Basic Math

The Basic Math components are used to perform low-level math operations. Remember that even simple math operations might use many DSP cycles. For example, the Divide processor will use about 30 cycles while ScaleAdd uses only about 10 for both a multiplication and addition. Avoid the Divide, SqRoot, and Modulus processors whenever possible.

This group includes the following components:

• AbsVal
• Bound
• Ceiling
• Compare
• Divide
• Floor
• Limit
• Min
• Max
• Modulus
• ScaleAdd
• Sign
• SqRoot
• Square
• StereoScale
• StereoSum
• Sum
• Mult

This group also includes the following components, if RPvdsEx Device Setup is configured for a high performance device, such as the RXn or RZn:

• MCAbsVal
• MCBound
• MCDotProd
• MCMatMult
• MCScale
• MCSign
• MCSum
• MCMult

AbsVal

Description:

AbsVal computes the absolute value of the signal.

Name	Description	Data Type
Input	Input	Floating Point
Output	Absolute value of Input	Floating Point

Equation:

Output = Abs (Input)

Example(s):

AbsVal (-2.3) = 2.3

AbsVal (2.3) = 2.3

Bound

Description:

Bound functions similar to the Limit component but evaluates to Vnan for inputs that produce a NaN (not a number) error.

Note:

NaN is output when a division by 0 is applied to a signal value.

Name	Description	Data Type
Input	Input	Floating Point
Output	Value no less than Min and no greater than Max.	Floating Point
Max	Maximum output value	Floating Point
Min	Minimum output value	Floating Point
Vnan	Value output in the event that input = Na N(not a number)	Floating Point

Equation:

If Input > Max then Output = Max

Else If Min \<= Input \<= Max then Output = Input

Else If Input \< Min then Output = Min

Else If Input = NaN then Output = Vnan

Ceiling

Description:

Ceiling rounds the input to the next highest integer value (returned in floating point format). If the input is a negative value, Ceiling rounds towards zero.

Name	Description	Data Type
Input	Input	Floating Point
Output	Rounded up value of Input	Floating Point

Equation:

Output = Ceiling (Input)

Example(s):

Ceiling (2.3) = 3.0

Ceiling (-2.3) = -2.0

Ceiling (-2.7) = -2.0

Compare

Description:

This component uses a specified test to compare the input signal to a specified value, K. The output reports the result, true or false, as a logical value. The comparison test can be any of the following: equal to, not equal to, greater than, less than, greater than or equal to, or less than or equal to. The Compare component can be thought of as an If... statement. For example, If the signal value equals K then the output is true (1).

Name	Description	Data Type
Input	Input	Floating Point
Output	1 if compare is true, 0 if false	Logic
K	Test value	Floating Point
Test	Comparison types: EQ: Equal NE: Not Equal GT: Greater Than LT: Less Than GE: Greater than or Equal to LE: Less than or Equal to	Static

Equation:

Output = Compare (Input Test K)

Example(s):

K = 20; Test = EQ

When Input = 20, Output = 1; otherwise Output = 0

K = 20; Test = GT

When Input > 20, Output = 1; otherwise Output = 0

Divide

Description:

This component divides the input signal by the denominator and passes the quotient to the output. Division by zero results in an error value. The Divide component can also be used to multiply by defining a Den value between zero and one.

The ScaleAdd and Mult components offer similar functionality and can also be used to divide. The ScaleAdd is the most efficient of these three components and should, therefore, be used whenever possible.

Name	Description	Data Type
Input	Input	Floating Point
Output	Input/Den	Floating Point
Den	Denominator for the divide	Floating Point

Equation:

Output = Input / Den (Denominator)

Example(s):

PowerBand, PowerBand.

Biquad Filter, Biquad.

Floor

Description:

Floor rounds the input to the next lowest integer value (returned in floating point format). If the input is a negative value Floor rounds away from zero.

Name	Description	Data Type
Input	Input	Floating Point
Output	Round down of Input	Floating Point

Equation:

Output = Floor (Input)

Example(s):

Floor (2.3) = 2.0

Floor (-2.3) = -3.0

Limit

Description:

This component limits the signal to a range defined by the Max and Min parameters. If the input is greater than Max, the signal out is the Max value. If the input is less than Min, the signal out is the Min value. If the input is between the Min and Max values it is passed through as the signal output without change.

Note:

If Max is defined as a value less than the defined Min value, the output will always be the defined Min, regardless of the input value.

Name	Description	Data Type
Input	Input	Floating Point
Output	Value no less than Min and no greater than Max	Floating Point
Max	Maximum output value	Floating Point
Min	Minimum output value	Floating Point

Equation:

If Input > Max then Output = Max

Else If Min \<= Input \<= Max then Output = Input

Else If Input \< Min then Output = Min

Min

Max

Description:

The Max and Min components evaluate multiple input signals and pass the maximum or minimum input to the output. All inputs signals must come from the primary output of another component. If it is necessary to route a parameter output to this function use a ConstF to make it a primary output.

Name	Description	Data Type
Input (multiple)	Input (multiple)	Floating Point
Output	Min or Max of inputs	Floating Point

Example(s):

F_o = Min (F_i1, F_i2, F_i3, F_i4, F_i5)

F_o = Max (F_i1, F_i2, F_i3, F_i4, F_i5)

Min (4.0, -12.3, 22.7) = -12.3

Max (-3.0, 4, 16.2) = 16.2

MCAbsVal

Description:

MCAbsVal computes the absolute value of the multi-channel signal.

Note:

This component is for use with only high performance processor devices, such as RXn or RZn.

Name	Description	Data Type
Input	Multi-channel input	Floating Point
Output	Absolute value of multi-channel Input	Floating Point
nChan	Number of channels of input/output	Integer (Static)

Equation:

F_oN = Abs(F_iN)

MCBound

Description:

MCBound functions similar to the Limit component but evaluates to Vnan for inputs that produce a NaN (not a number) error.

Note:

NaN is output when a division by 0 is applied to a signal value.

Note:

This component is for use with only high performance processor devices, such as RXn or RZn.

Name	Description	Data Type
Input	Multi-channel input	Floating Point
Output	Multi-channel Output, Value no less than Min and no greater than Max.	Floating Point
nChan	Number of channels of input/output	Integer (Static)
Max	Maximum output value	Floating Point
Min	Minimum output value	Floating Point
Vnan	Value output in the event that input = NaN (not a number)	Floating Point

Equation:

If F_iN > Max then F_oN = Max

Else If Min <= F_iN <= Max then F_oN = F_iN

Else If F_iN < Min then F_oN = Min

Else If F_iN = NaN then F_oN = Vnan

MCDotProd

Description:

MCDotProd computes the dot product of the multi-channel input signal and the vector data entered on {>K}. The number of elements for {>K} must match nChan (for example, when nChan is set to 4, {>K} is a 4 x 1 matrix).

Note:

This component is for use with only high performance processor devices, such as RXn or RZn.

Name	Description	Data Type
Input	Multi-channel input	Floating Point
Output	Single-channel output	Floating Point
nChan	Number of channels of input	Integer (Static)
>K	Scaling Matrix	Pointer

MCMatMult

Description:

MCMatMult performs matrix multiplication of the multi-channel input signal and the matrix data entered on >K. The dimensions for >K must match nChan (e.g., when nChan is set to 4, >K is a 4 x 4 matrix).

Note:

This component is for use with only high performance processor devices, such as RXn or RZn.

Name	Description	Data Type
Input	Multi-channel input signal	Floating Point
Output	Multi-channel input signal	Floating Point
nChan	Number of Channels (4 - 256)	Integer (Static)
>K	Scaling matrix	Pointer

Equation:

K x A = B

Where, K is the N x N scaling matrix. A is the input N x 1 matrix, one data point for each of the N input channels and B is the output N x 1 matrix, one data point for each of the N output channels. N is the total number of channels (nChan).

The operation is computed on every sample based on the current input provided.

B₁ = K_1,1 * A₁ + K_1,2 * A₂ + K_1,3 * A₃ + ... K_1,N * A_N

.

.

.

B_N = K_N,1 * A₁ + K_N,2 * A₂ + K_N,3 * A₃ + ... K_N,N * A_N

Ordering:

The matrix data for K must be loaded as a vector. Matrix row data is concatenated to form the vector. For example, to load a 4 x 4 identity matrix:

In RPvdsEx, the >K scaling matrix is typically loaded using a DataTable component. Load the K matrix as a column vector using the nRow Type/Format shown below. The No. Rows value is equal to N * N (or in this case 4 * 4 =16).

In this diagram, the DataTable K is used to load the identity matrix. The number pattern from above K = [1000 0100 0010 0001] is listed in the first column.

Note:

The DataTable component allows a maximum of 1024 rows. This would correspond to a 32 x 32 scaling matrix. This means that the maximum number of channels you can use with this component is 32. If you need to use a larger channel amount, a SourceFile component or parameter tag can be used to load in a larger scaling matrix.

MCScale

Description:

MCScale multiplies each signal in a multi-channel input by the value of the SF parameter. The scaled signals are output as a multi-channel signal. The SF parameter input can be used to update the scale factor dynamically.

Note:

This component is for use with only high performance processor devices, such as RXn or RZn.

Name	Description	Data Type
Input	Multi-channel signal input	Floating Point
Output	Multi-channel scaled output	Floating Point
nChan	Number of channels of input/output	Integer (Static)
SF	Scale factor	Floating Point

Equation:

Output[x] = Input[x] * SF

MCSign

Description:

This component determines the sign of the multi-channel input and outputs either -1 (signal with negative value), 0 (signal with no value), or 1 (signal with positive value).

Note:

This component is for use with only high performance processor devices, such as RXn or RZn.

Name	Description	Data Type
Input	Multi-channel signal input	Floating Point
Output	Sign value of multi-channel input: -1, 0, 1	Floating Point
nChan	Number of channels of input/output	Integer (Static)

Equation:

If F_iN \< 0.0 then F_oN = -1

Else If F_iN = 0.0 then F_oN = 0

Else If F_iN > 0.0 then F_oN = 1

MCSum

MCMult

Description:

These multi-input components perform basic summing and multiplying functions for two multi-channel inputs.

Note:

This component is for use with only high performance processor devices, such as RXn or RZn.

Name	Description	Data Type
Inputs (two)	Input	Floating Point
NChan	Number of Channels	Integer (Static)
Output	Multiplied or summed value of the inputs	Floating Point

Equation:

Output =(Input₁ChN + Input₂ChN)

Output =(Input₁ChN * Input₂ChN)

Examples:

This circuit acquires 16 channels of input, and performs digital subtraction of one channel from all the others. The channel to be subtracted is defined by the parameter tag named RefChan.

This circuit shows how to scale each channel of an MC input by a different scale factor.

Note:

Use the MCScale component when all signals are to be scaled by the same value.

Modulus

Description:

Returns the remainder after the input is divided by the modulus.

Note:

Check Known Anomalies for updates on this component.

Name	Description	Data Type
Input	Input	Floating Point
Output	Remainder of Input and Modulus	Floating Point
Mod	Modulus value (to calculate remainder)	Floating Point

Equation:

Output=Mod (Input)

For example: Input=5, Mod=2: Output = 1. (i.e. 5/2=2 with remainder of 1)

ScaleAdd

Description:

ScaleAdd multiplies a signal by the value of the SF parameter and then sums the result with the Shft value.

Note:

the SF and Shft parameters can be set to a constant value or connected to signal sources. This enables the ScaleAdd function to be used to multiply two signals, add two signals, or take the product of two signals and sum it to a third.

Using ScaleAdd to sum two signals is preferable to using the multi-input sum function because it saves DSP cycles.

Name	Description	Data Type
Input	Input	Floating Point
Output	Product of input and SF plus shft	Floating Point
SF	Scale factor (multiply)	Floating Point
Shft	Add value	Floating Point

Equation:

Output = (Input * SF) + Shft

Note that Shft can be another signal.

Sign

Description:

This component determines the sign of the input and outputs either -1 (signal with negative value), 0 (signal with no value), or 1 (signal with positive value).

Name	Description	Data Type
Input	Input	Floating Point
Output	Sign value of input: -1, 0, 1	Floating Point

Equation:

If F_i < 0.0 then F_o = -1

Else If F_i = 0.0 then F_o = 0

Else If F_i > 0.0 then F_o = 1

SqRoot

Description:

This component computes the mathematical square root operation. The function has a lower bound of 0.

Name	Description	Data Type
Input	Input	Floating Point
Output	Square root of input	Floating Point

Equation:

F_o = F_i^½

Example(s):

PowerBand, PowerBand.

Biquad Filter, Biquad.

Square

Description:

This component computes the mathematical square operation and passes the result to the output.

Name	Description	Data Type
Input	Input	Floating Point
Output	Square of input	Floating Point

Equation:

F_o = F_i²

Example:

Smooth, Smooth.

StereoScale

Description:

Scales a stereo signal. The left and right signals are scaled independently by SFL and SFR respectively.

Name	Description	Data Type
Input	Stereo signal	Floating Point
Output	Stereo signal	Floating Point
SFL	Scale signal right channel	Floating Point
SFR	Scale signal right channel	Floating Point

StereoSum

Description:

Sums up to five stereo inputs and outputs one stereo signal.

Name	Description	Data Type
Inputs	Stereo signal	Floating Point
Output	Summed stereo signal	Floating Point

Sum

Mult

Description:

These multi-input components perform basic summing and multiplying functions. They work most efficiently when three or more inputs are used. Unused inputs will be ignored. All multiple inputs must come from primary outputs. If it is necessary to route a parameter output to this function, use a CONSTF to convert the signal to a primary output.

Name	Description	Data Type
Input (multiple)	Input (multiple)	Floating Point
Output	Multiplied or summed value of the inputs	Floating Point

Equation:

F_o = F_i1 + F_i2 + F_i3 + F_i4 + F_i5

or

F_o = F_i1 * F_i2 * F_i3 * F_i4 * F_i5

Example:

Sum - This construct implements a typical 'Reverb' circuit. The first three long delays are summed to simulate early reflections. The 4^th delay is added back recursively to create the reverb chain. Try it out, it sounds like a big reverberant warehouse.