avr-libc  2.0.0 Standard C library for AVR-GCC  ## Example Projects

<math.h>: Mathematics

## Macros

#define M_E   2.7182818284590452354

#define M_LOG2E   1.4426950408889634074 /* log_2 e */

#define M_LOG10E   0.43429448190325182765 /* log_10 e */

#define M_LN2   0.69314718055994530942 /* log_e 2 */

#define M_LN10   2.30258509299404568402 /* log_e 10 */

#define M_PI   3.14159265358979323846 /* pi */

#define M_PI_2   1.57079632679489661923 /* pi/2 */

#define M_PI_4   0.78539816339744830962 /* pi/4 */

#define M_1_PI   0.31830988618379067154 /* 1/pi */

#define M_2_PI   0.63661977236758134308 /* 2/pi */

#define M_2_SQRTPI   1.12837916709551257390 /* 2/sqrt(pi) */

#define M_SQRT2   1.41421356237309504880 /* sqrt(2) */

#define M_SQRT1_2   0.70710678118654752440 /* 1/sqrt(2) */

#define NAN   __builtin_nan("")

#define INFINITY   __builtin_inf()

#define cosf   cos

#define sinf   sin

#define tanf   tan

#define fabsf   fabs

#define fmodf   fmod

#define cbrtf   cbrt

#define hypotf   hypot

#define squaref   square

#define floorf   floor

#define ceilf   ceil

#define frexpf   frexp

#define ldexpf   ldexp

#define expf   exp

#define coshf   cosh

#define sinhf   sinh

#define tanhf   tanh

#define acosf   acos

#define asinf   asin

#define atanf   atan

#define atan2f   atan2

#define logf   log

#define log10f   log10

#define powf   pow

#define isnanf   isnan

#define isinff   isinf

#define isfinitef   isfinite

#define copysignf   copysign

#define signbitf   signbit

#define fdimf   fdim

#define fmaf   fma

#define fmaxf   fmax

#define fminf   fmin

#define truncf   trunc

#define roundf   round

#define lroundf   lround

#define lrintf   lrint

## Functions

double cos (double __x)

double sin (double __x)

double tan (double __x)

double fabs (double __x)

double fmod (double __x, double __y)

double modf (double __x, double *__iptr)

float modff (float __x, float *__iptr)

double sqrt (double __x)

float sqrtf (float)

double cbrt (double __x)

double hypot (double __x, double __y)

double square (double __x)

double floor (double __x)

double ceil (double __x)

double frexp (double __x, int *__pexp)

double ldexp (double __x, int __exp)

double exp (double __x)

double cosh (double __x)

double sinh (double __x)

double tanh (double __x)

double acos (double __x)

double asin (double __x)

double atan (double __x)

double atan2 (double __y, double __x)

double log (double __x)

double log10 (double __x)

double pow (double __x, double __y)

int isnan (double __x)

int isinf (double __x)

static int isfinite (double __x)

static double copysign (double __x, double __y)

int signbit (double __x)

double fdim (double __x, double __y)

double fma (double __x, double __y, double __z)

double fmax (double __x, double __y)

double fmin (double __x, double __y)

double trunc (double __x)

double round (double __x)

long lround (double __x)

long lrint (double __x)

## Detailed Description

#include <math.h>

This header file declares basic mathematics constants and functions.

Notes:
• In order to access the functions declared herein, it is usually also required to additionally link against the library `libm.a`. See also the related FAQ entry.
• 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.

## Macro Definition Documentation

 #define acosf   acos

The alias for acos().

 #define asinf   asin

The alias for asin().

 #define atan2f   atan2

The alias for atan2().

 #define atanf   atan

The alias for atan().

 #define cbrtf   cbrt

The alias for cbrt().

 #define ceilf   ceil

The alias for ceil().

 #define copysignf   copysign

The alias for copysign().

 #define cosf   cos

The alias for cos().

 #define coshf   cosh

The alias for cosh().

 #define expf   exp

The alias for exp().

 #define fabsf   fabs

The alias for fabs().

 #define fdimf   fdim

The alias for fdim().

 #define floorf   floor

The alias for floor().

 #define fmaf   fma

The alias for fma().

 #define fmaxf   fmax

The alias for fmax().

 #define fminf   fmin

The alias for fmin().

 #define fmodf   fmod

The alias for fmod().

 #define frexpf   frexp

The alias for frexp().

 #define hypotf   hypot

The alias for hypot().

 #define INFINITY   __builtin_inf()

INFINITY constant.

 #define isfinitef   isfinite

The alias for isfinite().

 #define isinff   isinf

The alias for isinf().

 #define isnanf   isnan

The alias for isnan().

 #define ldexpf   ldexp

The alias for ldexp().

 #define log10f   log10

The alias for log10().

 #define logf   log

The alias for log().

 #define lrintf   lrint

The alias for lrint().

 #define lroundf   lround

The alias for lround().

 #define M_1_PI   0.31830988618379067154 /* 1/pi */

The constant 1/pi.

 #define M_2_PI   0.63661977236758134308 /* 2/pi */

The constant 2/pi.

 #define M_2_SQRTPI   1.12837916709551257390 /* 2/sqrt(pi) */

The constant 2/sqrt(pi).

 #define M_E   2.7182818284590452354

The constant e.

 #define M_LN10   2.30258509299404568402 /* log_e 10 */

The natural logarithm of the 10.

 #define M_LN2   0.69314718055994530942 /* log_e 2 */

The natural logarithm of the 2.

 #define M_LOG10E   0.43429448190325182765 /* log_10 e */

The logarithm of the e to base 10.

 #define M_LOG2E   1.4426950408889634074 /* log_2 e */

The logarithm of the e to base 2.

 #define M_PI   3.14159265358979323846 /* pi */

The constant pi.

 #define M_PI_2   1.57079632679489661923 /* pi/2 */

The constant pi/2.

 #define M_PI_4   0.78539816339744830962 /* pi/4 */

The constant pi/4.

 #define M_SQRT1_2   0.70710678118654752440 /* 1/sqrt(2) */

The constant 1/sqrt(2).

 #define M_SQRT2   1.41421356237309504880 /* sqrt(2) */

The square root of 2.

 #define NAN   __builtin_nan("")

NAN constant.

 #define powf   pow

The alias for pow().

 #define roundf   round

The alias for round().

 #define signbitf   signbit

The alias for signbit().

 #define sinf   sin

The alias for sin().

 #define sinhf   sinh

The alias for sinh().

 #define squaref   square

The alias for square().

 #define tanf   tan

The alias for tan().

 #define tanhf   tanh

The alias for tanh().

 #define truncf   trunc

The alias for trunc().

## Function Documentation

 double acos ( double __x )

The acos() 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].

 double asin ( double __x )

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. A domain error occurs for arguments not in the range [-1, +1].

 double atan ( double __x )

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 )

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.

 double cbrt ( double __x )

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

 double ceil ( double __x )

The ceil() 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 )
static

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

 double cos ( double __x )

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

 double cosh ( double __x )

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

 double exp ( double __x )

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

 double fabs ( double __x )

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

 double fdim ( double __x, double __y )

The fdim() function returns max(__x - __y, 0). If __x or __y or both are NaN, NaN is returned.

 double floor ( double __x )

The floor() 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 )

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.

 double fmax ( double __x, double __y )

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.

 double fmin ( double __x, double __y )

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.

 double fmod ( double __x, double __y )

The function fmod() returns the floating-point remainder of __x / __y.

 double frexp ( double __x, int * __pexp )

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.

Note
This implementation permits a zero pointer as a directive to skip a storing the exponent.
 double hypot ( double __x, double __y )

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.

 static int isfinite ( double __x )
static

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

 int isinf ( double __x )

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

Note
The GCC 4.3 can replace this function with inline code that returns the 1 value for both infinities (gcc bug #35509).
 int isnan ( double __x )

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

 double ldexp ( double __x, int __exp )

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 __exp.

 double log ( double __x )

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

 double log10 ( double __x )

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

 long lrint ( double __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).
 long lround ( double __x )

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).
 double modf ( double __x, double * __iptr )

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.

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.
 float modff ( float __x, float * __iptr )

An alias for modf().

 double pow ( double __x, double __y )

The function pow() returns the value of __x to the exponent __y.

 double round ( double __x )

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.
 int signbit ( double __x )

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.

 double sin ( double __x )

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

 double sinh ( double __x )

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

 double sqrt ( double __x )

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

 float sqrtf ( float )

An alias for sqrt().

 double square ( double __x )

The function square() returns __x * __x.

Note
This function does not belong to the C standard definition.
 double tan ( double __x )

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

 double tanh ( double __x )

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

 double trunc ( double __x )

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