> For the complete documentation index, see [llms.txt](https://bubblegum-reality.gitbook.io/bubblegum-reality-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://bubblegum-reality.gitbook.io/bubblegum-reality-docs/reference/math.md).

# Math Utilities

`src/lib/money.ts` — the only place token arithmetic happens. `decimal.js` is configured to 40-digit precision with `ROUND_DOWN`.

## Conversions

```ts
fromBaseUnits(value: bigint | string, decimals: number): Decimal
toBaseUnits(value: Decimal.Value, decimals: number): bigint
```

* `decimals` must be an integer in `[0, 36]` — otherwise it throws.
* `toBaseUnits` truncates excess precision downward and throws on negatives.

## Reference pricing

```ts
adjustedReference(rawPrice, multiplier): Decimal   // throws if multiplier ≤ 0
spreadBps(bid, ask): number | null                // null if either side ≤ 0
```

## Execution cost

```ts
executionCostBps({
  side: "buy" | "sell",
  usdgAmount: Decimal.Value,   // human USDG moved
  tokenAmount: Decimal.Value,  // human stock-token moved
  referencePrice: Decimal.Value,// multiplier-adjusted price of one token
}): number | null
```

Positive is always worse than reference, on both sides. `null` when any input is non-positive.

## Formatting

```ts
formatUsd(value, dp = 2)     // "$214.87"  | "—"
formatAmount(value, dp = 6)  // "12.345678"| "—"
formatBps(value)             // "+48.3 bps"| "—"
```

All three render `—` for `null` / `undefined`. `formatBps` prefixes `+` for positive values so direction is unambiguous.

## Rules

1. **Never `Number(amount)` on a token value.** Parse to `Decimal` or `bigint`.
2. **Never round up** a user-supplied amount.
3. **Return `null`, not `0`**, when a metric is undefined — `0 bps` is a claim, `—` is not.
4. **Throw on corrupt inputs** (non-positive multiplier, bad decimals) instead of degrading into a wrong number.

Covered by `src/lib/__tests__/money.test.ts`.


---

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