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<math.h>(P)		   POSIX Programmer's Manual		   <math.h>(P)

PROLOG
       This  manual  page is part of the POSIX Programmer's Manual.  The Linux
       implementation of this interface may differ (consult the	 corresponding
       Linux  manual page for details of Linux behavior), or the interface may
       not be implemented on Linux.

NAME
       math.h - mathematical declarations

SYNOPSIS
       #include <math.h>

DESCRIPTION
       Some of the functionality described on this reference page extends  the
       ISO C  standard. Applications shall define the appropriate feature test
       macro (see the System Interfaces volume of  IEEE Std 1003.1-2001,  Sec‐
       tion  2.2,  The	Compilation  Environment)  to enable the visibility of
       these symbols in this header.

       The <math.h> header shall include definitions for at least the  follow‐
       ing types:

       float_t
	      A real-floating type at least as wide as float.

       double_t
	      A real-floating type at least as wide as double, and at least as
	      wide as float_t.

       If FLT_EVAL_METHOD equals 0, float_t and double_t shall	be  float  and
       double,	respectively;  if FLT_EVAL_METHOD equals 1, they shall both be
       double; if FLT_EVAL_METHOD equals 2, they shall both  be	 long  double;
       for other values of FLT_EVAL_METHOD, they are otherwise implementation-
       defined.

       The <math.h> header shall define	 the  following	 macros,  where	 real-
       floating	 indicates  that  the argument shall be an expression of real-
       floating type:

	      int fpclassify(real-floating x);
	      int isfinite(real-floating x);
	      int isinf(real-floating x);
	      int isnan(real-floating x);
	      int isnormal(real-floating x);
	      int signbit(real-floating x);
	      int isgreater(real-floating x, real-floating y);
	      int isgreaterequal(real-floating x, real-floating y);
	      int isless(real-floating x, real-floating y);
	      int islessequal(real-floating x, real-floating y);
	      int islessgreater(real-floating x, real-floating y);
	      int isunordered(real-floating x, real-floating y);

       The <math.h> header shall provide for  the  following  constants.   The
       values  are of type double and are accurate within the precision of the
       double type.

       M_E    Value of e

       M_LOG2E
	      Value of log_2e

       M_LOG10E
	      Value of log_10e

       M_LN2  Value of log_e2

       M_LN10 Value of log_e10

       M_PI   Value of pi

       M_PI_2 Value of pi/2

       M_PI_4 Value of pi/4

       M_1_PI Value of 1/pi

       M_2_PI Value of 2/pi

       M_2_SQRTPI
	      Value of 2/ sqrt pi

       M_SQRT2
	      Value of sqrt 2

       M_SQRT1_2
	      Value of 1/sqrt 2

       The header shall define the following symbolic constants:

       MAXFLOAT
	      Value of maximum	non-infinite  single-precision	floating-point
	      number.

       HUGE_VAL
	      A positive double expression, not necessarily representable as a
	      float. Used as  an  error	 value	returned  by  the  mathematics
	      library.	HUGE_VAL  evaluates to +infinity on systems supporting
	      IEEE Std 754-1985.

       HUGE_VALF
	      A positive float constant expression. Used  as  an  error	 value
	      returned	by  the	 mathematics  library.	HUGE_VALF evaluates to
	      +infinity on systems supporting IEEE Std 754-1985.

       HUGE_VALL
	      A positive long double constant expression.  Used	 as  an	 error
	      value  returned  by the mathematics library. HUGE_VALL evaluates
	      to +infinity on systems supporting IEEE Std 754-1985.

       INFINITY
	      A constant expression of type  float  representing  positive  or
	      unsigned	infinity,  if  available;  else a positive constant of
	      type float that overflows at translation time.

       NAN    A constant expression of type float representing	a  quiet  NaN.
	      This  symbolic  constant	is  only defined if the implementation
	      supports quiet NaNs for the float type.

       The following macros shall be defined for number	 classification.  They
       represent  the  mutually-exclusive kinds of floating-point values. They
       expand to integer constant expressions with distinct values. Additional
       implementation-defined floating-point classifications, with macro defi‐
       nitions beginning with FP_ and an uppercase letter, may also be	speci‐
       fied by the implementation.

	      FP_INFINITE
	      FP_NAN
	      FP_NORMAL
	      FP_SUBNORMAL
	      FP_ZERO

       The  following  optional	 macros	 indicate  whether the fma() family of
       functions are fast compared with direct code:

	      FP_FAST_FMA
	      FP_FAST_FMAF
	      FP_FAST_FMAL

       The FP_FAST_FMA macro shall be defined to indicate that the fma() func‐
       tion  generally	executes  about as fast as, or faster than, a multiply
       and an add of double operands. The other	 macros	 have  the  equivalent
       meaning for the float and long double versions.

       The following macros shall expand to integer constant expressions whose
       values are returned by ilogb( x) if x is zero or NaN, respectively. The
       value  of FP_ILOGB0 shall be either {INT_MIN} or - {INT_MAX}. The value
       of FP_ILOGBNAN shall be either {INT_MAX} or {INT_MIN}.

	      FP_ILOGB0
	      FP_ILOGBNAN

       The following macros shall expand to the integer	 constants  1  and  2,
       respectively;

	      MATH_ERRNO
	      MATH_ERREXCEPT

       The following macro shall expand to an expression that has type int and
       the value MATH_ERRNO, MATH_ERREXCEPT, or the  bitwise-inclusive	OR  of
       both:

	      math_errhandling

       The  value of math_errhandling is constant for the duration of the pro‐
       gram. It is unspecified whether math_errhandling is a macro or an iden‐
       tifier  with external linkage. If a macro definition is suppressed or a
       program defines an identifier with  the	name  math_errhandling	,  the
       behavior	  is   undefined.   If	 the  expression  (math_errhandling  &
       MATH_ERREXCEPT) can be non-zero, the implementation  shall  define  the
       macros FE_DIVBYZERO, FE_INVALID, and FE_OVERFLOW in <fenv.h>.

       The following shall be declared as functions and may also be defined as
       macros. Function prototypes shall be provided.

	      double	  acos(double);
	      float	  acosf(float);
	      double	  acosh(double);
	      float	  acoshf(float);
	      long double acoshl(long double);
	      long double acosl(long double);
	      double	  asin(double);
	      float	  asinf(float);
	      double	  asinh(double);
	      float	  asinhf(float);
	      long double asinhl(long double);
	      long double asinl(long double);
	      double	  atan(double);
	      double	  atan2(double, double);
	      float	  atan2f(float, float);
	      long double atan2l(long double, long double);
	      float	  atanf(float);
	      double	  atanh(double);
	      float	  atanhf(float);
	      long double atanhl(long double);
	      long double atanl(long double);
	      double	  cbrt(double);
	      float	  cbrtf(float);
	      long double cbrtl(long double);
	      double	  ceil(double);
	      float	  ceilf(float);
	      long double ceill(long double);
	      double	  copysign(double, double);
	      float	  copysignf(float, float);
	      long double copysignl(long double, long double);
	      double	  cos(double);
	      float	  cosf(float);
	      double	  cosh(double);
	      float	  coshf(float);
	      long double coshl(long double);
	      long double cosl(long double);
	      double	  erf(double);
	      double	  erfc(double);
	      float	  erfcf(float);
	      long double erfcl(long double);
	      float	  erff(float);
	      long double erfl(long double);
	      double	  exp(double);
	      double	  exp2(double);
	      float	  exp2f(float);
	      long double exp2l(long double);
	      float	  expf(float);
	      long double expl(long double);
	      double	  expm1(double);
	      float	  expm1f(float);
	      long double expm1l(long double);
	      double	  fabs(double);
	      float	  fabsf(float);
	      long double fabsl(long double);
	      double	  fdim(double, double);
	      float	  fdimf(float, float);
	      long double fdiml(long double, long double);
	      double	  floor(double);
	      float	  floorf(float);
	      long double floorl(long double);
	      double	  fma(double, double, double);
	      float	  fmaf(float, float, float);
	      long double fmal(long double, long double, long double);
	      double	  fmax(double, double);
	      float	  fmaxf(float, float);
	      long double fmaxl(long double, long double);
	      double	  fmin(double, double);
	      float	  fminf(float, float);
	      long double fminl(long double, long double);
	      double	  fmod(double, double);
	      float	  fmodf(float, float);
	      long double fmodl(long double, long double);
	      double	  frexp(double, int *);
	      float	  frexpf(float value, int *);
	      long double frexpl(long double value, int *);
	      double	  hypot(double, double);
	      float	  hypotf(float, float);
	      long double hypotl(long double, long double);
	      int	  ilogb(double);
	      int	  ilogbf(float);
	      int	  ilogbl(long double);

	      double	  j0(double);
	      double	  j1(double);
	      double	  jn(int, double);

	      double	  ldexp(double, int);
	      float	  ldexpf(float, int);
	      long double ldexpl(long double, int);
	      double	  lgamma(double);
	      float	  lgammaf(float);
	      long double lgammal(long double);
	      long long	  llrint(double);
	      long long	  llrintf(float);
	      long long	  llrintl(long double);
	      long long	  llround(double);
	      long long	  llroundf(float);
	      long long	  llroundl(long double);
	      double	  log(double);
	      double	  log10(double);
	      float	  log10f(float);
	      long double log10l(long double);
	      double	  log1p(double);
	      float	  log1pf(float);
	      long double log1pl(long double);
	      double	  log2(double);
	      float	  log2f(float);
	      long double log2l(long double);
	      double	  logb(double);
	      float	  logbf(float);
	      long double logbl(long double);
	      float	  logf(float);
	      long double logl(long double);
	      long	  lrint(double);
	      long	  lrintf(float);
	      long	  lrintl(long double);
	      long	  lround(double);
	      long	  lroundf(float);
	      long	  lroundl(long double);
	      double	  modf(double, double *);
	      float	  modff(float, float *);
	      long double modfl(long double, long double *);
	      double	  nan(const char *);
	      float	  nanf(const char *);
	      long double nanl(const char *);
	      double	  nearbyint(double);
	      float	  nearbyintf(float);
	      long double nearbyintl(long double);
	      double	  nextafter(double, double);
	      float	  nextafterf(float, float);
	      long double nextafterl(long double, long double);
	      double	  nexttoward(double, long double);
	      float	  nexttowardf(float, long double);
	      long double nexttowardl(long double, long double);
	      double	  pow(double, double);
	      float	  powf(float, float);
	      long double powl(long double, long double);
	      double	  remainder(double, double);
	      float	  remainderf(float, float);
	      long double remainderl(long double, long double);
	      double	  remquo(double, double, int *);
	      float	  remquof(float, float, int *);
	      long double remquol(long double, long double, int *);
	      double	  rint(double);
	      float	  rintf(float);
	      long double rintl(long double);
	      double	  round(double);
	      float	  roundf(float);
	      long double roundl(long double);

	      double	  scalb(double, double);

	      double	  scalbln(double, long);
	      float	  scalblnf(float, long);
	      long double scalblnl(long double, long);
	      double	  scalbn(double, int);
	      float	  scalbnf(float, int);
	      long double scalbnl(long double, int);
	      double	  sin(double);
	      float	  sinf(float);
	      double	  sinh(double);
	      float	  sinhf(float);
	      long double sinhl(long double);
	      long double sinl(long double);
	      double	  sqrt(double);
	      float	  sqrtf(float);
	      long double sqrtl(long double);
	      double	  tan(double);
	      float	  tanf(float);
	      double	  tanh(double);
	      float	  tanhf(float);
	      long double tanhl(long double);
	      long double tanl(long double);
	      double	  tgamma(double);
	      float	  tgammaf(float);
	      long double tgammal(long double);
	      double	  trunc(double);
	      float	  truncf(float);
	      long double truncl(long double);

	      double	  y0(double);
	      double	  y1(double);
	      double	  yn(int, double);

       The following external variable shall be defined:

	      extern int signgam;

       The behavior of each of the functions defined in <math.h> is  specified
       in  the System Interfaces volume of IEEE Std 1003.1-2001 for all repre‐
       sentable values of its input arguments, except where stated  otherwise.
       Each  function  shall  execute as if it were a single operation without
       generating any externally visible exceptional conditions.

       The following sections are informative.

APPLICATION USAGE
       The FP_CONTRACT pragma can be used to allow (if the  state  is  on)  or
       disallow	 (if  the state is off) the implementation to contract expres‐
       sions. Each pragma can occur either outside  external  declarations  or
       preceding  all  explicit	 declarations and statements inside a compound
       statement. When outside external declarations, the pragma takes	effect
       from its occurrence until another FP_CONTRACT pragma is encountered, or
       until the end of the translation unit. When inside  a  compound	state‐
       ment, the pragma takes effect from its occurrence until another FP_CON‐
       TRACT pragma is encountered (including within a nested compound	state‐
       ment), or until the end of the compound statement; at the end of a com‐
       pound statement the state for the pragma is restored to	its  condition
       just before the compound statement. If this pragma is used in any other
       context, the behavior is undefined. The default state (on or  off)  for
       the pragma is implementation-defined.

RATIONALE
       Before  the  ISO/IEC 9899:1999  standard,  the math library was defined
       only for the floating type double. All the names	 formed	 by  appending
       'f' or 'l' to a name in <math.h> were reserved to allow for the defini‐
       tion of float and long  double  libraries;  and	the  ISO/IEC 9899:1999
       standard provides for all three versions of math functions.

       The  functions  ecvt(),	fcvt(),	 and gcvt() have been dropped from the
       ISO C standard since their capability is available  through  sprintf().
       These  are  provided  on	 XSI-conformant	 systems supporting the Legacy
       Option Group.

FUTURE DIRECTIONS
       None.

SEE ALSO
       <stddef.h>  ,  <sys/types.h>  ,	the  System   Interfaces   volume   of
       IEEE Std 1003.1-2001, acos(), acosh(), asin(), atan(), atan2(), cbrt(),
       ceil(), cos(), cosh(), erf(), exp(), expm1(), fabs(), floor(),  fmod(),
       frexp(),	 hypot(),  ilogb(),  isnan(),  j0(), ldexp(), lgamma(), log(),
       log10(), log1p(),  logb(),  modf(),  nextafter(),  pow(),  remainder(),
       rint(), scalb(), sin(), sinh(), sqrt(), tan(), tanh(), y0()

COPYRIGHT
       Portions	 of  this text are reprinted and reproduced in electronic form
       from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
       --  Portable  Operating	System	Interface (POSIX), The Open Group Base
       Specifications Issue 6, Copyright (C) 2001-2003	by  the	 Institute  of
       Electrical  and	Electronics  Engineers, Inc and The Open Group. In the
       event of any discrepancy between this version and the original IEEE and
       The  Open Group Standard, the original IEEE and The Open Group Standard
       is the referee document. The original Standard can be  obtained	online
       at http://www.opengroup.org/unix/online.html .

IEEE/The Open Group		     2003			   <math.h>(P)
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