Bash split stdin by null and pipe to pipeline - bash

Question

I have a stream that is null delimited, with an unknown number of sections. For each delimited section I want to pipe it into another pipeline until the last section has been read, and then terminate.
In practice, each section is very large (~1GB), so I would like to do this without reading each section into memory.
For example, imagine I have the stream created by:
for I in {3..5}; do seq $I; echo -ne '\0';
done
I'll get a steam that looks like:
1
2
3
^#1
2
3
4
^#1
2
3
4
5
^#
When piped through cat -v.
I would like to pipe each section through paste -sd+ | bc, so I get a stream that looks like:
6
10
15
This is simply an example. In actuality the stream is much larger and the pipeline is more complicated, so solutions that don't rely on streams are not feasible.
I've tried something like:
set -eo pipefail
while head -zn1 | head -c-1 | ifne -n false | paste -sd+ | bc; do :; done
but I only get
6
10
If I leave off bc I get
1+2+3
1+2+3+4
1+2+3+4+5
which is basically correct. This leads me to believe that the issue is potentially related to buffering and the way each process is actually interacting with the pipes between them.
Is there some way to fix the way that these commands exchange streams so that I can get the desired output? Or, alternatively, is there a way to accomplish this with other means?
In principle this is related to this question, and I could certainly write a program that reads stdin into a buffer, looks for the null character, and pipes the output to a spawned subprocess, as the accepted answer does for that question. Given the general support of streams and null delimiters in bash, I'm hoping to do something that's a little more "native". In particular, if I want to go this route, I'll have to escape the pipeline (paste -sd+ | bc) in a string instead of just letting the same shell interpret it. There's nothing too inherently bad about this, but it's a little ugly and will require a bunch of somewhat error prone escaping.
Edit
As was pointed out in an answer, head makes no guarantees about how much it buffers. Unless it only buffers single byte at a time, which would be impractical, this will never work. Thus, it seems like the only solution would be to read it into memory, or write a specific program.

Answer 1

The issue with your original code is that head doesn't guarantee that it won't read more than it outputs. Thus, it can consume more than one (NUL-delimited) chunk of input, even if it's emitting only one chunk of output.
read, by contrast, guarantees that it won't consume more than you ask it for.
set -o pipefail
while IFS= read -r -d '' line; do
bc <<<"${line//$'\n'/+}"
done < <(build_a_stream)
If you want native logic, there's nothing more native than just writing the whole thing in shell.
Calling external tools -- including bc, cut, paste, or others -- involves a fork() penalty. If you're only processing small amounts of data per invocation, the efficiency of the tools is overwhelmed by the cost of starting them.
while read -r -d '' -a numbers; do # read up to the next NUL into an array
sum=0 # initialize an accumulator
for number in "${numbers[#]}"; do # iterate over that array
(( sum += number )) # ...using an arithmetic context for our math
done
printf '%s\n' "$sum"
done < <(build_a_stream)
For all of the above, I tested with the following build_a_stream implementation:
build_a_stream() {
local i j IFS=$'\n'
local -a numbers
for ((i=3; i<=5; i++)); do
numbers=( )
for ((j=0; j<=i; j++)); do
numbers+=( "$j" )
done
printf '%s\0' "${numbers[*]}"
done
}

Answer 2

As discussed, the only real solution seemed to be writing a program to do this specifically. I wrote one in rust called xstream-util. After installing it with cargo install xstream-util, you can pipe the input into
xstream -0 -- bash -c 'paste -sd+ | bc'
to get the desired output
6
10
15
It doesn't avoid having to run the program in bash, so it still needs escaping if the pipeline is complicated. Also, it currently only supports single byte delimiters.