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Mathematical Synchronization Operators

A family of operators that perform arithmetic operations on synchronized numeric streams.

Common Properties​

All operators:

  • Accept two or more input ports (0 to n-1)
  • Produce one output port (0)
  • Synchronize input messages based on timestamps
  • Output messages only when all inputs have matching timestamps
  • Inherit buffering behavior from ReduceJoin

Available Operators​

Addition​

Computes the sum of all synchronized values.

Initial value: 0.0

For n inputs:

y(t_n) = x₀(t_n) + x₁(t_n) + ... + xₙ₋₁(t_n)

Multiplication​

Computes the product of all synchronized values.

Initial value: 1.0

For n inputs:

y(t_n) = x₀(t_n) × x₁(t_n) × ... × xₙ₋₁(t_n)

Subtraction​

Takes the first input and subtracts all subsequent inputs.

For n inputs:

y(t_n) = x₀(t_n) - (x₁(t_n) + x₂(t_n) + ... + xₙ₋₁(t_n))

With 2 inputs, reduces to standard subtraction:

y(t_n) = x₀(t_n) - x₁(t_n)

Division​

Takes the first input and divides by the product of all subsequent inputs. Returns no output if the product of denominators is zero.

For n inputs:

y(t_n) = x₀(t_n) ÷ (x₁(t_n) × x₂(t_n) × ... × xₙ₋₁(t_n))

With 2 inputs, reduces to standard division:

y(t_n) = x₀(t_n) ÷ x₁(t_n)  if x₁(t_n) ≠ 0

Example Message Flows​

Addition with 3 inputs:

Time | Port 0 | Port 1 | Port 2 | Output
-----|--------|--------|--------|--------
1    | 10.0   | -      | 5.0    | -
2    | -      | 5.0    | -      | -
3    | 15.0   | 15.0   | 15.0   | 45.0
5    | 20.0   | -      | 10.0   | -
7    | 25.0   | 25.0   | 25.0   | 75.0

Multiplication with 3 inputs:​

Time | Port 0 | Port 1 | Port 2 | Output
-----|--------|--------|--------|--------
1    | 2.0    | -      | 3.0    | -
2    | -      | 4.0    | -      | -
3    | 2.0    | 2.0    | 2.0    | 8.0
4    | 3.0    | 3.0    | 3.0    | 27.0

Subtraction with 3 inputs:​

Time | Port 0 | Port 1 | Port 2 | Output
-----|--------|--------|--------|--------
1    | 100.0  | 20.0   | 30.0   | 50.0   # 100 - (20 + 30)
2    | 50.0   | 10.0   | 15.0   | 25.0   # 50 - (10 + 15)

Division with 3 inputs:​

Time | Port 0 | Port 1 | Port 2 | Output
-----|--------|--------|--------|--------
1    | 100.0  | 2.0    | 5.0    | 10.0   # 100 ÷ (2 × 5)
2    | 200.0  | 4.0    | 5.0    | 10.0   # 200 ÷ (4 × 5)

Usage​

// Create operators using factory functions
auto add = make_addition("add1", 3);           // 3 inputs
auto mul = make_multiplication("mul1", 4);      // 4 inputs
auto sub = make_subtraction("sub1", 3);        // x₀ - (x₁ + x₂)
auto div = make_division("div1", 3);           // x₀ ÷ (x₁ × x₂)

Implementation Notes​

  1. Addition and Multiplication are commutative - order of inputs doesn't matter.

  2. Subtraction treats first input (x₀) as minuend and subtracts sum of all other inputs.

  3. Division treats first input (x₀) as numerator and divides by product of all other inputs.

  4. All operators maintain backward compatibility with previous binary behavior when used with 2 inputs.