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<math.h>(0P)		   POSIX Programmer's Manual		  <math.h>(0P)

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>(0P)
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