exblock_idx row = 0; row < n; row++){
+            for(pangulu_exblock_ptr idx = rowpointer[row]; idx < rowpointer[row+1]; idx++){
+                pangulu_exblock_idx col = columnindex[idx];
+                rowindex[aid_ptr_arr[col]] = row;
+                aid_ptr_arr[col]++;
+            }
+        }
+    }
+
+    pangulu_free(__FILE__, __LINE__, aid_ptr_arr);
+    if(free_csrmatrix){
+        pangulu_free(__FILE__, __LINE__, *csr_pointer);
+        pangulu_free(__FILE__, __LINE__, *csr_index);
+        pangulu_free(__FILE__, __LINE__, *csr_value);
+        *csr_pointer = NULL;
+        *csr_index = NULL;
+        *csr_value = NULL;
+    }
+    *csc_pointer = columnpointer;
+    *csc_index = rowindex;
+    if(csc_value){
+        *csc_value = value_csc;
+    }
+    // printf("[PanguLU LOG] pangulu_convert_csr_to_csc time : %.2lf ms\n", pangulu_time_stop(&start_time) * 1e3);
+}
+
+void pangulu_convert_ordered_halfsymcsc_to_csc_struct(
+    int free_halfmatrix,
+    int if_colsort,
+    pangulu_exblock_idx n,
+    pangulu_exblock_ptr** half_csc_pointer,
+    pangulu_exblock_idx** half_csc_index,
+    pangulu_exblock_ptr** csc_pointer,
+    pangulu_exblock_idx** csc_index
+){
+    pangulu_exblock_ptr* half_ptr = *half_csc_pointer;
+    pangulu_exblock_idx* half_idx = *half_csc_index;
+    pangulu_exblock_ptr nnz = half_ptr[n];
+    pangulu_exblock_ptr* at_ptr = (pangulu_exblock_ptr*)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
+    memset(at_ptr, 0, sizeof(pangulu_exblock_ptr) * (n + 1));
+    pangulu_exblock_idx* at_idx = (pangulu_exblock_idx*)pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * nnz);
+    for (pangulu_exblock_idx col = 0; col < n; col++) {
+        for (pangulu_exblock_ptr row_idx = half_ptr[col]; row_idx < half_ptr[col + 1]; row_idx++) {
+            pangulu_exblock_idx row = half_idx[row_idx];
+            at_ptr[row + 1]++;
+        }
+    }
+    for (pangulu_exblock_idx i = 1; i <= n; i++) {
+        at_ptr[i] += at_ptr[i - 1];
+    }
+
+    pangulu_exblock_ptr* a_aid_ptr = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
+    memcpy(a_aid_ptr, half_ptr, sizeof(pangulu_exblock_ptr) * (n + 1));
+    pangulu_exblock_ptr* at_aid_ptr = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
+    memcpy(at_aid_ptr, at_ptr, sizeof(pangulu_exblock_ptr) * (n + 1));
+    pangulu_exblock_idx stride = 10000;
+    // printf("stride = %d\n", stride);
+    pangulu_exblock_idx n_tile = PANGULU_ICEIL(n,stride);
+    for(pangulu_exblock_idx i_tile = 0; i_tile < n_tile; i_tile++){
+        pangulu_exblock_idx col_end = PANGULU_MIN((i_tile + 1) * stride, n);
+        for(pangulu_exblock_idx row = 0; row < n; row++){
+            pangulu_exblock_idx col;
+            while((a_aid_ptr[row] < half_ptr[row+1]) && ((col = half_idx[a_aid_ptr[row]]) < col_end)){
+                at_idx[at_aid_ptr[col]] = row;
+                at_aid_ptr[col]++;
+                a_aid_ptr[row]++;
+            }
+        }
+    }
+    pangulu_free(__FILE__, __LINE__, at_aid_ptr);
+    pangulu_free(__FILE__, __LINE__, a_aid_ptr);
+
+    pangulu_exblock_ptr* full_ptr = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_ptr) * (n + 1));
+    pangulu_exblock_idx* full_idx = pangulu_malloc(__FILE__, __LINE__, sizeof(pangulu_exblock_idx) * (2 * nnz - n));
+    full_ptr[0] = 0;
+    for(pangulu_exblock_idx row = 0; row < n; row++){
+        full_ptr[row + 1] = (half_ptr[row + 1] - half_ptr[row]) + (at_ptr[row + 1] - at_ptr[row]) - 1;
+    }
+    for(pangulu_exblock_idx row = 0; row < n; row++){
+        full_ptr[row + 1] += full_ptr[row];
+    }
+    #pragma omp parallel for
+    for(pangulu_exblock_idx row = 0; row < n; row++){
+        memcpy(&full_idx[full_ptr[row]], &at_idx[at_ptr[row]], sizeof(pangulu_exblock_idx) * (at_ptr[row+1] - at_ptr[row]));
+        memcpy(&full_idx[full_ptr[row] + (at_ptr[row+1] - at_ptr[row]) - 1], &half_idx[half_ptr[row]], sizeof(pangulu_exblock_idx) * (half_ptr[row+1] - half_ptr[row]));
+    }
+    
+    pangulu_free(__FILE__, __LINE__, at_ptr);
+    pangulu_free(__FILE__, __LINE__, at_idx);
+
+    if (free_halfmatrix) {
+        pangulu_free(__FILE__, __LINE__, *half_csc_pointer);
+        pangulu_free(__FILE__, __LINE__, *half_csc_index);
+        *half_csc_pointer = NULL;
+        *half_csc_index = NULL;
+    }
+
+    if(if_colsort){
+        pangulu_int32_t rank, nproc;
+        pangulu_cm_rank(&rank);
+        pangulu_cm_size(&nproc);
+        int nthread_sort = 2;
+        bind_to_core((rank * nthread_sort) % sysconf(_SC_NPROCESSORS_ONLN));
+        #pragma omp parallel num_threads(nthread_sort)
+        {
+            bind_to_core((rank * nthread_sort + omp_get_thread_num()) % sysconf(_SC_NPROCESSORS_ONLN));
+        }
+        pangulu_sort_exblock_struct(n, at_ptr, at_idx, nthread_sort);
+        bind_to_core(rank % sysconf(_SC_NPROCESSORS_ONLN));
+    }
+    
+    *csc_pointer = full_ptr;
+    *csc_index = full_idx;
+}
+
+void pangulu_convert_bcsc_fill_value_to_struct(
+    int free_valuebcsc,
+    pangulu_exblock_idx n,
+    pangulu_inblock_idx nb,
+
+    pangulu_exblock_ptr* value_bcsc_struct_pointer,
+    pangulu_exblock_idx* value_bcsc_struct_index,
+    pangulu_exblock_ptr* value_bcsc_struct_nnzptr,
+    pangulu_inblock_ptr** value_bcsc_inblock_pointers,
+    pangulu_inblock_idx** value_bcsc_inblock_indeces,
+    calculate_type** value_bcsc_values,
+
+    pangulu_exblock_ptr* struct_bcsc_struct_pointer,
+    pangulu_exblock_idx* struct_bcsc_struct_index,
+    pangulu_exblock_ptr* struct_bcsc_struct_nnzptr,
+    pangulu_inblock_ptr** struct_bcsc_inblock_pointers,
+    pangulu_inblock_idx** struct_bcsc_inblock_indeces,
+    calculate_type** struct_bcsc_values
+){
+    struct timeval start_time;
+    pangulu_time_start(&start_time);
+
+    pangulu_exblock_idx block_length = PANGULU_ICEIL(n , nb);
+
+    for(pangulu_exblock_idx sp = 0; sp < block_length; sp++)
+    {
+        pangulu_exblock_ptr ssi = struct_bcsc_struct_pointer[sp];
+        for(pangulu_exblock_ptr vsi = value_bcsc_struct_pointer[sp]; vsi < value_bcsc_struct_pointer[sp + 1]; vsi++)
+        {
+            while((struct_bcsc_struct_index[ssi] != value_bcsc_struct_index[vsi]) && (ssi < struct_bcsc_struct_pointer[sp+1]))
+            {
+                ssi++;
+            }
+            if(ssi >= struct_bcsc_struct_pointer[sp+1]){
+                break;
+            }
+            for(pangulu_exblock_idx ip = 0; ip < nb; ip++)
+            {
+                pangulu_inblock_ptr sii = struct_bcsc_inblock_pointers[ssi][ip];
+                for(pangulu_exblock_ptr vii = value_bcsc_inblock_pointers[vsi][ip]; vii < value_bcsc_inblock_pointers[vsi][ip + 1]; vii++)
+                {
+                    while((struct_bcsc_inblock_indeces[ssi][sii] != value_bcsc_inblock_indeces[vsi][vii]) && (sii < struct_bcsc_inblock_pointers[ssi][ip+1]))
+                    {
+                        sii++;
+                    }
+                    if(sii >= struct_bcsc_inblock_pointers[ssi][ip+1]){
+                        break;
+                    }
+                    struct_bcsc_values[ssi][sii] = value_bcsc_values[vsi][vii];
+                }
+            }
+        }
+    }
+    
+    if(free_valuebcsc)
+    {
+        if(value_bcsc_struct_pointer[block_length] > 0){
+            pangulu_free(__FILE__, __LINE__, value_bcsc_inblock_pointers[0]);            
+        }
+        pangulu_free(__FILE__, __LINE__, value_bcsc_inblock_pointers);
+        pangulu_free(__FILE__, __LINE__, value_bcsc_inblock_indeces);
+        pangulu_free(__FILE__, __LINE__, value_bcsc_values);
+        pangulu_free(__FILE__, __LINE__, value_bcsc_struct_pointer);
+        pangulu_free(__FILE__, __LINE__, value_bcsc_struct_index);
+        pangulu_free(__FILE__, __LINE__, value_bcsc_struct_nnzptr);
+    }
+
+    // printf("[PanguLU LOG] pangulu_convert_bcsc_fill_value_to_struct time : %.2lf ms\n", pangulu_time_stop(&start_time) * 1e3);
+}
+
 void pangulu_bip_init(pangulu_block_info_pool **BIP, pangulu_int64_t map_index_not_included)
 { // BIP : block info pool
     if(!BIP){
@@ -493,14 +1624,24 @@ void pangulu_read_pangulu_origin_smatrix(pangulu_origin_smatrix *s, int wcs_n, l
     s->value = csr_value;
 }
 
-void pangulu_time_start(pangulu_common *common)
-{
-    gettimeofday(&(common->start_time), NULL);
-}
+// void pangulu_time_start(pangulu_common *common)
+// {
+//     gettimeofday(&(common->start_time), NULL);
+// }
 
-void pangulu_time_stop(pangulu_common *common)
-{
-    gettimeofday(&(common->stop_time), NULL);
+// void pangulu_time_stop(pangulu_common *common)
+// {
+//     gettimeofday(&(common->stop_time), NULL);
+// }
+
+void pangulu_time_start(struct timeval* start){
+    gettimeofday(start, NULL);
+}
+double pangulu_time_stop(struct timeval* start){
+    struct timeval end;
+    gettimeofday(&end, NULL);
+    double time = ((double)end.tv_sec - start->tv_sec) + ((double)end.tv_usec - start->tv_usec) * 1e-6;
+    return time;
 }
 
 void pangulu_memcpy_zero_pangulu_smatrix_csc_value(pangulu_smatrix *s)
@@ -560,7 +1701,7 @@ double pangulu_get_spend_time(pangulu_common *common)
     return time / 1000.0;
 }
 
-void pangulu_transport_pangulu_smatrix_csc_to_csr(pangulu_smatrix *s)
+void pangulu_transpose_pangulu_smatrix_csc_to_csr(pangulu_smatrix *s)
 {
     for (pangulu_int64_t i = 0; i < s->nnz; i++)
     {
@@ -568,7 +1709,7 @@ void pangulu_transport_pangulu_smatrix_csc_to_csr(pangulu_smatrix *s)
         s->value[index] = s->value_csc[i];
     }
 }
-void pangulu_transport_pangulu_smatrix_csr_to_csc(pangulu_smatrix *s)
+void pangulu_transpose_pangulu_smatrix_csr_to_csc(pangulu_smatrix *s)
 {
     for (pangulu_int64_t i = 0; i < s->nnz; i++)
     {
@@ -1203,6 +2344,7 @@ void pangulu_sort_pangulu_matrix(pangulu_int64_t n, pangulu_exblock_ptr *rowpoin
 
 void pangulu_sort_pangulu_origin_smatrix(pangulu_origin_smatrix *s)
 {
+    #pragma omp parallel for
     for (pangulu_exblock_idx i = 0; i < s->row; i++)
     {
         pangulu_sort(s->columnindex, s->value, s->rowpointer[i], s->rowpointer[i + 1] - 1);
diff --git a/src/platforms/02_GPU/01_CUDA/000_CUDA/pangulu_cuda.cu b/src/platforms/02_GPU/01_CUDA/000_CUDA/pangulu_cuda.cu
index f0e6cb2..23393e7 100644
--- a/src/platforms/02_GPU/01_CUDA/000_CUDA/pangulu_cuda.cu
+++ b/src/platforms/02_GPU/01_CUDA/000_CUDA/pangulu_cuda.cu
@@ -2980,7 +2980,7 @@ __global__ void cuda_transform_d_to_s_col(pangulu_int64_t n,
     }
 }
 
-// void pangulu_cuda_transport_kernel_csc_to_csr(pangulu_int64_t nnz, calculate_type *d_val_csr, pangulu_inblock_idx *d_idx, calculate_type *d_val_csc)
+// void pangulu_cuda_transpose_kernel_csc_to_csr(pangulu_int64_t nnz, calculate_type *d_val_csr, pangulu_inblock_idx *d_idx, calculate_type *d_val_csc)
 // {
 
 //     pangulu_int64_t num_threads = warp_size * 2;
@@ -2990,7 +2990,7 @@ __global__ void cuda_transform_d_to_s_col(pangulu_int64_t n,
 //     cudaDeviceSynchronize();
 // }
 
-// void pangulu_cuda_transport_kernel_csr_to_csc(pangulu_int64_t nnz, calculate_type *d_val_csc, pangulu_inblock_idx *d_idx, calculate_type *d_val_csr)
+// void pangulu_cuda_transpose_kernel_csr_to_csc(pangulu_int64_t nnz, calculate_type *d_val_csc, pangulu_inblock_idx *d_idx, calculate_type *d_val_csr)
 // {
 
 //     pangulu_int64_t num_threads = warp_size * 2;
diff --git a/src/platforms/02_GPU/01_CUDA/000_CUDA/pangulu_cuda.h b/src/platforms/02_GPU/01_CUDA/000_CUDA/pangulu_cuda.h
index 0cffc47..595bda5 100644
--- a/src/platforms/02_GPU/01_CUDA/000_CUDA/pangulu_cuda.h
+++ b/src/platforms/02_GPU/01_CUDA/000_CUDA/pangulu_cuda.h
@@ -131,9 +131,9 @@ void pangulu_gessm_cuda_kernel_v11(pangulu_int64_t n,
                                    pangulu_inblock_idx *a_rowindex,
                                    calculate_type *a_value);
 
-// void pangulu_cuda_transport_kernel_csc_to_csr(pangulu_int64_t nnz, calculate_type *d_val_csr, pangulu_int64_t *d_idx, calculate_type *d_val_csc); 
+// void pangulu_cuda_transpose_kernel_csc_to_csr(pangulu_int64_t nnz, calculate_type *d_val_csr, pangulu_int64_t *d_idx, calculate_type *d_val_csc); 
 
-// void pangulu_cuda_transport_kernel_csr_to_csc(pangulu_int64_t nnz, calculate_type *d_val_csc, pangulu_int64_t *d_idx, calculate_type *d_val_csr);
+// void pangulu_cuda_transpose_kernel_csr_to_csc(pangulu_int64_t nnz, calculate_type *d_val_csc, pangulu_int64_t *d_idx, calculate_type *d_val_csr);
 
 void pangulu_getrf_cuda_kernel(pangulu_int64_t n,
                                pangulu_int64_t nnza,