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52 lines
1.2 KiB
Plaintext
52 lines
1.2 KiB
Plaintext
[section:mod_inverse Modular Multiplicative Inverse]
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[section Introduction]
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The modular multiplicative inverse of a number /a/ is that number /x/ which satisfies /ax/ = 1 mod /p/.
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A fast algorithm for computing modular multiplicative inverses based on the extended Euclidean algorithm exists and is provided by Boost.
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[endsect]
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[section Synopsis]
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#include <boost/integer/mod_inverse.hpp>
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namespace boost { namespace integer {
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template<class Z>
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boost::optional<Z> mod_inverse(Z a, Z p);
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}}
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[endsect]
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[section Usage]
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Multiplicative modular inverses exist if and only if /a/ and /p/ are coprime.
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So for example
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auto x = mod_inverse(2, 5);
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if (x)
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{
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int should_be_three = x.value();
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}
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auto y = mod_inverse(2, 4);
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if (!y)
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{
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std::cout << "There is no inverse of 2 mod 4\n";
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}
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[endsect]
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[section References]
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Wagstaff, Samuel S., ['The Joy of Factoring], Vol. 68. American Mathematical Soc., 2013.
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[endsect]
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[endsect]
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[/
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Copyright 2018 Nick Thompson.
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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