1 /* Declarations for math functions.
2 Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006
3 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <http://www.gnu.org/licenses/>. */
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 # include <bits/huge_valf.h>
36 # include <bits/huge_vall.h>
38 /* Get machine-dependent INFINITY value. */
39 # include <bits/inf.h>
41 /* Get machine-dependent NAN value (returned for some domain errors). */
42 # include <bits/nan.h>
43 #endif /* __USE_ISOC99 */
45 /* Get general and ISO C99 specific information. */
46 #include <bits/mathdef.h>
49 /* The file <bits/mathcalls.h> contains the prototypes for all the
50 actual math functions. These macros are used for those prototypes,
51 so we can easily declare each function as both `name' and `__name',
52 and can declare the float versions `namef' and `__namef'. */
54 #define __MATHDECL_1(type,function,suffix,args) \
55 extern type __MATH_PRECNAME(function,suffix) args __THROW
57 #define __MATHDECL(type,function,suffix,args) \
58 __MATHDECL_1(type,function,suffix,args);
60 #define __MATHCALL(function,suffix,args) \
61 __MATHDECL(_Mdouble_,function,suffix,args)
63 #define __MATHDECLX(type,function,suffix,args,attrib) \
64 __MATHDECL_1(type,function,suffix,args) __attribute__ (attrib); \
65 __MATH_maybe_libm_hidden_proto(function)
67 #define __MATHCALLX(function,suffix,args,attrib) \
68 __MATHDECLX(_Mdouble_,function,suffix,args,attrib)
70 /* Decls which are also used internally in libm.
71 Only the main variant is used internally, no need to try to avoid relocs
72 for the {l,f} variants. */
73 #define __MATHDECLI(type,function,suffix,args) \
74 __MATHDECL_1(type,function,suffix,args); \
75 __MATH_maybe_libm_hidden_proto(function)
77 #define __MATHCALLI(function,suffix,args) \
78 __MATHDECLI(_Mdouble_,function,suffix,args)
80 /* Private helpers for purely macro impls below.
81 Only make __foo{,f,l} visible but not (the macro-only) foo. */
83 # define __MATHDECL_PRIV(type,function,suffix,args,attrib) \
84 __MATHDECL_1(type,__CONCAT(__,function),suffix,args) __attribute__ (attrib); \
85 libm_hidden_proto(__MATH_PRECNAME(__##function,suffix))
87 # define __MATHDECL_PRIV(type,function,suffix,args,attrib) \
88 __MATHDECL_1(type,__CONCAT(__,function),suffix,args) __attribute__ (attrib);
92 /* Include the file of declarations, declaring double versions */
95 # define __MATH_maybe_libm_hidden_proto(x) libm_hidden_proto(x)
97 # define __MATH_maybe_libm_hidden_proto(x)
99 #define _Mdouble_ double
100 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
101 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
102 #define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD
103 #include <bits/mathcalls.h>
105 #undef _Mdouble_BEGIN_NAMESPACE
106 #undef _Mdouble_END_NAMESPACE
107 #undef __MATH_PRECNAME
108 #undef __MATH_maybe_libm_hidden_proto
111 #if defined __USE_MISC || defined __USE_ISOC99
113 /* Include the file of declarations again, this time using `float'
114 instead of `double' and appending f to each function name. */
116 # define __MATH_maybe_libm_hidden_proto(x)
118 # define _Mfloat_ float
120 # define _Mdouble_ _Mfloat_
122 # define __MATH_PRECNAME(name,r) name##f##r
124 # define __MATH_PRECNAME(name,r) name/**/f/**/r
126 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
127 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
128 # include <bits/mathcalls.h>
130 # undef _Mdouble_BEGIN_NAMESPACE
131 # undef _Mdouble_END_NAMESPACE
133 # undef __MATH_PRECNAME
134 # undef __MATH_maybe_libm_hidden_proto
137 # if (defined __STDC__ || defined __GNUC__) \
138 && (!defined __NO_LONG_DOUBLE_MATH || defined __LDBL_COMPAT)
139 # ifdef __LDBL_COMPAT
142 extern float __nldbl_nexttowardf (float __x
, long double __y
) __THROW
143 __attribute__ ((__const__
));
144 # ifdef __REDIRECT_NTH
145 extern float __REDIRECT_NTH (nexttowardf
, (float __x
, long double __y
), __nldbl_nexttowardf
)
146 __attribute__ ((__const__
));
147 extern double __REDIRECT_NTH (nexttoward
, (double __x
, long double __y
), nextafter
)
148 __attribute__ ((__const__
));
149 extern long double __REDIRECT_NTH (nexttowardl
, (long double __x
, long double __y
), nextafter
)
150 __attribute__ ((__const__
));
154 /* Include the file of declarations again, this time using `long double'
155 instead of `double' and appending l to each function name. */
158 # define __MATHDECL_2(type,function,suffix,args,alias) \
159 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix),args,alias)
160 # define __MATHDECL_1(type,function,suffix,args) \
161 __MATHDECL_2(type,function,suffix,args,__CONCAT(function,suffix))
164 # define __MATH_maybe_libm_hidden_proto(x)
165 # ifndef _Mlong_double_
166 # define _Mlong_double_ long double
168 # define _Mdouble_ _Mlong_double_
170 # define __MATH_PRECNAME(name,r) name##l##r
172 # define __MATH_PRECNAME(name,r) name/**/l/**/r
174 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
175 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
176 # include <bits/mathcalls.h>
178 # undef _Mdouble_BEGIN_NAMESPACE
179 # undef _Mdouble_END_NAMESPACE
180 # undef _Mlong_double_
181 # undef __MATH_PRECNAME
182 # undef __MATH_maybe_libm_hidden_proto
184 # endif /* __STDC__ || __GNUC__ */
186 #endif /* Use misc or ISO C99. */
192 #if defined __USE_MISC || defined __USE_XOPEN
193 /* This variable is used by `gamma' and `lgamma'. */
196 /* This is used when standart of libm
197 * should prevent lgamma(x) of modifying signgam variable.
199 # define lgammaf(arg) \
201 int local_signgam = 0; \
202 float result = lgammaf_r((float)arg, &local_signgam); \
206 # define lgamma(arg) \
208 int local_signgam = 0; \
209 double result = lgamma_r(arg, &local_signgam); \
213 # define lgammal(arg) \
215 int local_signgam = 0; \
216 long double result = lgammal_r(arg, &local_signgam); \
222 /* ISO C99 defines some generic macros which work on any data type. */
223 #if defined(__USE_ISOC99) || defined(__USE_BSD)
225 /* Get the architecture specific values describing the floating-point
226 evaluation. The following symbols will get defined:
228 float_t floating-point type at least as wide as `float' used
229 to evaluate `float' expressions
230 double_t floating-point type at least as wide as `double' used
231 to evaluate `double' expressions
235 0 if `float_t' is `float' and `double_t' is `double'
236 1 if `float_t' and `double_t' are `double'
237 2 if `float_t' and `double_t' are `long double'
238 else `float_t' and `double_t' are unspecified
240 INFINITY representation of the infinity value of type `float'
245 If defined it indicates that the `fma' function
246 generally executes about as fast as a multiply and an add.
247 This macro is defined only iff the `fma' function is
248 implemented directly with a hardware multiply-add instructions.
250 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
251 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
253 DECIMAL_DIG Number of decimal digits supported by conversion between
254 decimal and all internal floating-point formats.
258 /* All floating-point numbers can be put in one of these categories. */
262 # define FP_NAN FP_NAN
264 # define FP_INFINITE FP_INFINITE
266 # define FP_ZERO FP_ZERO
268 # define FP_SUBNORMAL FP_SUBNORMAL
270 # define FP_NORMAL FP_NORMAL
273 /* Return number of classification appropriate for X. */
274 # ifdef __NO_LONG_DOUBLE_MATH
275 # define fpclassify(x) \
276 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
278 # define fpclassify(x) \
279 (sizeof (x) == sizeof (float) \
280 ? __fpclassifyf (x) \
281 : sizeof (x) == sizeof (double) \
282 ? __fpclassify (x) : __fpclassifyl (x))
285 /* Return nonzero value if sign of X is negative. */
286 # ifdef __NO_LONG_DOUBLE_MATH
287 # define signbit(x) \
288 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
290 # define signbit(x) \
291 (sizeof (x) == sizeof (float) \
293 : sizeof (x) == sizeof (double) \
294 ? __signbit (x) : __signbitl (x))
297 /* Return nonzero value if X is not +-Inf or NaN. */
298 # ifdef __NO_LONG_DOUBLE_MATH
299 # define isfinite(x) \
300 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
302 # define isfinite(x) \
303 (sizeof (x) == sizeof (float) \
305 : sizeof (x) == sizeof (double) \
306 ? __finite (x) : __finitel (x))
309 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
310 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
312 /* Return nonzero value if X is a NaN. We could use `fpclassify' but
313 we already have this functions `__isnan' and it is faster. */
314 # ifdef __NO_LONG_DOUBLE_MATH
316 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
319 (sizeof (x) == sizeof (float) \
321 : sizeof (x) == sizeof (double) \
322 ? __isnan (x) : __isnanl (x))
325 /* Return nonzero value is X is positive or negative infinity. */
326 # ifdef __NO_LONG_DOUBLE_MATH
328 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
331 (sizeof (x) == sizeof (float) \
333 : sizeof (x) == sizeof (double) \
334 ? __isinf (x) : __isinfl (x))
337 /* Bitmasks for the math_errhandling macro. */
338 # define MATH_ERRNO 1 /* errno set by math functions. */
339 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
341 #endif /* Use ISO C99. */
344 #define finite(x) __finite(x)
345 #define finitef(x) __finitef(x)
346 #define finitel(x) __finitel(x)
349 /* Support for various different standard error handling behaviors. */
352 _IEEE_
= -1, /* According to IEEE 754/IEEE 854. */
353 _SVID_
, /* According to System V, release 4. */
354 _XOPEN_
, /* Nowadays also Unix98. */
356 _ISOC_
/* Actually this is ISO C99. */
359 /* This variable can be changed at run-time to any of the values above to
360 affect floating point error handling behavior (it may also be necessary
361 to change the hardware FPU exception settings). */
362 extern _LIB_VERSION_TYPE _LIB_VERSION
;
367 /* In SVID error handling, `matherr' is called with this description
368 of the exceptional condition.
370 We have a problem when using C++ since `exception' is a reserved
386 extern int matherr (struct __exception
*__exc
) throw ();
388 extern int __attribute__ ((weak
)) matherr (struct exception
*__exc
);
391 # define X_TLOSS 1.41484755040568800000e+16
393 /* Types of exceptions in the `type' field. */
401 /* SVID mode specifies returning this large value instead of infinity. */
402 # define HUGE 3.40282347e+38F
407 # ifdef __UCLIBC_SUSV4_LEGACY__
408 /* X/Open wants another strange constant. */
409 # define MAXFLOAT 3.40282347e+38F
416 /* Some useful constants. */
417 #if defined __USE_BSD || defined __USE_XOPEN
418 # define M_E 2.7182818284590452354 /* e */
419 # define M_LOG2E 1.4426950408889634074 /* log_2 e */
420 # define M_LOG10E 0.43429448190325182765 /* log_10 e */
421 # define M_LN2 0.69314718055994530942 /* log_e 2 */
422 # define M_LN10 2.30258509299404568402 /* log_e 10 */
423 # define M_PI 3.14159265358979323846 /* pi */
424 # define M_PI_2 1.57079632679489661923 /* pi/2 */
425 # define M_PI_4 0.78539816339744830962 /* pi/4 */
426 # define M_1_PI 0.31830988618379067154 /* 1/pi */
427 # define M_2_PI 0.63661977236758134308 /* 2/pi */
428 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
429 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
430 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
433 /* The above constants are not adequate for computation using `long double's.
434 Therefore we provide as an extension constants with similar names as a
435 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
437 # define M_El 2.7182818284590452353602874713526625L /* e */
438 # define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */
439 # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */
440 # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */
441 # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */
442 # define M_PIl 3.1415926535897932384626433832795029L /* pi */
443 # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
444 # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
445 # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
446 # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
447 # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
448 # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */
449 # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */
453 /* When compiling in strict ISO C compatible mode we must not use the
454 inline functions since they, among other things, do not set the
455 `errno' variable correctly. */
456 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
457 # define __NO_MATH_INLINES 1
460 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
461 /* ISO C99 defines some macros to compare number while taking care for
462 unordered numbers. Many FPUs provide special instructions to support
463 these operations. Generic support in GCC for these as builtins went
464 in before 3.0.0, but not all cpus added their patterns. We define
465 versions that use the builtins here, and <bits/mathinline.h> will
466 undef/redefine as appropriate for the specific GCC version in use. */
467 # define isgreater(x, y) __builtin_isgreater(x, y)
468 # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
469 # define isless(x, y) __builtin_isless(x, y)
470 # define islessequal(x, y) __builtin_islessequal(x, y)
471 # define islessgreater(x, y) __builtin_islessgreater(x, y)
472 # define isunordered(u, v) __builtin_isunordered(u, v)
475 /* Get machine-dependent inline versions (if there are any). */
476 #ifdef __USE_EXTERN_INLINES
477 # include <bits/mathinline.h>
481 /* If we've still got undefined comparison macros, provide defaults. */
483 /* Return nonzero value if X is greater than Y. */
485 # define isgreater(x, y) \
487 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
488 !isunordered (__x, __y) && __x > __y; }))
491 /* Return nonzero value if X is greater than or equal to Y. */
492 # ifndef isgreaterequal
493 # define isgreaterequal(x, y) \
495 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
496 !isunordered (__x, __y) && __x >= __y; }))
499 /* Return nonzero value if X is less than Y. */
501 # define isless(x, y) \
503 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
504 !isunordered (__x, __y) && __x < __y; }))
507 /* Return nonzero value if X is less than or equal to Y. */
509 # define islessequal(x, y) \
511 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
512 !isunordered (__x, __y) && __x <= __y; }))
515 /* Return nonzero value if either X is less than Y or Y is less than X. */
516 # ifndef islessgreater
517 # define islessgreater(x, y) \
519 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
520 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
523 /* Return nonzero value if arguments are unordered. */
525 # define isunordered(u, v) \
527 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
528 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))