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Arithmetic Scalar Operators

The ArithmeticScalar class serves as a base for operators that perform mathematical operations on a single numeric input stream. Each derived class implements a specific mathematical function that is applied to each input value.

Basic Operation​

All ArithmeticScalar operators:

  • Have one input port (port 0) for numeric data
  • Have one output port (port 0) for numeric results
  • Process messages immediately (no buffering)
  • Preserve message timestamps
  • Apply their mathematical operation to each input value

Available Operators​

Arithmetic Operators​

  1. Add (y = x + C)

    • Additional parameter: value (constant to add)
    {
      "id": "add1",
      "type": "Add",
      "value": 5.0
    }

  2. Scale (y = C × x)

    • Additional parameter: value (scaling factor)
    {
      "id": "scale1",
      "type": "Scale",
      "value": 2.0
    }

  3. Power (y = x^C)

    • Additional parameter: value (exponent)
    {
      "id": "pow1",
      "type": "Power",
      "value": 2.0
    }

Trigonometric Functions​

  1. Sin (y = sin(x))

    {
      "id": "sin1",
      "type": "Sin"
    }

  2. Cos (y = cos(x))

    {
      "id": "cos1",
      "type": "Cos"
    }

  3. Tan (y = tan(x))

    {
      "id": "tan1",
      "type": "Tan"
    }

Exponential and Logarithmic Functions​

  1. Exp (y = e^x)

    {
      "id": "exp1",
      "type": "Exp"
    }

  2. Log (y = ln(x))

    {
      "id": "log1",
      "type": "Log"
    }

  3. Log10 (y = log₁₀(x))

    {
      "id": "log10_1",
      "type": "Log10"
    }

Absolute Value and Sign Functions​

  1. Abs (y = |x|)

    {
      "id": "abs1",
      "type": "Abs"
    }

  2. Sign (y = sign(x))

    {
      "id": "sign1",
      "type": "Sign"
    }

Rounding Functions​

  1. Floor (y = ⌊x⌋)

    {
      "id": "floor1",
      "type": "Floor"
    }

  2. Ceil (y = ⌈x⌉)

    {
      "id": "ceil1",
      "type": "Ceil"
    }

  3. Round (y = round(x))

    {
      "id": "round1",
      "type": "Round"
    }

Example Usage​

Message Flow Example​

Consider an Add operator with value = 2.0:

TimeInputOutput
11.03.0
22.54.5
4-1.01.0
53.05.0

Note how:

  • Time gaps are preserved (no message at t=3)
  • Output timestamps match input timestamps
  • The constant value (2.0) is added to each input

Code Example​

// Create an Add operator
auto add = make_add("add1", 2.0);

// Create a Sine operator
auto sine = make_sin("sin1");

// Process some messages
add->receive_data(create_message<NumberData>(1, NumberData{1.0}), 0);
add->execute();

sine->receive_data(create_message<NumberData>(1, NumberData{M_PI/2}), 0);
sine->execute();

Error Handling​

Operators will throw exceptions for:

  • Invalid message types
  • Invalid input port indices
  • Mathematical errors (e.g., log of negative numbers)

Implementation Notes​

  1. Stateless Operation

    • No buffering of messages
    • Each output depends only on current input
    • Immediate processing

  2. Performance

    • O(1) processing per message
    • Constant memory usage
    • No allocation during normal operation

  3. Numerical Considerations

    • Uses IEEE 754 floating-point arithmetic
    • Handles special values (NaN, Inf) according to standard rules
    • Preserves numeric precision of underlying math functions

Factory Functions​

Each operator type has an associated factory function:

auto add = make_add("add1", 2.0);
auto sin = make_sin("sin1");
auto exp = make_exp("exp1");
// etc.