From e549de8152ce4c81616cadae70cef59116af728f Mon Sep 17 00:00:00 2001
From: Paul Razvan Berg <prberg@proton.me>
Date: Fri, 28 Jun 2024 23:01:49 +0300
Subject: [PATCH 1/2] docs: use comparison symbols

docs: fix #238
---
 src/casting/Uint128.sol     |  6 +++---
 src/casting/Uint256.sol     | 10 +++++-----
 src/sd1x18/Casting.sol      | 10 +++++-----
 src/sd21x18/Casting.sol     | 10 +++++-----
 src/sd59x18/Casting.sol     | 28 ++++++++++++++--------------
 src/sd59x18/Conversions.sol |  4 ++--
 src/sd59x18/Math.sol        | 18 +++++++++---------
 src/ud21x18/Casting.sol     |  2 +-
 src/ud2x18/Casting.sol      |  2 +-
 src/ud60x18/Casting.sol     | 14 +++++++-------
 src/ud60x18/Conversions.sol |  2 +-
 src/ud60x18/Errors.sol      |  2 +-
 src/ud60x18/Math.sol        | 14 +++++++-------
 13 files changed, 61 insertions(+), 61 deletions(-)

diff --git a/src/casting/Uint128.sol b/src/casting/Uint128.sol
index c2c3c180..d24c6e78 100644
--- a/src/casting/Uint128.sol
+++ b/src/casting/Uint128.sol
@@ -25,7 +25,7 @@ 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 `uMAX_SD1x18`.
+    /// - x ≤ uMAX_SD1x18
     function intoSD1x18(uint128 x) internal pure returns (SD1x18 result) {
         if (x > uint256(int256(uMAX_SD1x18))) {
             revert PRBMath_IntoSD1x18_Overflow(x);
@@ -35,7 +35,7 @@ library PRBMathCastingUint128 {
 
     /// @notice Casts a uint128 number to SD21x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `uMAX_SD21x18`.
+    /// - x ≤ uMAX_SD21x18
     function intoSD21x18(uint128 x) internal pure returns (SD21x18 result) {
         if (x > uint256(int256(uMAX_SD21x18))) {
             revert PRBMath_IntoSD21x18_Overflow(x);
@@ -51,7 +51,7 @@ library PRBMathCastingUint128 {
 
     /// @notice Casts a uint128 number to UD2x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `uMAX_UD2x18`.
+    /// - x ≤ uMAX_UD2x18
     function intoUD2x18(uint128 x) internal pure returns (UD2x18 result) {
         if (x > uint64(uMAX_UD2x18)) {
             revert PRBMath_IntoUD2x18_Overflow(x);
diff --git a/src/casting/Uint256.sol b/src/casting/Uint256.sol
index e98f207b..f75118c0 100644
--- a/src/casting/Uint256.sol
+++ b/src/casting/Uint256.sol
@@ -33,7 +33,7 @@ error PRBMath_IntoUD21x18_Overflow(uint256 x);
 library PRBMathCastingUint256 {
     /// @notice Casts a uint256 number to SD1x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `uMAX_SD1x18`.
+    /// - x ≤ uMAX_SD1x18
     function intoSD1x18(uint256 x) internal pure returns (SD1x18 result) {
         if (x > uint256(int256(uMAX_SD1x18))) {
             revert PRBMath_IntoSD1x18_Overflow(x);
@@ -43,7 +43,7 @@ library PRBMathCastingUint256 {
 
     /// @notice Casts a uint256 number to SD21x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `uMAX_SD21x18`.
+    /// - x ≤ uMAX_SD21x18
     function intoSD21x18(uint256 x) internal pure returns (SD21x18 result) {
         if (x > uint256(int256(uMAX_SD21x18))) {
             revert PRBMath_IntoSD21x18_Overflow(x);
@@ -53,7 +53,7 @@ library PRBMathCastingUint256 {
 
     /// @notice Casts a uint256 number to SD59x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `uMAX_SD59x18`.
+    /// - x ≤ uMAX_SD59x18
     function intoSD59x18(uint256 x) internal pure returns (SD59x18 result) {
         if (x > uint256(uMAX_SD59x18)) {
             revert PRBMath_IntoSD59x18_Overflow(x);
@@ -63,7 +63,7 @@ library PRBMathCastingUint256 {
 
     /// @notice Casts a uint256 number to UD2x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `uMAX_UD2x18`.
+    /// - x ≤ uMAX_UD2x18
     function intoUD2x18(uint256 x) internal pure returns (UD2x18 result) {
         if (x > uint256(uMAX_UD2x18)) {
             revert PRBMath_IntoUD2x18_Overflow(x);
@@ -73,7 +73,7 @@ library PRBMathCastingUint256 {
 
     /// @notice Casts a uint256 number to UD2x18.
     /// @dev Requirements:
-    /// - x must be less than or equal to `uMAX_UD21x18`.
+    /// - x ≤ uMAX_UD21x18
     function intoUD21x18(uint256 x) internal pure returns (UD21x18 result) {
         if (x > uint256(uMAX_UD21x18)) {
             revert PRBMath_IntoUD21x18_Overflow(x);
diff --git a/src/sd1x18/Casting.sol b/src/sd1x18/Casting.sol
index 860727d7..90ad105d 100644
--- a/src/sd1x18/Casting.sol
+++ b/src/sd1x18/Casting.sol
@@ -15,7 +15,7 @@ function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
 
 /// @notice Casts an SD1x18 number into UD60x18.
 /// @dev Requirements:
-/// - x must be positive.
+/// - x ≥ 0
 function intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {
     int64 xInt = SD1x18.unwrap(x);
     if (xInt < 0) {
@@ -26,7 +26,7 @@ function intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {
 
 /// @notice Casts an SD1x18 number into uint128.
 /// @dev Requirements:
-/// - x must be positive.
+/// - x ≥ 0
 function intoUint128(SD1x18 x) pure returns (uint128 result) {
     int64 xInt = SD1x18.unwrap(x);
     if (xInt < 0) {
@@ -37,7 +37,7 @@ function intoUint128(SD1x18 x) pure returns (uint128 result) {
 
 /// @notice Casts an SD1x18 number into uint256.
 /// @dev Requirements:
-/// - x must be positive.
+/// - x ≥ 0
 function intoUint256(SD1x18 x) pure returns (uint256 result) {
     int64 xInt = SD1x18.unwrap(x);
     if (xInt < 0) {
@@ -48,8 +48,8 @@ function intoUint256(SD1x18 x) pure returns (uint256 result) {
 
 /// @notice Casts an SD1x18 number into uint40.
 /// @dev Requirements:
-/// - x must be positive.
-/// - x must be less than or equal to `MAX_UINT40`.
+/// - x ≥ 0
+/// - x ≤ MAX_UINT40
 function intoUint40(SD1x18 x) pure returns (uint40 result) {
     int64 xInt = SD1x18.unwrap(x);
     if (xInt < 0) {
diff --git a/src/sd21x18/Casting.sol b/src/sd21x18/Casting.sol
index 35734693..da1b07be 100644
--- a/src/sd21x18/Casting.sol
+++ b/src/sd21x18/Casting.sol
@@ -15,7 +15,7 @@ function intoSD59x18(SD21x18 x) pure returns (SD59x18 result) {
 
 /// @notice Casts an SD21x18 number into UD60x18.
 /// @dev Requirements:
-/// - x must be positive.
+/// - x ≥ 0
 function intoUD60x18(SD21x18 x) pure returns (UD60x18 result) {
     int128 xInt = SD21x18.unwrap(x);
     if (xInt < 0) {
@@ -26,7 +26,7 @@ function intoUD60x18(SD21x18 x) pure returns (UD60x18 result) {
 
 /// @notice Casts an SD21x18 number into uint128.
 /// @dev Requirements:
-/// - x must be positive.
+/// - x ≥ 0
 function intoUint128(SD21x18 x) pure returns (uint128 result) {
     int128 xInt = SD21x18.unwrap(x);
     if (xInt < 0) {
@@ -37,7 +37,7 @@ function intoUint128(SD21x18 x) pure returns (uint128 result) {
 
 /// @notice Casts an SD21x18 number into uint256.
 /// @dev Requirements:
-/// - x must be positive.
+/// - x ≥ 0
 function intoUint256(SD21x18 x) pure returns (uint256 result) {
     int128 xInt = SD21x18.unwrap(x);
     if (xInt < 0) {
@@ -48,8 +48,8 @@ function intoUint256(SD21x18 x) pure returns (uint256 result) {
 
 /// @notice Casts an SD21x18 number into uint40.
 /// @dev Requirements:
-/// - x must be positive.
-/// - x must be less than or equal to `MAX_UINT40`.
+/// - x ≥ 0
+/// - x ≤ MAX_UINT40
 function intoUint40(SD21x18 x) pure returns (uint40 result) {
     int128 xInt = SD21x18.unwrap(x);
     if (xInt < 0) {
diff --git a/src/sd59x18/Casting.sol b/src/sd59x18/Casting.sol
index 9bee9fee..17dedc96 100644
--- a/src/sd59x18/Casting.sol
+++ b/src/sd59x18/Casting.sol
@@ -22,8 +22,8 @@ function intoInt256(SD59x18 x) pure returns (int256 result) {
 
 /// @notice Casts an SD59x18 number into SD1x18.
 /// @dev Requirements:
-/// - x must be greater than or equal to `uMIN_SD1x18`.
-/// - x must be less than or equal to `uMAX_SD1x18`.
+/// - x ≥ uMIN_SD1x18
+/// - x ≤ uMAX_SD1x18
 function intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {
     int256 xInt = SD59x18.unwrap(x);
     if (xInt < uMIN_SD1x18) {
@@ -37,8 +37,8 @@ function intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {
 
 /// @notice Casts an SD59x18 number into SD21x18.
 /// @dev Requirements:
-/// - x must be greater than or equal to `uMIN_SD21x18`.
-/// - x must be less than or equal to `uMAX_SD21x18`.
+/// - x ≥ uMIN_SD21x18
+/// - x ≤ uMAX_SD21x18
 function intoSD21x18(SD59x18 x) pure returns (SD21x18 result) {
     int256 xInt = SD59x18.unwrap(x);
     if (xInt < uMIN_SD21x18) {
@@ -52,8 +52,8 @@ function intoSD21x18(SD59x18 x) pure returns (SD21x18 result) {
 
 /// @notice Casts an SD59x18 number into UD2x18.
 /// @dev Requirements:
-/// - x must be positive.
-/// - x must be less than or equal to `uMAX_UD2x18`.
+/// - x ≥ 0
+/// - x ≤ uMAX_UD2x18
 function intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {
     int256 xInt = SD59x18.unwrap(x);
     if (xInt < 0) {
@@ -67,8 +67,8 @@ function intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {
 
 /// @notice Casts an SD59x18 number into UD21x18.
 /// @dev Requirements:
-/// - x must be positive.
-/// - x must be less than or equal to `uMAX_UD21x18`.
+/// - x ≥ 0
+/// - x ≤ uMAX_UD21x18
 function intoUD21x18(SD59x18 x) pure returns (UD21x18 result) {
     int256 xInt = SD59x18.unwrap(x);
     if (xInt < 0) {
@@ -82,7 +82,7 @@ function intoUD21x18(SD59x18 x) pure returns (UD21x18 result) {
 
 /// @notice Casts an SD59x18 number into UD60x18.
 /// @dev Requirements:
-/// - x must be positive.
+/// - x ≥ 0
 function intoUD60x18(SD59x18 x) pure returns (UD60x18 result) {
     int256 xInt = SD59x18.unwrap(x);
     if (xInt < 0) {
@@ -93,7 +93,7 @@ function intoUD60x18(SD59x18 x) pure returns (UD60x18 result) {
 
 /// @notice Casts an SD59x18 number into uint256.
 /// @dev Requirements:
-/// - x must be positive.
+/// - x ≥ 0
 function intoUint256(SD59x18 x) pure returns (uint256 result) {
     int256 xInt = SD59x18.unwrap(x);
     if (xInt < 0) {
@@ -104,8 +104,8 @@ function intoUint256(SD59x18 x) pure returns (uint256 result) {
 
 /// @notice Casts an SD59x18 number into uint128.
 /// @dev Requirements:
-/// - x must be positive.
-/// - x must be less than or equal to `uMAX_UINT128`.
+/// - x ≥ 0
+/// - x ≤ uMAX_UINT128
 function intoUint128(SD59x18 x) pure returns (uint128 result) {
     int256 xInt = SD59x18.unwrap(x);
     if (xInt < 0) {
@@ -119,8 +119,8 @@ function intoUint128(SD59x18 x) pure returns (uint128 result) {
 
 /// @notice Casts an SD59x18 number into uint40.
 /// @dev Requirements:
-/// - x must be positive.
-/// - x must be less than or equal to `MAX_UINT40`.
+/// - x ≥ 0
+/// - x ≤ MAX_UINT40
 function intoUint40(SD59x18 x) pure returns (uint40 result) {
     int256 xInt = SD59x18.unwrap(x);
     if (xInt < 0) {
diff --git a/src/sd59x18/Conversions.sol b/src/sd59x18/Conversions.sol
index 2252c3ad..fe5f9fd0 100644
--- a/src/sd59x18/Conversions.sol
+++ b/src/sd59x18/Conversions.sol
@@ -8,8 +8,8 @@ import { SD59x18 } from "./ValueType.sol";
 /// @notice Converts a simple integer to SD59x18 by multiplying it by `UNIT`.
 ///
 /// @dev Requirements:
-/// - x must be greater than or equal to `MIN_SD59x18 / UNIT`.
-/// - x must be less than or equal to `MAX_SD59x18 / UNIT`.
+/// - x ≥ `MIN_SD59x18 / UNIT`
+/// - x ≤ `MAX_SD59x18 / UNIT`
 ///
 /// @param x The basic integer to convert.
 /// @param result The same number converted to SD59x18.
diff --git a/src/sd59x18/Math.sol b/src/sd59x18/Math.sol
index 361838c4..0753afe3 100644
--- a/src/sd59x18/Math.sol
+++ b/src/sd59x18/Math.sol
@@ -26,7 +26,7 @@ import { SD59x18 } from "./ValueType.sol";
 /// @notice Calculates the absolute value of x.
 ///
 /// @dev Requirements:
-/// - x must be greater than `MIN_SD59x18`.
+/// - x > MIN_SD59x18.
 ///
 /// @param x The SD59x18 number for which to calculate the absolute value.
 /// @param result The absolute value of x as an SD59x18 number.
@@ -75,7 +75,7 @@ function avg(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
 /// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
 ///
 /// Requirements:
-/// - x must be less than or equal to `MAX_WHOLE_SD59x18`.
+/// - x ≤ MAX_WHOLE_SD59x18
 ///
 /// @param x The SD59x18 number to ceil.
 /// @param result The smallest whole number greater than or equal to x, as an SD59x18 number.
@@ -162,7 +162,7 @@ function div(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
 ///
 /// Requirements:
 /// - Refer to the requirements in {exp2}.
-/// - x must be less than 133_084258667509499441.
+/// - x < 133_084258667509499441.
 ///
 /// @param x The exponent as an SD59x18 number.
 /// @return result The result as an SD59x18 number.
@@ -197,10 +197,10 @@ function exp(SD59x18 x) pure returns (SD59x18 result) {
 /// @dev See https://ethereum.stackexchange.com/q/79903/24693.
 ///
 /// Notes:
-/// - If x is less than -59_794705707972522261, the result is zero.
+/// - If x < -59_794705707972522261, the result is zero.
 ///
 /// Requirements:
-/// - x must be less than 192e18.
+/// - x < 192e18.
 /// - The result must fit in SD59x18.
 ///
 /// @param x The exponent as an SD59x18 number.
@@ -240,7 +240,7 @@ function exp2(SD59x18 x) pure returns (SD59x18 result) {
 /// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
 ///
 /// Requirements:
-/// - x must be greater than or equal to `MIN_WHOLE_SD59x18`.
+/// - x ≥ MIN_WHOLE_SD59x18
 ///
 /// @param x The SD59x18 number to floor.
 /// @param result The greatest whole number less than or equal to x, as an SD59x18 number.
@@ -484,7 +484,7 @@ function log10(SD59x18 x) pure returns (SD59x18 result) {
 /// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
 ///
 /// Requirements:
-/// - x must be greater than zero.
+/// - x > 0
 ///
 /// @param x The SD59x18 number for which to calculate the binary logarithm.
 /// @return result The binary logarithm as an SD59x18 number.
@@ -687,8 +687,8 @@ function powu(SD59x18 x, uint256 y) pure returns (SD59x18 result) {
 /// - The result is rounded toward zero.
 ///
 /// Requirements:
-/// - x cannot be negative, since complex numbers are not supported.
-/// - x must be less than `MAX_SD59x18 / UNIT`.
+/// - x ≥ 0, since complex numbers are not supported.
+/// - x ≤ MAX_SD59x18 / UNIT
 ///
 /// @param x The SD59x18 number for which to calculate the square root.
 /// @return result The result as an SD59x18 number.
diff --git a/src/ud21x18/Casting.sol b/src/ud21x18/Casting.sol
index 34c52792..69480cb4 100644
--- a/src/ud21x18/Casting.sol
+++ b/src/ud21x18/Casting.sol
@@ -33,7 +33,7 @@ function intoUint256(UD21x18 x) pure returns (uint256 result) {
 
 /// @notice Casts a UD21x18 number into uint40.
 /// @dev Requirements:
-/// - x must be less than or equal to `MAX_UINT40`.
+/// - x ≤ MAX_UINT40
 function intoUint40(UD21x18 x) pure returns (uint40 result) {
     uint128 xUint = UD21x18.unwrap(x);
     if (xUint > uint128(Common.MAX_UINT40)) {
diff --git a/src/ud2x18/Casting.sol b/src/ud2x18/Casting.sol
index 4e9916b5..47a3b6bb 100644
--- a/src/ud2x18/Casting.sol
+++ b/src/ud2x18/Casting.sol
@@ -33,7 +33,7 @@ function intoUint256(UD2x18 x) pure returns (uint256 result) {
 
 /// @notice Casts a UD2x18 number into uint40.
 /// @dev Requirements:
-/// - x must be less than or equal to `MAX_UINT40`.
+/// - x ≤ MAX_UINT40
 function intoUint40(UD2x18 x) pure returns (uint40 result) {
     uint64 xUint = UD2x18.unwrap(x);
     if (xUint > uint64(Common.MAX_UINT40)) {
diff --git a/src/ud60x18/Casting.sol b/src/ud60x18/Casting.sol
index 7fadb45a..68dd63a4 100644
--- a/src/ud60x18/Casting.sol
+++ b/src/ud60x18/Casting.sol
@@ -17,7 +17,7 @@ import { UD60x18 } from "./ValueType.sol";
 
 /// @notice Casts a UD60x18 number into SD1x18.
 /// @dev Requirements:
-/// - x must be less than or equal to `uMAX_SD1x18`.
+/// - x ≤ uMAX_SD1x18
 function intoSD1x18(UD60x18 x) pure returns (SD1x18 result) {
     uint256 xUint = UD60x18.unwrap(x);
     if (xUint > uint256(int256(uMAX_SD1x18))) {
@@ -28,7 +28,7 @@ function intoSD1x18(UD60x18 x) pure returns (SD1x18 result) {
 
 /// @notice Casts a UD60x18 number into SD21x18.
 /// @dev Requirements:
-/// - x must be less than or equal to `uMAX_SD21x18`.
+/// - x ≤ uMAX_SD21x18
 function intoSD21x18(UD60x18 x) pure returns (SD21x18 result) {
     uint256 xUint = UD60x18.unwrap(x);
     if (xUint > uint256(int256(uMAX_SD21x18))) {
@@ -39,7 +39,7 @@ function intoSD21x18(UD60x18 x) pure returns (SD21x18 result) {
 
 /// @notice Casts a UD60x18 number into UD2x18.
 /// @dev Requirements:
-/// - x must be less than or equal to `uMAX_UD2x18`.
+/// - x ≤ uMAX_UD2x18
 function intoUD2x18(UD60x18 x) pure returns (UD2x18 result) {
     uint256 xUint = UD60x18.unwrap(x);
     if (xUint > uMAX_UD2x18) {
@@ -50,7 +50,7 @@ function intoUD2x18(UD60x18 x) pure returns (UD2x18 result) {
 
 /// @notice Casts a UD60x18 number into UD21x18.
 /// @dev Requirements:
-/// - x must be less than or equal to `uMAX_UD21x18`.
+/// - x ≤ uMAX_UD21x18
 function intoUD21x18(UD60x18 x) pure returns (UD21x18 result) {
     uint256 xUint = UD60x18.unwrap(x);
     if (xUint > uMAX_UD21x18) {
@@ -61,7 +61,7 @@ function intoUD21x18(UD60x18 x) pure returns (UD21x18 result) {
 
 /// @notice Casts a UD60x18 number into SD59x18.
 /// @dev Requirements:
-/// - x must be less than or equal to `uMAX_SD59x18`.
+/// - x ≤ uMAX_SD59x18
 function intoSD59x18(UD60x18 x) pure returns (SD59x18 result) {
     uint256 xUint = UD60x18.unwrap(x);
     if (xUint > uint256(uMAX_SD59x18)) {
@@ -78,7 +78,7 @@ function intoUint256(UD60x18 x) pure returns (uint256 result) {
 
 /// @notice Casts a UD60x18 number into uint128.
 /// @dev Requirements:
-/// - x must be less than or equal to `MAX_UINT128`.
+/// - x ≤ MAX_UINT128
 function intoUint128(UD60x18 x) pure returns (uint128 result) {
     uint256 xUint = UD60x18.unwrap(x);
     if (xUint > MAX_UINT128) {
@@ -89,7 +89,7 @@ function intoUint128(UD60x18 x) pure returns (uint128 result) {
 
 /// @notice Casts a UD60x18 number into uint40.
 /// @dev Requirements:
-/// - x must be less than or equal to `MAX_UINT40`.
+/// - x ≤ MAX_UINT40
 function intoUint40(UD60x18 x) pure returns (uint40 result) {
     uint256 xUint = UD60x18.unwrap(x);
     if (xUint > MAX_UINT40) {
diff --git a/src/ud60x18/Conversions.sol b/src/ud60x18/Conversions.sol
index 8ff23339..80e81e46 100644
--- a/src/ud60x18/Conversions.sol
+++ b/src/ud60x18/Conversions.sol
@@ -16,7 +16,7 @@ function convert(UD60x18 x) pure returns (uint256 result) {
 /// @notice Converts a simple integer to UD60x18 by multiplying it by `UNIT`.
 ///
 /// @dev Requirements:
-/// - x must be less than or equal to `MAX_UD60x18 / UNIT`.
+/// - x ≤ MAX_UD60x18 / UNIT
 ///
 /// @param x The basic integer to convert.
 /// @param result The same number converted to UD60x18.
diff --git a/src/ud60x18/Errors.sol b/src/ud60x18/Errors.sol
index fede85bb..321f1344 100644
--- a/src/ud60x18/Errors.sol
+++ b/src/ud60x18/Errors.sol
@@ -39,7 +39,7 @@ error PRBMath_UD60x18_IntoUint128_Overflow(UD60x18 x);
 /// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.
 error PRBMath_UD60x18_IntoUint40_Overflow(UD60x18 x);
 
-/// @notice Thrown when taking the logarithm of a number less than 1.
+/// @notice Thrown when taking the logarithm of a number less than UNIT.
 error PRBMath_UD60x18_Log_InputTooSmall(UD60x18 x);
 
 /// @notice Thrown when calculating the square root overflows UD60x18.
diff --git a/src/ud60x18/Math.sol b/src/ud60x18/Math.sol
index 4459b048..87c44897 100644
--- a/src/ud60x18/Math.sol
+++ b/src/ud60x18/Math.sol
@@ -59,7 +59,7 @@ function avg(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
 /// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
 ///
 /// Requirements:
-/// - x must be less than or equal to `MAX_WHOLE_UD60x18`.
+/// - x ≤ MAX_WHOLE_UD60x18
 ///
 /// @param x The UD60x18 number to ceil.
 /// @param result The smallest whole number greater than or equal to x, as a UD60x18 number.
@@ -107,7 +107,7 @@ function div(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
 /// $$
 ///
 /// @dev Requirements:
-/// - x must be less than 133_084258667509499441.
+/// - x ≤ 133_084258667509499440
 ///
 /// @param x The exponent as a UD60x18 number.
 /// @return result The result as a UD60x18 number.
@@ -132,7 +132,7 @@ function exp(UD60x18 x) pure returns (UD60x18 result) {
 /// @dev See https://ethereum.stackexchange.com/q/79903/24693
 ///
 /// Requirements:
-/// - x must be less than 192e18.
+/// - x < 192e18
 /// - The result must fit in UD60x18.
 ///
 /// @param x The exponent as a UD60x18 number.
@@ -384,7 +384,7 @@ function log10(UD60x18 x) pure returns (UD60x18 result) {
 /// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
 ///
 /// Requirements:
-/// - x must be greater than zero.
+/// - x ≥ UNIT
 ///
 /// @param x The UD60x18 number for which to calculate the binary logarithm.
 /// @return result The binary logarithm as a UD60x18 number.
@@ -500,11 +500,11 @@ function pow(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
         return x;
     }
 
-    // If x is greater than `UNIT`, use the standard formula.
+    // If x is > UNIT, use the standard formula.
     if (xUint > uUNIT) {
         result = exp2(mul(log2(x), y));
     }
-    // Conversely, if x is less than `UNIT`, use the equivalent formula.
+    // Conversely, if x < UNIT, use the equivalent formula.
     else {
         UD60x18 i = wrap(uUNIT_SQUARED / xUint);
         UD60x18 w = exp2(mul(log2(i), y));
@@ -553,7 +553,7 @@ function powu(UD60x18 x, uint256 y) pure returns (UD60x18 result) {
 /// - The result is rounded toward zero.
 ///
 /// Requirements:
-/// - x must be less than `MAX_UD60x18 / UNIT`.
+/// - x ≤ MAX_UD60x18 / UNIT
 ///
 /// @param x The UD60x18 number for which to calculate the square root.
 /// @return result The result as a UD60x18 number.

From 4d7c3e53795cc24339269f0b55490415402e5d12 Mon Sep 17 00:00:00 2001
From: Paul Razvan Berg <prberg@proton.me>
Date: Fri, 28 Jun 2024 23:48:33 +0300
Subject: [PATCH 2/2] docs: use inclusion symbols

---
 src/casting/Uint128.sol |  4 ++--
 src/casting/Uint40.sol  | 12 ++++++------
 src/sd1x18/Casting.sol  |  2 +-
 src/sd21x18/Casting.sol |  2 +-
 src/ud21x18/Casting.sol |  6 +++---
 src/ud2x18/Casting.sol  |  8 ++++----
 6 files changed, 17 insertions(+), 17 deletions(-)

diff --git a/src/casting/Uint128.sol b/src/casting/Uint128.sol
index d24c6e78..6a4f1d65 100644
--- a/src/casting/Uint128.sol
+++ b/src/casting/Uint128.sol
@@ -44,7 +44,7 @@ library PRBMathCastingUint128 {
     }
 
     /// @notice Casts a uint128 number to SD59x18.
-    /// @dev There is no overflow check because the domain of uint128 is a subset of SD59x18.
+    /// @dev There is no overflow check because uint128 ⊆ SD59x18.
     function intoSD59x18(uint128 x) internal pure returns (SD59x18 result) {
         result = SD59x18.wrap(int256(uint256(x)));
     }
@@ -65,7 +65,7 @@ library PRBMathCastingUint128 {
     }
 
     /// @notice Casts a uint128 number to UD60x18.
-    /// @dev There is no overflow check because the domain of uint128 is a subset of UD60x18.
+    /// @dev There is no overflow check because uint128 ⊆ UD60x18.
     function intoUD60x18(uint128 x) internal pure returns (UD60x18 result) {
         result = UD60x18.wrap(x);
     }
diff --git a/src/casting/Uint40.sol b/src/casting/Uint40.sol
index c93edb9a..df9b240d 100644
--- a/src/casting/Uint40.sol
+++ b/src/casting/Uint40.sol
@@ -12,37 +12,37 @@ import { UD60x18 } from "../ud60x18/ValueType.sol";
 /// @notice Casting utilities for uint40.
 library PRBMathCastingUint40 {
     /// @notice Casts a uint40 number into SD1x18.
-    /// @dev There is no overflow check because the domain of uint40 is a subset of SD1x18.
+    /// @dev There is no overflow check because uint40 ⊆ SD1x18.
     function intoSD1x18(uint40 x) internal pure returns (SD1x18 result) {
         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.
+    /// @dev There is no overflow check because uint40 ⊆ 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.
+    /// @dev There is no overflow check because uint40 ⊆ SD59x18.
     function intoSD59x18(uint40 x) internal pure returns (SD59x18 result) {
         result = SD59x18.wrap(int256(uint256(x)));
     }
 
     /// @notice Casts a uint40 number into UD2x18.
-    /// @dev There is no overflow check because the domain of uint40 is a subset of UD2x18.
+    /// @dev There is no overflow check because uint40 ⊆ UD2x18.
     function intoUD2x18(uint40 x) internal pure returns (UD2x18 result) {
         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.
+    /// @dev There is no overflow check because uint40 ⊆ 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.
+    /// @dev There is no overflow check because uint40 ⊆ UD60x18.
     function intoUD60x18(uint40 x) internal pure returns (UD60x18 result) {
         result = UD60x18.wrap(x);
     }
diff --git a/src/sd1x18/Casting.sol b/src/sd1x18/Casting.sol
index 90ad105d..9f9dd474 100644
--- a/src/sd1x18/Casting.sol
+++ b/src/sd1x18/Casting.sol
@@ -8,7 +8,7 @@ import { UD60x18 } from "../ud60x18/ValueType.sol";
 import { SD1x18 } from "./ValueType.sol";
 
 /// @notice Casts an SD1x18 number into SD59x18.
-/// @dev There is no overflow check because the domain of SD1x18 is a subset of SD59x18.
+/// @dev There is no overflow check because SD1x18 ⊆ SD59x18.
 function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
     result = SD59x18.wrap(int256(SD1x18.unwrap(x)));
 }
diff --git a/src/sd21x18/Casting.sol b/src/sd21x18/Casting.sol
index da1b07be..637aeeed 100644
--- a/src/sd21x18/Casting.sol
+++ b/src/sd21x18/Casting.sol
@@ -8,7 +8,7 @@ import { UD60x18 } from "../ud60x18/ValueType.sol";
 import { SD21x18 } from "./ValueType.sol";
 
 /// @notice Casts an SD21x18 number into SD59x18.
-/// @dev There is no overflow check because the domain of SD21x18 is a subset of SD59x18.
+/// @dev There is no overflow check because SD21x18 ⊆ SD59x18.
 function intoSD59x18(SD21x18 x) pure returns (SD59x18 result) {
     result = SD59x18.wrap(int256(SD21x18.unwrap(x)));
 }
diff --git a/src/ud21x18/Casting.sol b/src/ud21x18/Casting.sol
index 69480cb4..63482b52 100644
--- a/src/ud21x18/Casting.sol
+++ b/src/ud21x18/Casting.sol
@@ -8,13 +8,13 @@ import { UD60x18 } from "../ud60x18/ValueType.sol";
 import { UD21x18 } from "./ValueType.sol";
 
 /// @notice Casts a UD21x18 number into SD59x18.
-/// @dev There is no overflow check because the domain of UD21x18 is a subset of SD59x18.
+/// @dev There is no overflow check because UD21x18 ⊆ SD59x18.
 function intoSD59x18(UD21x18 x) pure returns (SD59x18 result) {
     result = SD59x18.wrap(int256(uint256(UD21x18.unwrap(x))));
 }
 
 /// @notice Casts a UD21x18 number into UD60x18.
-/// @dev There is no overflow check because the domain of UD21x18 is a subset of UD60x18.
+/// @dev There is no overflow check because UD21x18 ⊆ UD60x18.
 function intoUD60x18(UD21x18 x) pure returns (UD60x18 result) {
     result = UD60x18.wrap(UD21x18.unwrap(x));
 }
@@ -26,7 +26,7 @@ function intoUint128(UD21x18 x) pure returns (uint128 result) {
 }
 
 /// @notice Casts a UD21x18 number into uint256.
-/// @dev There is no overflow check because the domain of UD21x18 is a subset of uint256.
+/// @dev There is no overflow check because UD21x18 ⊆ uint256.
 function intoUint256(UD21x18 x) pure returns (uint256 result) {
     result = uint256(UD21x18.unwrap(x));
 }
diff --git a/src/ud2x18/Casting.sol b/src/ud2x18/Casting.sol
index 47a3b6bb..a5db8dc6 100644
--- a/src/ud2x18/Casting.sol
+++ b/src/ud2x18/Casting.sol
@@ -8,25 +8,25 @@ import { UD60x18 } from "../ud60x18/ValueType.sol";
 import { UD2x18 } from "./ValueType.sol";
 
 /// @notice Casts a UD2x18 number into SD59x18.
-/// @dev There is no overflow check because the domain of UD2x18 is a subset of SD59x18.
+/// @dev There is no overflow check because UD2x18 ⊆ SD59x18.
 function intoSD59x18(UD2x18 x) pure returns (SD59x18 result) {
     result = SD59x18.wrap(int256(uint256(UD2x18.unwrap(x))));
 }
 
 /// @notice Casts a UD2x18 number into UD60x18.
-/// @dev There is no overflow check because the domain of UD2x18 is a subset of UD60x18.
+/// @dev There is no overflow check because UD2x18 ⊆ UD60x18.
 function intoUD60x18(UD2x18 x) pure returns (UD60x18 result) {
     result = UD60x18.wrap(UD2x18.unwrap(x));
 }
 
 /// @notice Casts a UD2x18 number into uint128.
-/// @dev There is no overflow check because the domain of UD2x18 is a subset of uint128.
+/// @dev There is no overflow check because UD2x18 ⊆ uint128.
 function intoUint128(UD2x18 x) pure returns (uint128 result) {
     result = uint128(UD2x18.unwrap(x));
 }
 
 /// @notice Casts a UD2x18 number into uint256.
-/// @dev There is no overflow check because the domain of UD2x18 is a subset of uint256.
+/// @dev There is no overflow check because UD2x18 ⊆ uint256.
 function intoUint256(UD2x18 x) pure returns (uint256 result) {
     result = uint256(UD2x18.unwrap(x));
 }