every multiply and divide in the mint and burn paths is a full precision multiply then divide, rounding down. the largest intermediate is K times S squared, which is 2 to the 43rd times 10 to the 54th, about 8.8 times 10 to the 66th, well inside a 256 bit word. the square of S plus position stays inside the word for any position under a billion eth.
rounding down at every step means the contract under issues by at most one base unit per mint and under pays by at most one wei per burn, and never the other way. the site's curve module reproduces this with bigint and the tests in this build pin twelve values.
| expression | value |
|---|---|
| p(0) in wei per token | 7 629 394 531 250 |
| q(1 eth) − q(0) in base units | 130 688 997 564 302 786 422 413 |
| K × S² | 8 796 093 022 208 followed by 54 zeros |
| (7/8)^64 fp18 | 194 319 056 637 162 |
| (7/8)^512 fp18 | 0 |
| blocks of full budget from seed to pressure one | 36 |