Computing mod inverse - algorithm

Question

I want to compute the inverse element of a prime in modular arithmetic.
In order to speed things up I start a few goroutines which try to find the element in a certain range. When the first one finds the element, it sends it to the main goroutine and at this point I want to terminate the program. So I call close in the main goroutine, but I don't know if the goroutines will finish their execution (I guess not). So a few questions arise:
1) Is this a bad style, should I have something like a WaitGroup?
2) Is there a more idiomatic way to do this computation?
package main
import "fmt"
const (
Procs = 8
P = 1000099
Base = 1<<31 - 1
)
func compute(start, end uint64, finished chan struct{}, output chan uint64) {
for i := start; i < end; i++ {
select {
case <-finished:
return
default:
break
}
if i*P%Base == 1 {
output <- i
}
}
}
func main() {
finished := make(chan struct{})
output := make(chan uint64)
for i := uint64(0); i < Procs; i++ {
start := i * (Base / Procs)
end := (i + 1) * (Base / Procs)
go compute(start, end, finished, output)
}
fmt.Println(<-output)
close(finished)
}

Answer 1

Is there a more idiomatic way to do this computation?
You don't actually need a loop to compute this.
If you use the GCD function (part of the standard library), you get returned numbers x and y such that:
x*P+y*Base=1
this means that x is the answer you want (because x*P = 1 modulo Base):
package main
import (
"fmt"
"math/big"
)
const (
P = 1000099
Base = 1<<31 - 1
)
func main() {
bigP := big.NewInt(P)
bigBase := big.NewInt(Base)
// Compute inverse of bigP modulo bigBase
bigGcd := big.NewInt(0)
bigX := big.NewInt(0)
bigGcd.GCD(bigX,nil,bigP,bigBase)
// x*bigP+y*bigBase=1
// => x*bigP = 1 modulo bigBase
fmt.Println(bigX)
}

Answer 2

Is this a bad style, should I have something like a WaitGroup?
A wait group solves a different problem.
In general, to be a responsible go citizen here and ensure your code runs and tidies up behind itself, you may need to do a combination of:
Signal to the spawned goroutines to stop their calculations when the result of the computation has been found elsewhere.
Ensure a synchronous process waits for the goroutines to stop before returning. This is not mandatory if they properly respond to the signal in #1, but if you don't wait, there will be no guarantee they have terminated before the parent goroutine continues.
In your example program, which performs this task and then quits, there is strictly no need to do either. As this comment indicates, your program's main method terminates upon a satisfactory answer being found, at which point the program will end, any goroutines will be summarily terminated, and the operating system will tidy up any consumed resources. Waiting for goroutines to stop is unnecessary.
However, if you wrapped this code up into a library or it became part of a long running "inverse prime calculation" service, it would be desirable to tidy up the goroutines you spawned to avoid wasting cycles unnecessarily. Additionally, in general, you may have other scenarios in which goroutines store state, hold handles to external resources, or hold handles to internal objects which you risk leaking if not properly tidied away – it is desirable to properly close these.
Communicating the requirement to stop working
There are several approaches to communicate this. I don't claim this is an exhaustive list! (Please do suggest other general-purpose methods in the comments or by proposing edits to the post.)
Using a special channel
Signal the child goroutines by closing a special "shutdown" channel reserved for the purpose. This exploits the channel axiom:
A receive from a closed channel returns the zero value immediately
On receiving from the shutdown channel, the goroutine should immediately arrange to tidy any local state and return from the function. Your earlier question had example code which implemented this; a version of the pattern is:
func myGoRoutine(shutdownChan <-chan struct{}) {
select {
case <-shutdownChan:
// tidy up behaviour goes here
return
// You may choose to listen on other channels here to implement
// the primary behaviour of the goroutine.
}
}
func main() {
shutdownChan := make(chan struct{})
go myGoRoutine(shutdownChan)
// some time later
close(shutdownChan)
}
In this instance, the shutdown logic is wasted because the main() method will immediately return after the call to close. This will race with the shutdown of the goroutine, but we should assume it will not properly execute its tidy-up behaviour. Point 2 addresses ways to fix this.
Using a context
The context package provides the option to create a context which can be cancelled. On cancellation, a channel exposed by the context's Done() method will be closed, which signals time to return from the goroutine.
This approach is approximately the same as the previous method, with the exception of neater encapsulation and the availability of a context to pass to downstream calls in your goroutine to cancel nested calls where desired. Example:
func myGoRoutine(ctx context.Context) {
select {
case <-ctx.Done():
// tidy up behaviour goes here
return
// Put real behaviour for the goroutine here.
}
}
func main() {
// Get a context (or use an existing one if you are provided with one
// outside a `main` method:
ctx := context.Background()
// Create a derived context with a cancellation method
ctx, cancel := context.WithCancel(ctx)
go myGoRoutine(ctx)
// Later, when ready to quit
cancel()
}
This has the same bug as the other case in that the main method will not wait for the child goroutines to quit before returning.
Waiting (or "join"ing) for child goroutines to stop
The code which closes the shutdown channel or closes the context in the above examples will not wait for child goroutines to stop working before continuing. This may be acceptable in some instances, while in others you may require the guarantee that goroutines have stopped before continuing.
sync.WaitGroup can be used to implement this requirement. The documentation is comprehensive. A wait group is a counter which should be incremented using its Add method on starting a goroutine and decremented using its Done method when a goroutine completes. Code can wait for the counter to return to zero by calling its Wait method, which blocks until the condition is true. All calls to Add must occur before a call to Wait.
Example code:
func main() {
var wg sync.WaitGroup
// Increment the WaitGroup with the number of goroutines we're
// spawning.
wg.Add(1)
// It is common to wrap a goroutine in a function which performs
// the decrement on the WaitGroup once the called function returns
// to avoid passing references of this control logic to the
// downstream consumer.
go func() {
// TODO: implement a method to communicate shutdown.
callMyFunction()
wg.Done()
}()
// Indicate shutdown, e.g. by closing a channel or cancelling a
// context.
// Wait for goroutines to stop
wg.Wait()
}
Is there a more idiomatic way to do this computation?
This algorithm is certainly parallelizable through use of goroutines in the manner you have defined. As the work is CPU-bound, the limitation of goroutines to the number of available CPUs makes sense (in the absence of other work on the machine) to benefit from the available compute resource.
See peterSO's answer for a bug fix.