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       math.h - mathematical declarations


       #include <math.h>


       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:

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

              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

       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

              Value of log_2e

              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

              Value of 2/ sqrt pi

              Value of sqrt 2

              Value of 1/sqrt 2

       The header shall define the following symbolic constants:

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

              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.

              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.

              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.

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

       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

       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.


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


       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


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


       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:


       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.


       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.


       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.




       <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()


       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 .