Efficient parallel computation

yourbasic.org/golang
cpu

Dividing a large compu­tation into work units for parallel pro­cessing is more of an art than a science.

Here are some rules of thumb.

Whatever strategies you are using, don’t forget to benchmark and profile your code.

Example

The following example shows how to divide a costly computation and distribute it on all available CPUs. This is the code we want to optimize.

type Vector []float64

// Convolve computes w = u * v, where w[k] = Σ u[i]*v[j], i + j = k.
// Precondition: len(u) > 0, len(v) > 0.
func Convolve(u, v Vector) Vector {
    n := len(u) + len(v) - 1
    w := make(Vector, n)
    for k := 0; k < n; k++ {
        w[k] = mul(u, v, k)
    }
    return w
}

// mul returns Σ u[i]*v[j], i + j = k.
func mul(u, v Vector, k int) float64 {
    var res float64
    n := min(k+1, len(u))
    j := min(k, len(v)-1)
    for i := k - j; i < n; i, j = i+1, j-1 {
        res += u[i] * v[j]
    }
    return res
}

The idea is simple: identify work units of suitable size and then run each work unit in a separate goroutine. Here is a parallel version of Convolve.

func Convolve(u, v Vector) Vector {
    n := len(u) + len(v) - 1
    w := make(Vector, n)

    // Divide w into work units that take ~100μs-1ms to compute.
    size := max(1, 1000000/n)

    var wg sync.WaitGroup
    for i, j := 0, size; i < n; i, j = j, j+size {
        if j > n {
            j = n
        }
        // These goroutines share memory, but only for reading.
        wg.Add(1)
        go func(i, j int) {
            for k := i; k < j; k++ {
                w[k] = mul(u, v, k)
            }
            wg.Done()
        }(i, j)
    }
    wg.Wait()
    return w
}

When the work units have been defined, it’s often best to leave the scheduling to the runtime and the operating system. However, if needed, you can tell the runtime how many goroutines you want executing code simultaneously.

func init() {
    numcpu := runtime.NumCPU()
    runtime.GOMAXPROCS(numcpu) // Try to use all available CPUs.
}

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