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Chapter 26: Numerics
Chapter 26 deals with building block abstractions to aid in numerical computing:
- Template data structures such as
valarray<>andcomplex<>. - Template numerical functions such as
accumulate,inner_product,partial_sum, andadjacent_difference.
long, float, and
long double have been added for all of them.
Contents
Complex Number Processing
Using complex<> becomes even more comple- er, sorry,
complicated, with the not-quite-gratuitously-incompatible
addition of complex types to the C language. David Tribble has
compiled a list of C++98 and C99 conflict points; his description of
C's new type versus those of C++ and how to get them playing together
nicely is
here.
complex<> is intended to be instantiated with a
floating-point type. As long as you meet that and some other basic
requirements, then the resulting instantiation has all of the usual
math operators defined, as well as definitions of op<<
and op>> that work with iostreams: op<<
prints (u,v) and op>> can read u,
(u), and (u,v).
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Array Processing
One of the major reasons why FORTRAN can chew through numbers so well
is that it is defined to be free of pointer aliasing, an assumption
that C89 is not allowed to make, and neither is C++98. C99 adds a new
keyword, restrict, to apply to individual pointers. The
C++ solution is contained in the library rather than the language
(although many vendors can be expected to add this to their compilers
as an extension).
That library solution is a set of two classes, five template classes,
and "a whole bunch" of functions. The classes are required
to be free of pointer aliasing, so compilers can optimize the
daylights out of them the same way that they have been for FORTRAN.
They are collectively called valarray, although strictly
speaking this is only one of the five template classes, and they are
designed to be familiar to people who have worked with the BLAS
libraries before.
Some more stuff should go here once somebody has time to write it.
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Numerical Functions
There are four generalized functions in the <numeric> header that follow the same conventions as those in <algorithm>. Each of them is overloaded: one signature for common default operations, and a second for fully general operations. Their names are self-explanatory to anyone who works with numerics on a regular basis:
accumulateinner_productpartial_sumadjacent_difference
Here is a simple example of the two forms of accumulate.
int ar[50];
int someval = somefunction();
// ...initialize members of ar to something...
int sum = std::accumulate(ar,ar+50,0);
int sum_stuff = std::accumulate(ar,ar+50,someval);
int product = std::accumulate(ar,ar+50,1,std::multiplies<int>());
The first call adds all the members of the array, using zero as an
initial value for sum. The second does the same, but uses
someval as the starting value (thus, sum_stuff == sum +
someval). The final call uses the second of the two signatures,
and multiplies all the members of the array; here we must obviously
use 1 as a starting value instead of 0.
The other three functions have similar dual-signature forms.
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C99
In addition to the other topics on this page, we'll note here some of the C99 features that appear in libstdc++-v3.
The C99 features depend on the --enable-c99 configure flag.
This flag is already on by default, but it can be disabled by the
user. Also, the configuration machinery will disable it if the
necessary support for C99 (e.g., header files) cannot be found.
As of GCC 3.0, C99 support includes classification functions
such as isnormal, isgreater,
isnan, etc.
The functions used for 'long long' support such as strtoll
are supported, as is the lldiv_t typedef. Also supported
are the wide character functions using 'long long', like
wcstoll.
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