Add UD21x18 and SD21x18 types

README.md

@@ -184,14 +184,16 @@ the source code, which is well-documented with NatSpec comments.
 
 ### Adjacent Value Types
 
-PRBMath provides adjacent value types that serve as abstractions over other vanilla types such as `int64`. The types currently available are:
+PRBMath provides adjacent value types that serve as abstractions over other vanilla types:
 
 | Value Type | Underlying Type |
 | ---------- | --------------- |
 | `SD1x18`   | int64           |
+| `SD21x18`  | int128          |
 | `UD2x18`   | uint64          |
+| `UD21x18`  | uint128         |
 
-These are useful if you want to save gas by using a lower bit width integer, e.g. in a struct.
+These are useful if you want to save gas by using a lower bit width integer, e.g., in a struct.
 
 Note that these types don't have any mathematical functionality. To do math with them, you will have to unwrap them into a simple integer and then to
 the core types `SD59x18` and `UD60x18`.

src/Common.sol

@@ -32,6 +32,9 @@ uint128 constant MAX_UINT128 = type(uint128).max;
 /// @dev The maximum value a uint40 number can have.
 uint40 constant MAX_UINT40 = type(uint40).max;
 
+/// @dev The maximum value a uint64 number can have.
+uint64 constant MAX_UINT64 = type(uint64).max;
+
 /// @dev The unit number, which the decimal precision of the fixed-point types.
 uint256 constant UNIT = 1e18;
 

src/SD21x18.sol

@@ -0,0 +1,25 @@
+// SPDX-License-Identifier: MIT
+pragma solidity >=0.8.19;
+
+/*
+
+██████╗ ██████╗ ██████╗ ███╗   ███╗ █████╗ ████████╗██╗  ██╗
+██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║  ██║
+██████╔╝██████╔╝██████╔╝██╔████╔██║███████║   ██║   ███████║
+██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║   ██║   ██╔══██║
+██║     ██║  ██║██████╔╝██║ ╚═╝ ██║██║  ██║   ██║   ██║  ██║
+╚═╝     ╚═╝  ╚═╝╚═════╝ ╚═╝     ╚═╝╚═╝  ╚═╝   ╚═╝   ╚═╝  ╚═╝
+
+███████╗██████╗ ██████╗  ██╗██╗  ██╗ ██╗ █████╗
+██╔════╝██╔══██╗╚════██╗███║╚██╗██╔╝███║██╔══██╗
+███████╗██║  ██║ █████╔╝╚██║ ╚███╔╝ ╚██║╚█████╔╝
+╚════██║██║  ██║██╔═══╝  ██║ ██╔██╗  ██║██╔══██╗
+███████║██████╔╝███████╗ ██║██╔╝ ██╗ ██║╚█████╔╝
+╚══════╝╚═════╝ ╚══════╝ ╚═╝╚═╝  ╚═╝ ╚═╝ ╚════╝
+
+*/
+
+import "./sd21x18/Casting.sol";
+import "./sd21x18/Constants.sol";
+import "./sd21x18/Errors.sol";
+import "./sd21x18/ValueType.sol";

src/UD21x18.sol

@@ -0,0 +1,25 @@
+// SPDX-License-Identifier: MIT
+pragma solidity >=0.8.19;
+
+/*
+
+██████╗ ██████╗ ██████╗ ███╗   ███╗ █████╗ ████████╗██╗  ██╗
+██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║  ██║
+██████╔╝██████╔╝██████╔╝██╔████╔██║███████║   ██║   ███████║
+██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║   ██║   ██╔══██║
+██║     ██║  ██║██████╔╝██║ ╚═╝ ██║██║  ██║   ██║   ██║  ██║
+╚═╝     ╚═╝  ╚═╝╚═════╝ ╚═╝     ╚═╝╚═╝  ╚═╝   ╚═╝   ╚═╝  ╚═╝
+
+██╗   ██╗██████╗ ██████╗  ██╗██╗  ██╗ ██╗ █████╗ 
+██║   ██║██╔══██╗╚════██╗███║╚██╗██╔╝███║██╔══██╗
+██║   ██║██║  ██║ █████╔╝╚██║ ╚███╔╝ ╚██║╚█████╔╝
+██║   ██║██║  ██║██╔═══╝  ██║ ██╔██╗  ██║██╔══██╗
+╚██████╔╝██████╔╝███████╗ ██║██╔╝ ██╗ ██║╚█████╔╝
+ ╚═════╝ ╚═════╝ ╚══════╝ ╚═╝╚═╝  ╚═╝ ╚═╝ ╚════╝
+
+*/
+
+import "./ud21x18/Casting.sol";
+import "./ud21x18/Constants.sol";
+import "./ud21x18/Errors.sol";
+import "./ud21x18/ValueType.sol";

src/casting/Uint128.sol

@@ -3,14 +3,20 @@ pragma solidity >=0.8.19;
 
 import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
 import { SD1x18 } from "../sd1x18/ValueType.sol";
+import { uMAX_SD21x18 } from "../sd21x18/Constants.sol";
+import { SD21x18 } from "../sd21x18/ValueType.sol";
 import { SD59x18 } from "../sd59x18/ValueType.sol";
 import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
 import { UD2x18 } from "../ud2x18/ValueType.sol";
+import { UD21x18 } from "../ud21x18/ValueType.sol";
 import { UD60x18 } from "../ud60x18/ValueType.sol";
 
 /// @notice Thrown when trying to cast a uint128 that doesn't fit in SD1x18.
 error PRBMath_IntoSD1x18_Overflow(uint128 x);
 
+/// @notice Thrown when trying to cast a uint128 that doesn't fit in SD21x18.
+error PRBMath_IntoSD21x18_Overflow(uint128 x);
+
 /// @notice Thrown when trying to cast a uint128 that doesn't fit in UD2x18.
 error PRBMath_IntoUD2x18_Overflow(uint128 x);
 
@@ -19,14 +25,24 @@ error PRBMath_IntoUD2x18_Overflow(uint128 x);
 library PRBMathCastingUint128 {
     /// @notice Casts a uint128 number to SD1x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `MAX_SD1x18`.
+    /// - x must be less than or equal to `uMAX_SD1x18`.
     function intoSD1x18(uint128 x) internal pure returns (SD1x18 result) {
         if (x > uint256(int256(uMAX_SD1x18))) {
             revert PRBMath_IntoSD1x18_Overflow(x);
         }
         result = SD1x18.wrap(int64(uint64(x)));
     }
 
+    /// @notice Casts a uint128 number to SD21x18.
+    /// @dev Requirements:
+    /// - x must be less than or equal to `uMAX_SD21x18`.
+    function intoSD21x18(uint128 x) internal pure returns (SD21x18 result) {
+        if (x > uint256(int256(uMAX_SD21x18))) {
+            revert PRBMath_IntoSD21x18_Overflow(x);
+        }
+        result = SD21x18.wrap(int128(x));
+    }
+
     /// @notice Casts a uint128 number to SD59x18.
     /// @dev There is no overflow check because the domain of uint128 is a subset of SD59x18.
     function intoSD59x18(uint128 x) internal pure returns (SD59x18 result) {
@@ -35,17 +51,22 @@ library PRBMathCastingUint128 {
 
     /// @notice Casts a uint128 number to UD2x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `MAX_SD1x18`.
+    /// - x must be less than or equal to `uMAX_UD2x18`.
     function intoUD2x18(uint128 x) internal pure returns (UD2x18 result) {
         if (x > uint64(uMAX_UD2x18)) {
             revert PRBMath_IntoUD2x18_Overflow(x);
         }
         result = UD2x18.wrap(uint64(x));
     }
 
+    /// @notice Casts a uint128 number to UD21x18.
+    function intoUD21x18(uint128 x) internal pure returns (UD21x18 result) {
+        result = UD21x18.wrap(x);
+    }
+
     /// @notice Casts a uint128 number to UD60x18.
     /// @dev There is no overflow check because the domain of uint128 is a subset of UD60x18.
     function intoUD60x18(uint128 x) internal pure returns (UD60x18 result) {
-        result = UD60x18.wrap(uint256(x));
+        result = UD60x18.wrap(x);
     }
 }

src/casting/Uint256.sol

@@ -3,37 +3,57 @@ pragma solidity >=0.8.19;
 
 import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
 import { SD1x18 } from "../sd1x18/ValueType.sol";
+import { uMAX_SD21x18 } from "../sd21x18/Constants.sol";
+import { SD21x18 } from "../sd21x18/ValueType.sol";
 import { uMAX_SD59x18 } from "../sd59x18/Constants.sol";
 import { SD59x18 } from "../sd59x18/ValueType.sol";
 import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
 import { UD2x18 } from "../ud2x18/ValueType.sol";
+import { uMAX_UD21x18 } from "../ud21x18/Constants.sol";
+import { UD21x18 } from "../ud21x18/ValueType.sol";
 import { UD60x18 } from "../ud60x18/ValueType.sol";
 
 /// @notice Thrown when trying to cast a uint256 that doesn't fit in SD1x18.
 error PRBMath_IntoSD1x18_Overflow(uint256 x);
 
+/// @notice Thrown when trying to cast a uint256 that doesn't fit in SD21x18.
+error PRBMath_IntoSD21x18_Overflow(uint256 x);
+
 /// @notice Thrown when trying to cast a uint256 that doesn't fit in SD59x18.
 error PRBMath_IntoSD59x18_Overflow(uint256 x);
 
 /// @notice Thrown when trying to cast a uint256 that doesn't fit in UD2x18.
 error PRBMath_IntoUD2x18_Overflow(uint256 x);
 
+/// @notice Thrown when trying to cast a uint256 that doesn't fit in UD21x18.
+error PRBMath_IntoUD21x18_Overflow(uint256 x);
+
 /// @title PRBMathCastingUint256
 /// @notice Casting utilities for uint256.
 library PRBMathCastingUint256 {
     /// @notice Casts a uint256 number to SD1x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `MAX_SD1x18`.
+    /// - x must be less than or equal to `uMAX_SD1x18`.
     function intoSD1x18(uint256 x) internal pure returns (SD1x18 result) {
         if (x > uint256(int256(uMAX_SD1x18))) {
             revert PRBMath_IntoSD1x18_Overflow(x);
         }
         result = SD1x18.wrap(int64(int256(x)));
     }
 
+    /// @notice Casts a uint256 number to SD21x18.
+    /// @dev Requirements:
+    /// - x must be less than or equal to `uMAX_SD21x18`.
+    function intoSD21x18(uint256 x) internal pure returns (SD21x18 result) {
+        if (x > uint256(int256(uMAX_SD21x18))) {
+            revert PRBMath_IntoSD21x18_Overflow(x);
+        }
+        result = SD21x18.wrap(int128(int256(x)));
+    }
+
     /// @notice Casts a uint256 number to SD59x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `MAX_SD59x18`.
+    /// - x must be less than or equal to `uMAX_SD59x18`.
     function intoSD59x18(uint256 x) internal pure returns (SD59x18 result) {
         if (x > uint256(uMAX_SD59x18)) {
             revert PRBMath_IntoSD59x18_Overflow(x);
@@ -42,13 +62,25 @@ library PRBMathCastingUint256 {
     }
 
     /// @notice Casts a uint256 number to UD2x18.
+    /// @dev Requirements:
+    /// - x must be less than or equal to `uMAX_UD2x18`.
     function intoUD2x18(uint256 x) internal pure returns (UD2x18 result) {
         if (x > uint256(uMAX_UD2x18)) {
             revert PRBMath_IntoUD2x18_Overflow(x);
         }
         result = UD2x18.wrap(uint64(x));
     }
 
+    /// @notice Casts a uint256 number to UD2x18.
+    /// @dev Requirements:
+    /// - x must be less than or equal to `uMAX_UD21x18`.
+    function intoUD21x18(uint256 x) internal pure returns (UD21x18 result) {
+        if (x > uint256(uMAX_UD21x18)) {
+            revert PRBMath_IntoUD21x18_Overflow(x);
+        }
+        result = UD21x18.wrap(uint128(x));
+    }
+
     /// @notice Casts a uint256 number to UD60x18.
     function intoUD60x18(uint256 x) internal pure returns (UD60x18 result) {
         result = UD60x18.wrap(x);

src/casting/Uint40.sol

@@ -2,8 +2,10 @@
 pragma solidity >=0.8.19;
 
 import { SD1x18 } from "../sd1x18/ValueType.sol";
+import { SD21x18 } from "../sd21x18/ValueType.sol";
 import { SD59x18 } from "../sd59x18/ValueType.sol";
 import { UD2x18 } from "../ud2x18/ValueType.sol";
+import { UD21x18 } from "../ud21x18/ValueType.sol";
 import { UD60x18 } from "../ud60x18/ValueType.sol";
 
 /// @title PRBMathCastingUint40
@@ -15,6 +17,12 @@ library PRBMathCastingUint40 {
         result = SD1x18.wrap(int64(uint64(x)));
     }
 
+    /// @notice Casts a uint40 number into SD21x18.
+    /// @dev There is no overflow check because the domain of uint40 is a subset of SD21x18.
+    function intoSD21x18(uint40 x) internal pure returns (SD21x18 result) {
+        result = SD21x18.wrap(int128(uint128(x)));
+    }
+
     /// @notice Casts a uint40 number into SD59x18.
     /// @dev There is no overflow check because the domain of uint40 is a subset of SD59x18.
     function intoSD59x18(uint40 x) internal pure returns (SD59x18 result) {
@@ -24,12 +32,18 @@ library PRBMathCastingUint40 {
     /// @notice Casts a uint40 number into UD2x18.
     /// @dev There is no overflow check because the domain of uint40 is a subset of UD2x18.
     function intoUD2x18(uint40 x) internal pure returns (UD2x18 result) {
-        result = UD2x18.wrap(uint64(x));
+        result = UD2x18.wrap(x);
+    }
+
+    /// @notice Casts a uint40 number into UD21x18.
+    /// @dev There is no overflow check because the domain of uint40 is a subset of UD21x18.
+    function intoUD21x18(uint40 x) internal pure returns (UD21x18 result) {
+        result = UD21x18.wrap((x));
     }
 
     /// @notice Casts a uint40 number into UD60x18.
     /// @dev There is no overflow check because the domain of uint40 is a subset of UD60x18.
     function intoUD60x18(uint40 x) internal pure returns (UD60x18 result) {
-        result = UD60x18.wrap(uint256(x));
+        result = UD60x18.wrap(x);
     }
 }

src/sd1x18/Casting.sol

@@ -3,11 +3,19 @@ pragma solidity >=0.8.19;
 
 import "../Common.sol" as Common;
 import "./Errors.sol" as CastingErrors;
+import { SD21x18 } from "../sd21x18/ValueType.sol";
 import { SD59x18 } from "../sd59x18/ValueType.sol";
 import { UD2x18 } from "../ud2x18/ValueType.sol";
+import { UD21x18 } from "../ud21x18/ValueType.sol";
 import { UD60x18 } from "../ud60x18/ValueType.sol";
 import { SD1x18 } from "./ValueType.sol";
 
+/// @notice Casts an SD1x18 number into SD21x18.
+/// @dev There is no overflow check because the domain of SD1x18 is a subset of SD21x18.
+function intoSD21x18(SD1x18 x) pure returns (SD21x18 result) {
+    result = SD21x18.wrap(int128(int256(SD1x18.unwrap(x))));
+}
+
 /// @notice Casts an SD1x18 number into SD59x18.
 /// @dev There is no overflow check because the domain of SD1x18 is a subset of SD59x18.
 function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
@@ -24,6 +32,16 @@ function intoUD2x18(SD1x18 x) pure returns (UD2x18 result) {
     result = UD2x18.wrap(uint64(xInt));
 }
 
+/// @notice Casts an SD1x18 number into UD21x18.
+/// - x must be positive.
+function intoUD21x18(SD1x18 x) pure returns (UD21x18 result) {
+    int64 xInt = SD1x18.unwrap(x);
+    if (xInt < 0) {
+        revert CastingErrors.PRBMath_SD1x18_ToUD21x18_Underflow(x);
+    }
+    result = UD21x18.wrap(uint128(uint64(xInt)));
+}
+
 /// @notice Casts an SD1x18 number into UD60x18.
 /// @dev Requirements:
 /// - x must be positive.
@@ -35,26 +53,26 @@ function intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {
     result = UD60x18.wrap(uint64(xInt));
 }
 
-/// @notice Casts an SD1x18 number into uint256.
+/// @notice Casts an SD1x18 number into uint128.
 /// @dev Requirements:
 /// - x must be positive.
-function intoUint256(SD1x18 x) pure returns (uint256 result) {
+function intoUint128(SD1x18 x) pure returns (uint128 result) {
     int64 xInt = SD1x18.unwrap(x);
     if (xInt < 0) {
-        revert CastingErrors.PRBMath_SD1x18_ToUint256_Underflow(x);
+        revert CastingErrors.PRBMath_SD1x18_ToUint128_Underflow(x);
     }
-    result = uint256(uint64(xInt));
+    result = uint128(uint64(xInt));
 }
 
-/// @notice Casts an SD1x18 number into uint128.
+/// @notice Casts an SD1x18 number into uint256.
 /// @dev Requirements:
 /// - x must be positive.
-function intoUint128(SD1x18 x) pure returns (uint128 result) {
+function intoUint256(SD1x18 x) pure returns (uint256 result) {
     int64 xInt = SD1x18.unwrap(x);
     if (xInt < 0) {
-        revert CastingErrors.PRBMath_SD1x18_ToUint128_Underflow(x);
+        revert CastingErrors.PRBMath_SD1x18_ToUint256_Underflow(x);
     }
-    result = uint128(uint64(xInt));
+    result = uint256(uint64(xInt));
 }
 
 /// @notice Casts an SD1x18 number into uint40.

src/sd1x18/Constants.sol

@@ -10,7 +10,7 @@ SD1x18 constant E = SD1x18.wrap(2_718281828459045235);
 int64 constant uMAX_SD1x18 = 9_223372036854775807;
 SD1x18 constant MAX_SD1x18 = SD1x18.wrap(uMAX_SD1x18);
 
-/// @dev The maximum value an SD1x18 number can have.
+/// @dev The minimum value an SD1x18 number can have.
 int64 constant uMIN_SD1x18 = -9_223372036854775808;
 SD1x18 constant MIN_SD1x18 = SD1x18.wrap(uMIN_SD1x18);
 

src/sd1x18/Errors.sol

@@ -3,20 +3,23 @@ pragma solidity >=0.8.19;
 
 import { SD1x18 } from "./ValueType.sol";
 
-/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD2x18.
+/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in UD2x18.
 error PRBMath_SD1x18_ToUD2x18_Underflow(SD1x18 x);
 
-/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD60x18.
+/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in UD21x18.
+error PRBMath_SD1x18_ToUD21x18_Underflow(SD1x18 x);
+
+/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in UD60x18.
 error PRBMath_SD1x18_ToUD60x18_Underflow(SD1x18 x);
 
-/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint128.
+/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint128.
 error PRBMath_SD1x18_ToUint128_Underflow(SD1x18 x);
 
-/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint256.
+/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint256.
 error PRBMath_SD1x18_ToUint256_Underflow(SD1x18 x);
 
-/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint40.
+/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint40.
 error PRBMath_SD1x18_ToUint40_Overflow(SD1x18 x);
 
-/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint40.
+/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint40.
 error PRBMath_SD1x18_ToUint40_Underflow(SD1x18 x);