diff --git a/contracts/libraries/AddressStringUtil.sol b/contracts/libraries/AddressStringUtil.sol
index dd71ac38..245cf031 100644
--- a/contracts/libraries/AddressStringUtil.sol
+++ b/contracts/libraries/AddressStringUtil.sol
@@ -8,7 +8,7 @@ library AddressStringUtil {
         require(len % 2 == 0 && len > 0 && len <= 40, 'AddressStringUtil: INVALID_LEN');
 
         bytes memory s = new bytes(len);
-        uint256 addrNum = uint256(addr);
+        uint256 addrNum = uint160(addr);
         for (uint256 i = 0; i < len / 2; i++) {
             // shift right and truncate all but the least significant byte to extract the byte at position 19-i
             uint8 b = uint8(addrNum >> (8 * (19 - i)));
diff --git a/contracts/libraries/BitMath.sol b/contracts/libraries/BitMath.sol
index d570c2d6..6fc6d2ff 100644
--- a/contracts/libraries/BitMath.sol
+++ b/contracts/libraries/BitMath.sol
@@ -45,27 +45,27 @@ library BitMath {
         require(x > 0, 'BitMath::leastSignificantBit: zero');
 
         r = 255;
-        if (x & uint128(-1) > 0) {
+        if (x & type(uint128).max > 0) {
             r -= 128;
         } else {
             x >>= 128;
         }
-        if (x & uint64(-1) > 0) {
+        if (x & type(uint64).max > 0) {
             r -= 64;
         } else {
             x >>= 64;
         }
-        if (x & uint32(-1) > 0) {
+        if (x & type(uint32).max > 0) {
             r -= 32;
         } else {
             x >>= 32;
         }
-        if (x & uint16(-1) > 0) {
+        if (x & type(uint16).max > 0) {
             r -= 16;
         } else {
             x >>= 16;
         }
-        if (x & uint8(-1) > 0) {
+        if (x & type(uint8).max > 0) {
             r -= 8;
         } else {
             x >>= 8;
diff --git a/contracts/libraries/FixedPoint.sol b/contracts/libraries/FixedPoint.sol
index 27d0ed64..e800202c 100644
--- a/contracts/libraries/FixedPoint.sol
+++ b/contracts/libraries/FixedPoint.sol
@@ -19,9 +19,9 @@ library FixedPoint {
         uint256 _x;
     }
 
-    uint8 public constant RESOLUTION = 112;
-    uint256 public constant Q112 = 0x10000000000000000000000000000; // 2**112
-    uint256 private constant Q224 = 0x100000000000000000000000000000000000000000000000000000000; // 2**224
+    uint8 private constant RESOLUTION = 112;
+    uint256 private constant Q112 = 0x10000000000000000000000000000;
+    uint256 private constant Q224 = 0x100000000000000000000000000000000000000000000000000000000;
     uint256 private constant LOWER_MASK = 0xffffffffffffffffffffffffffff; // decimal of UQ*x112 (lower 112 bits)
 
     // encode a uint112 as a UQ112x112
@@ -78,13 +78,13 @@ library FixedPoint {
         uint224 uppero_lowers = uint224(upper_other) * lower_self; // * 2^-112
 
         // so the bit shift does not overflow
-        require(upper <= uint112(-1), 'FixedPoint::muluq: upper overflow');
+        require(upper <= type(uint112).max, 'FixedPoint::muluq: upper overflow');
 
         // this cannot exceed 256 bits, all values are 224 bits
         uint256 sum = uint256(upper << RESOLUTION) + uppers_lowero + uppero_lowers + (lower >> RESOLUTION);
 
         // so the cast does not overflow
-        require(sum <= uint224(-1), 'FixedPoint::muluq: sum overflow');
+        require(sum <= type(uint224).max, 'FixedPoint::muluq: sum overflow');
 
         return uq112x112(uint224(sum));
     }
@@ -95,30 +95,30 @@ library FixedPoint {
         if (self._x == other._x) {
             return uq112x112(uint224(Q112));
         }
-        if (self._x <= uint144(-1)) {
+        if (self._x <= type(uint144).max) {
             uint256 value = (uint256(self._x) << RESOLUTION) / other._x;
-            require(value <= uint224(-1), 'FixedPoint::divuq: overflow');
+            require(value <= type(uint224).max, 'FixedPoint::divuq: overflow');
             return uq112x112(uint224(value));
         }
 
         uint256 result = FullMath.mulDiv(Q112, self._x, other._x);
-        require(result <= uint224(-1), 'FixedPoint::divuq: overflow');
+        require(result <= type(uint224).max, 'FixedPoint::divuq: overflow');
         return uq112x112(uint224(result));
     }
 
     // returns a UQ112x112 which represents the ratio of the numerator to the denominator
-    // can be lossy
+    // lossy if either numerator or denominator is greater than 112 bits
     function fraction(uint256 numerator, uint256 denominator) internal pure returns (uq112x112 memory) {
         require(denominator > 0, 'FixedPoint::fraction: division by zero');
         if (numerator == 0) return FixedPoint.uq112x112(0);
 
-        if (numerator <= uint144(-1)) {
+        if (numerator <= type(uint144).max) {
             uint256 result = (numerator << RESOLUTION) / denominator;
-            require(result <= uint224(-1), 'FixedPoint::fraction: overflow');
+            require(result <= type(uint224).max, 'FixedPoint::fraction: overflow');
             return uq112x112(uint224(result));
         } else {
             uint256 result = FullMath.mulDiv(numerator, Q112, denominator);
-            require(result <= uint224(-1), 'FixedPoint::fraction: overflow');
+            require(result <= type(uint224).max, 'FixedPoint::fraction: overflow');
             return uq112x112(uint224(result));
         }
     }
@@ -135,7 +135,7 @@ library FixedPoint {
     // square root of a UQ112x112
     // lossy between 0/1 and 40 bits
     function sqrt(uq112x112 memory self) internal pure returns (uq112x112 memory) {
-        if (self._x <= uint144(-1)) {
+        if (self._x <= type(uint144).max) {
             return uq112x112(uint224(Babylonian.sqrt(uint256(self._x) << 112)));
         }
 
diff --git a/contracts/libraries/FullMath.sol b/contracts/libraries/FullMath.sol
index f06356c7..d6b6af73 100644
--- a/contracts/libraries/FullMath.sol
+++ b/contracts/libraries/FullMath.sol
@@ -5,7 +5,7 @@ pragma solidity >=0.4.0;
 // license is CC-BY-4.0
 library FullMath {
     function fullMul(uint256 x, uint256 y) internal pure returns (uint256 l, uint256 h) {
-        uint256 mm = mulmod(x, y, uint256(-1));
+        uint256 mm = mulmod(x, y, type(uint256).max);
         l = x * y;
         h = mm - l;
         if (mm < l) h -= 1;
@@ -16,10 +16,10 @@ library FullMath {
         uint256 h,
         uint256 d
     ) private pure returns (uint256) {
-        uint256 pow2 = d & -d;
+        uint256 pow2 = d & (~d+1);
         d /= pow2;
         l /= pow2;
-        l += h * ((-pow2) / pow2 + 1);
+        l += h * ((~pow2+1) / pow2 + 1);
         uint256 r = 1;
         r *= 2 - d * r;
         r *= 2 - d * r;
@@ -29,6 +29,7 @@ library FullMath {
         r *= 2 - d * r;
         r *= 2 - d * r;
         r *= 2 - d * r;
+        
         return l * r;
     }
 
@@ -48,4 +49,5 @@ library FullMath {
         require(h < d, 'FullMath: FULLDIV_OVERFLOW');
         return fullDiv(l, h, d);
     }
+    
 }