IEEE Std 1003.1-2017 (Revision of IEEE Std 1003.1-2008)

Copyright © 2001-2018 IEEE and The Open Group

math.h - mathematical declarations

#include <math.h>

^{[CX]}Some of the functionality described on this reference page extends the ISO C standard. Applications shall define the appropriate feature test macro (see XSHThe 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 asfloat_t.If FLT_EVAL_METHOD equals 0,

float_tanddouble_tshall befloatanddouble, respectively; if FLT_EVAL_METHOD equals 1, they shall both bedouble; if FLT_EVAL_METHOD equals 2, they shall both belong 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 typedoubleand shall be accurate to at least the precision of thedoubletype.

- M_E
^{[XSI]}Value ofe- M_LOG2E
^{[XSI]}Value of log_{2}e- M_LOG10E
^{[XSI]}Value of log_{10}e- M_LN2
^{[XSI]}Value of log_{e}2- M_LN10
^{[XSI]}Value of log_{e}10- M_PI
^{[XSI]}Value of- M_PI_2
^{[XSI]}Value of /2- M_PI_4
^{[XSI]}Value of /4- M_1_PI
^{[XSI]}Value of 1/- M_2_PI
^{[XSI]}Value of 2/- M_2_SQRTPI
^{[XSI]}Value of 2/- M_SQRT2
^{[XSI]}Value of 2- M_SQRT1_2
^{[XSI]}Value of 1/ 2The

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

- MAXFLOAT
^{[OB XSI]}Same value as FLT_MAX in<float.h>.The

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

- HUGE_VAL
- A positive
doubleconstant expression, not necessarily representable as afloat. 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
floatconstant 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 doubleconstant 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
floatrepresenting positive or unsigned infinity, if available; else a positive constant of typefloatthat overflows at translation time.- NAN
- A constant expression of type
floatrepresenting a quiet NaN. This macro is only defined if the implementation supports quiet NaNs for thefloattype.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_ZEROThe following optional macros indicate whether the

fma() family of functions are fast compared with direct code:FP_FAST_FMA FP_FAST_FMAF FP_FAST_FMALIf 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 ofdoubleoperands. If undefined, the speed of execution is unspecified. The other macros have the equivalent meaning for thefloatandlong doubleversions.The following macros shall expand to integer constant expressions whose values are returned by

ilogb(x) ifxis 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_ILOGBNANThe following macros shall expand to the integer constants 1 and 2, respectively;

MATH_ERRNO MATH_ERREXCEPTThe following macro shall expand to an expression that has type

intand the value MATH_ERRNO, MATH_ERREXCEPT, or the bitwise-inclusive OR of both:math_errhandlingThe 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);^{[XSI]}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);^{[XSI]}double y0(double); double y1(double); double yn(int, double);The following external variable shall be defined:

^{[XSI]}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 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_PIcan fail.

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 offloatandlong doublelibraries; and the ISO/IEC 9899:1999 standard provides for all three versions of math functions.The functions

ecvt(),fcvt(), andgcvt() have been dropped from the ISO C standard since their capability is available throughsprintf().

None.

<float.h>,<stddef.h>,<sys/types.h>XSH

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

First released in Issue 1.

This reference page is updated to align with the ISO/IEC 9899:1999 standard.

IEEE Std 1003.1-2001/Cor 2-2004, item XBD/TC2/D6/21 is applied, making it clear that the meaning of the FP_FAST_FMA macro is unspecified if the macro is undefined.

ISO/IEC 9899:1999 standard, Technical Corrigendum 2 #47 (SD5-XBD-ERN-52) is applied, clarifying the wording of the FP_FAST_FMA macro.

The MAXFLOAT constant is marked obsolescent.

This reference page is clarified with respect to macros and symbolic constants.

POSIX.1-2008, Technical Corrigendum 2, XBD/TC2-2008/0063 [801] and XBD/TC2-2008/0064 [801] are applied.

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