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xlnt/tests/detail/numeric_util_test_suite.cpp
Crzyrndm e183e37ae6 remove roundoff test, add test for exponential representations 
-- testing that a number with >15 significant digits rounded off to 15 failed on all tested platforms
2018-08-25 14:06:20 +12:00

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// Copyright (c) 2014-2018 Thomas Fussell
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, WRISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE
//
// @license: http://www.opensource.org/licenses/mit-license.php
// @author: see AUTHORS file
#include "../../source/detail/numeric_utils.hpp"
#include <helpers/test_suite.hpp>
class numeric_test_suite : public test_suite
{
public:
numeric_test_suite()
{
register_test(test_serialise_number);
register_test(test_float_equals_zero);
register_test(test_float_equals_large);
register_test(test_float_equals_fairness);
register_test(test_min);
register_test(test_max);
register_test(test_abs);
}
void test_serialise_number()
{
// excel serialises numbers as floating point values with <= 15 digits of precision
xlnt_assert(xlnt::detail::serialize_number_to_string(1) == "1");
// trailing zeroes are ignored
xlnt_assert(xlnt::detail::serialize_number_to_string(1.0) == "1");
xlnt_assert(xlnt::detail::serialize_number_to_string(1.0f) == "1");
// one to 1 relation
xlnt_assert(xlnt::detail::serialize_number_to_string(1.23456) == "1.23456");
xlnt_assert(xlnt::detail::serialize_number_to_string(1.23456789012345) == "1.23456789012345");
xlnt_assert(xlnt::detail::serialize_number_to_string(123456.789012345) == "123456.789012345");
xlnt_assert(xlnt::detail::serialize_number_to_string(1.23456789012345e+67) == "1.23456789012345e+67");
xlnt_assert(xlnt::detail::serialize_number_to_string(1.23456789012345e-67) == "1.23456789012345e-67");
}
void test_float_equals_zero()
{
// comparing relatively small numbers (2.3e-6) with 0 will be true by default
const float comp_val = 2.3e-6; // about the largest difference allowed by default
xlnt_assert(0.f != comp_val); // fail because not exactly equal
xlnt_assert(xlnt::detail::float_equals(0.0, comp_val));
xlnt_assert(xlnt::detail::float_equals(0.0, -comp_val));
// fail because diff is out of bounds for fuzzy equality
xlnt_assert(!xlnt::detail::float_equals(0.0, comp_val + 0.1e-6));
xlnt_assert(!xlnt::detail::float_equals(0.0, -(comp_val + 0.1e-6)));
// if the bounds of comparison are too loose, there are two tweakable knobs to tighten the comparison up
//==========================================================
// #1: reduce the epsilon_scale (default is 20)
// This can bring the range down to FLT_EPSILON (scale factor of 1)
xlnt_assert(!xlnt::detail::float_equals(0.0, comp_val, 10));
const float closer_comp_val = 1.1e-6;
xlnt_assert(xlnt::detail::float_equals(0.0, closer_comp_val, 10));
xlnt_assert(!xlnt::detail::float_equals(0.0, closer_comp_val + 0.1e-6, 10));
xlnt_assert(xlnt::detail::float_equals(0.0, -closer_comp_val, 10));
xlnt_assert(!xlnt::detail::float_equals(0.0, -(closer_comp_val + 0.1e-6), 10));
//==========================================================
// #2: specify the epsilon source as a higher precision type (e.g. double)
// This makes the epsilon range quite significantly less
xlnt_assert(!xlnt::detail::float_equals<double>(0.0, comp_val));
xlnt_assert(!xlnt::detail::float_equals<double>(0.0, closer_comp_val));
const float tiny_comp_val = 4.4e-15;
xlnt_assert(xlnt::detail::float_equals<double>(0.0, tiny_comp_val));
xlnt_assert(!xlnt::detail::float_equals<double>(0.0, tiny_comp_val + 0.1e-15));
xlnt_assert(xlnt::detail::float_equals<double>(0.0, -tiny_comp_val));
xlnt_assert(!xlnt::detail::float_equals<double>(0.0, -(tiny_comp_val + 0.1e-15)));
//==========================================================
// #3: combine #1 & #2
// for the tightest default precision, double with a scale of 1
xlnt_assert(!xlnt::detail::float_equals<double>(0.0, comp_val, 1));
xlnt_assert(!xlnt::detail::float_equals<double>(0.0, closer_comp_val, 1));
xlnt_assert(!xlnt::detail::float_equals<double>(0.0, tiny_comp_val, 1));
const float really_tiny_comp_val = 2.2e-16; // the limit is +/- std::numeric_limits<double>::epsilon()
xlnt_assert(xlnt::detail::float_equals<double>(0.0, really_tiny_comp_val, 1));
xlnt_assert(!xlnt::detail::float_equals<double>(0.0, really_tiny_comp_val + 0.1e-16, 1));
xlnt_assert(xlnt::detail::float_equals<double>(0.0, -really_tiny_comp_val, 1));
xlnt_assert(!xlnt::detail::float_equals<double>(0.0, -(really_tiny_comp_val + 0.1e-16), 1));
//==========================================================
// in the world of floats, 2.2e-16 is still significantly different to 0.f (smallest representable float is around 1e-38)
// if comparisons are known to involve extremely small numbers (such that +/- 2.2e-16 is too large a band),
// a type that specialises std::numeric_limits::epsilon may be passed as the first template parameter
// the type itself doesn't actually need to have any behaviour as it is only used as the source for epsilon
// struct super_precise{};
// namespace std {
// template<> numeric_limits<super_precise> {
// double epsilon() {
// return 1e-30;
// }
// }
// }
// float_equals<double>(0.0, 2e-30, 1); // returns true
// float_equals<super_precise>(0.0, 2e-30, 1); // returns false
}
void test_float_equals_large()
{
const float compare_to = 20e6;
// fp math with arguments of different magnitudes is wierd
xlnt_assert(compare_to == compare_to + 1); // x == x + 1 ...
xlnt_assert(compare_to != compare_to + 10); // x != x + 10
xlnt_assert(compare_to != compare_to - 10); // x != x - 10
// if the same epsilon was used for comparison of large values as the values around one
// we'd have all the issues around zero again
xlnt_assert(xlnt::detail::float_equals(compare_to, compare_to + 49));
xlnt_assert(!xlnt::detail::float_equals(compare_to, compare_to + 50));
xlnt_assert(xlnt::detail::float_equals(compare_to, compare_to - 49));
xlnt_assert(!xlnt::detail::float_equals(compare_to, compare_to - 50));
// float_equals also scales epsilon up to match the magnitude of its arguments
// all the same options are available for increasing/decreasing the precision of the comparison
// however the the epsilon source should always be of equal or lesser precision than the arguments when away from zero
}
void test_float_equals_nan()
{
const float nan = std::nan("");
// nans always compare false
xlnt_assert(!xlnt::detail::float_equals(nan, 0.f));
xlnt_assert(!xlnt::detail::float_equals(nan, nan));
xlnt_assert(!xlnt::detail::float_equals(nan, 1000.f));
}
void test_float_equals_fairness()
{
// tests for parameter ordering dependency
// (lhs ~= rhs) == (rhs ~= lhs)
const double test_val = 1.0;
const double test_diff_pass = 1.192092e-07; // should all pass with this
const double test_diff = 1.192093e-07; // difference enough to provide different results if the comparison is not "fair"
const double test_diff_fails = 1.192094e-07; // should all fail with this
// test_diff_pass
xlnt_assert(xlnt::detail::float_equals<float>((test_val + test_diff_pass), test_val, 1));
xlnt_assert(xlnt::detail::float_equals<float>(test_val, (test_val + test_diff_pass), 1));
xlnt_assert(xlnt::detail::float_equals<float>(-(test_val + test_diff_pass), -test_val, 1));
xlnt_assert(xlnt::detail::float_equals<float>(-test_val, -(test_val + test_diff_pass), 1));
// test_diff
xlnt_assert(xlnt::detail::float_equals<float>((test_val + test_diff), test_val, 1));
xlnt_assert(xlnt::detail::float_equals<float>(test_val, (test_val + test_diff), 1));
xlnt_assert(xlnt::detail::float_equals<float>(-(test_val + test_diff), -test_val, 1));
xlnt_assert(xlnt::detail::float_equals<float>(-test_val, -(test_val + test_diff), 1));
// test_diff_fails
xlnt_assert(!xlnt::detail::float_equals<float>((test_val + test_diff_fails), test_val, 1));
xlnt_assert(!xlnt::detail::float_equals<float>(test_val, (test_val + test_diff_fails), 1));
xlnt_assert(!xlnt::detail::float_equals<float>(-(test_val + test_diff_fails), -test_val, 1));
xlnt_assert(!xlnt::detail::float_equals<float>(-test_val, -(test_val + test_diff_fails), 1));
}
void test_min()
{
// simple
xlnt_assert(xlnt::detail::min(0, 1) == 0);
xlnt_assert(xlnt::detail::min(1, 0) == 0);
xlnt_assert(xlnt::detail::min(0.0, 1) == 0.0); // comparisons between different types just work
xlnt_assert(xlnt::detail::min(1, 0.0) == 0.0);
// negative numbers
xlnt_assert(xlnt::detail::min(0, -1) == -1.0);
xlnt_assert(xlnt::detail::min(-1, 0) == -1.0);
xlnt_assert(xlnt::detail::min(0.0, -1) == -1.0);
xlnt_assert(xlnt::detail::min(-1, 0.0) == -1.0);
// no zeroes
xlnt_assert(xlnt::detail::min(10, -10) == -10.0);
xlnt_assert(xlnt::detail::min(-10, 10) == -10.0);
xlnt_assert(xlnt::detail::min(10.0, -10) == -10.0);
xlnt_assert(xlnt::detail::min(-10, 10.0) == -10.0);
static_assert(xlnt::detail::min(-10, 10.0) == -10.0, "constexpr");
}
void test_max()
{
// simple
xlnt_assert(xlnt::detail::max(0, 1) == 1);
xlnt_assert(xlnt::detail::max(1, 0) == 1);
xlnt_assert(xlnt::detail::max(0.0, 1) == 1.0); // comparisons between different types just work
xlnt_assert(xlnt::detail::max(1, 0.0) == 1.0);
// negative numbers
xlnt_assert(xlnt::detail::max(0, -1) == 0.0);
xlnt_assert(xlnt::detail::max(-1, 0) == 0.0);
xlnt_assert(xlnt::detail::max(0.0, -1) == 0.0);
xlnt_assert(xlnt::detail::max(-1, 0.0) == 0.0);
// no zeroes
xlnt_assert(xlnt::detail::max(10, -10) == 10.0);
xlnt_assert(xlnt::detail::max(-10, 10) == 10.0);
xlnt_assert(xlnt::detail::max(10.0, -10) == 10.0);
xlnt_assert(xlnt::detail::max(-10, 10.0) == 10.0);
static_assert(xlnt::detail::max(-10, 10.0) == 10.0, "constexpr");
}
void test_abs()
{
xlnt_assert(xlnt::detail::abs(0) == 0);
xlnt_assert(xlnt::detail::abs(1) == 1);
xlnt_assert(xlnt::detail::abs(-1) == 1);
xlnt_assert(xlnt::detail::abs(0.0) == 0.0);
xlnt_assert(xlnt::detail::abs(1.5) == 1.5);
xlnt_assert(xlnt::detail::abs(-1.5) == 1.5);
static_assert(xlnt::detail::abs(-1.23) == 1.23, "constexpr");
}
};
static numeric_test_suite x;
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