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Res is not defined in the code. #359

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Res is not defined in the code. #359

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4 changes: 2 additions & 2 deletions content/english/hpc/number-theory/exponentiation.md
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Original file line number Diff line number Diff line change
Expand Up @@ -76,7 +76,7 @@ u64 binpow(u64 a, u64 n) {

while (n) {
if (n & 1)
r = res * a % M;
r = r * a % M;
a = a * a % M;
n >>= 1;
}
Expand All @@ -85,7 +85,7 @@ u64 binpow(u64 a, u64 n) {
}
```

The iterative implementation takes about 180ns per call. The heavy calculations are the same; the improvement mainly comes from the reduced dependency chain: `a = a * a % M` needs to finish before the loop can proceed, and it can now execute concurrently with `r = res * a % M`.
The iterative implementation takes about 180ns per call. The heavy calculations are the same; the improvement mainly comes from the reduced dependency chain: `a = a * a % M` needs to finish before the loop can proceed, and it can now execute concurrently with `r = r * a % M`.

The performance also benefits from $n$ being a constant, [making all branches predictable](/hpc/pipelining/branching/) and letting the scheduler know what needs to be executed in advance. The compiler, however, does not take advantage of it and does not unroll the `while(n) n >>= 1` loop. We can rewrite it as a `for` loop that performs constant 30 iterations:

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