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<H1> 3.5.4 Integer Types</H1>
<DIV Class="Paranum"><FONT SIZE=-2>1</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1599"></A><A NAME="I1600"></A><A NAME="I1601"></A>An
<FONT FACE="Arial, Helvetica">integer_type_definition</FONT> defines
an integer type; it defines either a <I>signed</I> integer type, or a
<I>modular</I> integer type. The base range of a signed integer type
includes at least the values of the specified range. A modular type is
an integer type with all arithmetic modulo a specified positive <I>modulus</I>;
such a type corresponds to an unsigned type with wrap-around semantics.
<A NAME="I1602"></A></DIV>
<H4 ALIGN=CENTER>Syntax</H4>
<DIV Class="Paranum"><FONT SIZE=-2>2</FONT></DIV>
<DIV Class="SyntaxIndented"><FONT FACE="Arial, Helvetica">integer_type_definition<A NAME="I1603"></A>
::= </FONT><A NAME="I1604"></A><FONT FACE="Arial, Helvetica">signed_integer_type_definition</FONT> | <A NAME="I1605"></A><FONT FACE="Arial, Helvetica">modular_type_definition</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>3</FONT></DIV>
<DIV Class="SyntaxIndented"><FONT FACE="Arial, Helvetica">signed_integer_type_definition<A NAME="I1606"></A>
::= </FONT><B>range</B> <I>static_</I><A NAME="I1607"></A><FONT FACE="Arial, Helvetica">simple_expression</FONT> .. <I>static_</I><A NAME="I1608"></A><FONT FACE="Arial, Helvetica">simple_expression</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>4</FONT></DIV>
<DIV Class="SyntaxIndented"><FONT FACE="Arial, Helvetica">modular_type_definition<A NAME="I1609"></A>
::= </FONT><B>mod</B> <I>static_</I><A NAME="I1610"></A><FONT FACE="Arial, Helvetica">expression</FONT></DIV>
<H4 ALIGN=CENTER>Name Resolution Rules</H4>
<DIV Class="Paranum"><FONT SIZE=-2>5</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1611"></A>Each <FONT FACE="Arial, Helvetica">simple_expression</FONT>
in a <FONT FACE="Arial, Helvetica">signed_integer_type_definition</FONT>
is expected to be of any integer type; they need not be of the same type.
<A NAME="I1612"></A>The <FONT FACE="Arial, Helvetica">expression</FONT>
in a <FONT FACE="Arial, Helvetica">modular_type_definition</FONT> is
likewise expected to be of any integer type. </DIV>
<H4 ALIGN=CENTER>Legality Rules</H4>
<DIV Class="Paranum"><FONT SIZE=-2>6</FONT></DIV>
<DIV Class="Normal"> The <FONT FACE="Arial, Helvetica">simple_expression</FONT>s
of a <FONT FACE="Arial, Helvetica">signed_integer_type_definition</FONT>
shall be static, and their values shall be in the range System.Min_Int
.. System.Max_Int.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>7</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1613"></A><A NAME="I1614"></A><A NAME="I1615"></A>The
<FONT FACE="Arial, Helvetica">expression</FONT> of a <FONT FACE="Arial, Helvetica">modular_type_definition</FONT>
shall be static, and its value (the <I>modulus</I>) shall be positive,
and shall be no greater than System.Max_Binary_Modulus if a power of
2, or no greater than System.Max_Nonbinary_Modulus if not. </DIV>
<H4 ALIGN=CENTER>Static Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>8</FONT></DIV>
<DIV Class="Normal"> The set of values for a signed integer type is
the (infinite) set of mathematical integers, though only values of the
base range of the type are fully supported for run-time operations. The
set of values for a modular integer type are the values from 0 to one
less than the modulus, inclusive.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>9</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1616"></A>A <FONT FACE="Arial, Helvetica">signed_integer_type_definition</FONT>
defines an integer type whose base range includes at least the values
of the <FONT FACE="Arial, Helvetica">simple_expression</FONT>s and is
symmetric about zero, excepting possibly an extra negative value. <A NAME="I1617"></A><A NAME="I1618"></A>A
<FONT FACE="Arial, Helvetica">signed_integer_type_definition</FONT> also
defines a constrained first subtype of the type, with a range whose bounds
are given by the values of the <FONT FACE="Arial, Helvetica">simple_expression</FONT>s,
converted to the type being defined. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>10</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1619"></A>A <FONT FACE="Arial, Helvetica">modular_type_definition</FONT>
defines a modular type whose base range is from zero to one less than
the given modulus. <A NAME="I1620"></A><A NAME="I1621"></A>A <FONT FACE="Arial, Helvetica">modular_type_definition</FONT>
also defines a constrained first subtype of the type with a range that
is the same as the base range of the type.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>11</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1622"></A>There is a predefined signed
integer subtype named Integer, declared in the visible part of package
Standard. It is constrained to the base range of its type. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>12</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> <A NAME="I1623"></A><A NAME="I1624"></A>Integer
has two predefined subtypes, declared in the visible part of package
Standard: </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>13</FONT></DIV>
<DIV Class="Examples"><TT><B>subtype</B> Natural <B>is</B> Integer <B>range</B> 0 .. Integer'Last;<BR>
<B>subtype</B> Positive <B>is</B> Integer <B>range</B> 1 .. Integer'Last;</TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>14</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1625"></A><A NAME="I1626"></A><A NAME="I1627"></A>A
type defined by an <FONT FACE="Arial, Helvetica">integer_type_definition</FONT>
is implicitly derived from <I>root_integer</I>, an anonymous predefined
(specific) integer type, whose base range is System.Min_Int .. System.Max_Int.
However, the base range of the new type is not inherited from <I>root_integer</I>,
but is instead determined by the range or modulus specified by the <FONT FACE="Arial, Helvetica">integer_type_definition</FONT>.
<A NAME="I1628"></A><A NAME="I1629"></A>Integer literals are all of the
type <I>universal_integer</I>, the universal type (see <A HREF="RM-3-4-1.html">3.4.1</A>)
for the class rooted at <I>root_integer</I>, allowing their use with
the operations of any integer type. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>15</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1630"></A>The <I>position number</I>
of an integer value is equal to the value.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>16</FONT></DIV>
<DIV Class="Wide" Style="margin-bottom: 0.4em"> For every modular
subtype S, the following attribute is defined: </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>17</FONT></DIV>
<DL Class="Hanging"><DT> S'Modulus<DD Class="Hanging">
<A NAME="I1631"></A><A NAME="I1632"></A>S'Modulus yields the modulus
of the type of S, as a value of the type <I>universal_integer</I>. </DL>
<H4 ALIGN=CENTER>Dynamic Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>18</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1633"></A>The elaboration of an <FONT FACE="Arial, Helvetica">integer_type_definition</FONT>
creates the integer type and its first subtype.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>19</FONT></DIV>
<DIV Class="Normal"> For a modular type, if the result of the execution
of a predefined operator (see <A HREF="RM-4-5.html">4.5</A>) is outside
the base range of the type, the result is reduced modulo the modulus
of the type to a value that is within the base range of the type.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>20</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1634"></A><A NAME="I1635"></A><A NAME="I1636"></A>For
a signed integer type, the exception Constraint_Error is raised by the
execution of an operation that cannot deliver the correct result because
it is outside the base range of the type. <A NAME="I1637"></A><A NAME="I1638"></A><A NAME="I1639"></A>For
any integer type, Constraint_Error is raised by the operators "/",
"<B>rem</B>", and "<B>mod</B>" if the right operand
is zero.</DIV>
<H4 ALIGN=CENTER>Implementation Requirements</H4>
<DIV Class="Paranum"><FONT SIZE=-2>21</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1640"></A>In an implementation, the
range of Integer shall include the range -2**15+1 .. +2**15-1.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>22</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1641"></A>If Long_Integer is predefined
for an implementation, then its range shall include the range -2**31+1
.. +2**31-1.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>23</FONT></DIV>
<DIV Class="Normal"> System.Max_Binary_Modulus shall be at least 2**16.
</DIV>
<H4 ALIGN=CENTER>Implementation Permissions</H4>
<DIV Class="Paranum"><FONT SIZE=-2>24</FONT></DIV>
<DIV Class="Normal"> For the execution of a predefined operation of
a signed integer type, the implementation need not raise Constraint_Error
if the result is outside the base range of the type, so long as the correct
result is produced. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>25</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1642"></A><A NAME="I1643"></A>An implementation
may provide additional predefined signed integer types, declared in the
visible part of Standard, whose first subtypes have names of the form
Short_Integer, Long_Integer, Short_Short_Integer, Long_Long_Integer,
etc. Different predefined integer types are allowed to have the same
base range. However, the range of Integer should be no wider than that
of Long_Integer. Similarly, the range of Short_Integer (if provided)
should be no wider than Integer. Corresponding recommendations apply
to any other predefined integer types. There need not be a named integer
type corresponding to each distinct base range supported by an implementation.
The range of each first subtype should be the base range of its type.
</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>26</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1644"></A>An implementation may provide
<I>nonstandard integer types</I>, descendants of <I>root_integer</I>
that are declared outside of the specification of package Standard, which
need not have all the standard characteristics of a type defined by an
<FONT FACE="Arial, Helvetica">integer_type_definition</FONT>. For example,
a nonstandard integer type might have an asymmetric base range or it
might not be allowed as an array or loop index (a very long integer).
Any type descended from a nonstandard integer type is also nonstandard.
An implementation may place arbitrary restrictions on the use of such
types; it is implementation defined whether operators that are predefined
for ``any integer type'' are defined for a particular nonstandard integer
type. In any case, such types are not permitted as <FONT FACE="Arial, Helvetica">explicit_generic_actual_parameter</FONT>s
for formal scalar types -- see <A HREF="RM-12-5-2.html">12.5.2</A>. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>27</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1645"></A>For a one's complement machine,
the high bound of the base range of a modular type whose modulus is one
less than a power of 2 may be equal to the modulus, rather than one less
than the modulus. It is implementation defined for which powers of 2,
if any, this permission is exercised.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>27.1/1</FONT></DIV>
<DIV Class="Normal"> For a one's complement machine, implementations
may support non-binary modulus values greater than System.Max_Nonbinary_Modulus.
It is implementation defined which specific values greater than System.Max_Nonbinary_Modulus,
if any, are supported. </DIV>
<H4 ALIGN=CENTER>Implementation Advice</H4>
<DIV Class="Paranum"><FONT SIZE=-2>28</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1646"></A>An implementation should
support Long_Integer in addition to Integer if the target machine supports
32-bit (or longer) arithmetic. No other named integer subtypes are recommended
for package Standard. Instead, appropriate named integer subtypes should
be provided in the library package Interfaces (see <A HREF="RM-B-2.html">B.2</A>).
</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>29</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1647"></A>An implementation for a two's
complement machine should support modular types with a binary modulus
up to System.Max_Int*2+2. An implementation should support a nonbinary
modulus up to Integer'Last. </DIV>
<DIV Class="NotesHeader"><FONT SIZE=-1>NOTES</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>30</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>25 <A NAME="I1648"></A><A NAME="I1649"></A>Integer
literals are of the anonymous predefined integer type <I>universal_integer</I>.
Other integer types have no literals. However, the overload resolution
rules (see <A HREF="RM-8-6.html">8.6</A>, ``<A HREF="RM-8-6.html">The
Context of Overload Resolution</A>'') allow expressions of the type <I>universal_integer</I>
whenever an integer type is expected.</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>31</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>26 The same arithmetic operators
are predefined for all signed integer types defined by a <FONT FACE="Arial, Helvetica">signed_integer_type_definition</FONT>
(see <A HREF="RM-4-5.html">4.5</A>, ``<A HREF="RM-4-5.html">Operators
and Expression Evaluation</A>''). For modular types, these same operators
are predefined, plus bit-wise logical operators (<B>and</B>, <B>or</B>,
<B>xor</B>, and <B>not</B>). In addition, for the unsigned types declared
in the language-defined package Interfaces (see <A HREF="RM-B-2.html">B.2</A>),
functions are defined that provide bit-wise shifting and rotating.</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>32</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>27 Modular types match a
<FONT FACE="Arial, Helvetica">generic_formal_parameter_declaration</FONT>
of the form "<B>type</B> T <B>is mod</B> <>;"; signed
integer types match "<B>type</B> T <B>is range</B> <>;"
(see <A HREF="RM-12-5-2.html">12.5.2</A>). </FONT></DIV>
<H4 ALIGN=CENTER>Examples</H4>
<DIV Class="Paranum"><FONT SIZE=-2>33</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> <I>Examples of
integer types and subtypes: </I></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>34</FONT></DIV>
<DIV Class="Examples"><TT><B>type</B> Page_Num <B>is</B> <B>range</B> 1 .. 2_000;<BR>
<B>type</B> Line_Size <B>is</B> <B>range</B> 1 .. Max_Line_Size;</TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>35</FONT></DIV>
<DIV Class="Examples"><TT><B>subtype</B> Small_Int <B>is</B> Integer <B>range</B> -10 .. 10;<BR>
<B>subtype</B> Column_Ptr <B>is</B> Line_Size <B>range</B> 1 .. 10;<BR>
<B>subtype</B> Buffer_Size <B>is</B> Integer <B>range</B> 0 .. Max;</TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>36</FONT></DIV>
<DIV Class="Examples"><TT><B>type</B> Byte <B>is</B> <B>mod</B> 256; <I>-- an unsigned byte</I><BR>
<B>type</B> Hash_Index <B>is</B> <B>mod</B> 97; <I>-- modulus is prime</I></TT></DIV>
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