feat(math): Upstream GDA based decimal type

docs/build/building-modules/18-decimal-handling.md

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+---
+sidebar_position: 1
+---
+# Decimal Handling in Cosmos SDK
+
+## Introduction
+
+In the Cosmos SDK, there are two types of decimals: `LegacyDec` and `Dec`. `LegacyDec` is the older decimal type that is still available for use, while `Dec` is the newer, more performant decimal type. The implementation of `Dec` is adapted from Regen Network's `regen-ledger`, specifically from [this module](https://github.com/regen-network/regen-ledger/tree/main/types/math). Migrating from `LegacyDec` to `Dec` involves state-breaking changes, specifically:
+
+* **Data Format**: The internal representation of decimals changes, affecting how data is stored and processed.
+* **Precision Handling**: `Dec` supports flexible precision up to 34 decimal places, unlike `LegacyDec` which has a fixed precision of 18 decimal places.
+
+These changes require a state migration to update existing decimal values to the new format. It is recommended to use `Dec` for new modules to leverage its enhanced performance and flexibility.
+
+## Why the Change?
+
+* Historically we have wrapped a `big.Int` to represent decimals in the Cosmos SDK and never had a decimal type. Finally, we have a decimal type that is more efficient and accurate.
+* `Dec` uses the [apd](https://github.com/cockroachdb/apd) library for arbitrary precision decimals, suitable for accurate financial calculations.
+* `Dec` operations are safer for concurrent use as they do not mutate the original values.
+* `Dec` operations are faster and more efficient than `LegacyDec`.
+
+## Using `Dec` in Modules that haven't used `LegacyDec`
+
+If you are creating a new module or updating an existing module that has not used `LegacyDec`, you can directly use `Dec` without any changes.
+
+-- math.NewLegacyDecFromInt64(100)
+++ math.NewDecFromInt64(100)
+
+-- math.LegacyNewDecWithPrec(100, 18)
+++ math.NewDecWithPrec(100, 18)
+
+-- math.LegacyNewDecFromStr("100")
+++ math.NewDecFromStr("100")
+
+-- math.LegacyNewDecFromStr("100.000000000000000000").Quo(math.LegacyNewDecFromInt(2))
+++ math.NewDecFromStr("100.000000000000000000").Quo(math.NewDecFromInt(2))
+
+-- math.LegacyNewDecFromStr("100.000000000000000000").Add(math.LegacyNewDecFromInt(2))
+++ math.NewDecFromStr("100.000000000000000000").Add(math.NewDecFromInt(2))
+
+-- math.LegacyNewDecFromStr("100.000000000000000000").Sub(math.LegacyNewDecFromInt(2))
+++ math.NewDecFromStr("100.000000000000000000").Sub(math.NewDecFromInt(2))
+
+
+## Modules migrating from `LegacyDec` to `Dec`
+
+When migrating from `LegacyDec` to `Dec`, you need to update your module to use the new decimal type. **These types are state breaking changes and require a migration.**
+
+## Precision Handling
+
+The reason for the state breaking change is the difference in precision handling between the two decimal types:
+
+* **LegacyDec**: Fixed precision of 18 decimal places.
+* **Dec**: Flexible precision up to 34 decimal places using the apd library.
+
+## Impact of Precision Change
+
+The increase in precision from 18 to 34 decimal places allows for more detailed decimal values but requires data migration. This change in how data is formatted and stored is a key aspect of why the transition is considered state-breaking.
+
+## Converting `LegacyDec` to `Dec` without storing the data
+
+If you would like to convert a `LegacyDec` to a `Dec` without a state migration changing how the data is handled internally within the application logic and not how it's stored or represented. You can use the following methods.
+
+```go
+func LegacyDecToDec(ld LegacyDec) (Dec, error) {
+    return NewDecFromString(ld.String())
+}
+```
+
+```go
+func DecToLegacyDec(ld Dec) (LegacyDec, error) {
+    return LegacyDecFromString(ld.String())
+}
+```
+