a = (1 << 52)
print((a + 0.5) == a)
Code Explanation:
- 1 << 52:
- The << operator is a bitwise left shift.
- 1 << 52 shifts the binary representation of 1 to the left by 52 places, resulting in .
- So, a = 1 << 52 sets a to , which is 4,503,599,627,370,496.
- a + 0.5:
- Adds 0.5 to the value of a. In this case, .
Equality Check (==):
- The expression (a + 0.5) == a compares whether is equal to .
Why does the result evaluate to True?
This happens because of the limitations of floating-point precision in Python:
- Python uses 64-bit floating-point numbers (IEEE 754 standard).
- A 64-bit floating-point number can precisely represent integers up to (inclusive), but not fractional values beyond this precision.
- is close to the upper limit of this precision. When adding 0.5 to , the fractional part (0.5) is effectively rounded off due to the lack of precision.
- As a result, is rounded back to , making (a + 0.5) == a evaluate to True.