Parallel calculations

Parallel calculations is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Many programming languages allow you to specify computations to be run in parallel. While Concurrent computing is focused on concurrency, the purpose of this task is to distribute time-consuming calculations on as many CPUs as possible.

Assume we have a collection of numbers, and want to find the one with the largest minimal prime factor (that is, the one that contains relatively large factors). To speed up the search, the factorization should be done in parallel using separate threads or processes, to take advantage of multi-core CPUs.

Show how this can be formulated in your language. Parallelize the factorization of those numbers, then search the returned list of numbers and factors for the largest minimal factor, and return that number and its prime factors.

For the prime number decomposition you may use the solution of the Prime decomposition task.

PicoLisp

The 'later' function is used in PicoLisp to start parallel computations. The following solution calls 'later' on the 'factor' function from Prime decomposition#PicoLisp, and then 'wait's until all results are available: <lang PicoLisp>(let Lst

  (mapcan
     '((N)
        (later (cons)               # When done,
           (cons N (factor N)) ) )  # return the number and its factors
     (quote
        188573867500151328137405845301  # Process a collection of 12 numbers
        3326500147448018653351160281
        979950537738920439376739947
        2297143294659738998811251
        136725986940237175592672413
        3922278474227311428906119
        839038954347805828784081
        42834604813424961061749793
        2651919914968647665159621
        967022047408233232418982157
        2532817738450130259664889
        122811709478644363796375689 ) )
  (wait NIL (full Lst))  # Wait until all computations are done
  (maxi '((L) (apply min L)) Lst) )  # Result: Number in CAR, factors in CDR</lang>

Output:

-> (2532817738450130259664889 6531761 146889539 2639871491)

Tcl

With Tcl, it is necessary to explicitly perform computations in other threads because each thread is strongly isolated from the others (except for inter-thread messaging). However, it is entirely practical to wrap up the communications so that only a small part of the code needs to know very much about it.

Works with: Tcl version 8.6

<lang tcl>package require Tcl 8.6 package require Thread

1. Pooled computation engine; runs event loop internally

namespace eval pooled {

   variable poolSize 3; # Needs to be tuned to system size

   proc computation {computationDefinition entryPoint values} {

variable result variable poolSize # Add communication shim append computationDefinition [subst -nocommands { proc poolcompute {value target} { set outcome [$entryPoint \$value] set msg [list set ::pooled::result(\$value) \$outcome] thread::send -async \$target \$msg } }]

# Set up the pool set pool [tpool::create -initcmd $computationDefinition \ -maxworkers $poolSize]

# Prepare to receive results unset -nocomplain result array set result {}

# Dispatch the computations foreach value $values { tpool::post $pool [list poolcompute $value [thread::id]] }

# Wait for results while {[array size result] < [llength $values]} {vwait pooled::result}

# Dispose of the pool tpool::release $pool

# Return the results return [array get result]

   }

}</lang> This is the definition of the prime factorization engine: <lang tcl># Code for computing the prime factors of a number set computationCode {

   namespace eval prime {

variable primes [list 2 3 5 7 11] proc restart {} { variable index -1 variable primes variable current [lindex $primes end] }

proc get_next_prime {} { variable primes variable index if {$index < [llength $primes]-1} { return [lindex $primes [incr index]] } variable current while 1 { incr current 2 set p 1 foreach prime $primes { if {$current % $prime} {} else { set p 0 break } } if {$p} { return [lindex [lappend primes $current] [incr index]] } } }

proc factors {num} { restart set factors [dict create] for {set i [get_next_prime]} {$i <= $num} {} { if {$num % $i == 0} { dict incr factors $i set num [expr {$num / $i}] continue } elseif {$i*$i > $num} { dict incr factors $num break } else { set i [get_next_prime] } } return $factors }

   }

}

1. The values to be factored

set values {

   188573867500151328137405845301
   3326500147448018653351160281
   979950537738920439376739947
   2297143294659738998811251
   136725986940237175592672413
   3922278474227311428906119
   839038954347805828784081
   42834604813424961061749793
   2651919914968647665159621
   967022047408233232418982157
   2532817738450130259664889
   122811709478644363796375689

}</lang> Putting everything together: <lang tcl># Do the computation, getting back a dictionary that maps

1. values to its results (itself an ordered dictionary)

set results [pooled::computation $computationCode prime::factors $values]

1. Find the maximum minimum factor with sorting magic

set best [lindex [lsort -integer -stride 2 -index {1 0} $results] end-1]

1. Print in human-readable form

proc renderFactors {factorDict} {

   dict for {factor times} $factorDict {

lappend v {*}[lrepeat $times $factor]

   }
   return [join $v "*"]

} puts "$best = [renderFactors [dict get $results $best]]"</lang>