1/* Copyright (C) 1997-2022 Free Software Foundation, Inc.
2 This file is part of the GNU C Library.
3
4 The GNU C Library is free software; you can redistribute it and/or
5 modify it under the terms of the GNU Lesser General Public
6 License as published by the Free Software Foundation; either
7 version 2.1 of the License, or (at your option) any later version.
8
9 The GNU C Library is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 Lesser General Public License for more details.
13
14 You should have received a copy of the GNU Lesser General Public
15 License along with the GNU C Library; if not, see
16 <https://www.gnu.org/licenses/>. */
17
18/*
19 * ISO C99 Standard: 7.22 Type-generic math <tgmath.h>
20 */
21
22#ifndef _TGMATH_H
23#define _TGMATH_H 1
24
25#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
26#include <bits/libc-header-start.h>
27
28/* Include the needed headers. */
29#include <bits/floatn.h>
30#include <math.h>
31#include <complex.h>
32
33
34/* There are two variant implementations of type-generic macros in
35 this file: one for GCC 8 and later, using __builtin_tgmath and
36 where each macro expands each of its arguments only once, and one
37 for older GCC, using other compiler extensions but with macros
38 expanding their arguments many times (so resulting in exponential
39 blowup of the size of expansions when calls to such macros are
40 nested inside arguments to such macros). */
41
42#define __HAVE_BUILTIN_TGMATH __GNUC_PREREQ (8, 0)
43
44#if __GNUC_PREREQ (2, 7)
45
46/* Certain cases of narrowing macros only need to call a single
47 function so cannot use __builtin_tgmath and do not need any
48 complicated logic. */
49# if __HAVE_FLOAT128X
50# error "Unsupported _Float128x type for <tgmath.h>."
51# endif
52# if ((__HAVE_FLOAT64X && !__HAVE_FLOAT128) \
53 || (__HAVE_FLOAT128 && !__HAVE_FLOAT64X))
54# error "Unsupported combination of types for <tgmath.h>."
55# endif
56# define __TGMATH_1_NARROW_D(F, X) \
57 (F ## l (X))
58# define __TGMATH_2_NARROW_D(F, X, Y) \
59 (F ## l (X, Y))
60# define __TGMATH_3_NARROW_D(F, X, Y, Z) \
61 (F ## l (X, Y, Z))
62# define __TGMATH_1_NARROW_F64X(F, X) \
63 (F ## f128 (X))
64# define __TGMATH_2_NARROW_F64X(F, X, Y) \
65 (F ## f128 (X, Y))
66# define __TGMATH_3_NARROW_F64X(F, X, Y, Z) \
67 (F ## f128 (X, Y, Z))
68# if !__HAVE_FLOAT128
69# define __TGMATH_1_NARROW_F32X(F, X) \
70 (F ## f64 (X))
71# define __TGMATH_2_NARROW_F32X(F, X, Y) \
72 (F ## f64 (X, Y))
73# define __TGMATH_3_NARROW_F32X(F, X, Y, Z) \
74 (F ## f64 (X, Y, Z))
75# endif
76
77# if __HAVE_BUILTIN_TGMATH
78
79# if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
80# define __TG_F16_ARG(X) X ## f16,
81# else
82# define __TG_F16_ARG(X)
83# endif
84# if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
85# define __TG_F32_ARG(X) X ## f32,
86# else
87# define __TG_F32_ARG(X)
88# endif
89# if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
90# define __TG_F64_ARG(X) X ## f64,
91# else
92# define __TG_F64_ARG(X)
93# endif
94# if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
95# define __TG_F128_ARG(X) X ## f128,
96# else
97# define __TG_F128_ARG(X)
98# endif
99# if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
100# define __TG_F32X_ARG(X) X ## f32x,
101# else
102# define __TG_F32X_ARG(X)
103# endif
104# if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
105# define __TG_F64X_ARG(X) X ## f64x,
106# else
107# define __TG_F64X_ARG(X)
108# endif
109# if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
110# define __TG_F128X_ARG(X) X ## f128x,
111# else
112# define __TG_F128X_ARG(X)
113# endif
114
115# define __TGMATH_FUNCS(X) X ## f, X, X ## l, \
116 __TG_F16_ARG (X) __TG_F32_ARG (X) __TG_F64_ARG (X) __TG_F128_ARG (X) \
117 __TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
118# define __TGMATH_RCFUNCS(F, C) __TGMATH_FUNCS (F) __TGMATH_FUNCS (C)
119# define __TGMATH_1(F, X) __builtin_tgmath (__TGMATH_FUNCS (F) (X))
120# define __TGMATH_2(F, X, Y) __builtin_tgmath (__TGMATH_FUNCS (F) (X), (Y))
121# define __TGMATH_2STD(F, X, Y) __builtin_tgmath (F ## f, F, F ## l, (X), (Y))
122# define __TGMATH_3(F, X, Y, Z) __builtin_tgmath (__TGMATH_FUNCS (F) \
123 (X), (Y), (Z))
124# define __TGMATH_1C(F, C, X) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) (X))
125# define __TGMATH_2C(F, C, X, Y) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) \
126 (X), (Y))
127
128# define __TGMATH_NARROW_FUNCS_F(X) X, X ## l,
129# define __TGMATH_NARROW_FUNCS_F16(X) \
130 __TG_F32_ARG (X) __TG_F64_ARG (X) __TG_F128_ARG (X) \
131 __TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
132# define __TGMATH_NARROW_FUNCS_F32(X) \
133 __TG_F64_ARG (X) __TG_F128_ARG (X) \
134 __TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
135# define __TGMATH_NARROW_FUNCS_F64(X) \
136 __TG_F128_ARG (X) \
137 __TG_F64X_ARG (X) __TG_F128X_ARG (X)
138# define __TGMATH_NARROW_FUNCS_F32X(X) \
139 __TG_F64X_ARG (X) __TG_F128X_ARG (X) \
140 __TG_F64_ARG (X) __TG_F128_ARG (X)
141
142# define __TGMATH_1_NARROW_F(F, X) \
143 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F (F) (X))
144# define __TGMATH_2_NARROW_F(F, X, Y) \
145 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F (F) (X), (Y))
146# define __TGMATH_3_NARROW_F(F, X, Y, Z) \
147 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F (F) (X), (Y), (Z))
148# define __TGMATH_1_NARROW_F16(F, X) \
149 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F16 (F) (X))
150# define __TGMATH_2_NARROW_F16(F, X, Y) \
151 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F16 (F) (X), (Y))
152# define __TGMATH_3_NARROW_F16(F, X, Y, Z) \
153 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F16 (F) (X), (Y), (Z))
154# define __TGMATH_1_NARROW_F32(F, X) \
155 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32 (F) (X))
156# define __TGMATH_2_NARROW_F32(F, X, Y) \
157 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32 (F) (X), (Y))
158# define __TGMATH_3_NARROW_F32(F, X, Y, Z) \
159 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32 (F) (X), (Y), (Z))
160# define __TGMATH_1_NARROW_F64(F, X) \
161 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F64 (F) (X))
162# define __TGMATH_2_NARROW_F64(F, X, Y) \
163 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F64 (F) (X), (Y))
164# define __TGMATH_3_NARROW_F64(F, X, Y, Z) \
165 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F64 (F) (X), (Y), (Z))
166# if __HAVE_FLOAT128
167# define __TGMATH_1_NARROW_F32X(F, X) \
168 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32X (F) (X))
169# define __TGMATH_2_NARROW_F32X(F, X, Y) \
170 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32X (F) (X), (Y))
171# define __TGMATH_3_NARROW_F32X(F, X, Y, Z) \
172 __builtin_tgmath (__TGMATH_NARROW_FUNCS_F32X (F) (X), (Y), (Z))
173# endif
174
175# else /* !__HAVE_BUILTIN_TGMATH. */
176
177# ifdef __NO_LONG_DOUBLE_MATH
178# define __tgml(fct) fct
179# else
180# define __tgml(fct) fct ## l
181# endif
182
183/* __floating_type expands to 1 if TYPE is a floating type (including
184 complex floating types), 0 if TYPE is an integer type (including
185 complex integer types). __real_integer_type expands to 1 if TYPE
186 is a real integer type. __complex_integer_type expands to 1 if
187 TYPE is a complex integer type. All these macros expand to integer
188 constant expressions. All these macros can assume their argument
189 has an arithmetic type (not vector, decimal floating-point or
190 fixed-point), valid to pass to tgmath.h macros. */
191# if __GNUC_PREREQ (3, 1)
192/* __builtin_classify_type expands to an integer constant expression
193 in GCC 3.1 and later. Default conversions applied to the argument
194 of __builtin_classify_type mean it always returns 1 for real
195 integer types rather than ever returning different values for
196 character, boolean or enumerated types. */
197# define __floating_type(type) \
198 (__builtin_classify_type (__real__ ((type) 0)) == 8)
199# define __real_integer_type(type) \
200 (__builtin_classify_type ((type) 0) == 1)
201# define __complex_integer_type(type) \
202 (__builtin_classify_type ((type) 0) == 9 \
203 && __builtin_classify_type (__real__ ((type) 0)) == 1)
204# else
205/* GCC versions predating __builtin_classify_type are also looser on
206 what counts as an integer constant expression. */
207# define __floating_type(type) (((type) 1.25) != 1)
208# define __real_integer_type(type) (((type) (1.25 + _Complex_I)) == 1)
209# define __complex_integer_type(type) \
210 (((type) (1.25 + _Complex_I)) == (1 + _Complex_I))
211# endif
212
213/* Whether an expression (of arithmetic type) has a real type. */
214# define __expr_is_real(E) (__builtin_classify_type (E) != 9)
215
216/* The tgmath real type for T, where E is 0 if T is an integer type
217 and 1 for a floating type. If T has a complex type, it is
218 unspecified whether the return type is real or complex (but it has
219 the correct corresponding real type). */
220# define __tgmath_real_type_sub(T, E) \
221 __typeof__ (*(0 ? (__typeof__ (0 ? (double *) 0 : (void *) (E))) 0 \
222 : (__typeof__ (0 ? (T *) 0 : (void *) (!(E)))) 0))
223
224/* The tgmath real type of EXPR. */
225# define __tgmath_real_type(expr) \
226 __tgmath_real_type_sub (__typeof__ ((__typeof__ (+(expr))) 0), \
227 __floating_type (__typeof__ (+(expr))))
228
229/* The tgmath complex type for T, where E1 is 1 if T has a floating
230 type and 0 otherwise, E2 is 1 if T has a real integer type and 0
231 otherwise, and E3 is 1 if T has a complex type and 0 otherwise. */
232# define __tgmath_complex_type_sub(T, E1, E2, E3) \
233 __typeof__ (*(0 \
234 ? (__typeof__ (0 ? (T *) 0 : (void *) (!(E1)))) 0 \
235 : (__typeof__ (0 \
236 ? (__typeof__ (0 \
237 ? (double *) 0 \
238 : (void *) (!(E2)))) 0 \
239 : (__typeof__ (0 \
240 ? (_Complex double *) 0 \
241 : (void *) (!(E3)))) 0)) 0))
242
243/* The tgmath complex type of EXPR. */
244# define __tgmath_complex_type(expr) \
245 __tgmath_complex_type_sub (__typeof__ ((__typeof__ (+(expr))) 0), \
246 __floating_type (__typeof__ (+(expr))), \
247 __real_integer_type (__typeof__ (+(expr))), \
248 __complex_integer_type (__typeof__ (+(expr))))
249
250# if (__HAVE_DISTINCT_FLOAT16 \
251 || __HAVE_DISTINCT_FLOAT32 \
252 || __HAVE_DISTINCT_FLOAT64 \
253 || __HAVE_DISTINCT_FLOAT32X \
254 || __HAVE_DISTINCT_FLOAT64X \
255 || __HAVE_DISTINCT_FLOAT128X)
256# error "Unsupported _FloatN or _FloatNx types for <tgmath.h>."
257# endif
258
259/* Expand to text that checks if ARG_COMB has type _Float128, and if
260 so calls the appropriately suffixed FCT (which may include a cast),
261 or FCT and CFCT for complex functions, with arguments ARG_CALL. */
262# if __HAVE_DISTINCT_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
263# if (!__HAVE_FLOAT64X \
264 || __HAVE_FLOAT64X_LONG_DOUBLE \
265 || !__HAVE_FLOATN_NOT_TYPEDEF)
266# define __TGMATH_F128(arg_comb, fct, arg_call) \
267 __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128) \
268 ? fct ## f128 arg_call :
269# define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) \
270 __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
271 ? (__expr_is_real (arg_comb) \
272 ? fct ## f128 arg_call \
273 : cfct ## f128 arg_call) :
274# else
275/* _Float64x is a distinct type at the C language level, which must be
276 handled like _Float128. */
277# define __TGMATH_F128(arg_comb, fct, arg_call) \
278 (__builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128) \
279 || __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float64x)) \
280 ? fct ## f128 arg_call :
281# define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) \
282 (__builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
283 || __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), \
284 _Float64x)) \
285 ? (__expr_is_real (arg_comb) \
286 ? fct ## f128 arg_call \
287 : cfct ## f128 arg_call) :
288# endif
289# else
290# define __TGMATH_F128(arg_comb, fct, arg_call) /* Nothing. */
291# define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) /* Nothing. */
292# endif
293
294# endif /* !__HAVE_BUILTIN_TGMATH. */
295
296/* We have two kinds of generic macros: to support functions which are
297 only defined on real valued parameters and those which are defined
298 for complex functions as well. */
299# if __HAVE_BUILTIN_TGMATH
300
301# define __TGMATH_UNARY_REAL_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
302# define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
303# define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
304 __TGMATH_2 (Fct, (Val1), (Val2))
305# define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct) \
306 __TGMATH_2STD (Fct, (Val1), (Val2))
307# define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
308 __TGMATH_2 (Fct, (Val1), (Val2))
309# define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct) \
310 __TGMATH_2STD (Fct, (Val1), (Val2))
311# define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
312 __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
313# define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
314 __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
315# define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct) \
316 __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
317# define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
318 __TGMATH_1C (Fct, Cfct, (Val))
319# define __TGMATH_UNARY_IMAG(Val, Cfct) __TGMATH_1 (Cfct, (Val))
320# define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
321 __TGMATH_1C (Fct, Cfct, (Val))
322# define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct) \
323 __TGMATH_1 (Cfct, (Val))
324# define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
325 __TGMATH_2C (Fct, Cfct, (Val1), (Val2))
326
327# else /* !__HAVE_BUILTIN_TGMATH. */
328
329# define __TGMATH_UNARY_REAL_ONLY(Val, Fct) \
330 (__extension__ ((sizeof (+(Val)) == sizeof (double) \
331 || __builtin_classify_type (Val) != 8) \
332 ? (__tgmath_real_type (Val)) Fct (Val) \
333 : (sizeof (+(Val)) == sizeof (float)) \
334 ? (__tgmath_real_type (Val)) Fct##f (Val) \
335 : __TGMATH_F128 ((Val), (__tgmath_real_type (Val)) Fct, \
336 (Val)) \
337 (__tgmath_real_type (Val)) __tgml(Fct) (Val)))
338
339# define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) \
340 (__extension__ ((sizeof (+(Val)) == sizeof (double) \
341 || __builtin_classify_type (Val) != 8) \
342 ? Fct (Val) \
343 : (sizeof (+(Val)) == sizeof (float)) \
344 ? Fct##f (Val) \
345 : __TGMATH_F128 ((Val), Fct, (Val)) \
346 __tgml(Fct) (Val)))
347
348# define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
349 (__extension__ ((sizeof (+(Val1)) == sizeof (double) \
350 || __builtin_classify_type (Val1) != 8) \
351 ? (__tgmath_real_type (Val1)) Fct (Val1, Val2) \
352 : (sizeof (+(Val1)) == sizeof (float)) \
353 ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2) \
354 : __TGMATH_F128 ((Val1), (__tgmath_real_type (Val1)) Fct, \
355 (Val1, Val2)) \
356 (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
357
358# define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct) \
359 (__extension__ ((sizeof (+(Val1)) == sizeof (double) \
360 || __builtin_classify_type (Val1) != 8) \
361 ? (__tgmath_real_type (Val1)) Fct (Val1, Val2) \
362 : (sizeof (+(Val1)) == sizeof (float)) \
363 ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2) \
364 : (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
365
366# define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
367 (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double) \
368 && __builtin_classify_type ((Val1) + (Val2)) == 8) \
369 ? __TGMATH_F128 ((Val1) + (Val2), \
370 (__typeof \
371 ((__tgmath_real_type (Val1)) 0 \
372 + (__tgmath_real_type (Val2)) 0)) Fct, \
373 (Val1, Val2)) \
374 (__typeof ((__tgmath_real_type (Val1)) 0 \
375 + (__tgmath_real_type (Val2)) 0)) \
376 __tgml(Fct) (Val1, Val2) \
377 : (sizeof (+(Val1)) == sizeof (double) \
378 || sizeof (+(Val2)) == sizeof (double) \
379 || __builtin_classify_type (Val1) != 8 \
380 || __builtin_classify_type (Val2) != 8) \
381 ? (__typeof ((__tgmath_real_type (Val1)) 0 \
382 + (__tgmath_real_type (Val2)) 0)) \
383 Fct (Val1, Val2) \
384 : (__typeof ((__tgmath_real_type (Val1)) 0 \
385 + (__tgmath_real_type (Val2)) 0)) \
386 Fct##f (Val1, Val2)))
387
388# define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct) \
389 (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double) \
390 && __builtin_classify_type ((Val1) + (Val2)) == 8) \
391 ? (__typeof ((__tgmath_real_type (Val1)) 0 \
392 + (__tgmath_real_type (Val2)) 0)) \
393 __tgml(Fct) (Val1, Val2) \
394 : (sizeof (+(Val1)) == sizeof (double) \
395 || sizeof (+(Val2)) == sizeof (double) \
396 || __builtin_classify_type (Val1) != 8 \
397 || __builtin_classify_type (Val2) != 8) \
398 ? (__typeof ((__tgmath_real_type (Val1)) 0 \
399 + (__tgmath_real_type (Val2)) 0)) \
400 Fct (Val1, Val2) \
401 : (__typeof ((__tgmath_real_type (Val1)) 0 \
402 + (__tgmath_real_type (Val2)) 0)) \
403 Fct##f (Val1, Val2)))
404
405# define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
406 (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double) \
407 && __builtin_classify_type ((Val1) + (Val2)) == 8) \
408 ? __TGMATH_F128 ((Val1) + (Val2), \
409 (__typeof \
410 ((__tgmath_real_type (Val1)) 0 \
411 + (__tgmath_real_type (Val2)) 0)) Fct, \
412 (Val1, Val2, Val3)) \
413 (__typeof ((__tgmath_real_type (Val1)) 0 \
414 + (__tgmath_real_type (Val2)) 0)) \
415 __tgml(Fct) (Val1, Val2, Val3) \
416 : (sizeof (+(Val1)) == sizeof (double) \
417 || sizeof (+(Val2)) == sizeof (double) \
418 || __builtin_classify_type (Val1) != 8 \
419 || __builtin_classify_type (Val2) != 8) \
420 ? (__typeof ((__tgmath_real_type (Val1)) 0 \
421 + (__tgmath_real_type (Val2)) 0)) \
422 Fct (Val1, Val2, Val3) \
423 : (__typeof ((__tgmath_real_type (Val1)) 0 \
424 + (__tgmath_real_type (Val2)) 0)) \
425 Fct##f (Val1, Val2, Val3)))
426
427# define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
428 (__extension__ ((sizeof ((Val1) + (Val2) + (Val3)) > sizeof (double) \
429 && __builtin_classify_type ((Val1) + (Val2) + (Val3)) \
430 == 8) \
431 ? __TGMATH_F128 ((Val1) + (Val2) + (Val3), \
432 (__typeof \
433 ((__tgmath_real_type (Val1)) 0 \
434 + (__tgmath_real_type (Val2)) 0 \
435 + (__tgmath_real_type (Val3)) 0)) Fct, \
436 (Val1, Val2, Val3)) \
437 (__typeof ((__tgmath_real_type (Val1)) 0 \
438 + (__tgmath_real_type (Val2)) 0 \
439 + (__tgmath_real_type (Val3)) 0)) \
440 __tgml(Fct) (Val1, Val2, Val3) \
441 : (sizeof (+(Val1)) == sizeof (double) \
442 || sizeof (+(Val2)) == sizeof (double) \
443 || sizeof (+(Val3)) == sizeof (double) \
444 || __builtin_classify_type (Val1) != 8 \
445 || __builtin_classify_type (Val2) != 8 \
446 || __builtin_classify_type (Val3) != 8) \
447 ? (__typeof ((__tgmath_real_type (Val1)) 0 \
448 + (__tgmath_real_type (Val2)) 0 \
449 + (__tgmath_real_type (Val3)) 0)) \
450 Fct (Val1, Val2, Val3) \
451 : (__typeof ((__tgmath_real_type (Val1)) 0 \
452 + (__tgmath_real_type (Val2)) 0 \
453 + (__tgmath_real_type (Val3)) 0)) \
454 Fct##f (Val1, Val2, Val3)))
455
456# define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct) \
457 (__extension__ ((sizeof (+(Val1)) == sizeof (double) \
458 || __builtin_classify_type (Val1) != 8) \
459 ? Fct (Val1, Val2, Val3) \
460 : (sizeof (+(Val1)) == sizeof (float)) \
461 ? Fct##f (Val1, Val2, Val3) \
462 : __TGMATH_F128 ((Val1), Fct, (Val1, Val2, Val3)) \
463 __tgml(Fct) (Val1, Val2, Val3)))
464
465/* XXX This definition has to be changed as soon as the compiler understands
466 the imaginary keyword. */
467# define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
468 (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double) \
469 || __builtin_classify_type (__real__ (Val)) != 8) \
470 ? (__expr_is_real (Val) \
471 ? (__tgmath_complex_type (Val)) Fct (Val) \
472 : (__tgmath_complex_type (Val)) Cfct (Val)) \
473 : (sizeof (+__real__ (Val)) == sizeof (float)) \
474 ? (__expr_is_real (Val) \
475 ? (__tgmath_complex_type (Val)) Fct##f (Val) \
476 : (__tgmath_complex_type (Val)) Cfct##f (Val)) \
477 : __TGMATH_CF128 ((Val), \
478 (__tgmath_complex_type (Val)) Fct, \
479 (__tgmath_complex_type (Val)) Cfct, \
480 (Val)) \
481 (__expr_is_real (Val) \
482 ? (__tgmath_complex_type (Val)) __tgml(Fct) (Val) \
483 : (__tgmath_complex_type (Val)) __tgml(Cfct) (Val))))
484
485# define __TGMATH_UNARY_IMAG(Val, Cfct) \
486 (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double) \
487 || __builtin_classify_type (__real__ (Val)) != 8) \
488 ? (__typeof__ ((__tgmath_real_type (Val)) 0 \
489 + _Complex_I)) Cfct (Val) \
490 : (sizeof (+__real__ (Val)) == sizeof (float)) \
491 ? (__typeof__ ((__tgmath_real_type (Val)) 0 \
492 + _Complex_I)) Cfct##f (Val) \
493 : __TGMATH_F128 (__real__ (Val), \
494 (__typeof__ \
495 ((__tgmath_real_type (Val)) 0 \
496 + _Complex_I)) Cfct, (Val)) \
497 (__typeof__ ((__tgmath_real_type (Val)) 0 \
498 + _Complex_I)) __tgml(Cfct) (Val)))
499
500/* XXX This definition has to be changed as soon as the compiler understands
501 the imaginary keyword. */
502# define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
503 (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double) \
504 || __builtin_classify_type (__real__ (Val)) != 8) \
505 ? (__expr_is_real (Val) \
506 ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
507 Fct (Val) \
508 : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
509 Cfct (Val)) \
510 : (sizeof (+__real__ (Val)) == sizeof (float)) \
511 ? (__expr_is_real (Val) \
512 ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
513 Fct##f (Val) \
514 : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
515 Cfct##f (Val)) \
516 : __TGMATH_CF128 ((Val), \
517 (__typeof__ \
518 (__real__ \
519 (__tgmath_real_type (Val)) 0)) Fct, \
520 (__typeof__ \
521 (__real__ \
522 (__tgmath_real_type (Val)) 0)) Cfct, \
523 (Val)) \
524 (__expr_is_real (Val) \
525 ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0)) \
526 __tgml(Fct) (Val) \
527 : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0)) \
528 __tgml(Cfct) (Val))))
529# define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct) \
530 __TGMATH_UNARY_REAL_IMAG_RET_REAL ((Val), Cfct, Cfct)
531
532/* XXX This definition has to be changed as soon as the compiler understands
533 the imaginary keyword. */
534# define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
535 (__extension__ ((sizeof (__real__ (Val1) \
536 + __real__ (Val2)) > sizeof (double) \
537 && __builtin_classify_type (__real__ (Val1) \
538 + __real__ (Val2)) == 8) \
539 ? __TGMATH_CF128 ((Val1) + (Val2), \
540 (__typeof \
541 ((__tgmath_complex_type (Val1)) 0 \
542 + (__tgmath_complex_type (Val2)) 0)) \
543 Fct, \
544 (__typeof \
545 ((__tgmath_complex_type (Val1)) 0 \
546 + (__tgmath_complex_type (Val2)) 0)) \
547 Cfct, \
548 (Val1, Val2)) \
549 (__expr_is_real ((Val1) + (Val2)) \
550 ? (__typeof ((__tgmath_complex_type (Val1)) 0 \
551 + (__tgmath_complex_type (Val2)) 0)) \
552 __tgml(Fct) (Val1, Val2) \
553 : (__typeof ((__tgmath_complex_type (Val1)) 0 \
554 + (__tgmath_complex_type (Val2)) 0)) \
555 __tgml(Cfct) (Val1, Val2)) \
556 : (sizeof (+__real__ (Val1)) == sizeof (double) \
557 || sizeof (+__real__ (Val2)) == sizeof (double) \
558 || __builtin_classify_type (__real__ (Val1)) != 8 \
559 || __builtin_classify_type (__real__ (Val2)) != 8) \
560 ? (__expr_is_real ((Val1) + (Val2)) \
561 ? (__typeof ((__tgmath_complex_type (Val1)) 0 \
562 + (__tgmath_complex_type (Val2)) 0)) \
563 Fct (Val1, Val2) \
564 : (__typeof ((__tgmath_complex_type (Val1)) 0 \
565 + (__tgmath_complex_type (Val2)) 0)) \
566 Cfct (Val1, Val2)) \
567 : (__expr_is_real ((Val1) + (Val2)) \
568 ? (__typeof ((__tgmath_complex_type (Val1)) 0 \
569 + (__tgmath_complex_type (Val2)) 0)) \
570 Fct##f (Val1, Val2) \
571 : (__typeof ((__tgmath_complex_type (Val1)) 0 \
572 + (__tgmath_complex_type (Val2)) 0)) \
573 Cfct##f (Val1, Val2))))
574
575# define __TGMATH_1_NARROW_F(F, X) \
576 (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (double) \
577 ? F ## l (X) \
578 : F (X)))
579# define __TGMATH_2_NARROW_F(F, X, Y) \
580 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
581 + (__tgmath_real_type (Y)) 0) > sizeof (double) \
582 ? F ## l (X, Y) \
583 : F (X, Y)))
584# define __TGMATH_3_NARROW_F(F, X, Y, Z) \
585 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
586 + (__tgmath_real_type (Y)) 0 \
587 + (__tgmath_real_type (Z)) 0) > sizeof (double) \
588 ? F ## l (X, Y, Z) \
589 : F (X, Y, Z)))
590/* In most cases, these narrowing macro definitions based on sizeof
591 ensure that the function called has the right argument format, as
592 for other <tgmath.h> macros for compilers before GCC 8, but may not
593 have exactly the argument type (among the types with that format)
594 specified in the standard logic.
595
596 In the case of macros for _Float32x return type, when _Float64x
597 exists, _Float64 arguments should result in the *f64 function being
598 called while _Float32x arguments should result in the *f64x
599 function being called. These cases cannot be distinguished using
600 sizeof (or at all if the types are typedefs rather than different
601 types). However, for these functions it is OK (does not affect the
602 final result) to call a function with any argument format at least
603 as wide as all the floating-point arguments, unless that affects
604 rounding of integer arguments. Integer arguments are considered to
605 have type _Float64, so the *f64 functions are preferred for f32x*
606 macros when no argument has a wider floating-point type. */
607# if __HAVE_FLOAT64X_LONG_DOUBLE && __HAVE_DISTINCT_FLOAT128
608# define __TGMATH_1_NARROW_F32(F, X) \
609 (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
610 ? __TGMATH_F128 ((X), F, (X)) \
611 F ## f64x (X) \
612 : F ## f64 (X)))
613# define __TGMATH_2_NARROW_F32(F, X, Y) \
614 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
615 + (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
616 ? __TGMATH_F128 ((X) + (Y), F, (X, Y)) \
617 F ## f64x (X, Y) \
618 : F ## f64 (X, Y)))
619# define __TGMATH_3_NARROW_F32(F, X, Y, Z) \
620 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
621 + (__tgmath_real_type (Y)) 0 \
622 + (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
623 ? __TGMATH_F128 ((X) + (Y) + (Z), F, (X, Y, Z)) \
624 F ## f64x (X, Y, Z) \
625 : F ## f64 (X, Y, Z)))
626# define __TGMATH_1_NARROW_F64(F, X) \
627 (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
628 ? __TGMATH_F128 ((X), F, (X)) \
629 F ## f64x (X) \
630 : F ## f128 (X)))
631# define __TGMATH_2_NARROW_F64(F, X, Y) \
632 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
633 + (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
634 ? __TGMATH_F128 ((X) + (Y), F, (X, Y)) \
635 F ## f64x (X, Y) \
636 : F ## f128 (X, Y)))
637# define __TGMATH_3_NARROW_F64(F, X, Y, Z) \
638 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
639 + (__tgmath_real_type (Y)) 0 \
640 + (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
641 ? __TGMATH_F128 ((X) + (Y) + (Z), F, (X, Y, Z)) \
642 F ## f64x (X, Y, Z) \
643 : F ## f128 (X, Y, Z)))
644# define __TGMATH_1_NARROW_F32X(F, X) \
645 (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
646 ? __TGMATH_F128 ((X), F, (X)) \
647 F ## f64x (X) \
648 : F ## f64 (X)))
649# define __TGMATH_2_NARROW_F32X(F, X, Y) \
650 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
651 + (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
652 ? __TGMATH_F128 ((X) + (Y), F, (X, Y)) \
653 F ## f64x (X, Y) \
654 : F ## f64 (X, Y)))
655# define __TGMATH_3_NARROW_F32X(F, X, Y, Z) \
656 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
657 + (__tgmath_real_type (Y)) 0 \
658 + (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
659 ? __TGMATH_F128 ((X) + (Y) + (Z), F, (X, Y, Z)) \
660 F ## f64x (X, Y, Z) \
661 : F ## f64 (X, Y, Z)))
662# elif __HAVE_FLOAT128
663# define __TGMATH_1_NARROW_F32(F, X) \
664 (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float64) \
665 ? F ## f128 (X) \
666 : F ## f64 (X)))
667# define __TGMATH_2_NARROW_F32(F, X, Y) \
668 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
669 + (__tgmath_real_type (Y)) 0) > sizeof (_Float64) \
670 ? F ## f128 (X, Y) \
671 : F ## f64 (X, Y)))
672# define __TGMATH_3_NARROW_F32(F, X, Y, Z) \
673 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
674 + (__tgmath_real_type (Y)) 0 \
675 + (__tgmath_real_type (Z)) 0) > sizeof (_Float64) \
676 ? F ## f128 (X, Y, Z) \
677 : F ## f64 (X, Y, Z)))
678# define __TGMATH_1_NARROW_F64(F, X) \
679 (F ## f128 (X))
680# define __TGMATH_2_NARROW_F64(F, X, Y) \
681 (F ## f128 (X, Y))
682# define __TGMATH_3_NARROW_F64(F, X, Y, Z) \
683 (F ## f128 (X, Y, Z))
684# define __TGMATH_1_NARROW_F32X(F, X) \
685 (__extension__ (sizeof ((__tgmath_real_type (X)) 0) > sizeof (_Float32x) \
686 ? F ## f64x (X) \
687 : F ## f64 (X)))
688# define __TGMATH_2_NARROW_F32X(F, X, Y) \
689 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
690 + (__tgmath_real_type (Y)) 0) > sizeof (_Float32x) \
691 ? F ## f64x (X, Y) \
692 : F ## f64 (X, Y)))
693# define __TGMATH_3_NARROW_F32X(F, X, Y, Z) \
694 (__extension__ (sizeof ((__tgmath_real_type (X)) 0 \
695 + (__tgmath_real_type (Y)) 0 \
696 + (__tgmath_real_type (Z)) 0) > sizeof (_Float32x) \
697 ? F ## f64x (X, Y, Z) \
698 : F ## f64 (X, Y, Z)))
699# else
700# define __TGMATH_1_NARROW_F32(F, X) \
701 (F ## f64 (X))
702# define __TGMATH_2_NARROW_F32(F, X, Y) \
703 (F ## f64 (X, Y))
704# define __TGMATH_3_NARROW_F32(F, X, Y, Z) \
705 (F ## f64 (X, Y, Z))
706# endif
707# endif /* !__HAVE_BUILTIN_TGMATH. */
708#else
709# error "Unsupported compiler; you cannot use <tgmath.h>"
710#endif
711
712
713/* Unary functions defined for real and complex values. */
714
715
716/* Trigonometric functions. */
717
718/* Arc cosine of X. */
719#define acos(Val) __TGMATH_UNARY_REAL_IMAG (Val, acos, cacos)
720/* Arc sine of X. */
721#define asin(Val) __TGMATH_UNARY_REAL_IMAG (Val, asin, casin)
722/* Arc tangent of X. */
723#define atan(Val) __TGMATH_UNARY_REAL_IMAG (Val, atan, catan)
724/* Arc tangent of Y/X. */
725#define atan2(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2)
726
727/* Cosine of X. */
728#define cos(Val) __TGMATH_UNARY_REAL_IMAG (Val, cos, ccos)
729/* Sine of X. */
730#define sin(Val) __TGMATH_UNARY_REAL_IMAG (Val, sin, csin)
731/* Tangent of X. */
732#define tan(Val) __TGMATH_UNARY_REAL_IMAG (Val, tan, ctan)
733
734
735/* Hyperbolic functions. */
736
737/* Hyperbolic arc cosine of X. */
738#define acosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, acosh, cacosh)
739/* Hyperbolic arc sine of X. */
740#define asinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, asinh, casinh)
741/* Hyperbolic arc tangent of X. */
742#define atanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, atanh, catanh)
743
744/* Hyperbolic cosine of X. */
745#define cosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, cosh, ccosh)
746/* Hyperbolic sine of X. */
747#define sinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, sinh, csinh)
748/* Hyperbolic tangent of X. */
749#define tanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, tanh, ctanh)
750
751
752/* Exponential and logarithmic functions. */
753
754/* Exponential function of X. */
755#define exp(Val) __TGMATH_UNARY_REAL_IMAG (Val, exp, cexp)
756
757/* Break VALUE into a normalized fraction and an integral power of 2. */
758#define frexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, frexp)
759
760/* X times (two to the EXP power). */
761#define ldexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, ldexp)
762
763/* Natural logarithm of X. */
764#define log(Val) __TGMATH_UNARY_REAL_IMAG (Val, log, clog)
765
766/* Base-ten logarithm of X. */
767#ifdef __USE_GNU
768# define log10(Val) __TGMATH_UNARY_REAL_IMAG (Val, log10, clog10)
769#else
770# define log10(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10)
771#endif
772
773/* Return exp(X) - 1. */
774#define expm1(Val) __TGMATH_UNARY_REAL_ONLY (Val, expm1)
775
776/* Return log(1 + X). */
777#define log1p(Val) __TGMATH_UNARY_REAL_ONLY (Val, log1p)
778
779/* Return the base 2 signed integral exponent of X. */
780#define logb(Val) __TGMATH_UNARY_REAL_ONLY (Val, logb)
781
782/* Compute base-2 exponential of X. */
783#define exp2(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2)
784
785/* Compute base-2 logarithm of X. */
786#define log2(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2)
787
788#if __GLIBC_USE (IEC_60559_FUNCS_EXT_C2X)
789/* Compute exponent to base ten. */
790#define exp10(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp10)
791#endif
792
793
794/* Power functions. */
795
796/* Return X to the Y power. */
797#define pow(Val1, Val2) __TGMATH_BINARY_REAL_IMAG (Val1, Val2, pow, cpow)
798
799/* Return the square root of X. */
800#define sqrt(Val) __TGMATH_UNARY_REAL_IMAG (Val, sqrt, csqrt)
801
802/* Return `sqrt(X*X + Y*Y)'. */
803#define hypot(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, hypot)
804
805/* Return the cube root of X. */
806#define cbrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, cbrt)
807
808
809/* Nearest integer, absolute value, and remainder functions. */
810
811/* Smallest integral value not less than X. */
812#define ceil(Val) __TGMATH_UNARY_REAL_ONLY (Val, ceil)
813
814/* Absolute value of X. */
815#define fabs(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, fabs, cabs)
816
817/* Largest integer not greater than X. */
818#define floor(Val) __TGMATH_UNARY_REAL_ONLY (Val, floor)
819
820/* Floating-point modulo remainder of X/Y. */
821#define fmod(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmod)
822
823/* Round X to integral valuein floating-point format using current
824 rounding direction, but do not raise inexact exception. */
825#define nearbyint(Val) __TGMATH_UNARY_REAL_ONLY (Val, nearbyint)
826
827/* Round X to nearest integral value, rounding halfway cases away from
828 zero. */
829#define round(Val) __TGMATH_UNARY_REAL_ONLY (Val, round)
830
831/* Round X to the integral value in floating-point format nearest but
832 not larger in magnitude. */
833#define trunc(Val) __TGMATH_UNARY_REAL_ONLY (Val, trunc)
834
835/* Compute remainder of X and Y and put in *QUO a value with sign of x/y
836 and magnitude congruent `mod 2^n' to the magnitude of the integral
837 quotient x/y, with n >= 3. */
838#define remquo(Val1, Val2, Val3) \
839 __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY (Val1, Val2, Val3, remquo)
840
841/* Round X to nearest integral value according to current rounding
842 direction. */
843#define lrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lrint)
844#define llrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llrint)
845
846/* Round X to nearest integral value, rounding halfway cases away from
847 zero. */
848#define lround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lround)
849#define llround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llround)
850
851
852/* Return X with its signed changed to Y's. */
853#define copysign(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, copysign)
854
855/* Error and gamma functions. */
856#define erf(Val) __TGMATH_UNARY_REAL_ONLY (Val, erf)
857#define erfc(Val) __TGMATH_UNARY_REAL_ONLY (Val, erfc)
858#define tgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, tgamma)
859#define lgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, lgamma)
860
861
862/* Return the integer nearest X in the direction of the
863 prevailing rounding mode. */
864#define rint(Val) __TGMATH_UNARY_REAL_ONLY (Val, rint)
865
866#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
867/* Return X - epsilon. */
868# define nextdown(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextdown)
869/* Return X + epsilon. */
870# define nextup(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextup)
871#endif
872
873/* Return X + epsilon if X < Y, X - epsilon if X > Y. */
874#define nextafter(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, nextafter)
875#define nexttoward(Val1, Val2) \
876 __TGMATH_BINARY_FIRST_REAL_STD_ONLY (Val1, Val2, nexttoward)
877
878/* Return the remainder of integer divison X / Y with infinite precision. */
879#define remainder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, remainder)
880
881/* Return X times (2 to the Nth power). */
882#ifdef __USE_MISC
883# define scalb(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, scalb)
884#endif
885
886/* Return X times (2 to the Nth power). */
887#define scalbn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbn)
888
889/* Return X times (2 to the Nth power). */
890#define scalbln(Val1, Val2) \
891 __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbln)
892
893/* Return the binary exponent of X, which must be nonzero. */
894#define ilogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, ilogb)
895
896
897/* Return positive difference between X and Y. */
898#define fdim(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fdim)
899
900#if __GLIBC_USE (ISOC2X) && !defined __USE_GNU
901/* Return maximum numeric value from X and Y. */
902# define fmax(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, fmax)
903
904/* Return minimum numeric value from X and Y. */
905# define fmin(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, fmin)
906#else
907/* Return maximum numeric value from X and Y. */
908# define fmax(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmax)
909
910/* Return minimum numeric value from X and Y. */
911# define fmin(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmin)
912#endif
913
914
915/* Multiply-add function computed as a ternary operation. */
916#define fma(Val1, Val2, Val3) \
917 __TGMATH_TERNARY_REAL_ONLY (Val1, Val2, Val3, fma)
918
919#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
920/* Round X to nearest integer value, rounding halfway cases to even. */
921# define roundeven(Val) __TGMATH_UNARY_REAL_ONLY (Val, roundeven)
922
923# define fromfp(Val1, Val2, Val3) \
924 __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfp)
925
926# define ufromfp(Val1, Val2, Val3) \
927 __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfp)
928
929# define fromfpx(Val1, Val2, Val3) \
930 __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfpx)
931
932# define ufromfpx(Val1, Val2, Val3) \
933 __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfpx)
934
935/* Like ilogb, but returning long int. */
936# define llogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llogb)
937#endif
938
939#if __GLIBC_USE (IEC_60559_BFP_EXT)
940/* Return value with maximum magnitude. */
941# define fmaxmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaxmag)
942
943/* Return value with minimum magnitude. */
944# define fminmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminmag)
945#endif
946
947#if __GLIBC_USE (ISOC2X)
948/* Return maximum value from X and Y. */
949# define fmaximum(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum)
950
951/* Return minimum value from X and Y. */
952# define fminimum(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum)
953
954/* Return maximum numeric value from X and Y. */
955# define fmaximum_num(Val1, Val2) \
956 __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_num)
957
958/* Return minimum numeric value from X and Y. */
959# define fminimum_num(Val1, Val2) \
960 __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_num)
961
962/* Return value with maximum magnitude. */
963# define fmaximum_mag(Val1, Val2) \
964 __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_mag)
965
966/* Return value with minimum magnitude. */
967# define fminimum_mag(Val1, Val2) \
968 __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_mag)
969
970/* Return numeric value with maximum magnitude. */
971# define fmaximum_mag_num(Val1, Val2) \
972 __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaximum_mag_num)
973
974/* Return numeric value with minimum magnitude. */
975# define fminimum_mag_num(Val1, Val2) \
976 __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminimum_mag_num)
977#endif
978
979
980/* Absolute value, conjugates, and projection. */
981
982/* Argument value of Z. */
983#define carg(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, carg)
984
985/* Complex conjugate of Z. */
986#define conj(Val) __TGMATH_UNARY_IMAG (Val, conj)
987
988/* Projection of Z onto the Riemann sphere. */
989#define cproj(Val) __TGMATH_UNARY_IMAG (Val, cproj)
990
991
992/* Decomposing complex values. */
993
994/* Imaginary part of Z. */
995#define cimag(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, cimag)
996
997/* Real part of Z. */
998#define creal(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, creal)
999
1000
1001/* Narrowing functions. */
1002
1003#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
1004
1005/* Add. */
1006# define fadd(Val1, Val2) __TGMATH_2_NARROW_F (fadd, Val1, Val2)
1007# define dadd(Val1, Val2) __TGMATH_2_NARROW_D (dadd, Val1, Val2)
1008
1009/* Divide. */
1010# define fdiv(Val1, Val2) __TGMATH_2_NARROW_F (fdiv, Val1, Val2)
1011# define ddiv(Val1, Val2) __TGMATH_2_NARROW_D (ddiv, Val1, Val2)
1012
1013/* Multiply. */
1014# define fmul(Val1, Val2) __TGMATH_2_NARROW_F (fmul, Val1, Val2)
1015# define dmul(Val1, Val2) __TGMATH_2_NARROW_D (dmul, Val1, Val2)
1016
1017/* Subtract. */
1018# define fsub(Val1, Val2) __TGMATH_2_NARROW_F (fsub, Val1, Val2)
1019# define dsub(Val1, Val2) __TGMATH_2_NARROW_D (dsub, Val1, Val2)
1020
1021/* Square root. */
1022# define fsqrt(Val) __TGMATH_1_NARROW_F (fsqrt, Val)
1023# define dsqrt(Val) __TGMATH_1_NARROW_D (dsqrt, Val)
1024
1025/* Fused multiply-add. */
1026# define ffma(Val1, Val2, Val3) __TGMATH_3_NARROW_F (ffma, Val1, Val2, Val3)
1027# define dfma(Val1, Val2, Val3) __TGMATH_3_NARROW_D (dfma, Val1, Val2, Val3)
1028
1029#endif
1030
1031#if __GLIBC_USE (IEC_60559_TYPES_EXT)
1032
1033# if __HAVE_FLOAT16
1034# define f16add(Val1, Val2) __TGMATH_2_NARROW_F16 (f16add, Val1, Val2)
1035# define f16div(Val1, Val2) __TGMATH_2_NARROW_F16 (f16div, Val1, Val2)
1036# define f16mul(Val1, Val2) __TGMATH_2_NARROW_F16 (f16mul, Val1, Val2)
1037# define f16sub(Val1, Val2) __TGMATH_2_NARROW_F16 (f16sub, Val1, Val2)
1038# define f16sqrt(Val) __TGMATH_1_NARROW_F16 (f16sqrt, Val)
1039# define f16fma(Val1, Val2, Val3) \
1040 __TGMATH_3_NARROW_F16 (f16fma, Val1, Val2, Val3)
1041# endif
1042
1043# if __HAVE_FLOAT32
1044# define f32add(Val1, Val2) __TGMATH_2_NARROW_F32 (f32add, Val1, Val2)
1045# define f32div(Val1, Val2) __TGMATH_2_NARROW_F32 (f32div, Val1, Val2)
1046# define f32mul(Val1, Val2) __TGMATH_2_NARROW_F32 (f32mul, Val1, Val2)
1047# define f32sub(Val1, Val2) __TGMATH_2_NARROW_F32 (f32sub, Val1, Val2)
1048# define f32sqrt(Val) __TGMATH_1_NARROW_F32 (f32sqrt, Val)
1049# define f32fma(Val1, Val2, Val3) \
1050 __TGMATH_3_NARROW_F32 (f32fma, Val1, Val2, Val3)
1051# endif
1052
1053# if __HAVE_FLOAT64 && (__HAVE_FLOAT64X || __HAVE_FLOAT128)
1054# define f64add(Val1, Val2) __TGMATH_2_NARROW_F64 (f64add, Val1, Val2)
1055# define f64div(Val1, Val2) __TGMATH_2_NARROW_F64 (f64div, Val1, Val2)
1056# define f64mul(Val1, Val2) __TGMATH_2_NARROW_F64 (f64mul, Val1, Val2)
1057# define f64sub(Val1, Val2) __TGMATH_2_NARROW_F64 (f64sub, Val1, Val2)
1058# define f64sqrt(Val) __TGMATH_1_NARROW_F64 (f64sqrt, Val)
1059# define f64fma(Val1, Val2, Val3) \
1060 __TGMATH_3_NARROW_F64 (f64fma, Val1, Val2, Val3)
1061# endif
1062
1063# if __HAVE_FLOAT32X
1064# define f32xadd(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xadd, Val1, Val2)
1065# define f32xdiv(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xdiv, Val1, Val2)
1066# define f32xmul(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xmul, Val1, Val2)
1067# define f32xsub(Val1, Val2) __TGMATH_2_NARROW_F32X (f32xsub, Val1, Val2)
1068# define f32xsqrt(Val) __TGMATH_1_NARROW_F32X (f32xsqrt, Val)
1069# define f32xfma(Val1, Val2, Val3) \
1070 __TGMATH_3_NARROW_F32X (f32xfma, Val1, Val2, Val3)
1071# endif
1072
1073# if __HAVE_FLOAT64X && (__HAVE_FLOAT128X || __HAVE_FLOAT128)
1074# define f64xadd(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xadd, Val1, Val2)
1075# define f64xdiv(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xdiv, Val1, Val2)
1076# define f64xmul(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xmul, Val1, Val2)
1077# define f64xsub(Val1, Val2) __TGMATH_2_NARROW_F64X (f64xsub, Val1, Val2)
1078# define f64xsqrt(Val) __TGMATH_1_NARROW_F64X (f64xsqrt, Val)
1079# define f64xfma(Val1, Val2, Val3) \
1080 __TGMATH_3_NARROW_F64X (f64xfma, Val1, Val2, Val3)
1081# endif
1082
1083#endif
1084
1085#endif /* tgmath.h */
1086

source code of glibc/math/tgmath.h