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‎LICENCE‎

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Apache License
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‎README.md‎

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# FixedPointsArduino
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A Fixed Points Library For Arduino
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# FixedPoints
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A portable fixed point arithmetic library.
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Some knowledge of how fixed point types are formatted is required to used this library to full effect.
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No knowledge of how these operations are implemented is required to use them.
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This library was written with Arduino in mind, as well as CPUs with limited floating point support.
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However, given the templated nature of the library, it should still function on a wide variety of CPUs.
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## Requirements:
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- The Compiler must be C++11 compliant.
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- The user should ideally be familar with the [Q number format](https://en.wikipedia.org/wiki/Q_(number_format)) for fixed points.
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## Licence
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This code uses the Apache 2.0 Licence.
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This means:
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- This code comes with no warranty.
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- The licensor and any contributors cannot be held liable for damages.
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- If you use this code, edited or unedited, you must:
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- Package a copy of LICENCE with your code.
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- Package a copy of NOTICE with your code.
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- You may modify the source code.
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- If you modify a file, you must state this prominently in the file (i.e. in a comment at the top).
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- Any modified code may use a different licence.
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- Any unmodified code must carry the same Apache 2.0 licence.
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- You may not use any trademarks owned by the licensor.
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## Contents
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This library supplies two core types and sixteen type aliases.
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### Core Types:
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The core types are provided by `FixedPoints.h`.
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- `UFixed<I, F>`: An unsigned fixed point type where I is the number of bits used for the integer part of the number and F is the number of bits used for the fractional part of the number.
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- `SFixed<I, F>`: An signed fixed point type where I is the number of bits used for the integer part of the number (excluding the implicit sign bit) and F is the number of bits used for the fractional part of the number.
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### Aliases:
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The common aliases are provided by `FixedPointsCommon.h`.
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- `UQ4x4`: An alias for `UFixed<4, 4>`, an 8-bit unsigned fixed point in the Q4.4 format.
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- `UQ8x8`: An alias for `UFixed<8, 8>`, a 16-bit unsigned fixed point in the Q8.8 format.
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- `UQ16x16`: An alias for `UFixed<16, 16>`, a 32-bit unsigned fixed point in the Q16.16 format.
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- `UQ32x32`: An alias for `UFixed<32, 32>`, a 64-bit unsigned fixed point in the Q32.32 format.
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- `UQ1x7`: An alias for `UFixed<1, 7>`, an 8-bit unsigned fixed point in the Q1.7 format.
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- `UQ1x15`: An alias for `UFixed<1, 15>`, a 16-bit unsigned fixed point in the Q1.15 format.
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- `UQ1x31`: An alias for `UFixed<1, 31>`, a 32-bit unsigned fixed point in the Q1.31 format.
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- `UQ1x63`: An alias for `UFixed<1, 63>`, a 64-bit unsigned fixed point in the Q1.63 format.
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- `SQ3x4`: An alias for `SFixed<3, 4>`, an 8-bit signed fixed point in the Q3.4 format with implicit sign bit.
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- `SQ7x8`: An alias for `SFixed<7, 8>`, a 16-bit signed fixed point in the Q7.8 format with implicit sign bit.
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- `SQ15x16`: An alias for `SFixed<15, 16>`, a 32-bit signed fixed point in the Q15.16 format with implicit sign bit.
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- `SQ31x32`: An alias for `SFixed<31, 32>`, a 64-bit signed fixed point in the Q31.32 format with implicit sign bit.
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- `SQ1x6`: An alias for `SFixed<1, 6>`, an 8-bit signed fixed point in the Q1.6 format with implicit sign bit.
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- `SQ1x14`: An alias for `SFixed<1, 14>`, a 16-bit signed fixed point in the Q1.14 format with implicit sign bit.
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- `SQ1x30`: An alias for `SFixed<1, 30>`, a 32-bit signed fixed point in the Q1.30 format with implicit sign bit.
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- `SQ1x62`: An alias for `SFixed<1, 62>`, a 64-bit signed fixed point in the Q1.62 format with implicit sign bit.
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([About Q Format](https://en.wikipedia.org/wiki/Q_(number_format)).)
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### Operators:
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- `+`: Adds two `UFixed`s or two `SFixed`s
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- `-`: Subtracts two `UFixed`s or two `SFixed`s
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- `*`: Multiplies two `UFixed`s or two `SFixed`s
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- `/`: Divides two `UFixed`s or two `SFixed`s
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- `==`: Compares two `UFixed`s or two `SFixed`s
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- `!=`: Compares two `UFixed`s or two `SFixed`s
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- `<`: Compares two `UFixed`s or two `SFixed`s
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- `<=`: Compares two `UFixed`s or two `SFixed`s
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- `>`: Compares two `UFixed`s or two `SFixed`s
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- `>=`: Compares two `UFixed`s or two `SFixed`s
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### Free Functions:
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- `floorFixed`: The floor operation.
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- `ceilFixed`: The Ceiling operation
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- `roundFixed`: Rounding operation.
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- `truncFixed`: Truncation operation.
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- `signbitFixed`: Returns `true` for signed numbers and `false` for unsigned numbers.
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- `copysignFixed`: Returns a value with the magnitude of the first argument and the sign of the second argument.
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- `multiply`: Multiplies two `UFixed`s or two `SFixed`s, returns a result that is twice the resolution of the input.
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### Member Functions:
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- `UFixed<I, F>::getInteger`: Gets the integer part of an unsigned fixed point.
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- `UFixed<I, F>::getFraction`: Gets the fractional part of an unsigned fixed point.
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- `UFixed<I, F>::getInternal`: Gets the internal representation of an unsigned fixed point.
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- `SFixed<I, F>::getInteger`: Gets the integer part of a signed fixed point.
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- `SFixed<I, F>::getFraction`: Gets the fractional part of a signed fixed point.
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- `SFixed<I, F>::getInternal`: Gets the internal representation of a signed fixed point.
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### Static Functions:
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- `UFixed<I, F>::fromInternal`: Produces an unsigned fixed point number from its internal representation.
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- `SFixed<I, F>::fromInternal`: Produces a signed fixed point number from its internal representation.
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## Construction:
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Note that both `UFixed<I, F>` and `SFixed<I, F>` are implicitly compile-time constructable from all integer and decimal literals.
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This means that you may write code such as `UFixed<8, 8> value = 0.5;` without incurring a runtime cost for converting from `double` to `UFixed<8, 8>` because the constructor is `constexpr`.
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`UFixed<I, F>` is constructable from:
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- Any integer literal type, regardless of sign.
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-- This constructs the fixed point as an integer with no fractional part.
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-- A value that does not fit shall be truncated without warning.
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-- If a constant value is used, the fixed point shall be constructed at compile time.
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- An unsigned integer part and an unsigned fractional part.
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-- The integer part is of the smallest type capable of representing `I` bits.
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-- The fractional part is of the smallest type capable of representing `F` bits.
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-- If constant values are used, the fixed point shall be constructed at compile time.
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- Any decimal literal type, regardless of sign.
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-- This constructs the fixed point as a best approximation of the provided value.
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-- A value that does not fit shall be truncated without warning.
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-- If a constant value is used, the fixed point shall be constructed at compile time.
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`SFixed<I, F>` is constructable from:
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- Any integer literal type, regardless of sign.
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-- This constructs the fixed point as an integer with no fractional part.
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-- A value that does not fit shall be truncated without warning.
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-- If a constant value is used, the fixed point shall be constructed at compile time.
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- A signed integer part and an unsigned fractional part.
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-- The integer part is of the smallest type capable of representing `I + 1` bits.
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-- The fractional part is of the smallest type capable of representing `F` bits.
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-- If constant values are used, the fixed point shall be constructed at compile time.
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- Any decimal literal type, regardless of sign.
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-- This constructs the fixed point as a best approximation of the provided value.
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-- A value that does not fit shall be truncated without warning.
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-- If a constant value is used, the fixed point shall be constructed at compile time.
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### Casts:
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`UFixed<I, F>` is explicitly convertible to:
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- `float`.
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- `double`.
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- The smallest unsigned type capable of holding its integer part. I.e. a type of at least `I` bits.
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- Another `UFixed` type of a different scale. E.g. `UFixed<4, 4>` may be converted to `UFixed<8, 8>` and vice versa.
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`SFixed<I, F>` is explicitly convertible to:
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- `float`.
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- `double`.
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- The smallest signed type capable of holding its integer part. I.e. a type of at least `I + 1` bits.
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- Another `SFixed` type of a different scale. E.g. `SFixed<3, 4>` may be converted to `SFixed<7, 8>` and vice versa.
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