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| 22 | <title>Division and Remainder (GNU C Language Manual)</title>
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| 30 | <link href="Symbol-Index.html" rel="index" title="Symbol Index">
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| 31 | <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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| 32 | <link href="Arithmetic.html" rel="up" title="Arithmetic">
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| 33 | <link href="Numeric-Comparisons.html" rel="next" title="Numeric Comparisons">
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| 55 | </head>
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| 56 |
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| 57 | <body lang="en">
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| 58 | <span id="Division-and-Remainder"></span><div class="header">
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| 59 | <p>
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| 60 | Next: <a href="Numeric-Comparisons.html" accesskey="n" rel="next">Numeric Comparisons</a>, Previous: <a href="Mixed-Mode.html" accesskey="p" rel="prev">Mixed Mode</a>, Up: <a href="Arithmetic.html" accesskey="u" rel="up">Arithmetic</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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| 61 | </div>
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| 62 | <hr>
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| 63 | <span id="Division-and-Remainder-1"></span><h3 class="section">6.5 Division and Remainder</h3>
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| 64 | <span id="index-remainder-operator"></span>
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| 65 | <span id="index-modulus"></span>
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| 66 | <span id="index-operator_002c-remainder"></span>
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| 67 |
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| 68 | <p>Division of integers in C rounds the result to an integer. The result
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| 69 | is always rounded towards zero.
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| 70 | </p>
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| 71 | <div class="example">
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| 72 | <pre class="example"> 16 / 3 ⇒ 5
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| 73 | -16 / 3 ⇒ -5
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| 74 | 16 / -3 ⇒ -5
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| 75 | -16 / -3 ⇒ 5
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| 76 | </pre></div>
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| 77 |
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| 78 | <p>To get the corresponding remainder, use the ‘<samp>%</samp>’ operator:
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| 79 | </p>
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| 80 | <div class="example">
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| 81 | <pre class="example"> 16 % 3 ⇒ 1
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| 82 | -16 % 3 ⇒ -1
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| 83 | 16 % -3 ⇒ 1
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| 84 | -16 % -3 ⇒ -1
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| 85 | </pre></div>
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| 86 |
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| 87 | <p>‘<samp>%</samp>’ has the same operator precedence as ‘<samp>/</samp>’ and ‘<samp>*</samp>’.
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| 88 | </p>
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| 89 | <p>From the rounded quotient and the remainder, you can reconstruct
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| 90 | the dividend, like this:
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| 91 | </p>
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| 92 | <div class="example">
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| 93 | <pre class="example">int
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| 94 | original_dividend (int divisor, int quotient, int remainder)
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| 95 | {
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| 96 | return divisor * quotient + remainder;
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| 97 | }
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| 98 | </pre></div>
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| 99 |
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| 100 | <p>To do unrounded division, use floating point. If only one operand is
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| 101 | floating point, ‘<samp>/</samp>’ converts the other operand to floating
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| 102 | point.
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| 103 | </p>
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| 104 | <div class="example">
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| 105 | <pre class="example">16.0 / 3 ⇒ 5.333333333333333
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| 106 | 16 / 3.0 ⇒ 5.333333333333333
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| 107 | 16.0 / 3.0 ⇒ 5.333333333333333
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| 108 | 16 / 3 ⇒ 5
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| 109 | </pre></div>
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| 110 |
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| 111 | <p>The remainder operator ‘<samp>%</samp>’ is not allowed for floating-point
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| 112 | operands, because it is not needed. The concept of remainder makes
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| 113 | sense for integers because the result of division of integers has to
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| 114 | be an integer. For floating point, the result of division is a
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| 115 | floating-point number, in other words a fraction, which will differ
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| 116 | from the exact result only by a very small amount.
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| 117 | </p>
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| 118 | <p>There are functions in the standard C library to calculate remainders
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| 119 | from integral-values division of floating-point numbers.
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| 120 | See <a href="https://www.gnu.org/software/libc/manual/html_node/Remainder-Functions.html#Remainder-Functions">The GNU C Library</a> in <cite>The GNU C Library
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| 121 | Reference Manual</cite>.
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| 122 | </p>
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| 123 | <p>Integer division overflows in one specific case: dividing the smallest
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| 124 | negative value for the data type (see <a href="Maximum-and-Minimum-Values.html">Maximum and Minimum Values</a>)
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| 125 | by -1. That’s because the correct result, which is the
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| 126 | corresponding positive number, does not fit (see <a href="Integer-Overflow.html">Integer Overflow</a>)
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| 127 | in the same number of bits. On some computers now in use, this always
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| 128 | causes a signal <code>SIGFPE</code> (see <a href="Signals.html">Signals</a>), the same behavior
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| 129 | that the option <samp>-ftrapv</samp> specifies (see <a href="Signed-Overflow.html">Signed Overflow</a>).
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| 130 | </p>
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| 131 | <p>Division by zero leads to unpredictable results—depending on the
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| 132 | type of computer, it might cause a signal <code>SIGFPE</code>, or it might
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| 133 | produce a numeric result.
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| 134 | </p>
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| 135 | <span id="index-division-by-zero"></span>
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| 136 | <span id="index-zero_002c-division-by"></span>
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| 137 | <p><strong>Watch out:</strong> Make sure the program does not divide by zero. If
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| 138 | you can’t prove that the divisor is not zero, test whether it is zero,
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| 139 | and skip the division if so.
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| 140 | </p>
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| 141 | <hr>
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| 142 | <div class="header">
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| 143 | <p>
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| 144 | Next: <a href="Numeric-Comparisons.html" accesskey="n" rel="next">Numeric Comparisons</a>, Previous: <a href="Mixed-Mode.html" accesskey="p" rel="prev">Mixed Mode</a>, Up: <a href="Arithmetic.html" accesskey="u" rel="up">Arithmetic</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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| 145 | </div>
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