Why Does Python's Floating-Point Math Sometimes Seem Inaccurate?

Why Python Floating-Point Math Can Seem Wrong

While Python is generally known for its versatility and ease of use, its handling of floating-point numbers has sometimes been questioned. This is because floating-point math in Python, as in many other languages, can exhibit subtle inaccuracies when dealing with non-integer values.

To understand this, it's important to delve into the realm of IEEE 754, the standard for floating-point arithmetic. This standard defines specific formats for representing real numbers as sequences of binary digits (bits). Floating-point numbers consist of three main parts:

• The sign bit
• The exponent
• The significand (or mantissa)

The exponent determines the magnitude of the number, while the significand represents its fractional part. The number of bits used to store the significand determines the precision of the floating-point representation.

When performing floating-point arithmetic, certain errors can arise:

• Rounding errors: When a number is represented in floating-point format with limited precision, some digits may be lost during rounding.
• Overflow: When the result of an operation is too large or too small to fit within the available number of bits, an overflow or underflow error occurs.

In Python, these errors can manifest in various ways. For example, the following code snippets demonstrate some of these inaccuracies:

>>> 4.2 - 1.8
2.4000000000000004
>>> 1.20 - 1.18
0.020000000000000018
>>> 5.1 - 4
1.0999999999999996
>>> 5 - 4
1
>>> 5.0 - 4.0
1.0

As you can see, the results can differ slightly from the expected exact values. This is because Python stores floating-point numbers in IEEE 754 format, and the rounding errors introduced during representation and arithmetic operations can lead to these discrepancies.

It's important to note that these errors are typically small and insignificant for most practical purposes. However, if extreme precision is required, it may be necessary to use specific libraries or programming techniques to mitigate these inaccuracies.

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