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math.h.0p (16867B)

    

  1. '\" et
  2. .TH math.h "0P" 2017 "IEEE/The Open Group" "POSIX Programmer's Manual"
  3. .\"
  4. .SH PROLOG
  5. This manual page is part of the POSIX Programmer's Manual.
  6. The Linux implementation of this interface may differ (consult
  7. the corresponding Linux manual page for details of Linux behavior),
  8. or the interface may not be implemented on Linux.
  9. .\"
  10. .EQ
  11. delim $$
  12. .EN
  13. .SH NAME
  14. math.h
  15. \(em mathematical declarations
  16. .SH SYNOPSIS
  17. .LP
  18. .nf
  19. #include <math.h>
  20. .fi
  21. .SH DESCRIPTION
  22. Some of the functionality described on this reference page extends the
  23. ISO\ C standard. Applications shall define the appropriate feature test macro
  24. (see the System Interfaces volume of POSIX.1\(hy2017,
  25. .IR "Section 2.2" ", " "The Compilation Environment")
  26. to enable the visibility of these symbols in this header.
  27. .P
  28. The
  29. .IR <math.h> 
  30. header shall define at least the following types:
  31. .IP "\fBfloat_t\fR" 12
  32. A real-floating type at least as wide as
  33. .BR float .
  34. .IP "\fBdouble_t\fR" 12
  35. A real-floating type at least as wide as
  36. .BR double ,
  37. and at least as wide as
  38. .BR float_t .
  39. .P
  40. If FLT_EVAL_METHOD equals 0,
  41. .BR float_t
  42. and
  43. .BR double_t
  44. shall be
  45. .BR float
  46. and
  47. .BR double ,
  48. respectively; if FLT_EVAL_METHOD equals 1, they shall both be
  49. .BR double ;
  50. if FLT_EVAL_METHOD equals 2, they shall both be
  51. .BR "long double" ;
  52. for other values of FLT_EVAL_METHOD, they are otherwise
  53. implementation-defined.
  54. .P
  55. The
  56. .IR <math.h> 
  57. header shall define the following macros, where real-floating indicates
  58. that the argument shall be an expression of real-floating type:
  59. .sp
  60. .RS 4
  61. .nf
  63. int fpclassify(real-floating x);
  64. int isfinite(real-floating x);
  65. int isgreater(real-floating x, real-floating y);
  66. int isgreaterequal(real-floating x, real-floating y);
  67. int isinf(real-floating x);
  68. int isless(real-floating x, real-floating y);
  69. int islessequal(real-floating x, real-floating y);
  70. int islessgreater(real-floating x, real-floating y);
  71. int isnan(real-floating x);
  72. int isnormal(real-floating x);
  73. int isunordered(real-floating x, real-floating y);
  74. int signbit(real-floating x);
  75. .fi
  76. .P
  77. .RE
  78. .P
  79. The
  80. .IR <math.h> 
  81. header shall define the following symbolic constants. The values
  82. shall have type
  83. .BR double
  84. and shall be accurate to at least the precision of the
  85. .BR double
  86. type.
  87. .IP M_E 12
  88. Value of $e$
  89. .IP M_LOG2E 12
  90. Value of $log_ 2" " e$
  91. .IP M_LOG10E 12
  92. Value of $log_ 10" " e$
  93. .IP M_LN2 12
  94. Value of $log_ e" " 2$
  95. .IP M_LN10 12
  96. Value of $log_ e" " 10$
  97. .IP M_PI 12
  98. Value of $pi$
  99. .IP M_PI_2 12
  100. Value of $pi /2$
  101. .IP M_PI_4 12
  102. Value of $pi /4$
  103. .IP M_1_PI 12
  104. Value of $1/ pi$
  105. .IP M_2_PI 12
  106. Value of $2/ pi$
  107. .IP M_2_SQRTPI 12
  108. Value of $2/ sqrt pi$
  109. .IP M_SQRT2 12
  110. Value of $sqrt 2$
  111. .IP M_SQRT1_2 12
  112. Value of $1/ sqrt 2$
  113. .P
  114. The
  115. .IR <math.h> 
  116. header shall define the following symbolic constant:
  117. .IP MAXFLOAT 12
  118. Same value as FLT_MAX in
  119. .IR <float.h> .
  120. .P
  121. The
  122. .IR <math.h> 
  123. header shall define the following macros:
  124. .IP HUGE_VAL 12
  125. A positive
  126. .BR double
  127. constant expression, not necessarily representable as a
  128. .BR float .
  129. Used as an error value returned by the mathematics library. HUGE_VAL
  130. evaluates to +infinity on systems supporting IEEE\ Std\ 754\(hy1985.
  131. .IP HUGE_VALF 12
  132. A positive
  133. .BR float
  134. constant expression. Used as an error value returned by the mathematics
  135. library. HUGE_VALF evaluates to +infinity on systems supporting IEEE\ Std\ 754\(hy1985.
  136. .IP HUGE_VALL 12
  137. A positive
  138. .BR "long double"
  139. constant expression. Used as an error value returned by the mathematics
  140. library. HUGE_VALL evaluates to +infinity on systems supporting IEEE\ Std\ 754\(hy1985.
  141. .IP INFINITY 12
  142. A constant expression of type
  143. .BR float
  144. representing positive or unsigned infinity, if available; else a
  145. positive constant of type
  146. .BR float
  147. that overflows at translation time.
  148. .IP NAN 12
  149. A constant expression of type
  150. .BR float
  151. representing a quiet NaN. This macro is only defined if the
  152. implementation supports quiet NaNs for the
  153. .BR float
  154. type.
  155. .P
  156. The following macros shall be defined for number classification. They
  157. represent the mutually-exclusive kinds of floating-point values. They
  158. expand to integer constant expressions with distinct values. Additional
  159. implementation-defined floating-point classifications, with macro
  160. definitions beginning with FP_ and an uppercase letter, may also be
  161. specified by the implementation.
  162. .sp
  163. .RS
  164. FP_INFINITE
  165. FP_NAN
  166. FP_NORMAL
  167. FP_SUBNORMAL
  168. FP_ZERO
  169. .RE
  170. .P
  171. The following optional macros indicate whether the
  172. \fIfma\fR()
  173. family of functions are fast compared with direct code:
  174. .sp
  175. .RS
  176. FP_FAST_FMA
  177. FP_FAST_FMAF
  178. FP_FAST_FMAL
  179. .RE
  180. .P
  181. If defined, the FP_FAST_FMA macro shall expand to the integer constant
  182. 1 and shall indicate that the
  183. \fIfma\fR()
  184. function generally executes about as fast as, or faster than, a
  185. multiply and an add of
  186. .BR double
  187. operands. If undefined, the speed of execution is unspecified. The
  188. other macros have the equivalent meaning for the
  189. .BR float
  190. and
  191. .BR "long double"
  192. versions.
  193. .P
  194. The following macros shall expand to integer constant expressions whose
  195. values are returned by
  196. .IR ilogb (\c
  197. .IR x )
  198. if
  199. .IR x
  200. is zero or NaN, respectively. The value of FP_ILOGB0 shall be either
  201. {INT_MIN}
  202. or \-\c
  203. {INT_MAX}.
  204. The value of FP_ILOGBNAN shall be either
  205. {INT_MAX}
  206. or
  207. {INT_MIN}.
  208. .sp
  209. .RS
  210. FP_ILOGB0
  211. FP_ILOGBNAN
  212. .RE
  213. .P
  214. The following macros shall expand to the integer constants 1 and 2,
  215. respectively;
  216. .sp
  217. .RS
  218. MATH_ERRNO
  219. MATH_ERREXCEPT
  220. .RE
  221. .P
  222. The following macro shall expand to an expression that has type
  223. .BR int
  224. and the value MATH_ERRNO, MATH_ERREXCEPT, or the bitwise-inclusive OR
  225. of both:
  226. .sp
  227. .RS
  228. math_errhandling
  229. .RE
  230. .P
  231. The value of math_errhandling is constant for the duration of the
  232. program. It is unspecified whether math_errhandling is a macro or an
  233. identifier with external linkage. If a macro definition is suppressed
  234. or a program defines an identifier with the name math_errhandling , the
  235. behavior is undefined. If the expression (math_errhandling &
  236. MATH_ERREXCEPT) can be non-zero, the implementation shall define the
  237. macros FE_DIVBYZERO, FE_INVALID, and FE_OVERFLOW in
  238. .IR <fenv.h> .
  239. .P
  240. The following shall be declared as functions and may also be defined as
  241. macros. Function prototypes shall be provided.
  242. .sp
  243. .RS 4
  244. .nf
  246. double      acos(double);
  247. float       acosf(float);
  248. double      acosh(double);
  249. float       acoshf(float);
  250. long double acoshl(long double);
  251. long double acosl(long double);
  252. double      asin(double);
  253. float       asinf(float);
  254. double      asinh(double);
  255. float       asinhf(float);
  256. long double asinhl(long double);
  257. long double asinl(long double);
  258. double      atan(double);
  259. double      atan2(double, double);
  260. float       atan2f(float, float);
  261. long double atan2l(long double, long double);
  262. float       atanf(float);
  263. double      atanh(double);
  264. float       atanhf(float);
  265. long double atanhl(long double);
  266. long double atanl(long double);
  267. double      cbrt(double);
  268. float       cbrtf(float);
  269. long double cbrtl(long double);
  270. double      ceil(double);
  271. float       ceilf(float);
  272. long double ceill(long double);
  273. double      copysign(double, double);
  274. float       copysignf(float, float);
  275. long double copysignl(long double, long double);
  276. double      cos(double);
  277. float       cosf(float);
  278. double      cosh(double);
  279. float       coshf(float);
  280. long double coshl(long double);
  281. long double cosl(long double);
  282. double      erf(double);
  283. double      erfc(double);
  284. float       erfcf(float);
  285. long double erfcl(long double);
  286. float       erff(float);
  287. long double erfl(long double);
  288. double      exp(double);
  289. double      exp2(double);
  290. float       exp2f(float);
  291. long double exp2l(long double);
  292. float       expf(float);
  293. long double expl(long double);
  294. double      expm1(double);
  295. float       expm1f(float);
  296. long double expm1l(long double);
  297. double      fabs(double);
  298. float       fabsf(float);
  299. long double fabsl(long double);
  300. double      fdim(double, double);
  301. float       fdimf(float, float);
  302. long double fdiml(long double, long double);
  303. double      floor(double);
  304. float       floorf(float);
  305. long double floorl(long double);
  306. double      fma(double, double, double);
  307. float       fmaf(float, float, float);
  308. long double fmal(long double, long double, long double);
  309. double      fmax(double, double);
  310. float       fmaxf(float, float);
  311. long double fmaxl(long double, long double);
  312. double      fmin(double, double);
  313. float       fminf(float, float);
  314. long double fminl(long double, long double);
  315. double      fmod(double, double);
  316. float       fmodf(float, float);
  317. long double fmodl(long double, long double);
  318. double      frexp(double, int *);
  319. float       frexpf(float, int *);
  320. long double frexpl(long double, int *);
  321. double      hypot(double, double);
  322. float       hypotf(float, float);
  323. long double hypotl(long double, long double);
  324. int         ilogb(double);
  325. int         ilogbf(float);
  326. int         ilogbl(long double);
  327. double      j0(double);
  328. double      j1(double);
  329. double      jn(int, double);
  330. double      ldexp(double, int);
  331. float       ldexpf(float, int);
  332. long double ldexpl(long double, int);
  333. double      lgamma(double);
  334. float       lgammaf(float);
  335. long double lgammal(long double);
  336. long long   llrint(double);
  337. long long   llrintf(float);
  338. long long   llrintl(long double);
  339. long long   llround(double);
  340. long long   llroundf(float);
  341. long long   llroundl(long double);
  342. double      log(double);
  343. double      log10(double);
  344. float       log10f(float);
  345. long double log10l(long double);
  346. double      log1p(double);
  347. float       log1pf(float);
  348. long double log1pl(long double);
  349. double      log2(double);
  350. float       log2f(float);
  351. long double log2l(long double);
  352. double      logb(double);
  353. float       logbf(float);
  354. long double logbl(long double);
  355. float       logf(float);
  356. long double logl(long double);
  357. long        lrint(double);
  358. long        lrintf(float);
  359. long        lrintl(long double);
  360. long        lround(double);
  361. long        lroundf(float);
  362. long        lroundl(long double);
  363. double      modf(double, double *);
  364. float       modff(float, float *);
  365. long double modfl(long double, long double *);
  366. double      nan(const char *);
  367. float       nanf(const char *);
  368. long double nanl(const char *);
  369. double      nearbyint(double);
  370. float       nearbyintf(float);
  371. long double nearbyintl(long double);
  372. double      nextafter(double, double);
  373. float       nextafterf(float, float);
  374. long double nextafterl(long double, long double);
  375. double      nexttoward(double, long double);
  376. float       nexttowardf(float, long double);
  377. long double nexttowardl(long double, long double);
  378. double      pow(double, double);
  379. float       powf(float, float);
  380. long double powl(long double, long double);
  381. double      remainder(double, double);
  382. float       remainderf(float, float);
  383. long double remainderl(long double, long double);
  384. double      remquo(double, double, int *);
  385. float       remquof(float, float, int *);
  386. long double remquol(long double, long double, int *);
  387. double      rint(double);
  388. float       rintf(float);
  389. long double rintl(long double);
  390. double      round(double);
  391. float       roundf(float);
  392. long double roundl(long double);
  393. double      scalbln(double, long);
  394. float       scalblnf(float, long);
  395. long double scalblnl(long double, long);
  396. double      scalbn(double, int);
  397. float       scalbnf(float, int);
  398. long double scalbnl(long double, int);
  399. double      sin(double);
  400. float       sinf(float);
  401. double      sinh(double);
  402. float       sinhf(float);
  403. long double sinhl(long double);
  404. long double sinl(long double);
  405. double      sqrt(double);
  406. float       sqrtf(float);
  407. long double sqrtl(long double);
  408. double      tan(double);
  409. float       tanf(float);
  410. double      tanh(double);
  411. float       tanhf(float);
  412. long double tanhl(long double);
  413. long double tanl(long double);
  414. double      tgamma(double);
  415. float       tgammaf(float);
  416. long double tgammal(long double);
  417. double      trunc(double);
  418. float       truncf(float);
  419. long double truncl(long double);
  420. double      y0(double);
  421. double      y1(double);
  422. double      yn(int, double);
  423. .fi
  424. .P
  425. .RE
  426. .P
  427. The following external variable shall be defined:
  428. .sp
  429. .RS 4
  430. .nf
  432. extern int signgam;
  433. .fi
  434. .P
  435. .RE
  436. .P
  437. The behavior of each of the functions defined in
  438. .IR <math.h> 
  439. is specified in the System Interfaces volume of POSIX.1\(hy2017 for all representable values of its input
  440. arguments, except where stated otherwise. Each function shall execute
  441. as if it were a single operation without generating any externally
  442. visible exceptional conditions.
  443. .LP
  444. .IR "The following sections are informative."
  445. .SH "APPLICATION USAGE"
  446. The FP_CONTRACT pragma can be used to allow (if the state is on) or
  447. disallow (if the state is off) the implementation to contract
  448. expressions. Each pragma can occur either outside external declarations
  449. or preceding all explicit declarations and statements inside a compound
  450. statement. When outside external declarations, the pragma takes effect
  451. from its occurrence until another FP_CONTRACT pragma is encountered, or
  452. until the end of the translation unit. When inside a compound
  453. statement, the pragma takes effect from its occurrence until another
  454. FP_CONTRACT pragma is encountered (including within a nested compound
  455. statement), or until the end of the compound statement; at the end of a
  456. compound statement the state for the pragma is restored to its
  457. condition just before the compound statement. If this pragma is used in
  458. any other context, the behavior is undefined. The default state (on or
  459. off) for the pragma is implementation-defined.
  460. .P
  461. Applications should use FLT_MAX as described in the
  462. .IR <float.h> 
  463. header instead of the obsolescent MAXFLOAT.
  464. .P
  465. Note that if FLT_EVAL_METHOD is neither 0 nor 1, then some constants might
  466. not compare equal as expected; for example, \fR(double)M_PI == M_PI\fR
  467. can fail.
  468. .SH RATIONALE
  469. Before the ISO/IEC\ 9899:\|1999 standard, the math library was defined only for the floating
  470. type
  471. .BR double .
  472. All the names formed by appending
  473. .BR 'f' 
  474. or
  475. .BR 'l' 
  476. to a name in
  477. .IR <math.h> 
  478. were reserved to allow for the definition of
  479. .BR float
  480. and
  481. .BR "long double"
  482. libraries; and the ISO/IEC\ 9899:\|1999 standard provides for all three versions of math
  483. functions.
  484. .P
  485. The functions
  486. .IR ecvt (\|),
  487. .IR fcvt (\|),
  488. and
  489. .IR gcvt (\|)
  490. have been dropped from the ISO\ C standard since their capability is available
  491. through
  492. \fIsprintf\fR().
  493. .SH "FUTURE DIRECTIONS"
  494. None.
  495. .SH "SEE ALSO"
  496. .IR "\fB<float.h>\fP",
  497. .IR "\fB<stddef.h>\fP",
  498. .IR "\fB<sys_types.h>\fP"
  499. .P
  500. The System Interfaces volume of POSIX.1\(hy2017,
  501. .IR "Section 2.2" ", " "The Compilation Environment",
  502. .IR "\fIacos\fR\^(\|)",
  503. .IR "\fIacosh\fR\^(\|)",
  504. .IR "\fIasin\fR\^(\|)",
  505. .IR "\fIasinh\fR\^(\|)",
  506. .IR "\fIatan\fR\^(\|)",
  507. .IR "\fIatan2\fR\^(\|)",
  508. .IR "\fIatanh\fR\^(\|)",
  509. .IR "\fIcbrt\fR\^(\|)",
  510. .IR "\fIceil\fR\^(\|)",
  511. .IR "\fIcopysign\fR\^(\|)",
  512. .IR "\fIcos\fR\^(\|)",
  513. .IR "\fIcosh\fR\^(\|)",
  514. .IR "\fIerf\fR\^(\|)",
  515. .IR "\fIerfc\fR\^(\|)",
  516. .IR "\fIexp\fR\^(\|)",
  517. .IR "\fIexp2\fR\^(\|)",
  518. .IR "\fIexpm1\fR\^(\|)",
  519. .IR "\fIfabs\fR\^(\|)",
  520. .IR "\fIfdim\fR\^(\|)",
  521. .IR "\fIfloor\fR\^(\|)",
  522. .IR "\fIfma\fR\^(\|)",
  523. .IR "\fIfmax\fR\^(\|)",
  524. .IR "\fIfmin\fR\^(\|)",
  525. .IR "\fIfmod\fR\^(\|)",
  526. .IR "\fIfpclassify\fR\^(\|)",
  527. .IR "\fIfrexp\fR\^(\|)",
  528. .IR "\fIhypot\fR\^(\|)",
  529. .IR "\fIilogb\fR\^(\|)",
  530. .IR "\fIisfinite\fR\^(\|)",
  531. .IR "\fIisgreater\fR\^(\|)",
  532. .IR "\fIisgreaterequal\fR\^(\|)",
  533. .IR "\fIisinf\fR\^(\|)",
  534. .IR "\fIisless\fR\^(\|)",
  535. .IR "\fIislessequal\fR\^(\|)",
  536. .IR "\fIislessgreater\fR\^(\|)",
  537. .IR "\fIisnan\fR\^(\|)",
  538. .IR "\fIisnormal\fR\^(\|)",
  539. .IR "\fIisunordered\fR\^(\|)",
  540. .IR "\fIj0\fR\^(\|)",
  541. .IR "\fIldexp\fR\^(\|)",
  542. .IR "\fIlgamma\fR\^(\|)",
  543. .IR "\fIllrint\fR\^(\|)",
  544. .IR "\fIllround\fR\^(\|)",
  545. .IR "\fIlog\fR\^(\|)",
  546. .IR "\fIlog10\fR\^(\|)",
  547. .IR "\fIlog1p\fR\^(\|)",
  548. .IR "\fIlog2\fR\^(\|)",
  549. .IR "\fIlogb\fR\^(\|)",
  550. .IR "\fIlrint\fR\^(\|)",
  551. .IR "\fIlround\fR\^(\|)",
  552. .IR "\fImodf\fR\^(\|)",
  553. .IR "\fInan\fR\^(\|)",
  554. .IR "\fInearbyint\fR\^(\|)",
  555. .IR "\fInextafter\fR\^(\|)",
  556. .IR "\fIpow\fR\^(\|)",
  557. .IR "\fIremainder\fR\^(\|)",
  558. .IR "\fIremquo\fR\^(\|)",
  559. .IR "\fIrint\fR\^(\|)",
  560. .IR "\fIround\fR\^(\|)",
  561. .IR "\fIscalbln\fR\^(\|)",
  562. .IR "\fIsignbit\fR\^(\|)",
  563. .IR "\fIsin\fR\^(\|)",
  564. .IR "\fIsinh\fR\^(\|)",
  565. .IR "\fIsqrt\fR\^(\|)",
  566. .IR "\fItan\fR\^(\|)",
  567. .IR "\fItanh\fR\^(\|)",
  568. .IR "\fItgamma\fR\^(\|)",
  569. .IR "\fItrunc\fR\^(\|)",
  570. .IR "\fIy0\fR\^(\|)"
  571. .\"
  572. .SH COPYRIGHT
  573. Portions of this text are reprinted and reproduced in electronic form
  574. from IEEE Std 1003.1-2017, Standard for Information Technology
  575. -- Portable Operating System Interface (POSIX), The Open Group Base
  576. Specifications Issue 7, 2018 Edition,
  577. Copyright (C) 2018 by the Institute of
  578. Electrical and Electronics Engineers, Inc and The Open Group.
  579. In the event of any discrepancy between this version and the original IEEE and
  580. The Open Group Standard, the original IEEE and The Open Group Standard
  581. is the referee document. The original Standard can be obtained online at
  582. http://www.opengroup.org/unix/online.html .
  583. .PP
  584. Any typographical or formatting errors that appear
  585. in this page are most likely
  586. to have been introduced during the conversion of the source files to
  587. man page format. To report such errors, see
  588. https://www.kernel.org/doc/man-pages/reporting_bugs.html .