Inconsistency when using `calculate_open_short` and `calculate_max_short` together

[DannyDelott]

Background

The sdk's calculate_max_short method takes a budget and returns a bond amount.

The calculate_open_short takes a bond amount and returns the trader deposit (ie: budget).

We expect that the outputs of one would reflect the inputs of the other, however the steps below show that this is not the case.

Steps to reproduce

1. Call calculate_max_short with a max uint256 budget to get the pool's max short (in bonds).
2. Feed this bond amount into calculate_open_short to get the actual traderDeposit needed.
3. Feed the traderDeposit back into calculate_max_short as the budget.

Expected

The bond amount returned from calculate_max_short should be the same as the bond amount we gave to calculate_open_short.

Actual

Feeding the traderDeposit back into calculate_max_short results in significantly fewer bonds shorted.

Usecase:
In the Open Short form, users can input either an amount to pay (budget) or the number of bonds to short.

Depending on which one they type into, either calculate_max_short or calculate_open_short will be called to update the form.

[DannyDelott]

We're currently not passing a conservative_price argument to calcMaxShort, there is prior art on how to calculate this here that we should try:

hyperdrive-rs/crates/hyperdrive-math/src/test_utils/agent.rs

Line 178 in e4fcc39

let conservative_price = {

[dpaiton]

Tasks :

• fix max_short_guess add calculate_approximate_short_bonds_given_base_deposit #198
• investigate, test, & possibly fix calculate_max_short_upper_bound
• fix calculate_absolute_max_short
• fix calculate_max_short add calculate_short_bonds_given_deposit #199
• fix or deprecate conservative LP price calculation