//
// Define object-based interface.
//
void bli_scalv( obj_t* alpha,
obj_t* x )
{
num_t dt = bli_obj_datatype( *x );
dim_t n = bli_obj_vector_dim( *x );
inc_t inc_x = bli_obj_vector_inc( *x );
void* buf_x = bli_obj_buffer_at_off( *x );
obj_t alpha_local;
void* buf_alpha;
FUNCPTR_T f = ftypes[dt];
if ( bli_error_checking_is_enabled() )
bli_scalv_check( alpha, x );
// Create a local copy-cast of alpha (and apply internal conjugation
// if needed).
bli_obj_scalar_init_detached_copy_of( dt,
BLIS_NO_CONJUGATE,
alpha,
&alpha_local );
// Extract the scalar buffer.
buf_alpha = bli_obj_buffer_for_1x1( dt, alpha_local );
// Invoke the void pointer-based function.
f( BLIS_NO_CONJUGATE, // conjugation applied during copy-cast.
n,
buf_alpha,
buf_x, inc_x );
}
void libblis_test_addv_check( obj_t* alpha,
obj_t* beta,
obj_t* x,
obj_t* y,
double* resid )
{
num_t dt = bli_obj_datatype( *x );
num_t dt_real = bli_obj_datatype_proj_to_real( *x );
dim_t m = bli_obj_vector_dim( *x );
conj_t conjx = bli_obj_conj_status( *x );
obj_t aplusb;
obj_t alpha_conj;
obj_t norm_r, m_r, temp_r;
double junk;
//
// Pre-conditions:
// - x is set to alpha.
// - y_orig is set to beta.
// Note:
// - alpha and beta should have non-zero imaginary components in the
// complex cases in order to more fully exercise the implementation.
//
// Under these conditions, we assume that the implementation for
//
// y := y_orig + conjx(x)
//
// is functioning correctly if
//
// fnormv(y) - sqrt( absqsc( beta + conjx(alpha) ) * m )
//
// is negligible.
//
bli_obj_scalar_init_detached( dt, &aplusb );
bli_obj_scalar_init_detached( dt_real, &temp_r );
bli_obj_scalar_init_detached( dt_real, &norm_r );
bli_obj_scalar_init_detached( dt_real, &m_r );
bli_obj_scalar_init_detached_copy_of( dt, conjx, alpha, &alpha_conj );
bli_fnormv( y, &norm_r );
bli_copysc( beta, &aplusb );
bli_addsc( &alpha_conj, &aplusb );
bli_setsc( ( double )m, 0.0, &m_r );
bli_absqsc( &aplusb, &temp_r );
bli_mulsc( &m_r, &temp_r );
bli_sqrtsc( &temp_r, &temp_r );
bli_subsc( &temp_r, &norm_r );
bli_getsc( &norm_r, resid, &junk );
}
void bli_obj_scalar_attach( conj_t conj,
obj_t* alpha,
obj_t* a )
{
obj_t alpha_cast;
// Make a copy-cast of alpha of the same datatype as A. This step
// gives us the opportunity to conjugate and/or typecast alpha.
bli_obj_scalar_init_detached_copy_of( bli_obj_datatype( *a ),
conj,
alpha,
&alpha_cast );
// Copy the internal scalar in alpha_cast to A.
bli_obj_copy_internal_scalar( alpha_cast, *a );
}
void bli_obj_scalar_apply_scalar( obj_t* alpha,
obj_t* a )
{
obj_t alpha_cast;
obj_t scalar_a;
// Make a copy-cast of alpha of the same datatype as A. This step
// gives us the opportunity to typecast alpha.
bli_obj_scalar_init_detached_copy_of( bli_obj_datatype( *a ),
BLIS_NO_CONJUGATE,
alpha,
&alpha_cast );
// Detach the scalar from A.
bli_obj_scalar_detach( a, &scalar_a );
// Scale the detached scalar by alpha.
bli_mulsc( &alpha_cast, &scalar_a );
// Copy the internal scalar in scalar_a to A.
bli_obj_copy_internal_scalar( scalar_a, *a );
}
//
// Define object-based interface.
//
void bli_setm( obj_t* beta,
obj_t* x )
{
num_t dt_x;
obj_t beta_local;
if ( bli_error_checking_is_enabled() )
bli_setm_check( beta, x );
// Use the datatype of x as the target type for beta (since we do
// not assume mixed domain/type support is enabled).
dt_x = bli_obj_datatype( *x );
// Create an object to hold a copy-cast of beta.
bli_obj_scalar_init_detached_copy_of( dt_x,
BLIS_NO_CONJUGATE,
beta,
&beta_local );
bli_setm_unb_var1( &beta_local, x );
}
void bli_syr2_front
(
obj_t* alpha,
obj_t* x,
obj_t* y,
obj_t* c,
cntx_t* cntx
)
{
her2_t* her2_cntl;
num_t dt_targ_x;
num_t dt_targ_y;
//num_t dt_targ_c;
bool_t x_has_unit_inc;
bool_t y_has_unit_inc;
bool_t c_has_unit_inc;
obj_t alpha_local;
num_t dt_alpha;
// Check parameters.
if ( bli_error_checking_is_enabled() )
bli_syr2_check( alpha, x, y, c );
// Query the target datatypes of each object.
dt_targ_x = bli_obj_target_dt( x );
dt_targ_y = bli_obj_target_dt( y );
//dt_targ_c = bli_obj_target_dt( c );
// Determine whether each operand with unit stride.
x_has_unit_inc = ( bli_obj_vector_inc( x ) == 1 );
y_has_unit_inc = ( bli_obj_vector_inc( y ) == 1 );
c_has_unit_inc = ( bli_obj_is_row_stored( c ) ||
bli_obj_is_col_stored( c ) );
// Create an object to hold a copy-cast of alpha. Notice that we use
// the type union of the datatypes of x and y.
dt_alpha = bli_dt_union( dt_targ_x, dt_targ_y );
bli_obj_scalar_init_detached_copy_of( dt_alpha,
BLIS_NO_CONJUGATE,
alpha,
&alpha_local );
// If all operands have unit stride, we choose a control tree for calling
// the unblocked implementation directly without any blocking.
if ( x_has_unit_inc &&
y_has_unit_inc &&
c_has_unit_inc )
{
// We use two control trees to handle the four cases corresponding to
// combinations of upper/lower triangular storage and row/column-storage.
// The row-stored lower triangular and column-stored upper triangular
// trees are identical. Same for the remaining two trees.
if ( bli_obj_is_lower( c ) )
{
if ( bli_obj_is_row_stored( c ) ) her2_cntl = her2_cntl_bs_ke_lrow_ucol;
else her2_cntl = her2_cntl_bs_ke_lcol_urow;
}
else // if ( bli_obj_is_upper( c ) )
{
if ( bli_obj_is_row_stored( c ) ) her2_cntl = her2_cntl_bs_ke_lcol_urow;
else her2_cntl = her2_cntl_bs_ke_lrow_ucol;
}
}
else
{
// Mark objects with unit stride as already being packed. This prevents
// unnecessary packing from happening within the blocked algorithm.
if ( x_has_unit_inc ) bli_obj_set_pack_schema( BLIS_PACKED_VECTOR, x );
if ( y_has_unit_inc ) bli_obj_set_pack_schema( BLIS_PACKED_VECTOR, y );
if ( c_has_unit_inc ) bli_obj_set_pack_schema( BLIS_PACKED_UNSPEC, c );
// Here, we make a similar choice as above, except that (1) we look
// at storage tilt, and (2) we choose a tree that performs blocking.
if ( bli_obj_is_lower( c ) )
{
if ( bli_obj_is_row_stored( c ) ) her2_cntl = her2_cntl_ge_lrow_ucol;
else her2_cntl = her2_cntl_ge_lcol_urow;
}
else // if ( bli_obj_is_upper( c ) )
{
if ( bli_obj_is_row_stored( c ) ) her2_cntl = her2_cntl_ge_lcol_urow;
else her2_cntl = her2_cntl_ge_lrow_ucol;
}
}
// Invoke the internal back-end with the copy-cast scalar and the
// chosen control tree. Set conjh to BLIS_NO_CONJUGATE to invoke the
// symmetric (and not Hermitian) algorithms.
bli_her2_int( BLIS_NO_CONJUGATE,
&alpha_local,
&alpha_local,
x,
y,
c,
cntx,
her2_cntl );
}
void bli_her2k_front( obj_t* alpha,
obj_t* a,
obj_t* b,
obj_t* beta,
obj_t* c,
herk_t* cntl )
{
obj_t alpha_conj;
obj_t c_local;
obj_t a_local;
obj_t bh_local;
obj_t b_local;
obj_t ah_local;
// Check parameters.
if ( bli_error_checking_is_enabled() )
bli_her2k_check( alpha, a, b, beta, c );
// If alpha is zero, scale by beta and return.
if ( bli_obj_equals( alpha, &BLIS_ZERO ) )
{
bli_scalm( beta, c );
return;
}
// Alias A, B, and C in case we need to apply transformations.
bli_obj_alias_to( *a, a_local );
bli_obj_alias_to( *b, b_local );
bli_obj_alias_to( *c, c_local );
bli_obj_set_as_root( c_local );
// For her2k, the first and second right-hand "B" operands are simply B'
// and A'.
bli_obj_alias_to( *b, bh_local );
bli_obj_induce_trans( bh_local );
bli_obj_toggle_conj( bh_local );
bli_obj_alias_to( *a, ah_local );
bli_obj_induce_trans( ah_local );
bli_obj_toggle_conj( ah_local );
// Initialize a conjugated copy of alpha.
bli_obj_scalar_init_detached_copy_of( bli_obj_datatype( *a ),
BLIS_CONJUGATE,
alpha,
&alpha_conj );
// An optimization: If C is row-stored, transpose the entire operation
// so as to allow the macro-kernel more favorable access patterns
// through C. (The effect of the transposition of A and A' is negligible
// because those operands are always packed to contiguous memory.)
if ( bli_obj_is_row_stored( c_local ) )
{
bli_obj_swap( a_local, bh_local );
bli_obj_swap( b_local, ah_local );
bli_obj_induce_trans( a_local );
bli_obj_induce_trans( bh_local );
bli_obj_induce_trans( b_local );
bli_obj_induce_trans( ah_local );
bli_obj_induce_trans( c_local );
}
#if 0
// Invoke the internal back-end.
bli_her2k_int( alpha,
&a_local,
&bh_local,
&alpha_conj,
&b_local,
&ah_local,
beta,
&c_local,
cntl );
#else
// Invoke herk twice, using beta only the first time.
bli_herk_int( alpha,
&a_local,
&bh_local,
beta,
&c_local,
cntl );
bli_herk_int( &alpha_conj,
&b_local,
&ah_local,
&BLIS_ONE,
&c_local,
cntl );
#endif
}
void bli_her2k_front( obj_t* alpha,
obj_t* a,
obj_t* b,
obj_t* beta,
obj_t* c,
gemm_t* cntl )
{
obj_t alpha_conj;
obj_t c_local;
obj_t a_local;
obj_t bh_local;
obj_t b_local;
obj_t ah_local;
// Check parameters.
if ( bli_error_checking_is_enabled() )
bli_her2k_check( alpha, a, b, beta, c );
// If alpha is zero, scale by beta, zero the imaginary components of
// the diagonal elements, and return.
if ( bli_obj_equals( alpha, &BLIS_ZERO ) )
{
bli_scalm( beta, c );
bli_setid( &BLIS_ZERO, c );
return;
}
// Alias A, B, and C in case we need to apply transformations.
bli_obj_alias_to( *a, a_local );
bli_obj_alias_to( *b, b_local );
bli_obj_alias_to( *c, c_local );
bli_obj_set_as_root( c_local );
// For her2k, the first and second right-hand "B" operands are simply B'
// and A'.
bli_obj_alias_to( *b, bh_local );
bli_obj_induce_trans( bh_local );
bli_obj_toggle_conj( bh_local );
bli_obj_alias_to( *a, ah_local );
bli_obj_induce_trans( ah_local );
bli_obj_toggle_conj( ah_local );
// Initialize a conjugated copy of alpha.
bli_obj_scalar_init_detached_copy_of( bli_obj_datatype( *a ),
BLIS_CONJUGATE,
alpha,
&alpha_conj );
// An optimization: If C is stored by rows and the micro-kernel prefers
// contiguous columns, or if C is stored by columns and the micro-kernel
// prefers contiguous rows, transpose the entire operation to allow the
// micro-kernel to access elements of C in its preferred manner.
if (
( bli_obj_is_row_stored( c_local ) &&
bli_func_prefers_contig_cols( bli_obj_datatype( c_local ),
bli_gemm_cntl_ukrs( cntl ) ) ) ||
( bli_obj_is_col_stored( c_local ) &&
bli_func_prefers_contig_rows( bli_obj_datatype( c_local ),
bli_gemm_cntl_ukrs( cntl ) ) )
)
{
bli_obj_swap( a_local, bh_local );
bli_obj_swap( b_local, ah_local );
bli_obj_induce_trans( a_local );
bli_obj_induce_trans( bh_local );
bli_obj_induce_trans( b_local );
bli_obj_induce_trans( ah_local );
bli_obj_induce_trans( c_local );
}
#if 0
// Invoke the internal back-end.
bli_her2k_int( alpha,
&a_local,
&bh_local,
&alpha_conj,
&b_local,
&ah_local,
beta,
&c_local,
cntl );
#else
// Invoke herk twice, using beta only the first time.
herk_thrinfo_t** infos = bli_create_herk_thrinfo_paths();
dim_t n_threads = thread_num_threads( infos[0] );
// Invoke the internal back-end.
bli_level3_thread_decorator( n_threads,
(level3_int_t) bli_herk_int,
alpha,
&a_local,
&bh_local,
beta,
&c_local,
(void*) cntl,
(void**) infos );
bli_level3_thread_decorator( n_threads,
(level3_int_t) bli_herk_int,
&alpha_conj,
&b_local,
&ah_local,
&BLIS_ONE,
&c_local,
(void*) cntl,
(void**) infos );
bli_herk_thrinfo_free_paths( infos, n_threads );
#endif
// The Hermitian rank-2k product was computed as A*B'+B*A', even for
// the diagonal elements. Mathematically, the imaginary components of
// diagonal elements of a Hermitian rank-2k product should always be
// zero. However, in practice, they sometimes accumulate meaningless
// non-zero values. To prevent this, we explicitly set those values
// to zero before returning.
bli_setid( &BLIS_ZERO, &c_local );
}
void libblis_test_gemv_check( obj_t* kappa,
obj_t* alpha,
obj_t* a,
obj_t* x,
obj_t* beta,
obj_t* y,
obj_t* y_orig,
double* resid )
{
num_t dt = bli_obj_datatype( *y );
num_t dt_real = bli_obj_datatype_proj_to_real( *y );
conj_t conja = bli_obj_conj_status( *a );
dim_t n_x = bli_obj_vector_dim( *x );
dim_t m_y = bli_obj_vector_dim( *y );
dim_t min_m_n = bli_min( m_y, n_x );
obj_t x_temp, y_temp;
obj_t kappac, norm;
obj_t xT_temp, yT_temp, yT;
double junk;
//
// Pre-conditions:
// - a is initialized to kappa along the diagonal.
// - x is randomized.
// - y_orig is randomized.
// Note:
// - alpha, beta, and kappa should have non-zero imaginary components in
// the complex cases in order to more fully exercise the implementation.
//
// Under these conditions, we assume that the implementation for
//
// y := beta * y_orig + alpha * transa(A) * conjx(x)
//
// is functioning correctly if
//
// normf( y - z )
//
// is negligible, where
//
// z = beta * y_orig + alpha * conja(kappa) * x
//
bli_obj_scalar_init_detached_copy_of( dt, conja, kappa, &kappac );
bli_obj_scalar_init_detached( dt_real, &norm );
bli_obj_create( dt, n_x, 1, 0, 0, &x_temp );
bli_obj_create( dt, m_y, 1, 0, 0, &y_temp );
bli_copyv( x, &x_temp );
bli_copyv( y_orig, &y_temp );
bli_acquire_vpart_f2b( BLIS_SUBPART1, 0, min_m_n,
&x_temp, &xT_temp );
bli_acquire_vpart_f2b( BLIS_SUBPART1, 0, min_m_n,
&y_temp, &yT_temp );
bli_acquire_vpart_f2b( BLIS_SUBPART1, 0, min_m_n,
y, &yT );
bli_scalv( &kappac, &xT_temp );
bli_scalv( beta, &yT_temp );
bli_axpyv( alpha, &xT_temp, &yT_temp );
bli_subv( &yT_temp, &yT );
bli_normfv( &yT, &norm );
bli_getsc( &norm, resid, &junk );
bli_obj_free( &x_temp );
bli_obj_free( &y_temp );
}
void bli_hemv( obj_t* alpha,
obj_t* a,
obj_t* x,
obj_t* beta,
obj_t* y )
{
hemv_t* hemv_cntl;
num_t dt_targ_a;
num_t dt_targ_x;
num_t dt_targ_y;
bool_t a_has_unit_inc;
bool_t x_has_unit_inc;
bool_t y_has_unit_inc;
obj_t alpha_local;
obj_t beta_local;
num_t dt_alpha;
num_t dt_beta;
// Check parameters.
if ( bli_error_checking_is_enabled() )
bli_hemv_check( alpha, a, x, beta, y );
// Query the target datatypes of each object.
dt_targ_a = bli_obj_target_datatype( *a );
dt_targ_x = bli_obj_target_datatype( *x );
dt_targ_y = bli_obj_target_datatype( *y );
// Determine whether each operand with unit stride.
a_has_unit_inc = ( bli_obj_is_row_stored( *a ) ||
bli_obj_is_col_stored( *a ) );
x_has_unit_inc = ( bli_obj_vector_inc( *x ) == 1 );
y_has_unit_inc = ( bli_obj_vector_inc( *y ) == 1 );
// Create an object to hold a copy-cast of alpha. Notice that we use
// the type union of the target datatypes of a and x to prevent any
// unnecessary loss of information during the computation.
dt_alpha = bli_datatype_union( dt_targ_a, dt_targ_x );
bli_obj_scalar_init_detached_copy_of( dt_alpha,
BLIS_NO_CONJUGATE,
alpha,
&alpha_local );
// Create an object to hold a copy-cast of beta. Notice that we use
// the datatype of y. Here's why: If y is real and beta is complex,
// there is no reason to keep beta_local in the complex domain since
// the complex part of beta*y will not be stored. If y is complex and
// beta is real then beta is harmlessly promoted to complex.
dt_beta = dt_targ_y;
bli_obj_scalar_init_detached_copy_of( dt_beta,
BLIS_NO_CONJUGATE,
beta,
&beta_local );
// If all operands have unit stride, we choose a control tree for calling
// the unblocked implementation directly without any blocking.
if ( a_has_unit_inc &&
x_has_unit_inc &&
y_has_unit_inc )
{
// We use two control trees to handle the four cases corresponding to
// combinations of upper/lower triangular storage and row/column-storage.
// The row-stored lower triangular and column-stored upper triangular
// trees are identical. Same for the remaining two trees.
if ( bli_obj_is_lower( *a ) )
{
if ( bli_obj_is_row_stored( *a ) ) hemv_cntl = hemv_cntl_bs_ke_lrow_ucol;
else hemv_cntl = hemv_cntl_bs_ke_lcol_urow;
}
else // if ( bli_obj_is_upper( *a ) )
{
if ( bli_obj_is_row_stored( *a ) ) hemv_cntl = hemv_cntl_bs_ke_lcol_urow;
else hemv_cntl = hemv_cntl_bs_ke_lrow_ucol;
}
}
else
{
// Mark objects with unit stride as already being packed. This prevents
// unnecessary packing from happening within the blocked algorithm.
if ( a_has_unit_inc ) bli_obj_set_pack_schema( BLIS_PACKED_UNSPEC, *a );
if ( x_has_unit_inc ) bli_obj_set_pack_schema( BLIS_PACKED_VECTOR, *x );
if ( y_has_unit_inc ) bli_obj_set_pack_schema( BLIS_PACKED_VECTOR, *y );
// Here, we make a similar choice as above, except that (1) we look
// at storage tilt, and (2) we choose a tree that performs blocking.
if ( bli_obj_is_lower( *a ) )
{
if ( bli_obj_is_row_tilted( *a ) ) hemv_cntl = hemv_cntl_ge_lrow_ucol;
else hemv_cntl = hemv_cntl_ge_lcol_urow;
}
else // if ( bli_obj_is_upper( *a ) )
{
if ( bli_obj_is_row_tilted( *a ) ) hemv_cntl = hemv_cntl_ge_lcol_urow;
else hemv_cntl = hemv_cntl_ge_lrow_ucol;
}
}
// Invoke the internal back-end with the copy-casts of scalars and the
// chosen control tree. Set conjh to BLIS_CONJUGATE to invoke the
// Hermitian (and not symmetric) algorithms.
bli_hemv_int( BLIS_CONJUGATE,
&alpha_local,
a,
x,
&beta_local,
y,
hemv_cntl );
}
void libblis_test_her2k_check
(
test_params_t* params,
obj_t* alpha,
obj_t* a,
obj_t* b,
obj_t* beta,
obj_t* c,
obj_t* c_orig,
double* resid
)
{
num_t dt = bli_obj_datatype( *c );
num_t dt_real = bli_obj_datatype_proj_to_real( *c );
dim_t m = bli_obj_length( *c );
dim_t k = bli_obj_width_after_trans( *a );
obj_t alphac, ah, bh;
obj_t norm;
obj_t t, v, w1, w2, z;
double junk;
//
// Pre-conditions:
// - a is randomized.
// - b is randomized.
// - c_orig is randomized and Hermitian.
// Note:
// - alpha should have a non-zero imaginary component in the
// complex cases in order to more fully exercise the implementation.
// - beta must be real-valued.
//
// Under these conditions, we assume that the implementation for
//
// C := beta * C_orig + alpha * transa(A) * transb(B)^H + conj(alpha) * transb(B) * transa(A)^H
//
// is functioning correctly if
//
// normf( v - z )
//
// is negligible, where
//
// v = C * t
// z = ( beta * C_orig + alpha * transa(A) * transb(B)^H + conj(alpha) * transb(B) * transa(A)^H ) * t
// = beta * C_orig * t + alpha * transa(A) * transb(B)^H * t + conj(alpha) * transb(B) * transa(A)^H * t
// = beta * C_orig * t + alpha * transa(A) * transb(B)^H * t + conj(alpha) * transb(B) * w2
// = beta * C_orig * t + alpha * transa(A) * w1 + conj(alpha) * transb(B) * w2
// = beta * C_orig * t + alpha * transa(A) * w1 + z
// = beta * C_orig * t + z
//
bli_obj_alias_with_trans( BLIS_CONJ_TRANSPOSE, *a, ah );
bli_obj_alias_with_trans( BLIS_CONJ_TRANSPOSE, *b, bh );
bli_obj_scalar_init_detached( dt_real, &norm );
bli_obj_scalar_init_detached_copy_of( dt, BLIS_CONJUGATE, alpha, &alphac );
bli_obj_create( dt, m, 1, 0, 0, &t );
bli_obj_create( dt, m, 1, 0, 0, &v );
bli_obj_create( dt, k, 1, 0, 0, &w1 );
bli_obj_create( dt, k, 1, 0, 0, &w2 );
bli_obj_create( dt, m, 1, 0, 0, &z );
libblis_test_vobj_randomize( params, TRUE, &t );
bli_hemv( &BLIS_ONE, c, &t, &BLIS_ZERO, &v );
bli_gemv( &BLIS_ONE, &ah, &t, &BLIS_ZERO, &w2 );
bli_gemv( &BLIS_ONE, &bh, &t, &BLIS_ZERO, &w1 );
bli_gemv( alpha, a, &w1, &BLIS_ZERO, &z );
bli_gemv( &alphac, b, &w2, &BLIS_ONE, &z );
bli_hemv( beta, c_orig, &t, &BLIS_ONE, &z );
bli_subv( &z, &v );
bli_normfv( &v, &norm );
bli_getsc( &norm, resid, &junk );
bli_obj_free( &t );
bli_obj_free( &v );
bli_obj_free( &w1 );
bli_obj_free( &w2 );
bli_obj_free( &z );
}
void bli_trmv_front
(
obj_t* alpha,
obj_t* a,
obj_t* x,
cntx_t* cntx
)
{
trmv_t* trmv_cntl;
num_t dt_targ_a;
num_t dt_targ_x;
bool_t a_has_unit_inc;
bool_t x_has_unit_inc;
obj_t alpha_local;
num_t dt_alpha;
// Check parameters.
if ( bli_error_checking_is_enabled() )
bli_trmv_check( alpha, a, x );
// Query the target datatypes of each object.
dt_targ_a = bli_obj_target_datatype( *a );
dt_targ_x = bli_obj_target_datatype( *x );
// Determine whether each operand with unit stride.
a_has_unit_inc = ( bli_obj_is_row_stored( *a ) ||
bli_obj_is_col_stored( *a ) );
x_has_unit_inc = ( bli_obj_vector_inc( *x ) == 1 );
// Create an object to hold a copy-cast of alpha. Notice that we use
// the type union of the target datatypes of a and x to prevent any
// unnecessary loss of information during the computation.
dt_alpha = bli_datatype_union( dt_targ_a, dt_targ_x );
bli_obj_scalar_init_detached_copy_of( dt_alpha,
BLIS_NO_CONJUGATE,
alpha,
&alpha_local );
// If all operands have unit stride, we choose a control tree for calling
// the unblocked implementation directly without any blocking.
if ( a_has_unit_inc &&
x_has_unit_inc )
{
// We use two control trees to handle the four cases corresponding to
// combinations of transposition and row/column-storage.
// The row-stored without transpose and column-stored with transpose
// trees are identical. Same for the remaining two trees.
if ( bli_obj_has_notrans( *a ) )
{
if ( bli_obj_is_row_stored( *a ) ) trmv_cntl = trmv_cntl_bs_ke_nrow_tcol;
else trmv_cntl = trmv_cntl_bs_ke_ncol_trow;
}
else // if ( bli_obj_has_trans( *a ) )
{
if ( bli_obj_is_row_stored( *a ) ) trmv_cntl = trmv_cntl_bs_ke_ncol_trow;
else trmv_cntl = trmv_cntl_bs_ke_nrow_tcol;
}
}
else
{
// Mark objects with unit stride as already being packed. This prevents
// unnecessary packing from happening within the blocked algorithm.
if ( a_has_unit_inc ) bli_obj_set_pack_schema( BLIS_PACKED_UNSPEC, *a );
if ( x_has_unit_inc ) bli_obj_set_pack_schema( BLIS_PACKED_VECTOR, *x );
// Here, we make a similar choice as above, except that (1) we look
// at storage tilt, and (2) we choose a tree that performs blocking.
if ( bli_obj_has_notrans( *a ) )
{
if ( bli_obj_is_row_tilted( *a ) ) trmv_cntl = trmv_cntl_ge_nrow_tcol;
else trmv_cntl = trmv_cntl_ge_ncol_trow;
}
else // if ( bli_obj_has_trans( *a ) )
{
if ( bli_obj_is_row_tilted( *a ) ) trmv_cntl = trmv_cntl_ge_ncol_trow;
else trmv_cntl = trmv_cntl_ge_nrow_tcol;
}
}
// Invoke the internal back-end with the copy-cast of alpha and the
// chosen control tree.
bli_trmv_int( &alpha_local,
a,
x,
cntx,
trmv_cntl );
}
void bli_her2_int( conj_t conjh,
obj_t* alpha,
obj_t* alpha_conj,
obj_t* x,
obj_t* y,
obj_t* c,
cntx_t* cntx,
her2_t* cntl )
{
varnum_t n;
impl_t i;
FUNCPTR_T f;
obj_t alpha_local;
obj_t alpha_conj_local;
obj_t x_local;
obj_t y_local;
obj_t c_local;
// Check parameters.
if ( bli_error_checking_is_enabled() )
{
if ( bli_is_conj( conjh ) ) bli_her2_check( alpha, x, y, c );
else bli_syr2_check( alpha, x, y, c );
}
// If C, x, or y has a zero dimension, return early.
if ( bli_obj_has_zero_dim( c ) ) return;
if ( bli_obj_has_zero_dim( x ) ) return;
if ( bli_obj_has_zero_dim( y ) ) return;
// Alias the operands in case we need to apply conjugations.
bli_obj_alias_to( x, &x_local );
bli_obj_alias_to( y, &y_local );
bli_obj_alias_to( c, &c_local );
// If matrix C is marked for conjugation, we interpret this as a request
// to apply a conjugation to the other operands.
if ( bli_obj_has_conj( &c_local ) )
{
bli_obj_toggle_conj( &c_local );
bli_obj_toggle_conj( &x_local );
bli_obj_toggle_conj( &y_local );
bli_obj_scalar_init_detached_copy_of( bli_obj_dt( alpha ),
BLIS_CONJUGATE,
alpha,
&alpha_local );
bli_obj_scalar_init_detached_copy_of( bli_obj_dt( alpha_conj ),
BLIS_CONJUGATE,
alpha_conj,
&alpha_conj_local );
}
else
{
bli_obj_alias_to( *alpha, alpha_local );
bli_obj_alias_to( *alpha_conj, alpha_conj_local );
}
// Extract the variant number and implementation type.
n = bli_cntl_var_num( cntl );
i = bli_cntl_impl_type( cntl );
// Index into the variant array to extract the correct function pointer.
f = vars[n][i];
// Invoke the variant.
f( conjh,
&alpha_local,
&alpha_conj_local,
&x_local,
&y_local,
&c_local,
cntx,
cntl );
}
void bli_her2k_front
(
obj_t* alpha,
obj_t* a,
obj_t* b,
obj_t* beta,
obj_t* c,
cntx_t* cntx,
cntl_t* cntl
)
{
bli_init_once();
obj_t alpha_conj;
obj_t c_local;
obj_t a_local;
obj_t bh_local;
obj_t b_local;
obj_t ah_local;
// Check parameters.
if ( bli_error_checking_is_enabled() )
bli_her2k_check( alpha, a, b, beta, c, cntx );
// If alpha is zero, scale by beta, zero the imaginary components of
// the diagonal elements, and return.
if ( bli_obj_equals( alpha, &BLIS_ZERO ) )
{
bli_scalm( beta, c );
bli_setid( &BLIS_ZERO, c );
return;
}
// Alias A, B, and C in case we need to apply transformations.
bli_obj_alias_to( a, &a_local );
bli_obj_alias_to( b, &b_local );
bli_obj_alias_to( c, &c_local );
bli_obj_set_as_root( &c_local );
// For her2k, the first and second right-hand "B" operands are simply B'
// and A'.
bli_obj_alias_to( b, &bh_local );
bli_obj_induce_trans( &bh_local );
bli_obj_toggle_conj( &bh_local );
bli_obj_alias_to( a, &ah_local );
bli_obj_induce_trans( &ah_local );
bli_obj_toggle_conj( &ah_local );
// Initialize a conjugated copy of alpha.
bli_obj_scalar_init_detached_copy_of( bli_obj_dt( a ),
BLIS_CONJUGATE,
alpha,
&alpha_conj );
// An optimization: If C is stored by rows and the micro-kernel prefers
// contiguous columns, or if C is stored by columns and the micro-kernel
// prefers contiguous rows, transpose the entire operation to allow the
// micro-kernel to access elements of C in its preferred manner.
if ( bli_cntx_l3_ukr_dislikes_storage_of( &c_local, BLIS_GEMM_UKR, cntx ) )
{
bli_obj_swap( &a_local, &bh_local );
bli_obj_swap( &b_local, &ah_local );
bli_obj_induce_trans( &a_local );
bli_obj_induce_trans( &bh_local );
bli_obj_induce_trans( &b_local );
bli_obj_induce_trans( &ah_local );
bli_obj_induce_trans( &c_local );
}
// Record the threading for each level within the context.
bli_cntx_set_thrloop_from_env( BLIS_HER2K, BLIS_LEFT, cntx,
bli_obj_length( &c_local ),
bli_obj_width( &c_local ),
bli_obj_width( &a_local ) );
// Invoke herk twice, using beta only the first time.
// Invoke the internal back-end.
bli_l3_thread_decorator
(
bli_gemm_int,
BLIS_HERK, // operation family id
alpha,
&a_local,
&bh_local,
beta,
&c_local,
cntx,
cntl
);
bli_l3_thread_decorator
(
bli_gemm_int,
BLIS_HERK, // operation family id
&alpha_conj,
&b_local,
&ah_local,
&BLIS_ONE,
&c_local,
cntx,
cntl
);
// The Hermitian rank-2k product was computed as A*B'+B*A', even for
// the diagonal elements. Mathematically, the imaginary components of
// diagonal elements of a Hermitian rank-2k product should always be
// zero. However, in practice, they sometimes accumulate meaningless
// non-zero values. To prevent this, we explicitly set those values
// to zero before returning.
bli_setid( &BLIS_ZERO, &c_local );
}
//
// Define object-based interface.
//
void bli_dotxf( obj_t* alpha,
obj_t* a,
obj_t* x,
obj_t* beta,
obj_t* y )
{
num_t dt = bli_obj_datatype( *x );
conj_t conja = bli_obj_conj_status( *a );
conj_t conjx = bli_obj_conj_status( *x );
dim_t m = bli_obj_vector_dim( *y );
dim_t b_n = bli_obj_vector_dim( *x );
void* buf_a = bli_obj_buffer_at_off( *a );
inc_t rs_a = bli_obj_row_stride( *a );
inc_t cs_a = bli_obj_col_stride( *a );
void* buf_x = bli_obj_buffer_at_off( *x );
inc_t inc_x = bli_obj_vector_inc( *x );
void* buf_y = bli_obj_buffer_at_off( *y );
inc_t inc_y = bli_obj_vector_inc( *y );
obj_t alpha_local;
void* buf_alpha;
obj_t beta_local;
void* buf_beta;
FUNCPTR_T f = ftypes[dt];
if ( bli_error_checking_is_enabled() )
bli_dotxf_check( alpha, a, x, beta, y );
// Create local copy-casts of the scalars (and apply internal conjugation
// if needed).
bli_obj_scalar_init_detached_copy_of( dt,
BLIS_NO_CONJUGATE,
alpha,
&alpha_local );
bli_obj_scalar_init_detached_copy_of( dt,
BLIS_NO_CONJUGATE,
beta,
&beta_local );
// Extract the scalar buffers.
buf_alpha = bli_obj_buffer_for_1x1( dt, alpha_local );
buf_beta = bli_obj_buffer_for_1x1( dt, beta_local );
// Support cases where matrix A requires a transposition.
if ( bli_obj_has_trans( *a ) ) { bli_swap_incs( rs_a, cs_a ); }
// Invoke the void pointer-based function.
f( conja,
conjx,
m,
b_n,
buf_alpha,
buf_a, rs_a, cs_a,
buf_x, inc_x,
buf_beta,
buf_y, inc_y );
}
void bli_ger_int( conj_t conjx,
conj_t conjy,
obj_t* alpha,
obj_t* x,
obj_t* y,
obj_t* a,
cntx_t* cntx,
ger_t* cntl )
{
varnum_t n;
impl_t i;
FUNCPTR_T f;
obj_t alpha_local;
obj_t x_local;
obj_t y_local;
obj_t a_local;
// Check parameters.
if ( bli_error_checking_is_enabled() )
bli_ger_check( alpha, x, y, a );
// If A has a zero dimension, return early.
if ( bli_obj_has_zero_dim( a ) ) return;
// If x or y has a zero dimension, return early.
if ( bli_obj_has_zero_dim( x ) ||
bli_obj_has_zero_dim( y ) ) return;
// Alias the objects, applying conjx and conjy to x and y, respectively.
bli_obj_alias_with_conj( conjx, x, &x_local );
bli_obj_alias_with_conj( conjy, y, &y_local );
bli_obj_alias_to( a, &a_local );
// If matrix A is marked for conjugation, we interpret this as a request
// to apply a conjugation to the other operands.
if ( bli_obj_has_conj( &a_local ) )
{
bli_obj_toggle_conj( &a_local );
bli_obj_toggle_conj( &x_local );
bli_obj_toggle_conj( &y_local );
bli_obj_scalar_init_detached_copy_of( bli_obj_dt( alpha ),
BLIS_CONJUGATE,
alpha,
&alpha_local );
}
else
{
bli_obj_alias_to( *alpha, alpha_local );
}
// If we are about the call a leaf-level implementation, and matrix A
// still needs a transposition, then we must induce one by swapping the
// strides and dimensions.
if ( bli_cntl_is_leaf( cntl ) && bli_obj_has_trans( &a_local ) )
{
bli_obj_induce_trans( &a_local );
bli_obj_set_onlytrans( BLIS_NO_TRANSPOSE, &a_local );
}
// Extract the variant number and implementation type.
n = bli_cntl_var_num( cntl );
i = bli_cntl_impl_type( cntl );
// Index into the variant array to extract the correct function pointer.
f = vars[n][i];
// Invoke the variant.
f( &alpha_local,
&x_local,
&y_local,
&a_local,
cntx,
cntl );
}
