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Added extra precision to interpolation points in general payout functions

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nkohen
2020-12-29 02:08:40 -06:00
parent 277ffe639b
commit c4fb12d95a
1 changed files with 11 additions and 1 deletions
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PayoutCurve.md
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@@ -71,13 +71,15 @@ In this section we detail the TLV serialization for a general `payout_function`.
* [`boolean`:`is_endpoint_1`]
* [`bigsize`:`event_outcome_1`]
* [`bigsize`:`outcome_payout_1`]
* [`u16`:`extra_precision_1`]
* ...
* [`boolean`:`is_endpoint_num_pts`]
* [`bigsize`:`event_outcome_num_pts`]
* [`bigsize`:`outcome_payout_num_pts`]
* [`u16`:`extra_precision_num_pts`]
`num_pts` is the number of points on the payout curve that will be provided for interpolation.
Each point consists of a `boolean` and two `bigsize` integers.
Each point consists of a `boolean` and two `bigsize` integers and a `u16`.
The `boolean` is called `is_endpoint` and if this is true, then this point marks the end of a
polynomial piece and the beginning of a new one. If this is false then this is a midpoint
@@ -86,6 +88,14 @@ The first integer is called `event_outcome` and contains the actual number that
(note: not in the serialization used by the oracle) which corresponds to an x-coordinate on the payout curve.
The second integer is called `outcome_payout` and is set equal to the local party's payout should
`event_outcome` be signed which corresponds to a y-coordinate on the payout curve.
The third integer, a `u16`, is called `extra_precision` and is set to be the first 16 bits of the payout after
the binary point which were rounded away.
This extra precision ensures that interpolation does not contain large errors due to error in the
`outcome_payout`s due to rounding.
To be precise, the points used for interpolation should be:
(`event_outcome`, `outcome_payout + double(extra_precision) >> 16`).
For the remainder of this document, the value `outcome_payout + double(extra_precision) >> 16`
is refered to as `outcome_payout`.
Note that this `payout_function` is from the offerer's point of view.
To evaluate the accepter's `payout_function`, you must evaluate the offerer's `payout_function` at a given