+++ /dev/null
-// Copyright ©2014 The Gonum Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package gonum
-
-import (
- "runtime"
- "sync"
-
- "gonum.org/v1/gonum/blas"
- "gonum.org/v1/gonum/internal/asm/f64"
-)
-
-// Dgemm computes
-// C = beta * C + alpha * A * B,
-// where A, B, and C are dense matrices, and alpha and beta are scalars.
-// tA and tB specify whether A or B are transposed.
-func (Implementation) Dgemm(tA, tB blas.Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) {
- if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
- panic(badTranspose)
- }
- if tB != blas.NoTrans && tB != blas.Trans && tB != blas.ConjTrans {
- panic(badTranspose)
- }
- aTrans := tA == blas.Trans || tA == blas.ConjTrans
- if aTrans {
- checkDMatrix('a', k, m, a, lda)
- } else {
- checkDMatrix('a', m, k, a, lda)
- }
- bTrans := tB == blas.Trans || tB == blas.ConjTrans
- if bTrans {
- checkDMatrix('b', n, k, b, ldb)
- } else {
- checkDMatrix('b', k, n, b, ldb)
- }
- checkDMatrix('c', m, n, c, ldc)
-
- // scale c
- if beta != 1 {
- if beta == 0 {
- for i := 0; i < m; i++ {
- ctmp := c[i*ldc : i*ldc+n]
- for j := range ctmp {
- ctmp[j] = 0
- }
- }
- } else {
- for i := 0; i < m; i++ {
- ctmp := c[i*ldc : i*ldc+n]
- for j := range ctmp {
- ctmp[j] *= beta
- }
- }
- }
- }
-
- dgemmParallel(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
-}
-
-func dgemmParallel(aTrans, bTrans bool, m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
- // dgemmParallel computes a parallel matrix multiplication by partitioning
- // a and b into sub-blocks, and updating c with the multiplication of the sub-block
- // In all cases,
- // A = [ A_11 A_12 ... A_1j
- // A_21 A_22 ... A_2j
- // ...
- // A_i1 A_i2 ... A_ij]
- //
- // and same for B. All of the submatrix sizes are blockSize×blockSize except
- // at the edges.
- //
- // In all cases, there is one dimension for each matrix along which
- // C must be updated sequentially.
- // Cij = \sum_k Aik Bki, (A * B)
- // Cij = \sum_k Aki Bkj, (A^T * B)
- // Cij = \sum_k Aik Bjk, (A * B^T)
- // Cij = \sum_k Aki Bjk, (A^T * B^T)
- //
- // This code computes one {i, j} block sequentially along the k dimension,
- // and computes all of the {i, j} blocks concurrently. This
- // partitioning allows Cij to be updated in-place without race-conditions.
- // Instead of launching a goroutine for each possible concurrent computation,
- // a number of worker goroutines are created and channels are used to pass
- // available and completed cases.
- //
- // http://alexkr.com/docs/matrixmult.pdf is a good reference on matrix-matrix
- // multiplies, though this code does not copy matrices to attempt to eliminate
- // cache misses.
-
- maxKLen := k
- parBlocks := blocks(m, blockSize) * blocks(n, blockSize)
- if parBlocks < minParBlock {
- // The matrix multiplication is small in the dimensions where it can be
- // computed concurrently. Just do it in serial.
- dgemmSerial(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
- return
- }
-
- nWorkers := runtime.GOMAXPROCS(0)
- if parBlocks < nWorkers {
- nWorkers = parBlocks
- }
- // There is a tradeoff between the workers having to wait for work
- // and a large buffer making operations slow.
- buf := buffMul * nWorkers
- if buf > parBlocks {
- buf = parBlocks
- }
-
- sendChan := make(chan subMul, buf)
-
- // Launch workers. A worker receives an {i, j} submatrix of c, and computes
- // A_ik B_ki (or the transposed version) storing the result in c_ij. When the
- // channel is finally closed, it signals to the waitgroup that it has finished
- // computing.
- var wg sync.WaitGroup
- for i := 0; i < nWorkers; i++ {
- wg.Add(1)
- go func() {
- defer wg.Done()
- // Make local copies of otherwise global variables to reduce shared memory.
- // This has a noticeable effect on benchmarks in some cases.
- alpha := alpha
- aTrans := aTrans
- bTrans := bTrans
- m := m
- n := n
- for sub := range sendChan {
- i := sub.i
- j := sub.j
- leni := blockSize
- if i+leni > m {
- leni = m - i
- }
- lenj := blockSize
- if j+lenj > n {
- lenj = n - j
- }
-
- cSub := sliceView64(c, ldc, i, j, leni, lenj)
-
- // Compute A_ik B_kj for all k
- for k := 0; k < maxKLen; k += blockSize {
- lenk := blockSize
- if k+lenk > maxKLen {
- lenk = maxKLen - k
- }
- var aSub, bSub []float64
- if aTrans {
- aSub = sliceView64(a, lda, k, i, lenk, leni)
- } else {
- aSub = sliceView64(a, lda, i, k, leni, lenk)
- }
- if bTrans {
- bSub = sliceView64(b, ldb, j, k, lenj, lenk)
- } else {
- bSub = sliceView64(b, ldb, k, j, lenk, lenj)
- }
- dgemmSerial(aTrans, bTrans, leni, lenj, lenk, aSub, lda, bSub, ldb, cSub, ldc, alpha)
- }
- }
- }()
- }
-
- // Send out all of the {i, j} subblocks for computation.
- for i := 0; i < m; i += blockSize {
- for j := 0; j < n; j += blockSize {
- sendChan <- subMul{
- i: i,
- j: j,
- }
- }
- }
- close(sendChan)
- wg.Wait()
-}
-
-// dgemmSerial is serial matrix multiply
-func dgemmSerial(aTrans, bTrans bool, m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
- switch {
- case !aTrans && !bTrans:
- dgemmSerialNotNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
- return
- case aTrans && !bTrans:
- dgemmSerialTransNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
- return
- case !aTrans && bTrans:
- dgemmSerialNotTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
- return
- case aTrans && bTrans:
- dgemmSerialTransTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
- return
- default:
- panic("unreachable")
- }
-}
-
-// dgemmSerial where neither a nor b are transposed
-func dgemmSerialNotNot(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
- // This style is used instead of the literal [i*stride +j]) is used because
- // approximately 5 times faster as of go 1.3.
- for i := 0; i < m; i++ {
- ctmp := c[i*ldc : i*ldc+n]
- for l, v := range a[i*lda : i*lda+k] {
- tmp := alpha * v
- if tmp != 0 {
- f64.AxpyUnitaryTo(ctmp, tmp, b[l*ldb:l*ldb+n], ctmp)
- }
- }
- }
-}
-
-// dgemmSerial where neither a is transposed and b is not
-func dgemmSerialTransNot(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
- // This style is used instead of the literal [i*stride +j]) is used because
- // approximately 5 times faster as of go 1.3.
- for l := 0; l < k; l++ {
- btmp := b[l*ldb : l*ldb+n]
- for i, v := range a[l*lda : l*lda+m] {
- tmp := alpha * v
- if tmp != 0 {
- ctmp := c[i*ldc : i*ldc+n]
- f64.AxpyUnitaryTo(ctmp, tmp, btmp, ctmp)
- }
- }
- }
-}
-
-// dgemmSerial where neither a is not transposed and b is
-func dgemmSerialNotTrans(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
- // This style is used instead of the literal [i*stride +j]) is used because
- // approximately 5 times faster as of go 1.3.
- for i := 0; i < m; i++ {
- atmp := a[i*lda : i*lda+k]
- ctmp := c[i*ldc : i*ldc+n]
- for j := 0; j < n; j++ {
- ctmp[j] += alpha * f64.DotUnitary(atmp, b[j*ldb:j*ldb+k])
- }
- }
-}
-
-// dgemmSerial where both are transposed
-func dgemmSerialTransTrans(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
- // This style is used instead of the literal [i*stride +j]) is used because
- // approximately 5 times faster as of go 1.3.
- for l := 0; l < k; l++ {
- for i, v := range a[l*lda : l*lda+m] {
- tmp := alpha * v
- if tmp != 0 {
- ctmp := c[i*ldc : i*ldc+n]
- f64.AxpyInc(tmp, b[l:], ctmp, uintptr(n), uintptr(ldb), 1, 0, 0)
- }
- }
- }
-}
-
-func sliceView64(a []float64, lda, i, j, r, c int) []float64 {
- return a[i*lda+j : (i+r-1)*lda+j+c]
-}
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