8. Consider the all-reduce operation in which each processor starts with an array of m words, and needs to get the global sum of the respective words in the array at each processor. This operation can be implemented on a ring using one of the followings. Note that log function in this chapter has base of 2, not 10. (i.e., log p is actually log2 p) a. All-to-all broadcast of all the arrays followed by a local computation of the sum of the respective elements of the array b. Single node accumulation of the elements of the array, followed by a one-to-all broadcast of the result array. (a) What is the time cost for each case in terms of m, t, and t? (5 points) (b) Assume that = 100, x = 1, and m is very large (i.e., 100). Which one is better? Justify your answer by comparing them in the plot with the number of processors (i.e., 2, 4, 6, ..., and 20). (10 points) (c) Assume that t=100, 1, and m is very small (i.e., 1). Which one is better? Justify your answer by comparing them in the plot with the number of processors (i.e., 2, 4, 6, ..., and 20). (10 points)