Presburger Arithmetic and Its Use in Verification

APPENDIX A. EXAMPLES OF MULTICORE PARALLELISM IN F#
(fun iloopState(local:float) −>
let x =(float i +0.5)∗steps
local +4.0/(1.0+x ∗ x)
),
(fun local −> lock (monitor) (fun () −> sum := !sum + local))) |>
ignore
!sum ∗ steps
// Overall best function
let compute2() =
let rangeSize = NUM_STEPS /(Environment.ProcessorCount ∗10)
let partitions = Partitioner.Create(0, NUM_STEPS, if rangeSize >= 1 then
rangeSize else 1)
let sum = ref 0.0
let monitor = new Object()
Parallel.ForEach(
partitions, new ParallelOptions(),
(fun () −> 0.0),
(fun (min, max) loopState l −>
let local = ref 0.0
for i in min .. max − 1 do
let x =(float i +0.5)∗steps
local := !local +4.0/(1.0+x ∗ x)
l +!local),
(fun local −> lock (monitor) (fun () −> sum := !sum + local))) |>
ignore
!sum ∗ steps
let sqr x = x ∗ x
module Linq =
// LINQ
let compute1() =
(Enumerable
.Range(0, NUM_STEPS)
.Select(fun i −> 4.0/(1.0+sqr ((float i +0.5)∗steps)))
.Sum()) ∗ steps
// PLINQ
let compute2() =
(ParallelEnumerable
.Range(0, NUM_STEPS)
.Select(fun i −> 4.0/(1.0+sqr ((float i +0.5)∗steps)))
.Sum()) ∗ steps
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