Recently I was reading an article on the EML operator (exp-min-log) that uses exponentiation and logarithm to build elementary math functions including arithmetic operations. There was a table of results from testing across languages.

  Language         Result of 2 x 3    Error
  ---
  Node.js v25.3.0  6.000000000000000  0
  Python 3.9.6     6.000000000000001  8.88e-16
  PHP 8.5.1        6.000000000000001  8.88e-16
  Go 1.26.2        6.000000000000000  0
  Rust             6.000000000000001  8.88e-16

It was speculated that this miniscule margin of error, 1 ULP (unit in the last place), is likely due to the difference in how log() is implemented by the language. Supposedly Python, PHP, and Rust use LLVM's libm (C math library) but maybe Go and Node.js internally compile to CPU instructions directly? There was no evidence presented, so I was skeptical of this explanation.

▲ purplesyringa a day ago | parent [-]

Python, PHP, and Rust do indeed use libm. Not LLVM's libm specifically, though, but rather just about anything they can find in runtime, and those libraries can have suboptimal accuracy.

Node uses V8, which notably implements a ton of math manually, because it needs the results to be deterministic across devices. It seemingly uses LLVM's libm, which IIRC promises 0.5 ulp for most operations. (https://github.com/v8/v8/blob/f24c62fbc342d616032734b714116e...)

Go avoids dynamic linking, so they also have their own implementation. (https://github.com/golang/go/blob/543ead71a8e7acc2bd6f326327...) They only promise 1 ulp, but I guess in this specific case it works out better than approximations used by the default libm on their system by pure chance?

▲

lioeters a day ago | parent [-]

Nice, thanks for tracking down those links, fascinating. Apparently being off by 1 ULP is within IEEE 754 floating-point spec, and "effectively negligible".

	▲	AlotOfReading a day ago \| parent [-]
		Correctly rounding transcendental functions is very difficult because of something called the table maker's dilemma, so the standard didn't want to impose a potentially extreme performance cost if they didn't have to. Correctly rounded single precision functions at a reasonable cost are much easier these days. LLVM 18+ implements them, but the gnu libraries have been slower to improve.