text: /*
      -- MAGMA (version 2.5.4) --
         Univ. of Tennessee, Knoxville
         Univ. of California, Berkeley
         Univ. of Colorado, Denver
         @date October 2020
  
         @author Mark Gates
         @author Azzam Haidar
         @author Tingxing Dong
  */
  
  // includes, system
  #include <stdlib.h>
  #include <stdio.h>
  #include <string.h>
  #include <math.h>
  
  // includes, project
  #include "flops.h"
  #include "magma_v2.h"
  #include "magma_lapack.h"
  #include "testings.h"
  
  #if CUDA_VERSION < 9020
  // conversion float to half are not defined for host in CUDA version <9.2
  // thus uses the conversion below when CUDA VERSION is < 9.2.
  #include <string.h>
  //
  // Copyright (c) 1993-2016, NVIDIA CORPORATION. All rights reserved.
  //
  // Redistribution and use in source and binary forms, with or without
  // modification, are permitted provided that the following conditions
  // are met:
  //  * Redistributions of source code must retain the above copyright
  //    notice, this list of conditions and the following disclaimer.
  //  * 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.
  //  * Neither the name of NVIDIA CORPORATION nor the names of its
  //    contributors may be used to endorse or promote products derived
  //    from this software without specific prior written permission.
  //
  // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``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 COPYRIGHT OWNER OR
  // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
  // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
  // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
  // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  
  // This code modified from the public domain code here:
  // https://gist.github.com/rygorous/2156668
  // The URL above includes more robust conversion routines
  // that handle Inf and NaN correctly.
  //
  // It is recommended to use the more robust versions in production code.
  
  typedef unsigned uint;
  
  union FP32
  {
      uint u;
      float f;
      struct
      {
          uint Mantissa : 23;
          uint Exponent : 8;
          uint Sign : 1;
      };
  };
  
  union FP16
  {
      unsigned short u;
      struct
      {
          uint Mantissa : 10;
          uint Exponent : 5;
          uint Sign : 1;
      };
  };
  
  // Approximate solution. This is faster but converts some sNaNs to
  // infinity and doesn't round correctly. Handle with care.
  // Approximate solution. This is faster but converts some sNaNs to
  // infinity and doesn't round correctly. Handle with care.
  static half approx_float_to_half(float fl)
  {
      FP32 f32infty = { 255 << 23 };
      FP32 f16max = { (127 + 16) << 23 };
      FP32 magic = { 15 << 23 };
      FP32 expinf = { (255 ^ 31) << 23 };
      uint sign_mask = 0x80000000u;
      FP16 o = { 0 };
  
      FP32 f = *((FP32*)&fl);
  
      uint sign = f.u & sign_mask;
      f.u ^= sign;
  
      if (!(f.f < f32infty.u)) // Inf or NaN
          o.u = f.u ^ expinf.u;
      else
          {
              if (f.f > f16max.f) f.f = f16max.f;
              f.f *= magic.f;
          }
      
      o.u = f.u >> 13; // Take the mantissa bits
      o.u |= sign >> 16;
      half tmp;
      memcpy(&tmp, &o, sizeof(half));
      //return *((half*)&o);
      return tmp;
  }
  
  // from half->float code - just for verification.                                                                         
  static float half_to_float(half hf)
  {
      FP16 h;
      memcpy(&h, &hf, sizeof(half));
  
      static const FP32 magic = { 113 << 23 };
      static const uint shifted_exp = 0x7c00 << 13; // exponent mask after shift
      FP32 o;
  
      o.u = (h.u & 0x7fff) << 13;     // exponent/mantissa bits
      uint exp = shifted_exp & o.u;   // just the exponent
      o.u += (127 - 15) << 23;        // exponent adjust
  
      // handle exponent special cases
      if (exp == shifted_exp) // Inf/NaN?
          o.u += (128 - 16) << 23;    // extra exp adjust
      else if (exp == 0) // Zero/Denormal?
          {
              o.u += 1 << 23;             // extra exp adjust
              o.f -= magic.f;             // renormalize
          }
  
      o.u |= (h.u & 0x8000) << 16;    // sign bit
      return o.f;
  }
  #endif
  
  #if defined(_OPENMP)
  #include <omp.h>
  #include "../control/magma_threadsetting.h"  // internal header
  #endif
  
  /* ////////////////////////////////////////////////////////////////////////////
     (1) converts a matrix from float to half on the GPU 
     (2) convert back to float and sent it to the CPU to compute the correct norm
  */
  void preprocess_matrix( 
              magma_int_t M, magma_int_t N, 
              float     *hA, magma_int_t lda, 
              magmaHalf *dA, magma_int_t ldda, 
              magma_queue_t queue )
  {
      float *dwork;
      magma_int_t info = 0; 
  
      
      TESTING_CHECK( magma_smalloc(&dwork, lda*N) );               // alloc. dwork on GPU
      magma_ssetmatrix(M, N, hA, lda, dwork, lda, queue);          // send to the GPU
      magmablas_slag2h(M, N, dwork, lda, dA, ldda, &info, queue);  // convert: s -> h
      if(info != 0)printf("preprocess_matrix: error at slag2h\n"); // check
      magmablas_hlag2s(M, N, dA, ldda, dwork, lda, queue );        // convert back: h -> hc
      magma_sgetmatrix(M, N, dwork, lda, hA, lda, queue);          // send to the CPU after conversion
  
      // free workspace
      magma_free( dwork );
  }
  
  /* ////////////////////////////////////////////////////////////////////////////
     (1) converts a matrix from half to float on the GPU 
     (2) send the converted matrix to the CPU
  */
  void postprocess_matrix( 
              magma_int_t M, magma_int_t N, 
              magmaHalf *dA, magma_int_t ldda, 
              float     *hA, magma_int_t lda, 
              magma_queue_t queue )
  {
      float *dwork;
  
      TESTING_CHECK( magma_smalloc(&dwork, lda*N) );
      magmablas_hlag2s(M, N, dA, ldda, dwork, lda, queue ); // convert h -> s
      magma_sgetmatrix(M, N, dwork, lda, hA, lda, queue);   // send to CPU 
  
      magma_free( dwork );
  }
  
  /* ////////////////////////////////////////////////////////////////////////////
     (1) converts a matrix from float to half on the GPU 
     (2) convert back to float and sent it to the CPU to compute the correct norm
     (3) matrices in the batch are assumed to be within a fixed stride of 
         lda*N (cpu) or ldda*N (gpu)
  */
  void preprocess_matrix_batched( 
              magma_int_t M, magma_int_t N, 
              float     *hA, magma_int_t lda, 
              magmaHalf *dA, magma_int_t ldda, 
              magma_int_t batchCount, magma_queue_t queue )
  {
      float *dwork;
      magma_int_t info = 0; 
  
      TESTING_CHECK( magma_smalloc(&dwork, batchCount*lda*N) );               // alloc. dwork on GPU
      magma_ssetmatrix(M, batchCount*N, hA, lda, dwork, lda, queue);          // send to the GPU
      magmablas_slag2h(M, batchCount*N, dwork, lda, dA, ldda, &info, queue);  // convert: s -> h
      if(info != 0)printf("preprocess_matrix: error at slag2h\n");            // check
      magmablas_hlag2s(M, batchCount*N, dA, ldda, dwork, lda, queue );        // convert back: h -> hc
      magma_sgetmatrix(M, batchCount*N, dwork, lda, hA, lda, queue);          // send to the CPU after conversion
  
      // free workspace
      magma_free( dwork );
  }
  
  /* ////////////////////////////////////////////////////////////////////////////
     (1) converts a matrix from half to float on the GPU 
     (2) send the converted matrix to the CPU
     (3) matrices in the batch are assumed to be within a fixed stride of 
         lda*N (cpu) or ldda*N (gpu)
  */
  void postprocess_matrix_batched( 
              magma_int_t M, magma_int_t N, 
              magmaHalf *dA, magma_int_t ldda, 
              float     *hA, magma_int_t lda, 
              magma_int_t batchCount, magma_queue_t queue )
  {
      float *dwork;
  
      TESTING_CHECK( magma_smalloc(&dwork, batchCount*lda*N) );
      magmablas_hlag2s(M, batchCount*N, dA, ldda, dwork, lda, queue ); // convert h -> s
      magma_sgetmatrix(M, batchCount*N, dwork, lda, hA, lda, queue);   // send to CPU 
  
      magma_free( dwork );
  }
  
  /* ////////////////////////////////////////////////////////////////////////////
     -- Testing hgemm_batched
  */
  int main( int argc, char** argv)
  {
      TESTING_CHECK( magma_init() );
      magma_print_environment();
  
      real_Double_t   gflops, magma_perf, magma_time, cublas_perf, cublas_time, cpu_perf, cpu_time;
      float          error, cublas_error, magma_error, normalize, work[1];
      magma_int_t M, N, K;
      magma_int_t Am, An, Bm, Bn;
      magma_int_t sizeA, sizeB, sizeC;
      magma_int_t lda, ldb, ldc, ldda, lddb, lddc;
      magma_int_t ione     = 1;
      magma_int_t ISEED[4] = {0,0,0,1};
      int status = 0;
      magma_int_t batchCount;
  
      float *hA, *hB, *hC, *hC_magma, *hC_cublas;
      magmaHalf *dA, *dB, *dC;
      float c_neg_one = MAGMA_S_NEG_ONE;
      #if CUDA_VERSION >= 9020
      magmaHalf alpha = 0.29;
      magmaHalf beta  = -0.48;
      #else
      magmaHalf alpha = approx_float_to_half(0.29); 
      magmaHalf beta  = approx_float_to_half(-0.48);
      #endif
  
      magmaHalf **dA_array = NULL;
      magmaHalf **dB_array = NULL;
      magmaHalf **dC_array = NULL;
  
      magma_opts opts( MagmaOptsBatched );
      opts.parse_opts( argc, argv );
      opts.lapack |= opts.check; // check (-c) implies lapack (-l)
      batchCount = opts.batchcount;
      
      float *Anorm, *Bnorm, *Cnorm;
      TESTING_CHECK( magma_smalloc_cpu( &Anorm, batchCount ));
      TESTING_CHECK( magma_smalloc_cpu( &Bnorm, batchCount ));
      TESTING_CHECK( magma_smalloc_cpu( &Cnorm, batchCount ));
  
      // See testing_sgemm about tolerance.
      // also see: https://blogs.mathworks.com/cleve/2017/05/08/half-precision-16-bit-floating-point-arithmetic
      float eps = (float)(0.00097656);
      float tol = 3*eps;
      
      printf("%% If running lapack (option --lapack), MAGMA and CUBLAS error are both computed\n"
             "%% relative to CPU BLAS result. Else, MAGMA error is computed relative to CUBLAS result.\n\n"
             "%% transA = %s, transB = %s\n",
             lapack_trans_const(opts.transA),
             lapack_trans_const(opts.transB));
      printf("%% BatchCount     M     N     K   MAGMA Gflop/s (ms)   CUBLAS Gflop/s (ms)   CPU Gflop/s   (ms)     MAGMA error   CUBLAS error\n");
      printf("%%                                (Half Precision)      (Half Precision)     (Single Precision)                               \n");
      printf("%%============================================================================================================================\n");
      
      for( int itest = 0; itest < opts.ntest; ++itest ) {
          for( int iter = 0; iter < opts.niter; ++iter ) {
              M = opts.msize[itest];
              N = opts.nsize[itest];
              K = opts.ksize[itest];
              gflops = FLOPS_SGEMM( M, N, K ) / 1e9 * batchCount;
  
              if ( opts.transA == MagmaNoTrans ) {
                  lda = Am = M;
                  An = K;
              }
              else {
                  lda = Am = K;
                  An = M;
              }
              
              if ( opts.transB == MagmaNoTrans ) {
                  ldb = Bm = K;
                  Bn = N;
              }
              else {
                  ldb = Bm = N;
                  Bn = K;
              }
              ldc = M;
  
              ldda = magma_roundup( lda, opts.align );  // multiple of 32 by default
              lddb = magma_roundup( ldb, opts.align );  // multiple of 32 by default
              lddc = magma_roundup( ldc, opts.align );  // multiple of 32 by default
  
              sizeA = lda*An*batchCount;
              sizeB = ldb*Bn*batchCount;
              sizeC = ldc*N*batchCount;
  
              TESTING_CHECK( magma_smalloc_cpu( &hA,  sizeA ));
              TESTING_CHECK( magma_smalloc_cpu( &hB,  sizeB ));
              TESTING_CHECK( magma_smalloc_cpu( &hC,  sizeC  ));
              TESTING_CHECK( magma_smalloc_cpu( &hC_magma,  sizeC  ));
              TESTING_CHECK( magma_smalloc_cpu( &hC_cublas, sizeC  ));
  
              TESTING_CHECK( magma_malloc( (void**) &dA, ldda*An*batchCount * sizeof(magmaHalf) ));
              TESTING_CHECK( magma_malloc( (void**) &dB, lddb*Bn*batchCount * sizeof(magmaHalf) ));
              TESTING_CHECK( magma_malloc( (void**) &dC, lddc*N*batchCount  * sizeof(magmaHalf) ));
  
              TESTING_CHECK( magma_malloc( (void**) &dA_array, batchCount * sizeof(magmaHalf*) ));
              TESTING_CHECK( magma_malloc( (void**) &dB_array, batchCount * sizeof(magmaHalf*) ));
              TESTING_CHECK( magma_malloc( (void**) &dC_array, batchCount * sizeof(magmaHalf*) ));
  
              /* Initialize the matrices */
              lapackf77_slarnv( &ione, ISEED, &sizeA, hA );
              lapackf77_slarnv( &ione, ISEED, &sizeB, hB );
              lapackf77_slarnv( &ione, ISEED, &sizeC, hC );
  
              /* preprocessing assumes one big matrix */
              preprocess_matrix(Am, batchCount*An, hA, lda, dA, ldda, opts.queue );
              preprocess_matrix(Bm, batchCount*Bn, hB, ldb, dB, lddb, opts.queue );
              preprocess_matrix( M, batchCount*N,  hC, ldc, dC, lddc, opts.queue );
  
              // Compute norms for error
              for (int s = 0; s < batchCount; ++s) {
                  Anorm[s] = lapackf77_slange( "F", &Am, &An, &hA[s*lda*An], &lda, work );
                  Bnorm[s] = lapackf77_slange( "F", &Bm, &Bn, &hB[s*ldb*Bn], &ldb, work );
                  Cnorm[s] = lapackf77_slange( "F", &M,  &N,  &hC[s*ldc*N],  &ldc, work );
              }
  
              /* =====================================================================
                 Performs operation using MAGMABLAS
                 =================================================================== */
              magma_hset_pointer( dA_array, dA, ldda, 0, 0, ldda*An, batchCount, opts.queue );
              magma_hset_pointer( dB_array, dB, lddb, 0, 0, lddb*Bn, batchCount, opts.queue );
              magma_hset_pointer( dC_array, dC, lddc, 0, 0, lddc*N,  batchCount, opts.queue );
  
              magma_time = magma_sync_wtime( opts.queue );
              magmablas_hgemm_batched( 
                          opts.transA, opts.transB, 
                          M, N, K, 
                          alpha, dA_array, ldda, 
                                 dB_array, lddb, 
                          beta,  dC_array, lddc, batchCount, opts.queue );
              magma_time = magma_sync_wtime( opts.queue ) - magma_time;
              magma_perf = gflops / magma_time;
              postprocess_matrix(M, batchCount*N, dC, lddc, hC_magma, ldc, opts.queue );
  
              /* =====================================================================
                 Performs operation using CUBLAS
                 =================================================================== */
              preprocess_matrix( M, batchCount*N,  hC, ldc, dC, lddc, opts.queue );
              cublasSetMathMode(opts.handle, CUBLAS_TENSOR_OP_MATH);
              
              cublas_time = magma_sync_wtime( opts.queue );
              cublasHgemmBatched(opts.handle, cublas_trans_const(opts.transA), cublas_trans_const(opts.transB),
                                 int(M), int(N), int(K),
                                 &alpha, (const magmaHalf**)dA_array, int(ldda),
                                         (const magmaHalf**)dB_array, int(lddb),
                                 &beta,                     dC_array, int(lddc), int(batchCount) );
              cublas_time = magma_sync_wtime( opts.queue ) - cublas_time;
              cublas_perf = gflops / cublas_time;
              postprocess_matrix(M, batchCount*N, dC, lddc, hC_cublas, ldc, opts.queue );
  
              /* =====================================================================
                 Performs operation using CPU BLAS
                 =================================================================== */
              if ( opts.lapack ) {
                  #if CUDA_VERSION >= 9020
                  float alpha_r32 = (float)alpha;
                  float beta_r32  = (float)beta;
                  #else
                  float alpha_r32 = half_to_float(alpha);
                  float beta_r32  = half_to_float(beta);
                  #endif
                  cpu_time = magma_wtime();
                  #if !defined (BATCHED_DISABLE_PARCPU) && defined(_OPENMP)
                  magma_int_t nthreads = magma_get_lapack_numthreads();
                  magma_set_lapack_numthreads(1);
                  magma_set_omp_numthreads(nthreads);
                  #pragma omp parallel for schedule(dynamic)
                  #endif
                  for (int i=0; i < batchCount; i++) {
                      blasf77_sgemm( lapack_trans_const(opts.transA),
                                     lapack_trans_const(opts.transB),
                                     &M, &N, &K,
                                     &alpha_r32, hA + i*lda*An, &lda,
                                             hB + i*ldb*Bn, &ldb,
                                     &beta_r32,  hC + i*ldc*N, &ldc );
                  }
                  #if !defined (BATCHED_DISABLE_PARCPU) && defined(_OPENMP)
                      magma_set_lapack_numthreads(nthreads);
                  #endif
                  cpu_time = magma_wtime() - cpu_time;
                  cpu_perf = gflops / cpu_time;
              }
              
              /* =====================================================================
                 Check the result
                 =================================================================== */
              if ( opts.lapack ) {
                  // compute error compared lapack
                  // error = |dC - C| / (gamma_{k+2}|A||B| + gamma_2|Cin|)
                  error = 0;
                  magma_error = 0;
                  cublas_error = 0;
  
                  for (int s=0; s < batchCount; s++) {
                      normalize = sqrt(float(K+2))*Anorm[s]*Bnorm[s] + 2*Cnorm[s];
                      if (normalize == 0)
                          normalize = 1;
                      magma_int_t Csize = ldc*N;
                      blasf77_saxpy( &Csize, &c_neg_one, &hC[s*ldc*N], &ione, &hC_magma[s*ldc*N], &ione );
                      error = lapackf77_slange( "F", &M, &N, &hC_magma[s*ldc*N], &ldc, work )
                            / normalize;
                      magma_error = magma_max_nan( error, magma_error );
                      
                      // cublas error
                      blasf77_saxpy( &Csize, &c_neg_one, &hC[s*ldc*N], &ione, &hC_cublas[s*ldc*N], &ione );
                      error = lapackf77_slange( "F", &M, &N, &hC_cublas[s*ldc*N], &ldc, work )
                            / normalize;
                      cublas_error = magma_max_nan( error, cublas_error );
                  }
  
                  bool okay = (magma_error < tol);
                  status += ! okay;
                  printf("  %10lld %5lld %5lld %5lld    %7.2f (%7.2f)    %7.2f (%7.2f)   %7.2f (%7.2f)       %8.2e      %8.2e   %s\n",
                         (long long) batchCount, (long long) M, (long long) N, (long long) K,
                         magma_perf,  1000.*magma_time,
                         cublas_perf, 1000.*cublas_time,
                         cpu_perf,    1000.*cpu_time,
                         magma_error, cublas_error, (okay ? "ok" : "failed") );
              }
              else {
                  // compute error compared cublas
                  // error = |dC - C| / (gamma_{k+2}|A||B| + gamma_2|Cin|)
                  error = 0;
                  magma_error = 0;
  
                  for (int s=0; s < batchCount; s++) {
                      normalize = sqrt(float(K+2))*Anorm[s]*Bnorm[s] + 2*Cnorm[s];
                      if (normalize == 0)
                          normalize = 1;
                      magma_int_t Csize = ldc*N;
                      blasf77_saxpy( &Csize, &c_neg_one, &hC_cublas[s*ldc*N], &ione, &hC_magma[s*ldc*N], &ione );
                      error = lapackf77_slange( "F", &M, &N, &hC_magma[s*ldc*N], &ldc, work )
                            / normalize;
                      magma_error = magma_max_nan( error, magma_error );
                  }
                  magma_error = magma_max_nan( error, magma_error );
  
                  bool okay = (magma_error < tol);
                  status += ! okay;
                  printf("  %10lld %5lld %5lld %5lld    %7.2f (%7.2f)    %7.2f (%7.2f)     ---   (  ---  )       %8.2e        ---      %s\n",
                         (long long) batchCount, (long long) M, (long long) N, (long long) K,
                         magma_perf,  1000.*magma_time,
                         cublas_perf, 1000.*cublas_time,
                         magma_error, (okay ? "ok" : "failed") );
              }
              
              magma_free_cpu( hA  );
              magma_free_cpu( hB  );
              magma_free_cpu( hC  );
              magma_free_cpu( hC_magma  );
              magma_free_cpu( hC_cublas );
  
              magma_free( dA );
              magma_free( dB );
              magma_free( dC );
              magma_free( dA_array );
              magma_free( dB_array );
              magma_free( dC_array );
  
              fflush( stdout);
          }
          if ( opts.niter > 1 ) {
              printf( "\n" );
          }
      }
  
      magma_free_cpu( Anorm );
      magma_free_cpu( Bnorm );
      magma_free_cpu( Cnorm );
  
      opts.cleanup();
      TESTING_CHECK( magma_finalize() );
      return status;
  }
  