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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.

NAME

       tgmath.h — type-generic macros

SYNOPSIS

       #include <tgmath.h>

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.1‐2017 defers to the ISO C standard.

       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(), j0(), j1(), jn(), y0(), y1(), and yn(),  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> Function<complex.h> FunctionType-Generic 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,  except  for modf(), j0(), j1(), jn(), y0(), y1(), and yn(), the corresponding type-generic macro
       has the same name as the function.  These type-generic macros are:

              atan2()      fma()      llround()      remainder()
              cbrt()       fmax()     log10()        remquo()
              ceil()       fmin()     log1p()        rint()
              copysign()   fmod()     log2()         round()
              erf()        frexp()    logb()         scalbln()
              erfc()       hypot()    lrint()        scalbn()
              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 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.

APPLICATION USAGE

       With the declarations:

           #include <tgmath.h>
           int n;
           float f;
           double d;
           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 following table:

                                  ┌─────────────────┬───────────────────────────────┐
                                  │     MacroUse Invokes          │
                                  ├─────────────────┼───────────────────────────────┤
                                  │exp(n)           │ exp(n), the function          │
                                  │acosh(f)         │ acoshf(f)                     │
                                  │sin(d)           │ sin(d), the function          │
                                  │atan(ld)         │ atanl(ld)                     │
                                  │log(fc)          │ clogf(fc)                     │
                                  │sqrt(dc)         │ csqrt(dc)                     │
                                  │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         │
                                  │cproj(f)         │ cprojf(f)                     │
                                  │creal(d)         │ creal(d), the function        │
                                  │cimag(ld)        │ cimagl(ld)                    │
                                  │cabs(fc)         │ cabsf(fc)                     │
                                  │carg(dc)         │ carg(dc), the function        │
                                  │cproj(ldc)       │ cprojl(ldc)                   │
                                  └─────────────────┴───────────────────────────────┘

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 '+' 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 POSIX.1‐2008
       specifies only for real arguments with the ability to invoke the complex functions.

       POSIX.1‐2008 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.

FUTURE DIRECTIONS

       None.

SEE ALSO

       <math.h>, <complex.h>

       The System Interfaces volume of POSIX.1‐2017, cabs(), fabs(), modf()

COPYRIGHT

       Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1-2017, Standard
       for  Information  Technology  --  Portable  Operating  System  Interface  (POSIX),  The  Open  Group Base
       Specifications Issue 7, 2018 Edition, Copyright (C) 2018 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 .

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