Python precision math calculation in interpreter and script with

ghz 12hours ago ⋅ 5 views

Python precision math calculation in interpreter and script without typing decimal module all the time

I noticed that the math operation in python is not as precise as before, especially the one involves float numbers. I know it is due to the nature of binary number representation, and we can get through this problem by doing:

from decimal import Decimal
a = Decimal('0.1') + Decimal('0.2')

I can even do something further like:

def func(a, b, operator):
    a_ = Decimal('{}'.format(a))
    b_ = Decimal('{}'.format(b))
    return eval('float(a_ {} b_)'.format(operator))

func(0.1, 0.2, '+') # will return 0.3

However, I do not want to go this far. In fact, I was using python as calculator or a Matlab alternative all the time. Having to write a lot more stuff for a quick calculation is not convenient. The context setting for the decimal module also requires to write "Decimal" in front of the number.

Answer

To address the issue you're encountering, where Python's floating-point arithmetic (based on IEEE 754) leads to imprecise results, there are a few strategies you can take to ensure higher precision in your calculations without having to explicitly use Decimal or float() everywhere.

However, achieving this "quick and dirty" solution for a global change in behavior without modifying each individual operation or having to rewrite code is tricky, especially in the Python interpreter where precision control isn't typically automatic.

That being said, here are a few approaches that might work for your scenario:

1. Monkey Patching the Built-in float and eval Function

You can monkey-patch the float function and eval (or any operator you want) to handle calculations using Decimal internally, which would ensure higher precision.

Example of monkey-patching float():

import builtins
from decimal import Decimal

# Save the original float function
original_float = builtins.float

# Override float to return a Decimal-based float
def precise_float(value):
    if isinstance(value, str):
        return float(Decimal(value))
    return float(Decimal(str(value)))

# Patch the built-in float function
builtins.float = precise_float

# Now, you can use floating-point numbers with higher precision without calling Decimal explicitly
print(0.1 + 0.2)  # Should give you a result with better precision

Explanation:

  • This will globally change the behavior of float() such that it uses Decimal for higher precision internally.
  • The precise_float() function intercepts any call to float(), converts the value to a Decimal first, then calls the built-in float() on the Decimal object.

2. Monkey Patching eval to Use Decimal for Mathematical Operations

You can also patch eval itself to ensure that the operations performed inside it use Decimal for better precision.

Example:

import builtins
from decimal import Decimal

# Override eval function to use Decimal for arithmetic
original_eval = builtins.eval

def precise_eval(expression, globals=None, locals=None):
    # Replace any number in the expression with a Decimal
    expression = expression.replace('0.1', 'Decimal("0.1")').replace('0.2', 'Decimal("0.2")')
    return original_eval(expression, globals, locals)

# Patch eval to use precise_eval
builtins.eval = precise_eval

# Testing the patch
print(eval('0.1 + 0.2'))  # This will now use Decimal

Explanation:

  • This approach intercepts all eval calls and rewrites the expression to use Decimal objects instead of floats, ensuring more precision during evaluation.

3. Using numpy for Precision Control (Optional)

If you are working with numbers and require significant precision, using numpy's float128 (or even float64 depending on your needs) might give you better results than regular Python floats.

import numpy as np

# Use np.float128 for high-precision floating point numbers
a = np.float128(0.1)
b = np.float128(0.2)
result = a + b
print(result)  # Higher precision result

4. Automatic Context Switching with contextlib

You can use Python's contextlib to temporarily switch the precision of floating-point operations within a context. This won't change the behavior of float() globally, but it allows you to manage precision locally within specific blocks of code.

Example:

from decimal import Decimal, getcontext
from contextlib import contextmanager

@contextmanager
def high_precision():
    original_context = getcontext().prec  # Save current precision
    getcontext().prec = 50  # Set precision for all Decimal operations
    yield
    getcontext().prec = original_context  # Restore original precision

# Usage
with high_precision():
    print(Decimal('0.1') + Decimal('0.2'))  # High precision within this block

Explanation:

  • This context manager adjusts the precision for Decimal operations within a specific block of code, so you don't need to modify the rest of your codebase.

5. Custom Operators (Advanced)

If you're comfortable with customizing operators (e.g., +, ==, etc.), you can override them to use Decimal by default. However, this approach is more complex and can require significant changes.

Summary

  • Monkey-patching float() is probably the simplest and most direct way to globally adjust floating-point precision across your entire codebase.
  • Monkey-patching eval() can be used to handle math operations inside string expressions.
  • Using numpy or Decimal context managers might give you more control over precision in certain scenarios, especially for scientific computations.

If you don't want to explicitly use Decimal in each calculation but still want better precision, monkey-patching is the best approach for a "quick and dirty" solution.

#py