Numeric utilities.
More...
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| template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>> |
| bool | Euclid::eq_almost (T a, T b, T epsilon=std::numeric_limits< T >::epsilon()) |
| | Two floating points are almost equal. More...
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| template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>> |
| bool | Euclid::eq_almost (T a, T b, T eps_rel, T eps_abs) |
| | Two floating points are almost equal. More...
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| template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>> |
| bool | Euclid::eq_rel_err (T a, T b, T epsilon=std::numeric_limits< T >::epsilon()) |
| | Two floating points are equal under a relative error bound. More...
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| template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>> |
| bool | Euclid::eq_abs_err (T a, T b, T epsilon=std::numeric_limits< T >::epsilon()) |
| | Two floating points are equal under an absolute error bound. More...
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| template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>> |
| bool | Euclid::eq_ulp (T a, T b, std::size_t max_ulps=4) |
| | Two floating points are equal under an ulp error bound. More...
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| template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>> |
| bool | Euclid::less_safe (T a, T b, T epsilon=std::numeric_limits< T >::epsilon()) |
| | Safer version of a < b. More...
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| template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>> |
| bool | Euclid::greater_safe (T a, T b, T epsilon=std::numeric_limits< T >::epsilon()) |
| | Safer version of a > b. More...
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This package provides functions for more robust floating point comparisons than using operator ==, !=, <, > directly.
Warnings
Choose epsilon according to your value range, otherwise you'll get undesired outcomes.
template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>>
| bool Euclid::eq_abs_err |
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epsilon = std::numeric_limits<T>::epsilon() |
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Only meaningful when you know the bounds of a, b and choose epsilon wisely.
- Parameters
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| a | |
| b | |
| epsilon | Default value is only useful for comparing to zero. You need to specify this value in order to be meaningful for your case. |
template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>>
| bool Euclid::eq_almost |
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T |
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b, |
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T |
epsilon = std::numeric_limits<T>::epsilon() |
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This is the most versatile equality check to use. It returns true when either a relative or absolute error bound is satified, with the assumption that the tolerance for both kinds of errors are the same.
- Parameters
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| a | |
| b | |
| epsilon | Default value is sufficient for common cases. However, when comparing very closed values less than one, try to increase epsilon because this senario is equivalent to using eq_abs_err(). |
template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>>
| bool Euclid::eq_almost |
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T |
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T |
b, |
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T |
eps_rel, |
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T |
eps_abs |
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This is the most versatile equality check to use. It returns true when either a relative or absolute error bound is satified.
template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>>
| bool Euclid::eq_rel_err |
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T |
a, |
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T |
b, |
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T |
epsilon = std::numeric_limits<T>::epsilon() |
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Faster than eq_almost() if not comparing zeros.
- Parameters
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| b | |
| epsilon | Default value is sufficient for most cases. However, when comparing very small values, epsilon might be very high. |
template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>>
| bool Euclid::eq_ulp |
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b, |
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std::size_t |
max_ulps = 4 |
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Units in the Last Place distance measures how much two floating points differs in their integer representations. It's also more accurate when comparing to an exact value, and robust in common cases.
- Parameters
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| a | |
| b | |
| max_ulps | The maximum ulp difference threshold, where 4 is enough for most cases. |
template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>>
| bool Euclid::greater_safe |
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T |
b, |
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T |
epsilon = std::numeric_limits<T>::epsilon() |
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Returns true even if a is less than b by a small margin, due to numeric error bounded by epsilon.
template<typename T , typename = std::enable_if_t<std::is_floating_point<T>::value>>
| bool Euclid::less_safe |
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T |
a, |
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T |
b, |
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T |
epsilon = std::numeric_limits<T>::epsilon() |
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Returns true even if a is greater than b by a small margin, due to numeric error bounded by epsilon.
1.8.11 
