feat: shortfall rework

[failingtwice]

A short summary of the changes.

Context

#1305

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Math

• LS = liability shares
• TVS = total value in shares (floor)
• B = 10000 (basis points base)
• T = thresholdBP
• M = B - T = mintRatio in bp.
• X = shortfall (misleading name btw)

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Vault is healthy if:

LS / TVS <= M / B

or

LS * B <= TVS * M

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Rebalance does the following

LS - X

rebalance(roundUp(X))

and

TVS - Y

Normally, X == Y

BUT

because rebalance rounds UP, in the worst case scenario

Y = X + 1

thus, we can derive the post-rebalance condition:

(LS - X) * B <= (TVS - X - 1) * M

OR (using distributive property)

LS * B - X * B <= TVS * M - X * M - M

add X * M to both sides

LS * B - X * B + X * M <= TVS * M - M

subtract LS * B

- X * B + X * M <= TVS * M - M - LS * B

or factor X

X (M - B) <= TVS * M - M - LS * B

because

T = M - B

X * (-T) <= TVS * M - M - LS * B

divide both sides by -T and flip the sign

X >= (TVS * M - M - LS * B) / (-T)

move minus to numerator

X >= -(TVS * M - M - LS * B) / T

factor -1

X >= (-TVS * M + M + L * B) / T

rearrange and get the final inequality

X >= (L * B - TVS * M + M) / T

AND after all of that we need to use ceiling division because the final inequality also includes division

X >= (L * B - TVS * M + M) + (T - 1) / T

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