Threshold check (#229)

* fix: threshold check in SD59x18 exp2 function * refactor: alphabetical ordering docs: improve writing refactor: change order of checks style: fix formatting issues test: order by value test: use MIN_SD59x18 * fix: Update threshold check in SD59x18 exp function, add EXP_MIN_THRESHOLD constant and add tests * fix: increase max_test_rejects to 100_000 * docs: improve explanation --------- Co-authored-by: Paul Razvan Berg <[email protected]>
PaulRBerg · May 6, 2024 · cceb7f6 · cceb7f6
1 parent 16419e5
commit cceb7f6
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Showing 5 changed files with 29 additions and 14 deletions.
diff --git a/foundry.toml b/foundry.toml
@@ -13,7 +13,7 @@
   test = "test"
 
 [profile.ci]
-  fuzz = { runs = 10_000 }
+  fuzz = { runs = 10_000, max_test_rejects = 100_000 }
   verbosity = 4
 
 [fmt]

diff --git a/src/sd59x18/Constants.sol b/src/sd59x18/Constants.sol
@@ -12,10 +12,18 @@ SD59x18 constant E = SD59x18.wrap(2_718281828459045235);
 int256 constant uEXP_MAX_INPUT = 133_084258667509499440;
 SD59x18 constant EXP_MAX_INPUT = SD59x18.wrap(uEXP_MAX_INPUT);
 
+/// @dev Any value less than this returns 0 in {exp}.
+int256 constant uEXP_MIN_THRESHOLD = -41_446531673892822322;
+SD59x18 constant EXP_MIN_THRESHOLD = SD59x18.wrap(uEXP_MIN_THRESHOLD);
+
 /// @dev The maximum input permitted in {exp2}.
 int256 constant uEXP2_MAX_INPUT = 192e18 - 1;
 SD59x18 constant EXP2_MAX_INPUT = SD59x18.wrap(uEXP2_MAX_INPUT);
 
+/// @dev Any value less than this returns 0 in {exp2}.
+int256 constant uEXP2_MIN_THRESHOLD = -59_794705707972522261;
+SD59x18 constant EXP2_MIN_THRESHOLD = SD59x18.wrap(uEXP2_MIN_THRESHOLD);
+
 /// @dev Half the UNIT number.
 int256 constant uHALF_UNIT = 0.5e18;
 SD59x18 constant HALF_UNIT = SD59x18.wrap(uHALF_UNIT);

diff --git a/src/sd59x18/Math.sol b/src/sd59x18/Math.sol
@@ -6,6 +6,8 @@ import "./Errors.sol" as Errors;
 import {
     uEXP_MAX_INPUT,
     uEXP2_MAX_INPUT,
+    uEXP_MIN_THRESHOLD,
+    uEXP2_MIN_THRESHOLD,
     uHALF_UNIT,
     uLOG2_10,
     uLOG2_E,
@@ -168,6 +170,12 @@ function div(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
 function exp(SD59x18 x) pure returns (SD59x18 result) {
     int256 xInt = x.unwrap();
 
+    // Any input less than the threshold returns zero.
+    // This check also prevents an overflow for very small numbers.
+    if (xInt < uEXP_MIN_THRESHOLD) {
+        return ZERO;
+    }
+
     // This check prevents values greater than 192e18 from being passed to {exp2}.
     if (xInt > uEXP_MAX_INPUT) {
         revert Errors.PRBMath_SD59x18_Exp_InputTooBig(x);
@@ -201,8 +209,8 @@ function exp(SD59x18 x) pure returns (SD59x18 result) {
 function exp2(SD59x18 x) pure returns (SD59x18 result) {
     int256 xInt = x.unwrap();
     if (xInt < 0) {
-        // The inverse of any number less than this is truncated to zero.
-        if (xInt < -59_794705707972522261) {
+        // The inverse of any number less than the threshold is truncated to zero.
+        if (xInt < uEXP2_MIN_THRESHOLD) {
             return ZERO;
         }
 

diff --git a/test/unit/sd59x18/math/exp/exp.t.sol b/test/unit/sd59x18/math/exp/exp.t.sol
@@ -2,16 +2,14 @@
 pragma solidity >=0.8.19 <0.9.0;
 
 import { sd } from "src/sd59x18/Casting.sol";
-import { E, EXP_MAX_INPUT, MIN_SD59x18, MIN_WHOLE_SD59x18, PI, UNIT, ZERO } from "src/sd59x18/Constants.sol";
+import { E, EXP_MAX_INPUT, EXP_MIN_THRESHOLD, MIN_SD59x18, MIN_WHOLE_SD59x18, PI, UNIT, ZERO } from "src/sd59x18/Constants.sol";
 import { PRBMath_SD59x18_Exp_InputTooBig } from "src/sd59x18/Errors.sol";
 import { exp } from "src/sd59x18/Math.sol";
 import { SD59x18 } from "src/sd59x18/ValueType.sol";
 
 import { SD59x18_Unit_Test } from "../../SD59x18.t.sol";
 
 contract Exp_Unit_Test is SD59x18_Unit_Test {
-    SD59x18 internal constant THRESHOLD = SD59x18.wrap(-41_446531673892822322);
-
     function test_Exp_Zero() external pure {
         SD59x18 x = ZERO;
         SD59x18 actual = exp(x);
@@ -27,7 +25,7 @@ contract Exp_Unit_Test is SD59x18_Unit_Test {
         delete sets;
         sets.push(set({ x: MIN_SD59x18 }));
         sets.push(set({ x: MIN_WHOLE_SD59x18 }));
-        sets.push(set({ x: THRESHOLD - sd(1) }));
+        sets.push(set({ x: EXP_MIN_THRESHOLD - sd(1) }));
         return sets;
     }
 
@@ -38,7 +36,9 @@ contract Exp_Unit_Test is SD59x18_Unit_Test {
 
     function negativeAndGteThreshold_Sets() internal returns (Set[] memory) {
         delete sets;
-        sets.push(set({ x: THRESHOLD, expected: 0.000000000000000001e18 }));
+        sets.push(set({ x: MIN_SD59x18, expected: 0 }));
+        sets.push(set({ x: EXP_MIN_THRESHOLD - sd(1), expected: 0 }));
+        sets.push(set({ x: EXP_MIN_THRESHOLD, expected: 0.000000000000000001e18 }));
         sets.push(set({ x: -33.333333e18, expected: 0.000000000000003338e18 }));
         sets.push(set({ x: -20.82e18, expected: 0.0000000009077973e18 }));
         sets.push(set({ x: -16e18, expected: 0.000000112535174719e18 }));

diff --git a/test/unit/sd59x18/math/exp2/exp2.t.sol b/test/unit/sd59x18/math/exp2/exp2.t.sol
@@ -2,17 +2,14 @@
 pragma solidity >=0.8.19 <0.9.0;
 
 import { sd } from "src/sd59x18/Casting.sol";
-import { E, EXP2_MAX_INPUT, MIN_SD59x18, MIN_WHOLE_SD59x18, PI, UNIT, ZERO } from "src/sd59x18/Constants.sol";
+import { E, EXP2_MAX_INPUT, EXP2_MIN_THRESHOLD, MIN_SD59x18, MIN_WHOLE_SD59x18, PI, UNIT, ZERO } from "src/sd59x18/Constants.sol";
 import { PRBMath_SD59x18_Exp2_InputTooBig } from "src/sd59x18/Errors.sol";
 import { exp2 } from "src/sd59x18/Math.sol";
 import { SD59x18 } from "src/sd59x18/ValueType.sol";
 
 import { SD59x18_Unit_Test } from "../../SD59x18.t.sol";
 
 contract Exp2_Unit_Test is SD59x18_Unit_Test {
-    /// @dev Any input smaller than this makes the result zero.
-    SD59x18 internal constant THRESHOLD = SD59x18.wrap(-59_794705707972522261);
-
     function test_Exp2_Zero() external pure {
         SD59x18 x = ZERO;
         SD59x18 actual = exp2(x);
@@ -28,7 +25,7 @@ contract Exp2_Unit_Test is SD59x18_Unit_Test {
         delete sets;
         sets.push(set({ x: MIN_SD59x18, expected: 0 }));
         sets.push(set({ x: MIN_WHOLE_SD59x18, expected: 0 }));
-        sets.push(set({ x: THRESHOLD - sd(1), expected: 0 }));
+        sets.push(set({ x: EXP2_MIN_THRESHOLD - sd(1), expected: 0 }));
         return sets;
     }
 
@@ -39,7 +36,9 @@ contract Exp2_Unit_Test is SD59x18_Unit_Test {
 
     function negativeAndGteMinPermitted_Sets() internal returns (Set[] memory) {
         delete sets;
-        sets.push(set({ x: THRESHOLD, expected: 0.000000000000000001e18 }));
+        sets.push(set({ x: MIN_SD59x18, expected: 0 }));
+        sets.push(set({ x: EXP2_MIN_THRESHOLD - sd(1), expected: 0 }));
+        sets.push(set({ x: EXP2_MIN_THRESHOLD, expected: 0.000000000000000001e18 }));
         sets.push(set({ x: -33.333333e18, expected: 0.000000000092398923e18 }));
         sets.push(set({ x: -20.82e18, expected: 0.000000540201132438e18 }));
         sets.push(set({ x: -16e18, expected: 0.0000152587890625e18 }));