text: /*
  
     BLIS    
     An object-based framework for developing high-performance BLAS-like
     libraries.
  
     Copyright (C) 2014, The University of Texas at Austin
  
     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 The University of Texas at Austin 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 AND CONTRIBUTORS
     "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
     HOLDER 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.
  
  */
  
  #include "blis.h"
  
  #define FUNCPTR_T gemm_fp
  
  typedef void (*FUNCPTR_T)(
                             doff_t  diagoffa,
                             pack_t  schema_a,
                             pack_t  schema_b,
                             dim_t   m,
                             dim_t   n,
                             dim_t   k,
                             void*   alpha1,
                             void*   a, inc_t cs_a, dim_t pd_a, inc_t ps_a,
                             void*   b, inc_t rs_b, dim_t pd_b, inc_t ps_b,
                             void*   alpha2,
                             void*   c, inc_t rs_c, inc_t cs_c,
                             cntx_t* cntx,
                             thrinfo_t* thread
                           );
  
  static FUNCPTR_T GENARRAY(ftypes,trsm_lu_ker_var2);
  
  
  void bli_trsm_lu_ker_var2
       (
         obj_t*  a,
         obj_t*  b,
         obj_t*  c,
         cntx_t* cntx,
         cntl_t* cntl,
         thrinfo_t* thread
       )
  {
  	num_t     dt_exec   = bli_obj_execution_datatype( *c );
  
  	doff_t    diagoffa  = bli_obj_diag_offset( *a );
  
  	pack_t    schema_a  = bli_obj_pack_schema( *a );
  	pack_t    schema_b  = bli_obj_pack_schema( *b );
  
  	dim_t     m         = bli_obj_length( *c );
  	dim_t     n         = bli_obj_width( *c );
  	dim_t     k         = bli_obj_width( *a );
  
  	void*     buf_a     = bli_obj_buffer_at_off( *a );
  	inc_t     cs_a      = bli_obj_col_stride( *a );
  	dim_t     pd_a      = bli_obj_panel_dim( *a );
  	inc_t     ps_a      = bli_obj_panel_stride( *a );
  
  	void*     buf_b     = bli_obj_buffer_at_off( *b );
  	inc_t     rs_b      = bli_obj_row_stride( *b );
  	dim_t     pd_b      = bli_obj_panel_dim( *b );
  	inc_t     ps_b      = bli_obj_panel_stride( *b );
  
  	void*     buf_c     = bli_obj_buffer_at_off( *c );
  	inc_t     rs_c      = bli_obj_row_stride( *c );
  	inc_t     cs_c      = bli_obj_col_stride( *c );
  
  	void*     buf_alpha1;
  	void*     buf_alpha2;
  
  	FUNCPTR_T f;
  
  	// Grab the address of the internal scalar buffer for the scalar
  	// attached to B (the non-triangular matrix). This will be the alpha
  	// scalar used in the gemmtrsm subproblems (ie: the scalar that would
  	// be applied to the packed copy of B prior to it being updated by
  	// the trsm subproblem). This scalar may be unit, if for example it
  	// was applied during packing.
  	buf_alpha1 = bli_obj_internal_scalar_buffer( *b );
  
  	// Grab the address of the internal scalar buffer for the scalar
  	// attached to C. This will be the "beta" scalar used in the gemm-only
  	// subproblems that correspond to micro-panels that do not intersect
  	// the diagonal. We need this separate scalar because it's possible
  	// that the alpha attached to B was reset, if it was applied during
  	// packing.
  	buf_alpha2 = bli_obj_internal_scalar_buffer( *c );
  
  	// Index into the type combination array to extract the correct
  	// function pointer.
  	f = ftypes[dt_exec];
  
  	// Invoke the function.
  	f( diagoffa,
  	   schema_a,
  	   schema_b,
  	   m,
  	   n,
  	   k,
  	   buf_alpha1,
  	   buf_a, cs_a, pd_a, ps_a,
  	   buf_b, rs_b, pd_b, ps_b,
  	   buf_alpha2,
  	   buf_c, rs_c, cs_c,
  	   cntx,
  	   thread );
  }
  
  
  #undef  GENTFUNC
  #define GENTFUNC( ctype, ch, varname ) \
  \
  void PASTEMAC(ch,varname) \
       ( \
         doff_t  diagoffa, \
         pack_t  schema_a, \
         pack_t  schema_b, \
         dim_t   m, \
         dim_t   n, \
         dim_t   k, \
         void*   alpha1, \
         void*   a, inc_t cs_a, dim_t pd_a, inc_t ps_a, \
         void*   b, inc_t rs_b, dim_t pd_b, inc_t ps_b, \
         void*   alpha2, \
         void*   c, inc_t rs_c, inc_t cs_c, \
         cntx_t* cntx, \
         thrinfo_t* thread  \
       ) \
  { \
  	const num_t     dt          = PASTEMAC(ch,type); \
  \
  	/* Alias some constants to simpler names. */ \
  	const dim_t     MR          = pd_a; \
  	const dim_t     NR          = pd_b; \
  	const dim_t     PACKMR      = cs_a; \
  	const dim_t     PACKNR      = rs_b; \
  \
  	/* Cast the micro-kernel address to its function pointer type. */ \
  	PASTECH(ch,gemmtrsm_ukr_ft) \
  	               gemmtrsm_ukr = bli_cntx_get_l3_ukr_dt( dt, BLIS_GEMMTRSM_U_UKR, cntx ); \
  	PASTECH(ch,gemm_ukr_ft) \
  	                   gemm_ukr = bli_cntx_get_l3_ukr_dt( dt, BLIS_GEMM_UKR, cntx ); \
  \
  	/* Temporary C buffer for edge cases. Note that the strides of this
  	   temporary buffer are set so that they match the storage of the
  	   original C matrix. For example, if C is column-stored, ct will be
  	   column-stored as well. */ \
  	ctype           ct[ BLIS_STACK_BUF_MAX_SIZE \
  	                    / sizeof( ctype ) ] \
  	                    __attribute__((aligned(BLIS_STACK_BUF_ALIGN_SIZE))); \
  	const bool_t    col_pref    = bli_cntx_l3_ukr_prefers_cols_dt( dt, BLIS_GEMM_UKR, cntx ); \
  	const inc_t     rs_ct       = ( col_pref ? 1 : NR ); \
  	const inc_t     cs_ct       = ( col_pref ? MR : 1 ); \
  \
  	ctype* restrict zero        = PASTEMAC(ch,0); \
  	ctype* restrict minus_one   = PASTEMAC(ch,m1); \
  	ctype* restrict a_cast      = a; \
  	ctype* restrict b_cast      = b; \
  	ctype* restrict c_cast      = c; \
  	ctype* restrict alpha1_cast = alpha1; \
  	ctype* restrict alpha2_cast = alpha2; \
  	ctype* restrict b1; \
  	ctype* restrict c1; \
  \
  	doff_t          diagoffa_i; \
  	dim_t           k_full; \
  	dim_t           m_iter, m_left; \
  	dim_t           n_iter, n_left; \
  	dim_t           m_cur; \
  	dim_t           n_cur; \
  	dim_t           k_a1112; \
  	dim_t           k_a11; \
  	dim_t           k_a12; \
  	dim_t           off_a11; \
  	dim_t           off_a12; \
  	dim_t           i, j, ib; \
  	inc_t           rstep_a; \
  	inc_t           cstep_b; \
  	inc_t           rstep_c, cstep_c; \
  	inc_t           istep_a; \
  	inc_t           istep_b; \
  	inc_t           off_scl; \
  	inc_t           ss_a_num; \
  	inc_t           ss_a_den; \
  	inc_t           ps_a_cur; \
  	inc_t           is_a_cur; \
  	auxinfo_t       aux; \
  \
  	/*
  	   Assumptions/assertions:
  	     rs_a == 1
  	     cs_a == PACKMR
  	     pd_a == MR
  	     ps_a == stride to next micro-panel of A
  	     rs_b == PACKNR
  	     cs_b == 1
  	     pd_b == NR
  	     ps_b == stride to next micro-panel of B
  	     rs_c == (no assumptions)
  	     cs_c == (no assumptions)
  	*/ \
  \
  	/* Safety trap: Certain indexing within this macro-kernel does not
  	   work as intended if both MR and NR are odd. */ \
  	if ( ( bli_is_odd( PACKMR ) && bli_is_odd( NR ) ) || \
  	     ( bli_is_odd( PACKNR ) && bli_is_odd( MR ) ) ) bli_abort(); \
  \
  	/* If any dimension is zero, return immediately. */ \
  	if ( bli_zero_dim3( m, n, k ) ) return; \
  \
  	/* Safeguard: If matrix A is below the diagonal, it is implicitly zero.
  	   So we do nothing. */ \
  	if ( bli_is_strictly_below_diag_n( diagoffa, m, k ) ) return; \
  \
  	/* Compute k_full as k inflated up to a multiple of MR. This is
  	   needed because some parameter combinations of trsm reduce k
  	   to advance past zero regions in the triangular matrix, and
  	   when computing the imaginary stride of B (the non-triangular
  	   matrix), which is used by 4m1/3m1 implementations, we need
  	   this unreduced value of k. */ \
  	k_full = ( k % MR != 0 ? k + MR - ( k % MR ) : k ); \
  \
  	/* Compute indexing scaling factor for for 4m or 3m. This is
  	   needed because one of the packing register blocksizes (PACKMR
  	   or PACKNR) is used to index into the micro-panels of the non-
  	   triangular matrix when computing with a diagonal-intersecting
  	   micro-panel of the triangular matrix. In the case of 4m or 3m,
  	   real values are stored in both sub-panels, and so the indexing
  	   needs to occur in units of real values. The value computed
  	   here is divided into the complex pointer offset to cause the
  	   pointer to be advanced by the correct value. */ \
  	if ( bli_is_4mi_packed( schema_a ) || \
  	     bli_is_3mi_packed( schema_a ) || \
  	     bli_is_rih_packed( schema_a ) ) off_scl = 2; \
  	else                                 off_scl = 1; \
  \
  	/* Compute the storage stride scaling. Usually this is just 1.
  	   However, in the case of interleaved 3m, we need to scale the
  	   offset by 3/2. Note that real-only, imag-only, and summed-only
  	   packing formats are not applicable here since trsm is a two-
  	   operand operation only (unlike trmm, which is capable of three-
  	   operand). */ \
  	if ( bli_is_3mi_packed( schema_a ) ) { ss_a_num = 3; ss_a_den = 2; } \
  	else                                 { ss_a_num = 1; ss_a_den = 1; } \
  \
  	/* If there is a zero region to the left of where the diagonal of A
  	   intersects the top edge of the block, adjust the pointer to B and
  	   treat this case as if the diagonal offset were zero. Note that we
  	   don't need to adjust the pointer to A since packm would have simply
  	   skipped over the region that was not stored. */ \
  	if ( diagoffa > 0 ) \
  	{ \
  		i        = diagoffa; \
  		k        = k - i; \
  		diagoffa = 0; \
  		b_cast   = b_cast + ( i * PACKNR ) / off_scl; \
  	} \
  \
  	/* If there is a zero region below where the diagonal of A intersects the
  	   right side of the block, shrink it to prevent "no-op" iterations from
  	   executing. */ \
  	if ( -diagoffa + k < m ) \
  	{ \
  		m = -diagoffa + k; \
  	} \
  \
  	/* Check the k dimension, which needs to be a multiple of MR. If k
  	   isn't a multiple of MR, we adjust it higher to satisfy the micro-
  	   kernel, which is expecting to perform an MR x MR triangular solve.
  	   This adjustment of k is consistent with what happened when A was
  	   packed: all of its bottom/right edges were zero-padded, and
  	   furthermore, the panel that stores the bottom-right corner of the
  	   matrix has its diagonal extended into the zero-padded region (as
  	   identity). This allows the trsm of that bottom-right panel to
  	   proceed without producing any infs or NaNs that would infect the
  	   "good" values of the corresponding block of B. */ \
  	if ( k % MR != 0 ) k += MR - ( k % MR ); \
  \
  	/* NOTE: We don't need to check that m is a multiple of PACKMR since we
  	   know that the underlying buffer was already allocated to have an m
  	   dimension that is a multiple of PACKMR, with the region between the
  	   last row and the next multiple of MR zero-padded accordingly. */ \
  \
  	/* Clear the temporary C buffer in case it has any infs or NaNs. */ \
  	PASTEMAC(ch,set0s_mxn)( MR, NR, \
  	                        ct, rs_ct, cs_ct ); \
  \
  	/* Compute number of primary and leftover components of the m and n
         dimensions. */ \
  	n_iter = n / NR; \
  	n_left = n % NR; \
  \
  	m_iter = m / MR; \
  	m_left = m % MR; \
  \
  	if ( n_left ) ++n_iter; \
  	if ( m_left ) ++m_iter; \
  \
  	/* Determine some increments used to step through A, B, and C. */ \
  	rstep_a = ps_a; \
  \
  	cstep_b = ps_b; \
  \
  	rstep_c = rs_c * MR; \
  	cstep_c = cs_c * NR; \
  \
  	istep_a = PACKMR * k; \
  	istep_b = PACKNR * k_full; \
  \
  	if ( bli_is_odd( istep_a ) ) istep_a += 1; \
  	if ( bli_is_odd( istep_b ) ) istep_b += 1; \
  \
  	/* Save the pack schemas of A and B to the auxinfo_t object. */ \
  	bli_auxinfo_set_schema_a( schema_a, &aux ); \
  	bli_auxinfo_set_schema_b( schema_b, &aux ); \
  \
  	/* Save the imaginary stride of B to the auxinfo_t object. */ \
  	bli_auxinfo_set_is_b( istep_b, &aux ); \
  \
  	b1 = b_cast; \
  	c1 = c_cast; \
  \
  	/* Loop over the n dimension (NR columns at a time). */ \
  	for ( j = 0; j < n_iter; ++j ) \
  	{ \
  		if( trsm_my_iter( j, thread ) ) { \
  \
  		ctype* restrict a1; \
  		ctype* restrict c11; \
  		ctype* restrict b2; \
  \
  		a1  = a_cast; \
  		c11 = c1 + (m_iter-1)*rstep_c; \
  \
  		n_cur = ( bli_is_not_edge_f( j, n_iter, n_left ) ? NR : n_left ); \
  \
  		/* Initialize our next panel of B to be the current panel of B. */ \
  		b2 = b1; \
  \
  		/* Loop over the m dimension (MR rows at a time). */ \
  		for ( ib = 0; ib < m_iter; ++ib ) \
  		{ \
  			i          = m_iter - 1 - ib; \
  			diagoffa_i = diagoffa + ( doff_t )i*MR; \
  \
  			m_cur = ( bli_is_not_edge_b( ib, m_iter, m_left ) ? MR : m_left ); \
  \
  			/* If the current panel of A intersects the diagonal, use a
  			   special micro-kernel that performs a fused gemm and trsm.
  			   If the current panel of A resides above the diagonal, use a
  			   a regular gemm micro-kernel. Otherwise, if it is below the
  			   diagonal, it was not packed (because it is implicitly zero)
  			   and so we do nothing. */ \
  			if ( bli_intersects_diag_n( diagoffa_i, MR, k ) ) \
  			{ \
  				ctype* restrict a11; \
  				ctype* restrict a12; \
  				ctype* restrict b11; \
  				ctype* restrict b21; \
  				ctype* restrict a2; \
  \
  				/* Compute various offsets into and lengths of parts of A. */ \
  				off_a11 = diagoffa_i; \
  				k_a1112 = k - off_a11;; \
  				k_a11   = MR; \
  				k_a12   = k_a1112 - MR; \
  				off_a12 = off_a11 + k_a11; \
  \
  				/* Compute the panel stride for the current diagonal-
  				   intersecting micro-panel. */ \
  				is_a_cur  = k_a1112 * PACKMR; \
  				is_a_cur += ( bli_is_odd( is_a_cur ) ? 1 : 0 ); \
  				ps_a_cur  = ( is_a_cur * ss_a_num ) / ss_a_den; \
  \
  				/* Compute the addresses of the triangular block A11 and the
  				   panel A12. */ \
  				a11 = a1; \
  				/* a12 = a1 + ( k_a11 * PACKMR ) / off_scl; */ \
  				bli_ptr_add( a12, a1, k_a11 * PACKMR, off_scl ); \
  \
  				/* Compute the addresses of the panel B01 and the block
  				   B11. */ \
  				b11 = b1 + ( off_a11 * PACKNR ) / off_scl; \
  				b21 = b1 + ( off_a12 * PACKNR ) / off_scl; \
  \
  				/* Compute the addresses of the next panels of A and B. */ \
  				a2 = a1 + ps_a_cur; \
  				if ( bli_is_last_iter( ib, m_iter, 0, 1 ) ) \
  				{ \
  					a2 = a_cast; \
  					b2 = b1; \
  					/*if ( bli_is_last_iter( j, n_iter, 0, 1 ) ) */\
  					if ( j + bli_thread_num_threads(thread) >= n_iter ) \
  						b2 = b_cast; \
  				} \
  \
  				/* Save addresses of next panels of A and B to the auxinfo_t
  				   object. */ \
  				bli_auxinfo_set_next_a( a2, &aux ); \
  				bli_auxinfo_set_next_b( b2, &aux ); \
  \
  				/* Save the 4m1/3m1 imaginary stride of A to the auxinfo_t
  				   object. */ \
  				bli_auxinfo_set_is_a( is_a_cur, &aux ); \
  \
  				/* Handle interior and edge cases separately. */ \
  				if ( m_cur == MR && n_cur == NR ) \
  				{ \
  					/* Invoke the fused gemm/trsm micro-kernel. */ \
  					gemmtrsm_ukr \
  					( \
  					  k_a12, \
  					  alpha1_cast, \
  					  a12, \
  					  a11, \
  					  b21, \
  					  b11, \
  					  c11, rs_c, cs_c, \
  					  &aux, \
  					  cntx  \
  					); \
  				} \
  				else \
  				{ \
  					/* Invoke the fused gemm/trsm micro-kernel. */ \
  					gemmtrsm_ukr \
  					( \
  					  k_a12, \
  					  alpha1_cast, \
  					  a12, \
  					  a11, \
  					  b21, \
  					  b11, \
  					  ct, rs_ct, cs_ct, \
  					  &aux, \
  					  cntx  \
  					); \
  \
  					/* Copy the result to the bottom edge of C. */ \
  					PASTEMAC(ch,copys_mxn)( m_cur, n_cur, \
  					                        ct,  rs_ct, cs_ct, \
  					                        c11, rs_c,  cs_c ); \
  				} \
  \
  				a1 += ps_a_cur; \
  			} \
  			else if ( bli_is_strictly_above_diag_n( diagoffa_i, MR, k ) ) \
  			{ \
  				ctype* restrict a2; \
  \
  				/* Compute the addresses of the next panels of A and B. */ \
  				a2 = a1 + rstep_a; \
  				if ( bli_is_last_iter( ib, m_iter, 0, 1 ) ) \
  				{ \
  					a2 = a_cast; \
  					b2 = b1; \
  					/*if ( bli_is_last_iter( j, n_iter, 0, 1 ) ) */\
  					if ( j + bli_thread_num_threads(thread) >= n_iter ) \
  						b2 = b_cast; \
  				} \
  \
  				/* Save addresses of next panels of A and B to the auxinfo_t
  				   object. */ \
  				bli_auxinfo_set_next_a( a2, &aux ); \
  				bli_auxinfo_set_next_b( b2, &aux ); \
  \
  				/* Save the 4m1/3m1 imaginary stride of A to the auxinfo_t
  				   object. */ \
  				bli_auxinfo_set_is_a( istep_a, &aux ); \
  \
  				/* Handle interior and edge cases separately. */ \
  				if ( m_cur == MR && n_cur == NR ) \
  				{ \
  					/* Invoke the gemm micro-kernel. */ \
  					gemm_ukr \
  					( \
  					  k, \
  					  minus_one, \
  					  a1, \
  					  b1, \
  					  alpha2_cast, \
  					  c11, rs_c, cs_c, \
  					  &aux, \
  					  cntx  \
  					); \
  				} \
  				else \
  				{ \
  					/* Invoke the gemm micro-kernel. */ \
  					gemm_ukr \
  					( \
  					  k, \
  					  minus_one, \
  					  a1, \
  					  b1, \
  					  zero, \
  					  ct, rs_ct, cs_ct, \
  					  &aux, \
  					  cntx  \
  					); \
  \
  					/* Add the result to the edge of C. */ \
  					PASTEMAC(ch,xpbys_mxn)( m_cur, n_cur, \
  					                        ct,  rs_ct, cs_ct, \
  					                        alpha2_cast, \
  					                        c11, rs_c,  cs_c ); \
  				} \
  \
  				a1 += rstep_a; \
  			} \
  \
  			c11 -= rstep_c; \
  		} \
  		} \
  \
  		b1 += cstep_b; \
  		c1 += cstep_c; \
  	} \
  \
  /*
  PASTEMAC(ch,fprintm)( stdout, "trsm_lu_ker_var2: a1 (diag)", MR, k_a1112, a1, 1, MR, "%5.2f", "" ); \
  PASTEMAC(ch,fprintm)( stdout, "trsm_lu_ker_var2: b11 (diag)", MR, NR, b11, NR, 1, "%6.3f", "" ); \
  printf( "m_iter     = %lu\n", m_iter ); \
  printf( "m_cur      = %lu\n", m_cur ); \
  printf( "k          = %lu\n", k ); \
  printf( "diagoffa_i = %lu\n", diagoffa_i ); \
  printf( "off_a1112  = %lu\n", off_a1112 ); \
  printf( "k_a1112    = %lu\n", k_a1112 ); \
  printf( "k_a12      = %lu\n", k_a12 ); \
  printf( "k_a11      = %lu\n", k_a11 ); \
  printf( "rs_c,cs_c  = %lu %lu\n", rs_c, cs_c ); \
  printf( "rs_ct,cs_ct= %lu %lu\n", rs_ct, cs_ct ); \
  */ \
  \
  /*
  PASTEMAC(ch,fprintm)( stdout, "trsm_lu_ker_var2: b11 after (diag)", MR, NR, b11, NR, 1, "%5.2f", "" ); \
  PASTEMAC(ch,fprintm)( stdout, "trsm_lu_ker_var2: b11 after (diag)", MR, NR, b11, NR, 1, "%5.2f", "" ); \
  PASTEMAC(ch,fprintm)( stdout, "trsm_lu_ker_var2: ct after (diag)", m_cur, n_cur, ct, rs_ct, cs_ct, "%5.2f", "" ); \
  */ \
  }
  
  INSERT_GENTFUNC_BASIC0( trsm_lu_ker_var2 )
  
  