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

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 POSIX.1‐2017, Section 2.2,
       The Compilation Environment) to enable the visibility of these symbols
       in this header.

       The <math.h> header shall define 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 isgreater(real-floating x, real-floating y);
	   int isgreaterequal(real-floating x, real-floating y);
	   int isinf(real-floating x);
	   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 isnan(real-floating x);
	   int isnormal(real-floating x);
	   int isunordered(real-floating x, real-floating y);
	   int signbit(real-floating x);

       The <math.h> header shall define the following symbolic constants. The
       values shall have type double and shall be accurate to at least the
       precision of the double type.

       M_E	   Value of e

       M_LOG2E	   Value of log _ 2   e

       M_LOG10E	   Value of log _ 10   e

       M_LN2	   Value of log _ e   2

       M_LN10	   Value of log _ e   10

       M_PI	   Value of π

       M_PI_2	   Value of π / 2

       M_PI_4	   Value of π / 4

       M_1_PI	   Value of 1 / π

       M_2_PI	   Value of 2 / π

       M_2_SQRTPI  Value of 2 / √(π)

       M_SQRT2	   Value of √(2)

       M_SQRT1_2   Value of 1 / √(2)

       The <math.h> header shall define the following symbolic constant:

       MAXFLOAT	   Same value as FLT_MAX in <float.h>.

       The <math.h> header shall define the following macros:

       HUGE_VAL	   A positive double constant 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 macro 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

       If defined, the FP_FAST_FMA macro shall expand to the integer constant
       1 and shall indicate that the fma() function generally executes about
       as fast as, or faster than, a multiply and an add of double operands.
       If undefined, the speed of execution is unspecified. 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, int *);
	   long double frexpl(long double, 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      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 POSIX.1‐2017 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.

       Applications should use FLT_MAX as described in the <float.h> header
       instead of the obsolescent MAXFLOAT.

       Note that if FLT_EVAL_METHOD is neither 0 nor 1, then some constants
       might not compare equal as expected; for example, (double)M_PI == M_PI
       can fail.

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().

FUTURE DIRECTIONS
       None.

SEE ALSO
       <float.h>, <stddef.h>, <sys_types.h>

       The System Interfaces volume of POSIX.1‐2017, Section 2.2, The
       Compilation Environment, acos(), acosh(), asin(), asinh(), atan(),
       atan2(), atanh(), cbrt(), ceil(), copysign(), cos(), cosh(), erf(),
       erfc(), exp(), exp2(), expm1(), fabs(), fdim(), floor(), fma(), fmax(),
       fmin(), fmod(), fpclassify(), frexp(), hypot(), ilogb(), isfinite(),
       isgreater(), isgreaterequal(), isinf(), isless(), islessequal(),
       islessgreater(), isnan(), isnormal(), isunordered(), j0(), ldexp(),
       lgamma(), llrint(), llround(), log(), log10(), log1p(), log2(), logb(),
       lrint(), lround(), modf(), nan(), nearbyint(), nextafter(), pow(),
       remainder(), remquo(), rint(), round(), scalbln(), signbit(), sin(),
       sinh(), sqrt(), tan(), tanh(), tgamma(), trunc(), y0()

COPYRIGHT
       Portions of this text are reprinted and reproduced in electronic form
       from IEEE Std 1003.1-2017, Standard for Information Technology --
       Portable Operating System Interface (POSIX), The Open Group Base
       Specifications Issue 7, 2018 Edition, Copyright (C) 2018 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 .

       Any typographical or formatting errors that appear in this page are
       most likely to have been introduced during the conversion of the source
       files to man page format. To report such errors, see
       https://www.kernel.org/doc/man-pages/reporting_bugs.html .

IEEE/The Open Group		     2017			    math.h(0P)