33 lines
1.3 KiB
C++
33 lines
1.3 KiB
C++
#include <algorithm>
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#include <cmath>
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#include <iostream>
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// return true if the difference between a and b is within epsilon percent of the larger of a and b
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bool approximatelyEqualRel(double a, double b, double relEpsilon)
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{
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return (std::abs(a - b) <= (std::max(std::abs(a), std::abs(b)) * relEpsilon));
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}
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bool approximatelyEqualAbsRel(double a, double b, double absEpsilon, double relEpsilon)
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{
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// Check if the numbers are really close -- needed when comparing numbers near zero.
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double diff{ std::abs(a - b) };
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if (diff <= absEpsilon)
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return true;
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// Otherwise fall back to Knuth's algorithm
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return (diff <= (std::max(std::abs(a), std::abs(b)) * relEpsilon));
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}
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int main()
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{
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// a is really close to 1.0, but has rounding errors
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double a{ 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 };
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std::cout << approximatelyEqualRel(a, 1.0, 1e-8) << '\n'; // compare "almost 1.0" to 1.0
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std::cout << approximatelyEqualRel(a-1.0, 0.0, 1e-8) << '\n'; // compare "almost 0.0" to 0.0
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std::cout << approximatelyEqualAbsRel(a, 1.0, 1e-12, 1e-8) << '\n'; // compare "almost 1.0" to 1.0
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std::cout << approximatelyEqualAbsRel(a-1.0, 0.0, 1e-12, 1e-8) << '\n'; // compare "almost 0.0" to 0.0
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}
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