Optimize gas for _getFraction in AmountDeriver

contracts/lib/AmountDeriver.sol

@@ -6,6 +6,8 @@ import {
     AmountDerivationErrors
 } from "../interfaces/AmountDerivationErrors.sol";
 
+import "./AmountDeriverConstants.sol";
+
 /**
  * @title AmountDeriver
  * @author 0age
@@ -98,16 +100,14 @@ contract AmountDeriver is AmountDerivationErrors {
 
         // Ensure fraction can be applied to the value with no remainder. Note
         // that the denominator cannot be zero.
-        bool exact;
         assembly {
             // Ensure new value contains no remainder via mulmod operator.
             // Credit to @hrkrshnn + @axic for proposing this optimal solution.
-            exact := iszero(mulmod(value, numerator, denominator))
-        }
-
-        // Ensure that division gave a final result with no remainder.
-        if (!exact) {
-            revert InexactFraction();
+            // Further optimization by @Chomtana and @0age
+            if mulmod(value, numerator, denominator) {
+                mstore(0, InexactFraction_error_signature)
+                revert(0, InexactFraction_error_len)
+            }
         }
 
         // Multiply the numerator by the value and ensure no overflow occurs.

contracts/lib/AmountDeriverConstants.sol

@@ -0,0 +1,42 @@
+// SPDX-License-Identifier: MIT
+pragma solidity >=0.8.7;
+
+/*
+ * -------------------------- Disambiguation & Other Notes ---------------------
+ *    - The term "head" is used as it is in the documentation for ABI encoding,
+ *      but only in reference to dynamic types, i.e. it always refers to the
+ *      offset or pointer to the body of a dynamic type. In calldata, the head
+ *      is always an offset (relative to the parent object), while in memory,
+ *      the head is always the pointer to the body. More information found here:
+ *      https://docs.soliditylang.org/en/v0.8.14/abi-spec.html#argument-encoding
+ *        - Note that the length of an array is separate from and precedes the
+ *          head of the array.
+ *
+ *    - The term "body" is used in place of the term "head" used in the ABI
+ *      documentation. It refers to the start of the data for a dynamic type,
+ *      e.g. the first word of a struct or the first word of the first element
+ *      in an array.
+ *
+ *    - The term "pointer" is used to describe the absolute position of a value
+ *      and never an offset relative to another value.
+ *        - The suffix "_ptr" refers to a memory pointer.
+ *        - The suffix "_cdPtr" refers to a calldata pointer.
+ *
+ *    - The term "offset" is used to describe the position of a value relative
+ *      to some parent value. For example, OrderParameters_conduit_offset is the
+ *      offset to the "conduit" value in the OrderParameters struct relative to
+ *      the start of the body.
+ *        - Note: Offsets are used to derive pointers.
+ *
+ *    - Some structs have pointers defined for all of their fields in this file.
+ *      Lines which are commented out are fields that are not used in the
+ *      codebase but have been left in for readability.
+ */
+
+// Declare constant for errors related to amount derivation.
+
+// error InexactFraction() @ AmountDerivationErrors.sol
+uint256 constant InexactFraction_error_signature = (
+    0xc63cf08900000000000000000000000000000000000000000000000000000000
+);
+uint256 constant InexactFraction_error_len = 0x20;