etl/docs/maths/constants.md

---
title: "Constants"
---

A set of compile time constants.

## log
```cpp
template <size_t N, size_t BASE>
struct log;
```

Header: *log.h*  

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
```cpp
template <size_t N>
struct log2;
```

Header: *log.h*  

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
```cpp
template <size_t N>
struct log10;
```

Header: *log.h*  

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
```cpp
template <size_t N, size_t POWER> 
struct power;
```

Header: *power.h*  

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
```cpp
template <size_t N> 
struct power_of_2_round_up;
```

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  
```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
```cpp
template <size_t N> 
struct power_of_2_round_down;
```

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  
```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
```cpp
template <size_t N> 
struct is_power_of_2;
```

Header: *power.h*  

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
```cpp
template <size_t N, size_t I = 1>
struct sqrt;
```

Header: *sqrt.h*  

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
```cpp
template <const size_t N> 
struct factorial;
```

Header: *factorial.h*  

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
```cpp
template <const size_t N> 
struct fibbonacci;
```

Header: *fibbonacci.h*  

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;
```

## Maths constants

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;
ETL_CONSTANT double e                = 2.71828182845905;
ETL_CONSTANT double e_reciprocal     = 0.36787944117144;
ETL_CONSTANT double e_squared        = 7.38905609893065;
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;
```