Factour out some functions from llm-utils repository

[nicovank]

A first set of factoring out of common method re-using those already in llm-utils.

This removes duplicate code but will also improve accuracy / quality of output.

Test Plan:

% pip install .
% g++ -g ./test/test-failed-assert.cpp
% gdb ./a.out
(gdb) % run
(gdb) % why
The issue arises from the function `fact(float n)` defined in the file `test-
failed-assert.cpp`. Specifically, the issue lies in the for-loop where the
factorial is being calculated.

In this loop, `i` is initialized to `0.0` and then on each iteration, the
variable `x` is multiplied by `i`. Thus, in the first iteration, `x` is zero
because it's being multiplied by `i`, which is `0.0`. The loop therefore sets
`x` to zero and it remains zero in all subsequent iterations, regardless of the
value of `n`. Then, immediately after the loop, there's an assertion checking
that `x` is not zero. Given `x` is always zero due to the loop, this assertion
always fails and calls `abort()`, resulting in the SIGABRT signal recorded in
the stack trace.

To fix this issue, start the for-loop counter `i` from `1.0` instead of `0.0`.
This will ensure that `x` is not set to zero on the first iteration, and give a
correct calculation for the factorial of `n`. The modified function would look
like this:

```c++
float fact(float n) {
  auto x = 1.0;
  for (auto i = 1.0; i <= n; i++) {
    x *= i;
  }
  assert(x != 0.0);
  return x;
}
```

This adjustment will skip the 0 and start multiplication from 1, so the function
should now calculate the factorial correctly for values of `n` greater than 0,
without failing the assertion.
(Total cost: approximately $0.04 USD.)

[ravenblood000]

Looks good to me! :)