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avr_math(3avr) avr_math(3avr)

avr_math - <math.h>: Mathematics


#define M_E 2.7182818284590452354
#define M_LOG2E 1.4426950408889634074
#define M_LOG10E 0.43429448190325182765
#define M_LN2 0.69314718055994530942
#define M_LN10 2.30258509299404568402
#define M_PI 3.14159265358979323846
#define M_PI_2 1.57079632679489661923
#define M_PI_4 0.78539816339744830962
#define M_1_PI 0.31830988618379067154
#define M_2_PI 0.63661977236758134308
#define M_2_SQRTPI 1.12837916709551257390
#define M_SQRT2 1.41421356237309504880
#define M_SQRT1_2 0.70710678118654752440
#define NAN __builtin_nan('')
#define nanf(__tagp) __builtin_nanf(__tag)
#define nan(__tag) __builtin_nan(__tag)
#define nanl(__tag) __builtin_nanl(__tag)
#define INFINITY __builtin_inf()
#define HUGE_VALF __builtin_huge_valf()
#define HUGE_VAL __builtin_huge_val()
#define HUGE_VALL __builtin_huge_vall()


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)


float squaref (float x)
double square (double x)
long double squarel (long double x) 

#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.

double infinity constant.

float infinity constant.

long double infinity constant.

double infinity constant.

The constant 1/pi.

The constant 2/pi.

The constant 2/sqrt(pi).

The constant Euler's number e.

The constant natural logarithm of 10.

The constant natural logarithm of 2.

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

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

The constant pi.

The constant pi/2.

The constant pi/4.

The constant 1/sqrt(2).

The square root of 2.

The double representation of a constant quiet NaN.

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

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

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

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.

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].

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.

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.

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].

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.

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.

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.

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.

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.

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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

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.

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.

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.

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.

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.

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.

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

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

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

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

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

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

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

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

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

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.

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.

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.

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

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

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

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

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

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

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

The rounded long integer value. If x is not a finite number or an overflow was, this realization returns the LONG_MIN value (0x80000000).

The lrintf() 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 rintf() function, but it differs in type of return value and in that an overflow is possible.

Returns

The rounded long integer value. If x is not a finite number or an overflow was, this realization returns the LONG_MIN value (0x80000000).

The lrintl() 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 rintl() function, but it differs in type of return value and in that an overflow is possible.

Returns

The rounded long integer value. If x is not a finite number or an overflow was, this realization returns the LONG_MIN value (0x80000000).

The lround() function rounds x to the nearest integer, but rounds halfway cases away from zero (instead of to the nearest even integer). This function is similar to round() function, but it differs in type of return value and in that an overflow is possible.

Returns

The rounded long integer value. If x is not a finite number or an overflow was, this realization returns the LONG_MIN value (0x80000000).

The lroundf() function rounds x to the nearest integer, but rounds halfway cases away from zero (instead of to the nearest even integer). This function is similar to round() function, but it differs in type of return value and in that an overflow is possible.

Returns

The rounded long integer value. If x is not a finite number or an overflow was, this realization returns the LONG_MIN value (0x80000000).

The lroundl() function rounds x to the nearest integer, but rounds halfway cases away from zero (instead of to the nearest even integer). This function is similar to round() function, but it differs in type of return value and in that an overflow is possible.

Returns

The rounded long integer value. If x is not a finite number or an overflow was, this realization returns the LONG_MIN value (0x80000000).

The modf() function breaks the argument x into integral and fractional parts, each of which has the same sign as the argument. It stores the integral part as a double in the object pointed to by iptr.

The modf() function returns the signed fractional part of x.

The modff() function breaks the argument x into integral and fractional parts, each of which has the same sign as the argument. It stores the integral part as a float in the object pointed to by iptr.

The modff() function returns the signed fractional part of x.

Note

This implementation skips writing by zero pointer. However, the GCC 4.3 can replace this function with inline code that does not permit to use NULL address for the avoiding of storing.

The modfl() function breaks the argument x into integral and fractional parts, each of which has the same sign as the argument. It stores the integral part as a long double in the object pointed to by iptr.

The modf() function returns the signed fractional part of x.

The function pow() returns the value of x to the exponent y.
Notice that for integer exponents, there is the more efficient double __builtin_powi(double x, int y).

The function powf() returns the value of x to the exponent y.
Notice that for integer exponents, there is the more efficient float __builtin_powif(float x, int y).

The function powl() returns the value of x to the exponent y.
Notice that for integer exponents, there is the more efficient long double __builtin_powil(long double x, int y).

The round() function rounds x to the nearest integer, but rounds halfway cases away from zero (instead of to the nearest even integer). Overflow is impossible.

Returns

The rounded value. If x is an integral or infinite, x itself is returned. If x is NaN, then NaN is returned.

The roundf() function rounds x to the nearest integer, but rounds halfway cases away from zero (instead of to the nearest even integer). Overflow is impossible.

Returns

The rounded value. If x is an integral or infinite, x itself is returned. If x is NaN, then NaN is returned.

The roundl() function rounds x to the nearest integer, but rounds halfway cases away from zero (instead of to the nearest even integer). Overflow is impossible.

Returns

The rounded value. If x is an integral or infinite, x itself is returned. If x is NaN, then NaN is returned.

The signbit() function returns a nonzero value if the value of x has its sign bit set. This is not the same as `x < 0.0', because IEEE 754 floating point allows zero to be signed. The comparison '0.0 < 0.0' is false, but `signbit (0.0)' will return a nonzero value.

The signbitf() function returns a nonzero value if the value of x has its sign bit set. This is not the same as `x < 0.0', because IEEE 754 floating point allows zero to be signed. The comparison '0.0 < 0.0' is false, but `signbit (0.0)' will return a nonzero value.

The signbitl() function returns a nonzero value if the value of x has its sign bit set. This is not the same as `x < 0.0', because IEEE 754 floating point allows zero to be signed. The comparison '0.0 < 0.0' is false, but `signbit (0.0)' will return a nonzero value.

The sin() function returns the sine of x, measured in radians.

The sinf() function returns the sine of x, measured in radians.

The sinh() function returns the hyperbolic sine of x.

The sinhf() function returns the hyperbolic sine of x.

The sinhl() function returns the hyperbolic sine of x.

The sinl() function returns the sine of x, measured in radians.

The sqrt() function returns the non-negative square root of x.

The sqrtf() function returns the non-negative square root of x.

The sqrtl() function returns the non-negative square root of x.

The function square() returns x * x.

Note

This function does not belong to the C standard definition.

The function squaref() returns x * x.

Note

This function does not belong to the C standard definition.

The function squarel() returns x * x.

Note

This function does not belong to the C standard definition.

The tan() function returns the tangent of x, measured in radians.

The tanf() function returns the tangent of x, measured in radians.

The tanh() function returns the hyperbolic tangent of x.

The tanhf() function returns the hyperbolic tangent of x.

The tanhl() function returns the hyperbolic tangent of x.

The tanl() function returns the tangent of x, measured in radians.

The trunc() function rounds x to the nearest integer not larger in absolute value.

The truncf() function rounds x to the nearest integer not larger in absolute value.

The truncl() function rounds x to the nearest integer not larger in absolute value.

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