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By Ronald Mak
* Non-theoretical causes of sensible numerical algorithms * Algorithms in motion with lively, interactive graphical Java courses and applets * Computational blunders and the way to take away them out of your codeUnderstand "computer math" and get the numbers you predict, reliably.In Java quantity Cruncher, writer Ronald Mak explains the right way to spot-and the right way to avoid-the refined programming miscues which can reason vexing calculation mistakes on your functions. an expert on mapping natural math to computing device math, he explains tips on how to use the often-overlooked computational positive factors of Java, and does so in a transparent, non-theoretical style.Without getting misplaced in mathematical element, you are going to study sensible numerical algorithms for properly summing numbers, discovering roots of equations, interpolation and approximation, numerical integration, fixing differential equations, matrix operations, and fixing units of simultaneous equations. you will additionally get pleasure from exciting issues resembling looking for styles in best numbers, producing random numbers, computing millions of digits of pi, and growing intricately attractive fractal images.Java quantity Cruncher comprises: * useful details all Java programmers should still be aware of * well known computational algorithms in Java-without over the top mathematical idea * Interactive graphical courses that convey the algorithms to existence at the visual display unit * Rounding blunders, the pitfalls of integer mathematics, Java's implementation of the IEEE 754 floating-point ordinary, and moreThis booklet comes in handy to all Java programmers, specifically if you are looking to know about numerical computation, and for builders of clinical, monetary, and information research purposes.
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Extra resources for Java Number Cruncher: The Java Programmer's Guide to Numerical Computing
Example text
Because 13 = 8 + 4 + 1, If we look at 1101, the binary encoding of 13, we can devise a more efficient algorithm. For each bit in the binary encoding of n, we repeatedly square the value of x, and so we compute x1, (x1)2 = x2, (x2)2 = x4, and (x4)2 = x8. We then multiply together the power of x corresponding to each 1 bit to give us Part I: Why Good Computations Go Bad 35 36 Part I: Why Good Computations Go Bad x8x4x1. This involves a total of five multiplications. The savings in multiplications is greater with larger values of n.
Substring(0, size)); validate(); } } /** * Convert the part to an integer value. toString()); } } /** * Convert the part to an long value. toString()); } } /** * Return the part as a string of characters '0' and '1'. toString(); } /** * Validate that the part consists only of '0' and '1'. "); } } } } /** * The IEEE 754 fraction part for a float. */ public static class FloatFraction extends Part { /** * Constructor. Exception */ public FloatFraction(String bits) throws Exception { super(FLOAT_FRACTION_SIZE, bits); } } /** * The IEEE 754 fraction part for a double.
The Java floating-point remainder operation is worth special mention. The floating-point operation is analogous to the integer operation. For any real values x and y, the remainder r is defined by where q is an integer value whose sign is the same as the sign of , and it is the integer value with the largest magnitude such that . Program 3-2 demonstrates the operation with some examples. See Listing 3-2. Listing 3-2 The float remainder operation. program3_2; /** * PROGRAM 3-2: Float Remainder * * Demonstrate the float remainder operation.