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1 : : // Copyright (c) 2014-2022 Thomas Fussell
2 : : // Copyright (c) 2024-2025 xlnt-community
3 : : //
4 : : // Permission is hereby granted, free of charge, to any person obtaining a copy
5 : : // of this software and associated documentation files (the "Software"), to deal
6 : : // in the Software without restriction, including without limitation the rights
7 : : // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
8 : : // copies of the Software, and to permit persons to whom the Software is
9 : : // furnished to do so, subject to the following conditions:
10 : : //
11 : : // The above copyright notice and this permission notice shall be included in
12 : : // all copies or substantial portions of the Software.
13 : : //
14 : : // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
15 : : // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
16 : : // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
17 : : // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
18 : : // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
19 : : // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
20 : : // THE SOFTWARE
21 : : //
22 : : // @license: http://www.opensource.org/licenses/mit-license.php
23 : : // @author: see AUTHORS file
24 : :
25 : : #pragma once
26 : :
27 : : #include <cmath>
28 : : #include <limits>
29 : : #include <type_traits>
30 : :
31 : : #undef min
32 : : #undef max
33 : :
34 : : namespace xlnt {
35 : : namespace detail {
36 : :
37 : : /// <summary>
38 : : /// constexpr abs
39 : : /// </summary>
40 : : template <typename Number>
41 :CBC 12582 : constexpr Number abs(Number val)
42 : : {
43 [ + + ]: 12582 : return (val < Number{0}) ? -val : val;
44 : : }
45 : :
46 : : /// <summary>
47 : : /// constexpr max
48 : : /// </summary>
49 : : template <typename NumberL, typename NumberR>
50 : 12588 : constexpr typename std::common_type<NumberL, NumberR>::type (max)(NumberL lval, NumberR rval)
51 : : {
52 [ + + ]: 12588 : return (lval < rval) ? rval : lval;
53 : : }
54 : :
55 : : /// <summary>
56 : : /// constexpr min
57 : : /// </summary>
58 : : template <typename NumberL, typename NumberR>
59 : 12 : constexpr typename std::common_type<NumberL, NumberR>::type (min)(NumberL lval, NumberR rval)
60 : : {
61 [ + + ]: 12 : return (lval < rval) ? lval : rval;
62 : : }
63 : :
64 : : /// <summary>
65 : : /// Floating point equality requires a bit of fuzzing due to the imprecise nature of fp calculation
66 : : /// References:
67 : : /// - Several blogs/articles were referenced with the following being the most useful
68 : : /// -- https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
69 : : /// -- http://realtimecollisiondetection.net/blog/?p=89
70 : : /// - Testing Frameworks {Catch2, Boost, Google}, primarily for selecting the default scale factor
71 : : /// -- None of these even remotely agree
72 : : /// </summary>
73 : : template <typename EpsilonType = float, // the type to extract epsilon from
74 : : typename LNumber, typename RNumber> // parameter types (deduced)
75 : 6288 : bool float_equals(const LNumber &lhs, const RNumber &rhs,
76 : : int epsilon_scale = 20) // scale the "fuzzy" equality. Higher value gives a more tolerant comparison
77 : : {
78 : : // a type that lhs and rhs can agree on
79 : : using common_t = typename std::common_type<LNumber, RNumber>::type;
80 : : // asserts for sane usage
81 : : static_assert(std::is_floating_point<LNumber>::value || std::is_floating_point<RNumber>::value,
82 : : "Using this function with two integers is just wasting time. Use ==");
83 : : static_assert(std::numeric_limits<EpsilonType>::epsilon() < EpsilonType{1},
84 : : "epsilon >= 1.0 will cause all comparisons to return true");
85 : :
86 : : // NANs always compare false with themselves
87 [ + - - + : 6288 : if (std::isnan(lhs) || std::isnan(rhs))
- + ]
88 : : {
89 :UBC 0 : return false;
90 : : }
91 : : // epsilon type defaults to float because even if both args are a higher precision type
92 : : // either or both could have been promoted by prior operations
93 : : // if a higher precision is required, the template type can be changed
94 :CBC 6288 : constexpr common_t epsilon = static_cast<common_t>(std::numeric_limits<EpsilonType>::epsilon());
95 : : // the "epsilon" then needs to be scaled into the comparison range
96 : : // epsilon for numeric_limits is valid when abs(x) <1.0, scaling only needs to be upwards
97 : : // in particular, this prevents a lhs of 0 from requiring an exact comparison
98 : : // additionally, a scale factor is applied.
99 : 6288 : common_t scaled_fuzz = epsilon_scale * epsilon * max(max(xlnt::detail::abs<common_t>(lhs),
100 : : xlnt::detail::abs<common_t>(rhs)), // |max| of parameters.
101 : : common_t{1}); // clamp
102 [ + + + + ]: 6288 : return ((lhs + scaled_fuzz) >= rhs) && ((rhs + scaled_fuzz) >= lhs);
103 : : }
104 : :
105 : : } // namespace detail
106 : : } // namespace xlnt
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