Trying to find smallest number

Question

In my program I'm trying to find the smallest number that python can give me. When I kept dividing a number by 2, I got 5 x 10^-324 (5e-324). I thought I could divide this by the biggest number I can use in python. I tried to get the biggest number in python by doing this:

z = 1
    while True:
        try:
            z = z+1
        except OverflowError:
            z = z-1
            break

---

Here is my full code:

from os import system
x = 76556758478567587
while True:
    x = x/2
    if x/2 == 0.0:
        break

print("Smallest number I can compute:", x)
print()
z = 1
while True:
    try:
        z = z+1
    except OverflowError:
        z = z-1
        break

print(str(x) + " divided by " + str(z) + " is...")
z = x/z
print(z)
system("pause >nul")

Every time I run this it does nothing. I suddenly recognize it's still trying to solve the problem so I open task manager and Python was eating up my CPU like a pack of wolves eating a dead cow.

---

I know the smallest number in python would be negative but I want to get the the smallest number above zero .

Answer 1

You may use sys.float_info to get the maximum/minimum representable finite float as:

>>> import sys
>>> sys.float_info.min
2.2250738585072014e-308
>>> sys.float_info.max
1.7976931348623157e+308

Python uses double-precision floats, which can hold values from about 10 to the -308 to 10 to the 308 power. Below is the experiment from the python prompt:

# for maximum
>>> 1e308
1e+308
>>> 1e+309
inf   <-- Infinite

You may even get numbers smaller than 1e-308 via denormals , but there is a significant performance hit to this and such numbers are represented with a loss of precision . I found that Python is able to handle 1e-323 but underflows on 1e-324 and returns 0.0 as the value.

# for minimum
>>> 1e-323
1e-323
>>> 1e-324
0.0

You can get denormalized minimum as sys.float_info.min * sys.float_info.epsilon , which comes as 5e-324 .

As per the document:

sys.float_info.max is maximum representable finite float

sys.float_info.min is minimum positive normalized float

To get more information check:sys.float_info :

sys.float_info is a struct sequence holding information about the float type. It contains low level information about the precision and internal representation. The values correspond to the various floating-point constants defined in the standard header file float.h for the 'C' programming language; see section 5.2.4.2.2 of the 1999 ISO/IEC C standard [C99], 'Characteristics of floating types', for details.

Answer 2

The smallest floating point number representable in Python is 5e-324 , or 2.0**-1075 .

The other two answers have each given you half of what you need to find this number. It can be found by multiplying sys.float_info.min ( 2.2250738585072014e-308 , the smallest normalized float) by sys.float_info.epsilon ( 2.220446049250313e-16 , the smallest proportion you can modify a number by while still getting a distinct value).

Answer 3

The key word that you're apparently missing is " epsilon ." If you search on Python epsilon value then it returns a links to StackOverflow: Value for epsilon in Python near the top of the results in Google.

Obviously it helps if you understand how the term is associated with this concept.