Explanation of this Python language feature? [x for x in x for x in x] (to flatten a nested list)

[Steven D'Aprano]

On Fri, 04 Apr 2014 09:43:15 +1100, Chris Angelico wrote:

> While I am interested in seeing a Decimal literal syntax in Python, and
> I would support a shift to have "1.2" evaluate as a Decimal (but not
> soon - it'd break backward compat *hugely*)

I used to think the same thing, but have since learned that it's not a 
coincidence or accident that people seriously interested in numerical 
computation nearly always stick to binary floats. I think it's a little 
harsh to say that only dilettantes and amateurs use base-10 floats, but 
only a little. Base-10 has one, and only one, thing going for it: the 
number you type (in decimal) is the number you get (within the limits of 
precision). Apart from that, in every way IEEE-754 binary floats are as 
good or better than any other choice of base, including decimal. The same 
floating-point complications that plague binary floats also plague 
decimal ones, only worse.

I really should stop being shocked by anything I learn about floating 
point numbers, but something that knocked my socks off when I learned it 
was that as simple an operation as taking the average of two floats is 
problematic in decimal. In base-2, and given round-to-nearest division, 
(x+y)/2 is always within the range x...y. But that's not necessarily the 
case in base-10 floats: sometimes the average of two numbers is not 
between those two numbers. Contrast binary floats:

py> x = 0.7777777777787516
py> y = 0.7777777777787518
py> (x + y) / 2
0.7777777777787517


with decimal:

py> from decimal import *
py> getcontext().prec = 16
py> x = Decimal("0.7777777777787516")
py> y = Decimal("0.7777777777787518")
py> (x + y) / 2
Decimal('0.7777777777787515')

"Guido, why can't Python do maths???"

(Oh lordy, can you imagine Ranting Rick getting onto that???)

I've changed my mind about Python using Decimal as the default numeric 
type. I think that would send a very strong message that Python is not 
for serious numeric work.



-- 
Steven D'Aprano
http://import-that.dreamwidth.org/