Editing Openai/6959ed27-accc-800e-8e87-21aa81e93c07 (section)

=========================================================

Great results! Let me summarize:

    0xfaded's r/q optimization works! - saves ~11% (40.9 → 36.4 ns)
    std::hypot is slow - 2.3x slower than manual sqrt (probably because it handles overflow/underflow carefully)
    Extreme eccentricity cases all work fine - no accuracy issues even at 1:1000 ratio
    With the optimization, 0xfaded's method is now faster than Claude's (36.4 vs 38.7 ns)

Let me present this nicely for the user to share.

Nice! His optimization works:

                     original   optimized   rotation (claude)
-----------------------------------------------------------
Time (ns/call)         40.9       36.4          38.7
Speedup                  --        11%           5%
sqrt per iteration        3          2             1
Accuracy             4.2e-7     4.2e-7        4.2e-7

Key findings:

    His r/q trick saves 11% — combining into one sqrt (40.9 → 36.4 ns)
    std::hypot is 2.3x SLOWER — it handles overflow/underflow carefully, which we don't need here
    Extreme eccentricity works fine — tested a=1, b=1000 and vice versa, no accuracy issues
    With his optimization, his method beats Claude's — 36.4 vs 38.7 ns

So the updated table for your HN reply:

  yours       yours+opt   claude
  ----------------------------------
  Time (ns)      40.5   36.4    38.3
  sqrt/iter         3      2       1
  Accuracy     4.8e-7 4.2e-7  4.8e-7

His own optimization makes his method the fastest again!

Nice. There a way to get, like, the number of instructions somehow in your environment?
9:47 PM

bash
which objdump && objdump --version | head -1

Output
/usr/bin/objdump
GNU objdump (GNU Binutils for Ubuntu) 2.42

Good, objdump is available. I can:

    Compile with symbols and disassemble
    Count instructions in each function

Let me create a simpler file with just the core functions marked so we can easily find them in the disassembly.

objdump is available. Let me compile with symbols and disassemble to count instructions:

bash
cd /home/claude && echo "