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:
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First, if any argument for generic parameters has type long double,
the type determined is long double.
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Otherwise, if any argument for generic parameters has type double
or is of integer type, the type determined is
double.
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Otherwise, the type determined is float.
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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
macros are:
atan2()
cbrt()
ceil()
copysign()
erf()
erfc()
exp2()
expm1()
fdim()
floor()
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fma()
fmax()
fmin()
fmod()
frexp()
hypot()
ilogb()
ldexp()
lgamma()
llrint()
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llround()
log10()
log1p()
log2()
logb()
lrint()
lround()
nearbyint()
nextafter()
nexttoward()
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remainder()
remquo()
rint()
round()
scalbn()
scalbln()
tgamma()
trunc()
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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.
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:
carg()
cimag()
conj()
cproj()
creal()
Use of the macro with any real or complex argument invokes a complex
function.
The following sections are informative.
Type-generic macros allow calling a function whose type is determined
by the argument type, as is the case for C operators such
as ’+’ and ’*’ . 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 Fortran’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 implemented with:
#undef sqrt
#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 implementation’s options
for efficiency, including inlining library functions.
