math.h 17 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, see
  15. <http://www.gnu.org/licenses/>. */
  16. /*
  17. * ISO C99 Standard: 7.12 Mathematics <math.h>
  18. */
  19. #ifndef _MATH_H
  20. #define _MATH_H 1
  21. #include <features.h>
  22. __BEGIN_DECLS
  23. /* Get machine-dependent HUGE_VAL value (returned on overflow).
  24. On all IEEE754 machines, this is +Infinity. */
  25. #include <bits/huge_val.h>
  26. #ifdef __USE_ISOC99
  27. # include <bits/huge_valf.h>
  28. # include <bits/huge_vall.h>
  29. /* Get machine-dependent INFINITY value. */
  30. # include <bits/inf.h>
  31. /* Get machine-dependent NAN value (returned for some domain errors). */
  32. # include <bits/nan.h>
  33. #endif /* __USE_ISOC99 */
  34. /* Get general and ISO C99 specific information. */
  35. #include <bits/mathdef.h>
  36. /* The file <bits/mathcalls.h> contains the prototypes for all the
  37. actual math functions. These macros are used for those prototypes,
  38. so we can easily declare each function as both `name' and `__name',
  39. and can declare the float versions `namef' and `__namef'. */
  40. #define __MATHDECL_1(type,function,suffix,args) \
  41. extern type __MATH_PRECNAME(function,suffix) args __THROW
  42. #define __MATHDECL(type,function,suffix,args) \
  43. __MATHDECL_1(type,function,suffix,args);
  44. #define __MATHCALL(function,suffix,args) \
  45. __MATHDECL(_Mdouble_,function,suffix,args)
  46. #define __MATHDECLX(type,function,suffix,args,attrib) \
  47. __MATHDECL_1(type,function,suffix,args) __attribute__ (attrib); \
  48. __MATH_maybe_libm_hidden_proto(function)
  49. #define __MATHCALLX(function,suffix,args,attrib) \
  50. __MATHDECLX(_Mdouble_,function,suffix,args,attrib)
  51. /* Decls which are also used internally in libm.
  52. Only the main variant is used internally, no need to try to avoid relocs
  53. for the {l,f} variants. */
  54. #define __MATHDECLI(type,function,suffix,args) \
  55. __MATHDECL_1(type,function,suffix,args); \
  56. __MATH_maybe_libm_hidden_proto(function)
  57. #define __MATHCALLI(function,suffix,args) \
  58. __MATHDECLI(_Mdouble_,function,suffix,args)
  59. /* Private helpers for purely macro impls below.
  60. Only make __foo{,f,l} visible but not (the macro-only) foo. */
  61. #if defined _LIBC
  62. # define __MATHDECL_PRIV(type,function,suffix,args,attrib) \
  63. __MATHDECL_1(type,__CONCAT(__,function),suffix,args) __attribute__ (attrib); \
  64. libm_hidden_proto(__MATH_PRECNAME(__##function,suffix))
  65. #else
  66. # define __MATHDECL_PRIV(type,function,suffix,args,attrib) \
  67. __MATHDECL_1(type,__CONCAT(__,function),suffix,args) __attribute__ (attrib);
  68. #endif
  69. /* Include the file of declarations, declaring double versions */
  70. #if defined _LIBC
  71. # define __MATH_maybe_libm_hidden_proto(x) libm_hidden_proto(x)
  72. #else
  73. # define __MATH_maybe_libm_hidden_proto(x)
  74. #endif
  75. #define _Mdouble_ double
  76. #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  77. #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
  78. #define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD
  79. #include <bits/mathcalls.h>
  80. #undef _Mdouble_
  81. #undef _Mdouble_BEGIN_NAMESPACE
  82. #undef _Mdouble_END_NAMESPACE
  83. #undef __MATH_PRECNAME
  84. #undef __MATH_maybe_libm_hidden_proto
  85. #if defined __USE_MISC || defined __USE_ISOC99
  86. /* Include the file of declarations again, this time using `float'
  87. instead of `double' and appending f to each function name. */
  88. # define __MATH_maybe_libm_hidden_proto(x)
  89. # ifndef _Mfloat_
  90. # define _Mfloat_ float
  91. # endif
  92. # define _Mdouble_ _Mfloat_
  93. # define _Mdouble_is_float_
  94. # ifdef __STDC__
  95. # define __MATH_PRECNAME(name,r) name##f##r
  96. # else
  97. # define __MATH_PRECNAME(name,r) name/**/f/**/r
  98. # endif
  99. # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
  100. # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
  101. # include <bits/mathcalls.h>
  102. # undef _Mdouble_is_float_
  103. # undef _Mdouble_
  104. # undef _Mdouble_BEGIN_NAMESPACE
  105. # undef _Mdouble_END_NAMESPACE
  106. # undef _Mfloat_
  107. # undef __MATH_PRECNAME
  108. # undef __MATH_maybe_libm_hidden_proto
  109. # if (defined __STDC__ || defined __GNUC__) \
  110. && (!defined __NO_LONG_DOUBLE_MATH || defined __LDBL_COMPAT)
  111. # ifdef __LDBL_COMPAT
  112. # ifdef __USE_ISOC99
  113. extern float __nldbl_nexttowardf (float __x, long double __y) __THROW
  114. __attribute__ ((__const__));
  115. # ifdef __REDIRECT_NTH
  116. extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y), __nldbl_nexttowardf)
  117. __attribute__ ((__const__));
  118. extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y), nextafter)
  119. __attribute__ ((__const__));
  120. extern long double __REDIRECT_NTH (nexttowardl, (long double __x, long double __y), nextafter)
  121. __attribute__ ((__const__));
  122. # endif
  123. # endif
  124. /* Include the file of declarations again, this time using `long double'
  125. instead of `double' and appending l to each function name. */
  126. # undef __MATHDECL_1
  127. # define __MATHDECL_2(type,function,suffix,args,alias) \
  128. extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix),args,alias)
  129. # define __MATHDECL_1(type,function,suffix,args) \
  130. __MATHDECL_2(type,function,suffix,args,__CONCAT(function,suffix))
  131. # endif
  132. # define __MATH_maybe_libm_hidden_proto(x)
  133. # ifndef _Mlong_double_
  134. # define _Mlong_double_ long double
  135. # endif
  136. # define _Mdouble_ _Mlong_double_
  137. # ifdef __STDC__
  138. # define __MATH_PRECNAME(name,r) name##l##r
  139. # else
  140. # define __MATH_PRECNAME(name,r) name/**/l/**/r
  141. # endif
  142. # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
  143. # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
  144. # include <bits/mathcalls.h>
  145. # undef _Mdouble_
  146. # undef _Mdouble_BEGIN_NAMESPACE
  147. # undef _Mdouble_END_NAMESPACE
  148. # undef _Mlong_double_
  149. # undef __MATH_PRECNAME
  150. # undef __MATH_maybe_libm_hidden_proto
  151. # endif /* __STDC__ || __GNUC__ */
  152. #endif /* Use misc or ISO C99. */
  153. #undef __MATHDECL_1
  154. #undef __MATHDECL
  155. #undef __MATHCALL
  156. #if defined __USE_MISC || defined __USE_XOPEN
  157. /* This variable is used by `gamma' and `lgamma'. */
  158. extern int signgam;
  159. #endif
  160. /* ISO C99 defines some generic macros which work on any data type. */
  161. #ifdef __USE_ISOC99
  162. /* Get the architecture specific values describing the floating-point
  163. evaluation. The following symbols will get defined:
  164. float_t floating-point type at least as wide as `float' used
  165. to evaluate `float' expressions
  166. double_t floating-point type at least as wide as `double' used
  167. to evaluate `double' expressions
  168. FLT_EVAL_METHOD
  169. Defined to
  170. 0 if `float_t' is `float' and `double_t' is `double'
  171. 1 if `float_t' and `double_t' are `double'
  172. 2 if `float_t' and `double_t' are `long double'
  173. else `float_t' and `double_t' are unspecified
  174. INFINITY representation of the infinity value of type `float'
  175. FP_FAST_FMA
  176. FP_FAST_FMAF
  177. FP_FAST_FMAL
  178. If defined it indicates that the `fma' function
  179. generally executes about as fast as a multiply and an add.
  180. This macro is defined only iff the `fma' function is
  181. implemented directly with a hardware multiply-add instructions.
  182. FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
  183. FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
  184. DECIMAL_DIG Number of decimal digits supported by conversion between
  185. decimal and all internal floating-point formats.
  186. */
  187. /* All floating-point numbers can be put in one of these categories. */
  188. enum
  189. {
  190. FP_NAN,
  191. # define FP_NAN FP_NAN
  192. FP_INFINITE,
  193. # define FP_INFINITE FP_INFINITE
  194. FP_ZERO,
  195. # define FP_ZERO FP_ZERO
  196. FP_SUBNORMAL,
  197. # define FP_SUBNORMAL FP_SUBNORMAL
  198. FP_NORMAL
  199. # define FP_NORMAL FP_NORMAL
  200. };
  201. /* Return number of classification appropriate for X. */
  202. # ifdef __NO_LONG_DOUBLE_MATH
  203. # define fpclassify(x) \
  204. (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
  205. # else
  206. # define fpclassify(x) \
  207. (sizeof (x) == sizeof (float) \
  208. ? __fpclassifyf (x) \
  209. : sizeof (x) == sizeof (double) \
  210. ? __fpclassify (x) : __fpclassifyl (x))
  211. # endif
  212. /* Return nonzero value if sign of X is negative. */
  213. # ifdef __NO_LONG_DOUBLE_MATH
  214. # define signbit(x) \
  215. (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
  216. # else
  217. # define signbit(x) \
  218. (sizeof (x) == sizeof (float) \
  219. ? __signbitf (x) \
  220. : sizeof (x) == sizeof (double) \
  221. ? __signbit (x) : __signbitl (x))
  222. # endif
  223. /* Return nonzero value if X is not +-Inf or NaN. */
  224. # ifdef __NO_LONG_DOUBLE_MATH
  225. # define isfinite(x) \
  226. (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
  227. # else
  228. # define isfinite(x) \
  229. (sizeof (x) == sizeof (float) \
  230. ? __finitef (x) \
  231. : sizeof (x) == sizeof (double) \
  232. ? __finite (x) : __finitel (x))
  233. # endif
  234. /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
  235. # define isnormal(x) (fpclassify (x) == FP_NORMAL)
  236. /* Return nonzero value if X is a NaN. We could use `fpclassify' but
  237. we already have this functions `__isnan' and it is faster. */
  238. # ifdef __NO_LONG_DOUBLE_MATH
  239. # define isnan(x) \
  240. (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
  241. # else
  242. # define isnan(x) \
  243. (sizeof (x) == sizeof (float) \
  244. ? __isnanf (x) \
  245. : sizeof (x) == sizeof (double) \
  246. ? __isnan (x) : __isnanl (x))
  247. # endif
  248. /* Return nonzero value is X is positive or negative infinity. */
  249. # ifdef __NO_LONG_DOUBLE_MATH
  250. # define isinf(x) \
  251. (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
  252. # else
  253. # define isinf(x) \
  254. (sizeof (x) == sizeof (float) \
  255. ? __isinff (x) \
  256. : sizeof (x) == sizeof (double) \
  257. ? __isinf (x) : __isinfl (x))
  258. # endif
  259. /* Bitmasks for the math_errhandling macro. */
  260. # define MATH_ERRNO 1 /* errno set by math functions. */
  261. # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
  262. #endif /* Use ISO C99. */
  263. #ifdef __USE_MISC
  264. /* Support for various different standard error handling behaviors. */
  265. typedef enum
  266. {
  267. _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
  268. _SVID_, /* According to System V, release 4. */
  269. _XOPEN_, /* Nowadays also Unix98. */
  270. _POSIX_,
  271. _ISOC_ /* Actually this is ISO C99. */
  272. } _LIB_VERSION_TYPE;
  273. /* This variable can be changed at run-time to any of the values above to
  274. affect floating point error handling behavior (it may also be necessary
  275. to change the hardware FPU exception settings). */
  276. extern _LIB_VERSION_TYPE _LIB_VERSION;
  277. #endif
  278. #ifdef __USE_SVID
  279. /* In SVID error handling, `matherr' is called with this description
  280. of the exceptional condition.
  281. We have a problem when using C++ since `exception' is a reserved
  282. name in C++. */
  283. # ifdef __cplusplus
  284. struct __exception
  285. # else
  286. struct exception
  287. # endif
  288. {
  289. int type;
  290. char *name;
  291. double arg1;
  292. double arg2;
  293. double retval;
  294. };
  295. # ifdef __cplusplus
  296. extern int matherr (struct __exception *__exc) throw ();
  297. # else
  298. extern int matherr (struct exception *__exc);
  299. # endif
  300. # define X_TLOSS 1.41484755040568800000e+16
  301. /* Types of exceptions in the `type' field. */
  302. # define DOMAIN 1
  303. # define SING 2
  304. # define OVERFLOW 3
  305. # define UNDERFLOW 4
  306. # define TLOSS 5
  307. # define PLOSS 6
  308. /* SVID mode specifies returning this large value instead of infinity. */
  309. # define HUGE 3.40282347e+38F
  310. #else /* !SVID */
  311. # ifdef __USE_XOPEN
  312. # ifdef __UCLIBC_SUSV4_LEGACY__
  313. /* X/Open wants another strange constant. */
  314. # define MAXFLOAT 3.40282347e+38F
  315. # endif
  316. # endif
  317. #endif /* SVID */
  318. /* Some useful constants. */
  319. #if defined __USE_BSD || defined __USE_XOPEN
  320. # define M_E 2.7182818284590452354 /* e */
  321. # define M_LOG2E 1.4426950408889634074 /* log_2 e */
  322. # define M_LOG10E 0.43429448190325182765 /* log_10 e */
  323. # define M_LN2 0.69314718055994530942 /* log_e 2 */
  324. # define M_LN10 2.30258509299404568402 /* log_e 10 */
  325. # define M_PI 3.14159265358979323846 /* pi */
  326. # define M_PI_2 1.57079632679489661923 /* pi/2 */
  327. # define M_PI_4 0.78539816339744830962 /* pi/4 */
  328. # define M_1_PI 0.31830988618379067154 /* 1/pi */
  329. # define M_2_PI 0.63661977236758134308 /* 2/pi */
  330. # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
  331. # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
  332. # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
  333. #endif
  334. /* The above constants are not adequate for computation using `long double's.
  335. Therefore we provide as an extension constants with similar names as a
  336. GNU extension. Provide enough digits for the 128-bit IEEE quad. */
  337. #ifdef __USE_GNU
  338. # define M_El 2.7182818284590452353602874713526625L /* e */
  339. # define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */
  340. # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */
  341. # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */
  342. # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */
  343. # define M_PIl 3.1415926535897932384626433832795029L /* pi */
  344. # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
  345. # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
  346. # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
  347. # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
  348. # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
  349. # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */
  350. # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */
  351. #endif
  352. /* When compiling in strict ISO C compatible mode we must not use the
  353. inline functions since they, among other things, do not set the
  354. `errno' variable correctly. */
  355. #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
  356. # define __NO_MATH_INLINES 1
  357. #endif
  358. #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
  359. /* ISO C99 defines some macros to compare number while taking care for
  360. unordered numbers. Many FPUs provide special instructions to support
  361. these operations. Generic support in GCC for these as builtins went
  362. in before 3.0.0, but not all cpus added their patterns. We define
  363. versions that use the builtins here, and <bits/mathinline.h> will
  364. undef/redefine as appropriate for the specific GCC version in use. */
  365. # define isgreater(x, y) __builtin_isgreater(x, y)
  366. # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
  367. # define isless(x, y) __builtin_isless(x, y)
  368. # define islessequal(x, y) __builtin_islessequal(x, y)
  369. # define islessgreater(x, y) __builtin_islessgreater(x, y)
  370. # define isunordered(u, v) __builtin_isunordered(u, v)
  371. #endif
  372. /* Get machine-dependent inline versions (if there are any). */
  373. #ifdef __USE_EXTERN_INLINES
  374. # include <bits/mathinline.h>
  375. #endif
  376. #ifdef __USE_ISOC99
  377. /* If we've still got undefined comparison macros, provide defaults. */
  378. /* Return nonzero value if X is greater than Y. */
  379. # ifndef isgreater
  380. # define isgreater(x, y) \
  381. (__extension__ \
  382. ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
  383. !isunordered (__x, __y) && __x > __y; }))
  384. # endif
  385. /* Return nonzero value if X is greater than or equal to Y. */
  386. # ifndef isgreaterequal
  387. # define isgreaterequal(x, y) \
  388. (__extension__ \
  389. ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
  390. !isunordered (__x, __y) && __x >= __y; }))
  391. # endif
  392. /* Return nonzero value if X is less than Y. */
  393. # ifndef isless
  394. # define isless(x, y) \
  395. (__extension__ \
  396. ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
  397. !isunordered (__x, __y) && __x < __y; }))
  398. # endif
  399. /* Return nonzero value if X is less than or equal to Y. */
  400. # ifndef islessequal
  401. # define islessequal(x, y) \
  402. (__extension__ \
  403. ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
  404. !isunordered (__x, __y) && __x <= __y; }))
  405. # endif
  406. /* Return nonzero value if either X is less than Y or Y is less than X. */
  407. # ifndef islessgreater
  408. # define islessgreater(x, y) \
  409. (__extension__ \
  410. ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
  411. !isunordered (__x, __y) && (__x < __y || __y < __x); }))
  412. # endif
  413. /* Return nonzero value if arguments are unordered. */
  414. # ifndef isunordered
  415. # define isunordered(u, v) \
  416. (__extension__ \
  417. ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
  418. fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
  419. # endif
  420. #endif
  421. __END_DECLS
  422. #endif /* math.h */