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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,
       Section 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
       following 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
       definitions  beginning  with  FP_  and an uppercase letter, may also be
       specified 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()
       function 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
       program.  It  is  unspecified whether math_errhandling is a macro or an
       identifier 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
       representable  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
       expressions. 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
       statement, the pragma takes effect from its  occurrence  until  another
       FP_CONTRACT  pragma  is encountered (including within a nested compound
       statement), or until the end of the compound statement; at the end of a
       compound  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
       definition    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 .