fig_3_16 dependency graph processing is doing x[i] calculations twice

[jnorwood]

I added logging to fig_3_16 dependency graph example and exercised it with several different block sizes. The block where it computes the x[i] values is sometimes being executed twice. Below is a log for block_size=1 and N=8 that shows the "calc" executions occurring twice. It also has multiple calc executions when block_size=2, so it isn't a block_size=1 issue.

r:c= calc x[0]=0,
r:c=0:1, calc x[1]=0.5,
r:c= calc x[1]=0.5,
r:c=0:2,
r:c=0:3,
r:c=0:4,
r:c=1:2, calc x[2]=0.5,
r:c=1:3,
r:c=0:5,
r:c=1:4,
r:c= calc x[2]=0.5,
r:c=0:6,
r:c=1:5,
r:c=2:3, calc x[3]=0.35,
r:c=1:6,
r:c=0:7,
r:c=2:4,
r:c=2:5,
r:c=2:6,
r:c= calc x[3]=0.35,
r:c=1:7,
r:c=2:7,
r:c=3:4, calc x[4]=0.261765,
r:c=3:5,
r:c=3:6,
r:c= calc x[4]=0.261765,
r:c=3:7,
r:c=4:5, calc x[5]=0.207805,
r:c= calc x[5]=0.207805,
r:c=4:6,
r:c=4:7,
r:c=5:6, calc x[6]=0.171998,
r:c=5:7,
r:c= calc x[6]=0.171998,
r:c=6:7, calc x[7]=0.146639,
r:c= calc x[7]=0.146639,

I'm attaching the modified fig_3_16 example with logging and random delays inserted.

fig_3_16.zip

[jnorwood]

In investigating this, I'm changing the initialization data to use non-zero values, since a 0 can hide processing errors. So, the question is why are x[i] values are computed twice. I'm logging for N=8 and for block_size values of 1, 2 ,4 and 8. I'm also fixing the r:c index order log in this version

r:c=0:0, calc x[0]=5, no ops
r:c=1:0, calc x[1]=0.5,
r:c=2:0,
r:c=1:1, calc x[1]=0.5, no ops
r:c=3:0,
r:c=2:1, calc x[2]=0.5,
r:c=4:0,
r:c=3:1,
r:c=5:0,
r:c=4:1,
r:c=6:0,
r:c=5:1,
r:c=2:2, calc x[2]=0.5, no ops
r:c=6:1,
r:c=3:2, calc x[3]=0.35,
r:c=7:0,
r:c=3:3, calc x[3]=0.35, no ops
r:c=7:1,
r:c=4:2,
r:c=5:2,
r:c=4:3, calc x[4]=0.261765,
r:c=6:2,
r:c=4:4, calc x[4]=0.261765, no ops
r:c=7:2,
r:c=5:3,
r:c=6:3,
r:c=5:4, calc x[5]=0.207805,
r:c=7:3,
r:c=5:5, calc x[5]=0.207805, no ops
r:c=6:4,
r:c=7:4,
r:c=6:5, calc x[6]=0.171998,
r:c=7:5,
r:c=6:6, calc x[6]=0.171998, no ops
r:c=7:6, calc x[7]=0.146639,
r:c=7:7, calc x[7]=0.146639, no ops
parallel_time block_count:1 == 0.172112 seconds
r:c=0:0, calc x[0]=5, calc x[1]=0.5,
r:c=2:0,2:1, calc x[2]=0.5, 3:0,3:1,
r:c=4:0,4:1,5:0,5:1,
r:c=2:2, calc x[2]=0.5, calc x[3]=0.35,
r:c=6:0,6:1,7:0,7:1,
r:c=4:2,4:3, calc x[4]=0.261765, 5:2,5:3,
r:c=4:4, calc x[4]=0.261765, calc x[5]=0.207805,
r:c=6:2,6:3,7:2,7:3,
r:c=6:4,6:5, calc x[6]=0.171998, 7:4,7:5,
r:c=6:6, calc x[6]=0.171998, calc x[7]=0.146639,
parallel_time block_count:2 == 0.0805095 seconds
r:c=0:0, calc x[0]=5, calc x[1]=0.5, 2:0,2:1, calc x[2]=0.5, 3:0,3:1,3:2, calc x[3]=0.35,
r:c=4:0,4:1,4:2,4:3, calc x[4]=0.261765, 5:0,5:1,5:2,5:3,6:0,6:1,6:2,6:3,7:0,7:1,7:2,7:3,
r:c=4:4, calc x[4]=0.261765, calc x[5]=0.207805, 6:4,6:5, calc x[6]=0.171998, 7:4,7:5,7:6, calc x[7]=0.146639,
parallel_time block_count:4 == 0.0131065 seconds
r:c=0:0, calc x[0]=5, calc x[1]=0.5, 2:0,2:1, calc x[2]=0.5, 3:0,3:1,3:2, calc x[3]=0.35, 4:0,4:1,4:2,4:3, calc x[4]=0.261765, 5:0,5:1,5:2,5:3,5:4, calc x[5]=0.207805, 6:0,6:1,6:2,6:3,6:4,6:5, calc x[6]=0.171998, 7:0,7:1,7:2,7:3,7:4,7:5,7:6, calc x[7]=0.146639,
parallel_time block_count:8 == 0.00705842 seconds

fig_3_16.zip