CN112148456A - FPGA high-level comprehensive scheduling method - Google Patents

FPGA high-level comprehensive scheduling method Download PDF

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CN112148456A
CN112148456A CN202011062643.0A CN202011062643A CN112148456A CN 112148456 A CN112148456 A CN 112148456A CN 202011062643 A CN202011062643 A CN 202011062643A CN 112148456 A CN112148456 A CN 112148456A
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control step
scheduling
time frame
force
scheduled
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CN112148456B (en
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刘乙力
白利琼
鞠瑜华
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Chengdu Sino Microelectronics Technology Co ltd
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Abstract

An FPGA high-level comprehensive scheduling method relates to an integrated circuit technology. The invention comprises the following steps: 1) calculating to obtain the length of a time frame of each operation; 2) calculating the sum of the occurrence probability of each operation in each control step according to the time frame to obtain probability distribution; 3) judging whether operations which are not scheduled exist, if so, calculating direct force and indirect force of all operations to be scheduled to each control step in the time frame, and selecting (op) with minimum resultant forcei，csj) Scheduling, and setting the length of the current operation time frame as 1, otherwise ending the scheduling; the inter-relay force is calculated by adopting the following method:
Figure DDA0002712870680000011
the invention has obvious improvement on reducing the operation amount of the scheduling algorithm.

Description

FPGA high-level comprehensive scheduling method
Technical Field
The present invention relates to integrated circuit technology.
Background
With the increase of logic scale and performance requirement of FPGA devices, optimization of a scheduling algorithm in a high-level integration process is of great importance. The quality of the scheduling algorithm directly affects the time characteristics such as the execution speed and the response delay of the device and the space characteristics such as the hardware resource cost.
Commonly used Scheduling algorithms mainly include ASAP (As Soon As Possible), ALAP (As Late As Possible), List Scheduling algorithm (LS, List Scheduling), and force-guided algorithm (FDS, F)race-Directed Scheduling). Paulin and Knight proposed in 1989 to apply force-guided algorithms to high-level synthesis, which is a construction algorithm for finding minimum resource scheduling based on time constraints. The algorithm simulates the state of the minimum stress of a spring to distribute a force to each movement according to the Hooke's law f-k x in mechanics, so that the resources are uniformly distributed to the maximum extent in each period. In the force guidance algorithm, k represents an initial pressure on a control step, x represents a probability variation amount of an operation occurring in the control step, f represents an acting force of the control step on the operation, and a larger f represents a larger repulsive force to the operation. f comprises direct forces and indirect forces, wherein direct forces characterize the operation opiScheduling to control step csjTime, to control step csjThe resulting influence, indirect force, characterizes the operation opiScheduling to control step csjThen, to opiThe effect of the predecessor and successor operations. FIG. 1 is a drawing of
The main flow of the traditional force guidance algorithm comprises the following steps:
1) running ASAP and ALAP scheduling algorithms to obtain a time frame of each operation;
2) calculating the sum of the occurrence probability of each operation in each control step according to the time frame to obtain a probability distribution map;
3) judging whether operations which are not scheduled exist, if so, calculating direct force and indirect force of all operations to be scheduled to each control step in the time frame, and selecting (op) with minimum resultant forcei,csj) Scheduling, and setting the length of the current operation time frame as 1, otherwise ending the scheduling;
4) updating the time frames of the direct predecessor and direct successor of the operation;
5) update the probability distribution map, go to 3).
Wherein, the operation opiMay be expressed as
Figure BDA0002712870660000021
ALAP(opi) Representing operations opiCan adjustThe latest control step of the degree is recorded as
Figure BDA0002712870660000022
Can be obtained by an ALAP scheduling algorithm; ASAP (op)i) To operate oniThe earliest control step that can be scheduled is recorded as
Figure BDA0002712870660000023
May be derived from the ASAP scheduling algorithm.
Operation opiIn a control step csjProbability P (op)i,csj) Is composed of
Figure BDA0002712870660000024
The probability distribution over each control step is then obtained as follows
Figure BDA0002712870660000025
Where n is the total number of operations of that type, K (cs)j) Can be regarded as k in the mechanical formula f ═ k × x, and is used for representing control step csjThe initial pressure of (a). Let x (cs)k) Represents an operation opiScheduling to control step csjWhen, P (op)i,csj) In a control step csjThe generated variation can be regarded as x in the mechanical formula. And drawing a probability distribution diagram through the probability distribution condition.
Solving the direct force and the indirect force to obtain the resultant force, i.e. the operation opiScheduling to control step csjThe direct forces generated are:
Figure BDA0002712870660000026
when cs isk＝csjX (cs) isk) 1-1/h; when cs isk≠csjX (cs) isk) -1/h. The above formula is modified to obtain:
Figure BDA0002712870660000027
the deformation formula avoids the pair x (cs)k) The direct acting force generated by the dispatching operation can be obtained by directly utilizing the initial pressure distribution condition. Considering operation opiScheduling to control step csjThe influence of the successor on the predecessor and successor is generated by the scheduling, and the indirect force formula is as follows
Figure BDA0002712870660000028
Wherein opwEither immediately preceding or succeeding the current operation,
Figure BDA0002712870660000029
is opwThe time frame of (a) is,
Figure BDA00027128706600000210
to operate oniPost-dispatch opwThe length of the time frame of the update,
Figure BDA0002712870660000031
aiming at the indirect force, the algorithm time complexity can reach
Figure BDA0002712870660000032
Will opiScheduling to csjThe resultant force calculation formula is as follows
F(opi,csj)＝Fdirect(opi,csj)+Findirect(opi,csj,opw) (7)
Disclosure of Invention
The invention aims to solve the technical problem of providing a rapid and efficient FPGA high-level comprehensive scheduling method in order to adapt to the continuous increase of the scale of FPGA devices.
The technical scheme adopted by the invention for solving the technical problems is that the FPGA high-level comprehensive scheduling method comprises the following steps:
1) the time frame length for each operation is calculated:
operation opiMay be expressed as
Figure BDA0002712870660000033
Wherein ALAP (op)i) Representing operations opiThe latest control step that can be scheduled is recorded as
Figure BDA0002712870660000034
ASAP(opi) To operate oniThe earliest control step that can be scheduled is recorded as
Figure BDA0002712870660000035
2) Calculating the sum of the probability of each operation in each control step according to the time frame to obtain probability distribution, namely operation opiIn a control step csjProbability P (op)i,csj) Comprises the following steps:
Figure BDA0002712870660000036
the probability distribution over each control step is as follows:
Figure BDA0002712870660000037
where n is the total number of operations of that type, K (cs)j) Indicating the control step csjAn initial pressure on;
3) judging whether operations which are not scheduled exist, if so, calculating direct force and indirect force of all operations to be scheduled to each control step in the time frame, and selecting (op) with minimum resultant forcei,csj) The scheduling is carried out, the length of the time frame of the current operation is set to be 1,otherwise, finishing the scheduling;
wherein the content of the first and second substances,
(3.a) calculating the direct force: let x (cs)k) Represents an operation opiScheduling to control step csjWhen, P (op)i,csj) In a control step csjThe generated variable is to be operated oniScheduling to control step csjThe direct forces generated are:
Figure BDA0002712870660000041
(3.b) calculating the inter-relay;
4) updating the time frames of the direct predecessor and direct successor of the operation;
5) updating the probability distribution, go to 3);
the method is characterized in that in the step (3.b), the inter-relay force is calculated by adopting the following method:
Figure BDA0002712870660000042
wherein opwEither immediately preceding or succeeding the current operation,
Figure BDA0002712870660000043
is opwThe length of the time frame of (a),
Figure BDA0002712870660000044
to operate oniPost-dispatch opwThe length of the time frame of the update,
Figure BDA0002712870660000045
Figure BDA0002712870660000046
the invention improves the existing scheduling algorithm, and simplifies the calculation of indirect force in the calculation of involution force. While solving for intermediate relay for any predecessor or successorThe algorithm needs to be calculated before improvement
Figure BDA0002712870660000047
Direct force generated by secondary predecessor or successor implicit scheduling is not needed to be considered independently in the improved algorithm, indirect force is calculated directly, and the time complexity of the algorithm can be changed from the original time
Figure BDA0002712870660000048
Is reduced to
Figure BDA0002712870660000049
For a large-scale integrated circuit, the invention obviously improves the reduction of the operation amount of the scheduling algorithm, and can effectively improve the running speed of the system without reducing the scheduling effect.
Drawings
FIG. 1 is a flow chart of an FPGA high-level scheduling algorithm.
Fig. 2 is a data flow diagram of embodiment 1.
Fig. 3 is a schematic diagram of the distribution of the operation time frames.
Fig. 4 is a diagram illustrating a scheduling result according to an embodiment.
Detailed Description
The invention improves the existing force guidance algorithm based on time frame length priority division, simplifies the calculation mode of indirect force, and avoids the complex calculation process of the indirect force when the length of the time frame of the predecessor or successor of the current operation is larger. The problem of excessive calculation in the force guidance algorithm can be further solved.
The invention is characterized in that the intermediate relay formula of the original algorithm is improved, and the intermediate relay formula (6) in the prior art is replaced by the following formula:
Figure BDA0002712870660000051
wherein the content of the first and second substances,
Figure BDA0002712870660000052
representing operations opiScheduling to control step csjThen at opwAn average value of the initial pressure within the schedulable time frame range;
Figure BDA0002712870660000053
represents opwInitial pressure average value in the range of the original time frame. Differencing the two terms may characterize the operation opiScheduling to control step csjIndirect effects of time. The algorithm time complexity of the improved intermediate relay can be reduced to
Figure BDA0002712870660000054
Selecting (op) with the smallest resultant forcei,csj) For scheduling, when the resultant force is the same, sigma can be selectedAlltypeK(csi) The smaller control step is scheduled.
And after the current operation scheduling is finished, updating the preceding time frame and the following time frame, and implicitly scheduling and deleting the operation to be scheduled, which can be determined by the child node after the parent node is scheduled.
When the probability distribution map needs to be updated, only the operation type and the time frame which affect the current operation type and the time frame thereof and the implicit scheduling are considered for updating.
To further illustrate the present invention, an analysis is performed according to the dataflow diagram shown in FIG. 2, assuming that all numbered operations are of the same type.
For the data stream shown in fig. 2, the operation time frame representation obtained by using the ASAP and ALAP algorithms is shown in fig. 3.
Wherein cs is1-cs5To control the step, op1-op10To operate, it can be seen that op1、op2、op4、op5、op8、op10For critical path operations, the only op to be scheduled is3、op6、op7、op9. (Note: conventional force-guided algorithms need to calculate the resultant force of all the operations, this documentIn the embodiment, the time frame is sorted according to the sorting length) and all the operation to be scheduled are sorted according to the time frame length and then are op6、op9、op3、op7And 2, the initial pressure distribution on each control step can be obtained through calculation and is shown in the table 1.
TABLE 1 initial pressure distribution over control steps
Control step Initial pressure (K (cs)i))
cs 1 1
cs 2 4/3
cs3 19/6
cs 4 8/3
cs5 11/6
First op6And (3) scheduling to obtain the following resultant force calculation formula:
(Note: since the scheduling of op6 to cs3 has no effect on predecessor successors, it is sufficient to directly calculate predecessor forces)
Figure BDA0002712870660000061
Figure BDA0002712870660000062
Selecting the operation-control step pair (op) with the smallest resultant force6,cs4) Will op6Scheduling to cs4，4.op9For its immediate successor operation, it can only be implicitly scheduled to cs5。
After updating probability distribution, p pairs3Scheduling is carried out to obtain
Figure BDA0002712870660000063
Figure BDA0002712870660000064
Will op3Scheduling to cs2. Subsequent op7Can be scheduled to cs3、cs4And cs5Updating the probability distribution map, F (op)7,cs3)＝0，F(op7,cs4)＝0，F(op7,cs5) And (4) performing scheduling in the optional control step, and performing scheduling for three times to obtain a final result as shown in fig. 4.

Claims (1)

  1. The FPGA high-level comprehensive scheduling method comprises the following steps:
    1) the time frame length for each operation is calculated:
    operation opiMay be expressed as
    Figure FDA0002712870650000011
    Wherein ALAP (op)i) Representing operations opiThe latest control step that can be scheduled is recorded as
    Figure FDA0002712870650000012
    ASAP(opi) To operate oniThe earliest control step that can be scheduled is recorded as
    Figure FDA0002712870650000013
    2) Calculating the sum of the occurrence probability of each operation in each control step according to the time frame to obtain probability distribution:
    operation opiIn a control step csjProbability P (op)i,csj) Comprises the following steps:
    Figure FDA0002712870650000014
    the probability distribution over each control step is as follows:
    Figure FDA0002712870650000015
    where n is the total number of operations of that type, K (cs)j) Indicating the control step csjAn initial pressure on;
    3) judging whether operations which are not scheduled exist, if so, calculating direct force and indirect force of all operations to be scheduled to each control step in the time frame, and selecting (op) with minimum resultant forcei,csj) Scheduling, and setting the length of the current operation time frame as 1, otherwise ending the scheduling;
    wherein the content of the first and second substances,
    (3.a) calculating the direct force: let x (cs)k) Represents an operation opiScheduling to control step csjWhen, P (op)i,csj) In a control step csjThe generated variable is to be operated oniScheduling to control step csjThe direct forces generated are:
    Figure FDA0002712870650000016
    (3.b) calculating the inter-relay;
    4) updating the time frames of the direct predecessor and direct successor of the operation;
    5) updating the probability distribution, go to 3);
    the method is characterized in that in the step (3.b), the inter-relay force is calculated by adopting the following method:
    Figure FDA0002712870650000021
    wherein opwEither immediately preceding or succeeding the current operation,
    Figure FDA0002712870650000022
    is opwThe length of the time frame of (a),
    Figure FDA0002712870650000023
    to operate oniPost-dispatch opwThe length of the time frame of the update,
    Figure FDA0002712870650000024
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