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55 lines
2.0 KiB
Plaintext
55 lines
2.0 KiB
Plaintext
@node gcd
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@section gcd: greatest common divisor
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@findex gcd
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@c Copyright (C) 2006, 2009-2017 Free Software Foundation, Inc.
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@c Permission is granted to copy, distribute and/or modify this document
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@c under the terms of the GNU Free Documentation License, Version 1.3 or
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@c any later version published by the Free Software Foundation; with no
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@c Invariant Sections, no Front-Cover Texts, and no Back-Cover
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@c Texts. A copy of the license is included in the ``GNU Free
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@c Documentation License'' file as part of this distribution.
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The @code{gcd} function returns the greatest common divisor of two numbers
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@code{a > 0} and @code{b > 0}. It is the caller's responsibility to ensure
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that the arguments are non-zero.
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If you need a gcd function for an integer type larger than
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@samp{unsigned long}, you can include the @file{gcd.c} implementation file
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with parametrization. The parameters are:
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@itemize @bullet
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@item WORD_T
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Define this to the unsigned integer type that you need this function for.
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@item GCD
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Define this to the name of the function to be created.
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@end itemize
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The created function has the prototype
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@smallexample
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WORD_T GCD (WORD_T a, WORD_T b);
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@end smallexample
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If you need the least common multiple of two numbers, it can be computed
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like this: @code{lcm(a,b) = (a / gcd(a,b)) * b} or
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@code{lcm(a,b) = a * (b / gcd(a,b))}.
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Avoid the formula @code{lcm(a,b) = (a * b) / gcd(a,b)} because---although
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mathematically correct---it can yield a wrong result, due to integer overflow.
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In some applications it is useful to have a function taking the gcd of two
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signed numbers. In this case, the gcd function result is usually normalized
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to be non-negative (so that two gcd results can be compared in magnitude
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or compared against 1, etc.). Note that in this case the prototype of the
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function has to be
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@smallexample
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unsigned long gcd (long a, long b);
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@end smallexample
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and not
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@smallexample
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long gcd (long a, long b);
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@end smallexample
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because @code{gcd(LONG_MIN,LONG_MIN) = -LONG_MIN = LONG_MAX + 1} does not
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fit into a signed @samp{long}.
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