Elementary Functions¶
argmax¶
- template<bool
minIndex= false, typenameT>
INLINE qVar_t<std::int32_t>qmath::argmax(qVar_t<T> qIn[], const std::int32_t tiles)¶Get the max index for an array of data.
- Return
the index of the max element
- Template Parameters
minIndex: by default, the function returns an arbitrary element in case of a tie, set minIndex to true if a min index is required, requiring a min index will incur some overhead
T: type for the input- Parameters
qIn: input, will be overwriteen with max value
tiles: the number of tiles
- template<bool
minIndex= false, typenameT>
INLINE qVar_t<std::int32_t>qmath::argmax(qVar_t<T> &qIn)¶Get the max index for a tile of data.
- Return
the index of the max element
- Template Parameters
minIndex: by default, the function returns an arbitrary element in case of a tie, set minIndex to true if a min index is required, requiring a min index will incur some overhead
T: type for the input- Parameters
qIn: input, will be overwriteen with max value
cos¶
- template<FracRepType
numFracBits, booltransformRange= false, typenameT, IfIntegerTy<T> = 0>
INLINE qVar_t<T>qmath::cos(const qVar_t<T> &inp)¶Computes cosine of input qVar.
- Template Parameters
T: Underlying type of qVar (deductible)
numIntBits: Number of bits used for integer part
numFracBits: Number of bits used for fractional part
transformRange: allows input with arbitrary value, produces additional overhead- Parameters
[in] inp: The input theta in radians (between -pi/2 and pi/2) qVar. Input type is 32-bit fixed point. `*. Error Table:* Number of Fractional Bits | Percent of Fixed Point computes w/ rel. error greater than 1e-4 | Maximum Absolute Error * 2 | 84.6 | 2.47e-1 * 3 | 92.0 | 1.25e-1 * 4 | 96.1 | 6.25e-2 * 5 | 98.0 | 3.12e-2 * 6 | 99.0 | 1.56e-2 * 7 | 98.5 | 7.81e-3 * 8 | 97.0 | 3.91e-3 * 9 | 95.5 | 1.95e-3 * 10 | 93.3 | 9.77e-4 * 11 | 87.9 | 4.88e-4 * 12 | 74.3 | 2.44e-4 * 13 | 48.0 | 1.22e-4 * 14 | 20.3 | 6.11e-5 * 15 | 10.0 | 3.05e-5 * 16 | 5.00 | 1.53e-5 * 17 | 2.40 | 7.66e-6 * 18 | 1.42 | 3.84e-6 * 19 | 0.678 | 1.94e-6 * 20 | 0.197 | 1.01e-6 * 21 | 0.197 | 5.36e-7 * 22 | 0.0480 | 2.98e-7 * 23 | 0.0480 | 1.79e-7 * 24 | 0.0256 | 1.79e-7 * 25 | 0.0220 | 1.49e-7 * 26 | 0.0203 | 1.27e-7 * 27 | 0.0195 | 1.19e-7 * 28 | 0.0193 | 1.19e-7 * 29 | 0.0193 | 1.19e-7 *
exp¶
- template<FracRepType
numFracBits, typenameT, IfIntegerTy<T> = 0>
INLINE qVar_t<T>qmath::exp(const qVar_t<T> &inp)¶Computes Natural Exponent of input variable.
- Template Parameters
numFracBits: Number of bits used for fractional part
T: Underlying type of qVar (deductible)- Parameters
[in] inp: The input value. Input type is 32-bit fixed point.
incrementMagnitudeByHalf¶
- template<FracRepType
numFracBits, typenameT>
INLINE const qVar_t<T>qmath::incrementMagnitudeByHalf(const qVar_t<T> &op)¶performs fixed point increment which involves adding (1 << (numFracBits - 1)) in magnitude
- Return
qVar_t<T> Fixed point result
- Template Parameters
numFracBits: Number of Fraction bits used to represent fixed point input- Parameters
op: represented in fixed point
inverseSqrt¶
- template<FracRepType
numFracBits, typenameT>
INLINE qVar_t<FixedPoint<T, numFracBits>>qmath::inverseSqrt(const qVar_t<FixedPoint<T, numFracBits>> &qX)¶Computes inverse sqrt of input qVar using Newton’s Method.
see
https://www.geometrictools.com/Documentation/ApproxInvSqrt.pdf
- Template Parameters
T: Underlying type of qVar (deductible)
numFracBits: Number of bits used for fractional part- Parameters
[in] x: The input of the square-root function
log¶
- template<FracRepType
numFracBits, typenameT>
INLINE qVar_t<FixedPoint<T, numFracBits>>qmath::log(const qVar_t<FixedPoint<T, numFracBits>> &inp)¶Computes natural logarithm of input qVar. The expected input type is signed 32-bit fixed-point with 16 bits for integer part and 16 bits for fractional part. The output will be generated in the same fashion.
https://www.quinapalus.com/efunc.html
- Template Parameters
T: Underlying type of qVar (deductible)
numIntBits: Number of bits used for integer part.
numFracBits: Number of bits used for fractional part.- Parameters
[in] inp: The input qVar. Input type is 32-bit fixed point.* Error Table: * Number of Fractional Bits | Percent of Fixed Point computes w/ rel. error greater than 1e-4 | Maximum Absolute Error * 5 | 95.8 | 1.40e-1 * 6 | 97.4 | 9.18e-2 * 7 | 95.4 | 5.25e-3 * 8 | 88.3 | 2.49e-2 * 9 | 63.4 | 1.04e-2 * 10 | 35.1 | 4.78e-3 * 11 | 2.84 | 2.10e-3 * 12 | 0.018 | 9.13e-4 * 13 | 0.00200 | 4.02e-4 * 14 | 0.000754 | 1.79e-4 * 15 | 0.000920 | 8.92e-5 * 16 | 0.00204 | 7.77e-5 * 17 | 0.00214 | 5.02e-5 * 18 | 0.00261 | 4.08e-5 * 19 | 0.00596 | 3.67e-5 * 20 | 0.0101 | 3.29e-5 * 21 | 0.0202 | 3.19e-5 * 22 | 0.0389 | 3.09e-5 * 23 | 0.0763 | 3.09e-5 * 24 | 0.152 | 3.05e-5 * 25 | 0.302 | 3.05e-5 * 26 | 0.604 | 3.05e-5 * 27 | 1.21 | 3.05e-5 | 3.05e-5 *
log2¶
sin¶
- template<FracRepType
numFracBits, booltransformRange= false, typenameT, IfIntegerTy<T> = 0>
INLINE qVar_t<T>qmath::sin(const qVar_t<T> &inp)¶Computes sine of input qVar.
- Template Parameters
T: Underlying type of qVar (deductible)
numIntBits: Number of bits used for integer part
numFracBits: Number of bits used for fractional part
transformRange: allows input with arbitrary value, produces additional overhead- Parameters
[in] inp: The input theta in radians (between -pi/2 and pi/2) qVar. Input type is 32-bit fixed point. . Error Table:* Number of Fractional Bits | Percent of Fixed Point computes w/ rel. error greater than 1e-4 | Maximum Absolute Error * 2 | 84.6 | 2.47e-1 * 3 | 92.0 | 1.25e-1 * 4 | 96.1 | 6.25e-2 * 5 | 98.0 | 3.12e-2 * 6 | 99.0 | 1.56e-2 * 7 | 98.5 | 7.81e-3 * 8 | 97.0 | 3.91e-3 * 9 | 95.5 | 1.95e-3 * 10 | 93.3 | 9.77e-4 * 11 | 87.9 | 4.88e-4 * 12 | 74.3 | 2.44e-4 * 13 | 48.0 | 1.22e-4 * 14 | 20.3 | 6.11e-5 * 15 | 10.0 | 3.05e-5 * 16 | 5.00 | 1.53e-5 * 17 | 2.40 | 7.66e-6 * 18 | 1.42 | 3.84e-6 * 19 | 0.678 | 1.94e-6 * 20 | 0.197 | 1.01e-6 * 21 | 0.197 | 5.36e-7 * 22 | 0.0480 | 2.98e-7 * 23 | 0.0480 | 1.79e-7 * 24 | 0.0256 | 1.79e-7 * 25 | 0.0220 | 1.49e-7 * 26 | 0.0203 | 1.27e-7 * 27 | 0.0195 | 1.19e-7 * 28 | 0.0193 | 1.19e-7 * 29 | 0.0193 | 1.19e-7 *
sqrt¶
- template<FracRepType
numFracBits, typenameT>
INLINE qVar_t<FixedPoint<T, numFracBits>>qmath::sqrt(qVar_t<FixedPoint<T, numFracBits>> qX)¶Computes sqrt of input qVar using Newton’s Method.
- Template Parameters
T: Underlying type of qVar (deductible)
numFracBits: Number of bits used for fractional part- Parameters
[in] x: The input of the square-root function
stdRound¶
- template<FracRepType
numFracBits, typenameT>
INLINE const qVar_t<T>qmath::stdRound(const qVar_t<T> &op)¶performs fixed point round which involves adding (1 << (numFracBits - 1)) then two shifts (and negation if necessary). Rounding at 0.5 is away from 0
- Return
qVar_t<T> Fixed point result
- Template Parameters
numFracBits: Number of Fraction bits used to represent fixed point input- Parameters
op: represented in fixed point
vectorMag¶
- template<FracRepType
numFracBits, typenameT, IfIntegerTy<T> = 0>
INLINE qVar_t<T>qmath::vectorMag(qVar_t<T> &x, qVar_t<T> &y)¶Computes magnitude of input qVar. Ranges will vary based on inputs but it recommended to use one more more integer bit to represent the largest input.
- Template Parameters
T: Underlying type of qVar (deductible)
numIntBits: Number of bits used for integer part
numFracBits: Number of bits used for fractional part- Parameters
[in] x: The input in the x dimension (gets flipped if negative). Input type is 32-bit fixed point.
[in] y: The input in the y dimension. Input type is 32-bit fixed point.