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      1 /* Copyright (C) 1997, 1998, 1999, 2000, 2001, 2003, 2004, 2005, 2007
      2    Free Software Foundation, Inc.
      3    This file is part of the GNU C Library.
      4 
      5    The GNU C Library is free software; you can redistribute it and/or
      6    modify it under the terms of the GNU Lesser General Public
      7    License as published by the Free Software Foundation; either
      8    version 2.1 of the License, or (at your option) any later version.
      9 
     10    The GNU C Library is distributed in the hope that it will be useful,
     11    but WITHOUT ANY WARRANTY; without even the implied warranty of
     12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
     13    Lesser General Public License for more details.
     14 
     15    You should have received a copy of the GNU Lesser General Public
     16    License along with the GNU C Library; if not, write to the Free
     17    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
     18    02111-1307 USA.  */
     19 
     20 /*
     21  *	ISO C99 Standard: 7.22 Type-generic math	<tgmath.h>
     22  */
     23 
     24 #ifndef _TGMATH_H
     25 #define _TGMATH_H	1
     26 
     27 /* Include the needed headers.  */
     28 #include <math.h>
     29 #include <complex.h>
     30 
     31 
     32 /* Since `complex' is currently not really implemented in most C compilers
     33    and if it is implemented, the implementations differ.  This makes it
     34    quite difficult to write a generic implementation of this header.  We
     35    do not try this for now and instead concentrate only on GNU CC.  Once
     36    we have more information support for other compilers might follow.  */
     37 
     38 #if __GNUC_PREREQ (2, 7)
     39 
     40 # ifdef __NO_LONG_DOUBLE_MATH
     41 #  define __tgml(fct) fct
     42 # else
     43 #  define __tgml(fct) fct ## l
     44 # endif
     45 
     46 /* This is ugly but unless gcc gets appropriate builtins we have to do
     47    something like this.  Don't ask how it works.  */
     48 
     49 /* 1 if 'type' is a floating type, 0 if 'type' is an integer type.
     50    Allows for _Bool.  Expands to an integer constant expression.  */
     51 # if __GNUC_PREREQ (3, 1)
     52 #  define __floating_type(type) \
     53   (__builtin_classify_type ((type) 0) == 8 \
     54    || (__builtin_classify_type ((type) 0) == 9 \
     55        && __builtin_classify_type (__real__ ((type) 0)) == 8))
     56 # else
     57 #  define __floating_type(type) (((type) 0.25) && ((type) 0.25 - 1))
     58 # endif
     59 
     60 /* The tgmath real type for T, where E is 0 if T is an integer type and
     61    1 for a floating type.  */
     62 # define __tgmath_real_type_sub(T, E) \
     63   __typeof__ (*(0 ? (__typeof__ (0 ? (double *) 0 : (void *) (E))) 0	      \
     64 		  : (__typeof__ (0 ? (T *) 0 : (void *) (!(E)))) 0))
     65 
     66 /* The tgmath real type of EXPR.  */
     67 # define __tgmath_real_type(expr) \
     68   __tgmath_real_type_sub (__typeof__ ((__typeof__ (expr)) 0),		      \
     69 			  __floating_type (__typeof__ (expr)))
     70 
     71 
     72 /* We have two kinds of generic macros: to support functions which are
     73    only defined on real valued parameters and those which are defined
     74    for complex functions as well.  */
     75 # define __TGMATH_UNARY_REAL_ONLY(Val, Fct) \
     76      (__extension__ ((sizeof (Val) == sizeof (double)			      \
     77 		      || __builtin_classify_type (Val) != 8)		      \
     78 		     ? (__tgmath_real_type (Val)) Fct (Val)		      \
     79 		     : (sizeof (Val) == sizeof (float))			      \
     80 		     ? (__tgmath_real_type (Val)) Fct##f (Val)		      \
     81 		     : (__tgmath_real_type (Val)) __tgml(Fct) (Val)))
     82 
     83 # define __TGMATH_UNARY_REAL_RET_ONLY(Val, RetType, Fct) \
     84      (__extension__ ((sizeof (Val) == sizeof (double)			      \
     85 		      || __builtin_classify_type (Val) != 8)		      \
     86 		     ? (RetType) Fct (Val)				      \
     87 		     : (sizeof (Val) == sizeof (float))			      \
     88 		     ? (RetType) Fct##f (Val)				      \
     89 		     : (RetType) __tgml(Fct) (Val)))
     90 
     91 # define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
     92      (__extension__ ((sizeof (Val1) == sizeof (double)			      \
     93 		      || __builtin_classify_type (Val1) != 8)		      \
     94 		     ? (__tgmath_real_type (Val1)) Fct (Val1, Val2)	      \
     95 		     : (sizeof (Val1) == sizeof (float))		      \
     96 		     ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2)	      \
     97 		     : (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
     98 
     99 # define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
    100      (__extension__ (((sizeof (Val1) > sizeof (double)			      \
    101 		       || sizeof (Val2) > sizeof (double))		      \
    102 		      && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
    103 		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
    104 				   + (__tgmath_real_type (Val2)) 0))	      \
    105 		       __tgml(Fct) (Val1, Val2)				      \
    106 		     : (sizeof (Val1) == sizeof (double)		      \
    107 			|| sizeof (Val2) == sizeof (double)		      \
    108 			|| __builtin_classify_type (Val1) != 8		      \
    109 			|| __builtin_classify_type (Val2) != 8)		      \
    110 		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
    111 				   + (__tgmath_real_type (Val2)) 0))	      \
    112 		       Fct (Val1, Val2)					      \
    113 		     : (__typeof ((__tgmath_real_type (Val1)) 0		      \
    114 				   + (__tgmath_real_type (Val2)) 0))	      \
    115 		       Fct##f (Val1, Val2)))
    116 
    117 # define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
    118      (__extension__ (((sizeof (Val1) > sizeof (double)			      \
    119 		       || sizeof (Val2) > sizeof (double))		      \
    120 		      && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
    121 		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
    122 				   + (__tgmath_real_type (Val2)) 0))	      \
    123 		       __tgml(Fct) (Val1, Val2, Val3)			      \
    124 		     : (sizeof (Val1) == sizeof (double)		      \
    125 			|| sizeof (Val2) == sizeof (double)		      \
    126 			|| __builtin_classify_type (Val1) != 8		      \
    127 			|| __builtin_classify_type (Val2) != 8)		      \
    128 		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
    129 				   + (__tgmath_real_type (Val2)) 0))	      \
    130 		       Fct (Val1, Val2, Val3)				      \
    131 		     : (__typeof ((__tgmath_real_type (Val1)) 0		      \
    132 				   + (__tgmath_real_type (Val2)) 0))	      \
    133 		       Fct##f (Val1, Val2, Val3)))
    134 
    135 # define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
    136      (__extension__ (((sizeof (Val1) > sizeof (double)			      \
    137 		       || sizeof (Val2) > sizeof (double)		      \
    138 		       || sizeof (Val3) > sizeof (double))		      \
    139 		      && __builtin_classify_type ((Val1) + (Val2) + (Val3))   \
    140 			 == 8)						      \
    141 		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
    142 				   + (__tgmath_real_type (Val2)) 0	      \
    143 				   + (__tgmath_real_type (Val3)) 0))	      \
    144 		       __tgml(Fct) (Val1, Val2, Val3)			      \
    145 		     : (sizeof (Val1) == sizeof (double)		      \
    146 			|| sizeof (Val2) == sizeof (double)		      \
    147 			|| sizeof (Val3) == sizeof (double)		      \
    148 			|| __builtin_classify_type (Val1) != 8		      \
    149 			|| __builtin_classify_type (Val2) != 8		      \
    150 			|| __builtin_classify_type (Val3) != 8)		      \
    151 		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
    152 				   + (__tgmath_real_type (Val2)) 0	      \
    153 				   + (__tgmath_real_type (Val3)) 0))	      \
    154 		       Fct (Val1, Val2, Val3)				      \
    155 		     : (__typeof ((__tgmath_real_type (Val1)) 0		      \
    156 				   + (__tgmath_real_type (Val2)) 0	      \
    157 				   + (__tgmath_real_type (Val3)) 0))	      \
    158 		       Fct##f (Val1, Val2, Val3)))
    159 
    160 /* XXX This definition has to be changed as soon as the compiler understands
    161    the imaginary keyword.  */
    162 # define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
    163      (__extension__ ((sizeof (__real__ (Val)) == sizeof (double)	      \
    164 		      || __builtin_classify_type (__real__ (Val)) != 8)	      \
    165 		     ? ((sizeof (__real__ (Val)) == sizeof (Val))	      \
    166 			? (__tgmath_real_type (Val)) Fct (Val)		      \
    167 			: (__tgmath_real_type (Val)) Cfct (Val))	      \
    168 		     : (sizeof (__real__ (Val)) == sizeof (float))	      \
    169 		     ? ((sizeof (__real__ (Val)) == sizeof (Val))	      \
    170 			? (__tgmath_real_type (Val)) Fct##f (Val)	      \
    171 			: (__tgmath_real_type (Val)) Cfct##f (Val))	      \
    172 		     : ((sizeof (__real__ (Val)) == sizeof (Val))	      \
    173 			? (__tgmath_real_type (Val)) __tgml(Fct) (Val)	      \
    174 			: (__tgmath_real_type (Val)) __tgml(Cfct) (Val))))
    175 
    176 # define __TGMATH_UNARY_IMAG(Val, Cfct) \
    177      (__extension__ ((sizeof (__real__ (Val)) == sizeof (double)	      \
    178 		      || __builtin_classify_type (__real__ (Val)) != 8)	      \
    179 		     ? (__typeof__ ((__tgmath_real_type (Val)) 0	      \
    180 				    + _Complex_I)) Cfct (Val)		      \
    181 		     : (sizeof (__real__ (Val)) == sizeof (float))	      \
    182 		     ? (__typeof__ ((__tgmath_real_type (Val)) 0	      \
    183 				    + _Complex_I)) Cfct##f (Val)	      \
    184 		     : (__typeof__ ((__tgmath_real_type (Val)) 0	      \
    185 				    + _Complex_I)) __tgml(Cfct) (Val)))
    186 
    187 /* XXX This definition has to be changed as soon as the compiler understands
    188    the imaginary keyword.  */
    189 # define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
    190      (__extension__ ((sizeof (__real__ (Val)) == sizeof (double)	      \
    191 		      || __builtin_classify_type (__real__ (Val)) != 8)	      \
    192 		     ? ((sizeof (__real__ (Val)) == sizeof (Val))	      \
    193 			? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
    194 			  Fct (Val)					      \
    195 			: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
    196 			  Cfct (Val))					      \
    197 		     : (sizeof (__real__ (Val)) == sizeof (float))	      \
    198 		     ? ((sizeof (__real__ (Val)) == sizeof (Val))	      \
    199 			? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
    200 			  Fct##f (Val)					      \
    201 			: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
    202 			  Cfct##f (Val))				      \
    203 		     : ((sizeof (__real__ (Val)) == sizeof (Val))	      \
    204 			? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
    205 			  __tgml(Fct) (Val)				      \
    206 			: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
    207 			  __tgml(Cfct) (Val))))
    208 
    209 /* XXX This definition has to be changed as soon as the compiler understands
    210    the imaginary keyword.  */
    211 # define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
    212      (__extension__ (((sizeof (__real__ (Val1)) > sizeof (double)	      \
    213 		       || sizeof (__real__ (Val2)) > sizeof (double))	      \
    214 		      && __builtin_classify_type (__real__ (Val1)	      \
    215 						  + __real__ (Val2)) == 8)    \
    216 		     ? ((sizeof (__real__ (Val1)) == sizeof (Val1)	      \
    217 			 && sizeof (__real__ (Val2)) == sizeof (Val2))	      \
    218 			? (__typeof ((__tgmath_real_type (Val1)) 0	      \
    219 				   + (__tgmath_real_type (Val2)) 0))	      \
    220 			  __tgml(Fct) (Val1, Val2)			      \
    221 			: (__typeof ((__tgmath_real_type (Val1)) 0	      \
    222 				   + (__tgmath_real_type (Val2)) 0))	      \
    223 			  __tgml(Cfct) (Val1, Val2))			      \
    224 		     : (sizeof (__real__ (Val1)) == sizeof (double)	      \
    225 			|| sizeof (__real__ (Val2)) == sizeof (double)	      \
    226 			|| __builtin_classify_type (__real__ (Val1)) != 8     \
    227 			|| __builtin_classify_type (__real__ (Val2)) != 8)    \
    228 		     ? ((sizeof (__real__ (Val1)) == sizeof (Val1)	      \
    229 			 && sizeof (__real__ (Val2)) == sizeof (Val2))	      \
    230 			? (__typeof ((__tgmath_real_type (Val1)) 0	      \
    231 				   + (__tgmath_real_type (Val2)) 0))	      \
    232 			  Fct (Val1, Val2)				      \
    233 			: (__typeof ((__tgmath_real_type (Val1)) 0	      \
    234 				   + (__tgmath_real_type (Val2)) 0))	      \
    235 			  Cfct (Val1, Val2))				      \
    236 		     : ((sizeof (__real__ (Val1)) == sizeof (Val1)	      \
    237 			 && sizeof (__real__ (Val2)) == sizeof (Val2))	      \
    238 			? (__typeof ((__tgmath_real_type (Val1)) 0	      \
    239 				   + (__tgmath_real_type (Val2)) 0))	      \
    240 			  Fct##f (Val1, Val2)				      \
    241 			: (__typeof ((__tgmath_real_type (Val1)) 0	      \
    242 				   + (__tgmath_real_type (Val2)) 0))	      \
    243 			  Cfct##f (Val1, Val2))))
    244 #else
    245 # error "Unsupported compiler; you cannot use <tgmath.h>"
    246 #endif
    247 
    248 
    249 /* Unary functions defined for real and complex values.  */
    250 
    251 
    252 /* Trigonometric functions.  */
    253 
    254 /* Arc cosine of X.  */
    255 #define acos(Val) __TGMATH_UNARY_REAL_IMAG (Val, acos, cacos)
    256 /* Arc sine of X.  */
    257 #define asin(Val) __TGMATH_UNARY_REAL_IMAG (Val, asin, casin)
    258 /* Arc tangent of X.  */
    259 #define atan(Val) __TGMATH_UNARY_REAL_IMAG (Val, atan, catan)
    260 /* Arc tangent of Y/X.  */
    261 #define atan2(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2)
    262 
    263 /* Cosine of X.  */
    264 #define cos(Val) __TGMATH_UNARY_REAL_IMAG (Val, cos, ccos)
    265 /* Sine of X.  */
    266 #define sin(Val) __TGMATH_UNARY_REAL_IMAG (Val, sin, csin)
    267 /* Tangent of X.  */
    268 #define tan(Val) __TGMATH_UNARY_REAL_IMAG (Val, tan, ctan)
    269 
    270 
    271 /* Hyperbolic functions.  */
    272 
    273 /* Hyperbolic arc cosine of X.  */
    274 #define acosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, acosh, cacosh)
    275 /* Hyperbolic arc sine of X.  */
    276 #define asinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, asinh, casinh)
    277 /* Hyperbolic arc tangent of X.  */
    278 #define atanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, atanh, catanh)
    279 
    280 /* Hyperbolic cosine of X.  */
    281 #define cosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, cosh, ccosh)
    282 /* Hyperbolic sine of X.  */
    283 #define sinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, sinh, csinh)
    284 /* Hyperbolic tangent of X.  */
    285 #define tanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, tanh, ctanh)
    286 
    287 
    288 /* Exponential and logarithmic functions.  */
    289 
    290 /* Exponential function of X.  */
    291 #define exp(Val) __TGMATH_UNARY_REAL_IMAG (Val, exp, cexp)
    292 
    293 /* Break VALUE into a normalized fraction and an integral power of 2.  */
    294 #define frexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, frexp)
    295 
    296 /* X times (two to the EXP power).  */
    297 #define ldexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, ldexp)
    298 
    299 /* Natural logarithm of X.  */
    300 #define log(Val) __TGMATH_UNARY_REAL_IMAG (Val, log, clog)
    301 
    302 /* Base-ten logarithm of X.  */
    303 #ifdef __USE_GNU
    304 # define log10(Val) __TGMATH_UNARY_REAL_IMAG (Val, log10, __clog10)
    305 #else
    306 # define log10(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10)
    307 #endif
    308 
    309 /* Return exp(X) - 1.  */
    310 #define expm1(Val) __TGMATH_UNARY_REAL_ONLY (Val, expm1)
    311 
    312 /* Return log(1 + X).  */
    313 #define log1p(Val) __TGMATH_UNARY_REAL_ONLY (Val, log1p)
    314 
    315 /* Return the base 2 signed integral exponent of X.  */
    316 #define logb(Val) __TGMATH_UNARY_REAL_ONLY (Val, logb)
    317 
    318 /* Compute base-2 exponential of X.  */
    319 #define exp2(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2)
    320 
    321 /* Compute base-2 logarithm of X.  */
    322 #define log2(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2)
    323 
    324 
    325 /* Power functions.  */
    326 
    327 /* Return X to the Y power.  */
    328 #define pow(Val1, Val2) __TGMATH_BINARY_REAL_IMAG (Val1, Val2, pow, cpow)
    329 
    330 /* Return the square root of X.  */
    331 #define sqrt(Val) __TGMATH_UNARY_REAL_IMAG (Val, sqrt, csqrt)
    332 
    333 /* Return `sqrt(X*X + Y*Y)'.  */
    334 #define hypot(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, hypot)
    335 
    336 /* Return the cube root of X.  */
    337 #define cbrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, cbrt)
    338 
    339 
    340 /* Nearest integer, absolute value, and remainder functions.  */
    341 
    342 /* Smallest integral value not less than X.  */
    343 #define ceil(Val) __TGMATH_UNARY_REAL_ONLY (Val, ceil)
    344 
    345 /* Absolute value of X.  */
    346 #define fabs(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, fabs, cabs)
    347 
    348 /* Largest integer not greater than X.  */
    349 #define floor(Val) __TGMATH_UNARY_REAL_ONLY (Val, floor)
    350 
    351 /* Floating-point modulo remainder of X/Y.  */
    352 #define fmod(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmod)
    353 
    354 /* Round X to integral valuein floating-point format using current
    355    rounding direction, but do not raise inexact exception.  */
    356 #define nearbyint(Val) __TGMATH_UNARY_REAL_ONLY (Val, nearbyint)
    357 
    358 /* Round X to nearest integral value, rounding halfway cases away from
    359    zero.  */
    360 #define round(Val) __TGMATH_UNARY_REAL_ONLY (Val, round)
    361 
    362 /* Round X to the integral value in floating-point format nearest but
    363    not larger in magnitude.  */
    364 #define trunc(Val) __TGMATH_UNARY_REAL_ONLY (Val, trunc)
    365 
    366 /* Compute remainder of X and Y and put in *QUO a value with sign of x/y
    367    and magnitude congruent `mod 2^n' to the magnitude of the integral
    368    quotient x/y, with n >= 3.  */
    369 #define remquo(Val1, Val2, Val3) \
    370      __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY (Val1, Val2, Val3, remquo)
    371 
    372 /* Round X to nearest integral value according to current rounding
    373    direction.  */
    374 #define lrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long int, lrint)
    375 #define llrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long long int, llrint)
    376 
    377 /* Round X to nearest integral value, rounding halfway cases away from
    378    zero.  */
    379 #define lround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long int, lround)
    380 #define llround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long long int, llround)
    381 
    382 
    383 /* Return X with its signed changed to Y's.  */
    384 #define copysign(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, copysign)
    385 
    386 /* Error and gamma functions.  */
    387 #define erf(Val) __TGMATH_UNARY_REAL_ONLY (Val, erf)
    388 #define erfc(Val) __TGMATH_UNARY_REAL_ONLY (Val, erfc)
    389 #define tgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, tgamma)
    390 #define lgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, lgamma)
    391 
    392 
    393 /* Return the integer nearest X in the direction of the
    394    prevailing rounding mode.  */
    395 #define rint(Val) __TGMATH_UNARY_REAL_ONLY (Val, rint)
    396 
    397 /* Return X + epsilon if X < Y, X - epsilon if X > Y.  */
    398 #define nextafter(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, nextafter)
    399 #define nexttoward(Val1, Val2) \
    400      __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, nexttoward)
    401 
    402 /* Return the remainder of integer divison X / Y with infinite precision.  */
    403 #define remainder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, remainder)
    404 
    405 /* Return X times (2 to the Nth power).  */
    406 #if defined __USE_MISC || defined __USE_XOPEN_EXTENDED
    407 # define scalb(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, scalb)
    408 #endif
    409 
    410 /* Return X times (2 to the Nth power).  */
    411 #define scalbn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbn)
    412 
    413 /* Return X times (2 to the Nth power).  */
    414 #define scalbln(Val1, Val2) \
    415      __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbln)
    416 
    417 /* Return the binary exponent of X, which must be nonzero.  */
    418 #define ilogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, int, ilogb)
    419 
    420 
    421 /* Return positive difference between X and Y.  */
    422 #define fdim(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fdim)
    423 
    424 /* Return maximum numeric value from X and Y.  */
    425 #define fmax(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmax)
    426 
    427 /* Return minimum numeric value from X and Y.  */
    428 #define fmin(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmin)
    429 
    430 
    431 /* Multiply-add function computed as a ternary operation.  */
    432 #define fma(Val1, Val2, Val3) \
    433      __TGMATH_TERNARY_REAL_ONLY (Val1, Val2, Val3, fma)
    434 
    435 
    436 /* Absolute value, conjugates, and projection.  */
    437 
    438 /* Argument value of Z.  */
    439 #define carg(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, carg, carg)
    440 
    441 /* Complex conjugate of Z.  */
    442 #define conj(Val) __TGMATH_UNARY_IMAG (Val, conj)
    443 
    444 /* Projection of Z onto the Riemann sphere.  */
    445 #define cproj(Val) __TGMATH_UNARY_IMAG (Val, cproj)
    446 
    447 
    448 /* Decomposing complex values.  */
    449 
    450 /* Imaginary part of Z.  */
    451 #define cimag(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, cimag, cimag)
    452 
    453 /* Real part of Z.  */
    454 #define creal(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, creal, creal)
    455 
    456 #endif /* tgmath.h */
    457