Question

ActionScript3 states the following:

Note: The Math functions acos, asin, atan, atan2, cos, exp, log, pow, sin, and sqrt may result in slightly different values depending on the algorithms used by the CPU or operating system. Flash runtimes call on the CPU (or operating system if the CPU doesn’t support floating point calculations) when performing the calculations for the listed functions, and results have shown slight variations depending upon the CPU or operating system in use.

My web application works with very large and small numbers that I suspect may see a difference depending on which machine is running it (especially with mobile devices whose processors aren’t as powerful as desktop machines’). My question is, is this behavior a function of the language?

That is, I assume some languages implement their own algorithms for the above functions, and so may be more consistent (except for differences in round-off errors introduced by the choice of processor/CPU that would exist for all languages).

Anyone know if Javascript has it’s own algorithms, or does it outsource them to the CPU/processor like ActionScript?

Answer 1

Excerpt from the ECMAScript 5 standard, 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. For other argument values, these
functions are intended to compute approximations to the results of
familiar mathematical functions, but some latitude is allowed in the
choice of approximation algorithms. The general intent is that an
implementer should be able to use the same mathematical library for
ECMAScript on a given hardware platform that is available to C
programmers on that platform.

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
(http://www.netlib.org/fdlibm)

Essentially that means that every implementation (including every browser) can decide how they want to deal with those functions. As recommended, I presume the vast majority use fdlibm although checking that will be left as an exercise for the reader.