# MPI Trapezoidal - 79135

Request Posted by ## sdave92

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Price: \$10
• From: Computer Science, Programming
• Due on: Mon 05 Dec, 2016 (02:35pm)
• Asked on: Mon 28 Nov, 2016
• Due date has passed, but you can still Post Solution.
Description
1. Supposewetossdartsrandomlyatasquaredartboard,whosebullseyeisatthe origin, and whose sides are 2 feet in length. Suppose also that there’s a circle inscribed in the square dartboard. The radius of the circle is 1 foot, and it’s area is ? square feet. If the points that are hit by the darts are uniformly distributed (and we always hit the square), then the number of darts that hit inside the circle should approximately satisfy the equation

number in circle = ? , total number of tosses 4

since the ratio of the area of the circle to the area of the square is ?/4.
We can use this formula to estimate the value of
? with a random number

generator:

number in circle = 0;
for (toss = 0; toss < number of tosses; toss++) {

x = random double between 1 and 1;
y = random
double between 1 and 1;
distance squared = x
?x + y?y;
if (distance squared <= 1) number in circle++;

p} i estimate = 4?number in circle/((double) number of tosses);                 This is called a “Monte Carlo” method, since it uses randomness (the dart tosses).

Write an MPI program that uses a Monte Carlo method to estimate ?. Process 0 should read in the total number of tosses and broadcast it to the other processes. Use MPI Reduce to find the global sum of the local variable number in circle, and have process 0 print the result. You may want to use long long ints for the number of hits in the circle and the number of tosses, since both may have to be very large to get a reasonable estimate of ?

1 Solution for MPI Trapezoidal
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MPI_Toss as discussed
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