mirror of
https://github.com/gonum/gonum.git
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281 lines
8.0 KiB
Go
281 lines
8.0 KiB
Go
// Code generated by "go generate github.com/gonum/blas/native"; DO NOT EDIT.
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// Copyright ©2014 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package native
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import (
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"runtime"
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"sync"
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/internal/asm/f32"
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)
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// Sgemm computes
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// C = beta * C + alpha * A * B,
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// where A, B, and C are dense matrices, and alpha and beta are scalars.
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// tA and tB specify whether A or B are transposed.
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//
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// Float32 implementations are autogenerated and not directly tested.
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func (Implementation) Sgemm(tA, tB blas.Transpose, m, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) {
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if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
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panic(badTranspose)
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}
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if tB != blas.NoTrans && tB != blas.Trans && tB != blas.ConjTrans {
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panic(badTranspose)
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}
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aTrans := tA == blas.Trans || tA == blas.ConjTrans
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if aTrans {
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checkMatrix32(k, m, a, lda)
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} else {
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checkMatrix32(m, k, a, lda)
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}
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bTrans := tB == blas.Trans || tB == blas.ConjTrans
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if bTrans {
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checkMatrix32(n, k, b, ldb)
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} else {
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checkMatrix32(k, n, b, ldb)
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}
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checkMatrix32(m, n, c, ldc)
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// scale c
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if beta != 1 {
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if beta == 0 {
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for i := 0; i < m; i++ {
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ctmp := c[i*ldc : i*ldc+n]
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for j := range ctmp {
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ctmp[j] = 0
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}
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}
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} else {
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for i := 0; i < m; i++ {
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ctmp := c[i*ldc : i*ldc+n]
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for j := range ctmp {
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ctmp[j] *= beta
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}
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}
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}
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}
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sgemmParallel(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
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}
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func sgemmParallel(aTrans, bTrans bool, m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
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// dgemmParallel computes a parallel matrix multiplication by partitioning
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// a and b into sub-blocks, and updating c with the multiplication of the sub-block
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// In all cases,
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// A = [ A_11 A_12 ... A_1j
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// A_21 A_22 ... A_2j
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// ...
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// A_i1 A_i2 ... A_ij]
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//
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// and same for B. All of the submatrix sizes are blockSize×blockSize except
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// at the edges.
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//
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// In all cases, there is one dimension for each matrix along which
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// C must be updated sequentially.
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// Cij = \sum_k Aik Bki, (A * B)
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// Cij = \sum_k Aki Bkj, (A^T * B)
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// Cij = \sum_k Aik Bjk, (A * B^T)
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// Cij = \sum_k Aki Bjk, (A^T * B^T)
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//
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// This code computes one {i, j} block sequentially along the k dimension,
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// and computes all of the {i, j} blocks concurrently. This
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// partitioning allows Cij to be updated in-place without race-conditions.
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// Instead of launching a goroutine for each possible concurrent computation,
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// a number of worker goroutines are created and channels are used to pass
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// available and completed cases.
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//
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// http://alexkr.com/docs/matrixmult.pdf is a good reference on matrix-matrix
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// multiplies, though this code does not copy matrices to attempt to eliminate
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// cache misses.
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maxKLen := k
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parBlocks := blocks(m, blockSize) * blocks(n, blockSize)
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if parBlocks < minParBlock {
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// The matrix multiplication is small in the dimensions where it can be
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// computed concurrently. Just do it in serial.
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sgemmSerial(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
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return
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}
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nWorkers := runtime.GOMAXPROCS(0)
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if parBlocks < nWorkers {
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nWorkers = parBlocks
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}
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// There is a tradeoff between the workers having to wait for work
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// and a large buffer making operations slow.
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buf := buffMul * nWorkers
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if buf > parBlocks {
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buf = parBlocks
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}
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sendChan := make(chan subMul, buf)
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// Launch workers. A worker receives an {i, j} submatrix of c, and computes
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// A_ik B_ki (or the transposed version) storing the result in c_ij. When the
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// channel is finally closed, it signals to the waitgroup that it has finished
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// computing.
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var wg sync.WaitGroup
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for i := 0; i < nWorkers; i++ {
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wg.Add(1)
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go func() {
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defer wg.Done()
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// Make local copies of otherwise global variables to reduce shared memory.
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// This has a noticable effect on benchmarks in some cases.
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alpha := alpha
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aTrans := aTrans
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bTrans := bTrans
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m := m
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n := n
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for sub := range sendChan {
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i := sub.i
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j := sub.j
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leni := blockSize
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if i+leni > m {
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leni = m - i
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}
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lenj := blockSize
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if j+lenj > n {
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lenj = n - j
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}
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cSub := sliceView32(c, ldc, i, j, leni, lenj)
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// Compute A_ik B_kj for all k
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for k := 0; k < maxKLen; k += blockSize {
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lenk := blockSize
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if k+lenk > maxKLen {
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lenk = maxKLen - k
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}
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var aSub, bSub []float32
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if aTrans {
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aSub = sliceView32(a, lda, k, i, lenk, leni)
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} else {
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aSub = sliceView32(a, lda, i, k, leni, lenk)
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}
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if bTrans {
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bSub = sliceView32(b, ldb, j, k, lenj, lenk)
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} else {
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bSub = sliceView32(b, ldb, k, j, lenk, lenj)
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}
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sgemmSerial(aTrans, bTrans, leni, lenj, lenk, aSub, lda, bSub, ldb, cSub, ldc, alpha)
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}
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}
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}()
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}
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// Send out all of the {i, j} subblocks for computation.
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for i := 0; i < m; i += blockSize {
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for j := 0; j < n; j += blockSize {
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sendChan <- subMul{
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i: i,
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j: j,
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}
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}
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}
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close(sendChan)
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wg.Wait()
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}
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// sgemmSerial is serial matrix multiply
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func sgemmSerial(aTrans, bTrans bool, m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
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switch {
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case !aTrans && !bTrans:
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sgemmSerialNotNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
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return
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case aTrans && !bTrans:
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sgemmSerialTransNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
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return
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case !aTrans && bTrans:
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sgemmSerialNotTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
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return
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case aTrans && bTrans:
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sgemmSerialTransTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
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return
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default:
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panic("unreachable")
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}
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}
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// sgemmSerial where neither a nor b are transposed
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func sgemmSerialNotNot(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
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// This style is used instead of the literal [i*stride +j]) is used because
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// approximately 5 times faster as of go 1.3.
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for i := 0; i < m; i++ {
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ctmp := c[i*ldc : i*ldc+n]
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for l, v := range a[i*lda : i*lda+k] {
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tmp := alpha * v
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if tmp != 0 {
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f32.AxpyUnitaryTo(ctmp, tmp, b[l*ldb:l*ldb+n], ctmp)
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}
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}
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}
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}
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// sgemmSerial where neither a is transposed and b is not
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func sgemmSerialTransNot(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
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// This style is used instead of the literal [i*stride +j]) is used because
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// approximately 5 times faster as of go 1.3.
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for l := 0; l < k; l++ {
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btmp := b[l*ldb : l*ldb+n]
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for i, v := range a[l*lda : l*lda+m] {
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tmp := alpha * v
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if tmp != 0 {
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ctmp := c[i*ldc : i*ldc+n]
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f32.AxpyUnitaryTo(ctmp, tmp, btmp, ctmp)
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}
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}
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}
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}
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// sgemmSerial where neither a is not transposed and b is
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func sgemmSerialNotTrans(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
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// This style is used instead of the literal [i*stride +j]) is used because
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// approximately 5 times faster as of go 1.3.
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for i := 0; i < m; i++ {
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atmp := a[i*lda : i*lda+k]
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ctmp := c[i*ldc : i*ldc+n]
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for j := 0; j < n; j++ {
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ctmp[j] += alpha * f32.DotUnitary(atmp, b[j*ldb:j*ldb+k])
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}
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}
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}
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// sgemmSerial where both are transposed
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func sgemmSerialTransTrans(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
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// This style is used instead of the literal [i*stride +j]) is used because
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// approximately 5 times faster as of go 1.3.
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for l := 0; l < k; l++ {
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for i, v := range a[l*lda : l*lda+m] {
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tmp := alpha * v
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if tmp != 0 {
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ctmp := c[i*ldc : i*ldc+n]
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f32.AxpyInc(tmp, b[l:], ctmp, uintptr(n), uintptr(ldb), 1, 0, 0)
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}
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}
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}
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}
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func sliceView32(a []float32, lda, i, j, r, c int) []float32 {
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return a[i*lda+j : (i+r-1)*lda+j+c]
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}
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func checkMatrix32(m, n int, a []float32, lda int) {
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if m < 0 {
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panic("blas: rows < 0")
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}
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if n < 0 {
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panic("blas: cols < 0")
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}
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if lda < n {
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panic("blas: illegal stride")
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}
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if len(a) < (m-1)*lda+n {
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panic("blas: insufficient matrix slice length")
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}
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}
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