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1 | // (C) Copyright John Maddock 2006. |
2 | // Use, modification and distribution are subject to the | |
3 | // Boost Software License, Version 1.0. (See accompanying file | |
4 | // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
5 | ||
6 | #ifndef BOOST_MATH_SQRT1PM1 | |
7 | #define BOOST_MATH_SQRT1PM1 | |
8 | ||
9 | #ifdef _MSC_VER | |
10 | #pragma once | |
11 | #endif | |
12 | ||
13 | #include <boost/math/special_functions/math_fwd.hpp> | |
14 | #include <boost/math/special_functions/log1p.hpp> | |
15 | #include <boost/math/special_functions/expm1.hpp> | |
16 | ||
17 | // | |
18 | // This algorithm computes sqrt(1+x)-1 for small x: | |
19 | // | |
20 | ||
21 | namespace boost{ namespace math{ | |
22 | ||
23 | template <class T, class Policy> | |
24 | inline typename tools::promote_args<T>::type sqrt1pm1(const T& val, const Policy& pol) | |
25 | { | |
26 | typedef typename tools::promote_args<T>::type result_type; | |
27 | BOOST_MATH_STD_USING | |
28 | ||
29 | if(fabs(result_type(val)) > 0.75) | |
30 | return sqrt(1 + result_type(val)) - 1; | |
31 | return boost::math::expm1(boost::math::log1p(val, pol) / 2, pol); | |
32 | } | |
33 | ||
34 | template <class T> | |
35 | inline typename tools::promote_args<T>::type sqrt1pm1(const T& val) | |
36 | { | |
37 | return sqrt1pm1(val, policies::policy<>()); | |
38 | } | |
39 | ||
40 | } // namespace math | |
41 | } // namespace boost | |
42 | ||
43 | #endif // BOOST_MATH_SQRT1PM1 | |
44 | ||
45 | ||
46 | ||
47 | ||
48 |