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systolic.py
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systolic.py
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#################################################################################
## Abstraction of a Systolic Array HW
##
##
##################################################################################
from collections import namedtuple
MatrixElement = namedtuple(
'MatrixElement', [
'value',
'row',
'column'
]
)
Matrix = namedtuple(
'Matrix', [
'elements',
'M',
'N'
]
)
###
## if last row >= current row
## == it means that I am stuck with a vector composed of only one element
## > drop of index means that we went back in the sequence
###
def row_marker(last, current):
return last.row >= current.row
###
## if last column >= current column
## == it means that I am stuck with a vector composed of only one element
## > drop of index means that we went back in the sequence
###
def column_marker(last, current):
return last.column >= current.column
class FIFOQueue:
## N length
## x possible contents
## marker function to tell me when the contents have reached the end
def __init__(self,
N,
x=None,
marker =None):
self.max = N
self.fifo = [] if x is None else x
self.m = marker
self.ghost = None
def reset(self):
return False
def insert(self,x):
if len(self.fifo)< self.max:
self.fifo.append(x)
return x
return None
def pop(self):
if (len(self.fifo)>0):
self.ghost = self.fifo[0]
return self.fifo.pop(0)
return None
def top(self):
if (len(self.fifo)>0):
return self.fifo[0]
return None
def last(self):
return len(self.fifo)==1
def empty(self):
return len(self.fifo)==0
def marker(self):
if self.empty() or self.ghost is None :
return False
return self.m(self.ghost,self.fifo[0])
class CircularQueue:
## N length
## x vector of length N
def __init__(self,x, marker=None):
self.max = len(X)
self.X = x
self.index=0
self.m = marker
self.ghost = None
def top(self):
return self.X[self.index]
def pop(self):
self.ghost = self.X[self.index]
self.index +=1
self.index = self.index % self.max
return self.X[self.index]
def insert(self,x):
self.X[self.index] =x
self.index +=1
self.index = self.index % self.max
def reset(self,X=None):
if not X is None:
self.X = X
self.max = len(X)
self.index=0
return True
def last(self):
return len(self.X)==self.index+1
def empty(self):
return len(self.X)==self.index+1
def marker(self):
if self.empty() or self.ghost is None :
return False
return self.m(self.ghost,self.top())
##
## a += b*c graph style
##
def mul(a,b):
return a+b
def add(a,b):
return min(a,b)
def multiplyadd(a,b,c):
return add(a, mul(b.value+c.value))
def identity():
return int(float("inf"))
class SystolicElement:
## X Queue (left horizontal input)
## Y Queue (up vertical input)
## Z Queue (down vertical output)
## Out Queue to accumulate
def __init__(self,
X, ## circular
Y,
Z,
Out,
func = multiplyadd
identity = identity()
):
self.left = X
self.up = Y
self.down = Z
self.output = Out
self.func = func
self.pushstalls = 0
self.pullstalls = 0
self.accumulator = identity()
self.identity = identity
###
## Computation step
###
def compute(self):
count = 0
## If either input is empty, nothing to do
## We wait for the data to come.
if self.up.empty():
self.pullstalls = self.pullstalls + 1
return 0
## if left is empty ... we are pretty much done
if self.left.empty():
return -1
x = self.left.top() ## row vector(s)
y = self.up.top() ## column vector
if x.row < y.col:
self.left.pop()
elif x.row > y.col:
zip = self.down.append(y)
if zip:
self.up.pop()
count += 1
else:
self.pushstalls = self.pushstalls + 1
elif x.row == y.col:
zip = self.down.append(y)
if zip:
count +=1
self.accumulator = self.func(self.accumulator,x,y)
self.left.pop()
self.up.pop()
if self.left.marker() or self.up.marker()<0:
self.output.insert(MatrixElement(self.accumulator,x.row,y.col))
self.accumulator = self.identity()
l = self.left.marker()
u = self.up.marker()
if l: self.up.reset()
if False and u: self.left.reset()
return count
class SystolicArray:
## X Matrix
## y vector
## x = Xy
## N number of systolic elements
def __init__(self,
X,
y,
N
):
self.y = CircularQueue(y,column_marker)
self.z = FIFOQueue(N*N,column_marker)
self.Xs = SystolicArray.split(X,N) # circular queue
self.N = N
def split(X,N):
active=1
E = X.elements[0]
for e in X.elements:
if e.row != E.row:
active +=1
E =e
M = active // N