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<title>Integers and Arithmetic Operatio</title>
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Integers and Arithmetic Operations</h4>
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We have seen that the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">if</code><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">while</code><span class="Apple-converted-space"> </span>statements
allow programs to make decisions by using the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">bool</code><span class="Apple-converted-space"> </span>type
in the form of logical expressions. In this chapter, we will see arithmetic
operations on the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">integer</i><span class="Apple-converted-space"> </span>types
of D. These features will allow us to write much more useful programs.</p>
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Although arithmetic operations are a part of our daily lives and are actually
simple, there are very important concepts that a programmer must be aware of in
order to produce correct programs:<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">bit
length of a type</i>,<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">overflow</i>,<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">underflow</i>,
and<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">truncation</i>.</p>
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Before going further, I would like to summarize the arithmetic operations in the
following table as a reference:</p>
<table border="1" cellpadding="4" cellspacing="0" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;" width="550">
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Operator</th>
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Effect</th>
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Sample</th>
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<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
++</tt></td>
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increments by one</td>
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++variable</td>
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<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
--</tt></td>
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decrements by one</td>
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--variable</td>
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<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
+</tt></td>
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the result of adding two values</td>
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first + second</td>
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<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
-</tt></td>
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the result of subtracting 'second' from 'first'</td>
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first - second</td>
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<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
*</tt></td>
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the result of multiplying two values</td>
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first * second</td>
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<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
/</tt></td>
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the result of dividing 'first' by 'second'</td>
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first / second</td>
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<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
%</tt></td>
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the remainder of dividing 'first' by 'second'</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
first % second</td>
</tr>
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<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
^^</tt></td>
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the result of raising 'first' to the power of 'second'<br />
(multiplying 'first' by itself 'second' times)</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
first ^^ second</td>
</tr>
</table>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Most of those operators have counterparts that have an<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">=</code><span class="Apple-converted-space"> </span>sign
attached:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">+=</code>,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">-=</code>,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">*=</code>,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">/=</code>,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">%=</code>,
and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">^^=</code>.
The difference with these operators is that they assign the result to the
left-hand side:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> variable += 10;
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
That expression adds the value of<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">variable</code><span class="Apple-converted-space"> </span>and
10 and assigns the result to<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">variable</code>.
In the end, the value of<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">variable</code><span class="Apple-converted-space"> </span>would
be increased by 10. It is the equivalent of the following expression:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> variable = variable + 10;
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
I would like also to summarize two important concepts here before elaborating on
them below.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<b style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Overflow:</b><span class="Apple-converted-space"> </span>Not all values can fit
in a type, in which case<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">the
value overflows</i>. For example, a variable of type<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">ubyte</code><span class="Apple-converted-space"> </span>can
have values only in the range of 0 to 255; so when assigned 260, the value
overflows and becomes 4.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<b style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Underflow:</b><span class="Apple-converted-space"> </span>Similarly, values may
not be less than the minimum value that a type can have.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<b style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Truncation:</b><span class="Apple-converted-space"> </span>Integer types cannot
have values with fractional parts. For example, the value of the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">int</code><span class="Apple-converted-space"> </span>expression<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">3/2</code><span class="Apple-converted-space"> </span>is
1, not 1.5.</p>
<h5 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.25em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
More Information</h5>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
We encounter arithmetic operations daily without much surprises: if a bagel is
$1, two bagels are $2; if four sandwiches are $15, one sandwich is $3.75, etc.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Unfortunately things are not as simple with arithmetic operations in computers.
If we don't understand how values are stored in a computer, we may be surprised
to see that a company's debt is<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">reduced</i><span class="Apple-converted-space"> </span>to
$1.7 billions when it borrows $3 billions more on top of its existing debt of $3
billions! Or when a box of ice cream serves 4 kids, an arithmetic operation may
claim that 2 boxes would be sufficient for 11 kids!</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Programmers must understand how integers are stored in computers.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Integer types</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Integer types are the types that can have only whole values like -2, 0, 10, etc.
These types cannot have fractional parts as in 2.5. All of the integer types
that we have seen in the<span class="Apple-converted-space"> </span><a href="http://ddili.org/ders/d.en/types.html" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: purple; text-decoration: none; background-position: initial initial; background-repeat: initial initial;">Fundamental
Types chapter</a><span class="Apple-converted-space"> </span>are the following:</p>
<table border="1" cellpadding="4" cellspacing="0" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;" width="200">
<tbody style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tr style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<br />
Type</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Number of<br />
Bits</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Initial<br />
Value</th>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
byte</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
8</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
ubyte</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
8</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
short</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
16</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
ushort</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
16</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
int</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
32</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
uint</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
32</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
long</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
64</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0L</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
ulong</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
64</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0L</td>
</tr>
</table>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">u</code><span class="Apple-converted-space"> </span>at
the beginning of the type names stands for "unsigned" and indicates that such
types cannot have values less than zero.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Number of bits of a type</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
In today's computer systems, the smallest unit of information is called a<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">bit</i>.
At the physical level, a bit is represented by electrical signals at certain
points in the circuitry of a computer. A bit can be in one of two states that
correspond to the presence and absence of electrical signals at the point that
defines that particular bit. These two states are arbitrarily defined to have
the values 0 and 1. As a result, a bit can have one of these two values.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
As there aren't many concepts that can be represented by just two states, bit is
not a very useful type. It can only be useful for concepts with two states like
heads or tails or whether a light switch is on or off.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
If we consider two bits at a time, the total number of information that can be
represented multiplies. Based on each bit having a value of 0 or 1 individually,
there are a total of 4 possible states. Assuming that the left and right digits
represent the first and second bit respectively, these states are 00, 01, 10,
and 11. Let's add one more bit to see this effect better; three bits can be in 8
different states: 000, 001, 010, 011, 100, 101, 110, 111. As can be seen, each
added bit doubles the total number of states that can be represented.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The values to which these eight states correspond to are defined by conventions.
The following table shows these values for the signed and unsigned
representations of 3 bits:</p>
<table border="1" cellpadding="4" cellspacing="0" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;" width="250">
<tbody style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Bit<br />
State</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Unsigned<br />
Value</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Signed<br />
Value</th>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
000</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
001</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
1</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
1</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
010</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
2</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
2</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
011</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
3</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
3</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
100</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
4</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
-4</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
101</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
5</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
-3</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
110</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
6</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
-2</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
111</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
7</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
-1</td>
</tr>
</table>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
We can produce the following table by adding more bits:</p>
<table border="1" cellpadding="4" cellspacing="0" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 0.9em; vertical-align: baseline; background-color: transparent; font-family: monospace; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;" width="570">
<tbody style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Bits</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Number of Distinct Values</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
D Type</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Minimum Value</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Maximum Value</th>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
2</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
2</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
4</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
3</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
8</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
4</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
16</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
5</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
32</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
6</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
64</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
7</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
128</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
8</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
256</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
byte<br />
ubyte</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
-128<br />
0</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
127<br />
255</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
...</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
...</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
16</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
65,536</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
short<br />
ushort</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
-32768<br />
0</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
32767<br />
65535</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
...</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
...</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
32</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
4,294,967,296</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
int<br />
uint</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
-2147483648<br />
0</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
2147483647<br />
4294967295</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
...</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
...</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
64</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
18,446,744,073,709,551,616</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
long<br />
ulong</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
-9223372036854775808<br />
0</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
9223372036854775807<br />
18446744073709551615</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
...</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
...</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 12px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
</td>
</tr>
</table>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
I have skipped many rows in the table, and indicated the signed and unsigned
versions of the D types that have the same number of bits on the same row (e.g.<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">int</code><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">uint</code><span class="Apple-converted-space"> </span>are
both on the 32-bit row).</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Choosing a type</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Since a 3-bit type can only have 8 distinct values, it can only represent
concepts like the value of a die or the number of the day of the week. (This is
just an example; there isn't a 3-bit type in D.)</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
On the other hand, although<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">uint</code><span class="Apple-converted-space"> </span>is
a very large type, it cannot represent the concept of an ID number for each
living person; as its maximum value is less than the world population of 7
billion.<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">long</code><span class="Apple-converted-space"> </span>and<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">ulong</code><span class="Apple-converted-space"> </span>would
be more than enough to represent many concepts.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
As a general rule, as long as there is no specific reason not to, you can use<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">int</code><span class="Apple-converted-space"> </span>for
integer values.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Overflow</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The fact that types can have a limited range of values may cause unexpected
results. For example, although adding two<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">uint</code><span class="Apple-converted-space"> </span>variables
with values of 3 billion each should produce 6 billion, because that sum is
greater than the maximum value that a<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">uint</code><span class="Apple-converted-space"> </span>variable
can hold (about 4 billion), this sum<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">overflows</i>.
Without any warning, only the difference of 6 and 4 billion gets stored. (A
little more accurately, 6 minus 4.3 billion.)</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Truncation</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Since integers cannot have values with fractional parts, they lose the part
after the decimal point. For example, assuming that a box of ice cream serves 4
kids, although 11 kids would actually need 2.75 boxes, 2.75 can only be stored
as 2 in an integer type.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
I will show limited techniques to help reduce the effects of overflow,
underflow, and truncation later in the chapter.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">
.min</code><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">.max</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
I will take advantage of the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">.min</code><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">.max</code><span class="Apple-converted-space"> </span>properties
below, which we have seen in the fundamental types chapter. These properties
provide the minimum and maximum values that an integer type can have.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Increment:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">++</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator is used with a single variable (more generally, with a single
expression) and is written before the name of that variable. It increments the
value of that variable by 1:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number = 10;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">++</span>number;
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"New value: "</span>, number);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">New value: 11
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The increment operator is the equivalent of using the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">add-and-assign</i>operator
with the value of 1:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> number += 1; <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// same as ++number
</span></pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
If the result of the increment operation is greater than the maximum value of
that type, the result<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">overflows</i><span class="Apple-converted-space"> </span>and
becomes the minimum value. We can see this effect by incrementing a variable
that initially has the value<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">int.max</code>:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"minimum int value : "</span>, <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span>.min);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"maximum int value : "</span>, <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span>.max);
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number = <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span>.max;
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"before the increment: "</span>, number);
++number;
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"after the increment : "</span>, number);
}
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The value becomes<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">int.min</code><span class="Apple-converted-space"> </span>after
the increment:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">minimum int value : -2147483648
maximum int value : 2147483647
before the increment: 2147483647
after the increment : -2147483648
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This is a very important observation, because the value changes from the maximum
to the minimum as a result of<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">incrementing</i><span class="Apple-converted-space"> </span>and
without any warning! This effect is called<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">overflow</i>.
We will see similar effects with other operations.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Decrement:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">--</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator is similar to the increment operator; the difference is that the
value is decreased by 1:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> --number; <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// the value decreases by 1
</span></pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The decrement operation is the equivalent of using the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">subtract-and-assign</i><span class="Apple-converted-space"> </span>operator
with the value of 1:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> number -= 1; <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// same as --number
</span></pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Similar to the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">++</code><span class="Apple-converted-space"> </span>operator,
if the value is the minimum value to begin with, it becomes the maximum value.
This effect is called<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">underflow</i>.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Addition: +</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator is used with two expressions and adds their values:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> first = 12;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> second = 100;
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"Result: "</span>, first <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">+</span> second);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"With a constant expression: "</span>, 1000 <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">+</span> second);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">Result: 112
With a constant expression: 1100
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
If the result is greater than the sum of the two expressions, it again overflows
and becomes a value that is less than both of the expressions:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// 3 billions each
</span> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> first = 3000000000;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> second = 3000000000;
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"maximum value of uint: "</span>, <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span>.max);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" first: "</span>, first);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" second: "</span>, second);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" sum: "</span>, first + second);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"OVERFLOW! The result is not 6 billions!"</span>);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">maximum value of uint: 4294967295
first: 3000000000
second: 3000000000
sum: 1705032704
OVERFLOW! The result is not 6 billions!
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Subtraction:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">-</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator is used with two expressions and gives the difference between the
first and the second:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number_1 = 10;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number_2 = 20;
writeln(number_1 <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">-</span> number_2);
writeln(number_2 <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">-</span> number_1);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">-10
10
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
It is again surprising if the actual result is less than zero and is stored in
an unsigned type. Let's rewrite the program using the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">uint</code>type:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> number_1 = 10;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> number_2 = 20;
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"PROBLEM! uint cannot have negative values:"</span>);
writeln(number_1 - number_2);
writeln(number_2 - number_1);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">PROBLEM! uint cannot have negative values:
4294967286
10
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
It is a good guideline to use signed types to represent concepts that may ever
be subtracted. As long as there is no specific reason not to, you can choose<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">int</code>.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Multiplication:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">*</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator multiplies the values of two expressions; the result is again
subject to overflow:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> number_1 = 6;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> number_2 = 7;
writeln(number_1 <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">*</span> number_2);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">42
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Division:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">/</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator divides the first expression by the second expression. Since
integer types cannot have fractional values, the fractional part of the value is
discarded. This effect is called<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">truncation</i>.
As a result, the following program prints 3, not 3.5:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
writeln(7 <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">/</span> 2);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">3
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
For calculations where fractional parts matter,<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">floating
point types</i>must be used instead of integers. We will see floating point
types in the next chapter.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Remainder: %</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator divides the first expression by the second expression and produces
the remainder of the division:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
writeln(10 <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">%</span> 6);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">4
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
A common application of this operator is to determine whether a value is odd or
even. Since the remainder of dividing an even number by 2 is always 0, comparing
the result against 0 is sufficient to make that distinction:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">if</span> ((number % 2) == 0) {
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"even number"</span>);
} <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">else</span> {
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"odd number"</span>);
}
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Power: ^^</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator raises the first expression to the power of the second expression.
For example, raising 3 to the power of 4 is multiplying 3 by itself 4 times:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
writeln(3 <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">^^</span> 4);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">81
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Arithmetic operations with assignment</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
All of the operators that take two expressions have<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">assignment</i>counterparts.
These operators assign the result back to the expression that is on the
left-hand side:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number = 10;
number += 20; <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// same as number = number + 20; now 30
</span> number -= 5; <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// same as number = number - 5; now 25
</span> number *= 2; <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// same as number = number * 2; now 50
</span> number /= 3; <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// same as number = number / 3; now 16
</span> number %= 7; <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// same as number = number % 7; now 2
</span> number ^^= 6; <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// same as number = number ^^ 6; now 64
</span>
writeln(number);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">64
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Negation:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">-</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator converts the value of the expression from negative to positive or
positive to negative:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number_1 = 1;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number_2 = -2;
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">-</span>number_1);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">-</span>number_2);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">-1
2
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The type of the result of this operation is the same as the type of the
expression. Since unsigned types cannot have negative values, the result of
using this operator with unsigned types can be surprising:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span></span> number = 1;
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"negation: "</span>, -number);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The type of<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">-number</code><span class="Apple-converted-space"> </span>is<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">uint</code><span class="Apple-converted-space"> </span>as
well, which cannot have negative values:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">negation: 4294967295
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Plus sign:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">+</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator has no effect and exists only for symmetry with the negation
operator. Positive values stay positive and negative values stay negative:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number_1 = 1;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number_2 = -2;
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">+</span>number_1);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">+</span>number_2);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">1
-2
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Post-increment:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">++</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
<b style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Note:</b><span class="Apple-converted-space"> </span>Unless there is a strong
reason, always use the regular increment operator (which is sometimes called the
pre-increment operator).</i></p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Contrary to the regular increment operator, it is written after the expression
and still increments the value of the expression by 1. The difference is, the
post-increment operation itself produces the old value of the expression. To see
this difference, let's compare it with the regular increment operator:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> incremented_regularly = 1;
writeln(++incremented_regularly); <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// prints 2
</span> writeln(incremented_regularly); <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// prints 2
</span>
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> post_incremented = 1;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// Gets incremented, but its old value is used:
</span> writeln(post_incremented<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">++</span>); <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// prints 1
</span> writeln(post_incremented); <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// prints 2
</span>}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">2
2
1
2
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">writeln(post_incremented++);</code><span class="Apple-converted-space"> </span>statement
above is the equivalent of the following code:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> old_value = post_incremented;
++post_incremented;
writeln(old_value); <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// prints 1
</span></pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Post-decrement:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">--</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
<b style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Note:</b><span class="Apple-converted-space"> </span>Unless there is a strong
reason, always use the regular decrement operator (which is sometimes called the
pre-decrement operator).</i></p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Behaves the same as the post-increment operator but decrements.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Operator precedence</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The operators we've discussed above have all been used in operations on their
own with only one or two expressions. However, similar to logical expressions,
it is common to combine these operators to form more complex arithmetic
expressions:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> value = 77;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> result = (((value + 8) * 3) / (value - 1)) % 5;
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
As with logical operators, arithmetic operators also obey operator precedence
rules. For example, the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">*</code><span class="Apple-converted-space"> </span>operator
has precedence over the<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">+</code><span class="Apple-converted-space"> </span>operator.
For that reason, when parentheses are not used (e.g. in the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">value + 8 * 3</code><span class="Apple-converted-space"> </span>expression),
the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">*</code><span class="Apple-converted-space"> </span>operator
is evaluated before the<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">+</code><span class="Apple-converted-space"> </span>operator.
As a result, that expression becomes the equivalent of<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">value + 24</code>,
which is quite different from<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">(value + 8) * 3</code>.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Using parentheses is useful both for ensuring correct results and for
communicating the intent of the code to programmers who may work on the code in
the future.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Potential remedy against overflow</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
If the result of an operation cannot fit in the type of the result, then there
is nothing that can be done. Sometimes, although the ultimate result would fit
in a certain type, the intermediate calculations may overflow and cause
incorrect results.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
As an example, let's assume that we need to plant an apple tree per 1000 square
meters of an area that is 40 by 60 kilometers. How many trees are needed?</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
When we solve this problem on paper, we see that the result is 40000 times 60000
divided by 1000, being equal to 2.4 million trees. Let's write a program that
executes this calculation:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> width = 40000;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> length = 60000;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> areaPerTree = 1000;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> treesNeeded = width * length / areaPerTree;
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"Number of trees needed: "</span>, treesNeeded);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">Number of trees needed: -1894967
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Not to mention it's not even close, the result is also less than zero! In this
case, the intermediate calculation<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">width * length</code><span class="Apple-converted-space"> </span>overflows
and the subsequent calculation of<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">/ areaPerTree</code><span class="Apple-converted-space"> </span>produces
an incorrect result.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
One way of avoiding the overflow in this example is to change the order of
operations:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> treesNeeded = width / areaPerTree * length ;
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The result would now be correct:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">Number of trees needed: 2400000
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The reason this method works is the fact that all of the steps of the
calculation now fit the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">int</code><span class="Apple-converted-space"> </span>type.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Please note that this is not a complete solution because this time the
intermediate value is prone to truncation, which may affect the result
significantly in certain other calculations. Another solution might be to use a
floating point type instead of an integer type:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">float</code>,<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">double</code>,
or<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">real</code>.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Potential remedy against truncation</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Changing the order of operations may be a solution to truncation as well. An
interesting example of truncation can be seen by dividing and multiplying a
value with the same number. We would expect the result of 10/9*9 to be 10, but
it comes out as 9:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
writeln(10 / 9 * 9);
}
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">9
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The result is correct when truncation is avoided by changing the order of
operations:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> writeln(10 * 9 / 9);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">10
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This too is not a complete solution: This time the intermediate calculation
could be prone to overflow. Using a floating point type may be another solution
to truncation in certain calculations.</p>
<h5 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.25em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Exercises</h5>
<ol style="margin: 1em 1em 0.75em 1.5em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Write a program that takes two integers from the user, prints the integer
quotient resulting from the division of the first by the second, and also
prints the remainder. For example, when 7 and 3 are entered, have the
program print the following equation:<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; background-position: initial initial; background-repeat: initial initial;">7 = 3 * 2 + 1
</pre>
</li>
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Modify the program to print shorter output when the remainder is 0. For
example, when 10 and 5 are entered, it should not print "10 = 5 * 2 + 0" but
just the following:<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; background-position: initial initial; background-repeat: initial initial;">10 = 5 * 2
</pre>
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<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Write a simple calculator that supports the four basic arithmetic
operations. Have the program let the operation to be selected from a menu
and apply that operation to the two values that are entered. You can ignore
overflow and truncation in this program.</li>
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Write a program that prints the values from 1 to 10, each on a separate
line, with the exception of value 7. Do not use repeated lines like the
following:<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// Do not do this!
</span> writeln(1);
writeln(2);
writeln(3);
writeln(4);
writeln(5);
writeln(6);
writeln(8);
writeln(9);
writeln(10);
}
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); background-position: initial initial; background-repeat: initial initial;">
Instead, imagine a variable whose value is incremented in a loop. You may
need to take advantage of the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">is
not equal to</i><span class="Apple-converted-space"> </span>operator<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">!=</code>here.</p>
</li>
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<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
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... the solutions</i></a></p>
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