1 /* Declarations for math functions.
2 Copyright (C) 1991,92,93,95,96,97,98,99,2001 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 C99 Standard: 7.12 Mathematics <math.h>
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). */
37 # include <bits/nan.h>
39 /* Get general and ISO C99 specific information. */
40 #include <bits/mathdef.h>
43 /* The file <bits/mathcalls.h> contains the prototypes for all the
44 actual math functions. These macros are used for those prototypes,
45 so we can easily declare each function as both `name' and `__name',
46 and can declare the float versions `namef' and `__namef'. */
48 #define __MATHCALL(function,suffix, args) \
49 __MATHDECL (_Mdouble_,function,suffix, args)
50 #define __MATHDECL(type, function,suffix, args) \
51 __MATHDECL_1(type, function,suffix, args); \
52 __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
53 #define __MATHCALLX(function,suffix, args, attrib) \
54 __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
55 #define __MATHDECLX(type, function,suffix, args, attrib) \
56 __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
57 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
58 #define __MATHDECL_1(type, function,suffix, args) \
59 extern type __MATH_PRECNAME(function,suffix) args __THROW
61 #define _Mdouble_ double
62 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
63 #include <bits/mathcalls.h>
65 #undef __MATH_PRECNAME
67 #if defined __USE_MISC || defined __USE_ISOC99
70 /* Include the file of declarations again, this time using `float'
71 instead of `double' and appending f to each function name. */
74 # define _Mfloat_ float
76 # define _Mdouble_ _Mfloat_
78 # define __MATH_PRECNAME(name,r) name##f##r
80 # define __MATH_PRECNAME(name,r) name/**/f/**/r
82 # include <bits/mathcalls.h>
84 # undef __MATH_PRECNAME
86 # if (__STDC__ - 0 || __GNUC__ - 0) && !defined __NO_LONG_DOUBLE_MATH
87 /* Include the file of declarations again, this time using `long double'
88 instead of `double' and appending l to each function name. */
90 # ifndef _Mlong_double_
91 # define _Mlong_double_ long double
93 # define _Mdouble_ _Mlong_double_
95 # define __MATH_PRECNAME(name,r) name##l##r
97 # define __MATH_PRECNAME(name,r) name/**/l/**/r
99 # include <bits/mathcalls.h>
101 # undef __MATH_PRECNAME
103 # endif /* __STDC__ || __GNUC__ */
105 #endif /* Use misc or ISO C99. */
111 #if defined __USE_MISC || defined __USE_XOPEN
112 /* This variable is used by `gamma' and `lgamma'. */
117 /* ISO C99 defines some generic macros which work on any data type. */
120 /* Get the architecture specific values describing the floating-point
121 evaluation. The following symbols will get defined:
123 float_t floating-point type at least as wide as `float' used
124 to evaluate `float' expressions
125 double_t floating-point type at least as wide as `double' used
126 to evaluate `double' expressions
130 0 if `float_t' is `float' and `double_t' is `double'
131 1 if `float_t' and `double_t' are `double'
132 2 if `float_t' and `double_t' are `long double'
133 else `float_t' and `double_t' are unspecified
135 INFINITY representation of the infinity value of type `float'
140 If defined it indicates that the `fma' function
141 generally executes about as fast as a multiply and an add.
142 This macro is defined only iff the `fma' function is
143 implemented directly with a hardware multiply-add instructions.
145 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
146 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
148 DECIMAL_DIG Number of decimal digits supported by conversion between
149 decimal and all internal floating-point formats.
153 /* All floating-point numbers can be put in one of these categories. */
157 # define FP_NAN FP_NAN
159 # define FP_INFINITE FP_INFINITE
161 # define FP_ZERO FP_ZERO
163 # define FP_SUBNORMAL FP_SUBNORMAL
165 # define FP_NORMAL FP_NORMAL
168 /* Return number of classification appropriate for X. */
169 # ifdef __NO_LONG_DOUBLE_MATH
170 # define fpclassify(x) \
171 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
173 # define fpclassify(x) \
174 (sizeof (x) == sizeof (float) \
175 ? __fpclassifyf (x) \
176 : sizeof (x) == sizeof (double) \
177 ? __fpclassify (x) : __fpclassifyl (x))
180 /* Return nonzero value if sign of X is negative. */
181 # ifdef __NO_LONG_DOUBLE_MATH
182 # define signbit(x) \
183 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
185 # define signbit(x) \
186 (sizeof (x) == sizeof (float) \
188 : sizeof (x) == sizeof (double) \
189 ? __signbit (x) : __signbitl (x))
192 /* Return nonzero value if X is not +-Inf or NaN. */
193 # ifdef __NO_LONG_DOUBLE_MATH
194 # define isfinite(x) \
195 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
197 # define isfinite(x) \
198 (sizeof (x) == sizeof (float) \
200 : sizeof (x) == sizeof (double) \
201 ? __finite (x) : __finitel (x))
204 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
205 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
207 /* Return nonzero value if X is a NaN. We could use `fpclassify' but
208 we already have this functions `__isnan' and it is faster. */
209 # ifdef __NO_LONG_DOUBLE_MATH
211 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
214 (sizeof (x) == sizeof (float) \
216 : sizeof (x) == sizeof (double) \
217 ? __isnan (x) : __isnanl (x))
220 /* Return nonzero value is X is positive or negative infinity. */
221 # ifdef __NO_LONG_DOUBLE_MATH
223 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
226 (sizeof (x) == sizeof (float) \
228 : sizeof (x) == sizeof (double) \
229 ? __isinf (x) : __isinfl (x))
232 /* Bitmasks for the math_errhandling macro. */
233 # define MATH_ERRNO 1 /* errno set by math functions. */
234 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
236 #endif /* Use ISO C99. */
239 /* Support for various different standard error handling behaviors. */
242 _IEEE_
= -1, /* According to IEEE 754/IEEE 854. */
243 _SVID_
, /* According to System V, release 4. */
244 _XOPEN_
, /* Nowadays also Unix98. */
246 _ISOC_
/* Actually this is ISO C99. */
249 /* This variable can be changed at run-time to any of the values above to
250 affect floating point error handling behavior (it may also be necessary
251 to change the hardware FPU exception settings). */
252 extern _LIB_VERSION_TYPE _LIB_VERSION
;
257 /* In SVID error handling, `matherr' is called with this description
258 of the exceptional condition.
260 We have a problem when using C++ since `exception' is a reserved
276 extern int matherr (struct __exception
*__exc
) throw ();
278 extern int matherr (struct exception
*__exc
);
281 # define X_TLOSS 1.41484755040568800000e+16
283 /* Types of exceptions in the `type' field. */
291 /* SVID mode specifies returning this large value instead of infinity. */
292 # define HUGE 3.40282347e+38F
297 /* X/Open wants another strange constant. */
298 # define MAXFLOAT 3.40282347e+38F
304 /* Some useful constants. */
305 #if defined __USE_BSD || defined __USE_XOPEN
306 # define M_E 2.7182818284590452354 /* e */
307 # define M_LOG2E 1.4426950408889634074 /* log_2 e */
308 # define M_LOG10E 0.43429448190325182765 /* log_10 e */
309 # define M_LN2 0.69314718055994530942 /* log_e 2 */
310 # define M_LN10 2.30258509299404568402 /* log_e 10 */
311 # define M_PI 3.14159265358979323846 /* pi */
312 # define M_PI_2 1.57079632679489661923 /* pi/2 */
313 # define M_PI_4 0.78539816339744830962 /* pi/4 */
314 # define M_1_PI 0.31830988618379067154 /* 1/pi */
315 # define M_2_PI 0.63661977236758134308 /* 2/pi */
316 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
317 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
318 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
321 /* The above constants are not adequate for computation using `long double's.
322 Therefore we provide as an extension constants with similar names as a
323 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
325 # define M_El 2.7182818284590452353602874713526625L /* e */
326 # define M_LOG2El 1.4426950408889634073599246810018922L /* log_2 e */
327 # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */
328 # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */
329 # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */
330 # define M_PIl 3.1415926535897932384626433832795029L /* pi */
331 # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
332 # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
333 # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
334 # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
335 # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
336 # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */
337 # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */
341 /* When compiling in strict ISO C compatible mode we must not use the
342 inline functions since they, among other things, do not set the
343 `errno' variable correctly. */
344 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
345 # define __NO_MATH_INLINES 1
348 /* Get machine-dependent inline versions (if there are any). */
349 #ifdef __USE_EXTERN_INLINES
350 # include <bits/mathinline.h>
355 /* ISO C99 defines some macros to compare number while taking care
356 for unordered numbers. Since many FPUs provide special
357 instructions to support these operations and these tests are
358 defined in <bits/mathinline.h>, we define the generic macros at
359 this late point and only if they are not defined yet. */
361 /* Return nonzero value if X is greater than Y. */
363 # define isgreater(x, y) \
365 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
366 !isunordered (__x, __y) && __x > __y; }))
369 /* Return nonzero value if X is greater than or equal to Y. */
370 # ifndef isgreaterequal
371 # define isgreaterequal(x, y) \
373 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
374 !isunordered (__x, __y) && __x >= __y; }))
377 /* Return nonzero value if X is less than Y. */
379 # define isless(x, y) \
381 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
382 !isunordered (__x, __y) && __x < __y; }))
385 /* Return nonzero value if X is less than or equal to Y. */
387 # define islessequal(x, y) \
389 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
390 !isunordered (__x, __y) && __x <= __y; }))
393 /* Return nonzero value if either X is less than Y or Y is less than X. */
394 # ifndef islessgreater
395 # define islessgreater(x, y) \
397 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
398 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
401 /* Return nonzero value if arguments are unordered. */
403 # define isunordered(u, v) \
405 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
406 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))