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| <h1>Module <code>bit32</code></h1> |
| |
| <p>Bitwise Operations.</p> |
| |
| |
| <p>This library provides bitwise operations. It provides all its functions inside the table <code>bit32</code>. |
| Unless otherwise stated, all functions accept numeric arguments in the range <code>(-2^51,+2^51);</code> |
| each argument is normalized to the remainder of its division by <code>2^32</code> and truncated to an integer |
| (in some unspecified way), so that its final value falls in the range <code>[0,2^32 - 1]</code>. |
| Similarly, all results are in the range <code>[0,2^32 - 1]</code>. Note that <code>bit32.bnot(0)</code> is <code>0xFFFFFFFF</code>, |
| which is different from <code>-1</code>.</p> |
| |
| <h2><a id="#(bit32)" >Type <code>bit32</code></a></h2> |
| <table class="function_list"> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).arshift">bit32.arshift(x, disp)</a></td> |
| <td class="summary"> |
| <p>Returns the number <code>x</code> shifted <code>disp</code> bits to the right.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).band">bit32.band()</a></td> |
| <td class="summary"> |
| <p>Returns the bitwise <code>and</code> of its operands.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).bnot">bit32.bnot(x)</a></td> |
| <td class="summary"> |
| <p>Returns the bitwise negation of <code>x</code>.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).bor">bit32.bor()</a></td> |
| <td class="summary"> |
| <p>Returns the bitwise <code>or</code> of its operands.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).btest">bit32.btest()</a></td> |
| <td class="summary"> |
| <p>Returns a boolean signaling whether the bitwise <code>and</code> of its operands is different from zero.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).bxor">bit32.bxor()</a></td> |
| <td class="summary"> |
| <p>Returns the bitwise exclusive <code>or</code> of its operands.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).extract">bit32.extract(n, width)</a></td> |
| <td class="summary"> |
| <p>Returns the unsigned number formed by the bits <code>field</code> to <code>field + width - 1</code> from <code>n</code>.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).lrotate">bit32.lrotate(x, disp)</a></td> |
| <td class="summary"> |
| <p>Returns the number <code>x</code> rotated <code>disp</code> bits to the left.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).lshift">bit32.lshift(x, disp)</a></td> |
| <td class="summary"> |
| <p>Returns the number <code>x</code> shifted <code>disp</code> bits to the left.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).replace">bit32.replace(n, v, width)</a></td> |
| <td class="summary"> |
| <p>Returns a copy of <code>n</code> with the bits <code>field</code> to <code>field + width - 1</code> replaced by the value <code>v</code>.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).rrotate">bit32.rrotate(x, disp)</a></td> |
| <td class="summary"> |
| <p>Returns the number <code>x</code> rotated <code>disp</code> bits to the right.</p> |
| </td> |
| </tr> |
| <tr> |
| <td class="name" nowrap="nowrap"><a href="##(bit32).rshift">bit32.rshift(x, disp)</a></td> |
| <td class="summary"> |
| <p>Returns the number <code>x</code> shifted <code>disp</code> bits to the right.</p> |
| </td> |
| </tr> |
| </table> |
| |
| <h2><a id="#(bit32)" >Type <code>bit32</code></a></h2> |
| <h3>Field(s)</h3> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).arshift" > |
| <strong>bit32.arshift(x, disp)</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns the number <code>x</code> shifted <code>disp</code> bits to the right.</p> |
| |
| |
| <p>The number <code>disp</code> may be any |
| representable integer. Negative displacements shift to the left.</p> |
| |
| <p>This shift operation is what is called arithmetic shift. |
| Vacant bits on the left are filled with copies of the higher bit of <code>x</code>; |
| vacant bits on the right are filled with zeros. In particular, displacements with |
| absolute values higher than 31 result in zero or <code>0xFFFFFFFF</code> |
| (all original bits are shifted out).</p> |
| |
| |
| <h3>Parameters</h3> |
| <ul> |
| <li> |
| |
| <p><code><em>#number x </em></code>: |
| value to shift</p> |
| |
| </li> |
| <li> |
| |
| <p><code><em>#number disp </em></code>: |
| the number of shift, may an positive or negative integer</p> |
| |
| </li> |
| </ul> |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| shifted number</p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).band" > |
| <strong>bit32.band()</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns the bitwise <code>and</code> of its operands.</p> |
| |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| bitwise <code>and</code> of operands</p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).bnot" > |
| <strong>bit32.bnot(x)</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns the bitwise negation of <code>x</code>.</p> |
| |
| |
| <p>For any integer <code>x</code>, the following identity holds:</p> |
| |
| <pre><code> assert(bit32.bnot(x) == (-1 - x) % 2^32) |
| |
| </code></pre> |
| |
| <h3>Parameter</h3> |
| <ul> |
| <li> |
| |
| <p><code><em>#number x </em></code>: |
| Number to proceed</p> |
| |
| </li> |
| </ul> |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| bitwise negation </p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).bor" > |
| <strong>bit32.bor()</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns the bitwise <code>or</code> of its operands.</p> |
| |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| bitwise <code>or</code> of operands</p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).btest" > |
| <strong>bit32.btest()</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns a boolean signaling whether the bitwise <code>and</code> of its operands is different from zero.</p> |
| |
| <h3>Return value</h3> |
| |
| <p><em>#boolean:</em> |
| true if the bitwise <code>and</code> of its operands is different from zero</p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).bxor" > |
| <strong>bit32.bxor()</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns the bitwise exclusive <code>or</code> of its operands.</p> |
| |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| bitwise exclusive <code>or</code> of its operands.</p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).extract" > |
| <strong>bit32.extract(n, width)</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns the unsigned number formed by the bits <code>field</code> to <code>field + width - 1</code> from <code>n</code>.</p> |
| |
| |
| <p>Bits are numbered from <code>0</code> (least significant) to <code>31</code> (most significant). |
| All accessed bits must be in the range <code>[0, 31]</code>.</p> |
| |
| <p>The default for <code>width</code> is <code>1</code>.</p> |
| |
| |
| <h3>Parameters</h3> |
| <ul> |
| <li> |
| |
| <p><code><em>#number n </em></code>: |
| input number</p> |
| |
| </li> |
| <li> |
| |
| <p><code><em>#number width </em></code>: |
| the number of bit to take in account (optional, 1 by default)</p> |
| |
| </li> |
| </ul> |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| extracted number</p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).lrotate" > |
| <strong>bit32.lrotate(x, disp)</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns the number <code>x</code> rotated <code>disp</code> bits to the left.</p> |
| |
| |
| <p>The number <code>disp</code> may be |
| any representable integer. |
| For any valid displacement, the following identity holds:</p> |
| |
| <pre><code>assert(bit32.lrotate(x, disp) == bit32.lrotate(x, disp % 32)) |
| </code></pre> |
| |
| <p>In particular, negative displacements rotate to the right.</p> |
| |
| <h3>Parameters</h3> |
| <ul> |
| <li> |
| |
| <p><code><em>#number x </em></code>: |
| original number</p> |
| |
| </li> |
| <li> |
| |
| <p><code><em>#number disp </em></code>: |
| number of rotate</p> |
| |
| </li> |
| </ul> |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| rotated number</p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).lshift" > |
| <strong>bit32.lshift(x, disp)</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns the number <code>x</code> shifted <code>disp</code> bits to the left.</p> |
| |
| |
| <p>The number <code>disp</code> may be any representable integer. |
| Negative displacements shift to the right. In any direction, vacant bits are filled with zeros. |
| In particular, displacements with absolute values higher than <code>31</code> result in zero (all bits are shifted out). |
| For positive displacements, the following equality holds:</p> |
| |
| <pre><code> assert(bit32.lshift(b, disp) == (b * 2^disp) % 2^32) |
| </code></pre> |
| |
| |
| <h3>Parameters</h3> |
| <ul> |
| <li> |
| |
| <p><code><em>#number x </em></code>: |
| original number</p> |
| |
| </li> |
| <li> |
| |
| <p><code><em>#number disp </em></code>: |
| the number of shift</p> |
| |
| </li> |
| </ul> |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| shifted number</p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).replace" > |
| <strong>bit32.replace(n, v, width)</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns a copy of <code>n</code> with the bits <code>field</code> to <code>field + width - 1</code> replaced by the value <code>v</code>.</p> |
| |
| |
| <p>See <code>bit32.extract</code> for details about field and width.</p> |
| |
| <h3>Parameters</h3> |
| <ul> |
| <li> |
| |
| <p><code><em>#number n </em></code>: |
| the number to copy</p> |
| |
| </li> |
| <li> |
| |
| <p><code><em>#number v </em></code>: |
| the value v</p> |
| |
| </li> |
| <li> |
| |
| <p><code><em>#number width </em></code>: |
| the number of bit to take in account (optional, 1 by default)</p> |
| |
| </li> |
| </ul> |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| replaced number</p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).rrotate" > |
| <strong>bit32.rrotate(x, disp)</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns the number <code>x</code> rotated <code>disp</code> bits to the right.</p> |
| |
| |
| <p>The number <code>disp</code> may be any representable integer. |
| For any valid displacement, the following identity holds:</p> |
| |
| <pre><code> assert(bit32.rrotate(x, disp) == bit32.rrotate(x, disp % 32)) |
| </code></pre> |
| |
| <p>In particular, negative displacements rotate to the left.</p> |
| |
| <h3>Parameters</h3> |
| <ul> |
| <li> |
| |
| <p><code><em>#number x </em></code>: |
| original number</p> |
| |
| </li> |
| <li> |
| |
| <p><code><em>#number disp </em></code>: |
| number of bits to rotate</p> |
| |
| </li> |
| </ul> |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| rotated number</p> |
| |
| |
| </dd> |
| </dl> |
| <dl class="function"> |
| <dt> |
| <a id="#(bit32).rshift" > |
| <strong>bit32.rshift(x, disp)</strong> |
| </a> |
| </dt> |
| <dd> |
| |
| <p>Returns the number <code>x</code> shifted <code>disp</code> bits to the right.</p> |
| |
| |
| <p>The number <code>disp</code> may be any |
| representable integer. Negative displacements shift to the left. In any direction, |
| vacant bits are filled with zeros. In particular, displacements with absolute |
| values higher than <code>31</code> result in zero (all bits are shifted out).</p> |
| |
| <p>For positive displacements, the following equality holds:</p> |
| |
| <pre><code> assert(bit32.rshift(b, disp) == math.floor(b % 2^32 / 2^disp)) |
| </code></pre> |
| |
| <p>This shift operation is what is called logical shift. </p> |
| |
| <h3>Parameters</h3> |
| <ul> |
| <li> |
| |
| <p><code><em>#number x </em></code>: |
| original number</p> |
| |
| </li> |
| <li> |
| |
| <p><code><em>#number disp </em></code>: |
| the number of shift</p> |
| |
| </li> |
| </ul> |
| <h3>Return value</h3> |
| |
| <p><em>#number:</em> |
| shifted number</p> |
| |
| |
| </dd> |
| </dl> |
| |
| </div> |
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