/* 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(s) of the copyright holder(s) 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" void bli_zaxpyf_template_noopt ( conj_t conja, conj_t conjx, dim_t m, dim_t b_n, dcomplex* restrict alpha, dcomplex* restrict a, inc_t inca, inc_t lda, dcomplex* restrict x, inc_t incx, dcomplex* restrict y, inc_t incy, cntx_t* cntx ) { /* Template axpyf kernel implementation This function contains a template implementation for a double-precision complex kernel, coded in C, which can serve as the starting point for one to write an optimized kernel on an arbitrary architecture. (We show a template implementation for only double-precision complex because the templates for the other three floating-point types would be similar, with the real instantiations being noticeably simpler due to the disappearance of conjugation in the real domain.) This kernel performs the following gemv-like operation: y := y + alpha * conja( A ) * conjx( x ) where A is an m x b_n matrix, x is a vector of length b_n, y is a vector of length m, and alpha is a scalar. The operation is performed as a series of fused axpyv operations, and therefore A should be column-stored. Parameters: - conja: Compute with conjugated values of A? - conjx: Compute with conjugated values of x? - m: The number of rows in matrix A. - b_n: The number of columns in matrix A. Must be equal to or less than the fusing factor. - alpha: The address of a scalar. - a: The address of matrix A. - inca: The row stride of A. inca should be unit unless the implementation makes special accomodation for non-unit values. - lda: The column stride of A. - x: The address of vector x. - incx: The vector increment of x. - y: The address of vector y. - incy: The vector increment of y. incy should be unit unless the implementation makes special accomodation for non-unit values. This template code calls the reference implementation if any of the following conditions are true: - Either of the strides inca or incy is non-unit. - The address of A, the second column of A, and y are unaligned with different offsets. If the first/second columns of A and address of y are aligned, or unaligned by the same offset, then optimized code can be used for the bulk of the computation. This template shows how the front-edge case can be handled so that the remaining computation is aligned. (This template guarantees alignment in the main loops to be BLIS_SIMD_ALIGN_SIZE.) Additional things to consider: - When optimizing, you should fully unroll the loops over b_n. This is the dimension across which we are fusing axpyv operations. - This template code chooses to call the reference implementation whenever b_n is less than the fusing factor, so as to avoid having to handle edge cases. One may choose to optimize this edge case, if desired. - Because conjugation disappears in the real domain, real instances of this kernel can safely ignore the values of any conjugation parameters, thereby simplifying the implementation. For more info, please refer to the BLIS website and/or contact the blis-devel mailing list. -FGVZ */ const dim_t n_elem_per_reg = 1; const dim_t n_iter_unroll = 1; const dim_t n_elem_per_iter = n_elem_per_reg * n_iter_unroll; const siz_t type_size = sizeof( *a ); dcomplex* ap[ bli_zaxpyf_fusefac ]; dcomplex* xp[ bli_zaxpyf_fusefac ]; dcomplex* yp; dcomplex alpha_x[ bli_zaxpyf_fusefac ]; bool use_ref = FALSE; dim_t m_pre = 0; dim_t m_iter; dim_t m_left; dim_t off_a, off_a2, off_y; dim_t i, j; // Return early if possible. if ( bli_zero_dim2( m, b_n ) ) return; // If there is anything that would interfere with our use of aligned // vector loads/stores, call the reference implementation. if ( b_n < bli_zaxpyf_fusefac ) { use_ref = TRUE; } else if ( bli_has_nonunit_inc3( inca, incx, incy ) ) { use_ref = TRUE; } else if ( bli_is_unaligned_to( a, BLIS_SIMD_ALIGN_SIZE ) || bli_is_unaligned_to( a+lda, BLIS_SIMD_ALIGN_SIZE ) || bli_is_unaligned_to( y, BLIS_SIMD_ALIGN_SIZE ) ) { use_ref = TRUE; // If a, the second column of a, and y are unaligned by the same // offset, then we can still use an implementation that depends on // alignment for most of the operation. off_a = bli_offset_from_alignment( a, BLIS_SIMD_ALIGN_SIZE ); off_a2 = bli_offset_from_alignment( a+lda, BLIS_SIMD_ALIGN_SIZE ); off_y = bli_offset_from_alignment( y, BLIS_SIMD_ALIGN_SIZE ); if ( off_a == off_y && off_a == off_a2 ) { use_ref = FALSE; m_pre = off_a / type_size; } } // Call the reference implementation if needed. if ( use_ref == TRUE ) { zaxpyf_ft f = bli_zaxpyf_template_ref; f ( conja, conjx, m, b_n, alpha, a, inca, lda, x, incx, y, incy, cntx ); return; } // Compute the number of unrolled and leftover (edge) iterations. m_iter = ( m - m_pre ) / n_elem_per_iter; m_left = ( m - m_pre ) % n_elem_per_iter; // Initialize pointers into the columns of A and elements of x. for ( j = 0; j < b_n; ++j ) { ap[ j ] = a + (j )*lda; xp[ j ] = x + (j )*incx; } yp = y; // Load elements of x or conj(x) into alpha_x and scale by alpha. if ( bli_is_noconj( conjx ) ) { for ( j = 0; j < b_n; ++j ) { bli_zcopys( *xp[ j ], alpha_x[ j ] ); bli_zscals( *alpha, alpha_x[ j ] ); } } else // if ( bli_is_conj( conjx ) ) { for ( j = 0; j < b_n; ++j ) { bli_zcopyjs( *xp[ j ], alpha_x[ j ] ); bli_zscals( *alpha, alpha_x[ j ] ); } } // Iterate over rows of A and y to compute: // y += conja( A )*conjx( x ); if ( bli_is_noconj( conja ) ) { // Compute front edge cases if a and y were unaligned. for ( i = 0; i < m_pre; ++i ) { for ( j = 0; j < b_n; ++j ) { bli_zaxpys( alpha_x[ j ], *ap[ j ], *yp ); ap[ j ] += 1; } yp += 1; } // The bulk of the operation is executed here. For best performance, // the elements of alpha_x should be loaded once prior to the m_iter // loop, and the b_n loop should be fully unrolled. The addresses in // ap[] and yp are guaranteed to be aligned to // BLIS_SIMD_ALIGN_SIZE. for ( i = 0; i < m_iter; ++i ) { for ( j = 0; j < b_n; ++j ) { bli_zaxpys( alpha_x[ j ], *ap[ j ], *yp ); ap[ j ] += n_elem_per_iter; } yp += n_elem_per_iter; } // Compute tail edge cases, if applicable. for ( i = 0; i < m_left; ++i ) { for ( j = 0; j < b_n; ++j ) { bli_zaxpys( alpha_x[ j ], *ap[ j ], *yp ); ap[ j ] += 1; } yp += 1; } } else // if ( bli_is_conj( conja ) ) { // Compute front edge cases if a and y were unaligned. for ( i = 0; i < m_pre; ++i ) { for ( j = 0; j < b_n; ++j ) { bli_zaxpyjs( alpha_x[ j ], *ap[ j ], *yp ); ap[ j ] += 1; } yp += 1; } // The bulk of the operation is executed here. For best performance, // the elements of alpha_x should be loaded once prior to the m_iter // loop, and the b_n loop should be fully unrolled. The addresses in // ap[] and yp are guaranteed to be aligned to // BLIS_SIMD_ALIGN_SIZE. for ( i = 0; i < m_iter; ++i ) { for ( j = 0; j < b_n; ++j ) { bli_zaxpyjs( alpha_x[ j ], *ap[ j ], *yp ); ap[ j ] += n_elem_per_iter; } yp += n_elem_per_iter; } // Compute tail edge cases. for ( i = 0; i < m_left; ++i ) { for ( j = 0; j < b_n; ++j ) { bli_zaxpyjs( alpha_x[ j ], *ap[ j ], *yp ); ap[ j ] += 1; } yp += 1; } } }