1/* Prototype declarations for math functions; helper file for <math.h>. 
2 Copyright (C) 1996-2022 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, see 
17 <https://www.gnu.org/licenses/>. */ 
18 
19/* NOTE: Because of the special way this file is used by <math.h>, this 
20 file must NOT be protected from multiple inclusion as header files 
21 usually are. 
22 
23 This file provides prototype declarations for the math functions. 
24 Most functions are declared using the macro: 
25 
26 __MATHCALL (NAME,[_r], (ARGS...)); 
27 
28 This means there is a function `NAME' returning `double' and a function 
29 `NAMEf' returning `float'. Each place `_Mdouble_' appears in the 
30 prototype, that is actually `double' in the prototype for `NAME' and 
31 `float' in the prototype for `NAMEf'. Reentrant variant functions are 
32 called `NAME_r' and `NAMEf_r'. 
33 
34 Functions returning other types like `int' are declared using the macro: 
35 
36 __MATHDECL (TYPE, NAME,[_r], (ARGS...)); 
37 
38 This is just like __MATHCALL but for a function returning `TYPE' 
39 instead of `_Mdouble_'. In all of these cases, there is still 
40 both a `NAME' and a `NAMEf' that takes `float' arguments. 
41 
42 Note that there must be no whitespace before the argument passed for 
43 NAME, to make token pasting work with -traditional. */ 
44 
45#ifndef _MATH_H 
46# error "Never include <bits/mathcalls.h> directly; include <math.h> instead." 
47#endif 
48 
49 
50/* Trigonometric functions. */ 
51 
52/* Arc cosine of X. */ 
53__MATHCALL_VEC (acos,, (_Mdouble_ __x)); 
54/* Arc sine of X. */ 
55__MATHCALL_VEC (asin,, (_Mdouble_ __x)); 
56/* Arc tangent of X. */ 
57__MATHCALL_VEC (atan,, (_Mdouble_ __x)); 
58/* Arc tangent of Y/X. */ 
59__MATHCALL_VEC (atan2,, (_Mdouble_ __y, _Mdouble_ __x)); 
60 
61/* Cosine of X. */ 
62__MATHCALL_VEC (cos,, (_Mdouble_ __x)); 
63/* Sine of X. */ 
64__MATHCALL_VEC (sin,, (_Mdouble_ __x)); 
65/* Tangent of X. */ 
66__MATHCALL_VEC (tan,, (_Mdouble_ __x)); 
67 
68/* Hyperbolic functions. */ 
69 
70/* Hyperbolic cosine of X. */ 
71__MATHCALL_VEC (cosh,, (_Mdouble_ __x)); 
72/* Hyperbolic sine of X. */ 
73__MATHCALL_VEC (sinh,, (_Mdouble_ __x)); 
74/* Hyperbolic tangent of X. */ 
75__MATHCALL_VEC (tanh,, (_Mdouble_ __x)); 
76 
77#ifdef __USE_GNU 
78/* Cosine and sine of X. */ 
79__MATHDECL_VEC (void,sincos,, 
80 (_Mdouble_ __x, _Mdouble_ *__sinx, _Mdouble_ *__cosx)); 
81#endif 
82 
83#if defined __USE_XOPEN_EXTENDED || defined __USE_ISOC99 
84/* Hyperbolic arc cosine of X. */ 
85__MATHCALL_VEC (acosh,, (_Mdouble_ __x)); 
86/* Hyperbolic arc sine of X. */ 
87__MATHCALL_VEC (asinh,, (_Mdouble_ __x)); 
88/* Hyperbolic arc tangent of X. */ 
89__MATHCALL_VEC (atanh,, (_Mdouble_ __x)); 
90#endif 
91 
92/* Exponential and logarithmic functions. */ 
93 
94/* Exponential function of X. */ 
95__MATHCALL_VEC (exp,, (_Mdouble_ __x)); 
96 
97/* Break VALUE into a normalized fraction and an integral power of 2. */ 
98__MATHCALL (frexp,, (_Mdouble_ __x, int *__exponent)); 
99 
100/* X times (two to the EXP power). */ 
101__MATHCALL (ldexp,, (_Mdouble_ __x, int __exponent)); 
102 
103/* Natural logarithm of X. */ 
104__MATHCALL_VEC (log,, (_Mdouble_ __x)); 
105 
106/* Base-ten logarithm of X. */ 
107__MATHCALL_VEC (log10,, (_Mdouble_ __x)); 
108 
109/* Break VALUE into integral and fractional parts. */ 
110__MATHCALL (modf,, (_Mdouble_ __x, _Mdouble_ *__iptr)) __nonnull ((2)); 
111 
112#if __GLIBC_USE (IEC_60559_FUNCS_EXT_C2X) 
113/* Compute exponent to base ten. */ 
114__MATHCALL_VEC (exp10,, (_Mdouble_ __x)); 
115#endif 
116 
117#if defined __USE_XOPEN_EXTENDED || defined __USE_ISOC99 
118/* Return exp(X) - 1. */ 
119__MATHCALL_VEC (expm1,, (_Mdouble_ __x)); 
120 
121/* Return log(1 + X). */ 
122__MATHCALL_VEC (log1p,, (_Mdouble_ __x)); 
123 
124/* Return the base 2 signed integral exponent of X. */ 
125__MATHCALL (logb,, (_Mdouble_ __x)); 
126#endif 
127 
128#ifdef __USE_ISOC99 
129/* Compute base-2 exponential of X. */ 
130__MATHCALL_VEC (exp2,, (_Mdouble_ __x)); 
131 
132/* Compute base-2 logarithm of X. */ 
133__MATHCALL_VEC (log2,, (_Mdouble_ __x)); 
134#endif 
135 
136 
137/* Power functions. */ 
138 
139/* Return X to the Y power. */ 
140__MATHCALL_VEC (pow,, (_Mdouble_ __x, _Mdouble_ __y)); 
141 
142/* Return the square root of X. */ 
143__MATHCALL (sqrt,, (_Mdouble_ __x)); 
144 
145#if defined __USE_XOPEN || defined __USE_ISOC99 
146/* Return `sqrt(X*X + Y*Y)'. */ 
147__MATHCALL_VEC (hypot,, (_Mdouble_ __x, _Mdouble_ __y)); 
148#endif 
149 
150#if defined __USE_XOPEN_EXTENDED || defined __USE_ISOC99 
151/* Return the cube root of X. */ 
152__MATHCALL_VEC (cbrt,, (_Mdouble_ __x)); 
153#endif 
154 
155 
156/* Nearest integer, absolute value, and remainder functions. */ 
157 
158/* Smallest integral value not less than X. */ 
159__MATHCALLX (ceil,, (_Mdouble_ __x), (__const__)); 
160 
161/* Absolute value of X. */ 
162__MATHCALLX (fabs,, (_Mdouble_ __x), (__const__)); 
163 
164/* Largest integer not greater than X. */ 
165__MATHCALLX (floor,, (_Mdouble_ __x), (__const__)); 
166 
167/* Floating-point modulo remainder of X/Y. */ 
168__MATHCALL (fmod,, (_Mdouble_ __x, _Mdouble_ __y)); 
169 
170#ifdef __USE_MISC 
171# if ((!defined __cplusplus \ 
172 || __cplusplus < 201103L /* isinf conflicts with C++11. */ \ 
173 || __MATH_DECLARING_DOUBLE == 0)) /* isinff or isinfl don't. */ \ 
174 && !__MATH_DECLARING_FLOATN 
175/* Return 0 if VALUE is finite or NaN, +1 if it 
176 is +Infinity, -1 if it is -Infinity. */ 
177__MATHDECL_ALIAS (int,isinf,, (_Mdouble_ __value), isinf) 
178 __attribute__ ((__const__)); 
179# endif 
180 
181# if !__MATH_DECLARING_FLOATN 
182/* Return nonzero if VALUE is finite and not NaN. */ 
183__MATHDECL_ALIAS (int,finite,, (_Mdouble_ __value), finite) 
184 __attribute__ ((__const__)); 
185 
186/* Return the remainder of X/Y. */ 
187__MATHCALL (drem,, (_Mdouble_ __x, _Mdouble_ __y)); 
188 
189 
190/* Return the fractional part of X after dividing out `ilogb (X)'. */ 
191__MATHCALL (significand,, (_Mdouble_ __x)); 
192# endif 
193 
194#endif /* Use misc. */ 
195 
196#ifdef __USE_ISOC99 
197/* Return X with its signed changed to Y's. */ 
198__MATHCALLX (copysign,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
199#endif 
200 
201#ifdef __USE_ISOC99 
202/* Return representation of qNaN for double type. */ 
203__MATHCALL (nan,, (const char *__tagb)); 
204#endif 
205 
206 
207#if defined __USE_MISC || (defined __USE_XOPEN && !defined __USE_XOPEN2K) 
208# if ((!defined __cplusplus \ 
209 || __cplusplus < 201103L /* isnan conflicts with C++11. */ \ 
210 || __MATH_DECLARING_DOUBLE == 0)) /* isnanf or isnanl don't. */ \ 
211 && !__MATH_DECLARING_FLOATN 
212/* Return nonzero if VALUE is not a number. */ 
213__MATHDECL_ALIAS (int,isnan,, (_Mdouble_ __value), isnan) 
214 __attribute__ ((__const__)); 
215# endif 
216#endif 
217 
218#if defined __USE_MISC || (defined __USE_XOPEN && __MATH_DECLARING_DOUBLE) 
219/* Bessel functions. */ 
220__MATHCALL (j0,, (_Mdouble_)); 
221__MATHCALL (j1,, (_Mdouble_)); 
222__MATHCALL (jn,, (int, _Mdouble_)); 
223__MATHCALL (y0,, (_Mdouble_)); 
224__MATHCALL (y1,, (_Mdouble_)); 
225__MATHCALL (yn,, (int, _Mdouble_)); 
226#endif 
227 
228 
229#if defined __USE_XOPEN || defined __USE_ISOC99 
230/* Error and gamma functions. */ 
231__MATHCALL_VEC (erf,, (_Mdouble_)); 
232__MATHCALL_VEC (erfc,, (_Mdouble_)); 
233__MATHCALL (lgamma,, (_Mdouble_)); 
234#endif 
235 
236#ifdef __USE_ISOC99 
237/* True gamma function. */ 
238__MATHCALL (tgamma,, (_Mdouble_)); 
239#endif 
240 
241#if defined __USE_MISC || (defined __USE_XOPEN && !defined __USE_XOPEN2K) 
242# if !__MATH_DECLARING_FLOATN 
243/* Obsolete alias for `lgamma'. */ 
244__MATHCALL (gamma,, (_Mdouble_)); 
245# endif 
246#endif 
247 
248#ifdef __USE_MISC 
249/* Reentrant version of lgamma. This function uses the global variable 
250 `signgam'. The reentrant version instead takes a pointer and stores 
251 the value through it. */ 
252__MATHCALL (lgamma,_r, (_Mdouble_, int *__signgamp)); 
253#endif 
254 
255 
256#if defined __USE_XOPEN_EXTENDED || defined __USE_ISOC99 
257/* Return the integer nearest X in the direction of the 
258 prevailing rounding mode. */ 
259__MATHCALL (rint,, (_Mdouble_ __x)); 
260 
261/* Return X + epsilon if X < Y, X - epsilon if X > Y. */ 
262__MATHCALL (nextafter,, (_Mdouble_ __x, _Mdouble_ __y)); 
263# if defined __USE_ISOC99 && !defined __LDBL_COMPAT && !__MATH_DECLARING_FLOATN 
264__MATHCALL (nexttoward,, (_Mdouble_ __x, long double __y)); 
265# endif 
266 
267# if __GLIBC_USE (IEC_60559_BFP_EXT_C2X) || __MATH_DECLARING_FLOATN 
268/* Return X - epsilon. */ 
269__MATHCALL (nextdown,, (_Mdouble_ __x)); 
270/* Return X + epsilon. */ 
271__MATHCALL (nextup,, (_Mdouble_ __x)); 
272# endif 
273 
274/* Return the remainder of integer divison X / Y with infinite precision. */ 
275__MATHCALL (remainder,, (_Mdouble_ __x, _Mdouble_ __y)); 
276 
277# ifdef __USE_ISOC99 
278/* Return X times (2 to the Nth power). */ 
279__MATHCALL (scalbn,, (_Mdouble_ __x, int __n)); 
280# endif 
281 
282/* Return the binary exponent of X, which must be nonzero. */ 
283__MATHDECL (int,ilogb,, (_Mdouble_ __x)); 
284#endif 
285 
286#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X) || __MATH_DECLARING_FLOATN 
287/* Like ilogb, but returning long int. */ 
288__MATHDECL (long int, llogb,, (_Mdouble_ __x)); 
289#endif 
290 
291#ifdef __USE_ISOC99 
292/* Return X times (2 to the Nth power). */ 
293__MATHCALL (scalbln,, (_Mdouble_ __x, long int __n)); 
294 
295/* Round X to integral value in floating-point format using current 
296 rounding direction, but do not raise inexact exception. */ 
297__MATHCALL (nearbyint,, (_Mdouble_ __x)); 
298 
299/* Round X to nearest integral value, rounding halfway cases away from 
300 zero. */ 
301__MATHCALLX (round,, (_Mdouble_ __x), (__const__)); 
302 
303/* Round X to the integral value in floating-point format nearest but 
304 not larger in magnitude. */ 
305__MATHCALLX (trunc,, (_Mdouble_ __x), (__const__)); 
306 
307/* Compute remainder of X and Y and put in *QUO a value with sign of x/y 
308 and magnitude congruent `mod 2^n' to the magnitude of the integral 
309 quotient x/y, with n >= 3. */ 
310__MATHCALL (remquo,, (_Mdouble_ __x, _Mdouble_ __y, int *__quo)); 
311 
312 
313/* Conversion functions. */ 
314 
315/* Round X to nearest integral value according to current rounding 
316 direction. */ 
317__MATHDECL (long int,lrint,, (_Mdouble_ __x)); 
318__extension__ 
319__MATHDECL (long long int,llrint,, (_Mdouble_ __x)); 
320 
321/* Round X to nearest integral value, rounding halfway cases away from 
322 zero. */ 
323__MATHDECL (long int,lround,, (_Mdouble_ __x)); 
324__extension__ 
325__MATHDECL (long long int,llround,, (_Mdouble_ __x)); 
326 
327 
328/* Return positive difference between X and Y. */ 
329__MATHCALL (fdim,, (_Mdouble_ __x, _Mdouble_ __y)); 
330 
331# if !__MATH_DECLARING_FLOATN || defined __USE_GNU || !__GLIBC_USE (ISOC2X) 
332/* Return maximum numeric value from X and Y. */ 
333__MATHCALLX (fmax,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
334 
335/* Return minimum numeric value from X and Y. */ 
336__MATHCALLX (fmin,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
337# endif 
338 
339/* Multiply-add function computed as a ternary operation. */ 
340__MATHCALL (fma,, (_Mdouble_ __x, _Mdouble_ __y, _Mdouble_ __z)); 
341#endif /* Use ISO C99. */ 
342 
343#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X) || __MATH_DECLARING_FLOATN 
344/* Round X to nearest integer value, rounding halfway cases to even. */ 
345__MATHCALLX (roundeven,, (_Mdouble_ __x), (__const__)); 
346 
347/* Round X to nearest signed integer value, not raising inexact, with 
348 control of rounding direction and width of result. */ 
349__MATHDECL (__intmax_t, fromfp,, (_Mdouble_ __x, int __round, 
350 unsigned int __width)); 
351 
352/* Round X to nearest unsigned integer value, not raising inexact, 
353 with control of rounding direction and width of result. */ 
354__MATHDECL (__uintmax_t, ufromfp,, (_Mdouble_ __x, int __round, 
355 unsigned int __width)); 
356 
357/* Round X to nearest signed integer value, raising inexact for 
358 non-integers, with control of rounding direction and width of 
359 result. */ 
360__MATHDECL (__intmax_t, fromfpx,, (_Mdouble_ __x, int __round, 
361 unsigned int __width)); 
362 
363/* Round X to nearest unsigned integer value, raising inexact for 
364 non-integers, with control of rounding direction and width of 
365 result. */ 
366__MATHDECL (__uintmax_t, ufromfpx,, (_Mdouble_ __x, int __round, 
367 unsigned int __width)); 
368 
369/* Canonicalize floating-point representation. */ 
370__MATHDECL_1 (int, canonicalize,, (_Mdouble_ *__cx, const _Mdouble_ *__x)); 
371#endif 
372 
373#if (__GLIBC_USE (IEC_60559_BFP_EXT) \ 
374 || (__MATH_DECLARING_FLOATN \ 
375 && (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))) 
376/* Return value with maximum magnitude. */ 
377__MATHCALLX (fmaxmag,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
378 
379/* Return value with minimum magnitude. */ 
380__MATHCALLX (fminmag,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
381#endif 
382 
383#if __GLIBC_USE (ISOC2X) 
384/* Return maximum value from X and Y. */ 
385__MATHCALLX (fmaximum,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
386 
387/* Return minimum value from X and Y. */ 
388__MATHCALLX (fminimum,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
389 
390/* Return maximum numeric value from X and Y. */ 
391__MATHCALLX (fmaximum_num,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
392 
393/* Return minimum numeric value from X and Y. */ 
394__MATHCALLX (fminimum_num,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
395 
396/* Return value with maximum magnitude. */ 
397__MATHCALLX (fmaximum_mag,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
398 
399/* Return value with minimum magnitude. */ 
400__MATHCALLX (fminimum_mag,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
401 
402/* Return numeric value with maximum magnitude. */ 
403__MATHCALLX (fmaximum_mag_num,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
404 
405/* Return numeric value with minimum magnitude. */ 
406__MATHCALLX (fminimum_mag_num,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); 
407#endif 
408 
409#if __GLIBC_USE (IEC_60559_EXT) || __MATH_DECLARING_FLOATN 
410/* Total order operation. */ 
411__MATHDECL_1 (int, totalorder,, (const _Mdouble_ *__x, 
412 const _Mdouble_ *__y)) 
413 __attribute_pure__; 
414 
415/* Total order operation on absolute values. */ 
416__MATHDECL_1 (int, totalordermag,, (const _Mdouble_ *__x, 
417 const _Mdouble_ *__y)) 
418 __attribute_pure__; 
419 
420/* Get NaN payload. */ 
421__MATHCALL (getpayload,, (const _Mdouble_ *__x)); 
422 
423/* Set quiet NaN payload. */ 
424__MATHDECL_1 (int, setpayload,, (_Mdouble_ *__x, _Mdouble_ __payload)); 
425 
426/* Set signaling NaN payload. */ 
427__MATHDECL_1 (int, setpayloadsig,, (_Mdouble_ *__x, _Mdouble_ __payload)); 
428#endif 
429 
430#if (defined __USE_MISC || (defined __USE_XOPEN_EXTENDED \ 
431 && __MATH_DECLARING_DOUBLE \ 
432 && !defined __USE_XOPEN2K8)) \ 
433 && !__MATH_DECLARING_FLOATN 
434/* Return X times (2 to the Nth power). */ 
435__MATHCALL (scalb,, (_Mdouble_ __x, _Mdouble_ __n)); 
436#endif 
437