Do Floating-Point Numbers Offer Arbitrary Precision in Python and Other Languages?

Can Floating-Point Numbers Provide Arbitrary Precision?

In Python, floating-point numbers exhibit precision limitations. A question arose regarding the Python code's inability to identify certain large Grafting numbers due to this limitation. The user attempted to verify this behavior using a C program and observed similar results.

Python's Limitations:

The Python floating-point implementation truncates trailing bits, leading to loss of precision in certain operations. As a result, the code misses numbers like 9999999998, which should be a Grafting number but is lost due to truncation.

Alternative Options:

Python offers alternative modules like decimal and mpmath that provide higher precision in mathematical operations. However, certain functions in these modules may not always align with their corresponding functions in the standard math module.

For example, math.sqrt and decimal.sqrt may provide different results for high-precision values:

>>> from decimal import *
>>> from math import sqrt
>>> getcontext().prec = 30
>>> num = Decimal(1) / Decimal(7)
>>> print("   math.sqrt:", Decimal(sqrt(num)))
>>> print("decimal.sqrt:", num.sqrt())
   math.sqrt: 0.37796447300922719758631274089566431939601898193359375
decimal.sqrt: 0.377964473009227227214516536234

Recommendation:

To handle such precision requirements, consider using external libraries such as GMP or switching to languages like C/C that provide built-in support for arbitrary precision arithmetic.

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