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Java Example of a Routine to Compare Floating-Point Numbers
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double const ACCEPTABLE_DELTA = 0.00001; boolean Equals( double Term1, double Term2 ) { if ( Math.abs( Term1 - Term2 ) < ACCEPTABLE_DELTA ) { return true; } else { return false; } }
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If the code in the bad comparison of floating-point numbers example were converted so that this routine could be used for comparisons, the new comparison would look like this:
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if ( Equals( Nominal, Sum ) ) ...
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The output from the program when it uses this test is
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Numbers are the same.
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Depending on the demands of your application, it might be inappropriate to use a hard-coded value for AcceptableDelta. You might need to compute AcceptableDelta based on the size of the two numbers being compared.
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Anticipate rounding errors Rounding-error problems are no different from the problem of numbers with greatly different magnitudes. The same issue is involved, and many of the same techniques help to solve rounding problems. In addition, here are common specific solutions to rounding problems:
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First, change to a variable type that has greater precision. If you re using singleprecision floating point, change to double-precision floating point, and so on. Second, change to binary coded decimal (BCD) variables. The BCD scheme is typically slower and takes up more storage space but prevents many rounding errors. This is particularly valuable if the variables you re using represent dollars and cents or other quantities that must balance precisely. Third, change from floating-point to integer variables. This is a roll-your-own approach to BCD variables. You will probably have to use 64-bit integers to get the precision you want. This technique requires you to keep track of the fractional part of your numbers yourself. Suppose you were originally keeping track of dollars using floating point with cents expressed as fractional parts of
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de Complete
12. Fundamental Data Types
Page 8
dollars. This is a normal way to handle dollars and cents. When you switch to integers, you have to keep track of cents using integers and of dollars using multiples of 100 cents. In other words, you multiply dollars by 100 and keep the cents in the 0-to-99 range of the variable. This might seem absurd at first glance, but it s an effective solution in terms of both speed and accuracy. You can make these manipulations easier by creating a DollarsAndCents class that hides the integer representation and supports the necessary numeric operations.
Check language and library support for specific data types Some languages including Visual Basic have data types such as Currency that specifically support data that is sensitive to rounding errors. If your language has a built-in data type that provides such functionality, use it!
12.4 Characters and Strings
Here are some tips for using strings. The first applies to strings in all languages.
Issu
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9 es for using magic characters
and strings are similar to those for magic numbers 1 discussed in Section 12.1, 2 Numbers in General.
Avoid magic characters and strings Magic characters are literal characters (such as <;$QS>A<;$QS>) and magic strings are literal strings (such as <;$QD>Gigamatic Accounting Program<;$QD>) that appear throughout a program. If you program in a language that supports the use of named constants, use them instead. Otherwise, use global variables. Several reasons for avoiding literal strings follow.
For commonly occurring strings like the name of your program, command names, report titles, and so on, you might at some point need to change the string s contents. For example, Gigamatic Accounting Program might change to New and Improved! Gigamatic Accounting Program for a later version. International markets are becoming increasingly important, and it s easier to translate strings that are grouped in a string resource file than it is to translate to them in situ throughout a program. String literals tend to take up a lot of space. They re used for menus, messages, help screens, entry forms, and so on. If you have too many, they grow beyond control and cause memory problems. String space isn t a concern in many environments, but in embedded systems programming and other applications in which storage space is at a premium, solutions to string-space problems are easier to implement if the strings are relatively independent of the source code. Character and string literals are cryptic. Comments or named constants clarify your intentions. In the example below, the meaning of
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