Basics

0, 0 = 0

0, 1 = 0

1, 0 = 0

1, 1 = 1

1. The fast carry chain is a dedicated connection for routing carry signals between adjacent cells implementing full adders to realize fast adders (which are fundamental units in many arithmetic circuits)

2. Accelerate propagation of carry signals, speeds up arithmetic circuits

1. With Nearest Neighbor interconnect, only connections to neighboring logic blocks are possible.

2. With Segmented interconnect, connection blocks and switch boxed are introduced (extending Nearest Neighbor), which allow general routing to non-neighboring logic blocks. Different wire lengths spanning more than one logic block enable an efficient implementation.

3. With Hierarchical interconnect, clusters are built from a 2 × 2 array of logic blocks that realize a Nearest Neighbor interconnect. Next, a 4 × 4 cluster is build from a 2 × 2 array of 2 × 2 clusters, again using a Nearest Neighbor interconnect. This pattern is repeated to larger clusters. This leads wire lengths spanning more than one logic block, similar to Segmented interconnect

With Nearest Neighbor interconnect, only connections to neighboring logic blocks are possible.

With Segmented interconnect, connection blocks and switch boxed are introduced (extending Nearest Neighbor), which allow general routing to non-neighboring logic blocks. Different wire lengths spanning more than one logic block enable an efficient implementation.

With Hierarchical interconnect, clusters are built from a 2 × 2 array of logic blocks that realize a Nearest Neighbor interconnect. Next, a 4 × 4 cluster is build from a 2 × 2 array of 2 × 2 clusters, again using a Nearest Neighbor interconnect. This pattern is repeated to larger clusters. This leads wire lengths spanning more than one logic block, similar to Segmented interconnect

An External RCU refers to a Remote Control Unit that is physically separate from the main device or system it controls. It connects to the main system via external ports or wireless communication. This setup allows for greater flexibility in positioning the control unit and can be used in scenarios where the main system is not easily accessible.

An Attached RCU is a Remote Control Unit that is physically connected to the main device or system it controls. This connection could be through a cable or a docking mechanism. This type of RCU is typically used for convenience and to ensure a stable connection, reducing the chance of signal interference or loss.

A Peer Processor RCU involves a remote control unit that operates in conjunction with another processor of equal standing within a network or system. This configuration allows for parallel processing and can enhance system performance by distributing tasks among multiple processors.

A Co-Processor RCU refers to a Remote Control Unit that works alongside a primary processor to perform specific functions. The co-processor is designed to handle particular tasks more efficiently than the main processor, such as mathematical computations or graphic processing, thereby improving overall system performance.

RCU as a Functional Unit means that the Remote Control Unit is integrated as a core component within a system or device, performing essential functions that are critical to the operation of the system. This configuration implies that the RCU is not just an accessory but a vital part of the system's architecture, contributing to its primary operations.

wobei:

S(N) = speedup with N processors

P = fraction of the task that is parallelizable

N = numer of processors

für N→∞

bedeutet:

𝑃 / 𝑁 →0

daher:

Amdahl’s law assumes that the problem size is kept constant. By adding more processing units the same problem gets solved faster. In reconfigurable computing it is often the case that bigger computers are used to solve bigger problems, not to solve old problems faster. If the sequential part of the program does not increase when increasing the problem (or increases sublinearly) then we can run on a large number of cores!

• Start every operation as soon as ist predecessors have completed

• Optimize overally latency of computation

• No care for resources

As late as possible

• Difference between schedule times from ALAP and ASAP

• length of the path from the current node to the output node

• All operations that already have scheduled predecessors

D: time constraint

V: vertices

E: edges

a_T: allocation

X als set binärer Zahlen mit

D: time constraint

V: vertices

E: edges

a_T: allocation

X als set binärer Zahlen mit

1. Initiation Interval (II):

   • The fixed number of cycles after which a new iteration of the loop begins execution.

   • The goal is to minimize II to maximize throughput.

2. Stage Scheduling:

   • Each operation in the loop is assigned to a specific stage within the initiation interval.

   • The same stage of different iterations should not conflict with resource constraints.

3. Resource Constraints:

   • Constraints ensuring that the available resources (e.g., functional units like multipliers, ALUs) are not overused in any cycle.

4. Dependence Constraints:

   • Constraints ensuring that data dependencies between operations are respected.

• II: Interval

• b_{ij}: ?

• ϕj: step/schedule time of o_j

• ϕ_i: step/schedule time of o_i

• δ(o_i​): t_REG

• T_min: minimum clock period

• t_{p,CQ}: time to propagate flip flops

• t_{p,max}: critical path (in ns)

• t_{su}: time to setup flip flops

• T_min: minimum clock period

• f_{max}: max. frequency

f_{max} = 1 / T_{min}

• T_min: minimum clock period

• f_{max}: max. frequency

f: frequency in MHz

T: time in nanoseconds

f = 1000 / T

T = 1000 / f