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tgmath.h - type-generic macros
The <tgmath.h> header shall include the headers <math.h> and
<complex.h> and shall define several type-generic macros.
Of the functions contained within the <math.h> and <complex.h> headers
without an f ( float) or l ( long double) suffix, several have one or
more parameters whose corresponding real type is double. For each such
function, except modf(), there shall be a corresponding type-generic
macro. The parameters whose corresponding real type is 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.
Use of the macro invokes a function whose generic parameters have the
corresponding real type determined as follows:
* First, if any argument for generic parameters has type long double,
the type determined is long double.
* Otherwise, if any argument for generic parameters has type double or
is of integer type, the type determined is double.
* Otherwise, the type determined is float.
For each unsuffixed function in the <math.h> header for which there is
a function in the <complex.h> header with the same name except for a c
prefix, the corresponding type-generic macro (for both functions) has
the same name as the function in the <math.h> header. The corresponding
type-generic macro for fabs() and cabs() is fabs().
<math.h> <complex.h> Type-Generic
Function Function Macro
acos() cacos() acos()
asin() casin() asin()
atan() catan() atan()
acosh() cacosh() acosh()
asinh() casinh() asinh()
atanh() catanh() atanh()
cos() ccos() cos()
sin() csin() sin()
tan() ctan() tan()
cosh() ccosh() cosh()
sinh() csinh() sinh()
tanh() ctanh() tanh()
exp() cexp() exp()
log() clog() log()
pow() cpow() pow()
sqrt() csqrt() sqrt()
fabs() cabs() fabs()
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.
For each unsuffixed function in the <math.h> header without a c-
prefixed counterpart in the <complex.h> header, the corresponding type-
generic macro has the same name as the function. These type-generic
atan2() fma() llround() remainder()
cbrt() fmax() log10() remquo()
ceil() fmin() log1p() rint()
copysign() fmod() log2() round()
erf() frexp() logb() scalbn()
erfc() hypot() lrint() scalbln()
exp2() ilogb() lround() tgamma()
expm1() ldexp() nearbyint() trunc()
fdim() lgamma() nextafter()
floor() llrint() nexttoward()
If all arguments for generic parameters are real, then use of the macro
invokes a real function; otherwise, use of the macro results in
For each unsuffixed function in the <complex.h> header that is not a c-
prefixed counterpart to a function in the <math.h> header, the
corresponding type-generic macro has the same name as the function.
These type-generic macros are:
Use of the macro with any real or complex argument invokes a complex
The following sections are informative.
With the declarations:
long double ld;
float complex fc;
double complex dc;
long double complex ldc;
functions invoked by use of type-generic macros are shown in the
Macro Use Invokes
exp(n) exp(n), the function
sin(d) sin(d), the function
pow(ldc,f) cpowl(ldc, f)
remainder(n,n) remainder(n, n), the function
nextafter(d,f) nextafter(d, f), the function
nexttoward(f,ld) nexttowardf(f, ld)
copysign(n,ld) copysignl(n, ld)
ceil(fc) Undefined behavior
rint(dc) Undefined behavior
fmax(ldc,ld) Undefined behavior
carg(n) carg(n), the function
creal(d) creal(d), the function
carg(dc) carg(dc), the function
Type-generic macros allow calling a function whose type is determined
by the argument type, as is the case for C operators such as â€â€™+â€â€™ and
â€â€™*â€â€™ . For example, with a type-generic cos() macro, the expression
cos(( float) x) will have type 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.
The only arguments that affect the type resolution are the arguments
corresponding to the parameters that have type double in the synopsis.
Hence the type of a type-generic call to nexttoward(), whose second
parameter is long double in the synopsis, is determined solely by the
type of the first argument.
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 Fortranâ€™s generic functions than to C++ overloading.
The macros are placed in their own header in order not to silently
break old programs that include the <math.h> header; for example, with:
printf ("%e", sin(x))
modf( double, double *) is excluded because no way was seen to make it
safe without complicating the type resolution.
The implementation might, as an extension, endow appropriate ones of
the macros that IEEE Std 1003.1-2001 specifies only for real arguments
with the ability to invoke the complex functions.
IEEE Std 1003.1-2001 does not prescribe any particular implementation
mechanism for generic macros. It could be implemented simply with
built-in macros. The generic macro for sqrt(), for example, could be
#define sqrt(x) __BUILTIN_GENERIC_sqrt(x)
Generic macros are designed for a useful level of consistency with C++
overloaded math functions.
The great majority of existing C programs are expected to be unaffected
when the <tgmath.h> header is included instead of the <math.h> or
<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.
The ability to overload on integer as well as floating types would have
been useful for some functions; for example, copysign(). Overloading
with different numbers of arguments would have allowed reusing names;
for example, remainder() for remquo(). However, these facilities would
have complicated the specification; and their natural consistent use,
such as for a floating abs() or a two-argument atan(), would have
introduced further inconsistencies with the ISO/IEC 9899:1999 standard
for insufficient benefit.
The ISO C standard in no way limits the implementationâ€™s options for
efficiency, including inlining library functions.
<math.h> , <complex.h> , the System Interfaces volume of
IEEE Std 1003.1-2001, cabs(), fabs(), modf()
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
-- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of
Electrical and Electronics Engineers, Inc and The Open Group. 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.opengroup.org/unix/online.html .