Math functions

qm.qua.lib.Math

abs staticmethod

Computes the absolute value of x

PARAMETER	DESCRIPTION
x	a QUA variable

RETURNS	DESCRIPTION
	a QUA fixed

aelu staticmethod

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

PARAMETER	DESCRIPTION
x	a QUA fixed

RETURNS	DESCRIPTION
	a QUA fixed

argmax staticmethod

Return the index of the maximum of an array

PARAMETER	DESCRIPTION
x	a QUA array

RETURNS	DESCRIPTION
	the index of maximum value of array, a QUA Integer

argmin staticmethod

Return the index of the minimum of an array

PARAMETER	DESCRIPTION
x	a QUA array

RETURNS	DESCRIPTION
	the index of minimum value of array, a QUA Integer

cos staticmethod

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

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

RETURNS	DESCRIPTION
	a QUA fixed

cos2pi staticmethod

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 periodcity of the cosine function.

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

RETURNS	DESCRIPTION
	a QUA fixed

div staticmethod

Computes the division between two same-type variables \(x/y\)

PARAMETER	DESCRIPTION
x	a QUA parameter
y	a QUA parameter not equal to 0

RETURNS	DESCRIPTION
	a QUA fixed

dot staticmethod

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

PARAMETER	DESCRIPTION
x	a QUA array
y	a QUA array

RETURNS	DESCRIPTION
	The dot product of x and y, has same type as x and y

Example

assign(c, dot(a, b))

elu staticmethod

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

RETURNS	DESCRIPTION
	a QUA fixed

exp staticmethod

Computes \(e^{x}\)

PARAMETER	DESCRIPTION
x	a QUA fixed smaller than ln(8)=2.0794415416

RETURNS	DESCRIPTION
	a QUA fixed

inv staticmethod

Computes the inverse of x

PARAMETER	DESCRIPTION
x	a QUA fixed which is x<=-1/8 or 1/8<x

RETURNS	DESCRIPTION
	a QUA fixed

inv_sqrt staticmethod

Computes the inverse square root of x

PARAMETER	DESCRIPTION
x	a QUA fixed larger than 1/64

RETURNS	DESCRIPTION
	a QUA fixed

ln staticmethod

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

PARAMETER	DESCRIPTION
x	a QUA fixed larger than exp(-8)=0.0003354627

RETURNS	DESCRIPTION
	a QUA fixed

log staticmethod

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

PARAMETER	DESCRIPTION
x	a QUA fixed larger than pow2(-8)=0.00390625
base	a QUA fixed larger than pow2(1/8)=1.09051

RETURNS	DESCRIPTION
	a QUA fixed

log10 staticmethod

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

PARAMETER	DESCRIPTION
x	a QUA fixed larger than pow10(-8)=0.00000001

RETURNS	DESCRIPTION
	a QUA fixed

log2 staticmethod

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

PARAMETER	DESCRIPTION
x	a QUA fixed larger than pow2(-8)=0.00390625

RETURNS	DESCRIPTION
	a QUA fixed

lrelu staticmethod

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

RETURNS	DESCRIPTION
	a QUA fixed

max staticmethod

Computes the max of an array x

PARAMETER	DESCRIPTION
x	a QUA array

RETURNS	DESCRIPTION
	the max value of the array, has same type as x

min staticmethod

Computes the min of an array x

PARAMETER	DESCRIPTION
x	a QUA array

RETURNS	DESCRIPTION
	the min value of the array, has same type as x

msb staticmethod

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

RETURNS	DESCRIPTION
	a QUA int

plrelu staticmethod

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
a	a QUA fixed

RETURNS	DESCRIPTION
	a QUA fixed

pow staticmethod

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
x	a QUA fixed

RETURNS	DESCRIPTION
	a QUA fixed

pow2 staticmethod

Computes \(2^{x}\)

PARAMETER	DESCRIPTION
x	a QUA fixed smaller than 3 (to avoid overflow)

RETURNS	DESCRIPTION
	a QUA fixed

relu staticmethod

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

PARAMETER	DESCRIPTION
x	a QUA fixed

RETURNS	DESCRIPTION
	a QUA fixed

selu staticmethod

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

RETURNS	DESCRIPTION
	a QUA fixed

sin staticmethod

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

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

RETURNS	DESCRIPTION
	a QUA fixed

sin2pi staticmethod

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
	a QUA fixed

sqrt staticmethod

Computes the square root of x

PARAMETER	DESCRIPTION
x	a non-negative QUA fixed

RETURNS	DESCRIPTION
	a QUA fixed

sum staticmethod

Computes the sum of an array x

PARAMETER	DESCRIPTION
x	a QUA array

RETURNS	DESCRIPTION
	the sum of the array, has same type as x