Importing variables non-deterministic?

[Steven D'Aprano]

On Mon, 19 Aug 2013 22:34:00 +0200, Antoon Pardon wrote:

> Op 19-08-13 19:05, Steven D'Aprano schreef:
> 
> 
>> I wish Python had stronger support for enforcing constantness, to whit,
>> some way to say "you can't rebind or delete this name once it is
>> bound". You can do it with attributes, by use of property, or in C
>> extensions, but you cannot do it with top-level name bindings. It makes
>> me terribly sad that you can do this:
>>
>> import math
>> math.pi = 3.0
>>
>>
>> although I can't decide whether I am less sad or more sad to see that
>> the behaviour of math.sin and friends doesn't depend on math.pi.
> 
> Why should you expect math.sin and friends be dependant on math.pi?
> AfAIR the numerical algorithms for calulating sin and friends don't
> depend on (the value of) pi. So there is no reason to suspect that
> altering math.pi would have any effect on the results of these
> functions.


Of course they depend on pi. Or rather, they depend on the geometric 
properties of circles, which are related to pi. If the ratio of the 
circumference of a circle to its diameter was exactly 3, instead of 
3.1415..., then sine and cosine functions would be periodic with period 6 
rather than τ = 2π.

If you consider the implementation of sin and cos functions, they usually 
reduce the argument modulo π to something in the first quadrant, and then 
use symmetry to adjust the value. So changing the value of pi could, in 
principle, change the implementation of sin, cos and tan.


-- 
Steven