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Write an MPI program 'Estimate-Pi.c' from the scratch to estimate the value of Pi (π) using a Monte Carlo method. Your program should perform necessary error checking for inputs.

Write an MPI program 'Estimate-Pi.c' from the scratch to estimate the value of Pi (π) using a Monte Carlo method. Your program should perform necessary error checking for inputs.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Write an MPI program 'Estimate-Pi.c' from the scratch to estimate the value of Pi (π) using a Monte Carlo method. Your program should perform necessary error checking for inputs.

This is called a “Monte Carlo" method, since it uses randomness (the dart tosses). Specifically, the MPI program can be implemented in the following way. (1) Process 0 should read in the total number of tosses and broadcast it to the other processes. (2) Use MPI_Reduce to find the global sum of the local variable number_in_circle, and have process 0 print the result. (3) You may want to use long long ints for the number of hits in the cirele and the number of tosses, since both may have to be very large to get a reasonable estimate of n. 1.
Transcribed Image Text:This is called a “Monte Carlo" method, since it uses randomness (the dart tosses). Specifically, the MPI program can be implemented in the following way. (1) Process 0 should read in the total number of tosses and broadcast it to the other processes. (2) Use MPI_Reduce to find the global sum of the local variable number_in_circle, and have process 0 print the result. (3) You may want to use long long ints for the number of hits in the cirele and the number of tosses, since both may have to be very large to get a reasonable estimate of n. 1.
Write an MPI program that uses a Monte Carlo method to estimate a. Suppose we toss darts randomly at a square dartboard, whose bullseye is at the 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 its area is a 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 a/4. We can use this formula to estimate the value of a 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_cirele++; } pi_estimate = 4*number_in_circle/((double) number_of_tosses); This is called a “Monte Carlo" method, since it uses randomness (the dart tosses). Specifically, the MPI program can be implemented in the following way.
Transcribed Image Text:Write an MPI program that uses a Monte Carlo method to estimate a. Suppose we toss darts randomly at a square dartboard, whose bullseye is at the 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 its area is a 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 a/4. We can use this formula to estimate the value of a 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_cirele++; } pi_estimate = 4*number_in_circle/((double) number_of_tosses); This is called a “Monte Carlo" method, since it uses randomness (the dart tosses). Specifically, the MPI program can be implemented in the following way.
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