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| 22 | <title>Integer Arithmetic (GNU C Language Manual)</title>
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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="Integer-Overflow.html" rel="next" title="Integer Overflow">
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| 55 | </head>
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| 57 | <body lang="en">
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| 58 | <span id="Integer-Arithmetic"></span><div class="header">
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| 59 | <p>
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| 60 | Next: <a href="Integer-Overflow.html" accesskey="n" rel="next">Integer Overflow</a>, Previous: <a href="Basic-Arithmetic.html" accesskey="p" rel="prev">Basic Arithmetic</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="Integer-Arithmetic-1"></span><h3 class="section">6.2 Integer Arithmetic</h3>
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| 64 | <span id="index-integer-arithmetic"></span>
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| 65 |
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| 66 | <p>Each of the basic arithmetic operations in C has two variants for
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| 67 | integers: <em>signed</em> and <em>unsigned</em>. The choice is determined
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| 68 | by the data types of their operands.
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| 69 | </p>
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| 70 | <p>Each integer data type in C is either <em>signed</em> or <em>unsigned</em>.
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| 71 | A signed type can hold a range of positive and negative numbers, with
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| 72 | zero near the middle of the range. An unsigned type can hold only
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| 73 | nonnegative numbers; its range starts with zero and runs upward.
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| 74 | </p>
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| 75 | <p>The most basic integer types are <code>int</code>, which normally can hold
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| 76 | numbers from -2,147,483,648 to 2,147,483,647, and <code>unsigned
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| 77 | int</code>, which normally can hold numbers from 0 to 4,294.967,295. (This
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| 78 | assumes <code>int</code> is 32 bits wide, always true for GNU C on real
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| 79 | computers but not always on embedded controllers.) See <a href="Integer-Types.html">Integer Types</a>, for full information about integer types.
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| 80 | </p>
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| 81 | <p>When a basic arithmetic operation is given two signed operands, it
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| 82 | does signed arithmetic. Given two unsigned operands, it does
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| 83 | unsigned arithmetic.
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| 84 | </p>
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| 85 | <p>If one operand is <code>unsigned int</code> and the other is <code>int</code>, the
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| 86 | operator treats them both as unsigned. More generally, the common
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| 87 | type of the operands determines whether the operation is signed or
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| 88 | not. See <a href="Common-Type.html">Common Type</a>.
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| 89 | </p>
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| 90 | <p>Printing the results of unsigned arithmetic with <code>printf</code> using
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| 91 | ‘<samp>%d</samp>’ can produce surprising results for values far away from
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| 92 | zero. Even though the rules above say that the computation was done
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| 93 | with unsigned arithmetic, the printed result may appear to be signed!
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| 94 | </p>
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| 95 | <p>The explanation is that the bit pattern resulting from addition,
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| 96 | subtraction or multiplication is actually the same for signed and
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| 97 | unsigned operations. The difference is only in the data type of the
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| 98 | result, which affects the <em>interpretation</em> of the result bit pattern,
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| 99 | and whether the arithmetic operation can overflow (see the next section).
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| 100 | </p>
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| 101 | <p>But ‘<samp>%d</samp>’ doesn’t know its argument’s data type. It sees only the
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| 102 | value’s bit pattern, and it is defined to interpret that as
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| 103 | <code>signed int</code>. To print it as unsigned requires using ‘<samp>%u</samp>’
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| 104 | instead of ‘<samp>%d</samp>’. See <a href="https://www.gnu.org/software/libc/manual/html_node/Formatted-Output.html#Formatted-Output">The GNU C Library</a> in <cite>The GNU C Library Reference Manual</cite>.
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| 105 | </p>
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| 106 | <p>Arithmetic in C never operates directly on narrow integer types (those
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| 107 | with fewer bits than <code>int</code>; <a href="Narrow-Integers.html">Narrow Integers</a>). Instead it
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| 108 | “promotes” them to <code>int</code>. See <a href="Operand-Promotions.html">Operand Promotions</a>.
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| 109 | </p>
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| 110 | <hr>
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| 111 | <div class="header">
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| 112 | <p>
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| 113 | Next: <a href="Integer-Overflow.html" accesskey="n" rel="next">Integer Overflow</a>, Previous: <a href="Basic-Arithmetic.html" accesskey="p" rel="prev">Basic Arithmetic</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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