--- /dev/null
+/* Copyright (C) 1997-2018 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+/*
+ * ISO C99 Standard: 7.22 Type-generic math <tgmath.h>
+ */
+
+#ifndef _TGMATH_H
+#define _TGMATH_H 1
+
+#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
+#include <bits/libc-header-start.h>
+
+/* Include the needed headers. */
+#include <bits/floatn.h>
+#include <math.h>
+#include <complex.h>
+
+
+/* There are two variant implementations of type-generic macros in
+ this file: one for GCC 8 and later, using __builtin_tgmath and
+ where each macro expands each of its arguments only once, and one
+ for older GCC, using other compiler extensions but with macros
+ expanding their arguments many times (so resulting in exponential
+ blowup of the size of expansions when calls to such macros are
+ nested inside arguments to such macros). */
+
+#define __HAVE_BUILTIN_TGMATH __GNUC_PREREQ (8, 0)
+
+#if __GNUC_PREREQ (2, 7)
+
+# if __HAVE_BUILTIN_TGMATH
+
+# if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define __TG_F16_ARG(X) X ## f16,
+# else
+# define __TG_F16_ARG(X)
+# endif
+# if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define __TG_F32_ARG(X) X ## f32,
+# else
+# define __TG_F32_ARG(X)
+# endif
+# if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define __TG_F64_ARG(X) X ## f64,
+# else
+# define __TG_F64_ARG(X)
+# endif
+# if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define __TG_F128_ARG(X) X ## f128,
+# else
+# define __TG_F128_ARG(X)
+# endif
+# if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define __TG_F32X_ARG(X) X ## f32x,
+# else
+# define __TG_F32X_ARG(X)
+# endif
+# if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define __TG_F64X_ARG(X) X ## f64x,
+# else
+# define __TG_F64X_ARG(X)
+# endif
+# if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define __TG_F128X_ARG(X) X ## f128x,
+# else
+# define __TG_F128X_ARG(X)
+# endif
+
+# define __TGMATH_FUNCS(X) X ## f, X, X ## l, \
+ __TG_F16_ARG (X) __TG_F32_ARG (X) __TG_F64_ARG (X) __TG_F128_ARG (X) \
+ __TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
+# define __TGMATH_RCFUNCS(F, C) __TGMATH_FUNCS (F) __TGMATH_FUNCS (C)
+# define __TGMATH_1(F, X) __builtin_tgmath (__TGMATH_FUNCS (F) (X))
+# define __TGMATH_2(F, X, Y) __builtin_tgmath (__TGMATH_FUNCS (F) (X), (Y))
+# define __TGMATH_2STD(F, X, Y) __builtin_tgmath (F ## f, F, F ## l, (X), (Y))
+# define __TGMATH_3(F, X, Y, Z) __builtin_tgmath (__TGMATH_FUNCS (F) \
+ (X), (Y), (Z))
+# define __TGMATH_1C(F, C, X) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) (X))
+# define __TGMATH_2C(F, C, X, Y) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) \
+ (X), (Y))
+
+# else /* !__HAVE_BUILTIN_TGMATH. */
+
+# ifdef __NO_LONG_DOUBLE_MATH
+# define __tgml(fct) fct
+# else
+# define __tgml(fct) fct ## l
+# endif
+
+/* __floating_type expands to 1 if TYPE is a floating type (including
+ complex floating types), 0 if TYPE is an integer type (including
+ complex integer types). __real_integer_type expands to 1 if TYPE
+ is a real integer type. __complex_integer_type expands to 1 if
+ TYPE is a complex integer type. All these macros expand to integer
+ constant expressions. All these macros can assume their argument
+ has an arithmetic type (not vector, decimal floating-point or
+ fixed-point), valid to pass to tgmath.h macros. */
+# if __GNUC_PREREQ (3, 1)
+/* __builtin_classify_type expands to an integer constant expression
+ in GCC 3.1 and later. Default conversions applied to the argument
+ of __builtin_classify_type mean it always returns 1 for real
+ integer types rather than ever returning different values for
+ character, boolean or enumerated types. */
+# define __floating_type(type) \
+ (__builtin_classify_type (__real__ ((type) 0)) == 8)
+# define __real_integer_type(type) \
+ (__builtin_classify_type ((type) 0) == 1)
+# define __complex_integer_type(type) \
+ (__builtin_classify_type ((type) 0) == 9 \
+ && __builtin_classify_type (__real__ ((type) 0)) == 1)
+# else
+/* GCC versions predating __builtin_classify_type are also looser on
+ what counts as an integer constant expression. */
+# define __floating_type(type) (((type) 1.25) != 1)
+# define __real_integer_type(type) (((type) (1.25 + _Complex_I)) == 1)
+# define __complex_integer_type(type) \
+ (((type) (1.25 + _Complex_I)) == (1 + _Complex_I))
+# endif
+
+/* Whether an expression (of arithmetic type) has a real type. */
+# define __expr_is_real(E) (__builtin_classify_type (E) != 9)
+
+/* The tgmath real type for T, where E is 0 if T is an integer type
+ and 1 for a floating type. If T has a complex type, it is
+ unspecified whether the return type is real or complex (but it has
+ the correct corresponding real type). */
+# define __tgmath_real_type_sub(T, E) \
+ __typeof__ (*(0 ? (__typeof__ (0 ? (double *) 0 : (void *) (E))) 0 \
+ : (__typeof__ (0 ? (T *) 0 : (void *) (!(E)))) 0))
+
+/* The tgmath real type of EXPR. */
+# define __tgmath_real_type(expr) \
+ __tgmath_real_type_sub (__typeof__ ((__typeof__ (+(expr))) 0), \
+ __floating_type (__typeof__ (+(expr))))
+
+/* The tgmath complex type for T, where E1 is 1 if T has a floating
+ type and 0 otherwise, E2 is 1 if T has a real integer type and 0
+ otherwise, and E3 is 1 if T has a complex type and 0 otherwise. */
+# define __tgmath_complex_type_sub(T, E1, E2, E3) \
+ __typeof__ (*(0 \
+ ? (__typeof__ (0 ? (T *) 0 : (void *) (!(E1)))) 0 \
+ : (__typeof__ (0 \
+ ? (__typeof__ (0 \
+ ? (double *) 0 \
+ : (void *) (!(E2)))) 0 \
+ : (__typeof__ (0 \
+ ? (_Complex double *) 0 \
+ : (void *) (!(E3)))) 0)) 0))
+
+/* The tgmath complex type of EXPR. */
+# define __tgmath_complex_type(expr) \
+ __tgmath_complex_type_sub (__typeof__ ((__typeof__ (+(expr))) 0), \
+ __floating_type (__typeof__ (+(expr))), \
+ __real_integer_type (__typeof__ (+(expr))), \
+ __complex_integer_type (__typeof__ (+(expr))))
+
+# if (__HAVE_DISTINCT_FLOAT16 \
+ || __HAVE_DISTINCT_FLOAT32 \
+ || __HAVE_DISTINCT_FLOAT64 \
+ || __HAVE_DISTINCT_FLOAT32X \
+ || __HAVE_DISTINCT_FLOAT64X \
+ || __HAVE_DISTINCT_FLOAT128X)
+# error "Unsupported _FloatN or _FloatNx types for <tgmath.h>."
+# endif
+
+/* Expand to text that checks if ARG_COMB has type _Float128, and if
+ so calls the appropriately suffixed FCT (which may include a cast),
+ or FCT and CFCT for complex functions, with arguments ARG_CALL. */
+# if __HAVE_DISTINCT_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# if (!__HAVE_FLOAT64X \
+ || __HAVE_FLOAT64X_LONG_DOUBLE \
+ || !__HAVE_FLOATN_NOT_TYPEDEF)
+# define __TGMATH_F128(arg_comb, fct, arg_call) \
+ __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128) \
+ ? fct ## f128 arg_call :
+# define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) \
+ __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
+ ? (__expr_is_real (arg_comb) \
+ ? fct ## f128 arg_call \
+ : cfct ## f128 arg_call) :
+# else
+/* _Float64x is a distinct type at the C language level, which must be
+ handled like _Float128. */
+# define __TGMATH_F128(arg_comb, fct, arg_call) \
+ (__builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128) \
+ || __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float64x)) \
+ ? fct ## f128 arg_call :
+# define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) \
+ (__builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
+ || __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), \
+ _Float64x)) \
+ ? (__expr_is_real (arg_comb) \
+ ? fct ## f128 arg_call \
+ : cfct ## f128 arg_call) :
+# endif
+# else
+# define __TGMATH_F128(arg_comb, fct, arg_call) /* Nothing. */
+# define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) /* Nothing. */
+# endif
+
+# endif /* !__HAVE_BUILTIN_TGMATH. */
+
+/* We have two kinds of generic macros: to support functions which are
+ only defined on real valued parameters and those which are defined
+ for complex functions as well. */
+# if __HAVE_BUILTIN_TGMATH
+
+# define __TGMATH_UNARY_REAL_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
+# define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
+# define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
+ __TGMATH_2 (Fct, (Val1), (Val2))
+# define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct) \
+ __TGMATH_2STD (Fct, (Val1), (Val2))
+# define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
+ __TGMATH_2 (Fct, (Val1), (Val2))
+# define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct) \
+ __TGMATH_2STD (Fct, (Val1), (Val2))
+# define __TGMATH_BINARY_REAL_RET_ONLY(Val1, Val2, Fct) \
+ __TGMATH_2 (Fct, (Val1), (Val2))
+# define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
+ __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
+# define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
+ __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
+# define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct) \
+ __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
+# define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
+ __TGMATH_1C (Fct, Cfct, (Val))
+# define __TGMATH_UNARY_IMAG(Val, Cfct) __TGMATH_1 (Cfct, (Val))
+# define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
+ __TGMATH_1C (Fct, Cfct, (Val))
+# define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct) \
+ __TGMATH_1 (Cfct, (Val))
+# define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
+ __TGMATH_2C (Fct, Cfct, (Val1), (Val2))
+
+# else /* !__HAVE_BUILTIN_TGMATH. */
+
+# define __TGMATH_UNARY_REAL_ONLY(Val, Fct) \
+ (__extension__ ((sizeof (+(Val)) == sizeof (double) \
+ || __builtin_classify_type (Val) != 8) \
+ ? (__tgmath_real_type (Val)) Fct (Val) \
+ : (sizeof (+(Val)) == sizeof (float)) \
+ ? (__tgmath_real_type (Val)) Fct##f (Val) \
+ : __TGMATH_F128 ((Val), (__tgmath_real_type (Val)) Fct, \
+ (Val)) \
+ (__tgmath_real_type (Val)) __tgml(Fct) (Val)))
+
+# define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) \
+ (__extension__ ((sizeof (+(Val)) == sizeof (double) \
+ || __builtin_classify_type (Val) != 8) \
+ ? Fct (Val) \
+ : (sizeof (+(Val)) == sizeof (float)) \
+ ? Fct##f (Val) \
+ : __TGMATH_F128 ((Val), Fct, (Val)) \
+ __tgml(Fct) (Val)))
+
+# define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
+ (__extension__ ((sizeof (+(Val1)) == sizeof (double) \
+ || __builtin_classify_type (Val1) != 8) \
+ ? (__tgmath_real_type (Val1)) Fct (Val1, Val2) \
+ : (sizeof (+(Val1)) == sizeof (float)) \
+ ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2) \
+ : __TGMATH_F128 ((Val1), (__tgmath_real_type (Val1)) Fct, \
+ (Val1, Val2)) \
+ (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
+
+# define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct) \
+ (__extension__ ((sizeof (+(Val1)) == sizeof (double) \
+ || __builtin_classify_type (Val1) != 8) \
+ ? (__tgmath_real_type (Val1)) Fct (Val1, Val2) \
+ : (sizeof (+(Val1)) == sizeof (float)) \
+ ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2) \
+ : (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
+
+# define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
+ (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double) \
+ && __builtin_classify_type ((Val1) + (Val2)) == 8) \
+ ? __TGMATH_F128 ((Val1) + (Val2), \
+ (__typeof \
+ ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) Fct, \
+ (Val1, Val2)) \
+ (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) \
+ __tgml(Fct) (Val1, Val2) \
+ : (sizeof (+(Val1)) == sizeof (double) \
+ || sizeof (+(Val2)) == sizeof (double) \
+ || __builtin_classify_type (Val1) != 8 \
+ || __builtin_classify_type (Val2) != 8) \
+ ? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) \
+ Fct (Val1, Val2) \
+ : (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) \
+ Fct##f (Val1, Val2)))
+
+# define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct) \
+ (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double) \
+ && __builtin_classify_type ((Val1) + (Val2)) == 8) \
+ ? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) \
+ __tgml(Fct) (Val1, Val2) \
+ : (sizeof (+(Val1)) == sizeof (double) \
+ || sizeof (+(Val2)) == sizeof (double) \
+ || __builtin_classify_type (Val1) != 8 \
+ || __builtin_classify_type (Val2) != 8) \
+ ? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) \
+ Fct (Val1, Val2) \
+ : (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) \
+ Fct##f (Val1, Val2)))
+
+# define __TGMATH_BINARY_REAL_RET_ONLY(Val1, Val2, Fct) \
+ (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double) \
+ && __builtin_classify_type ((Val1) + (Val2)) == 8) \
+ ? __TGMATH_F128 ((Val1) + (Val2), Fct, (Val1, Val2)) \
+ __tgml(Fct) (Val1, Val2) \
+ : (sizeof (+(Val1)) == sizeof (double) \
+ || sizeof (+(Val2)) == sizeof (double) \
+ || __builtin_classify_type (Val1) != 8 \
+ || __builtin_classify_type (Val2) != 8) \
+ ? Fct (Val1, Val2) \
+ : Fct##f (Val1, Val2)))
+
+# define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
+ (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double) \
+ && __builtin_classify_type ((Val1) + (Val2)) == 8) \
+ ? __TGMATH_F128 ((Val1) + (Val2), \
+ (__typeof \
+ ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) Fct, \
+ (Val1, Val2, Val3)) \
+ (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) \
+ __tgml(Fct) (Val1, Val2, Val3) \
+ : (sizeof (+(Val1)) == sizeof (double) \
+ || sizeof (+(Val2)) == sizeof (double) \
+ || __builtin_classify_type (Val1) != 8 \
+ || __builtin_classify_type (Val2) != 8) \
+ ? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) \
+ Fct (Val1, Val2, Val3) \
+ : (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0)) \
+ Fct##f (Val1, Val2, Val3)))
+
+# define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
+ (__extension__ ((sizeof ((Val1) + (Val2) + (Val3)) > sizeof (double) \
+ && __builtin_classify_type ((Val1) + (Val2) + (Val3)) \
+ == 8) \
+ ? __TGMATH_F128 ((Val1) + (Val2) + (Val3), \
+ (__typeof \
+ ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0 \
+ + (__tgmath_real_type (Val3)) 0)) Fct, \
+ (Val1, Val2, Val3)) \
+ (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0 \
+ + (__tgmath_real_type (Val3)) 0)) \
+ __tgml(Fct) (Val1, Val2, Val3) \
+ : (sizeof (+(Val1)) == sizeof (double) \
+ || sizeof (+(Val2)) == sizeof (double) \
+ || sizeof (+(Val3)) == sizeof (double) \
+ || __builtin_classify_type (Val1) != 8 \
+ || __builtin_classify_type (Val2) != 8 \
+ || __builtin_classify_type (Val3) != 8) \
+ ? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0 \
+ + (__tgmath_real_type (Val3)) 0)) \
+ Fct (Val1, Val2, Val3) \
+ : (__typeof ((__tgmath_real_type (Val1)) 0 \
+ + (__tgmath_real_type (Val2)) 0 \
+ + (__tgmath_real_type (Val3)) 0)) \
+ Fct##f (Val1, Val2, Val3)))
+
+# define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct) \
+ (__extension__ ((sizeof (+(Val1)) == sizeof (double) \
+ || __builtin_classify_type (Val1) != 8) \
+ ? Fct (Val1, Val2, Val3) \
+ : (sizeof (+(Val1)) == sizeof (float)) \
+ ? Fct##f (Val1, Val2, Val3) \
+ : __TGMATH_F128 ((Val1), Fct, (Val1, Val2, Val3)) \
+ __tgml(Fct) (Val1, Val2, Val3)))
+
+/* XXX This definition has to be changed as soon as the compiler understands
+ the imaginary keyword. */
+# define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
+ (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double) \
+ || __builtin_classify_type (__real__ (Val)) != 8) \
+ ? (__expr_is_real (Val) \
+ ? (__tgmath_complex_type (Val)) Fct (Val) \
+ : (__tgmath_complex_type (Val)) Cfct (Val)) \
+ : (sizeof (+__real__ (Val)) == sizeof (float)) \
+ ? (__expr_is_real (Val) \
+ ? (__tgmath_complex_type (Val)) Fct##f (Val) \
+ : (__tgmath_complex_type (Val)) Cfct##f (Val)) \
+ : __TGMATH_CF128 ((Val), \
+ (__tgmath_complex_type (Val)) Fct, \
+ (__tgmath_complex_type (Val)) Cfct, \
+ (Val)) \
+ (__expr_is_real (Val) \
+ ? (__tgmath_complex_type (Val)) __tgml(Fct) (Val) \
+ : (__tgmath_complex_type (Val)) __tgml(Cfct) (Val))))
+
+# define __TGMATH_UNARY_IMAG(Val, Cfct) \
+ (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double) \
+ || __builtin_classify_type (__real__ (Val)) != 8) \
+ ? (__typeof__ ((__tgmath_real_type (Val)) 0 \
+ + _Complex_I)) Cfct (Val) \
+ : (sizeof (+__real__ (Val)) == sizeof (float)) \
+ ? (__typeof__ ((__tgmath_real_type (Val)) 0 \
+ + _Complex_I)) Cfct##f (Val) \
+ : __TGMATH_F128 (__real__ (Val), \
+ (__typeof__ \
+ ((__tgmath_real_type (Val)) 0 \
+ + _Complex_I)) Cfct, (Val)) \
+ (__typeof__ ((__tgmath_real_type (Val)) 0 \
+ + _Complex_I)) __tgml(Cfct) (Val)))
+
+/* XXX This definition has to be changed as soon as the compiler understands
+ the imaginary keyword. */
+# define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
+ (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double) \
+ || __builtin_classify_type (__real__ (Val)) != 8) \
+ ? (__expr_is_real (Val) \
+ ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
+ Fct (Val) \
+ : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
+ Cfct (Val)) \
+ : (sizeof (+__real__ (Val)) == sizeof (float)) \
+ ? (__expr_is_real (Val) \
+ ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
+ Fct##f (Val) \
+ : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
+ Cfct##f (Val)) \
+ : __TGMATH_CF128 ((Val), \
+ (__typeof__ \
+ (__real__ \
+ (__tgmath_real_type (Val)) 0)) Fct, \
+ (__typeof__ \
+ (__real__ \
+ (__tgmath_real_type (Val)) 0)) Cfct, \
+ (Val)) \
+ (__expr_is_real (Val) \
+ ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0)) \
+ __tgml(Fct) (Val) \
+ : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0)) \
+ __tgml(Cfct) (Val))))
+# define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct) \
+ __TGMATH_UNARY_REAL_IMAG_RET_REAL ((Val), Cfct, Cfct)
+
+/* XXX This definition has to be changed as soon as the compiler understands
+ the imaginary keyword. */
+# define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
+ (__extension__ ((sizeof (__real__ (Val1) \
+ + __real__ (Val2)) > sizeof (double) \
+ && __builtin_classify_type (__real__ (Val1) \
+ + __real__ (Val2)) == 8) \
+ ? __TGMATH_CF128 ((Val1) + (Val2), \
+ (__typeof \
+ ((__tgmath_complex_type (Val1)) 0 \
+ + (__tgmath_complex_type (Val2)) 0)) \
+ Fct, \
+ (__typeof \
+ ((__tgmath_complex_type (Val1)) 0 \
+ + (__tgmath_complex_type (Val2)) 0)) \
+ Cfct, \
+ (Val1, Val2)) \
+ (__expr_is_real ((Val1) + (Val2)) \
+ ? (__typeof ((__tgmath_complex_type (Val1)) 0 \
+ + (__tgmath_complex_type (Val2)) 0)) \
+ __tgml(Fct) (Val1, Val2) \
+ : (__typeof ((__tgmath_complex_type (Val1)) 0 \
+ + (__tgmath_complex_type (Val2)) 0)) \
+ __tgml(Cfct) (Val1, Val2)) \
+ : (sizeof (+__real__ (Val1)) == sizeof (double) \
+ || sizeof (+__real__ (Val2)) == sizeof (double) \
+ || __builtin_classify_type (__real__ (Val1)) != 8 \
+ || __builtin_classify_type (__real__ (Val2)) != 8) \
+ ? (__expr_is_real ((Val1) + (Val2)) \
+ ? (__typeof ((__tgmath_complex_type (Val1)) 0 \
+ + (__tgmath_complex_type (Val2)) 0)) \
+ Fct (Val1, Val2) \
+ : (__typeof ((__tgmath_complex_type (Val1)) 0 \
+ + (__tgmath_complex_type (Val2)) 0)) \
+ Cfct (Val1, Val2)) \
+ : (__expr_is_real ((Val1) + (Val2)) \
+ ? (__typeof ((__tgmath_complex_type (Val1)) 0 \
+ + (__tgmath_complex_type (Val2)) 0)) \
+ Fct##f (Val1, Val2) \
+ : (__typeof ((__tgmath_complex_type (Val1)) 0 \
+ + (__tgmath_complex_type (Val2)) 0)) \
+ Cfct##f (Val1, Val2))))
+# endif /* !__HAVE_BUILTIN_TGMATH. */
+#else
+# error "Unsupported compiler; you cannot use <tgmath.h>"
+#endif
+
+
+/* Unary functions defined for real and complex values. */
+
+
+/* Trigonometric functions. */
+
+/* Arc cosine of X. */
+#define acos(Val) __TGMATH_UNARY_REAL_IMAG (Val, acos, cacos)
+/* Arc sine of X. */
+#define asin(Val) __TGMATH_UNARY_REAL_IMAG (Val, asin, casin)
+/* Arc tangent of X. */
+#define atan(Val) __TGMATH_UNARY_REAL_IMAG (Val, atan, catan)
+/* Arc tangent of Y/X. */
+#define atan2(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2)
+
+/* Cosine of X. */
+#define cos(Val) __TGMATH_UNARY_REAL_IMAG (Val, cos, ccos)
+/* Sine of X. */
+#define sin(Val) __TGMATH_UNARY_REAL_IMAG (Val, sin, csin)
+/* Tangent of X. */
+#define tan(Val) __TGMATH_UNARY_REAL_IMAG (Val, tan, ctan)
+
+
+/* Hyperbolic functions. */
+
+/* Hyperbolic arc cosine of X. */
+#define acosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, acosh, cacosh)
+/* Hyperbolic arc sine of X. */
+#define asinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, asinh, casinh)
+/* Hyperbolic arc tangent of X. */
+#define atanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, atanh, catanh)
+
+/* Hyperbolic cosine of X. */
+#define cosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, cosh, ccosh)
+/* Hyperbolic sine of X. */
+#define sinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, sinh, csinh)
+/* Hyperbolic tangent of X. */
+#define tanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, tanh, ctanh)
+
+
+/* Exponential and logarithmic functions. */
+
+/* Exponential function of X. */
+#define exp(Val) __TGMATH_UNARY_REAL_IMAG (Val, exp, cexp)
+
+/* Break VALUE into a normalized fraction and an integral power of 2. */
+#define frexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, frexp)
+
+/* X times (two to the EXP power). */
+#define ldexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, ldexp)
+
+/* Natural logarithm of X. */
+#define log(Val) __TGMATH_UNARY_REAL_IMAG (Val, log, clog)
+
+/* Base-ten logarithm of X. */
+#ifdef __USE_GNU
+# define log10(Val) __TGMATH_UNARY_REAL_IMAG (Val, log10, clog10)
+#else
+# define log10(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10)
+#endif
+
+/* Return exp(X) - 1. */
+#define expm1(Val) __TGMATH_UNARY_REAL_ONLY (Val, expm1)
+
+/* Return log(1 + X). */
+#define log1p(Val) __TGMATH_UNARY_REAL_ONLY (Val, log1p)
+
+/* Return the base 2 signed integral exponent of X. */
+#define logb(Val) __TGMATH_UNARY_REAL_ONLY (Val, logb)
+
+/* Compute base-2 exponential of X. */
+#define exp2(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2)
+
+/* Compute base-2 logarithm of X. */
+#define log2(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2)
+
+
+/* Power functions. */
+
+/* Return X to the Y power. */
+#define pow(Val1, Val2) __TGMATH_BINARY_REAL_IMAG (Val1, Val2, pow, cpow)
+
+/* Return the square root of X. */
+#define sqrt(Val) __TGMATH_UNARY_REAL_IMAG (Val, sqrt, csqrt)
+
+/* Return `sqrt(X*X + Y*Y)'. */
+#define hypot(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, hypot)
+
+/* Return the cube root of X. */
+#define cbrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, cbrt)
+
+
+/* Nearest integer, absolute value, and remainder functions. */
+
+/* Smallest integral value not less than X. */
+#define ceil(Val) __TGMATH_UNARY_REAL_ONLY (Val, ceil)
+
+/* Absolute value of X. */
+#define fabs(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, fabs, cabs)
+
+/* Largest integer not greater than X. */
+#define floor(Val) __TGMATH_UNARY_REAL_ONLY (Val, floor)
+
+/* Floating-point modulo remainder of X/Y. */
+#define fmod(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmod)
+
+/* Round X to integral valuein floating-point format using current
+ rounding direction, but do not raise inexact exception. */
+#define nearbyint(Val) __TGMATH_UNARY_REAL_ONLY (Val, nearbyint)
+
+/* Round X to nearest integral value, rounding halfway cases away from
+ zero. */
+#define round(Val) __TGMATH_UNARY_REAL_ONLY (Val, round)
+
+/* Round X to the integral value in floating-point format nearest but
+ not larger in magnitude. */
+#define trunc(Val) __TGMATH_UNARY_REAL_ONLY (Val, trunc)
+
+/* Compute remainder of X and Y and put in *QUO a value with sign of x/y
+ and magnitude congruent `mod 2^n' to the magnitude of the integral
+ quotient x/y, with n >= 3. */
+#define remquo(Val1, Val2, Val3) \
+ __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY (Val1, Val2, Val3, remquo)
+
+/* Round X to nearest integral value according to current rounding
+ direction. */
+#define lrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lrint)
+#define llrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llrint)
+
+/* Round X to nearest integral value, rounding halfway cases away from
+ zero. */
+#define lround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lround)
+#define llround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llround)
+
+
+/* Return X with its signed changed to Y's. */
+#define copysign(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, copysign)
+
+/* Error and gamma functions. */
+#define erf(Val) __TGMATH_UNARY_REAL_ONLY (Val, erf)
+#define erfc(Val) __TGMATH_UNARY_REAL_ONLY (Val, erfc)
+#define tgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, tgamma)
+#define lgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, lgamma)
+
+
+/* Return the integer nearest X in the direction of the
+ prevailing rounding mode. */
+#define rint(Val) __TGMATH_UNARY_REAL_ONLY (Val, rint)
+
+#if __GLIBC_USE (IEC_60559_BFP_EXT)
+/* Return X - epsilon. */
+# define nextdown(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextdown)
+/* Return X + epsilon. */
+# define nextup(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextup)
+#endif
+
+/* Return X + epsilon if X < Y, X - epsilon if X > Y. */
+#define nextafter(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, nextafter)
+#define nexttoward(Val1, Val2) \
+ __TGMATH_BINARY_FIRST_REAL_STD_ONLY (Val1, Val2, nexttoward)
+
+/* Return the remainder of integer divison X / Y with infinite precision. */
+#define remainder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, remainder)
+
+/* Return X times (2 to the Nth power). */
+#ifdef __USE_MISC
+# define scalb(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, scalb)
+#endif
+
+/* Return X times (2 to the Nth power). */
+#define scalbn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbn)
+
+/* Return X times (2 to the Nth power). */
+#define scalbln(Val1, Val2) \
+ __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbln)
+
+/* Return the binary exponent of X, which must be nonzero. */
+#define ilogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, ilogb)
+
+
+/* Return positive difference between X and Y. */
+#define fdim(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fdim)
+
+/* Return maximum numeric value from X and Y. */
+#define fmax(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmax)
+
+/* Return minimum numeric value from X and Y. */
+#define fmin(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmin)
+
+
+/* Multiply-add function computed as a ternary operation. */
+#define fma(Val1, Val2, Val3) \
+ __TGMATH_TERNARY_REAL_ONLY (Val1, Val2, Val3, fma)
+
+#if __GLIBC_USE (IEC_60559_BFP_EXT)
+/* Round X to nearest integer value, rounding halfway cases to even. */
+# define roundeven(Val) __TGMATH_UNARY_REAL_ONLY (Val, roundeven)
+
+# define fromfp(Val1, Val2, Val3) \
+ __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfp)
+
+# define ufromfp(Val1, Val2, Val3) \
+ __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfp)
+
+# define fromfpx(Val1, Val2, Val3) \
+ __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfpx)
+
+# define ufromfpx(Val1, Val2, Val3) \
+ __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfpx)
+
+/* Like ilogb, but returning long int. */
+# define llogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llogb)
+
+/* Return value with maximum magnitude. */
+# define fmaxmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaxmag)
+
+/* Return value with minimum magnitude. */
+# define fminmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminmag)
+
+/* Total order operation. */
+# define totalorder(Val1, Val2) \
+ __TGMATH_BINARY_REAL_RET_ONLY (Val1, Val2, totalorder)
+
+/* Total order operation on absolute values. */
+# define totalordermag(Val1, Val2) \
+ __TGMATH_BINARY_REAL_RET_ONLY (Val1, Val2, totalordermag)
+#endif
+
+
+/* Absolute value, conjugates, and projection. */
+
+/* Argument value of Z. */
+#define carg(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, carg)
+
+/* Complex conjugate of Z. */
+#define conj(Val) __TGMATH_UNARY_IMAG (Val, conj)
+
+/* Projection of Z onto the Riemann sphere. */
+#define cproj(Val) __TGMATH_UNARY_IMAG (Val, cproj)
+
+
+/* Decomposing complex values. */
+
+/* Imaginary part of Z. */
+#define cimag(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, cimag)
+
+/* Real part of Z. */
+#define creal(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, creal)
+
+#endif /* tgmath.h */
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