Preallocate witness before synthesis

[winston-h-zhang]

Addresses #137 and replaces #138.

This PR uses the new API in WitnessCS to preallocate the witness buffers before calling synthesize. This ensures that we do not unnecessarily grow and reallocate these large witness buffers, which adds overhead.

[winston-h-zhang]

Benchmarks

Table of Contents

• Benchmark Results
  • LEM Fibonacci Prove Fresh - rc = 100
  • LEM Fibonacci Prove Fresh - rc = 600
  • LEM Fibonacci Prove Load - rc = 100
  • LEM Fibonacci Prove Load - rc = 600

Benchmark Results

LEM Fibonacci Prove Fresh - rc = 100

	new-witness-cs/fib	all-ops/fib
num-100	6.37 s	6.30 s
num-200	13.06 s	12.76 s
adthrpt	224.2	247.7

LEM Fibonacci Prove Fresh - rc = 600

	new-witness-cs/fib	all-ops/fib
num-100	4.41 s	4.43 s
num-200	10.43 s	10.27 s
adthrpt	299.0	308.2

LEM Fibonacci Prove Load - rc = 100

	new-witness-cs/fib	all-ops/fib
num-100	6.24 s	6.22 s
num-200	12.71 s	12.66 s
adthrpt	247.3	248.4

LEM Fibonacci Prove Load - rc = 600

	new-witness-cs/fib	all-ops/fib
num-100	5.00 s	4.72 s
num-200	11.49 s	10.74 s
adthrpt	277.4	299.0

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Made with criterion-table

[winston-h-zhang]

I've pasted benchmarks comparing this PR to #118. After #139 and the changes in this PR, we're still missing some performance. So the rest of the gap can reasonably be attributed to the remaining large-vector allocations (edit: #144) that #118 removes.

[huitseeker]

Excellent overall, thanks a lot!