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copied!<p>You are dividing using the true division operator <code>/</code>, which will <em>always</em> result in floating point values. Use floor division instead, <code>//</code>, to get integer results:</p> <pre><code>>>> a = 313585730727764141482831584863 >>> b = a*2 >>> c = b // 2 >>> a == c True </code></pre> <p>Your computer hardware cannot handle float values with the required precision.</p> <p>The alternative is to use <a href="http://docs.python.org/3/library/decimal.html" rel="nofollow"><code>decimal.Decimal()</code> values</a>, but this will result in slower arithmetic operations.</p> <p>In Python 2, the <code>/</code> operator <em>is</em> the floor division operator, but when applied to integers <em>only</em>. To get the same behaviour in Python 2, add:</p> <pre><code>from __future__ import division </code></pre> <p>The behaviour was changed because the difference between using only integer operators and using at least one float argument was confusing.</p> <p>In other words, the standard Python 2 <code>/</code> operator is a <em>different</em> beast from the Python 3 <code>/</code> division operator. When applied to two integer operands, it acts just like the <code>//</code> floor division operator in Python 3. But if either one of the two operands is a float instead, then it acts like the <code>/</code> float division operator <em>instead</em>. The above <code>__future__</code> import swaps out the Python 2 <code>/</code> operator for the true division operator found in Python 3.</p> <p>You can see this when disassembling Python bytecode:</p> <pre><code>>>> import dis >>> def olddivision(x, y): return x / y ... >>> dis.dis(olddivision) 1 0 LOAD_FAST 0 (x) 3 LOAD_FAST 1 (y) 6 BINARY_DIVIDE 7 RETURN_VALUE >>> from __future__ import division >>> def newdivision(x, y): return x / y ... >>> dis.dis(newdivision) 1 0 LOAD_FAST 0 (x) 3 LOAD_FAST 1 (y) 6 BINARY_TRUE_DIVIDE 7 RETURN_VALUE </code></pre> <p>the <code>__future__</code> import caused the Python compiler to use a different bytecode for the division operator, swapping <code>BINARY_DIVIDE</code> for <code>BINARY_TRUE_DIVIDE</code>.</p>

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