math.h 16 KB

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  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.
  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. 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. You should have received a copy of the GNU Lesser General Public
  14. License along with the GNU C Library; if not, write to the Free
  15. Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  16. 02111-1307 USA. */
  17. /*
  18. * ISO C99 Standard: 7.12 Mathematics <math.h>
  19. */
  20. #ifndef _MATH_H
  21. #define _MATH_H 1
  22. #include <features.h>
  23. __BEGIN_DECLS
  24. /* Get machine-dependent HUGE_VAL value (returned on overflow).
  25. On all IEEE754 machines, this is +Infinity. */
  26. #include <bits/huge_val.h>
  27. #ifdef __USE_ISOC99
  28. # include <bits/huge_valf.h>
  29. # include <bits/huge_vall.h>
  30. /* Get machine-dependent INFINITY value. */
  31. # include <bits/inf.h>
  32. /* Get machine-dependent NAN value (returned for some domain errors). */
  33. # include <bits/nan.h>
  34. #endif /* __USE_ISOC99 */
  35. /* Get general and ISO C99 specific information. */
  36. #include <bits/mathdef.h>
  37. #if !(defined _LIBC && (defined NOT_IN_libc && defined IS_IN_libm))
  38. # define libm_hidden_proto(name, attrs...)
  39. #endif
  40. /* The file <bits/mathcalls.h> contains the prototypes for all the
  41. actual math functions. These macros are used for those prototypes,
  42. so we can easily declare each function as both `name' and `__name',
  43. and can declare the float versions `namef' and `__namef'. */
  44. #define __MATHCALL(function,suffix, args) \
  45. __MATHDECL (_Mdouble_,function,suffix, args)
  46. #define __MATHDECL(type, function,suffix, args) \
  47. __MATHDECL_1(type, function,suffix, args);
  48. #define __MATHCALLX(function,suffix, args, attrib) \
  49. __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  50. #define __MATHDECLX(type, function,suffix, args, attrib) \
  51. __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  52. __MATHDECLI_MAINVARIANT(function)
  53. #define __MATHDECL_1(type, function,suffix, args) \
  54. extern type __MATH_PRECNAME(function,suffix) args __THROW
  55. /* Decls which are also used internally in libm.
  56. Only the main variant is used internally, no need to try to avoid relocs
  57. for the {l,f} variants. */
  58. #define __MATHCALLI(function,suffix, args) \
  59. __MATHDECLI (_Mdouble_,function,suffix, args)
  60. #define __MATHDECLI(type, function,suffix, args) \
  61. __MATHDECL_1(type, function,suffix, args); \
  62. __MATHDECLI_MAINVARIANT(function)
  63. /* Private helpers for purely macro impls below.
  64. Only make __foo{,f,l} visible but not (the macro-only) foo. */
  65. #define __MATHDECL_PRIV(type, function,suffix, args, attrib) \
  66. __MATHDECL_1(type, __CONCAT(__,function),suffix, args) \
  67. __attribute__ (attrib); \
  68. libm_hidden_proto(__MATH_PRECNAME(__##function,suffix))
  69. #define __MATHDECLI_MAINVARIANT libm_hidden_proto
  70. #define _Mdouble_ double
  71. #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  72. # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
  73. # define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD
  74. #include <bits/mathcalls.h>
  75. #undef _Mdouble_
  76. #undef _Mdouble_BEGIN_NAMESPACE
  77. #undef _Mdouble_END_NAMESPACE
  78. #undef __MATH_PRECNAME
  79. #undef __MATHDECLI_MAINVARIANT
  80. #define __MATHDECLI_MAINVARIANT(x)
  81. #if defined __USE_MISC || defined __USE_ISOC99
  82. /* Include the file of declarations again, this time using `float'
  83. instead of `double' and appending f to each function name. */
  84. # ifndef _Mfloat_
  85. # define _Mfloat_ float
  86. # endif
  87. # define _Mdouble_ _Mfloat_
  88. # ifdef __STDC__
  89. # define __MATH_PRECNAME(name,r) name##f##r
  90. # else
  91. # define __MATH_PRECNAME(name,r) name/**/f/**/r
  92. # endif
  93. # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
  94. # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
  95. # include <bits/mathcalls.h>
  96. # undef _Mdouble_
  97. # undef _Mdouble_BEGIN_NAMESPACE
  98. # undef _Mdouble_END_NAMESPACE
  99. # undef __MATH_PRECNAME
  100. # if (__STDC__ - 0 || __GNUC__ - 0) \
  101. && (defined __UCLIBC_HAS_LONG_DOUBLE_MATH__ || defined __LDBL_COMPAT)
  102. # ifdef __LDBL_COMPAT
  103. # ifdef __USE_ISOC99
  104. extern float __nldbl_nexttowardf (float __x, long double __y)
  105. __THROW __attribute__ ((__const__));
  106. # ifdef __REDIRECT_NTH
  107. extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
  108. __nldbl_nexttowardf)
  109. __attribute__ ((__const__));
  110. extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
  111. nextafter) __attribute__ ((__const__));
  112. extern long double __REDIRECT_NTH (nexttowardl,
  113. (long double __x, long double __y),
  114. nextafter) __attribute__ ((__const__));
  115. # endif
  116. # endif
  117. /* Include the file of declarations again, this time using `long double'
  118. instead of `double' and appending l to each function name. */
  119. # undef __MATHDECL_1
  120. # define __MATHDECL_2(type, function,suffix, args, alias) \
  121. extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
  122. args, alias)
  123. # define __MATHDECL_1(type, function,suffix, args) \
  124. __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
  125. # endif
  126. # ifndef _Mlong_double_
  127. # define _Mlong_double_ long double
  128. # endif
  129. # define _Mdouble_ _Mlong_double_
  130. # ifdef __STDC__
  131. # define __MATH_PRECNAME(name,r) name##l##r
  132. # else
  133. # define __MATH_PRECNAME(name,r) name/**/l/**/r
  134. # endif
  135. # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
  136. # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
  137. # include <bits/mathcalls.h>
  138. # undef _Mdouble_
  139. # undef _Mdouble_BEGIN_NAMESPACE
  140. # undef _Mdouble_END_NAMESPACE
  141. # undef __MATH_PRECNAME
  142. # endif /* __STDC__ || __GNUC__ */
  143. #endif /* Use misc or ISO C99. */
  144. #undef __MATHDECL_1
  145. #undef __MATHDECL
  146. #undef __MATHCALL
  147. #if defined __USE_MISC || defined __USE_XOPEN
  148. /* This variable is used by `gamma' and `lgamma'. */
  149. extern int signgam;
  150. #endif
  151. /* ISO C99 defines some generic macros which work on any data type. */
  152. #ifdef __USE_ISOC99
  153. /* Get the architecture specific values describing the floating-point
  154. evaluation. The following symbols will get defined:
  155. float_t floating-point type at least as wide as `float' used
  156. to evaluate `float' expressions
  157. double_t floating-point type at least as wide as `double' used
  158. to evaluate `double' expressions
  159. FLT_EVAL_METHOD
  160. Defined to
  161. 0 if `float_t' is `float' and `double_t' is `double'
  162. 1 if `float_t' and `double_t' are `double'
  163. 2 if `float_t' and `double_t' are `long double'
  164. else `float_t' and `double_t' are unspecified
  165. INFINITY representation of the infinity value of type `float'
  166. FP_FAST_FMA
  167. FP_FAST_FMAF
  168. FP_FAST_FMAL
  169. If defined it indicates that the `fma' function
  170. generally executes about as fast as a multiply and an add.
  171. This macro is defined only iff the `fma' function is
  172. implemented directly with a hardware multiply-add instructions.
  173. FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
  174. FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
  175. DECIMAL_DIG Number of decimal digits supported by conversion between
  176. decimal and all internal floating-point formats.
  177. */
  178. /* All floating-point numbers can be put in one of these categories. */
  179. enum
  180. {
  181. FP_NAN,
  182. # define FP_NAN FP_NAN
  183. FP_INFINITE,
  184. # define FP_INFINITE FP_INFINITE
  185. FP_ZERO,
  186. # define FP_ZERO FP_ZERO
  187. FP_SUBNORMAL,
  188. # define FP_SUBNORMAL FP_SUBNORMAL
  189. FP_NORMAL
  190. # define FP_NORMAL FP_NORMAL
  191. };
  192. /* Return number of classification appropriate for X. */
  193. # ifndef __UCLIBC_HAS_LONG_DOUBLE_MATH__
  194. # define fpclassify(x) \
  195. (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
  196. # else
  197. # define fpclassify(x) \
  198. (sizeof (x) == sizeof (float) \
  199. ? __fpclassifyf (x) \
  200. : sizeof (x) == sizeof (double) \
  201. ? __fpclassify (x) : __fpclassifyl (x))
  202. # endif
  203. /* Return nonzero value if sign of X is negative. */
  204. # ifndef __UCLIBC_HAS_LONG_DOUBLE_MATH__
  205. # define signbit(x) \
  206. (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
  207. # else
  208. # define signbit(x) \
  209. (sizeof (x) == sizeof (float) \
  210. ? __signbitf (x) \
  211. : sizeof (x) == sizeof (double) \
  212. ? __signbit (x) : __signbitl (x))
  213. # endif
  214. /* Return nonzero value if X is not +-Inf or NaN. */
  215. # ifndef __UCLIBC_HAS_LONG_DOUBLE_MATH__
  216. # define isfinite(x) \
  217. (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
  218. # else
  219. # define isfinite(x) \
  220. (sizeof (x) == sizeof (float) \
  221. ? __finitef (x) \
  222. : sizeof (x) == sizeof (double) \
  223. ? __finite (x) : __finitel (x))
  224. # endif
  225. /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
  226. # define isnormal(x) (fpclassify (x) == FP_NORMAL)
  227. /* Return nonzero value if X is a NaN. We could use `fpclassify' but
  228. we already have this functions `__isnan' and it is faster. */
  229. # ifndef __UCLIBC_HAS_LONG_DOUBLE_MATH__
  230. # define isnan(x) \
  231. (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
  232. # else
  233. # define isnan(x) \
  234. (sizeof (x) == sizeof (float) \
  235. ? __isnanf (x) \
  236. : sizeof (x) == sizeof (double) \
  237. ? __isnan (x) : __isnanl (x))
  238. # endif
  239. /* Return nonzero value is X is positive or negative infinity. */
  240. # ifndef __UCLIBC_HAS_LONG_DOUBLE_MATH__
  241. # define isinf(x) \
  242. (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
  243. # else
  244. # define isinf(x) \
  245. (sizeof (x) == sizeof (float) \
  246. ? __isinff (x) \
  247. : sizeof (x) == sizeof (double) \
  248. ? __isinf (x) : __isinfl (x))
  249. # endif
  250. /* Bitmasks for the math_errhandling macro. */
  251. # define MATH_ERRNO 1 /* errno set by math functions. */
  252. # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
  253. #endif /* Use ISO C99. */
  254. #ifdef __USE_MISC
  255. /* Support for various different standard error handling behaviors. */
  256. typedef enum
  257. {
  258. _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
  259. _SVID_, /* According to System V, release 4. */
  260. _XOPEN_, /* Nowadays also Unix98. */
  261. _POSIX_,
  262. _ISOC_ /* Actually this is ISO C99. */
  263. } _LIB_VERSION_TYPE;
  264. /* This variable can be changed at run-time to any of the values above to
  265. affect floating point error handling behavior (it may also be necessary
  266. to change the hardware FPU exception settings). */
  267. extern _LIB_VERSION_TYPE _LIB_VERSION;
  268. #endif
  269. #ifdef __USE_SVID
  270. /* In SVID error handling, `matherr' is called with this description
  271. of the exceptional condition.
  272. We have a problem when using C++ since `exception' is a reserved
  273. name in C++. */
  274. # ifdef __cplusplus
  275. struct __exception
  276. # else
  277. struct exception
  278. # endif
  279. {
  280. int type;
  281. char *name;
  282. double arg1;
  283. double arg2;
  284. double retval;
  285. };
  286. # ifdef __cplusplus
  287. extern int matherr (struct __exception *__exc) throw ();
  288. # else
  289. extern int matherr (struct exception *__exc);
  290. # endif
  291. # define X_TLOSS 1.41484755040568800000e+16
  292. /* Types of exceptions in the `type' field. */
  293. # define DOMAIN 1
  294. # define SING 2
  295. # define OVERFLOW 3
  296. # define UNDERFLOW 4
  297. # define TLOSS 5
  298. # define PLOSS 6
  299. /* SVID mode specifies returning this large value instead of infinity. */
  300. # define HUGE 3.40282347e+38F
  301. #else /* !SVID */
  302. # ifdef __USE_XOPEN
  303. /* X/Open wants another strange constant. */
  304. # define MAXFLOAT 3.40282347e+38F
  305. # endif
  306. #endif /* SVID */
  307. /* Some useful constants. */
  308. #if defined __USE_BSD || defined __USE_XOPEN
  309. # define M_E 2.7182818284590452354 /* e */
  310. # define M_LOG2E 1.4426950408889634074 /* log_2 e */
  311. # define M_LOG10E 0.43429448190325182765 /* log_10 e */
  312. # define M_LN2 0.69314718055994530942 /* log_e 2 */
  313. # define M_LN10 2.30258509299404568402 /* log_e 10 */
  314. # define M_PI 3.14159265358979323846 /* pi */
  315. # define M_PI_2 1.57079632679489661923 /* pi/2 */
  316. # define M_PI_4 0.78539816339744830962 /* pi/4 */
  317. # define M_1_PI 0.31830988618379067154 /* 1/pi */
  318. # define M_2_PI 0.63661977236758134308 /* 2/pi */
  319. # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
  320. # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
  321. # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
  322. #endif
  323. /* The above constants are not adequate for computation using `long double's.
  324. Therefore we provide as an extension constants with similar names as a
  325. GNU extension. Provide enough digits for the 128-bit IEEE quad. */
  326. #ifdef __USE_GNU
  327. # define M_El 2.7182818284590452353602874713526625L /* e */
  328. # define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */
  329. # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */
  330. # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */
  331. # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */
  332. # define M_PIl 3.1415926535897932384626433832795029L /* pi */
  333. # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
  334. # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
  335. # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
  336. # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
  337. # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
  338. # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */
  339. # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */
  340. #endif
  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
  346. #endif
  347. #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
  348. /* ISO C99 defines some macros to compare number while taking care for
  349. unordered numbers. Many FPUs provide special instructions to support
  350. these operations. Generic support in GCC for these as builtins went
  351. in before 3.0.0, but not all cpus added their patterns. We define
  352. versions that use the builtins here, and <bits/mathinline.h> will
  353. undef/redefine as appropriate for the specific GCC version in use. */
  354. # define isgreater(x, y) __builtin_isgreater(x, y)
  355. # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
  356. # define isless(x, y) __builtin_isless(x, y)
  357. # define islessequal(x, y) __builtin_islessequal(x, y)
  358. # define islessgreater(x, y) __builtin_islessgreater(x, y)
  359. # define isunordered(u, v) __builtin_isunordered(u, v)
  360. #endif
  361. /* Get machine-dependent inline versions (if there are any). */
  362. #ifdef __USE_EXTERN_INLINES
  363. # include <bits/mathinline.h>
  364. #endif
  365. #ifdef __USE_ISOC99
  366. /* If we've still got undefined comparison macros, provide defaults. */
  367. /* Return nonzero value if X is greater than Y. */
  368. # ifndef isgreater
  369. # define isgreater(x, y) \
  370. (__extension__ \
  371. ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
  372. !isunordered (__x, __y) && __x > __y; }))
  373. # endif
  374. /* Return nonzero value if X is greater than or equal to Y. */
  375. # ifndef isgreaterequal
  376. # define isgreaterequal(x, y) \
  377. (__extension__ \
  378. ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
  379. !isunordered (__x, __y) && __x >= __y; }))
  380. # endif
  381. /* Return nonzero value if X is less than Y. */
  382. # ifndef isless
  383. # define isless(x, y) \
  384. (__extension__ \
  385. ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
  386. !isunordered (__x, __y) && __x < __y; }))
  387. # endif
  388. /* Return nonzero value if X is less than or equal to Y. */
  389. # ifndef islessequal
  390. # define islessequal(x, y) \
  391. (__extension__ \
  392. ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
  393. !isunordered (__x, __y) && __x <= __y; }))
  394. # endif
  395. /* Return nonzero value if either X is less than Y or Y is less than X. */
  396. # ifndef islessgreater
  397. # define islessgreater(x, y) \
  398. (__extension__ \
  399. ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
  400. !isunordered (__x, __y) && (__x < __y || __y < __x); }))
  401. # endif
  402. /* Return nonzero value if arguments are unordered. */
  403. # ifndef isunordered
  404. # define isunordered(u, v) \
  405. (__extension__ \
  406. ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
  407. fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
  408. # endif
  409. #endif
  410. __END_DECLS
  411. #endif /* math.h */