[Grammar] Update 10-2 Replace branches with arithmetic.md

chapters/10-Optimizing-Branch-Prediction/10-2 Replace branches with arithmetic.md

@@ -36,6 +36,6 @@ test    edi, edi                      xor     eax, edi
 cmovns  eax, ecx
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-In our example, we shift left the input value regardless if it is positive or negative. In addition, if the input value is negative, we also XOR it with a constant (exact value is irrelevant for this scenario). In the modified version, we leverage the fact that arithmetic right shift (`>>`) turns the sign of `x` (the high order bit) into a mask of all zeros or all ones. The subsequent AND (`&`) operation produces either zero or the desired constant. The original version of the function takes ~4 cycles, while the modified version takes only 3 cycles. It's worth mentioning that Clang 17 compiler replaced the branch with a conditional select (CMOVNS) instruction, which we will cover in the next section. Nevertheless, with some smart bit manipulation we were able to improve it even further.
+In our example, we shift left the input value regardless if it is positive or negative. In addition, if the input value is negative, we also XOR it with a constant (the exact value is irrelevant for this scenario). In the modified version, we leverage the fact that arithmetic right shift (`>>`) turns the sign of `x` (the high order bit) into a mask of all zeros or all ones. The subsequent AND (`&`) operation produces either zero or the desired constant. The original version of the function takes ~4 cycles, while the modified version takes only 3 cycles. It's worth mentioning that the Clang 17 compiler replaced the branch with a conditional select (CMOVNS) instruction, which we will cover in the next section. Nevertheless, with some smart bit manipulation, we were able to improve it even further.
 
-As of the year 2024, compilers are usually unable to find these shortcuts on their own, so it is up to the programmer to do it manually. If you can find a way to replace a frequently mispredicted branch with arithmetic, you will likely see a performance improvement. You can find more examples of bit manipulation tricks in other books, for example [@HackersDelight].
+As of the year 2024, compilers are usually unable to find these shortcuts on their own, so it is up to the programmer to do it manually. If you can find a way to replace a frequently mispredicted branch with arithmetic, you will likely see a performance improvement. You can find more examples of bit manipulation tricks in other books, for example [@HackersDelight].