Xilinx
TM
Block Preview

Introduction

This block performs IEEE 754 floating-point subtraction using the Xilinx Floating Point IP core. The component supports Time Multiplexing (TM): multiple parallel computation units (phases) share the same clock cycle, enabling high sample rates with predictable latency.

On every rising edge of CLK, if A_CE = 1, B_CE = 1, and READY_IN = 1, the operator performs

$$ \mathrm{F}(n) = \mathrm{A}(n) - \mathrm{B}(n), $$

where all operands are IEEE 754 floating-point values. The TM Factor property determines how many parallel instances are instantiated.

Pin Description

A Input Variable bit TM

Floating-point input A, always TM. Width: (Exponent + Mantissa) × TMFactor

  • Single: 32 bits/phase → total 32×TMFactor
  • Double: 64 bits/phase → total 64×TMFactor IEEE 754 format minuend (first operand) for subtraction.
Default: Must be connected
A_CE Input 1 bit BIT
Input A clock enable, active high. When A_CE = 0 the A input is not accepted. Maps to s_axis_a_tvalid in the AXI Stream interface.
B Input Variable bit TM

Floating-point input B.

  • If B is TM = YES: TM bus of width same as A
  • If B is TM = NO: Scalar of single phase width (replicated to all phases) IEEE 754 format subtrahend (second operand) for subtraction.
Default: Must be connected
B_CE Input 1 bit BIT
Input B clock enable, active high. When B_CE = 0 the B input is not accepted. Maps to s_axis_b_tvalid in the AXI Stream interface.
READY_IN Input 1 bit BIT
Downstream ready signal, active high. Indicates that downstream logic can accept new data. Maps to m_axis_result_tready. Default: ‘1’ if not connected.
CLK Input 1 bit BIT
Global clock. Every rising edge triggers computation in all TM phases and advances pipeline registers.
Default: Default Board Clock
F Output Variable bit TM
Floating-point output, always TM. Width: Same as input A Each phase produces A - B in IEEE 754 format. Valid after 12 clock cycles from inputs.
DV Output 1 bit BIT
Data Valid output, active high. Asserted when all TM phases have valid output data. Maps to AND of all m_axis_result_tvalid signals.
A_READY Output 1 bit BIT
Input A ready output, active high. Indicates operator is ready to accept new input A. Maps to AND of all s_axis_a_tready signals.
B_READY Output 1 bit BIT
Input B ready output, active high. Indicates operator is ready to accept new input B. Maps to AND of all s_axis_b_tready signals.

Properties

Property window

TM Factor TMFactor

Time Multiplexing factor (number of phases)

Number of time-multiplexed phases (parallel computation units). Range: 1 – 32. Higher values increase throughput proportionally but consume more FPGA resources (N instances of the Xilinx IP).

Default: 4

Range: 1 – 32

Float Format FloatFormat

Select between single precision 32 bit and double precision 64 bit

Floating-point format for all inputs and output:

  • Single → IEEE 754 single precision (32-bit): 8 exp + 24 mantissa
  • Double → IEEE 754 double precision (64-bit): 11 exp + 53 mantissa

Determines precision and range of the computation.

Default: Single

Options: Single Double

B is TM B_IsTM

Select if input B is Time Multiplexed or the same for all phases

Selects input B mode:

  • YES → Input B is a TM bus; each phase gets its slice
  • NO → Input B is scalar; replicated to all phases

Use NO for subtracting a constant from all TM channels.

Default: YES

Options: NO YES

DSP Usage DSPUsage

DSP Usage. Single precision: No [0], Full[2]. Double precision: No[0], Full[3]

DSP slice usage mode:

  • No_Usage → Minimize DSP usage (more LUTs)
  • Full_Usage → Maximize DSP usage (fewer LUTs)

Single precision DSP count: No [0], Full[2] Double precision DSP count: No[0], Full[3]

Default: Full_Usage

Options: No_Usage Full_Usage

Functional description

The component wraps the Xilinx Floating Point IP (operation type: Subtract) and replicates it N times (where N = TM Factor) to support time-multiplexed data streams.

Input modes

  • Input A is always TM, with width (Exponent + Mantissa) × TMFactor
  • Input B can be either:
    • TM mode (B is TM = YES): Same width as A, each phase gets its slice
    • Broadcast mode (B is TM = NO): Single value replicated to all phases

Output

  • Output F is always TM, with the same width as input A

Data valid and ready handshake

  • A_CE (input): Input A clock enable
  • B_CE (input): Input B clock enable
  • DV (output): Output data valid, asserted when all phases have valid output
  • A_READY (output): Ready to accept new input A (AND of all phase ready signals)
  • B_READY (output): Ready to accept new input B (AND of all phase ready signals)
  • READY_IN (input): Downstream ready signal

Mathematical background

IEEE 754 floating-point subtraction with proper rounding and special case handling:

$$ x - y = \text{round}(x - y) $$

Special cases:

  • $x - 0 = x$
  • $x - x = 0$ (with proper sign handling)
  • $\infty - x = \infty$ (for finite $x$)
  • $\infty - \infty = \text{NaN}$
  • $\text{NaN} - x = \text{NaN}$

Properties:

  • $x - y = x + (-y)$
  • Non-commutative: $x - y \neq y - x$ in general

Timing

The Xilinx Floating Point IP has a fixed latency of 12 clock cycles per phase:

Property Latency (clock cycles)
Subtraction 12

Total system delay: T_delay = 12 × T_CLK.

In TM mode, all phases operate in parallel with the same latency, producing TMFactor outputs per cycle after the initial pipeline fill.

DSP Usage

Subtraction can be implemented with different DSP slice usage:

  • Single precision: No [0], Full[2]
  • Double precision: No[0], Full[3]

Higher DSP usage typically provides better performance but consumes more FPGA resources.

Typical use cases

  • Difference calculations
  • Error computation (measurement - reference)
  • Baseline subtraction
  • Derivative approximation
  • Signal comparison

Waveform example

Example with TM Factor = 4, Single precision, B is TM = YES.

Note: 12 clock cycles of latency from input to output.