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long y2 = COS_TABLE[x2]; long k = Floatdiv(Floatsub(y2, y1), Floatsub(x2, x1)); return sign * Floatadd(y1, Floatmul(k, Floatsub(abs, x1))); } // Perform the tangent function on a float public static long tan(long value) { return Floatdiv(Floatsin(value), Floatcos(value)); } // Convert a value from radians to degrees public static long toDeg(long value) { return Floatdiv(Floatmul( value, FloatcreateFloat(180)), FloatPI); } // Convert a value from degrees to radians public static long toRad(long value) { return Floatdiv(Floatmul(value, FloatPI), FloatcreateFloat(180)); } }

In this chapter we also drop the formalism of patterns Most of the implementation mechanisms are included within the major parallel programming environments Hence, rather than use patterns, we provide a high level description of each implementation mechanism and then investigate how the mechanism maps onto our three target programming environments: OpenMP, MPI, and Java This mapping will in some cases be trivial and require little more than presenting an existing construct in an API or language The discussion will become interesting when we look at operations native to one programming model, but foreign to another For example, it is possible to do message passing in OpenMP It is not pretty, but it works and can be useful at times We assume that the reader is familiar with OpenMP, MPI, and Java and how they are used for writing parallel programs Although we cover specific features of these APIs in this chapter, the details of using them are left to the appendixes

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Listing 171 creates a library that isn't complete, but offers enough functionality to move sprites in a game All functions are static, enabling any other class to easily access the methods The float value is represented as a long integer You must carefully keep track of numbers you use in the game some long integers will actually be floating-point numbers The constant VALUE_ONE represents the number 10, and the number of zeros shows how many decimal places are reserved after the decimal point You can change this value to offer different levels of precision By increasing the constant, the maximum float value decreases Some values in mathematical libraries are represented as constants The most commonly used constants are pi ( ) and E Because the game needs only trigonometric functions, the constant E is not needed Pi has the value 3142 to provide the highest precision possible with three decimal places after the decimal point A floating-point number can be created with two createFloat() methods One method accepts just an integer value, and the other accepts an additional fraction part If method parameters exceed the maximum value, an exception is thrown To retrieve the integer part of a floating number, your game can call the getInteger() method To retrieve the fraction part, call the getFraction() method Addition and subtraction are done in the traditional way When multiplying, however, the result must be divided with the VALUE_ONE constant at the end to keep the result at the same decimal point precision During division, the result is multiplied by VALUE_ONE to keep the same decimal point precision To avoid additional precision losses, the numbers must be multiplied before dividing them

An RMI server or client can be configured with a codebase a list of one or more URLs, each of which specifies a global location for Java class files RMI transmits the codebase associated with each transmitted class The receiving end can automatically use this information to retrieve any classes it doesn't have installed locally Figure 91 illustrates classes being downloaded dynamically from an HTTP server on request by a client

Parallel programs exploit concurrency by mapping instructions onto multiple UEs At a very basic level, every parallel program needs to (1) create the set of UEs, (2) manage interactions between them and their access to shared resources, (3) exchange information between UEs, and (4) shut them down in an orderly manner This suggests the following categories of implementation mechanisms

There are also two tables in the code with results for major angles of sine and cosine Both tables can be easily merged because they are mirrored However, it is sometimes quicker to have more tables and less execution code

Synchronization Enforcing constraints on the ordering of events occurring in different UEs This is primarily used to ensure that shared resources are accessed by a collection of UEs in such a way that the program is correct regardless of how the UEs are scheduled Communication The exchange of information between UEs

Now we're almost ready to move some sprites First off, however, each sprite's initial condition must be set Sprites must be placed at their starting positions and given initial values (for example, level of energy, x velocity, y velocity, and so on) If your game contains a timer, it should be reset When your game is over, the initial conditions should be set once again Listing 172 expands Micro Racer's GameCanvas class to initialize the player sprite as well as the enemy sprites Listing 172 Initializing It All

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