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<P>&copy;Copyright 1996 Rogue Wave Software</P>
<H2>Numeric Limit Members</H2>
<P>Since a number of the fields in the <SAMP>numeric_limits</SAMP> structure are meaningful only for floating point values, it is useful to separate the description of the members into common fields and floating-point specific fields.</P>
<A NAME="memberscommontoalltypes"><H3>Members Common to All Types</H3></A>
<P>The following table summarizes the information available through the <A HREF="../stdref/num_5679.htm"><B><I>numeric_limits</I></B></A> static member data fields and functions.</P>
<CENTER><TABLE BORDER CELLSPACING=3 CELLPADDING=3>
<TR VALIGN=top>
<TD>
Type<BR>
</TD>

<TD>
Name<BR>
</TD>

<TD>
Meaning <BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>is_specialized</SAMP><BR>
</TD>

<TD>
true if a specialization exists, false otherwise <BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>T</SAMP><BR>
</TD>

<TD>
<SAMP>min()</SAMP><BR>
</TD>

<TD>
smallest finite value<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>T</SAMP><BR>
</TD>

<TD>
<SAMP>max()</SAMP><BR>
</TD>

<TD>
largest finite value<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>int</SAMP><BR>
</TD>

<TD>
<SAMP>radix</SAMP><BR>
</TD>

<TD>
the base of the representation<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>int</SAMP><BR>
</TD>

<TD>
<SAMP>digits</SAMP><BR>
</TD>

<TD>
number of <SAMP>radix</SAMP> digits that can be represented without change<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>int</SAMP><BR>
</TD>

<TD>
<SAMP>digits10</SAMP><BR>
</TD>

<TD>
number of base-10 digits that can be represented without change<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>is_signed</SAMP><BR>
</TD>

<TD>
true if the type is signed<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>is_integer</SAMP><BR>
</TD>

<TD>
true if the type is integer<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>is_exact</SAMP><BR>
</TD>

<TD>
true if the representation is exact<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>is_bounded</SAMP><BR>
</TD>

<TD>
true if representation is finite<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>is_modulo</SAMP><BR>
</TD>

<TD>
true if type is modulo<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>traps</SAMP><BR>
</TD>

<TD>
true if trapping is implemented for the type<BR>
</TD>
</TR>
</TABLE></CENTER>
<P>Radix represents the internal base for the representation.  For example, most machines use a base 2 radix for integer data values, however some may also support a representation, such as BCD, that uses a different base.  The <SAMP>digits</SAMP> field then represents the number of such radix values that can be held in a value.  For an integer type, this would be the number of non-sign bits in the representation.</P>
<P>All fundamental types are bounded.  However, an implementation might choose to include, for example, an infinite precision integer package that would not be bounded.</P>
<P>A type is <I>modulo</I> if the value resulting from the addition of two values can wrap around, that is, be smaller than either argument. The fundamental unsigned integer types are all modulo.</P>
<A NAME="membersspecifictofloatingpointvalues"><H3>Members Specific to Floating Point Values</H3></A>
<P>The following members are either specific to floating point values, or have a meaning slightly different for floating point values than the one described earlier for non-floating data types.</P>
<CENTER><TABLE BORDER CELLSPACING=3 CELLPADDING=3>
<TR VALIGN=top>
<TD>
Type<BR>
</TD>

<TD>
Name<BR>
</TD>

<TD>
Meaning<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>T</SAMP><BR>
</TD>

<TD>
<SAMP>min()</SAMP><BR>
</TD>

<TD>
the minimum positive normalized value<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>int</SAMP><BR>
</TD>

<TD>
<SAMP>digits</SAMP><BR>
</TD>

<TD>
the number of digits in the mantissa<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>int</SAMP><BR>
</TD>

<TD>
<SAMP>radix</SAMP><BR>
</TD>

<TD>
the base (or radix) of the exponent representation<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>T</SAMP><BR>
</TD>

<TD>
<SAMP>epsilon()</SAMP><BR>
</TD>

<TD>
the difference between 1 and the least representable value greater than 1<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>T</SAMP><BR>
</TD>

<TD>
<SAMP>round_error()</SAMP><BR>
</TD>

<TD>
a measurement of the rounding error<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>int</SAMP><BR>
</TD>

<TD>
<SAMP>min_exponent</SAMP><BR>
</TD>

<TD>
minimum negative exponent<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>int</SAMP><BR>
</TD>

<TD>
<SAMP>min_exponent10</SAMP><BR>
</TD>

<TD>
minimum value such that 10 raised to that power is in range<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>int</SAMP><BR>
</TD>

<TD>
<SAMP>max_exponent</SAMP><BR>
</TD>

<TD>
maximum positive exponent<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>int</SAMP><BR>
</TD>

<TD>
<SAMP>max_exponent10</SAMP><BR>
</TD>

<TD>
maximum value such that 10 raised to that power is in range<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>has_infinity</SAMP><BR>
</TD>

<TD>
true if the type has a representation of positive infinity<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>T</SAMP><BR>
</TD>

<TD>
<SAMP>infinity()</SAMP><BR>
</TD>

<TD>
representation of infinity, if available<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>has_quiet_NaN</SAMP><BR>
</TD>

<TD>
true if there is a representation of a quiet ``Not a Number"<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>T</SAMP><BR>
</TD>

<TD>
<SAMP>quiet_NaN()</SAMP><BR>
</TD>

<TD>
representation of quiet NaN, if available<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>has_signaling_NaN</SAMP><BR>
</TD>

<TD>
true if there is a representation for a signaling NaN<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>T</SAMP><BR>
</TD>

<TD>
<SAMP>signaling_NaN()</SAMP><BR>
</TD>

<TD>
representation of signaling NaN, if available<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>has_denorm</SAMP><BR>
</TD>

<TD>
true if the representation allows denormalized values<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>T</SAMP><BR>
</TD>

<TD>
<SAMP>denorm_min()</SAMP><BR>
</TD>

<TD>
Minimum positive denormalized value <BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>is_iec559</SAMP><BR>
</TD>

<TD>
true if representation adheres to IEC 559 standard.<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>
<SAMP>bool</SAMP><BR>
</TD>

<TD>
<SAMP>tinyness_before</SAMP><BR>
</TD>

<TD>
true if tinyness is detected before rounding<BR>
</TD>
</TR>

<TR VALIGN=top>
<TD>&nbsp;</TD>

<TD>
<SAMP>round_style</SAMP><BR>
</TD>

<TD>
rounding style for type<BR>
</TD>
</TR>
</TABLE></CENTER>
<P>For the <SAMP>float </SAMP>data type, the value in field <SAMP>radix</SAMP>, which represents the base of the exponential representation, is equivalent to the symbolic constant <SAMP>FLT_RADIX</SAMP>.</P>
<P>For the types <SAMP>float, double</SAMP> and <SAMP>long double</SAMP> the value of <SAMP>epsilon</SAMP> is also available as <SAMP>FLT_EPSILON, DBL_EPSILON</SAMP>, and <SAMP>LDBL_EPSILON</SAMP>.</P>
<P>A NaN is a "Not a Number."  It is a representable value that nevertheless does not correspond to any numeric quantity.  Many numeric algorithms manipulate such values.</P>
<P>The IEC 559 standard is a standard approved by the International Electrotechnical Commission.  It is the same as the IEEE standard 754.</P>
<P>Value returned by the function <SAMP>round_style()</SAMP> is one of the following: <SAMP>round_indeterminate, round_toward_zero, round_to_nearest, round_toward_infinity</SAMP>, or<SAMP> round_toward_neg_infinity.</SAMP></P>
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