Detailed Description

Mathematics helper functions. Min/max functions, functions to uniformly increase the effective bit depth, etc.

Collaboration diagram for Math Utilities:

Topics
	Math Types
	Vector and Quaternion types with the necessary operators and functions.

Functions
template<class T >
constexpr std::enable_if< std::is_floating_point< T >::value, T >::type	rad2deg (T r)
	Convert radians to degrees.

template<class T >
constexpr std::enable_if< std::is_floating_point< T >::value, T >::type	deg2rad (T d)
	Convert degrees to radians.

template<size_t Bits_out, size_t Bits_in, class T_out , class T_in >
T_out	increaseBitDepth (T_in in)
	Increase the bit depth of the given value from `Bits_in` bits wide to `Bits_out` bits wide, (approximately) evenly distributing the error across the entire range, such that the error for each element is between -1 and +1.

template<size_t Bits_out, size_t Bits_in, class T_out , class T_in >
T_out	increaseBitDepthMiddle (T_in in)
	Increase the bit depth of the given value from `Bits_in` bits wide to `Bits_out` bits wide, while ensuring that the middle of the input range maps exactly to the middle of the output range, i.e.

template<class T , class U >
constexpr auto	min (const T &a, const U &b) -> decltype(b< a ? b :a)
	Return the smaller of two numbers/objects.

template<class T , class U >
constexpr auto	max (const T &a, const U &b) -> decltype(a< b ? b :a)
	Return the larger of two numbers/objects.

Function Documentation

◆ rad2deg()

template<class T >

constexpr std::enable_if< std::is_floating_point< T >::value, T >::type rad2deg ( T r )

inlineconstexpr

Convert radians to degrees.

Definition at line 24 of file Degrees.hpp.

◆ deg2rad()

template<class T >

constexpr std::enable_if< std::is_floating_point< T >::value, T >::type deg2rad ( T d )

inlineconstexpr

Convert degrees to radians.

Definition at line 31 of file Degrees.hpp.

◆ increaseBitDepth()

template<size_t Bits_out, size_t Bits_in, class T_out , class T_in >

T_out increaseBitDepth ( T_in in )

Increase the bit depth of the given value from Bits_in bits wide to Bits_out bits wide, (approximately) evenly distributing the error across the entire range, such that the error for each element is between -1 and +1.

See also: increaseBitDepthMiddle

For example, converting 3-bit numbers to 7-bit numbers would result in the following:

in (dec)	in (bin)	out (bin)	out (dec)	exact	error
0	000	000'0000	0	0.00	+0.00
1	001	001'0010	18	18.14	+0.14
2	010	010'0100	36	36.29	+0.29
3	011	011'0110	54	54.43	+0.43
4	100	100'1001	73	72.57	-0.43
5	101	101'1011	91	90.71	-0.29
6	110	110'1101	109	108.86	-0.14
7	111	111'1111	127	127.00	+0.00

The following is a comparison to the increaseBitDepthMiddle function.

Template Parameters

Bits_out	The number of bits of the output range.
Bits_in	The number of bits of the input range.
T_out	The type of the output (return type).
T_in	The type of the input.

Parameters

in	The value to scale up.

Returns: The scaled up value.

Definition at line 77 of file IncreaseBitDepth.hpp.

◆ increaseBitDepthMiddle()

template<size_t Bits_out, size_t Bits_in, class T_out , class T_in >

T_out increaseBitDepthMiddle ( T_in in )

Increase the bit depth of the given value from Bits_in bits wide to Bits_out bits wide, while ensuring that the middle of the input range maps exactly to the middle of the output range, i.e.

\( 2^{\texttt{Bits\_in} - 1} \) maps to \( 2^{\texttt{Bits\_out} - 1} \).

See also: increaseBitDepth

For example, converting 3-bit numbers to 7-bit numbers would result in the following:

in (dec)	in (bin)	out (bin)	out (dec)	exact	error
0	000	000'0000	0	0.00	+0.00
1	001	001'0000	16	18.14	-2.14
2	010	010'0000	32	36.29	-4.29
3	011	011'0000	48	54.43	-6.43
4	100	100'0000	64	72.57	-8.57
5	101	101'0101	85	90.71	-5.71
6	110	110'1010	106	108.86	-2.86
7	111	111'1111	127	127.00	+0.00

The following is a comparison to the increaseBitDepth function.

Template Parameters

Bits_out	The number of bits of the output range.
Bits_in	The number of bits of the input range.
T_out	The type of the output (return type).
T_in	The type of the input.

Parameters

in	The value to scale up.

Returns: The scaled up value.

Definition at line 125 of file IncreaseBitDepth.hpp.

◆ min()

template<class T , class U >

constexpr auto min	(	const T &	a,
		const U &	b ) -> decltype(b < a ? b : a)

constexpr

Return the smaller of two numbers/objects.

Examples: Blink-Frequency-Buttons.ino.

Definition at line 12 of file MinMaxFix.hpp.

◆ max()