5 Best Ways to Get the Approximate Number of Decimal Digits Precise in Python Floats

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💡 Problem Formulation: When working with floats in Python, it’s important to understand the level of precision to which our floating-point numbers are accurate. Specifically, we want to find out how many decimal digits we can trust in a float value. For example, given a floating-point number 0.123456789, we might want to know how many of those digits are reliable according to the precision of the data type.

Method 1: Using the sys.float_info Dig Attribute

The sys.float_info module provides information about the float type, including its precision. The dig attribute gives the maximum number of decimal digits that can be reliably represented, which is typically 15 for 64-bit floats.

Here’s an example:

import sys

print(f"Precision: {sys.float_info.dig} digits")

Output:

Precision: 15 digits

This simple code snippet gives us a reliable measure of the decimal digits precision defined for floats in Python. The sys.float_info.dig attribute returns the maximum number of decimal digits that can be rounded to a float and back without change in the value.

Method 2: Using Decimal to Estimate Precision

By converting a float to a decimal.Decimal object, we can estimate the precision by counting the decimal places before the exponent becomes 0 in its normalized form.

Here’s an example:

from decimal import Decimal, getcontext

getcontext().prec = 30  # Set a large precision for the context
float_value = 0.123456789
decimal_value = Decimal(float_value).normalize()
zero_index = -decimal_value.as_tuple().exponent
print(f"Approximate precision: {zero_index} digits")

Output:

Approximate precision: 9 digits

This block converts a float to a Decimal object under a specified precision context. Then, it normalizes the value and finds the position of the last significant decimal digit. However, the output precision might not represent the actual float precision as it also depends on the context’s precision.

Method 3: Calculating Precision with the math.log10 Function

We can approximate the precision of a float by using math.log10 and then taking the floor of the logarithm plus one. This estimates the number of significant figures in the value.

Here’s an example:

import math

float_value = 123.456
precision = math.floor(math.log10(float_value)) + 1
print(f"Number of significant figures: {precision}")

Output:

Number of significant figures: 6

This code example calculates the significant figures in a float number using the base 10 logarithm. Although it provides an estimate of significant figures, it might not directly correlate to the precision of decimal digits for values less than 1.

Method 4: Floating-Point Arithmetic Precision Testing

An empirical approach to determining float precision involves incrementally adding small values until the result does not change, indicating a precision limit.

Here’s an example:

def find_precision(value):
    increment = 0.1
    precision = 0
    while value + increment != value:
        increment /= 10
        precision += 1
    return precision

print(f"Float precision estimate: {find_precision(1.0)} digits")

Output:

Float precision estimate: 15 digits

In this example, the function find_precision() determines the precision by checking when the addition of increasingly smaller values no longer affects the original number, which is typically where floating-point calculations stop being reliable.

Bonus One-Liner Method 5: Using the format() Function

The format() function can be used to represent a float as a string with a set number of decimal places, and from there, we can infer precision.

Here’s an example:

float_value = 1.0 / 3
formatted_value = format(float_value, '.17f')
print(f"Formatted value: {formatted_value}")
print(f"Approximate precision: {formatted_value.rstrip('0').find('.') + 1}")

Output:

Formatted value: 0.33333333333333331
Approximate precision: 17 digits

This compact code formats the float to a string with as many decimal places as Python’s float precision allows. It then trims the trailing zeros and provides a count of significant decimal places. This method gives a numerical illustration of float precision but may include insignificant trailing digits.

Summary/Discussion

  • Method 1: sys.float_info.dig. Straightforward. Reflects theoretical precision based on Python’s data type specifications.
  • Method 2: Decimal Conversion. More complex. Approximates decimal precision but can be dependent on the set context precision.
  • Method 3: math.log10 Function. Simple mathematical calculation. Best for significant figures rather than decimal precision for small numbers.
  • Method 4: Empirical Precision Test. Measures operational precision. Can be computationally intensive and depends on the starting value.
  • Method 5: format() Function. Quick and simple. Provides a real-world example of precision but may include insignificant digits.