Math functions¶

qm.qua.lib.Math ¶

MSB `staticmethod` ¶

MSB(x: Scalar[NumberT]) -> QuaLibFunctionOutput[int]

Finds the index of the most significant bit in the parameter x. Notes:

Result is independent of sign, for example, +3 and -3 will return the same msb
The returned value will be the closet log2, rounded down.

This is given by \(\mathrm{floor}(\mathrm{log}_2(|x|))\).

For example:

msb(0.1) will return -4.
msb(5) will return 2.
For an integer, msb(0) will return 0.
For a fixed point number, msb(0) will return -28.

PARAMETER	DESCRIPTION
`x`	a QUA fixed or a QUA int TYPE: `Scalar[NumberT]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[int]`	a QUA int

abs `staticmethod` ¶

abs(x: ScalarOfAnyType) -> QuaLibFunctionOutput[float]

Computes the absolute value of x

PARAMETER	DESCRIPTION
`x`	a QUA variable TYPE: `ScalarOfAnyType`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

aelu `staticmethod` ¶

aelu(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes faster an approximated Exponential Linear Unit activation function of x \(\mathrm{aELU}(x) \sim \mathrm{ELU}(x)\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

argmax `staticmethod` ¶

argmax(x: Vector[NumberT]) -> QuaLibFunctionOutput[int]

Return the index of the maximum of an array

PARAMETER	DESCRIPTION
`x`	a QUA array TYPE: `Vector[NumberT]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[int]`	the index of maximum value of array, a QUA Integer

argmin `staticmethod` ¶

argmin(x: Vector[NumberT]) -> QuaLibFunctionOutput[int]

Return the index of the minimum of an array

PARAMETER	DESCRIPTION
`x`	a QUA array TYPE: `Vector[NumberT]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[int]`	the index of minimum value of array, a QUA Integer

atan `staticmethod` ¶

atan(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{atan}(x)\)

-- Available from QOP 2.4 --

PARAMETER	DESCRIPTION
`x`	the tangent ratio (opposite/adjacent) TYPE: `a QUA fixed which is -1 <= x <= 1`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

atan2 `staticmethod` ¶

atan2(
    y: Scalar[float], x: Scalar[float]
) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{atan2}(y,x)\)

-- Available from QOP 2.4 --

PARAMETER	DESCRIPTION
`y`	the coordinate y (opposite) TYPE: `a QUA fixed`
`x`	the coordinate x (adjacent) TYPE: `a QUA fixed`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

atan2_2pi `staticmethod` ¶

atan2_2pi(
    y: Scalar[float], x: Scalar[float]
) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{1/2 \pi * atan2}(y,x)\)

-- Available from QOP 2.4 --

PARAMETER	DESCRIPTION
`y`	The coordinate y (opposite) TYPE: `a QUA fixed`
`x`	The coordinate x (adjacent) TYPE: `a QUA fixed`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

atan_2pi `staticmethod` ¶

atan_2pi(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{1/2 \pi * atan}(x)\)

-- Available from QOP 2.4 --

PARAMETER	DESCRIPTION
`x`	The tangent ratio (opposite/adjacent) TYPE: `a QUA fixed`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

cos `staticmethod` ¶

cos(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{cos}(x)\)

PARAMETER	DESCRIPTION
`x`	the angle in radians TYPE: `QUA variable of type fixed`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

cos2pi `staticmethod` ¶

cos2pi(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{cos}(2 \pi x)\). This is more efficient than Math.cos(\(2 \pi x\)). In addition, this function is immune to overflows: An overflow means that the argument gets a :math:\pm 16, which does not change the result due to the periodicity of the cosine function.

PARAMETER	DESCRIPTION
`x`	the angle in radians TYPE: `QUA variable of type fixed`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

div `staticmethod` ¶

div(x: Scalar[int], y: Scalar[int]) -> Any

div(
    x: Scalar[float], y: Scalar[float]
) -> QuaLibFunctionOutput[float]

div(
    x: Scalar[NumberT], y: Scalar[NumberT]
) -> QuaLibFunctionOutput[float]

Computes the division between two same-type variables \(x/y\). Takes integer and fixed variables as long as both are of the same type. When both inputs are integer, the actual result type (int or fixed) is determined by how the result is used - e.g. the type of the variable it is assigned to. When assigned to an int variable, the result is \(floor(x/y)\).

PARAMETER	DESCRIPTION
`x`	a QUA int or fixed TYPE: `Scalar[NumberT]`
`y`	a QUA int or fixed TYPE: `Scalar[NumberT]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA int or fixed

dot `staticmethod` ¶

dot(
    x: Union[Vector[int], Vector[bool]],
    y: Union[Vector[int], Vector[bool]],
) -> QuaLibFunctionOutput[int]

dot(
    x: Vector[float], y: VectorOfAnyType
) -> QuaLibFunctionOutput[float]

dot(
    x: VectorOfAnyType, y: Vector[float]
) -> QuaLibFunctionOutput[float]

dot(
    x: VectorOfAnyType, y: VectorOfAnyType
) -> Union[
    QuaLibFunctionOutput[float], QuaLibFunctionOutput[int]
]

Calculates a dot product of two QUA arrays of identical size.

PARAMETER	DESCRIPTION
`x`	a QUA array TYPE: `VectorOfAnyType`
`y`	a QUA array TYPE: `VectorOfAnyType`

RETURNS	DESCRIPTION
`Union[QuaLibFunctionOutput[float], QuaLibFunctionOutput[int]]`	The dot product of x and y.
`Union[QuaLibFunctionOutput[float], QuaLibFunctionOutput[int]]`	If either x or y is an array of type `Fixed`, then the result is `Fixed`. Otherwise, it is an `Int`

Example

assign(c, dot(a, b))

elu `staticmethod` ¶

elu(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes the Exponential Linear Unit activation function of x \(\mathrm{ELU(x)} = \mathrm{max}(0, x) + \mathrm{min}(0, \mathrm{exp}(x)-1)\).

PARAMETER	DESCRIPTION
`x`	a QUA fixed TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

exp `staticmethod` ¶

exp(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(e^{x}\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed smaller than ln(8)=2.0794415416 TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

inv `staticmethod` ¶

inv(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes the inverse of x

PARAMETER	DESCRIPTION
`x`	a QUA fixed which is x<=-1/8 or 1/8<x TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

inv_sqrt `staticmethod` ¶

inv_sqrt(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes the inverse square root of x

PARAMETER	DESCRIPTION
`x`	a QUA fixed larger than 1/64 TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

ln `staticmethod` ¶

ln(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{ln}(x)\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed larger than exp(-8)=0.0003354627 TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

log `staticmethod` ¶

log(
    x: Scalar[float], base: Scalar[float]
) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{log}_{base}(x)\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed larger than pow2(-8)=0.00390625 TYPE: `Scalar[float]`
`base`	a QUA fixed larger than pow2(1/8)=1.09051 TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

log10 `staticmethod` ¶

log10(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{log}_{10}(x)\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed larger than pow10(-8)=0.00000001 TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

log2 `staticmethod` ¶

log2(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{log}_{2}(x)\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed larger than pow2(-8)=0.00390625 TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

lrelu `staticmethod` ¶

lrelu(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes the Leaky Rectified Linear Unit activation function of x \(\mathrm{LReLU}(x)=\mathrm{max}(0, x)+0.01*\mathrm{min}(0, x)\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

max `staticmethod` ¶

max(x: Vector[NumberT]) -> QuaLibFunctionOutput[NumberT]

Computes the max of an array x

PARAMETER	DESCRIPTION
`x`	a QUA array TYPE: `Vector[NumberT]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[NumberT]`	the max value of the array, has same type as x

min `staticmethod` ¶

min(x: Vector[NumberT]) -> QuaLibFunctionOutput[NumberT]

Computes the min of an array x

PARAMETER	DESCRIPTION
`x`	a QUA array TYPE: `Vector[NumberT]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[NumberT]`	the min value of the array, has same type as x

plrelu `staticmethod` ¶

plrelu(
    x: Scalar[float], a: Scalar[float]
) -> QuaLibFunctionOutput[float]

Computes the Parametric Leaky Rectified Linear Unit activation function of x \(\mathrm{PLReLU}(x, a) = \mathrm{max}(0, x)+a*\mathrm{min}(0, x)\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed TYPE: `Scalar[float]`
`a`	a QUA fixed TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

pow `staticmethod` ¶

pow(
    base: Scalar[float], x: Scalar[float]
) -> QuaLibFunctionOutput[float]

Computes \({base}^{x}\). Does not support base=1, nor the case where both base=0 & x=0.

PARAMETER	DESCRIPTION
`base`	a non-negative QUA fixed TYPE: `Scalar[float]`
`x`	a QUA fixed TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

pow2 `staticmethod` ¶

pow2(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(2^{x}\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed smaller than 3 (to avoid overflow) TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

relu `staticmethod` ¶

relu(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes the Rectified Linear Unit activation function of x \(\mathrm{ReLU}(x) = \mathrm{max}(0, x)\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

selu `staticmethod` ¶

selu(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes the Scaled Exponential Linear Unit activation function of x \(\mathrm{SELU}(x) = s*(\mathrm{max}(0, x)+a*\mathrm{min}(0, \mathrm{exp}(x)-1))\), \(a=1.67326324\), \(s=1.05070098\)

PARAMETER	DESCRIPTION
`x`	a QUA fixed TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

sin `staticmethod` ¶

sin(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{sin}(x)\)

PARAMETER	DESCRIPTION
`x`	the angle in radians TYPE: `QUA variable of type fixed`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

sin2pi `staticmethod` ¶

sin2pi(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes \(\mathrm{sin}(2 \pi x)\). This is more efficient than Math.sin(2*np.pi*x). In addition, this function is immune to overflows: An overflow means that the argument gets a \(\pm 16\), which does not change the result due to the periodicity of the sine function.

PARAMETER	DESCRIPTION
`x`	the angle in radians TYPE: `QUA variable of type fixed`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

sqrt `staticmethod` ¶

sqrt(x: Scalar[float]) -> QuaLibFunctionOutput[float]

Computes the square root of x

PARAMETER	DESCRIPTION
`x`	a non-negative QUA fixed TYPE: `Scalar[float]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[float]`	a QUA fixed

sum `staticmethod` ¶

sum(x: Vector[NumberT]) -> QuaLibFunctionOutput[NumberT]

Computes the sum of an array x

PARAMETER	DESCRIPTION
`x`	a QUA array TYPE: `Vector[NumberT]`

RETURNS	DESCRIPTION
`QuaLibFunctionOutput[NumberT]`	the sum of the array, has same type as x

Math functions¶

qm.qua.lib.Math ¶

MSB staticmethod ¶

abs staticmethod ¶

aelu staticmethod ¶

argmax staticmethod ¶

argmin staticmethod ¶

atan staticmethod ¶

atan2 staticmethod ¶

atan2_2pi staticmethod ¶

atan_2pi staticmethod ¶

cos staticmethod ¶

cos2pi staticmethod ¶

div staticmethod ¶

dot staticmethod ¶

elu staticmethod ¶

exp staticmethod ¶

inv staticmethod ¶

inv_sqrt staticmethod ¶

ln staticmethod ¶

log staticmethod ¶

log10 staticmethod ¶

log2 staticmethod ¶

lrelu staticmethod ¶

max staticmethod ¶

min staticmethod ¶

plrelu staticmethod ¶

pow staticmethod ¶

pow2 staticmethod ¶

relu staticmethod ¶

selu staticmethod ¶

sin staticmethod ¶

sin2pi staticmethod ¶

sqrt staticmethod ¶

sum staticmethod ¶

MSB `staticmethod` ¶

abs `staticmethod` ¶

aelu `staticmethod` ¶

argmax `staticmethod` ¶

argmin `staticmethod` ¶

atan `staticmethod` ¶

atan2 `staticmethod` ¶

atan2_2pi `staticmethod` ¶

atan_2pi `staticmethod` ¶

cos `staticmethod` ¶

cos2pi `staticmethod` ¶

div `staticmethod` ¶

dot `staticmethod` ¶

elu `staticmethod` ¶

exp `staticmethod` ¶

inv `staticmethod` ¶

inv_sqrt `staticmethod` ¶

ln `staticmethod` ¶

log `staticmethod` ¶

log10 `staticmethod` ¶

log2 `staticmethod` ¶

lrelu `staticmethod` ¶

max `staticmethod` ¶

min `staticmethod` ¶

plrelu `staticmethod` ¶

pow `staticmethod` ¶

pow2 `staticmethod` ¶

relu `staticmethod` ¶

selu `staticmethod` ¶

sin `staticmethod` ¶

sin2pi `staticmethod` ¶

sqrt `staticmethod` ¶

sum `staticmethod` ¶