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1 /* Declarations for math functions.
2 Copyright (C) 1991, 92, 93, 95, 96, 97, 98 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Library General Public License as
7 published by the Free Software Foundation; either version 2 of the
8 License, or (at your option) any later version.
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 Library General Public License for more details.
15 You should have received a copy of the GNU Library General Public
16 License along with the GNU C Library; see the file COPYING.LIB. If not,
17 write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
18 Boston, MA 02111-1307, USA. */
21 * ISO C Standard: 4.5 MATHEMATICS <math.h>
24 #ifndef _MATH_H
25 #define _MATH_H 1
27 #include <features.h>
29 __BEGIN_DECLS
31 /* Get machine-dependent HUGE_VAL value (returned on overflow).
32 On all IEEE754 machines, this is +Infinity. */
33 #include <bits/huge_val.h>
35 /* Get machine-dependent NAN value (returned for some domain errors). */
36 #ifdef __USE_ISOC9X
37 # include <bits/nan.h>
38 #endif
41 /* The file <bits/mathcalls.h> contains the prototypes for all the
42 actual math functions. These macros are used for those prototypes,
43 so we can easily declare each function as both `name' and `__name',
44 and can declare the float versions `namef' and `__namef'. */
46 #define __MATHCALL(function,suffix, args) \
47 __MATHDECL (_Mdouble_,function,suffix, args)
48 #define __MATHDECL(type, function,suffix, args) \
49 __MATHDECL_1(type, function,suffix, args); \
50 __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
51 #define __MATHCALLX(function,suffix, args, attrib) \
52 __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
53 #define __MATHDECLX(type, function,suffix, args, attrib) \
54 __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
55 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
56 #define __MATHDECL_1(type, function,suffix, args) \
57 extern type __MATH_PRECNAME(function,suffix) args
59 #define _Mdouble_ double
60 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
61 #include <bits/mathcalls.h>
62 #undef _Mdouble_
63 #undef __MATH_PRECNAME
65 #if defined __USE_MISC || defined __USE_ISOC9X
68 /* Include the file of declarations again, this time using `float'
69 instead of `double' and appending f to each function name. */
71 # ifndef _Mfloat_
72 # define _Mfloat_ float
73 # endif
74 # define _Mdouble_ _Mfloat_
75 # ifdef __STDC__
76 # define __MATH_PRECNAME(name,r) name##f##r
77 # else
78 # define __MATH_PRECNAME(name,r) name/**/f/**/r
79 # endif
80 # include <bits/mathcalls.h>
81 # undef _Mdouble_
82 # undef __MATH_PRECNAME
84 # if __STDC__ - 0 || __GNUC__ - 0
85 /* Include the file of declarations again, this time using `long double'
86 instead of `double' and appending l to each function name. */
88 # ifndef _Mlong_double_
89 # define _Mlong_double_ long double
90 # endif
91 # define _Mdouble_ _Mlong_double_
92 # ifdef __STDC__
93 # define __MATH_PRECNAME(name,r) name##l##r
94 # else
95 # define __MATH_PRECNAME(name,r) name/**/l/**/r
96 # endif
97 # include <bits/mathcalls.h>
98 # undef _Mdouble_
99 # undef __MATH_PRECNAME
101 # endif /* __STDC__ || __GNUC__ */
103 #endif /* Use misc or ISO C 9X. */
104 #undef __MATHDECL_1
105 #undef __MATHDECL
106 #undef __MATHCALL
109 #if defined __USE_MISC || defined __USE_XOPEN || defined __USE_ISOC9X
110 /* This variable is used by `gamma' and `lgamma'. */
111 extern int signgam;
112 #endif
115 /* ISO C 9X defines some generic macros which work on any data type. */
116 #if __USE_ISOC9X
118 /* Get the architecture specific values describing the floating-point
119 evaluation. The following symbols will get defined:
121 float_t floating-point type at least as wide as `float' used
122 to evaluate `float' expressions
123 double_t floating-point type at least as wide as `double' used
124 to evaluate `double' expressions
126 FLT_EVAL_METHOD
127 Defined to
128 0 if `float_t' is `float' and `double_t' is `double'
129 1 if `float_t' and `double_t' are `double'
130 2 if `float_t' and `double_t' are `long double'
131 else `float_t' and `double_t' are unspecified
133 INFINITY representation of the infinity value of type `float'
135 FP_FAST_FMA
136 FP_FAST_FMAF
137 FP_FAST_FMAL
138 If defined it indicates that the `fma' function
139 generally executes about as fast as a multiply and an add.
140 This macro is defined only iff the `fma' function is
141 implemented directly with a hardware multiply-add instructions.
143 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
144 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
146 DECIMAL_DIG Number of decimal digits supported by conversion between
147 decimal and all internal floating-point formats.
150 # include <bits/mathdef.h>
152 /* All floating-point numbers can be put in one of these categories. */
153 enum
155 FP_NAN,
156 # define FP_NAN FP_NAN
157 FP_INFINITE,
158 # define FP_INFINITE FP_INFINITE
159 FP_ZERO,
160 # define FP_ZERO FP_ZERO
161 FP_SUBNORMAL,
162 # define FP_SUBNORMAL FP_SUBNORMAL
163 FP_NORMAL
164 # define FP_NORMAL FP_NORMAL
167 /* Return number of classification appropriate for X. */
168 # define fpclassify(x) \
169 (sizeof (x) == sizeof (float) ? \
170 __fpclassifyf (x) \
171 : sizeof (x) == sizeof (double) ? \
172 __fpclassify (x) : __fpclassifyl (x))
174 /* Return nonzero value if sign of X is negative. */
175 # define signbit(x) \
176 (sizeof (x) == sizeof (float) ? \
177 __signbitf (x) \
178 : sizeof (x) == sizeof (double) ? \
179 __signbit (x) : __signbitl (x))
181 /* Return nonzero value if X is not +-Inf or NaN. */
182 # define isfinite(x) \
183 (sizeof (x) == sizeof (float) ? \
184 __finitef (x) \
185 : sizeof (x) == sizeof (double) ? \
186 __finite (x) : __finitel (x))
188 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
189 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
191 /* Return nonzero value if X is a NaN. We could use `fpclassify' but
192 we already have this functions `__isnan' and it is faster. */
193 # define isnan(x) \
194 (sizeof (x) == sizeof (float) ? \
195 __isnanf (x) \
196 : sizeof (x) == sizeof (double) ? \
197 __isnan (x) : __isnanl (x))
199 #endif /* Use ISO C 9X. */
201 #ifdef __USE_MISC
202 /* Support for various different standard error handling behaviors. */
203 typedef enum
205 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
206 _SVID_, /* According to System V, release 4. */
207 _XOPEN_, /* Nowadays also Unix98. */
208 _POSIX_,
209 _ISOC_ /* Actually this is ISO C 9X. */
210 } _LIB_VERSION_TYPE;
212 /* This variable can be changed at run-time to any of the values above to
213 affect floating point error handling behavior (it may also be necessary
214 to change the hardware FPU exception settings). */
215 extern _LIB_VERSION_TYPE _LIB_VERSION;
216 #endif
219 #ifdef __USE_SVID
220 /* In SVID error handling, `matherr' is called with this description
221 of the exceptional condition.
223 We have a problem when using C++ since `exception' is a reserved
224 name in C++. */
225 # ifdef __cplusplus
226 struct __exception
227 # else
228 struct exception
229 # endif
231 int type;
232 char *name;
233 double arg1;
234 double arg2;
235 double retval;
238 # ifdef __cplusplus
239 extern int __matherr __P ((struct __exception *__exc));
240 extern int matherr __P ((struct __exception *__exc));
241 # else
242 extern int __matherr __P ((struct exception *__exc));
243 extern int matherr __P ((struct exception *__exc));
244 # endif
246 # define X_TLOSS 1.41484755040568800000e+16
248 /* Types of exceptions in the `type' field. */
249 # define DOMAIN 1
250 # define SING 2
251 # define OVERFLOW 3
252 # define UNDERFLOW 4
253 # define TLOSS 5
254 # define PLOSS 6
256 /* SVID mode specifies returning this large value instead of infinity. */
257 # define HUGE FLT_MAX
258 # include <float.h> /* Defines FLT_MAX. */
260 #else /* !SVID */
262 # ifdef __USE_XOPEN
263 /* X/Open wants another strange constant. */
264 # define MAXFLOAT FLT_MAX
265 # include <float.h>
266 # endif
268 #endif /* SVID */
271 /* Some useful constants. */
272 #if defined __USE_BSD || defined __USE_UNIX98
273 # define M_E 2.7182818284590452354 /* e */
274 # define M_LOG2E 1.4426950408889634074 /* log_2 e */
275 # define M_LOG10E 0.43429448190325182765 /* log_10 e */
276 # define M_LN2 0.69314718055994530942 /* log_e 2 */
277 # define M_LN10 2.30258509299404568402 /* log_e 10 */
278 # define M_PI 3.14159265358979323846 /* pi */
279 # define M_PI_2 1.57079632679489661923 /* pi/2 */
280 # define M_PI_4 0.78539816339744830962 /* pi/4 */
281 # define M_1_PI 0.31830988618379067154 /* 1/pi */
282 # define M_2_PI 0.63661977236758134308 /* 2/pi */
283 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
284 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
285 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
286 #endif
288 /* The above constants are not adequate for computation using `long double's.
289 Therefore we provide as an extension constants with similar names as a
290 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
291 #ifdef __USE_GNU
292 # define M_El 2.7182818284590452353602874713526625L /* e */
293 # define M_LOG2El 1.4426950408889634073599246810018922L /* log_2 e */
294 # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */
295 # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */
296 # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */
297 # define M_PIl 3.1415926535897932384626433832795029L /* pi */
298 # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
299 # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
300 # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
301 # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
302 # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
303 # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */
304 # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */
305 #endif
308 /* Get machine-dependent inline versions (if there are any). */
309 #ifdef __OPTIMIZE__
310 # include <bits/mathinline.h>
311 #endif
314 #if __USE_ISOC9X
315 /* ISO C 9X defines some macros to compare number while taking care
316 for unordered numbers. Since many FPUs provide special
317 instructions to support these operations and these tests are
318 defined in <bits/mathinline.h>, we define the generic macros at
319 this late point and only if they are not defined yet. */
321 /* Return nonzero value if X is greater than Y. */
322 # ifndef isgreater
323 # define isgreater(x, y) \
324 (__extension__ \
325 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
326 !isunordered (__x, __y) && __x > __y; }))
327 # endif
329 /* Return nonzero value if X is greater than or equal to Y. */
330 # ifndef isgreaterequal
331 # define isgreaterequal(x, y) \
332 (__extension__ \
333 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
334 !isunordered (__x, __y) && __x >= __y; }))
335 # endif
337 /* Return nonzero value if X is less than Y. */
338 # ifndef isless
339 # define isless(x, y) \
340 (__extension__ \
341 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
342 !isunordered (__x, __y) && __x < __y; }))
343 # endif
345 /* Return nonzero value if X is less than or equal to Y. */
346 # ifndef islessequal
347 # define islessequal(x, y) \
348 (__extension__ \
349 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
350 !isunordered (__x, __y) && __x <= __y; }))
351 # endif
353 /* Return nonzero value if either X is less than Y or Y is less than X. */
354 # ifndef islessgreater
355 # define islessgreater(x, y) \
356 (__extension__ \
357 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
358 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
359 # endif
361 /* Return nonzero value if arguments are unordered. */
362 # ifndef isunordered
363 # define isunordered(u, v) \
364 (__extension__ \
365 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
366 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
367 # endif
369 #endif
371 __END_DECLS
374 #endif /* math.h */