stan-dev / stan-dev/math

Slight rounding errors in constants

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C++
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Description

In constants.hpp, I noticed there are some constants that get a small unnecessary rounding error due to how they are defined.

For example, with 64bit precision floating point, we have:

LOG_TWO_PI = LOG_TWO + LOG_PI = 0.6931471805599453 + 1.1447298858494002 =
1.8378770664093453

However, a mathematically more precise value is $\log(2\pi) \approx 1.83787706640934548356065947281123527972279494727556682563430308096553139185$

This is better rounded to the 64bit value

1.8378770664093456

which means the current value has an unnecessary error in the order of E-16.

I guess there could be a similar type of issue for other constants as well.

I suppose this is pretty much negligible for any practical purpose and perhaps one may argue the current implementation is better readable. But my OCD is kinda forcing me to point this out haha

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Research direction

Start in constants.hpp by reviewing LOG_TWO_PI and nearby constants for values formed from rounded components. Check which constants differ from their more precisely rounded 64-bit values and define the scope of the correction. Done means the identified constants use the better-rounded values without changing unrelated definitions.

Written by the indexing model from the issue text.

Assessment

Tech stack
cpp
Domain
backend
Issue type
Bug
Difficulty
2/5
Estimated time
1-3 hours
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
45/100

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