Arduino - Math Library

The Arduino Math library (math.h) includes a number of useful mathematical functions for manipulating floating-point numbers.
Following are the macros defined in the header math.h −
1.4426950408889634074
/* log_2 e */
0.31830988618379067154
/* 1/pi */
0.63661977236758134308
/* 2/pi */
1.12837916709551257390
/* 2/sqrt(pi) */
2.30258509299404568402
/* log_e 10 */
0.69314718055994530942
/* log_e 2 */
0.43429448190325182765
/* log_10 e */
3.14159265358979323846
/* pi */
3.3V1.57079632679489661923
/* pi/2 */
0.78539816339744830962
/* pi/4 */
0.70710678118654752440
/* 1/sqrt(2) */
1.41421356237309504880
/* sqrt(2) */
The following functions are defined in the header math.h −
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)
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 the 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 the 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)
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, 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)
The 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.
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.
The following example shows how to use the most common math.h library functions −
double double__x = 45.45 ;
double double__y = 30.20 ;

void setup() {
   Serial.begin(9600);
   Serial.print("cos num = ");
   Serial.println (cos (double__x) ); // returns cosine of x
   Serial.print("absolute value of num = ");
   Serial.println (fabs (double__x) ); // absolute value of a float
   Serial.print("floating point modulo = ");
   Serial.println (fmod (double__x, double__y)); // floating point modulo
   Serial.print("sine of num = ");
   Serial.println (sin (double__x) ) ;// returns sine of x
   Serial.print("square root of num : ");
   Serial.println ( sqrt (double__x) );// returns square root of x
   Serial.print("tangent of num : ");
   Serial.println ( tan (double__x) ); // returns tangent of x
   Serial.print("exponential value of num : ");
   Serial.println ( exp (double__x) ); // function returns the exponential value of x.
   Serial.print("cos num : ");

   Serial.println (atan (double__x) ); // arc tangent of x
   Serial.print("tangent of num : ");
   Serial.println (atan2 (double__y, double__x) );// arc tangent of y/x
   Serial.print("arc tangent of num : ");
   Serial.println (log (double__x) ) ; // natural logarithm of x
   Serial.print("cos num : ");
   Serial.println ( log10 (double__x)); // logarithm of x to base 10.
   Serial.print("logarithm of num to base 10 : ");
   Serial.println (pow (double__x, double__y) );// x to power of y
   Serial.print("power of num : ");
   Serial.println (square (double__x)); // square of x
}

void loop() {

}
cos num = 0.10
absolute value of num = 45.45
floating point modulo =15.25
sine of num = 0.99
square root of num : 6.74
tangent of num : 9.67
exponential value of num : ovf
cos num : 1.55
tangent of num : 0.59
arc tangent of num : 3.82
cos num : 1.66
logarithm of num to base 10 : inf
power of num : 2065.70


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