Node:Exponents and Logarithms, Next:, Previous:Inverse Trig Functions, Up:Mathematics


Exponentiation and Logarithms

double exp (double x) Function
float expf (float x) Function
long double expl (long double x) Function
These functions compute e (the base of natural logarithms) raised to the power x.

If the magnitude of the result is too large to be representable, exp signals overflow.

double exp2 (double x) Function
float exp2f (float x) Function
long double exp2l (long double x) Function
These functions compute 2 raised to the power x. Mathematically, exp2 (x) is the same as exp (x * log (2)).

double exp10 (double x) Function
float exp10f (float x) Function
long double exp10l (long double x) Function
double pow10 (double x) Function
float pow10f (float x) Function
long double pow10l (long double x) Function
These functions compute 10 raised to the power x. Mathematically, exp10 (x) is the same as exp (x * log (10)).

These functions are GNU extensions. The name exp10 is preferred, since it is analogous to exp and exp2.

double log (double x) Function
float logf (float x) Function
long double logl (long double x) Function
These functions compute the natural logarithm of x. exp (log (x)) equals x, exactly in mathematics and approximately in C.

If x is negative, log signals a domain error. If x is zero, it returns negative infinity; if x is too close to zero, it may signal overflow.

double log10 (double x) Function
float log10f (float x) Function
long double log10l (long double x) Function
These functions return the base-10 logarithm of x. log10 (x) equals log (x) / log (10).

double log2 (double x) Function
float log2f (float x) Function
long double log2l (long double x) Function
These functions return the base-2 logarithm of x. log2 (x) equals log (x) / log (2).

double logb (double x) Function
float logbf (float x) Function
long double logbl (long double x) Function
These functions extract the exponent of x and return it as a floating-point value. If FLT_RADIX is two, logb is equal to floor (log2 (x)), except it's probably faster.

If x is de-normalized, logb returns the exponent x would have if it were normalized. If x is infinity (positive or negative), logb returns ∞. If x is zero, logb returns ∞. It does not signal.

int ilogb (double x) Function
int ilogbf (float x) Function
int ilogbl (long double x) Function
These functions are equivalent to the corresponding logb functions except that they return signed integer values.

Since integers cannot represent infinity and NaN, ilogb instead returns an integer that can't be the exponent of a normal floating-point number. math.h defines constants so you can check for this.

int FP_ILOGB0 Macro
ilogb returns this value if its argument is 0. The numeric value is either INT_MIN or -INT_MAX.

This macro is defined in ISO C99.

int FP_ILOGBNAN Macro
ilogb returns this value if its argument is NaN. The numeric value is either INT_MIN or INT_MAX.

This macro is defined in ISO C99.

These values are system specific. They might even be the same. The proper way to test the result of ilogb is as follows: 

i = ilogb (f);
if (i == FP_ILOGB0 || i == FP_ILOGBNAN)
  {
    if (isnan (f))
      {
        /* Handle NaN.  */
      }
    else if (f  == 0.0)
      {
        /* Handle 0.0.  */
      }
    else
      {
        /* Some other value with large exponent,
           perhaps +Inf.  */
      }
  }

double pow (double base, double power) Function
float powf (float base, float power) Function
long double powl (long double base, long double power) Function
These are general exponentiation functions, returning base raised to power.

Mathematically, pow would return a complex number when base is negative and power is not an integral value. pow can't do that, so instead it signals a domain error. pow may also underflow or overflow the destination type.

double sqrt (double x) Function
float sqrtf (float x) Function
long double sqrtl (long double x) Function
These functions return the nonnegative square root of x.

If x is negative, sqrt signals a domain error. Mathematically, it should return a complex number.

double cbrt (double x) Function
float cbrtf (float x) Function
long double cbrtl (long double x) Function
These functions return the cube root of x. They cannot fail; every representable real value has a representable real cube root.

double hypot (double x, double y) Function
float hypotf (float x, float y) Function
long double hypotl (long double x, long double y) Function
These functions return 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. See also the function cabs in Absolute Value.

double expm1 (double x) Function
float expm1f (float x) Function
long double expm1l (long double x) Function
These functions return a value equivalent to exp (x) - 1. They are computed in a way that is accurate even if x is near zero--a case where exp (x) - 1 would be inaccurate owing to subtraction of two numbers that are nearly equal.

double log1p (double x) Function
float log1pf (float x) Function
long double log1pl (long double x) Function
These functions returns a value equivalent to log (1 + x). They are computed in a way that is accurate even if x is near zero.

ISO C99 defines complex variants of some of the exponentiation and logarithm functions.

complex double cexp (complex double z) Function
complex float cexpf (complex float z) Function
complex long double cexpl (complex long double z) Function
These functions return e (the base of natural logarithms) raised to the power of z. Mathematically, this corresponds to the value

exp (z) = exp (creal (z)) * (cos (cimag (z)) + I * sin (cimag (z)))

complex double clog (complex double z) Function
complex float clogf (complex float z) Function
complex long double clogl (complex long double z) Function
These functions return the natural logarithm of z. Mathematically, this corresponds to the value

log (z) = log (cabs (z)) + I * carg (z)

clog has a pole at 0, and will signal overflow if z equals or is very close to 0. It is well-defined for all other values of z.

complex double clog10 (complex double z) Function
complex float clog10f (complex float z) Function
complex long double clog10l (complex long double z) Function
These functions return the base 10 logarithm of the complex value z. Mathematically, this corresponds to the value

log (z) = log10 (cabs (z)) + I * carg (z)

These functions are GNU extensions.

complex double csqrt (complex double z) Function
complex float csqrtf (complex float z) Function
complex long double csqrtl (complex long double z) Function
These functions return the complex square root of the argument z. Unlike the real-valued functions, they are defined for all values of z.

complex double cpow (complex double base, complex double power) Function
complex float cpowf (complex float base, complex float power) Function
complex long double cpowl (complex long double base, complex long double power) Function
These functions return base raised to the power of power. This is equivalent to cexp (y * clog (x))