经过太多分歧后，Python会变为0.0

Question

So, I have the following code:

    half= 1/2.0
    print(half)
    for x in range(1,1075):
        half=half/2.0
        print(half)

But right at the last part of the loop, python decides that half is now 0.0

    1.265e-321
    6.3e-322
    3.16e-322
    1.6e-322
    8e-323
    4e-323
    2e-323
    1e-323
    5e-324
    0.0

Did I reach python's limit? Do I need to install a package to go farther? I'm not sure why this is happening, but I'm assuming that python just reached limit

Answer 1

TLDR : try Fraction

half = Fraction(1, 2)
for x in range(1, 1075):
    half = half / 2
    print(half)

will give

1/4
1/8
...
1/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784
1/404804506614621236704990693437834614099113299528284236713802716054860679135990693783920767402874248990374155728633623822779617474771586953734026799881477019843034848553132722728933815484186432682479535356945490137124014966849385397236206711298319112681620113024717539104666829230461005064372655017292012526615415482186989568

---

You can find out the smallest available positive float with

>>> import sys
>>> sys.float_info.min
2.2250738585072014e-308

then following your example we will find that

>>> 2 * sys.float_info.min > pow(2, -1074)
True

ie next division by 2 seems to be less than smallest available positive float .

Btw their difference is equal to

>>> diff = 2 * sys.float_info.min - pow(2, -1074)
>>> diff
4.4501477170144023e-308

but it is interesting that

>>> diff == 2 * sys.float_info.min
False

while

>>> diff / 2 == sys.float_info.min
True

---

PS : dividing Fraction objects by float s will give us float

>>> half = Fraction(1, 2)
>>> half = half / 2.0
>>> type(half)
<class 'float'>

so your code with dividing by 2.0 will give the same result and for correct working with Fraction s you should add/subtract/divide/multiply it with int s or other Fraction s like

half = Fraction(1, 2)
for x in range(1, 1075):
    half = half / Fraction(2.0)
    print(half)

---

PPS : there is a convention about using underscore as a name for unused object, so it will be better to write

half = Fraction(1, 2)
for _ in range(1, 1075):
    half = half / 2
    print(half)

Answer 2

Yes, essentially, you have reached the Python's limit. The decimals lose precision as you go on.

One possible way would be to use the Fraction class, as suggested by Azat.

However, you can also use the Decimal class.

Here is the example provided on the page linked above. This treats the number as an object and not as a primitive/built-in variable:

>>> from decimal import *
>>> getcontext().prec = 6
>>> Decimal(1) / Decimal(7)
Decimal('0.142857')
>>> getcontext().prec = 28
>>> Decimal(1) / Decimal(7)
Decimal('0.1428571428571428571428571429')

getcontext().prec = 6 line is the one that sets the precision. You can change the number 6 to whatever you need.

Usually, the precision to 324th decimal place (as in your example) is not necessary, so Python only stores a few digits as binary fractions . Using the Fraction or the Decimal classes allows you to extend the functionality, but it can also slow down the code significantly if you use it repetitively (in loops for example).