Draft 2002-06-13

<cmath>

The <cmath> header declares a number of mathematical functions (from the C standard <math.h>). Most functions have multiple, overloaded versions for different parameter types; each function's syntax description shows all the overloaded functions.

If an argument is out of range, a domain error occurs. The function sets errno to EDOM and returns an error value. The value is defined by the implementation, so the only portable way test for a domain error is to check errno. If the function's result is an overflow, a range error occurs. The function returns HUGE_VAL and sets errno to ERANGE. If underflow occurs, the function returns zero, and may or may not set errno to ERANGE.

Warning

HUGE_VAL is defined to be a double, and the C++ standard does not define a suitable value for the float and long double versions of the math functions. If you are using a system that has infinity as an explicit floating point value (such as IEC 60559/IEEE 754, which is found on PCs, Macintoshes, and modern workstations), most likely the overloaded versions of a function return infinity for overflow, so there is no problem with the float and long double versions of the functions. For maximum portability, though, use only the double versions of the math functions.

All the trigonometric functions use radians.

Several other headers in the standard library declare additional mathematical functions:

<complex>
The <complex> header declares types and functions for working with complex numbers.
<cstdlib>
The <cstdlib> header declares integer absolute value functions, and functions that compute quotient and remainder in a single operation.
<numeric>
The <numeric> header declares generic numerical algorithms.
<limits>
The <limits> header for the limits of the numerical types, e.g., the largest float, the precision of double, and so on.
<valarray>
The <valarray> header declares types and functions that work with arrays of numbers.

abs function

Absolute value

float abs(float x)
double abs(double x)
long double abs(long double x)

The abs function returns the absolute value of its argument: if x < 0, it returns -x ; otherwise, it returns x.

The abs function is the same as fabs. The <cstdlib> header declares integer versions of the abs function.

See Also

abs function in <cstdlib>, fabs function

acos function

Inverse cosine

float acos(float x)
double acos(double x)
long double acos(long double x)

The acos function returns the inverse cosine of its argument. The parameter x must be in the range [-1, 1], or a domain error occurs. The return value is in the range [0, pi ].

asin function

Inverse sine

float asin(float x)
double asin(double x)
long double asin(long double x)

The asin function returns the inverse sine of its argument. The parameter x must be in the range [-1, 1], or a domain error occurs. The return value is in the range [-pi /2, pi /2].

atan function

Inverse tangent

float atan(float x)
double atan(double x)
long double atan(long double x)

The atan function returns the inverse tangent of its argument. The return value is in the range [-pi /2, pi /2].

atan2 function

Inverse tangent

float atan2(float y, float x)
double atan2(double y, double x)
long double atan2(long double y, long double x)

The atan2 function returns the inverse tangent of y/x, using the sign of both numbers to determine the quadrant for the return value. It correctly handles the case where x is 0 (that is, pi /2 times the sign of y for non-zero y; if y is zero, the result is implementation-defined and might be a range error). The return value is in the range [-pi , pi ].

ceil function

Ceiling

float ceil(float x)
double ceil(double x)
long double ceil(long double x)

The ceil function returns the smallest integer that is greater than or equal to x.

See Also

floor function

cos function

Cosine

float cos(float x)
double cos(double x)
long double cos(long double x)

The cos function returns the cosine of its argument. The return value is in the range [-1, 1].

cosh function

Hyperbolic cosine

float cosh(float x)
double cosh(double x)
long double cosh(long double x)

The cosh function returns the hyperbolic cosine of its argument. Note that there are no inverse hyperbolic trigonometric functions.

exp function

Exponential

float exp(float x)
double exp(double x)
long double exp(long double x)

The exp function returns ex. If x is too large, a range error occurs.

See Also

log function, pow function

fabs function

Absolute value

float fabs(float x)
double fabs(double x)
long double fabs(long double x)

The fabs function returns the absolute value of its argument: if x < 0, it returns -x ; otherwise, it returns x.

The fabs function is the same as abs for floating point numbers. It exists only for compatibility with C.

See Also

abs function, abs function in <cstdlib>

floor function

Floor

float floor(float x)
double floor(double x)
long double floor(long double x)

The floor function returns the largest integer that is less than or equal to x.

See Also

ceil function

fmod function

Modulus

float fmod(float x, float y)
double fmod(double x, double y)
long double fmod(long double x, long double y)

The fmod function returns the floating point remainder of dividing x by y. If y is zero, the behavior is implementation defined: the return value might be zero, or a domain error can occur. If y is not zero, the return value is x - i × y, such that the result has the same sign as x and an absolute value less than the absolute value of y.

frexp function

Fraction and exponent

float frexp(float x, int* exp)
double frexp(double x, int* exp)
long double frexp(long double x, int* exp)

The frexp function separates a floating point number into a fraction and an exponent (with a base of 2). The exponent is stored in *exp. The return value is the normalized fractional part of x in the range [1/2, 1) or zero. If x is zero, the return value and *exp are zero.

See Also

ldexp function, modf function

HUGE_VAL macro

Range error value

double HUGE_VAL

When an overflow occurs, most functions set errno to ERANGE and return HUGE_VAL, with the correct sign of the result. The exact value of HUGE_VAL is implementation-defined. It might be a value that can be returned as a valid result from the function. In that case, the only way to discover whether an overflow occurred is to test errno, as shown in Example 13-6.

Example 13-6. Computing a logarithm to any base.

// Return the logarithm of x to the base n.
template<typename T>
T logn(T x, T n)
{
  errno = 0;
  T logx = log(x);
  if (errno == ERANGE)
    return logx;    // should be HUGE_VAL
  else if (errno != 0)
    return logx;    // implementation defined
  T logn = log(n);
  if (errno == ERANGE)
    return logn;    // should be HUGE_VAL
  else if (errno != 0)
    return logn;    // implementation defined
  if (logn == 0) {
    errno = EDOM;
    return 0;
  }
  return logx / logn;
}

See Also

<cerrno>

ldexp function

Floating point from fraction and exponent

float ldexp(float frac, int exp)
double ldexp(double frac, int exp)
long double ldexp(long double frac, int exp)

The ldexp function returns a floating point number that it constructs from a fractional part and an exponent (base 2). The return value is frac × 2exp.

See Also

frexp function, modf function

log function

Natural logarithm

float log(float x)
double log(double x)
long double log(long double x)

The log function returns the natural (base e) logarithm of its argument. A domain error occurs if x is negative. A range error might occur is x is zero.

log10 function

Common logarithm

float log10(float x)
double log10(double x)
long double log10(long double x)

Description

The log10 function returns the common (base 10) logarithm of its argument. A domain error occurs if x is negative. A range error might occur is x is zero.

modf function

Integer and fraction parts

float modf(float x, float* iptr)
double modf(double x, double* iptr)
long double modf(long double x, long double* iptr)

Description

The modf function splits a floating point number into integral and fractional parts. Both parts have the same sign as x. The integral part is stored in *iptr; the return value is the fractional part.

See Also

frexp function, ldexp function

pow function

Power

float pow(float x, float y)
float pow(float x, int y)
double pow(double x, double y)
double pow(double x, int y)
long double pow(long double x, long double y)
long double pow(long double x, int y)

The pow function raises x to the y power. If x is negative and y is not an integral value, a domain error occurs. If x is zero, and y is less than or equal to zero, and the result cannot be represented as a real number, a domain error occurs. A range error can occur if the result is out of range.

See Also

exp function

sin function

Sine

float sin(float x)
double sin(double x)
long double sin(long double x)

The sin function returns the sine of its argument. The return value is in the range [-1, 1].

sinh function

Hyperbolic sine

float sinh(float x)
double sinh(double x)
long double sinh(long double x)

The sinh function returns the hyperbolic sine of its argument. Note that there are no inverse hyperbolic trigonometric functions.

sqrt function

Square root

float sqrt(float x)
double sqrt(double x)
long double sqrt(long double x)

The sqrt function returns the square root or its argument. If x is negative, a domain error occurs. The return value is always positive or zero.

tan function

Tangent

float tan(float x)
double tan(double x)
long double tan(long double x)

The tan function returns the tangent of its argument. The standard does not specify the result when the tangent is undefined (that is, where x is kpi +pi /2 for any integer k), but a reasonable result is a range error. Due to the nature of the tangent function, the sign of the return value (HUGE_VAL) can be positive or negative.

tanh function

Hyperbolic tangent

float tanh(float x)
double tanh(double x)
long double tanh(long double x)

The tanh function returns the hyperbolic tangent of its argument. Note that there are no inverse hyperbolic trigonometric functions.