```# source code of yield-based parallel reduction schedule:
from preduce import preduce_y
from copy import copy

def preduce(vl, vec, pred):
vec = copy(vec)
step = 1
print(" start", step, pred, vec)
while step < vl:
step *= 2
for i in range(0, vl, step):
other = i + step // 2
other_pred = other < vl and pred[other]
if pred[i] and other_pred:
vec[i] += vec[other]
elif other_pred:
vec[i] = vec[other]
print("   row", step, pred, vec)
return vec

def preducei(vl, vec, pred):
vec = copy(vec)
step = 1
ix = list(range(vl)) # indices move rather than copy data
print(" start", step, pred, vec)
while step < vl:
step *= 2
for i in range(0, vl, step):
other = i + step // 2
ci = ix[i]
oi = ix[other] if other < vl else None
other_pred = other < vl and pred[oi]
if pred[ci] and other_pred:
vec[ci] += vec[oi]
elif other_pred:
ix[i] = oi # leave data in-place, copy index instead
print("   row", step, pred, vec, ix)
return vec

if __name__ == '__main__':
vec = [1, 2, 3, 4, 9, 5, 6]
prd = [0, 1, 1, 1, 0, 0, 1]
print (vec)
res = preduce(len(vec), vec, prd)
print (res)
res2 = preducei(len(vec), vec, prd)
print (res2)
print ()
preduce_y(len(vec), vec, prd)
print (vec)
print ()
assert vec == res2

vec = [1, 2, 3, 4, 9, 5, 6]
prd = [1, 0, 0, 1, 1, 0, 1]
print (vec)
res = preduce(len(vec), vec, prd)
print (res)
res2 = preducei(len(vec), vec, prd)
print (res2)
print ()
preduce_y(len(vec), vec, prd)
print (vec)
print ()
assert vec == res2

vec = [1, 2, 3, 4, 9, 5, 6, 8]
prd = [0, 0, 0, 0, 1, 1, 1, 1]
print (vec)
res = preduce(len(vec), vec, prd)
print (res)
res2 = preducei(len(vec), vec, prd)
print (res2)
print ()
preduce_y(len(vec), vec, prd)
print (vec)
print ()
assert vec == res2

vec = [1, 2, 3, 4, 9, 5, 6, 8]
prd = [0, 1, 0, 0, 0, 1, 0, 1]
print (vec)
res = preduce(len(vec), vec, prd)
print (res)
res2 = preducei(len(vec), vec, prd)
print (res2)
print ()
preduce_y(len(vec), vec, prd)
print (vec)
print ()
assert vec == res2

vec = [1, 2, 3, 4, 9, 5, 6]
prd = [1, 0, 1, 1, 0, 0, 1]
print (vec)
res = preduce(len(vec), vec, prd)
print (res)
res2 = preducei(len(vec), vec, prd)
print (res2)
print ()
preduce_y(len(vec), vec, prd)
print (vec)
print ()
assert vec == res2

```