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In this case, no iteration of the inner loop depends on the previous iteration's results; the entire inner loop can be executed in parallel. Indeed, given a(i, j) = a[i-j][j] then a(i, j) only depends on a(i - 1, x), with {,}. (However, each iteration of the outer loop does depend on previous iterations.)
The two examples below, written in Python, present a while loop with an inner for loop and a while loop without an inner loop. Although both have the same terminating condition for their while loops, the first example will finish faster because of the inner for loop. The variable innermax is a fraction of the maxticketno variable in the first ...
Modeling photon propagation with Monte Carlo methods is a flexible yet rigorous approach to simulate photon transport. In the method, local rules of photon transport are expressed as probability distributions which describe the step size of photon movement between sites of photon-matter interaction and the angles of deflection in a photon's trajectory when a scattering event occurs.
Concept art of hyperloop inner workings. Hyperloop is a proposed high-speed transportation system for both passengers and freight. [1] The concept behind the Hyperloop originated in the late 17th century with the invention of the world's first artificial vacuum, which led to designs for underground rapid transit systems powered by pneumatics in the decades that followed.
Loop interchange on this example can improve the cache performance of accessing b(j,i), but it will ruin the reuse of a(i) and c(i) in the inner loop, as it introduces two extra loads (for a(i) and for c(i)) and one extra store (for a(i)) during each iteration. As a result, the overall performance may be degraded after loop interchange.
Loop skewing: By "skewing" the logical shape of an array, this loop optimization can (when combined with loop interchange) eliminate loop-carried dependencies, allowing an inner loop to be parallelized. [citation needed] Loop unswitching moves loop invariants out of a loop, reducing the number of conditional branches in each loop. [1]
In more concrete terms this allows parallel transport to be described explicitly using the transport equation. Parallel transport along a curve c(t), with t taking values in [0,1], starting from a tangent from a tangent vector v 0 also amounts to finding a map v(t) from [0,1] to R 3 such that v(t) is a tangent vector to M at c(t) with v(0) = v 0.
SATURN (Simulation and Assignment of Traffic to Urban Road Networks) [1] is a computer program that calculates transport assignment on road networks. [2] It is developed by the University of Leeds and Atkins. Saturn competes with VISUM by PTV. [3]