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So far, we've managed to create a bunch of sprites and draw them on the screen But we're not painting a still life here; we're programming a game! To make a game a game, it must read input events from the keyboard or the screen and move sprites accordingly The game must also set up initial conditions, check controls for game operability, and provide artificial intelligence for computer-controlled characters or game moves

This equation, sometimes known as Gustafson's law, was attributed in [Gus88] to E Barsis Equation 214

Before we get too excited, though, there's one thing we're going to have to get out of the way: MIDP does not support floating-point math Why is floating-point math important for games Imagine a game hero that can move in different directions, such as the enemy cars in our Micro Racer game You'll want the cars to move at a constant speed, regardless of which direction the sprite is moving To create this type of smooth movement, you would use a pair of simple trigonometric formulas:

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This gives exactly the same speedup as Amdahl's law, but allows a different question to be asked when the number of processors is increased Since scaled depends on P, the result of taking the limit isn't immediately obvious, but would give the same result as the limit in Amdahl's law However, suppose we take the limit in P while holding Tcompute and thus scaled constant The interpretation is that we are increasing the size of the problem so that the total running time remains constant when more processors are added (This contains the implicit assumption that the execution time of the serial terms does not change as the problem size grows) In this case, the speedup is linear in P Thus, while adding more processors to solve a fixed problem may hit the speedup limits of Amdahl's law with a relatively small number of processors, if the problem grows as more processors are added, Amdahl's law will be pessimistic These two models of speedup, along with a fixed memory version of speedup, are discussed in [SN90]

Vx = V * cos(tau)

261 Latency and Bandwidth A simple but useful model characterizes the total time for message transfer as the sum of a fixed cost

Vy = V * sin(tau)

Remote method invocation has the same semantics except as follows:

where tau is an angle starting at the 3 o'clock position and increasing counterclockwise, as illustrated in Figure 171 Figure 171 Velocity components

The fixed cost is called latency and is essentially the time it takes to send an empty message over the communication medium, from the time the send routine is called to the time the data is received by the recipient Latency (given in some appropriate time unit) includes overhead due to software and network hardware plus the time it takes for the message to traverse the communication medium The bandwidth (given in some measure of bytes per time unit) is a measure of the capacity of the communication medium N is the length of the message The latency and bandwidth can vary significantly between systems depending on both the hardware used and the quality of the software implementing the communication protocols Because these values can be measured with fairly simple benchmarks [DD97], it is sometimes worthwhile to measure values for and , as these can help guide optimizations to improve communication performance For example, in a system in which is relatively large, it might be worthwhile to try to restructure a program that sends many small messages to aggregate the communication into a few large messages instead Data for several recent systems has been presented in [BBC 03 + ]

Unfortunately, the results of these formulas are going to involve decimal places If you round things off, movement becomes nonlinear Additionally, 3D games are becoming very popular It's conceivable that 3D engines, or isometric engines (games that simulate depth of scene, such as the view of a maze by peeking over its outer wall), will soon be feasible on smaller devices In order to transform 3D polygons and draw 3D worlds, accurate linear algebra and trigonometric functions are imperative This involves precise floating-point support

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