The major source of determinism in floating point calculations is IEEE 754 standard.
Most of the implementations adhere to IEEE 754 standard (more info about it here: https://en.wikipedia.org/wiki/IEEE_754-2008_revision)
C and C++ do not guarantee to adhere to IEEE 754 standard, therefore any software which was compiled using C/C++ may not necessarily adhere to IEEE 754
- Errors of none IEEE 754 can be really anything
The best explanation (yet not 100% accurate or complete) of it is here: https://neerc.ifmo.ru/wiki/index.php?title=Представление_вещественных_чисел
And this cool video is also helpful: https://www.youtube.com/watch?v=RuKkePyo9zk
Sources of error in IEEE 754-compliant systems:
- Precision error, which will be different depending on how you get the number
- Current rounding mode selected (more of those here: https://www.gnu.org/software/libc/manual/html_node/Rounding.html)
- Different optimization settings of the CPU: https://www.cppstories.com/2021/06/floating-point-myths/#2-they-are-non-deterministic
- Different CPU (for example Intel has DAZ optimization flag which affects precision and AMD does not have it)
- Old CPU instruction magic can make floating point numbers truly non-deterministic https://twitter.com/j_bikker/status/1372273107197698054
- Some functions are not specified in IEEE 754 at all, such as
sin/cos/exp, so their values can differ on different platforms (see https://www.appinf.com/download/FPIssues.pdf)