roundl3avr

<math.h>: mathematics

Part of avr_math(3avr).

Usage

Functions

float cosf (float x)

double cos (double x)

long double cosl (long double x)

float sinf (float x)

double sin (double x)

long double sinl (long double x)

float tanf (float x)

double tan (double x)

long double tanl (long double x)

static float fabsf (float __x)

static double fabs (double __x)

static long double fabsl (long double __x)

float fmodf (float x, float y)

double fmod (double x, double y)

long double fmodl (long double x, long double y)

float modff (float x, float *iptr)

double modf (double x, double *iptr)

long double modfl (long double x, long double *iptr)

float sqrtf (float x)

double sqrt (double x)

long double sqrtl (long double x)

float cbrtf (float x)

double cbrt (double x)

long double cbrtl (long double x)

float hypotf (float x, float y)

double hypot (double x, double y)

long double hypotl (long double x, long double y)

float floorf (float x)

double floor (double x)

long double floorl (long double x)

float ceilf (float x)

double ceil (double x)

long double ceill (long double x)

float frexpf (float x, int *pexp)

double frexp (double x, int *pexp)

long double frexpl (long double x, int *pexp)

float ldexpf (float x, int iexp)

double ldexp (double x, int iexp)

long double ldexpl (long double x, int iexp)

float expf (float x)

double exp (double x)

long double expl (long double x)

float coshf (float x)

double cosh (double x)

long double coshl (long double x)

float sinhf (float x)

double sinh (double x)

long double sinhl (long double x)

float tanhf (float x)

double tanh (double x)

long double tanhl (long double x)

float acosf (float x)

double acos (double x)

long double acosl (long double x)

float asinf (float x)

double asin (double x)

long double asinl (long double x)

float atanf (float x)

double atan (double x)

long double atanl (long double x)

float atan2f (float y, float x)

double atan2 (double y, double x)

long double atan2l (long double y, long double x)

float logf (float x)

double log (double x)

long double logl (long double x)

float log10f (float x)

double log10 (double x)

long double log10l (long double x)

float powf (float x, float y)

double pow (double x, double y)

long double powl (long double x, long double y)

int isnanf (float x)

int isnan (double x)

int isnanl (long double x)

int isinff (float x)

int isinf (double x)

int isinfl (long double x)

static int isfinitef (float __x)

static int isfinite (double __x)

static int isfinitel (long double __x)

static float copysignf (float __x, float __y)

static double copysign (double __x, double __y)

static long double copysignl (long double __x, long double __y)

int signbitf (float x)

int signbit (double x)

int signbitl (long double x)

float fdimf (float x, float y)

double fdim (double x, double y)

long double fdiml (long double x, long double y)

float fmaf (float x, float y, float z)

double fma (double x, double y, double z)

long double fmal (long double x, long double y, long double z)

float fmaxf (float x, float y)

double fmax (double x, double y)

long double fmaxl (long double x, long double y)

float fminf (float x, float y)

double fmin (double x, double y)

long double fminl (long double x, long double y)

float truncf (float x)

double trunc (double x)

long double truncl (long double x)

float roundf (float x)

double round (double x)

long double roundl (long double x)

long lroundf (float x)

long lround (double x)

long lroundl (long double x)

long lrintf (float x)

long lrint (double x)

long lrintl (long double x)

Non-Standard Math Functions

float squaref (float x)

double square (double x)

long double squarel (long double x)

Detailed Description

#include <math.h>

This header file declares basic mathematics constants and functions.

Notes:

•: Math functions do not raise exceptions and do not change the errno variable. Therefore the majority of them are declared with const attribute, for better optimization by GCC.

•: 64-bit floating-point arithmetic is only available in avr-gcc v10 and up. The size of the double and long double type can be selected at compile-time with options like -mdouble=64 and -mlong-double=32. Whether such options are available, and their default values, depend on how the compiler has been configured.

•: The implementation of 64-bit floating-point arithmetic has some shortcomings and limitations, see the avr-gcc Wiki for details.

•: In order to access the float functions, in avr-gcc v4.6 and older it is usually also required to link with -lm. In avr-gcc v4.7 and up, -lm is added automatically to all linker invocations.

Macro Definition Documentation

#define HUGE_VAL __builtin_huge_val()

double infinity constant.

#define HUGE_VALF __builtin_huge_valf()

float infinity constant.

#define HUGE_VALL __builtin_huge_vall()

long double infinity constant.

#define INFINITY __builtin_inf()

double infinity constant.

#define M_1_PI 0.31830988618379067154

The constant 1/pi.

#define M_2_PI 0.63661977236758134308

The constant 2/pi.

#define M_2_SQRTPI 1.12837916709551257390

The constant 2/sqrt(pi).

#define M_E 2.7182818284590452354

The constant Euler's number e.

#define M_LN10 2.30258509299404568402

The constant natural logarithm of 10.

#define M_LN2 0.69314718055994530942

The constant natural logarithm of 2.

#define M_LOG10E 0.43429448190325182765

The constant logarithm of Euler's number e to base 10.

#define M_LOG2E 1.4426950408889634074

The constant logarithm of Euler's number e to base 2.

#define M_PI 3.14159265358979323846

The constant pi.

#define M_PI_2 1.57079632679489661923

The constant pi/2.

#define M_PI_4 0.78539816339744830962

The constant pi/4.

#define M_SQRT1_2 0.70710678118654752440

The constant 1/sqrt(2).

#define M_SQRT2 1.41421356237309504880

The square root of 2.

#define NAN __builtin_nan('')

The double representation of a constant quiet NaN.

#define nan(tag) builtin_nan(__tag)

The double representation of a constant quiet NaN. __tag is a string constant like '' or '123'.

#define nanf(tagp) builtin_nanf(__tag)

The float representation of a constant quiet NaN. __tag is a string constant like '' or '123'.

#define nanl(tag) builtin_nanl(__tag)

The long double representation of a constant quiet NaN. __tag is a string constant like '' or '123'.

Function Documentation

double acos (double x) [extern]

The acos() function computes the principal value of the arc cosine of x. The returned value is in the range [0, pi] radians or NaN.

float acosf (float x) [extern]

The acosf() function computes the principal value of the arc cosine of x. The returned value is in the range [0, pi] radians. A domain error occurs for arguments not in the range [1, +1].

long double acosl (long double x) [extern]

The acosl() function computes the principal value of the arc cosine of x. The returned value is in the range [0, pi] radians or NaN.

double asin (double x) [extern]

The asin() function computes the principal value of the arc sine of x. The returned value is in the range [pi/2, pi/2] radians or NaN.

float asinf (float x) [extern]

The asinf() function computes the principal value of the arc sine of x. The returned value is in the range [pi/2, pi/2] radians. A domain error occurs for arguments not in the range [1, +1].

long double asinl (long double x) [extern]

The asinl() function computes the principal value of the arc sine of x. The returned value is in the range [pi/2, pi/2] radians or NaN.

double atan (double x) [extern]

The atan() function computes the principal value of the arc tangent of x. The returned value is in the range [pi/2, pi/2] radians.

double atan2 (double y, double x) [extern]

The atan2() function computes the principal value of the arc tangent of y / x, using the signs of both arguments to determine the quadrant of the return value. The returned value is in the range [pi, +pi] radians.

float atan2f (float y, float x) [extern]

The atan2f() function computes the principal value of the arc tangent of y / x, using the signs of both arguments to determine the quadrant of the return value. The returned value is in the range [pi, +pi] radians.

long double atan2l (long double y, long double x) [extern]

The atan2l() function computes the principal value of the arc tangent of y / x, using the signs of both arguments to determine the quadrant of the return value. The returned value is in the range [pi, +pi] radians.

float atanf (float x) [extern]

The atanf() function computes the principal value of the arc tangent of x. The returned value is in the range [pi/2, pi/2] radians.

long double atanl (long double x) [extern]

The atanl() function computes the principal value of the arc tangent of x. The returned value is in the range [pi/2, pi/2] radians.

double cbrt (double x) [extern]

The cbrt() function returns the cube root of x.

float cbrtf (float x) [extern]

The cbrtf() function returns the cube root of x.

long double cbrtl (long double x) [extern]

The cbrtl() function returns the cube root of x.

double ceil (double x) [extern]

The ceil() function returns the smallest integral value greater than or equal to x, expressed as a floating-point number.

float ceilf (float x) [extern]

The ceilf() function returns the smallest integral value greater than or equal to x, expressed as a floating-point number.

long double ceill (long double x) [extern]

The ceill() function returns the smallest integral value greater than or equal to x, expressed as a floating-point number.

static double copysign (double x, double y) [inline], [static]

The copysign() function returns __x but with the sign of __y. They work even if __x or __y are NaN or zero.

static float copysignf (float x, float y) [inline], [static]

The copysignf() function returns __x but with the sign of __y. They work even if __x or __y are NaN or zero.

static long double copysignl (long double x, long double y) [inline], [static]

The copysignl() function returns __x but with the sign of __y. They work even if __x or __y are NaN or zero.

double cos (double x) [extern]

The cos() function returns the cosine of x, measured in radians.

float cosf (float x) [extern]

The cosf() function returns the cosine of x, measured in radians.

double cosh (double x) [extern]

The cosh() function returns the hyperbolic cosine of x.

float coshf (float x) [extern]

The coshf() function returns the hyperbolic cosine of x.

long double coshl (long double x) [extern]

The coshl() function returns the hyperbolic cosine of x.

long double cosl (long double x) [extern]

The cosl() function returns the cosine of x, measured in radians.

double exp (double x) [extern]

The exp() function returns the exponential value of x.

float expf (float x) [extern]

The expf() function returns the exponential value of x.

long double expl (long double x) [extern]

The expl() function returns the exponential value of x.

static double fabs (double __x) [inline], [static]

The fabs() function computes the absolute value of a floating-point number x.

static float fabsf (float __x) [inline], [static]

The fabsf() function computes the absolute value of a floating-point number x.

static long double fabsl (long double __x) [inline], [static]

The fabsl() function computes the absolute value of a floating-point number x.

double fdim (double x, double y) [extern]

The fdim() function returns max(x y, 0). If x or y or both are NaN, NaN is returned.

float fdimf (float x, float y) [extern]

The fdimf() function returns max(x y, 0). If x or y or both are NaN, NaN is returned.

long double fdiml (long double x, long double y) [extern]

The fdiml() function returns max(x y, 0). If x or y or both are NaN, NaN is returned.

double floor (double x) [extern]

The floor() function returns the largest integral value less than or equal to x, expressed as a floating-point number.

float floorf (float x) [extern]

The floorf() function returns the largest integral value less than or equal to x, expressed as a floating-point number.

long double floorl (long double x) [extern]

The floorl() function returns the largest integral value less than or equal to x, expressed as a floating-point number.

double fma (double x, double y, double z) [extern]

The fma() function performs floating-point multiply-add. This is the operation (x * y) + z, but the intermediate result is not rounded to the destination type. This can sometimes improve the precision of a calculation.

float fmaf (float x, float y, float z) [extern]

The fmaf() function performs floating-point multiply-add. This is the operation (x * y) + z, but the intermediate result is not rounded to the destination type. This can sometimes improve the precision of a calculation.

long double fmal (long double x, long double y, long double z) [extern]

The fmal() function performs floating-point multiply-add. This is the operation (x * y) + z, but the intermediate result is not rounded to the destination type. This can sometimes improve the precision of a calculation.

double fmax (double x, double y) [extern]

The fmax() function returns the greater of the two values x and y. If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned.

float fmaxf (float x, float y) [extern]

The fmaxf() function returns the greater of the two values x and y. If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned.

long double fmaxl (long double x, long double y) [extern]

The fmaxl() function returns the greater of the two values x and y. If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned.

double fmin (double x, double y) [extern]

The fmin() function returns the lesser of the two values x and y. If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned.

float fminf (float x, float y) [extern]

The fminf() function returns the lesser of the two values x and y. If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned.

long double fminl (long double x, long double y) [extern]

The fminl() function returns the lesser of the two values x and y. If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned.

double fmod (double x, double y) [extern]

The function fmod() returns the floating-point remainder of x / y.

float fmodf (float x, float y) [extern]

The function fmodf() returns the floating-point remainder of x / y.

long double fmodl (long double x, long double y) [extern]

The function fmodl() returns the floating-point remainder of x / y.

double frexp (double x, int * pexp) [extern]

The frexp() function breaks a floating-point number into a normalized fraction and an integral power of 2. It stores the integer in the int object pointed to by pexp.

If x is a normal float point number, the frexp() function returns the value v, such that v has a magnitude in the interval [1/2, 1) or zero, and x equals v times 2 raised to the power pexp. If x is zero, both parts of the result are zero. If x is not a finite number, the frexp() returns x as is and stores 0 by pexp.

float frexpf (float x, int * pexp) [extern]

The frexpf() function breaks a floating-point number into a normalized fraction and an integral power of 2. It stores the integer in the int object pointed to by pexp.

If x is a normal float point number, the frexpf() function returns the value v, such that v has a magnitude in the interval [1/2, 1) or zero, and x equals v times 2 raised to the power pexp. If x is zero, both parts of the result are zero. If x is not a finite number, the frexpf() returns x as is and stores 0 by pexp.

Note

This implementation permits a zero pointer as a directive to skip a storing the exponent.

long double frexpl (long double x, int * pexp) [extern]

The frexpl() function breaks a floating-point number into a normalized fraction and an integral power of 2. It stores the integer in the int object pointed to by pexp.

If x is a normal float point number, the frexpl() function returns the value v, such that v has a magnitude in the interval [1/2, 1) or zero, and x equals v times 2 raised to the power pexp. If x is zero, both parts of the result are zero. If x is not a finite number, the frexpl() returns x as is and stores 0 by pexp.

double hypot (double x, double y) [extern]

The hypot() function returns sqrt(x*x + y*y). This is the length of the hypotenuse of a right triangle with sides of length x and y, or the distance of the point (x, y) from the origin. Using this function instead of the direct formula is wise, since the error is much smaller. No underflow with small x and y. No overflow if result is in range.

float hypotf (float x, float y) [extern]

The hypotf() function returns sqrtf(x*x + y*y). This is the length of the hypotenuse of a right triangle with sides of length x and y, or the distance of the point (x, y) from the origin. Using this function instead of the direct formula is wise, since the error is much smaller. No underflow with small x and y. No overflow if result is in range.

long double hypotl (long double x, long double y) [extern]

The hypotl() function returns sqrtl(x*x + y*y). This is the length of the hypotenuse of a right triangle with sides of length x and y, or the distance of the point (x, y) from the origin. Using this function instead of the direct formula is wise, since the error is much smaller. No underflow with small x and y. No overflow if result is in range.

static int isfinite (double __x) [inline], [static]

The isfinite() function returns a nonzero value if __x is finite: not plus or minus infinity, and not NaN.

static int isfinitef (float __x) [inline], [static]

The isfinitef() function returns a nonzero value if __x is finite: not plus or minus infinity, and not NaN.

static int isfinitel (long double __x) [inline], [static]

The isfinite() function returns a nonzero value if __x is finite: not plus or minus infinity, and not NaN.

int isinf (double x) [extern]

The function isinf() returns 1 if the argument x is positive infinity, 1 if x is negative infinity, and 0 otherwise.

int isinff (float x) [extern]

The function isinff() returns 1 if the argument x is positive infinity, 1 if x is negative infinity, and 0 otherwise.

int isinfl (long double x) [extern]

The function isinfl() returns 1 if the argument x is positive infinity, 1 if x is negative infinity, and 0 otherwise.

int isnan (double x) [extern]

The function isnan() returns 1 if the argument x represents a 'not-a-number' (NaN) object, otherwise 0.

int isnanf (float x) [extern]

The function isnanf() returns 1 if the argument x represents a 'not-a-number' (NaN) object, otherwise 0.

int isnanl (long double x) [extern]

The function isnanl() returns 1 if the argument x represents a 'not-a-number' (NaN) object, otherwise 0.

double ldexp (double x, int iexp) [extern]

The ldexp() function multiplies a floating-point number by an integral power of 2. It returns the value of x times 2 raised to the power iexp.

float ldexpf (float x, int iexp) [extern]

The ldexpf() function multiplies a floating-point number by an integral power of 2. It returns the value of x times 2 raised to the power iexp.

long double ldexpl (long double x, int iexp) [extern]

The ldexpl() function multiplies a floating-point number by an integral power of 2. It returns the value of x times 2 raised to the power iexp.

double log (double x) [extern]

The log() function returns the natural logarithm of argument x.

double log10 (double x) [extern]

The log10() function returns the logarithm of argument x to base 10.

float log10f (float x) [extern]

The log10f() function returns the logarithm of argument x to base 10.

long double log10l (long double x) [extern]

The log10l() function returns the logarithm of argument x to base 10.

float logf (float x) [extern]

The logf() function returns the natural logarithm of argument x.

long double logl (long double x) [extern]

The logl() function returns the natural logarithm of argument x.

long lrint (double x) [extern]

The lrint() function rounds x to the nearest integer, rounding the halfway cases to the even integer direction. (That is both 1.5 and 2.5 values are rounded to 2). This function is similar to rint() function, but it differs in type of return value and in that an overflow is possible.

Returns