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