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* @license Apache-2.0
*
* Copyright (c) 2025 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/* eslint-disable max-len, max-params */
'use strict';
// MODULES //
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var gdot = require( '@stdlib/blas/base/gdot' ).ndarray;
var blockSize = require( '@stdlib/ndarray/base/unary-tiling-block-size' );
// VARIABLES //
var bsize = blockSize( 'float64' ); // TODO: consider using a larger block size
// FUNCTIONS //
/**
* Tests whether a provided string indicates to transpose a matrix.
*
* @private
* @param {string} str - input string
* @returns {boolean} boolean indicating whether to transpose a matrix
*
* @example
* var bool = isTransposed( 'transpose' );
* // returns true
*
* @example
* var bool = isTransposed( 'conjugate-transpose' );
* // returns true
*
* @example
* var bool = isTransposed( 'no-transpose' );
* // returns false
*/
function isTransposed( str ) { // TODO: consider moving to a separate helper utility package
return ( str !== 'no-transpose' );
}
/**
* Fills a matrix with zeros.
*
* @private
* @param {NonNegativeInteger} M - number of rows
* @param {NonNegativeInteger} N - number of columns
* @param {Object} X - matrix object to fill
* @param {Collection} X.data - matrix data to fill
* @param {Array<Function>} X.accessors - array element accessors
* @param {integer} strideX1 - stride of the first dimension of `X`
* @param {integer} strideX2 - stride of the second dimension of `X`
* @param {NonNegativeInteger} offsetX - starting index for `X`
* @returns {Collection} matrix object to fill
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* var X = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
*
* zeros( 2, 3, arraylike2object( toAccessorArray( X ) ), 3, 1, 0 );
* // X => [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* var X = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
*
* zeros( 2, 3, arraylike2object( toAccessorArray( X ) ), 1, 2, 0 );
* // X => [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
*/
function zeros( M, N, X, strideX1, strideX2, offsetX ) { // TODO: consider moving to a separate package
var xbuf;
var set;
var dx0;
var dx1;
var S0;
var S1;
var i0;
var i1;
var ix;
// Cache references to array data:
xbuf = X.data;
// Cache references to element accessors:
set = X.accessors[ 1 ];
if ( isRowMajor( [ strideX1, strideX2 ] ) ) {
// For row-major matrices, the last dimension has the fastest changing index...
S0 = N;
S1 = M;
dx0 = strideX2; // offset increment for innermost loop
dx1 = strideX1 - ( S0*strideX2 ); // offset increment for outermost loop
} else { // column-major
// For column-major matrices, the first dimension has the fastest changing index...
S0 = M;
S1 = N;
dx0 = strideX1; // offset increment for innermost loop
dx1 = strideX2 - ( S0*strideX1 ); // offset increment for outermost loop
}
ix = offsetX;
for ( i1 = 0; i1 < S1; i1++ ) {
for ( i0 = 0; i0 < S0; i0++ ) {
set( xbuf, ix, 0.0 );
ix += dx0;
}
ix += dx1;
}
return X;
}
/**
* Scales each element in a matrix by a scalar `β`.
*
* @private
* @param {NonNegativeInteger} M - number of rows
* @param {NonNegativeInteger} N - number of columns
* @param {number} beta - scalar
* @param {Object} X - matrix object to fill
* @param {Collection} X.data - matrix data to fill
* @param {Array<Function>} X.accessors - array element accessors
* @param {integer} strideX1 - stride of the first dimension of `X`
* @param {integer} strideX2 - stride of the second dimension of `X`
* @param {NonNegativeInteger} offsetX - starting index for `X`
* @returns {Collection} matrix object to fill
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* var X = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
*
* scal( 2, 3, 5.0, arraylike2object( toAccessorArray( X ) ), 3, 1, 0 );
* // X => [ 5.0, 10.0, 15.0, 20.0, 25.0, 30.0 ]
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* var X = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
*
* scal( 2, 3, 5.0, arraylike2object( toAccessorArray( X ) ), 1, 2, 0 );
* // X => [ 5.0, 10.0, 15.0, 20.0, 25.0, 30.0 ]
*/
function scal( M, N, beta, X, strideX1, strideX2, offsetX ) { // TODO: consider moving to a separate package
var xbuf;
var get;
var set;
var dx0;
var dx1;
var S0;
var S1;
var i0;
var i1;
var ix;
// Cache references to array data:
xbuf = X.data;
// Cache references to element accessors:
get = X.accessors[ 0 ];
set = X.accessors[ 1 ];
if ( isRowMajor( [ strideX1, strideX2 ] ) ) {
// For row-major matrices, the last dimension has the fastest changing index...
S0 = N;
S1 = M;
dx0 = strideX2; // offset increment for innermost loop
dx1 = strideX1 - ( S0*strideX2 ); // offset increment for outermost loop
} else { // column-major
// For column-major matrices, the first dimension has the fastest changing index...
S0 = M;
S1 = N;
dx0 = strideX1; // offset increment for innermost loop
dx1 = strideX2 - ( S0*strideX1 ); // offset increment for outermost loop
}
ix = offsetX;
for ( i1 = 0; i1 < S1; i1++ ) {
for ( i0 = 0; i0 < S0; i0++ ) {
set( xbuf, ix, get( xbuf, ix ) * beta );
ix += dx0;
}
ix += dx1;
}
return X;
}
/**
* Performs matrix multiplication using a naive algorithm which is cache-optimal when `A` is row-major and `B` is column-major.
*
* @private
* @param {NonNegativeInteger} M - number of rows in the matrix `op(A)` and in the matrix `C`
* @param {NonNegativeInteger} N - number of columns in the matrix `op(B)` and in the matrix `C`
* @param {NonNegativeInteger} K - number of columns in the matrix `op(A)` and number of rows in the matrix `op(B)`
* @param {number} alpha - scalar constant
* @param {Object} A - first matrix object
* @param {Collection} A.data - first matrix data
* @param {Array<Function>} A.accessors - array element accessors
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {Object} B - second matrix object
* @param {Collection} B.data - second matrix data
* @param {Array<Function>} B.accessors - array element accessors
* @param {integer} strideB1 - stride of the first dimension of `B`
* @param {integer} strideB2 - stride of the second dimension of `B`
* @param {NonNegativeInteger} offsetB - starting index for `B`
* @param {Object} C - third matrix object
* @param {Collection} C.data - third matrix data
* @param {Array<Function>} C.accessors - array element accessors
* @param {integer} strideC1 - stride of the first dimension of `C`
* @param {integer} strideC2 - stride of the second dimension of `C`
* @param {NonNegativeInteger} offsetC - starting index for `C`
* @returns {Float64Array} `C`
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* var A = [ 1.0, 2.0, 3.0, 4.0 ];
* var B = [ 1.0, 1.0, 0.0, 1.0 ];
* var C = [ 1.0, 2.0, 3.0, 4.0 ];
*
* naive( 2, 2, 2, 1.0, arraylike2object( toAccessorArray( A ) ), 2, 1, 0, arraylike2object( toAccessorArray( B ) ), 2, 1, 0, arraylike2object( toAccessorArray( C ) ), 2, 1, 0 );
* // C => [ 2.0, 5.0, 6.0, 11.0 ]
*/
function naive( M, N, K, alpha, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB, C, strideC1, strideC2, offsetC ) {
var abuf;
var bbuf;
var cbuf;
var get;
var set;
var da0;
var db0;
var dc0;
var dc1;
var S0;
var S1;
var i0;
var i1;
var ia;
var ib;
var ic;
var v;
// Note on variable naming convention: S#, da#, db#, dc#, i# where # corresponds to the loop number, with `0` being the innermost loop...
S0 = N;
S1 = M;
da0 = strideA2;
db0 = strideB1;
dc0 = strideC2; // offset increment for innermost loop
dc1 = strideC1 - ( S0*strideC2 ); // offset increment for outermost loop
// Cache references to array data:
abuf = A.data;
bbuf = B.data;
cbuf = C.data;
// Cache references to element accessors:
get = C.accessors[ 0 ];
set = C.accessors[ 1 ];
ic = offsetC;
for ( i1 = 0; i1 < S1; i1++ ) {
ia = offsetA + ( i1*strideA1 );
for ( i0 = 0; i0 < S0; i0++ ) {
ib = offsetB + ( i0*strideB2 );
v = alpha * gdot( K, abuf, da0, ia, bbuf, db0, ib );
set( cbuf, ic, get( cbuf, ic ) + v );
ic += dc0;
}
ic += dc1;
}
return C;
}
/**
* Performs matrix multiplication using loop tiling.
*
* @private
* @param {NonNegativeInteger} M - number of rows in the matrix `op(A)` and in the matrix `C`
* @param {NonNegativeInteger} N - number of columns in the matrix `op(B)` and in the matrix `C`
* @param {NonNegativeInteger} K - number of columns in the matrix `op(A)` and number of rows in the matrix `op(B)`
* @param {number} alpha - scalar constant
* @param {Object} A - first matrix object
* @param {Collection} A.data - first matrix data
* @param {Array<Function>} A.accessors - array element accessors
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {Object} B - second matrix object
* @param {Collection} B.data - second matrix data
* @param {Array<Function>} B.accessors - array element accessors
* @param {integer} strideB1 - stride of the first dimension of `B`
* @param {integer} strideB2 - stride of the second dimension of `B`
* @param {NonNegativeInteger} offsetB - starting index for `B`
* @param {Object} C - third matrix object
* @param {Collection} C.data - third matrix data
* @param {Array<Function>} C.accessors - array element accessors
* @param {integer} strideC1 - stride of the first dimension of `C`
* @param {integer} strideC2 - stride of the second dimension of `C`
* @param {NonNegativeInteger} offsetC - starting index for `C`
* @returns {Float64Array} `C`
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* var A = [ 1.0, 2.0, 3.0, 4.0 ];
* var B = [ 1.0, 1.0, 0.0, 1.0 ];
* var C = [ 1.0, 2.0, 3.0, 4.0 ];
*
* blocked( 2, 2, 2, 1.0, arraylike2object( toAccessorArray( A ) ), 2, 1, 0, arraylike2object( toAccessorArray( B ) ), 2, 1, 0, arraylike2object( toAccessorArray( C ) ), 2, 1, 0 );
* // C => [ 2.0, 5.0, 6.0, 11.0 ]
*/
function blocked( M, N, K, alpha, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB, C, strideC1, strideC2, offsetC ) {
var abuf;
var bbuf;
var cbuf;
var get;
var set;
var da0;
var db0;
var dc0;
var dc1;
var oa1;
var ob0;
var oc0;
var oc1;
var S0;
var S1;
var s0;
var s1;
var sk;
var i0;
var i1;
var j0;
var j1;
var ia;
var ib;
var ic;
var oa;
var ob;
var k;
var v;
// Note on variable naming convention: S#, da#, db#, dc#, i#, j# where # corresponds to the loop number, with `0` being the innermost loop...
S0 = N;
S1 = M;
// Define increments for the innermost loop:
da0 = strideA2;
db0 = strideB1;
dc0 = strideC2;
// Cache references to array data:
abuf = A.data;
bbuf = B.data;
cbuf = C.data;
// Cache references to element accessors:
get = C.accessors[ 0 ];
set = C.accessors[ 1 ];
// Iterate over blocks...
for ( j1 = S1; j1 > 0; ) {
if ( j1 < bsize ) {
s1 = j1;
j1 = 0;
} else {
s1 = bsize;
j1 -= bsize;
}
oa1 = offsetA + ( j1*strideA1 );
oc1 = offsetC + ( j1*strideC1 );
for ( j0 = S0; j0 > 0; ) {
if ( j0 < bsize ) {
s0 = j0;
j0 = 0;
} else {
s0 = bsize;
j0 -= bsize;
}
ob0 = offsetB + ( j0*strideB2 );
oc0 = oc1 + ( j0*strideC2 ); // index offset for `C` for the current block
dc1 = strideC1 - ( s0*strideC2 ); // loop offset increment for `C`
for ( k = K; k > 0; ) {
if ( k < bsize ) {
sk = k;
k = 0;
} else {
sk = bsize;
k -= bsize;
}
oa = oa1 + ( k*strideA2 );
ob = ob0 + ( k*strideB1 );
ic = oc0;
for ( i1 = 0; i1 < s1; i1++ ) {
ia = oa + ( i1*strideA1 );
for ( i0 = 0; i0 < s0; i0++ ) {
ib = ob + ( i0*strideB2 );
v = alpha * gdot( sk, abuf, da0, ia, bbuf, db0, ib );
set( cbuf, ic, get( cbuf, ic ) + v );
ic += dc0;
}
ic += dc1;
}
}
}
}
return C;
}
// MAIN //
/**
* Performs the matrix-matrix operation `C = α*op(A)*op(B) + β*C` where `op(X)` is either `op(X) = X` or `op(X) = X^T`, `α` and `β` are scalars, `A`, `B`, and `C` are matrices, with `op(A)` an `M` by `K` matrix, `op(B)` a `K` by `N` matrix, and `C` an `M` by `N` matrix.
*
* @private
* @param {string} transA - specifies whether `A` should be transposed, conjugate-transposed, or not transposed
* @param {string} transB - specifies whether `B` should be transposed, conjugate-transposed, or not transposed
* @param {NonNegativeInteger} M - number of rows in the matrix `op(A)` and in the matrix `C`
* @param {NonNegativeInteger} N - number of columns in the matrix `op(B)` and in the matrix `C`
* @param {NonNegativeInteger} K - number of columns in the matrix `op(A)` and number of rows in the matrix `op(B)`
* @param {number} alpha - scalar constant
* @param {Object} A - first matrix object
* @param {Collection} A.data - first matrix data
* @param {Array<Function>} A.accessors - array element accessors
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {Object} B - second matrix object
* @param {Collection} B.data - second matrix data
* @param {Array<Function>} B.accessors - array element accessors
* @param {integer} strideB1 - stride of the first dimension of `B`
* @param {integer} strideB2 - stride of the second dimension of `B`
* @param {NonNegativeInteger} offsetB - starting index for `B`
* @param {number} beta - scalar constant
* @param {Object} C - third matrix object
* @param {Collection} C.data - third matrix data
* @param {Array<Function>} C.accessors - array element accessors
* @param {integer} strideC1 - stride of the first dimension of `C`
* @param {integer} strideC2 - stride of the second dimension of `C`
* @param {NonNegativeInteger} offsetC - starting index for `C`
* @returns {Float64Array} `C`
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* var A = [ 1.0, 2.0, 3.0, 4.0 ];
* var B = [ 1.0, 1.0, 0.0, 1.0 ];
* var C = [ 1.0, 2.0, 3.0, 4.0 ];
*
* ggemm( 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, arraylike2object( toAccessorArray( A ) ), 2, 1, 0, arraylike2object( toAccessorArray( B ) ), 2, 1, 0, 1.0, arraylike2object( toAccessorArray( C ) ), 2, 1, 0 );
* // C => [ 2.0, 5.0, 6.0, 11.0 ]
*/
function ggemm( transA, transB, M, N, K, alpha, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB, beta, C, strideC1, strideC2, offsetC ) {
var isrma;
var isrmb;
var sa1;
var sa2;
var sb1;
var sb2;
if ( M === 0 || N === 0 || ( ( beta === 1.0 ) && ( ( alpha === 0.0 ) || ( K === 0 ) ) ) ) {
return C;
}
// Form: C = β⋅C
if ( beta === 0.0 ) {
C = zeros( M, N, C, strideC1, strideC2, offsetC );
} else if ( beta !== 1.0 ) {
C = scal( M, N, beta, C, strideC1, strideC2, offsetC );
}
// Check whether we can early return...
if ( alpha === 0.0 ) {
return C;
}
// Determine the memory layouts of `A` and `B`...
isrma = isRowMajor( [ strideA1, strideA2 ] );
isrmb = isRowMajor( [ strideB1, strideB2 ] );
// Check whether we can avoid loop tiling and simply use the "naive" (cache-optimal) algorithm for performing matrix multiplication...
if ( isrma ) { // orderA === 'row-major'
if ( !isTransposed( transA ) ) {
if ( !isrmb && !isTransposed( transB ) ) { // orderB === 'column-major'
// Form: C = α⋅A⋅B + C
return naive( M, N, K, alpha, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB, C, strideC1, strideC2, offsetC );
}
if ( isrmb && isTransposed( transB ) ) { // orderB === 'row-major'
// Form: C = α⋅A⋅B^T + C
return naive( M, N, K, alpha, A, strideA1, strideA2, offsetA, B, strideB2, strideB1, offsetB, C, strideC1, strideC2, offsetC );
}
}
} else if ( isTransposed( transA ) ) { // orderA === 'column-major'
if ( isrmb && isTransposed( transB ) ) { // orderB === 'row-major'
// Form: C = α⋅A^T⋅B^T + C
return naive( M, N, K, alpha, A, strideA2, strideA1, offsetA, B, strideB2, strideB1, offsetB, C, strideC1, strideC2, offsetC );
}
if ( !isrmb && !isTransposed( transB ) ) { // orderB === 'column-major'
// Form: C = α⋅A^T⋅B + C
return naive( M, N, K, alpha, A, strideA2, strideA1, offsetA, B, strideB1, strideB2, offsetB, C, strideC1, strideC2, offsetC );
}
}
// Swap strides to perform transposes...
if ( isTransposed( transA ) ) {
sa1 = strideA2;
sa2 = strideA1;
} else {
sa1 = strideA1;
sa2 = strideA2;
}
if ( isTransposed( transB ) ) {
sb1 = strideB2;
sb2 = strideB1;
} else {
sb1 = strideB1;
sb2 = strideB2;
}
// Perform loop tiling to promote cache locality:
return blocked( M, N, K, alpha, A, sa1, sa2, offsetA, B, sb1, sb2, offsetB, C, strideC1, strideC2, offsetC );
}
// EXPORTS //
module.exports = ggemm;
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