CODEWITHSUNDEEP
python
Lily
Lily

Reputation: 11

Python calculation including e

enter image description here

print(0.5+0.5+0.5+0.5+1e+16): 1.0000000000000002e+16


print(1e+16+0.5+0.5+0.5+0.5): 1e+16

Why these two answers differ?

Upvotes: 1

Views: 80

Answers (1)

Roland Smith
Roland Smith

Reputation: 43533

It is because how Python parses the expressions.

Let's use the ast module to see:

In [1]: import ast

In [2]: print(ast.dump(ast.parse("0.5+0.5+0.5+0.5+1e+16"), indent=4))
Module(
    body=[
        Expr(
            value=BinOp(
                left=BinOp(
                    left=BinOp(
                        left=BinOp(
                            left=Constant(value=0.5),
                            op=Add(),
                            right=Constant(value=0.5)),
                        op=Add(),
                        right=Constant(value=0.5)),
                    op=Add(),
                    right=Constant(value=0.5)),
                op=Add(),
                right=Constant(value=1e+16)))],
    type_ignores=[])

The code above basically first adds all the 0.5 values (yielding 2.0) and then adds that to 1e16.

In [6]: 1e16+2
Out[6]: 1.0000000000000002e+16

In [3]: print(ast.dump(ast.parse("1e+16+0.5+0.5+0.5+0.5"), indent=4))
Module(
    body=[
        Expr(
            value=BinOp(
                left=BinOp(
                    left=BinOp(
                        left=BinOp(
                            left=Constant(value=1e+16),
                            op=Add(),
                            right=Constant(value=0.5)),
                        op=Add(),
                        right=Constant(value=0.5)),
                    op=Add(),
                    right=Constant(value=0.5)),
                op=Add(),
                right=Constant(value=0.5)))],
    type_ignores=[])

The other code adds 0.5 to 1e16 four times. However, this doesn't work because 0.5 is too small to change 1e16:

In [7]: 1e16+0.5 == 1e16
Out[7]: True

This basically has to do with the nature of floating point numbers. Look at sys.float_info.dig; this will tell you how many digits the float type can handle on your machine:

In [23]: import sys

In [24]: sys.float_info.dig
Out[24]: 15

In a case like this, consider using decimal.Decimal numbers:

In [21]: from decimal import Decimal

In [22]: Decimal("1e16")+Decimal("0.5")+Decimal("0.5")+Decimal("0.5")+Decimal("0.5")
Out[22]: Decimal('10000000000000002.0')

Upvotes: 1

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