OpenBLAS/driver/level3/level3_thread.c

/*********************************************************************/
/* Copyright 2009, 2010 The University of Texas at Austin.           */
/* All rights reserved.                                              */
/*                                                                   */
/* Redistribution and use in source and binary forms, with or        */
/* without modification, are permitted provided that the following   */
/* conditions are met:                                               */
/*                                                                   */
/*   1. Redistributions of source code must retain the above         */
/*      copyright notice, this list of conditions and the following  */
/*      disclaimer.                                                  */
/*                                                                   */
/*   2. Redistributions in binary form must reproduce the above      */
/*      copyright notice, this list of conditions and the following  */
/*      disclaimer in the documentation and/or other materials       */
/*      provided with the distribution.                              */
/*                                                                   */
/*    THIS  SOFTWARE IS PROVIDED  BY THE  UNIVERSITY OF  TEXAS AT    */
/*    AUSTIN  ``AS IS''  AND ANY  EXPRESS OR  IMPLIED WARRANTIES,    */
/*    INCLUDING, BUT  NOT LIMITED  TO, THE IMPLIED  WARRANTIES OF    */
/*    MERCHANTABILITY  AND FITNESS FOR  A PARTICULAR  PURPOSE ARE    */
/*    DISCLAIMED.  IN  NO EVENT SHALL THE UNIVERSITY  OF TEXAS AT    */
/*    AUSTIN OR CONTRIBUTORS BE  LIABLE FOR ANY DIRECT, INDIRECT,    */
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/* documentation are those of the authors and should not be          */
/* interpreted as representing official policies, either expressed   */
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/*********************************************************************/

#ifndef CACHE_LINE_SIZE
#define CACHE_LINE_SIZE 8
#endif

#ifndef DIVIDE_RATE
#define DIVIDE_RATE 2
#endif

#ifndef SWITCH_RATIO
#define SWITCH_RATIO 2
#endif

//The array of job_t may overflow the stack.
//Instead, use malloc to alloc job_t.
#if MAX_CPU_NUMBER > BLAS3_MEM_ALLOC_THRESHOLD
#define USE_ALLOC_HEAP
#endif

#ifndef GEMM_LOCAL
#if   defined(NN)
#define GEMM_LOCAL    GEMM_NN
#elif defined(NT)
#define GEMM_LOCAL    GEMM_NT
#elif defined(NR)
#define GEMM_LOCAL    GEMM_NR
#elif defined(NC)
#define GEMM_LOCAL    GEMM_NC
#elif defined(TN)
#define GEMM_LOCAL    GEMM_TN
#elif defined(TT)
#define GEMM_LOCAL    GEMM_TT
#elif defined(TR)
#define GEMM_LOCAL    GEMM_TR
#elif defined(TC)
#define GEMM_LOCAL    GEMM_TC
#elif defined(RN)
#define GEMM_LOCAL    GEMM_RN
#elif defined(RT)
#define GEMM_LOCAL    GEMM_RT
#elif defined(RR)
#define GEMM_LOCAL    GEMM_RR
#elif defined(RC)
#define GEMM_LOCAL    GEMM_RC
#elif defined(CN)
#define GEMM_LOCAL    GEMM_CN
#elif defined(CT)
#define GEMM_LOCAL    GEMM_CT
#elif defined(CR)
#define GEMM_LOCAL    GEMM_CR
#elif defined(CC)
#define GEMM_LOCAL    GEMM_CC
#endif
#endif

typedef struct {
#if _STDC_VERSION__ >= 201112L
_Atomic
#else  
  volatile
#endif
   BLASLONG working[MAX_CPU_NUMBER][CACHE_LINE_SIZE * DIVIDE_RATE];
} job_t;


#ifndef BETA_OPERATION
#ifndef COMPLEX
#define BETA_OPERATION(M_FROM, M_TO, N_FROM, N_TO, BETA, C, LDC)        \
  GEMM_BETA((M_TO) - (M_FROM), (N_TO - N_FROM), 0,                      \
            BETA[0], NULL, 0, NULL, 0,                                  \
            (FLOAT *)(C) + ((M_FROM) + (N_FROM) * (LDC)) * COMPSIZE, LDC)
#else
#define BETA_OPERATION(M_FROM, M_TO, N_FROM, N_TO, BETA, C, LDC)        \
  GEMM_BETA((M_TO) - (M_FROM), (N_TO - N_FROM), 0,                      \
            BETA[0], BETA[1], NULL, 0, NULL, 0,                         \
            (FLOAT *)(C) + ((M_FROM) + (N_FROM) * (LDC)) * COMPSIZE, LDC)
#endif
#endif

#ifndef ICOPY_OPERATION
#if defined(NN) || defined(NT) || defined(NC) || defined(NR) || \
  defined(RN) || defined(RT) || defined(RC) || defined(RR)
#define ICOPY_OPERATION(M, N, A, LDA, X, Y, BUFFER) GEMM_ITCOPY(M, N, (FLOAT *)(A) + ((Y) + (X) * (LDA)) * COMPSIZE, LDA, BUFFER);
#else
#define ICOPY_OPERATION(M, N, A, LDA, X, Y, BUFFER) GEMM_INCOPY(M, N, (FLOAT *)(A) + ((X) + (Y) * (LDA)) * COMPSIZE, LDA, BUFFER);
#endif
#endif

#ifndef OCOPY_OPERATION
#if defined(NN) || defined(TN) || defined(CN) || defined(RN) || \
  defined(NR) || defined(TR) || defined(CR) || defined(RR)
#define OCOPY_OPERATION(M, N, A, LDA, X, Y, BUFFER) GEMM_ONCOPY(M, N, (FLOAT *)(A) + ((X) + (Y) * (LDA)) * COMPSIZE, LDA, BUFFER);
#else
#define OCOPY_OPERATION(M, N, A, LDA, X, Y, BUFFER) GEMM_OTCOPY(M, N, (FLOAT *)(A) + ((Y) + (X) * (LDA)) * COMPSIZE, LDA, BUFFER);
#endif
#endif

#ifndef KERNEL_FUNC
#if defined(NN) || defined(NT) || defined(TN) || defined(TT)
#define KERNEL_FUNC	GEMM_KERNEL_N
#endif
#if defined(CN) || defined(CT) || defined(RN) || defined(RT)
#define KERNEL_FUNC	GEMM_KERNEL_L
#endif
#if defined(NC) || defined(TC) || defined(NR) || defined(TR)
#define KERNEL_FUNC	GEMM_KERNEL_R
#endif
#if defined(CC) || defined(CR) || defined(RC) || defined(RR)
#define KERNEL_FUNC	GEMM_KERNEL_B
#endif
#endif

#ifndef KERNEL_OPERATION
#ifndef COMPLEX
#define KERNEL_OPERATION(M, N, K, ALPHA, SA, SB, C, LDC, X, Y)          \
  KERNEL_FUNC(M, N, K, ALPHA[0], SA, SB, (FLOAT *)(C) + ((X) + (Y) * LDC) * COMPSIZE, LDC)
#else
#define KERNEL_OPERATION(M, N, K, ALPHA, SA, SB, C, LDC, X, Y)          \
  KERNEL_FUNC(M, N, K, ALPHA[0], ALPHA[1], SA, SB, (FLOAT *)(C) + ((X) + (Y) * LDC) * COMPSIZE, LDC)
#endif
#endif

#ifndef FUSED_KERNEL_OPERATION
#if defined(NN) || defined(TN) || defined(CN) || defined(RN) || \
  defined(NR) || defined(TR) || defined(CR) || defined(RR)
#ifndef COMPLEX
#define FUSED_KERNEL_OPERATION(M, N, K, ALPHA, SA, SB, B, LDB, C, LDC, I, J, L) \
  FUSED_GEMM_KERNEL_N(M, N, K, ALPHA[0], SA, SB,                        \
                      (FLOAT *)(B) + ((L) + (J) * LDB) * COMPSIZE, LDB, (FLOAT *)(C) + ((I) + (J) * LDC) * COMPSIZE, LDC)
#else
#define FUSED_KERNEL_OPERATION(M, N, K, ALPHA, SA, SB, B, LDB, C, LDC, I, J, L) \
  FUSED_GEMM_KERNEL_N(M, N, K, ALPHA[0], ALPHA[1], SA, SB,              \
                      (FLOAT *)(B) + ((L) + (J) * LDB) * COMPSIZE, LDB, (FLOAT *)(C) + ((I) + (J) * LDC) * COMPSIZE, LDC)

#endif
#else
#ifndef COMPLEX
#define FUSED_KERNEL_OPERATION(M, N, K, ALPHA, SA, SB, B, LDB, C, LDC, I, J, L) \
  FUSED_GEMM_KERNEL_T(M, N, K, ALPHA[0], SA, SB,                        \
                      (FLOAT *)(B) + ((J) + (L) * LDB) * COMPSIZE, LDB, (FLOAT *)(C) + ((I) + (J) * LDC) * COMPSIZE, LDC)
#else
#define FUSED_KERNEL_OPERATION(M, N, K, ALPHA, SA, SB, B, LDB, C, LDC, I, J, L) \
  FUSED_GEMM_KERNEL_T(M, N, K, ALPHA[0], ALPHA[1], SA, SB,              \
                      (FLOAT *)(B) + ((J) + (L) * LDB) * COMPSIZE, LDB, (FLOAT *)(C) + ((I) + (J) * LDC) * COMPSIZE, LDC)
#endif
#endif
#endif

#ifndef A
#define A	args -> a
#endif
#ifndef LDA
#define LDA	args -> lda
#endif
#ifndef B
#define B	args -> b
#endif
#ifndef LDB
#define LDB	args -> ldb
#endif
#ifndef C
#define C	args -> c
#endif
#ifndef LDC
#define LDC	args -> ldc
#endif
#ifndef M
#define M	args -> m
#endif
#ifndef N
#define N	args -> n
#endif
#ifndef K
#define K	args -> k
#endif

#ifdef TIMING
#define START_RPCC()		rpcc_counter = rpcc()
#define STOP_RPCC(COUNTER)	COUNTER  += rpcc() - rpcc_counter
#else
#define START_RPCC()
#define STOP_RPCC(COUNTER)
#endif

static int inner_thread(blas_arg_t *args, BLASLONG *range_m, BLASLONG *range_n, FLOAT *sa, FLOAT *sb, BLASLONG mypos){

  FLOAT *buffer[DIVIDE_RATE];

  BLASLONG k, lda, ldb, ldc;
  BLASLONG m_from, m_to, n_from, n_to;

  FLOAT *alpha, *beta;
  FLOAT *a, *b, *c;
  job_t *job = (job_t *)args -> common;

  BLASLONG nthreads_m;
  BLASLONG mypos_m, mypos_n;

  BLASLONG is, js, ls, bufferside, jjs;
  BLASLONG min_i, min_l, div_n, min_jj;

  BLASLONG i, current;
  BLASLONG l1stride;

#ifdef TIMING
  BLASULONG rpcc_counter;
  BLASULONG copy_A = 0;
  BLASULONG copy_B = 0;
  BLASULONG kernel = 0;
  BLASULONG waiting1 = 0;
  BLASULONG waiting2 = 0;
  BLASULONG waiting3 = 0;
  BLASULONG waiting6[MAX_CPU_NUMBER];
  BLASULONG ops    = 0;

  for (i = 0; i < args -> nthreads; i++) waiting6[i] = 0;
#endif

  k = K;

  a = (FLOAT *)A;
  b = (FLOAT *)B;
  c = (FLOAT *)C;

  lda = LDA;
  ldb = LDB;
  ldc = LDC;

  alpha = (FLOAT *)args -> alpha;
  beta  = (FLOAT *)args -> beta;

  /* Initialize 2D CPU distribution */
  nthreads_m = args -> nthreads;
  if (range_m) {
    nthreads_m = range_m[-1];
  }
  mypos_n = blas_quickdivide(mypos, nthreads_m);  /* mypos_n = mypos / nthreads_m */
  mypos_m = mypos - mypos_n * nthreads_m;         /* mypos_m = mypos % nthreads_m */

  /* Initialize m and n */
  m_from = 0;
  m_to   = M;
  if (range_m) {
    m_from = range_m[mypos_m + 0];
    m_to   = range_m[mypos_m + 1];
  }
  n_from = 0;
  n_to   = N;
  if (range_n) {
    n_from = range_n[mypos + 0];
    n_to   = range_n[mypos + 1];
  }

  /* Multiply C by beta if needed */
  if (beta) {
#ifndef COMPLEX
    if (beta[0] != ONE)
#else
    if ((beta[0] != ONE) || (beta[1] != ZERO))
#endif
      BETA_OPERATION(m_from, m_to, range_n[mypos_n * nthreads_m], range_n[(mypos_n + 1) * nthreads_m], beta, c, ldc);
  }

  /* Return early if no more computation is needed */
  if ((k == 0) || (alpha == NULL)) return 0;
  if (alpha[0] == ZERO
#ifdef COMPLEX
      && alpha[1] == ZERO
#endif
      ) return 0;

  /* Initialize workspace for local region of B */
  div_n = (n_to - n_from + DIVIDE_RATE - 1) / DIVIDE_RATE;
  buffer[0] = sb;
  for (i = 1; i < DIVIDE_RATE; i++) {
    buffer[i] = buffer[i - 1] + GEMM_Q * ((div_n + GEMM_UNROLL_N - 1)/GEMM_UNROLL_N) * GEMM_UNROLL_N * COMPSIZE;
  }

  /* Iterate through steps of k */
  for(ls = 0; ls < k; ls += min_l){

    /* Determine step size in k */
    min_l = k - ls;
    if (min_l >= GEMM_Q * 2) {
      min_l  = GEMM_Q;
    } else {
      if (min_l > GEMM_Q) min_l = (min_l + 1) / 2;
    }

    /* Determine step size in m
     * Note: We are currently on the first step in m
     */
    l1stride = 1;
    min_i = m_to - m_from;
    if (min_i >= GEMM_P * 2) {
      min_i = GEMM_P;
    } else {
      if (min_i > GEMM_P) {
	min_i = ((min_i / 2 + GEMM_UNROLL_M - 1)/GEMM_UNROLL_M) * GEMM_UNROLL_M;
      } else {
	if (args -> nthreads == 1) l1stride = 0;
      }
    }

    /* Copy local region of A into workspace */
    START_RPCC();
    ICOPY_OPERATION(min_l, min_i, a, lda, ls, m_from, sa);
    STOP_RPCC(copy_A);

    /* Copy local region of B into workspace and apply kernel */
    div_n = (n_to - n_from + DIVIDE_RATE - 1) / DIVIDE_RATE;
    for (js = n_from, bufferside = 0; js < n_to; js += div_n, bufferside ++) {

      /* Make sure if no one is using workspace */
      START_RPCC();
      for (i = 0; i < args -> nthreads; i++)
	while (job[mypos].working[i][CACHE_LINE_SIZE * bufferside]) {YIELDING;};
      STOP_RPCC(waiting1);

#if defined(FUSED_GEMM) && !defined(TIMING)

      /* Fused operation to copy region of B into workspace and apply kernel */
      FUSED_KERNEL_OPERATION(min_i, MIN(n_to, js + div_n) - js, min_l, alpha,
			     sa, buffer[bufferside], b, ldb, c, ldc, m_from, js, ls);

#else

      /* Split local region of B into parts */
      for(jjs = js; jjs < MIN(n_to, js + div_n); jjs += min_jj){
	min_jj = MIN(n_to, js + div_n) - jjs;
	if (min_jj >= 3*GEMM_UNROLL_N) min_jj = 3*GEMM_UNROLL_N;
	else
          if (min_jj >= 2*GEMM_UNROLL_N) min_jj = 2*GEMM_UNROLL_N;
          else
            if (min_jj > GEMM_UNROLL_N) min_jj = GEMM_UNROLL_N;

        /* Copy part of local region of B into workspace */
	START_RPCC();
	OCOPY_OPERATION(min_l, min_jj, b, ldb, ls, jjs,
			buffer[bufferside] + min_l * (jjs - js) * COMPSIZE * l1stride);
	STOP_RPCC(copy_B);

        /* Apply kernel with local region of A and part of local region of B */
	START_RPCC();
	KERNEL_OPERATION(min_i, min_jj, min_l, alpha,
			 sa, buffer[bufferside] + min_l * (jjs - js) * COMPSIZE * l1stride,
			 c, ldc, m_from, jjs);
	STOP_RPCC(kernel);

#ifdef TIMING
        ops += 2 * min_i * min_jj * min_l;
#endif

      }
#endif

      /* Set flag so other threads can access local region of B */
      for (i = mypos_n * nthreads_m; i < (mypos_n + 1) * nthreads_m; i++)
        job[mypos].working[i][CACHE_LINE_SIZE * bufferside] = (BLASLONG)buffer[bufferside];
      WMB;
    }

    /* Get regions of B from other threads and apply kernel */
    current = mypos;
    do {

      /* This thread accesses regions of B from threads in the range
       * [ mypos_n * nthreads_m, (mypos_n+1) * nthreads_m ) */
      current ++;
      if (current >= (mypos_n + 1) * nthreads_m) current = mypos_n * nthreads_m;

      /* Split other region of B into parts */
      div_n = (range_n[current + 1]  - range_n[current] + DIVIDE_RATE - 1) / DIVIDE_RATE;
      for (js = range_n[current], bufferside = 0; js < range_n[current + 1]; js += div_n, bufferside ++) {
        if (current != mypos) {

	  /* Wait until other region of B is initialized */
	  START_RPCC();
	  while(job[current].working[mypos][CACHE_LINE_SIZE * bufferside] == 0) {YIELDING;};
	  STOP_RPCC(waiting2);

          /* Apply kernel with local region of A and part of other region of B */
	  START_RPCC();
	  KERNEL_OPERATION(min_i, MIN(range_n[current + 1]  - js,  div_n), min_l, alpha,
			   sa, (FLOAT *)job[current].working[mypos][CACHE_LINE_SIZE * bufferside],
			   c, ldc, m_from, js);
          STOP_RPCC(kernel);

#ifdef TIMING
	  ops += 2 * min_i * MIN(range_n[current + 1]  - js,  div_n) * min_l;
#endif
	}

        /* Clear synchronization flag if this thread is done with other region of B */
	if (m_to - m_from == min_i) {
	  job[current].working[mypos][CACHE_LINE_SIZE * bufferside] &= 0;
	}
      }
    } while (current != mypos);

    /* Iterate through steps of m 
     * Note: First step has already been finished */
    for(is = m_from + min_i; is < m_to; is += min_i){
      min_i = m_to - is;
      if (min_i >= GEMM_P * 2) {
	min_i = GEMM_P;
      } else
	if (min_i > GEMM_P) {
	  min_i = (((min_i + 1) / 2 + GEMM_UNROLL_M - 1)/GEMM_UNROLL_M) * GEMM_UNROLL_M;
	}

      /* Copy local region of A into workspace */
      START_RPCC();
      ICOPY_OPERATION(min_l, min_i, a, lda, ls, is, sa);
      STOP_RPCC(copy_A);

      /* Get regions of B and apply kernel */
      current = mypos;
      do {

        /* Split region of B into parts and apply kernel */
	div_n = (range_n[current + 1]  - range_n[current] + DIVIDE_RATE - 1) / DIVIDE_RATE;
	for (js = range_n[current], bufferside = 0; js < range_n[current + 1]; js += div_n, bufferside ++) {

          /* Apply kernel with local region of A and part of region of B */
	  START_RPCC();
	  KERNEL_OPERATION(min_i, MIN(range_n[current + 1] - js, div_n), min_l, alpha,
			   sa, (FLOAT *)job[current].working[mypos][CACHE_LINE_SIZE * bufferside],
			   c, ldc, is, js);
          STOP_RPCC(kernel);
          
#ifdef TIMING
          ops += 2 * min_i * MIN(range_n[current + 1]  - js, div_n) * min_l;
#endif
          
          /* Clear synchronization flag if this thread is done with region of B */
          if (is + min_i >= m_to) {
            job[current].working[mypos][CACHE_LINE_SIZE * bufferside] &= 0;
            WMB;
          }
	}

        /* This thread accesses regions of B from threads in the range
         * [ mypos_n * nthreads_m, (mypos_n+1) * nthreads_m ) */
	current ++;
	if (current >= (mypos_n + 1) * nthreads_m) current = mypos_n * nthreads_m;

      } while (current != mypos);

    }

  }

  /* Wait until all other threads are done with local region of B */
  START_RPCC();
  for (i = 0; i < args -> nthreads; i++) {
    for (js = 0; js < DIVIDE_RATE; js++) {
      while (job[mypos].working[i][CACHE_LINE_SIZE * js] ) {YIELDING;};
    }
  }
  STOP_RPCC(waiting3);

#ifdef TIMING
  BLASLONG waiting = waiting1 + waiting2 + waiting3;
  BLASLONG total = copy_A + copy_B + kernel + waiting;

  fprintf(stderr, "GEMM   [%2ld] Copy_A : %6.2f  Copy_B : %6.2f  Wait1 : %6.2f Wait2 : %6.2f Wait3 : %6.2f Kernel : %6.2f",
	  mypos, (double)copy_A /(double)total * 100., (double)copy_B /(double)total * 100.,
	  (double)waiting1 /(double)total * 100.,
	  (double)waiting2 /(double)total * 100.,
	  (double)waiting3 /(double)total * 100.,
	  (double)ops/(double)kernel / 4. * 100.);
  fprintf(stderr, "\n");
#endif

  return 0;
}

static int gemm_driver(blas_arg_t *args, BLASLONG *range_m, BLASLONG
		       *range_n, FLOAT *sa, FLOAT *sb,
                       BLASLONG nthreads_m, BLASLONG nthreads_n) {

  blas_arg_t newarg;

#ifndef USE_ALLOC_HEAP
  job_t          job[MAX_CPU_NUMBER];
#else
  job_t *        job = NULL;
#endif

  blas_queue_t queue[MAX_CPU_NUMBER];

  BLASLONG range_M_buffer[MAX_CPU_NUMBER + 2];
  BLASLONG range_N_buffer[MAX_CPU_NUMBER + 2];
  BLASLONG *range_M, *range_N;
  BLASLONG num_parts;

  BLASLONG nthreads = args -> nthreads;

  BLASLONG width, i, j, k, js;
  BLASLONG m, n, n_from, n_to;
  int mode;

  /* Get execution mode */
#ifndef COMPLEX
#ifdef XDOUBLE
  mode  =  BLAS_XDOUBLE | BLAS_REAL | BLAS_NODE;
#elif defined(DOUBLE)
  mode  =  BLAS_DOUBLE  | BLAS_REAL | BLAS_NODE;
#else
  mode  =  BLAS_SINGLE  | BLAS_REAL | BLAS_NODE;
#endif
#else
#ifdef XDOUBLE
  mode  =  BLAS_XDOUBLE | BLAS_COMPLEX | BLAS_NODE;
#elif defined(DOUBLE)
  mode  =  BLAS_DOUBLE  | BLAS_COMPLEX | BLAS_NODE;
#else
  mode  =  BLAS_SINGLE  | BLAS_COMPLEX | BLAS_NODE;
#endif
#endif

#ifdef USE_ALLOC_HEAP
  /* Dynamically allocate workspace */
  job = (job_t*)malloc(MAX_CPU_NUMBER * sizeof(job_t));
  if(job==NULL){
    fprintf(stderr, "OpenBLAS: malloc failed in %s\n", __func__);
    exit(1);
  }
#endif

  /* Initialize struct for arguments */
  newarg.m        = args -> m;
  newarg.n        = args -> n;
  newarg.k        = args -> k;
  newarg.a        = args -> a;
  newarg.b        = args -> b;
  newarg.c        = args -> c;
  newarg.lda      = args -> lda;
  newarg.ldb      = args -> ldb;
  newarg.ldc      = args -> ldc;
  newarg.alpha    = args -> alpha;
  newarg.beta     = args -> beta;
  newarg.nthreads = args -> nthreads;
  newarg.common   = (void *)job;
#ifdef PARAMTEST
  newarg.gemm_p   = args -> gemm_p;
  newarg.gemm_q   = args -> gemm_q;
  newarg.gemm_r   = args -> gemm_r;
#endif

  /* Initialize partitions in m and n
   * Note: The number of CPU partitions is stored in the -1 entry */
  range_M = &range_M_buffer[1];
  range_N = &range_N_buffer[1];
  range_M[-1] = nthreads_m;
  range_N[-1] = nthreads_n;
  if (!range_m) {
    range_M[0] = 0;
    m          = args -> m;
  } else {
    range_M[0] = range_m[0];
    m          = range_m[1] - range_m[0];
  }

  /* Partition m into nthreads_m regions */
  num_parts = 0;
  while (m > 0){
    width = blas_quickdivide(m + nthreads_m - num_parts - 1, nthreads_m - num_parts);
    m -= width;
    if (m < 0) width = width + m;
    range_M[num_parts + 1] = range_M[num_parts] + width;
    num_parts ++;
  }
  for (i = num_parts; i < MAX_CPU_NUMBER; i++) {
    range_M[i + 1] = range_M[num_parts];
  }

  /* Initialize parameters for parallel execution */
  for (i = 0; i < nthreads; i++) {
    queue[i].mode    = mode;
    queue[i].routine = inner_thread;
    queue[i].args    = &newarg;
    queue[i].range_m = range_M;
    queue[i].range_n = range_N;
    queue[i].sa      = NULL;
    queue[i].sb      = NULL;
    queue[i].next    = &queue[i + 1];
  }
  queue[0].sa = sa;
  queue[0].sb = sb;
  queue[nthreads - 1].next = NULL;

  /* Iterate through steps of n */
  if (!range_n) {
    n_from = 0;
    n_to   = args -> n;
  } else {
    n_from = range_n[0];
    n_to   = range_n[1];
  }
  for(js = n_from; js < n_to; js += GEMM_R * nthreads){
    n = n_to - js;
    if (n > GEMM_R * nthreads) n = GEMM_R * nthreads;

    /* Partition (a step of) n into nthreads regions */
    range_N[0] = js;
    num_parts  = 0;
    while (n > 0){
      width = blas_quickdivide(n + nthreads - num_parts - 1, nthreads - num_parts);
      if (width < SWITCH_RATIO) {
        width = SWITCH_RATIO;
      }
      n -= width;
      if (n < 0) width = width + n;
      range_N[num_parts + 1] = range_N[num_parts] + width;
      num_parts ++;
    }
    for (j = num_parts; j < MAX_CPU_NUMBER; j++) {
      range_N[j + 1] = range_N[num_parts];
    }

    /* Clear synchronization flags */
    for (i = 0; i < MAX_CPU_NUMBER; i++) {
      for (j = 0; j < MAX_CPU_NUMBER; j++) {
	for (k = 0; k < DIVIDE_RATE; k++) {
	  job[i].working[j][CACHE_LINE_SIZE * k] = 0;
	}
      }
    }

    /* Execute parallel computation */
    exec_blas(nthreads, queue);
  }

#ifdef USE_ALLOC_HEAP
  free(job);
#endif

  return 0;
}

int CNAME(blas_arg_t *args, BLASLONG *range_m, BLASLONG *range_n, FLOAT *sa, FLOAT *sb, BLASLONG mypos){

  BLASLONG m = args -> m;
  BLASLONG n = args -> n;
  BLASLONG nthreads_m, nthreads_n;

  /* Get dimensions from index ranges if available */
  if (range_m) {
    m = range_m[1] - range_m[0];
  }
  if (range_n) {
    n = range_n[1] - range_n[0];
  }

  /* Partitions in m should have at least SWITCH_RATIO rows */
  if (m < 2 * SWITCH_RATIO) {
    nthreads_m = 1;
  } else {
    nthreads_m = args -> nthreads;
    while (m < nthreads_m * SWITCH_RATIO) {
      nthreads_m = nthreads_m / 2;
    }
  }

  /* Partitions in n should have at most SWITCH_RATIO * nthreads_m columns */
  if (n < SWITCH_RATIO * nthreads_m) {
    nthreads_n = 1;
  } else {
    nthreads_n = (n + SWITCH_RATIO * nthreads_m - 1) / (SWITCH_RATIO * nthreads_m);
    if (nthreads_m * nthreads_n > args -> nthreads) {
      nthreads_n = blas_quickdivide(args -> nthreads, nthreads_m);
    }
  }

  /* Execute serial or parallel computation */
  if (nthreads_m * nthreads_n <= 1) {
    GEMM_LOCAL(args, range_m, range_n, sa, sb, 0);
  } else {
    args -> nthreads = nthreads_m * nthreads_n;
    gemm_driver(args, range_m, range_n, sa, sb, nthreads_m, nthreads_n);
  }

  return 0;
}