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Maths functions documentation

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---
title: "Maths"
weight: 100
---

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---
title: "absolute"
---
A template functions that return the absolute value.
```cpp
template <typename T>
ETL_CONSTEXPR T absolute(T value)
```
**Return**
The absolute of `value`.
If T is `int8_t`:-
`0` => `0`
`127` => `127`
`-127` => `127`
**Error**
Asserts if `value == etl::integral_limits<T>::min`.
---
```cpp
template <typename T>
ETL_CONSTEXPR etl::make_unsigned_t<T> absolute_unsigned(T value)
```
**Return**
The absolute of `value`, cast to the unsigned version of type `T`.
If T is `int8_t`:-
Return type is `etl::make_unsigned_t<T>`
`0` => `0`
`127` => `127`
`-127` => `127`
`-128` => `128`

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Checksums & hashes
---
title: "Checksums & hashes"
---
A set of algorithms for producing checksums and hashes from data.
____________________________________________________________________________________________________
Generic hashes
## Generic hashes
```
Type Class Header
Checksum checksum checksum.h (8, 16, 32 or 64 bit)
BSD Checksum bsd_checksum checksum.h (8, 16, 32 or 64 bit)
@ -19,11 +23,17 @@ Jenkins jenkins jenkins.h
Pearson pearson pearson.h
Murmur3 murmur3 murmur3.h (32 or 64 bit)
____________________________________________________________________________________________________
CRC hashes
```
## CRC1
```
Type Class Table size Header
CRC1 crc1 0 crc1.h, crc.h
```
## CRC8
```
Type Class Table size Header
CRC8 CCITT crc8_ccitt 256 crc8_ccitt.h, crc.h
crc8_ccitt_t4 4
crc8_ccitt_t16 16
@ -95,7 +105,10 @@ CRC8 WCDMA crc8_wcdma 256 crc8_wcdma.h, cr
crc8_wcdma_t16 16
crc8_wcdma_t256 256
crc8_wcdma_t<N> N = 4, 16, 256
____________________________________________________________________________________________________
```
## CRC16
```
Type Class Table size Header
CRC16 crc16 256 crc16.h, crc.h
crc16_t4 4
crc16_t16 16
@ -251,7 +264,11 @@ CRC16 XMODEM crc16_xmodem 256 crc16_xmodem.h,
crc16_xmodem_t16 16
crc16_xmodem_t256 256
crc16_xmodem_t<N> N = 4, 16, 256
____________________________________________________________________________________________________
```
## CRC32
```
Type Class Table size Header
CRC32 crc32 256 crc32.h, crc.h
crc32_t4 4
crc32_t16 16
@ -305,7 +322,11 @@ CRC32 XFER crc32_xfer 256 crc32_xfer.h,
crc32_xfer_t16 16
crc32_xfer_t256 256
crc32_xfer_t<N> N = 4, 16, 256
____________________________________________________________________________________________________
```
## CRC32
```
Type Class Table size Header
CRC64 ECMA crc64_ecma 256 crc64_ecma.h, crc.h
crc32_ecma_t4 4
crc32_ecma_t16 16
@ -317,56 +338,85 @@ CRC64 ISO crc64_iso 256 crc64_iso.h, cr
crc32_iso_t16 16
crc32_iso_t256 256
crc32_iso_t<N> N = 4, 16, 256
```
The library also includes etl::hash which is a reverse engineered version of std::hash in hash.h
## Hash
The library also includes etl::hash which is a reverse engineered version of `std::hash` in `hash.h`
All hashing templates have the same API, apart from the members returning the hash value, which return the appropriate type.
A hash that requires finalising before the value is read should do it in the conversion operator and value() member functions. Trying to add values after finalisation should result in an etl::hash_finalised error being asserted. Construction or reset should clear any finalisation flag.
____________________________________________________________________________________________________
Hash API
A hash that requires finalising before the value is read should do it in the conversion operator and `value()` member functions. Trying to add values after finalisation should result in an `etl::hash_finalised error` being asserted. Construction or reset should clear any finalisation flag.
## Hash API
All hashing algorithms supply the following API.
Default constructor
Initialises the hash value to its appropriate starting value.
____________________________________________________________________________________________________
Constructor from a range. (Any iterator type)
Creates a hash from the supplied range.
____________________________________________________________________________________________________
```cpp
void reset();
```
**Decsription**
Resets the hash to the initial condition.
____________________________________________________________________________________________________
---
```cpp
void add(uint8_t value);
Adds a uint8_t to the hash.
____________________________________________________________________________________________________
```
Adds a `uint8_t` to the hash.
```cpp
template <typename TIterator>
void add(TIterator begin, Titerator end);
```
**Description**
Adds a range of values to the hash.
If the type pointed to must be default castable to uint8_t.
____________________________________________________________________________________________________
value_type value() const;
Returns the hash value.
The hash will be finalised if required.
____________________________________________________________________________________________________
operator value_type() const;
Returns the hash value.
The hash will be finalised if required.
__________________________________________________________________________________________________
iterator input()
Returns an iterator that allows the input of new values.
If the type pointed to must be default castable to `uint8_t`.
Example
---
```cpp
value_type value() const;
```
**Return**
The hash value.
The hash will be finalised if required.
---
```cpp
operator value_type() const;
```
**Return**
The hash value.
The hash will be finalised if required.
---
```cpp
iterator input()
```
**Return**
An iterator that allows the input of new values.
**Example**
```cpp
std::array data{ 9, 1, 8, 2, 7, 3, 6, 4, 5 };
etl::crc32 crc_calculator;
std::copy(data.begin(), data.end(), crc_calculator.input());
uint32_t crc = crc_calculator.value();
____________________________________________________________________________________________________
Creating a new frame check type.
```
## Creating a new frame check type.
The frame_check_sequence class may be customised with new policies that contain the expected typedef and member functions:-
Example
**Example**
```cpp
struct special_16
{
typedef uint16_t value_type;
@ -386,9 +436,11 @@ struct special_16
return ~sum; // How to read the final value.
}
};
```
The hash class would be declared as follows.
```cpp
//*************************************************************************
/// Special checksum
//*************************************************************************
@ -416,4 +468,4 @@ public:
this->add(begin, end);
}
};
```

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---
title: "Combinations / Permutations"
---
Templates to provide combinations and permutations constants.
## Combinations
See [Combinations](https://en.wikipedia.org/wiki/Combination)
```cpp
template <size_t N, size_t K>
struct combinations
```
**Member const**
Number of combinations of K items from a total of N.
```cpp
static ETL_CONSTEXPR size_t value
```
If C++17 is supported.
```cpp
template <size_t N, size_t K>
inline constexpr size_t combinations_v = combinations<N, K>::value;
```
## Permutations
See [Permutations](https://en.wikipedia.org/wiki/Permutation)
```cpp
template <size_t N, size_t K>
struct permutations
```
**Member const**
Number of permutations of K items from a total of N.
```cpp
static ETL_CONSTEXPR size_t value
```
If C++17 is supported.
```cpp
template <size_t N, size_t K>
inline constexpr size_t permutations_v = permutations<N, K>::value;
```

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Constants
---
title: "Constants"
---
A set of compile time constants.
____________________________________________________________________________________________________
log.h
log
## log
```cpp
template <size_t N, size_t BASE>
struct log;
```
Defines the member value as the log of N to base BASE.
Set to the integer below the ideal floating point value.
Header: *log.h*
C++17 and above
Defines the member value as the log of N to base BASE.
Set to the integer below the ideal floating point value.
C++17 and above
```cpp
template <size_t N, size_t BASE>
inline constexpr size_t log_v = log<N, BASE>::value;
____________________________________________________________________________________________________
log2
```
## log2
```cpp
template <size_t N>
struct log2;
```
Defines the member value as the log of N to base 2
Set to the integer below the ideal floating point value.
Header: *log.h*
C++17 and above
Defines the member value as the log of N to base 2
Set to the integer below the ideal floating point value.
C++17 and above
```cpp
template <size_t N>
inline constexpr size_t log2_v = log2<N>::value;
``
____________________________________________________________________________________________________
log10
## log10
```cpp
template <size_t N>
struct log10;
```
Defines the member value as the log of N to base 10
Set to the integer below the ideal floating point value.
Header: *log.h*
C++17 and above
Defines the member value as the log of N to base 10
Set to the integer below the ideal floating point value.
C++17 and above
```cpp
template <size_t N>
inline constexpr size_t log10_v = log10<N>::value;
```
____________________________________________________________________________________________________
power.h
power
## power
```cpp
template <size_t N, size_t POWER>
struct power;
```
Defines the member value as N raised to the power POWER.
Header: *power.h*
C++17 and above
Defines the member value as N raised to the power `POWER`.
C++17 and above
```cpp
template <size_t N, size_t POWER>
inline constexpr size_t power_v = power<N, POWER>::value;
```
____________________________________________________________________________________________________
power_of_2_round_up
## power_of_2_round_up
```cpp
template <size_t N>
struct power_of_2_round_up;
```
Defines the member value to the next equal or higher power of 2.
Header: *power.h*
Defines the member value to the next equal or higher power of 2.
```cpp
power_of_2_round_up<7> -> 8
power_of_2_round_up<8> -> 8
power_of_2_round_up<9> -> 16
```
C++17 and above
C++17 and above
```cpp
template <size_t N, size_t POWER>
inline constexpr size_t power_of_2_round_up_v = power_of_2_round_up<N, POWER>::value;
____________________________________________________________________________________________________
power_of_2_round_down
```
## power_of_2_round_down
```cpp
template <size_t N>
struct power_of_2_round_down;
```
Defines the member value to the next equal or lower power of 2.
Header: *power.h*
Defines the member value to the next equal or lower power of 2.
```cpp
power_of_2_round_down<7> -> 4
power_of_2_round_down<8> -> 4
power_of_2_round_down<9> -> 8
```
C++17 and above
C++17 and above
```cpp
template <size_t N, size_t POWER>
inline constexpr size_t power_of_2_round_down_v = power_of_2_round_down<N, POWER>::value;
```
____________________________________________________________________________________________________
is_power_of_2
## is_power_of_2
```cpp
template <size_t N>
struct is_power_of_2;
```
Defines the member value to true if N is a power of 2, otherwise false.
Header: *power.h*
C++17 and above
Defines the member value to true if N is a power of 2, otherwise false.
C++17 and above
```cpp
template <size_t N, size_t POWER>
inline constexpr size_t is_power_of_2_v = is_power_of_2<N, POWER>::value;
```
____________________________________________________________________________________________________
sqrt.h
sqrt
## sqrt
```cpp
template <size_t N, size_t I = 1>
struct sqrt;
```
Defines the member value as the largest integer that, when squared, is at less than or equal to N.
Header: *sqrt.h*
C++17 and above
Defines the member value as the largest integer that, when squared, is at less than or equal to N.
C++17 and above
```cpp
template <size_t N, size_t I = 1>
inline constexpr size_t sqrt_v = sqrt<N, POWER>::value;
```
____________________________________________________________________________________________________
factorial.h
factorial
## factorial
```cpp
template <const size_t N>
struct factorial;
```
Defines the member value as the Nth factorial.
Header: *factorial.h*
C++17 and above
Defines the member value as the Nth factorial.
C++17 and above
```cpp
template <size_t N>
inline constexpr size_t factorial_v = factorial<N>::value;
```
____________________________________________________________________________________________________
fibbonacci.h
fibbonacci
## fibbonacci
```cpp
template <const size_t N>
struct fibbonacci;
```
Defines the member value as the Nth in the Fibbonacci sequence
Header: *fibbonacci.h*
C++17 and above
Defines the member value as the Nth in the Fibbonacci sequence
C++17 and above
```cpp
template <size_t N>
inline constexpr size_t fibbonacci_v = fibbonacci<N>::value;
```
____________________________________________________________________________________________________
math_constants.h
## Maths constants
Namespace : etl::math
Header: *math_constants.h*
Namespace : *etl::math*
```cpp
ETL_CONSTANT double pi = 3.14159265358979;
ETL_CONSTANT double pi_reciprocal = 0.31830988618379;
ETL_CONSTANT double pi_squared = 9.86960440108936;
@ -140,4 +195,4 @@ ETL_CONSTANT double root2 = 1.41421356237310;
ETL_CONSTANT double root2_reciprocal = 0.70710678118655;
ETL_CONSTANT double euler = 0.57721566490153;
ETL_CONSTANT double golden_ratio = 1.61803398874989;
```

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Correlation
20.9.0
---
title: "Correlation"
---
{{< callout type="info">}}
Header: `correlation.h`
Since: `20.9.0`
{{< /callout >}}
Calculates the correlation of two sets of data.
```cpp
template <bool Correlation_Type, typename TInput, typename TCalc = TInput>
class correlation : public etl::binary_function<TInput, TInput, void>
```
`Correlation_Type` `Population` or `Sample`.
`TInput` The input data type.
`TCalc` The type to use for internal calculations. By default, equal to `TInput`.
Correlation_Type Population or Sample.
TInput The input data type.
TCalc The type to use for internal calculations. By default, equal to TInput.
____________________________________________________________________________________________________
correlation_type
etl::correlation_type::Sample
etl::correlation_type::Population
____________________________________________________________________________________________________
correlation
**correlation_type**
`etl::correlation_type::Sample`
`etl::correlation_type::Population`
## Construction
```cpp
correlation()
```
**Description**
Default constructor.
---
```cpp
template <typename TIterator>
correlation(TIterator first1, TIterator last1, TIterator first2)
```
**Decsription**
Construct from two iterator ranges.
____________________________________________________________________________________________________
```cpp
void add(TInput value1, TInput value2)
```
**Description**
Add a pair of values.
## Member functions
```cpp
template <typename TIterator>
void add(TIterator first1, TIterator last1, TIterator first2)
```
**Description**
Add a range of values.
____________________________________________________________________________________________________
```cpp
void operator()(TInput value1, TInput value2)
```
Add a pair of values.
---
```cpp
template <typename TIterator>
void operator()(TIterator first1, TIterator last1, TIterator first2)
```
**Description**
Add a range of values.
____________________________________________________________________________________________________
double get_covariance() const
Returns the calculated covariance for the data.
____________________________________________________________________________________________________
double get_correlation() const
Returns the calculated correlation for the data.
____________________________________________________________________________________________________
operator double() const
Returns the calculated correlation for the data.
____________________________________________________________________________________________________
size_t count() const
Get the total number added entries.
____________________________________________________________________________________________________
void clear()
Clear the correlation.
____________________________________________________________________________________________________
Example
---
```cpp
double get_covariance() const
```
**Decsription**
Returns the calculated covariance for the data.
---
```cpp
double get_correlation() const
```
**Description**
Returns the calculated correlation for the data.
---
```cpp
operator double() const
```
**Description**
Returns the calculated correlation for the data.
---
```cpp
size_t count() const
```
**Description**
Get the total number added entries.
---
```cpp
void clear()
```
**Description**
Clear the correlation.
## Example
```cpp
std::array<char, 10> input_c
{
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
@ -71,4 +128,4 @@ double covariance_result;
correlation_result = correlation; // correlation_result == -1.0
covariance_result = correlation.get_covariance(); // covariance_result == -8.25
```

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---
title: "Covariance"
---
{{< callout type="info">}}
Header: `covariance.h`
Since: `20.9.0`
{{< /callout >}}
```cpp
template <bool Covariance_Type, typename TInput, typename TCalc = TInput>
class covariance : public etl::binary_function<TInput, TInput, void>
```
`Covariance_Type` `Population` or `Sample`.
`TInput` The input data type.
`TCalc` The type to use for internal calculations. By default, equal to `TInput`.
## covariance_type
`etl::covariance_type::Sample`
`etl::covariance_type::Population`
## Constructor
```cpp
covariance()
```
Default constructor.
---
```cpp
template <typename TIterator>
covariance(TIterator first1, TIterator last1, TIterator first2)
```
**Description**
Construct from two iterator ranges.
## Member functions
```cpp
void add(TInput value1, TInput value2)
```
**Description**
Add a pair of values.
```cpp
template <typename TIterator>
void add(TIterator first1, TIterator last1, TIterator first2)
```
**Description**
Add a range of values.
---
```cpp
void operator()(TInput value1, TInput value2)
```
**Description**
Add a pair of values.
---
```cpp
template <typename TIterator>
void operator()(TIterator first1, TIterator last1, TIterator first2)
```
**Description**
Add a range of values.
---
```cpp
double get_covariance() const
```
**Return**
The calculated covariance for the data.
---
```cpp
operator double() const
```
**Return**
The calculated covariance for the data.
---
```cpp
size_t count() const
```
**Description**
Get the total number added entries.
```cpp
void clear()
```
**Description**
Clear the covariance.
## Example
```cpp
std::array<char, 10> input_c
{
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
};
std::array<char, 10> input_c_inv
{
0, -1, -2, -3, -4, -5, -6, -7, -8, -9
};
etl::covariance<etl::covariance_type::Population, char, int32_t> covariance(input_c.begin(),
input_c.end(),
input_c_inv.begin());
double covariance_result;
covariance_result = covariance; // covariance_result == -8.25
```

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Gamma
20.9.0
---
title: "Gamma"
---
There are two gamma functors, gamma_encode and gamma_decode.
{{< callout type="info">}}
Header: `gamma.h`
Since: `20.9.0`
{{< /callout >}}
There are two gamma functors, `gamma_encode` and `gamma_decode`.
```cpp
template <typename TInput>
class gamma_encode : public etl::unary_function<TInput, TInput>
```
```cpp
template <typename TInput>
class gamma_decode : public etl::unary_function<TInput, TInput>
```
TInput The input data type.
____________________________________________________________________________________________________
`TInput` The input data type.
```cpp
gamma_encode(double gamma, TInput maximum)
```
**Description**
Constructor.
____________________________________________________________________________________________________
TInput operator()(TInput value) const
Gamma a value.
____________________________________________________________________________________________________
gamma_decode(double gamma, TInput maximum)
Constructor.
____________________________________________________________________________________________________
TInput operator()(TInput value) const
Gamma a value.
____________________________________________________________________________________________________
Example
---
```cpp
TInput operator()(TInput value) const
```
**Description**
Gamma a value.
---
```cpp
gamma_decode(double gamma, TInput maximum)
```
**Decsription**
Constructor.
---
```cpp
TInput operator()(TInput value) const
```
**Description**
Gamma a value.
## Example
```cpp
std::array<double, 10> input
{
0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0
@ -45,4 +72,4 @@ etl::gamma_decode<double> gamma_decode(0.5, 9.0);
std::transform(output_encode.begin(), output_encode.end(), output_decode.begin(), gamma_decode);
// output_decode == 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0
```

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---
title: "Histgram"
---
{{< callout type="info">}}
Header: `histogram.h`
Since: `20.9.0`
{{< /callout >}}
## Member types
`const_iterator` The iterator used to traverse the histogram data.
`key_type` The index type for the histogram.
`count_type` The type used for the histogram counter.
`value_type` The type returned from the histogram.
## Constants
`Max_Size` The maximum number of elements in the histogram.
## histogram
```cpp
template <typename TKey, typename TCount, size_t Max_Keys>
class histogram
```
**Description**
A histogram where the start index of the keys is defined in the constructor.
## Member functions
```cpp
histogram()
```
**Description**
Default constructor.
---
```cpp
template <typename TIterator>
histogram(TIterator first, TIterator last)
```
**Description**
Construct from an iterator range.
---
## histogram
```cpp
template <typename TKey, typename TCount, size_t Max_Keys, size_t Start_Index>
class histogram
```
**Description**
A histogram where the start index of the keys is defined as a template parameter.
## Member functions
```cpp
histogram()
```
**Description**
Default constructor.
---
```cpp
template <typename TIterator>
histogram(TIterator first, TIterator last)
```
**Description**
Construct from an iterator range.
---
```cpp
histogram(const histogram& other)
```
**Description**
Copy constructor.
---
```cpp
histogram(histogram&& other)
```
**Description**
Move constructor.
---
```cpp
histogram& operator =(const histogram& rhs)
```
**Description**
Assignment operator.
---
```cpp
histogram& operator =(histogram&& rhs)
```
**Description**
Move assignment operator.
---
```cpp
void add(key_type key)
```
**Description**
Increment the count for the key.
---
```cpp
template <typename TIterator>
void add(TIterator first, TIterator last)
```
**Description**
Increment the counts for the keys from an iterator range.
---
```cpp
void operator ()(key_type key)
```
**Description**
Increment the count for the key.
---
```cpp
template <typename TIterator>
void operator ()(TIterator first, TIterator last)
```
**Description**
Increment the counts for the keys from an iterator range.
---
```cpp
value_type operator [](key_type key) const
```
**Description**
Get the count for a key.
---
```cpp
const_iterator begin() const
const_iterator cbegin() const
```
**Description**
Get the iterator to the first histogram entry.
---
```cpp
const_iterator end() const
const_iterator cend() const
```
**Description**
Get the iterator to the last + 1 histogram entry.
---
```cpp
void clear()
```
**Description**
Clear the counts to zero.
---
```cpp
ETL_CONSTEXPR size_t size() const
```
Get the number of items in the histogram.
**Description**
Always equal to max_size().
---
```cpp
ETL_CONSTEXPR size_t max_size() const
```
**Description**
Get the number of items in the histogram.
---
```cpp
size_t count() const
```
**Description**
Get the total of all the counts.
## sparse_histogram
```cpp
template <typename TKey, typename TCount, size_t Max_Keys>
class sparse_histogram
```
**Description**
A histogram where the keys are sparse or non-integral types.
## Types
`const_iterator` The iterator used to traverse the histogram data.
`key_type` The index type for the histogram.
`count_type` The type used for the histogram counter.
`value_type` The type returned from the histogram. A pair containing the key and count.
## Constants
`Max_Size` The maximum number of elements in the histogram.
## Member functions
```cpp
sparse_histogram()
```
**Description**
Default constructor.
---
```cpp
template <typename TIterator>
sparse_histogram(TIterator first, TIterator last)
```
**Description**
Construct from an iterator range.
---
```cpp
sparse_histogram(const sparse_histogram& other)
```
**Description**
Copy constructor.
---
```cpp
sparse_histogram(sparse_histogram&& other)
```
**Description**
Move constructor.
---
```cpp
sparse_histogram& operator =(const sparse_histogram& rhs)
```
**Description**
Assignment operator.
---
```cpp
sparse_histogram& operator =(sparse_histogram&& rhs)
```
**Description**
Move assignment operator.
---
```cpp
void add(key_type key)
```
**Description**
Increment the count for the key.
---
```cpp
template <typename TIterator>
void add(TIterator first, TIterator last)
```
**Description**
Increment the counts for the keys from an iterator range.
---
```cpp
void operator ()(key_type key)
```
**Description**
Increment the count for the key.
---
```cpp
template <typename TIterator>
void operator ()(TIterator first, TIterator last)
```
**Description**
Increment the counts for the keys from an iterator range.
---
```cpp
const value_type& operator [](key_type key) const
```
**Description**
Get the count for a key.
---
```cpp
const_iterator begin() const
const_iterator cbegin() const
```
**Description**
Get the iterator to the first histogram entry.
---
```cpp
const_iterator end() const
const_iterator cend() const
```
**Description**
Get the iterator to the last + 1 histogram entry.
---
```cpp
void clear()
```
**Description**
Clear the counts to zero.
---
```cpp
ETL_CONSTEXPR size_t size() const
```
**Description**
Get the number of items in the histogram.
---
```cpp
ETL_CONSTEXPR size_t max_size() const
```
**Description**
Get the number of items in the histogram.
---
```cpp
size_t count() const
```
**Description**
Get the total of all the counts.

67
docs/raw/maths/Covariance.txt
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Covariance
20.9.0
template <bool Correlation_Type, typename TInput, typename TCalc = TInput>
class correlation : public etl::binary_function<TInput, TInput, void>
Covariance_Type Population or Sample.
TInput The input data type.
TCalc The type to use for internal calculations. By default, equal to TInput.
____________________________________________________________________________________________________
covariance_type
etl::covariance_type::Sample
etl::covariance_type::Population
____________________________________________________________________________________________________
covariance
covariance()
Default constructor.
template <typename TIterator>
covariance(TIterator first1, TIterator last1, TIterator first2)
Construct from two iterator ranges.
____________________________________________________________________________________________________
void add(TInput value1, TInput value2)
Add a pair of values.
template <typename TIterator>
void add(TIterator first1, TIterator last1, TIterator first2)
Add a range of values.
____________________________________________________________________________________________________
void operator()(TInput value1, TInput value2)
Add a pair of values.
template <typename TIterator>
void operator()(TIterator first1, TIterator last1, TIterator first2)
Add a range of values.
____________________________________________________________________________________________________
double get_covariance() const
Returns the calculated covariance for the data.
____________________________________________________________________________________________________
operator double() const
Returns the calculated covariance for the data.
____________________________________________________________________________________________________
size_t count() const
Get the total number added entries.
____________________________________________________________________________________________________
void clear()
Clear the covariance.
____________________________________________________________________________________________________
Example
std::array<char, 10> input_c
{
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
};
std::array<char, 10> input_c_inv
{
0, -1, -2, -3, -4, -5, -6, -7, -8, -9
};
etl::covariance<etl::covariance_type::Population, char, int32_t> covariance(input_c.begin(),
input_c.end(),
input_c_inv.begin());
double covariance_result;
covariance_result = covariance; // covariance_result == -8.25

157
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Histogram
20.9.0
____________________________________________________________________________________________________
histogram
Types
const_iterator The iterator used to traverse the histogram data.
key_type The index type for the histogram.
count_type The type used for the histogram counter.
value_type The type returned from the histogram.
____________________________________________________________________________________________________
Constants
Max_Size The maximum number of elements in the histogram.
____________________________________________________________________________________________________
template <typename TKey, typename TCount, size_t Max_Keys>
class histogram
A histogram where the start index of the keys is defined in the constructor.
histogram()
Default constructor.
template <typename TIterator>
histogram(TIterator first, TIterator last)
Construct from an iterator range.
____________________________________________________________________________________________________
template <typename TKey, typename TCount, size_t Max_Keys, size_t Start_Index>
class histogram
A histogram where the start index of the keys is defined as a template parameter.
histogram()
Default constructor.
template <typename TIterator>
histogram(TIterator first, TIterator last)
Construct from an iterator range.
____________________________________________________________________________________________________
histogram(const histogram& other)
Copy constructor.
histogram(histogram&& other)
Move constructor.
histogram& operator =(const histogram& rhs)
Assignment operator.
histogram& operator =(histogram&& rhs)
Move assignment operator.
____________________________________________________________________________________________________
void add(key_type key)
Increment the count for the key.
template <typename TIterator>
void add(TIterator first, TIterator last)
Increment the counts for the keys from an iterator range.
____________________________________________________________________________________________________
void operator ()(key_type key)
Increment the count for the key.
template <typename TIterator>
void operator ()(TIterator first, TIterator last)
Increment the counts for the keys from an iterator range.
____________________________________________________________________________________________________
value_type operator [](key_type key) const
Get the count for a key.
____________________________________________________________________________________________________
const_iterator begin() const
const_iterator cbegin() const
Get the iterator to the first histogram entry.
____________________________________________________________________________________________________
const_iterator end() const
const_iterator cend() const
Get the iterator to the last + 1 histogram entry.
____________________________________________________________________________________________________
void clear()
Clear the counts to zero.
____________________________________________________________________________________________________
ETL_CONSTEXPR size_t size() const
Get the number of items in the histogram.
Always equal to max_size().
____________________________________________________________________________________________________
ETL_CONSTEXPR size_t max_size() const
Get the number of items in the histogram.
____________________________________________________________________________________________________
size_t count() const
Get the total of all the counts.
____________________________________________________________________________________________________
sparse_histogram
Types
const_iterator The iterator used to traverse the histogram data.
key_type The index type for the histogram.
count_type The type used for the histogram counter.
value_type The type returned from the histogram. A pair containing the key and count.
____________________________________________________________________________________________________
Constants
Max_Size The maximum number of elements in the histogram.
____________________________________________________________________________________________________
template <typename TKey, typename TCount, size_t Max_Keys>
class sparse_histogram
A histogram where the keys are sparse or non-integral types.
sparse_histogram()
Default constructor.
template <typename TIterator>
sparse_histogram(TIterator first, TIterator last)
Construct from an iterator range.
sparse_histogram(const sparse_histogram& other)
Copy constructor.
sparse_histogram(sparse_histogram&& other)
Move constructor.
sparse_histogram& operator =(const sparse_histogram& rhs)
Assignment operator.
sparse_histogram& operator =(sparse_histogram&& rhs)
Move assignment operator.
____________________________________________________________________________________________________
void add(key_type key)
Increment the count for the key.
template <typename TIterator>
void add(TIterator first, TIterator last)
Increment the counts for the keys from an iterator range.
____________________________________________________________________________________________________
void operator ()(key_type key)
Increment the count for the key.
template <typename TIterator>
void operator ()(TIterator first, TIterator last)
Increment the counts for the keys from an iterator range.
____________________________________________________________________________________________________
const value_type& operator [](key_type key) const
Get the count for a key.
____________________________________________________________________________________________________
const_iterator begin() const
const_iterator cbegin() const
Get the iterator to the first histogram entry.
____________________________________________________________________________________________________
const_iterator end() const
const_iterator cend() const
Get the iterator to the last + 1 histogram entry.
____________________________________________________________________________________________________
void clear()
Clear the counts to zero.
____________________________________________________________________________________________________
ETL_CONSTEXPR size_t size() const
Get the number of items in the histogram.
____________________________________________________________________________________________________
ETL_CONSTEXPR size_t max_size() const
Get the number of items in the histogram.
____________________________________________________________________________________________________
size_t count() const
Get the total of all the counts.

24
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absolute
A template functions that return the absolute value.
____________________________________________________________________________________________________
template <typename T>
ETL_CONSTEXPR T absolute(T value)
Returns the absolute of value.
If T is int8_t:-
0 => 0
127 => 127
-127 => 127
____________________________________________________________________________________________________
template <typename T>
ETL_CONSTEXPR etl::make_unsigned_t<T> absolute_unsigned(T value)
Returns the absolute of value, cast to the unsigned version of type T.
If T is int8_t:-
Return type is etl::make_unsigned_t<T>
0 => 0
127 => 127
-127 => 127
-128 => 128

30
docs/raw/maths/comb-perm.txt
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Combinations / Permutations
Templates to provide combinations and permutations constants.
____________________________________________________________________________________________________
Combinations
template <size_t N, size_t K>
struct combinations
Member const
static ETL_CONSTEXPR size_t value = Number of combinations of K items from a total of N
If C++17 is supported.
template <size_t N, size_t K>
inline constexpr size_t combinations_v = combinations<N, K>::value;
____________________________________________________________________________________________________
Permutations
template <size_t N, size_t K>
struct permutations
Member const
static ETL_CONSTEXPR size_t value = Number of permutations of K items from a total of N
If C++17 is supported.
template <size_t N, size_t K>
inline constexpr size_t permutations_v = permutations<N, K>::value;