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<H1> G.2 Numeric Performance Requirements</H1>
<H4 ALIGN=CENTER>Implementation Requirements</H4>
<DIV Class="Paranum"><FONT SIZE=-2>1</FONT></DIV>
<DIV Class="Normal"> <A NAME="I7249"></A><A NAME="I7250"></A>Implementations
shall provide a user-selectable mode in which the accuracy and other
numeric performance requirements detailed in the following subclauses
are observed. This mode, referred to as the <I>strict mode</I>, may or
may not be the default mode; it directly affects the results of the predefined
arithmetic operations of real types and the results of the subprograms
in children of the Numerics package, and indirectly affects the operations
in other language defined packages. <A NAME="I7251"></A>Implementations
shall also provide the opposing mode, which is known as the <I>relaxed
mode</I>. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>1.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Reason: </B>On the assumption
that the users of an implementation that does not support the Numerics
Annex have no particular need for numerical performance, such an implementation
has no obligation to meet any particular requirements in this area. On
the other hand, users of an implementation that does support the Numerics
Annex are provided with a way of ensuring that their programs achieve
a known level of numerical performance and that the performance is portable
to other such implementations. The relaxed mode is provided to allow
implementers to offer an efficient but not fully accurate alternative
in the case that the strict mode entails a time overhead that some users
may find excessive. In some of its areas of impact, the relaxed mode
may be fully equivalent to the strict mode. </FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>1.b</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Implementation Note: </B>The
relaxed mode may, for example, be used to exploit the implementation
of (some of) the elementary functions in hardware, when available. Such
implementations often do not meet the accuracy requirements of the strict
mode, or do not meet them over the specified range of parameter values,
but compensate in other ways that may be important to the user, such
as their extreme speed. </FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>1.c</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Ramification: </B>For implementations
supporting the Numerics Annex, the choice of mode has no effect on the
selection of a representation for a real type or on the values of attributes
of a real type. </FONT></DIV>
<H4 ALIGN=CENTER>Implementation Permissions</H4>
<DIV Class="Paranum"><FONT SIZE=-2>2</FONT></DIV>
<DIV Class="Normal"> Either mode may be the default mode. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>2.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Implementation defined: </B>Whether
the strict mode or the relaxed mode is the default.</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>3</FONT></DIV>
<DIV Class="Normal"> The two modes need not actually be different.
</DIV>
<H4 ALIGN=CENTER>Extensions to Ada 83</H4>
<DIV Class="Paranum"><FONT SIZE=-2>3.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><A NAME="I7252"></A>The choice
between strict and relaxed numeric performance was not available in Ada
83. </FONT></DIV>
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