'\" et
.TH tgmath.h "0P" 2013 "IEEE/The Open Group" "POSIX Programmer's Manual"
.SH PROLOG
This manual page is part of the POSIX Programmer's Manual.
The Linux implementation of this interface may differ (consult
the corresponding Linux manual page for details of Linux behavior),
or the interface may not be implemented on Linux.

.SH NAME
tgmath.h
\(em type-generic macros
.SH SYNOPSIS
.LP
.nf
#include <tgmath.h>
.fi
.SH DESCRIPTION
The functionality described on this reference page is aligned with the
ISO\ C standard. Any conflict between the requirements described here and the
ISO\ C standard is unintentional. This volume of POSIX.1\(hy2008 defers to the ISO\ C standard.
.P
The
.IR <tgmath.h> 
header shall include the headers
.IR <math.h> 
and
.IR <complex.h> 
and shall define several type-generic macros.
.P
Of the functions contained within the
.IR <math.h> 
and
.IR <complex.h> 
headers without an
.IR f
(\c
.BR float )
or
.IR l
(\c
.BR "long double" )
suffix, several have one or more parameters whose corresponding real
type is
.BR double .
For each such function, except
\fImodf\fR(),
\fIj0\fR(),
\fIj1\fR(),
\fIjn\fR(),
\fIy0\fR(),
\fIy1\fR(),
and
\fIyn\fR(),
there shall be a corresponding type-generic macro. The parameters
whose corresponding real type is
.BR double
in the function synopsis are generic parameters. Use of the macro
invokes a function whose corresponding real type and type domain are
determined by the arguments for the generic parameters.
.P
Use of the macro invokes a function whose generic parameters have the
corresponding real type determined as follows:
.IP " *" 4
First, if any argument for generic parameters has type
.BR "long double" ,
the type determined is
.BR "long double" .
.IP " *" 4
Otherwise, if any argument for generic parameters has type
.BR double
or is of integer type, the type determined is
.BR double .
.IP " *" 4
Otherwise, the type determined is
.BR float .
.P
For each unsuffixed function in the
.IR <math.h> 
header for which there is a function in the
.IR <complex.h> 
header with the same name except for a
.IR c
prefix, the corresponding type-generic macro (for both functions) has
the same name as the function in the
.IR <math.h> 
header. The corresponding type-generic macro for
\fIfabs\fR()
and
\fIcabs\fR()
is
\fIfabs\fR().
.TS
center box tab(!);
cB | cB | cB
l | l | l.
<math.h> Function!<complex.h> Function!Type-Generic Macro
_
\fIacos\fR\^(\|)!\fIcacos\fR\^(\|)!\fIacos\fR\^(\|)
\fIasin\fR\^(\|)!\fIcasin\fR\^(\|)!\fIasin\fR\^(\|)
\fIatan\fR\^(\|)!\fIcatan\fR\^(\|)!\fIatan\fR\^(\|)
\fIacosh\fR\^(\|)!\fIcacosh\fR\^(\|)!\fIacosh\fR\^(\|)
\fIasinh\fR\^(\|)!\fIcasinh\fR\^(\|)!\fIasinh\fR\^(\|)
\fIatanh\fR\^(\|)!\fIcatanh\fR\^(\|)!\fIatanh\fR\^(\|)
\fIcos\fR\^(\|)!\fIccos\fR\^(\|)!\fIcos\fR\^(\|)
\fIsin\fR\^(\|)!\fIcsin\fR\^(\|)!\fIsin\fR\^(\|)
\fItan\fR\^(\|)!\fIctan\fR\^(\|)!\fItan\fR\^(\|)
\fIcosh\fR\^(\|)!\fIccosh\fR\^(\|)!\fIcosh\fR\^(\|)
\fIsinh\fR\^(\|)!\fIcsinh\fR\^(\|)!\fIsinh\fR\^(\|)
\fItanh\fR\^(\|)!\fIctanh\fR\^(\|)!\fItanh\fR\^(\|)
\fIexp\fR\^(\|)!\fIcexp\fR\^(\|)!\fIexp\fR\^(\|)
\fIlog\fR\^(\|)!\fIclog\fR\^(\|)!\fIlog\fR\^(\|)
\fIpow\fR\^(\|)!\fIcpow\fR\^(\|)!\fIpow\fR\^(\|)
\fIsqrt\fR\^(\|)!\fIcsqrt\fR\^(\|)!\fIsqrt\fR\^(\|)
\fIfabs\fR\^(\|)!\fIcabs\fR\^(\|)!\fIfabs\fR\^(\|)
.TE
.P
If at least one argument for a generic parameter is complex, then use
of the macro invokes a complex function; otherwise, use of the macro
invokes a real function.
.P
For each unsuffixed function in the
.IR <math.h> 
header without a
.IR c -prefixed
counterpart in the
.IR <complex.h> 
header, except for
\fImodf\fR(),
\fIj0\fR(),
\fIj1\fR(),
\fIjn\fR(),
\fIy0\fR(),
\fIy1\fR(),
and
\fIyn\fR(),
the corresponding type-generic macro has the same name as the function.
These type-generic macros are:
.sp
.RS
.TS
tab(!);
l l l l.
T{
.nf
\fIatan2\fR()
\fIcbrt\fR()
\fIceil\fR()
\fIcopysign\fR()
\fIerf\fR()
\fIerfc\fR()
\fIexp2\fR()
\fIexpm1\fR()
\fIfdim\fR()
\fIfloor\fR()
T}!T{
.nf
\fIfma\fR()
\fIfmax\fR()
\fIfmin\fR()
\fIfmod\fR()
\fIfrexp\fR()
\fIhypot\fR()
\fIilogb\fR()
\fIldexp\fR()
\fIlgamma\fR()
\fIllrint\fR()
T}!T{
.nf
\fIllround\fR()
\fIlog10\fR()
\fIlog1p\fR()
\fIlog2\fR()
\fIlogb\fR()
\fIlrint\fR()
\fIlround\fR()
\fInearbyint\fR()
\fInextafter\fR()
\fInexttoward\fR()
T}!T{
.nf
\fIremainder\fR()
\fIremquo\fR()
\fIrint\fR()
\fIround\fR()
\fIscalbln\fR()
\fIscalbn\fR()
\fItgamma\fR()
\fItrunc\fR()
.fi
T}
.TE
.RE
.P
If all arguments for generic parameters are real, then use of the macro
invokes a real function; otherwise, use of the macro results in
undefined behavior.
.P
For each unsuffixed function in the
.IR <complex.h> 
header that is not a
.IR c -prefixed
counterpart to a function in the
.IR <math.h> 
header, the corresponding type-generic macro has the same name as the
function. These type-generic macros are:
.sp
.RS
\fIcarg\fR()
\fIcimag\fR()
\fIconj\fR()
\fIcproj\fR()
\fIcreal\fR()
.RE
.P
Use of the macro with any real or complex argument invokes a complex
function.
.LP
.IR "The following sections are informative."
.SH "APPLICATION USAGE"
With the declarations:
.sp
.RS 4
.nf
\fB
#include <tgmath.h>
int n;
float f;
double d;
long double ld;
float complex fc;
double complex dc;
long double complex ldc;
.fi \fR
.P
.RE
.P
functions invoked by use of type-generic macros are shown in the
following table:
.TS
center box tab(!);
cB | cB
l | l.
Macro!Use Invokes
_
\fIexp\fR(\fIn\fR)!\fIexp\fR(\fIn\fR), the function
\fIacosh\fR(\fIf\fR)!\fIacoshf\fR(\fIf\fR)
\fIsin\fR(\fId\fR)!\fIsin\fR(\fId\fR), the function
\fIatan\fR(\fIld\fR)!\fIatanl\fR(\fIld\fR)
\fIlog\fR(\fIfc\fR)!\fIclogf\fR(\fIfc\fR)
\fIsqrt\fR(\fIdc\fR)!\fIcsqrt\fR(\fIdc\fR)
\fIpow\fR(\fIldc,f\fR)!\fIcpowl\fR(\fIldc, f\fR)
\fIremainder\fR(\fIn,n\fR)!\fIremainder\fR(\fIn, n\fR), the function
\fInextafter\fR(\fId,f\fR)!\fInextafter\fR(\fId, f\fR), the function
\fInexttoward\fR(\fIf,ld\fR)!\fInexttowardf\fR(\fIf, ld\fR)
\fIcopysign\fR(\fIn,ld\fR)!\fIcopysignl\fR(\fIn, ld\fR)
\fIceil\fR(\fIfc\fR)!Undefined behavior
\fIrint\fR(\fIdc\fR)!Undefined behavior
\fIfmax\fR(\fIldc,ld\fR)!Undefined behavior
\fIcarg\fR(\fIn\fR)!\fIcarg\fR(\fIn\fR), the function
\fIcproj\fR(\fIf\fR)!\fIcprojf\fR(\fIf\fR)
\fIcreal\fR(\fId\fR)!\fIcreal\fR(\fId\fR), the function
\fIcimag\fR(\fIld\fR)!\fIcimagl\fR(\fIld\fR)
\fIcabs\fR(\fIfc\fR)!\fIcabsf\fR(\fIfc\fR)
\fIcarg\fR(\fIdc\fR)!\fIcarg\fR(\fIdc\fR), the function
\fIcproj\fR(\fIldc\fR)!\fIcprojl\fR(\fIldc\fR)
.TE
.SH RATIONALE
Type-generic macros allow calling a function whose type is determined
by the argument type, as is the case for C operators such as
.BR '+' 
and
.BR '*' .
For example, with a type-generic
\fIcos\fR()
macro, the expression
.IR cos ((\c
.BR float )\c
.IR x )
will have type
.BR float .
This feature enables writing more portably efficient code and
alleviates need for awkward casting and suffixing in the process of
porting or adjusting precision. Generic math functions are a widely
appreciated feature of Fortran.
.P
The only arguments that affect the type resolution are the arguments
corresponding to the parameters that have type
.BR double
in the synopsis. Hence the type of a type-generic call to
\fInexttoward\fR(),
whose second parameter is
.BR "long double"
in the synopsis, is determined solely by the type of the first
argument.
.P
The term ``type-generic'' was chosen over the proposed alternatives of
intrinsic and overloading. The term is more specific than intrinsic,
which already is widely used with a more general meaning, and reflects
a closer match to Fortran's generic functions than to C++ overloading.
.P
The macros are placed in their own header in order not to silently
break old programs that include the
.IR <math.h> 
header; for example, with:
.sp
.RS 4
.nf
\fB
printf ("%e", sin(x))
.fi \fR
.P
.RE
.P
.IR modf (\c
.BR double ,
.BR "double *" )
is excluded because no way was seen to make it safe without
complicating the type resolution.
.P
The implementation might, as an extension, endow appropriate ones of
the macros that POSIX.1\(hy2008 specifies only for real arguments with the
ability to invoke the complex functions.
.P
POSIX.1\(hy2008 does not prescribe any particular implementation mechanism
for generic macros. It could be implemented simply with built-in
macros. The generic macro for
\fIsqrt\fR(),
for example, could be implemented with:
.sp
.RS 4
.nf
\fB
#undef sqrt
#define sqrt(x) __BUILTIN_GENERIC_sqrt(x)
.fi \fR
.P
.RE
.P
Generic macros are designed for a useful level of consistency with C++
overloaded math functions.
.P
The great majority of existing C programs are expected to be unaffected
when the
.IR <tgmath.h> 
header is included instead of the
.IR <math.h> 
or
.IR <complex.h> 
headers. Generic macros are similar to the ISO/IEC\ 9899:\|1999 standard library masking
macros, though the semantic types of return values differ.
.P
The ability to overload on integer as well as floating types would have
been useful for some functions; for example,
\fIcopysign\fR().
Overloading with different numbers of arguments would have allowed
reusing names; for example,
\fIremainder\fR()
for
\fIremquo\fR().
However, these facilities would have complicated the specification; and
their natural consistent use, such as for a floating
\fIabs\fR()
or a two-argument
\fIatan\fR(),
would have introduced further inconsistencies with the ISO/IEC\ 9899:\|1999 standard for
insufficient benefit.
.P
The ISO\ C standard in no way limits the implementation's options for efficiency,
including inlining library functions.
.SH "FUTURE DIRECTIONS"
None.
.SH "SEE ALSO"
.IR "\fB<math.h>\fP",
.IR "\fB<complex.h>\fP"
.P
The System Interfaces volume of POSIX.1\(hy2008,
.IR "\fIcabs\fR\^(\|)",
.IR "\fIfabs\fR\^(\|)",
.IR "\fImodf\fR\^(\|)"
.SH COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
-- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 7, Copyright (C) 2013 by the Institute of
Electrical and Electronics Engineers, Inc and The Open Group.
(This is POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) In the
event of any discrepancy between this version and the original IEEE and
The Open Group Standard, the original IEEE and The Open Group Standard
is the referee document. The original Standard can be obtained online at
http://www.unix.org/online.html .

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