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very large geographical area (100 to 200 kilometers on a side) to a resolution of 100 meters Storing this as a large rectangular array exceeded the memory available on the target machine and would have caused unacceptable paging behavior But over large regions, the terrain and signal strength values are likely to be the same, so a hierarchical representation that coalesces regions of the same value into a single cell makes the problem manageable Variations on this theme are frequent, and so are specific representations, but all share the same basic idea: store the common value or values implicitly or in a compact form, and spend more time and space on the remaining values If the most common values are really common, this is a win The program should be organized so that the specific data representation of complex types is hidden in a class or set of functions operating on a private data type This precaution ensures that the rest of the program will not be affected if the representation changes Space efficiency concerns sometimes manifest themselves in the external representation of information as well, both conversion and storage In general, it is best to store information as text wherever feasible rather than in some binary representation Text is portable, easy to read, and amenable to processing by all kinds of tools; binary representations have none of these advantages The argument in favor of binary is usually based on "speed," but this should be treated with some skepticism, since the disparity between text and binary forms may not be all that great Space efficiency often comes with a cost in run-time One application had to transfer a big image from one program to another Images in a simple format called PPM were typically a megabyte, so we thought it would be much faster to encode them for transfer in the compressed GIF format instead; those files were more like 50K bytes But the encoding and decoding of GIF took as much time as was saved by transferring a shorter file, so nothing was gained The code to handle the GIF format is about 500 lines long; the PPM source is about 10 lines For ease of maintenance, therefore, the GIF encoding was dropped and the application continues to use PPM exclusively Of course the tradeoff would be different if the file were to be sent across a slow network instead; then a GIF encoding would be much more costeffective
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It's hard to estimate ahead of time how fast a program will be, and it's doubly hard to estimate the cost of specific language statements or machine instructions It's easy, though, to create a cost model for a language or a system, which will give you at least a rough idea of how long important operations take One approach that is often used for conventional programming languages is a program that times representative code sequences There are operational difficulties, like getting reproducible results and canceling out irrelevant overheads, but it is possible
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to get useful insights without much effort For example, we have a C and C++ cost model program that estimates the costs of individual statements by enclosing them in a loop that runs them many millions of times, then computes an average time On a 250 MHz MIPS R10000,it produces this data, with times in nanoseconds per operation
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I n t Operations i + 1 + il = i 2 + i 3 il = i 2 - i 3 il = i 2 u i 3 il = i 2 / i 3 il = i 2 % i 3 F l o a t Operations f l = f2 f l = f 2 + f3 f l = f 2 - f3 f l = f2 * f3 f l = f2 / f3 Double dl = dl = dl = dl = dl = Operations d2 d2 + d3 d2 - d3 d2 * d3 d2 / d3
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