Menu
Can the same mathematical operation return different results in different architectures or browsers ?
504
Floating-point is deterministic. The same floating-point operations, run on the same hardware, always produces the same result. There is no black magic, noise, randomness, fuzzing, or any of the other things that people commonly attribute to floating-point.
The short answer is that FP calculations are entirely deterministic, as per the IEEE Floating Point Standard, but that doesn't mean they're entirely reproducible across machines, compilers, OS's, etc.
The representation of floating points in JavaScript follows the IEEE-754 format. It is a double precision format where 64 bits are allocated for every floating point.
Because often-times, they are approximating rationals that cannot be represented finitely in base 2 (the digits repeat), and in general they are approximating real (possibly irrational) numbers which may not be representable in finitely many digits in any base.
The other answers are incorrect. According to the ECMAScript 5.1 specs (section 15.8.2)
NOTE The behaviour of the functions acos, asin, atan, atan2, cos, exp, log, pow, sin, sqrt, and tan is not precisely specified here except to require specific results for certain argument values that represent boundary cases of interest.
...
Although the choice of algorithms is left to the implementation, it is recommended (but not specified by this standard) that implementations use the approximation algorithms for IEEE 754 arithmetic contained in fdlibm, the freely distributable mathematical library from Sun Microsystems
However, even if the implementations were specified, the exact results of all floating-point operations would still be dependent on browser/architecture. That includes simple operations like multiplication and division!!
The reason is that IEEE-754 allows systems to do 64-bit floating-point calculations at a higher-precision than the result, leading to different rounding results than systems which use the same precision as the result. This is exactly what the x86 (Intel) architecture does, which is why in C (and javascript) we can sometimes have cos(x) != cos(y) even though x == y, even on the same machine!
This is a big issue for networked peer-to-peer games, since this means, if the higher-precision calculations can't be disabled (as is the case for C#), those games pretty much can't use floating-point calculations at all. However, this is typically not an issue for Javascript games, since they are usually client-server.
59
If we assume that every browser vendor follows the IEEE standards + ECMA specs and there is no human error while implementing, no there can't be any difference.
3
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With
