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7.4.7 <math.h>

Performs various mathematical operations.

The following constants (macros) are all implementation-defined.

Type	Definition Name	Description
Constant (macro)	EDOM	Indicates the value to be set in errno if the value of a parameter input to a function is outside the range of values defined in the function.
	ERANGE	Indicates the value to be set in errno if the result of a function cannot be represented as a double type value, or if an overflow or an underflow occurs.
	HUGE_VAL HUGE_VALF <-lang=c99> HUGE_VALL <-lang=c99>	Indicates the value for the function return value if the result of a function overflows.
	INFINITY <-lang=c99>	Expanded to a float-type constant expression that represents positive or unsigned infinity.
	NAN <-lang=c99>	Defined when float-type qNaN is supported.
	FP_INFINITE <-lang=c99> FP_NAN <-lang=c99> FP_NORMAL <-lang=c99> FP_SUBNORMAL <-lang=c99> FP_ZERO <-lang=c99>	These indicate exclusive types of floating-point values.
	FP_FAST_FMA <-lang=c99> FP_FAST_FMA <-lang=c99> FFP_FAST_FMAFL <-lang=c99>	Defined when the fma function is executed at the same or higher speed than a multiplication and an addition with double-type operands.
	FP_ILOGB0 <-lang=c99> FP_ILOGBNAN <-lang=c99>	These are expanded to an integer constant expression of the value returned by ilogb when they are 0 or not-a-number, respectively.
	MATH_ERRNO <-lang=c99> MATH_ERREXCEPT <-lang=c99>	These are expanded to integer constants 1 and 2, respectively.
	math_errhandling <-lang=c99>	Expanded to an int-type expression whose value is a bitwise logical OR of MATH_ERRNO and MATH_ERREXCEPT.
Type	float_t <-lang=c99> double_t <-lang=c99>	These are floating-point types having the same width as float and double, respectively.
Function (macro)	fpclassify <-lang=c99>	Classifies argument values into not-a-number, infinity, normalized number, denormalized number, and 0.
	isfinite <-lang=c99>	Determines whether the argument is a finite value.
	isinf <-lang=c99>	Determines whether the argument is infinity.
	isnan <-lang=c99>	Determines whether the argument is a not-a-number.
	isnormal <-lang=c99>	Determines whether the argument is a normalized number.
	signbit <-lang=c99>	Determines whether the sign of the argument is negative.
	isgreater <-lang=c99>	Determines whether the first argument is greater than the second argument.
	isgreaterequal <-lang=c99>	Determines whether the first argument is equal to or greater than the second argument.
	isless <-lang=c99>	Determines whether the first argument is smaller than the second argument.
	islessequal <-lang=c99>	Determines whether the first argument is equal to or smaller than the second argument.
	islessgreater <-lang=c99>	Determines whether the first argument is smaller or greater than the second argument.
	isunordered <-lang=c99>	Determines whether the arguments are not ordered.
Function	acos / acosf / acosl	Calculates the arc cosine of a floating-point number.
	asin / asinf / asinl	Calculates the arc sine of a floating-point number.
	atan / atanf / atanl	Calculates the arc tangent of a floating-point number.
	atan2 / atan2f / atan2l	Calculates the arc tangent of the result of a division of two floating-point numbers.
	cos / cosf / cosl	Calculates the cosine of a floating-point radian value.
	sin / sinf / sinl	Calculates the sine of a floating-point radian value.
	tan / tanf / tanl	Calculates the tangent of a floating-point radian value.
	cosh / coshf / coshl	Calculates the hyperbolic cosine of a floating-point number.
	sinh / sinhf / sinhl	Calculates the hyperbolic sine of a floating-point number.
	tanh / tanhf / tanhl	Calculates the hyperbolic tangent of a floating-point number.
	exp / expf / expl	Calculates the exponential function of a floating-point number.
	frexp / frexpf / frexpl	Breaks a floating-point number into a [0.5, 1.0) value and a power of 2.
	ldexp / ldexpf / ldexpl	Multiplies a floating-point number by a power of 2.
	log / logf / logl	Calculates the natural logarithm of a floating-point number.
	log10 / log10f / log10l	Calculates the base-ten logarithm of a floating-point number.
	modf / modff / modfl	Breaks a floating-point number into integral and fractional parts.
	pow / powf / powl	Calculates a power of a floating-point number.
	sqrt / sqrtf / sqrtl	Calculates the positive square root of a floating-point number.
Function	ceil / ceilf / ceill	Calculates the smallest integral value not less than or equal to the given floating-point number.
	fabs / fabsf / fabsl	Calculates the absolute value of a floating-point number.
	floor / floorf / floorl	Calculates the largest integral value not greater than or equal to the given floating-point number.
	fmod / fmodf / fmodl	Calculates the remainder of a division of two floating-point numbers.
	acosh / acoshf / acoshl <-lang=c99>	Calculates the hyperbolic arc cosine of a floating-point number.
	asinh / asinhf / asinhl <-lang=c99>	Calculates the hyperbolic arc sine of a floating-point number.
	atanh / atanhf / atanhl <-lang=c99>	Calculates the hyperbolic arc tangent of a floating-point number.
	exp2 / exp2f / exp2l <-lang=c99>	Calculates the value of 2 raised to the power x.
	expm1 / expm1f / expm1l <-lang=c99>	Calculates the natural logarithm raised to the power x and subtracts 1 from the result.
	ilogb / ilogbf / ilogbl <-lang=c99>	Extracts the exponent of x as a signed int value.
	log1p / log1pf / log1pl <-lang=c99>	Calculates the natural logarithm of the argument + 1.
	log2 / log2f / log2l <-lang=c99>	Calculates the base-2 logarithm.
	logb / logbf / logbl <-lang=c99>	Extracts the exponent of x as a signed integer.
	scalbn / scalbnf / scalbnl / scalbln / scalblnf / scalblnl <-lang=c99>	Calculates x × FLT_RADIXn.
	cbrt / cbrtf / cbrtl <-lang=c99>	Calculates the cube root of a floating-point number.
	hypot / hypotf / hypotl <-lang=c99>	Calculates the square root of the sum of squares of two parameters ( ).
	erf / erff / erfl <-lang=c99>	Calculates the error function.
	erfc / erfcf / erfcl <-lang=c99>	Calculates the complementary error function.
	lgamma / lgammaf / lgammal <-lang=c99>	Calculates the natural logarithm of the absolute value of the gamma function.
	tgamma / tgammaf / tgammal <-lang=c99>	Calculates the gamma function.
	nearbyint / nearbyintf / nearbyintl <-lang=c99>	Rounds a floating-point number to an integer in the floating-point representation according to the current rounding direction.
	rint / rintf / rintl <-lang=c99>	Equivalent to nearbyint except that this function group may generate floating-point exception.
Function	lrint / lrintf / lrintl / llrint / llrintf / llrintl <-lang=c99>	Rounds a floating-point number to the nearest integer according to the rounding direction.
	round / roundf / roundl <-lang=c99>	Rounds a floating-point number to the nearest integer in the floating-point representation.
	lround / lroundf / lroundl / llround / llroundf / llroundl <-lang=c99>	Rounds a floating-point number to the nearest integer.
	trunc / truncf / truncl <-lang=c99>	Rounds a floating-point number to the nearest integer in the floating-point representation.
	remainder / remainderf / remainderl <-lang=c99>	Calculates remainder x REM y specified in the IEEE60559 standard.
	remquo / remquof / remquol <-lang=c99>	Calculates the value having the same sign as x/y and the absolute value congruent modulo-2n to the absolute value of the quotient.
	copysign / copysignf / copysignl <-lang=c99>	Generates a value consisting of the given absolute value and sign.
	nan / nanf / nanl <-lang=c99>	nan("n string") is equivalent to ("NAN(n string)", (char**) NULL).
	nextafter / nextafterf / nextafterl <-lang=c99>	Converts a floating-point number to the type of the function and calculates the representable value following the converted number on the real axis.
	nexttoward / nexttowardf / nexttowardl <-lang=c99>	Equivalent to the nextafter function group except that the second argument is of type long double and returns the second argument after conversion to the type of the function.
	fdim / fdimf / fdiml <-lang=c99>	Calculates the positive difference.
	fmax / fmaxf / fmaxl <-lang=c99>	Obtains the greater of two values.
	fmin / fminf / fminl <-lang=c99>	Obtains the smaller of two values.
	fma / fmaf / fmal <-lang=c99>	Calculates (d1 * d2) + d3 as a single ternary operation.

Operation in the event of an error is described below.

(1)	Domain error

A domain error occurs if the value of a parameter input to a function is outside the domain over which the mathematical function is defined. In this case, the value of EDOM is set in errno. The function return value in implementation-defined.

(2)	Range error

A range error occurs if the result of a function cannot be represented as a value of the double type. In this case, the value of ERANGE is set in errno. If the result overflows, the function returns the value of HUGE_VAL, HUGE_VALF, or HUGE_VALL with the same sign as the correct value of the function. If the result underflows, 0 is returned as the return value.

Notes 1.

If there is a possibility of a domain error resulting from a <math.h> function call, it is dangerous to use the resultant value directly. The value of errno should always be checked before using the result in such cases.

[Format]

         1   x=asin(a);

         2   if (errno==EDOM)

         3       printf ("error\n");

         4   else

         5       printf ("result is : %lf\n",x);

In line 1, the arc sine value is computed using the asin function. If the value of argument a is outside the asin function domain [–1.0, 1.0], the EDOM value is set in errno. Line 2 determines whether a domain error has occurred. If a domain error has occurred, error is output in line 3. If there is no domain error, the arc sine value is output in line 5.

Notes 2.

Whether or not a range error occurs depends on the internal representation format of floating-point types determined by the compiler. For example, if an internal representation format that allows an infinity to be represented as a value is used, <math.h> library functions can be implemented without causing range errors.

Implementation-Defined Specifications

Item	Compiler Specifications
Value returned by a mathematical function if an input argument is out of the range	A not-a-number is returned. For details on the format of not-a-numbers, refer to section "(5) Floating-Point Number Specifications" in "4.1.5 Internal Data Representation and Areas".
Whether errno is set to the value of macro ERANGE if an underflow error occurs in a mathematical function	For the functions that set errno to the value of ERANGE, see "10.5.6 Standard Library Error Messages". The other functions do not set errno to ERANGE.
Whether a range error occurs if the second argument in the fmod function is 0	A range error occurs. For details of the return value from fmod, see "fmod / fmodf / fmodl" in "7.4.7 <math.h>".