This header was originally in the C standard library as <math.h>.
This header is part of the numeric library.
Types |
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| float_t
(C++11) | most efficient floating-point type at least as wide as float (typedef) |
| double_t
(C++11) | most efficient floating-point type at least as wide as double (typedef) |
Macros |
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(C++11)(C++11) | indicates the overflow value for float, double and long double respectively (macro constant) |
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(C++11) | evaluates to positive infinity or the value guaranteed to overflow a float (macro constant) |
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(C++11) | evaluates to a quiet NaN of type float (macro constant) |
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(C++11)(C++11)(C++11) | defines the error handling mechanism used by the common mathematical functions (macro constant) |
Classification |
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(C++11)(C++11)(C++11)(C++11)(C++11) | indicates a floating-point category (macro constant) |
Functions |
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Basic operations |
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(C++11)(C++11) | absolute value of a floating point value (\(\small{|x|}\)|x|) (function) |
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(C++11)(C++11) | remainder of the floating point division operation (function) |
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(C++11)(C++11)(C++11) | signed remainder of the division operation (function) |
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(C++11)(C++11)(C++11) | signed remainder as well as the three last bits of the division operation (function) |
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(C++11)(C++11)(C++11) | fused multiply-add operation (function) |
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(C++11)(C++11)(C++11) | larger of two floating-point values (function) |
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(C++11)(C++11)(C++11) | smaller of two floating point values (function) |
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(C++11)(C++11)(C++11) | positive difference of two floating point values (\({\small\max{(0, x-y)} }\)max(0, x-y)) (function) |
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(C++11)(C++11)(C++11) | not-a-number (NaN) (function) |
Linear interpolation |
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(C++20) | linear interpolation function (function) |
Exponential functions |
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(C++11)(C++11) | returns e raised to the given power (\({\small e^x}\)ex) (function) |
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(C++11)(C++11)(C++11) | returns 2 raised to the given power (\({\small 2^x}\)2x) (function) |
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(C++11)(C++11)(C++11) | returns e raised to the given power, minus one (\({\small e^x-1}\)ex-1) (function) |
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(C++11)(C++11) | computes natural (base e) logarithm (\({\small \ln{x} }\)ln(x)) (function) |
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(C++11)(C++11) | computes common (base 10) logarithm (\({\small \log_{10}{x} }\)log10(x)) (function) |
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(C++11)(C++11)(C++11) | base 2 logarithm of the given number (\({\small \log_{2}{x} }\)log2(x)) (function) |
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(C++11)(C++11)(C++11) | natural logarithm (to base e) of 1 plus the given number (\({\small \ln{(1+x)} }\)ln(1+x)) (function) |
Power functions |
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(C++11)(C++11) | raises a number to the given power (\(\small{x^y}\)xy) (function) |
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(C++11)(C++11) | computes square root (\(\small{\sqrt{x} }\)√x) (function) |
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(C++11)(C++11)(C++11) | computes cube root (\(\small{\sqrt[3]{x} }\)3√x) (function) |
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(C++11)(C++11)(C++11) | computes square root of the sum of the squares of two or three (since C++17) given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)√x2 +y2 ), (\(\scriptsize{\sqrt{x^2+y^2+z^2} }\)√x2 +y2 +z2 ) (since C++17) (function) |
Trigonometric functions |
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(C++11)(C++11) | computes sine (\({\small\sin{x} }\)sin(x)) (function) |
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(C++11)(C++11) | computes cosine (\({\small\cos{x} }\)cos(x)) (function) |
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(C++11)(C++11) | computes tangent (\({\small\tan{x} }\)tan(x)) (function) |
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(C++11)(C++11) | computes arc sine (\({\small\arcsin{x} }\)arcsin(x)) (function) |
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(C++11)(C++11) | computes arc cosine (\({\small\arccos{x} }\)arccos(x)) (function) |
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(C++11)(C++11) | computes arc tangent (\({\small\arctan{x} }\)arctan(x)) (function) |
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(C++11)(C++11) | arc tangent, using signs to determine quadrants (function) |
Hyperbolic functions |
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(C++11)(C++11) | computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function) |
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(C++11)(C++11) | computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x)) (function) |
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(C++11)(C++11) | computes hyperbolic tangent (\({\small\tanh{x} }\)tanh(x)) (function) |
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(C++11)(C++11)(C++11) | computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x} }\)arsinh(x)) (function) |
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(C++11)(C++11)(C++11) | computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x)) (function) |
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(C++11)(C++11)(C++11) | computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\)artanh(x)) (function) |
Error and gamma functions |
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(C++11)(C++11)(C++11) | error function (function) |
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(C++11)(C++11)(C++11) | complementary error function (function) |
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(C++11)(C++11)(C++11) | gamma function (function) |
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(C++11)(C++11)(C++11) | natural logarithm of the gamma function (function) |
Nearest integer floating-point operations |
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(C++11)(C++11) | nearest integer not less than the given value (function) |
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(C++11)(C++11) | nearest integer not greater than the given value (function) |
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(C++11)(C++11)(C++11) | nearest integer not greater in magnitude than the given value (function) |
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(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11) | nearest integer, rounding away from zero in halfway cases (function) |
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(C++11)(C++11)(C++11) | nearest integer using current rounding mode (function) |
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(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11) | nearest integer using current rounding mode with exception if the result differs (function) |
Floating-point manipulation functions |
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(C++11)(C++11) | decomposes a number into significand and a power of 2 (function) |
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(C++11)(C++11) | multiplies a number by 2 raised to a power (function) |
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(C++11)(C++11) | decomposes a number into integer and fractional parts (function) |
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(C++11)(C++11)(C++11)(C++11)(C++11)(C++11) | multiplies a number by FLT_RADIX raised to a power (function) |
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(C++11)(C++11)(C++11) | extracts exponent of the number (function) |
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(C++11)(C++11)(C++11) | extracts exponent of the number (function) |
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(C++11)(C++11) (C++11)(C++11)(C++11)(C++11) | next representable floating point value towards the given value (function) |
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(C++11)(C++11)(C++11) | copies the sign of a floating point value (function) |
Classification and comparison |
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(C++11) | categorizes the given floating-point value (function) |
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(C++11) | checks if the given number has finite value (function) |
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(C++11) | checks if the given number is infinite (function) |
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(C++11) | checks if the given number is NaN (function) |
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(C++11) | checks if the given number is normal (function) |
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(C++11) | checks if the given number is negative (function) |
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(C++11) | checks if the first floating-point argument is greater than the second (function) |
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(C++11) | checks if the first floating-point argument is greater or equal than the second (function) |
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(C++11) | checks if the first floating-point argument is less than the second (function) |
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(C++11) | checks if the first floating-point argument is less or equal than the second (function) |
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(C++11) | checks if the first floating-point argument is less or greater than the second (function) |
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(C++11) | checks if two floating-point values are unordered (function) |
Mathematical special functions |
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(C++17)(C++17)(C++17) | associated Laguerre polynomials (function) |
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(C++17)(C++17)(C++17) | associated Legendre polynomials (function) |
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(C++17)(C++17)(C++17) | beta function (function) |
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(C++17)(C++17)(C++17) | (complete) elliptic integral of the first kind (function) |
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(C++17)(C++17)(C++17) | (complete) elliptic integral of the second kind (function) |
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(C++17)(C++17)(C++17) | (complete) elliptic integral of the third kind (function) |
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(C++17)(C++17)(C++17) | regular modified cylindrical Bessel functions (function) |
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(C++17)(C++17)(C++17) | cylindrical Bessel functions (of the first kind) (function) |
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(C++17)(C++17)(C++17) | irregular modified cylindrical Bessel functions (function) |
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(C++17)(C++17)(C++17) | cylindrical Neumann functions (function) |
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(C++17)(C++17)(C++17) | (incomplete) elliptic integral of the first kind (function) |
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(C++17)(C++17)(C++17) | (incomplete) elliptic integral of the second kind (function) |
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(C++17)(C++17)(C++17) | (incomplete) elliptic integral of the third kind (function) |
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(C++17)(C++17)(C++17) | exponential integral (function) |
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(C++17)(C++17)(C++17) | Hermite polynomials (function) |
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(C++17)(C++17)(C++17) | Legendre polynomials (function) |
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(C++17)(C++17)(C++17) | Laguerre polynomials (function) |
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(C++17)(C++17)(C++17) | Riemann zeta function (function) |
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(C++17)(C++17)(C++17) | spherical Bessel functions (of the first kind) (function) |
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(C++17)(C++17)(C++17) | spherical associated Legendre functions (function) |
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(C++17)(C++17)(C++17) | spherical Neumann functions (function) |
For each function with at least one parameter of type /* floating-point-type */, an overload for each cv-unqualified floating-point type is provided where all uses of /* floating-point-type */ in the function signature are replaced with that floating-point type.
For each function with at least one parameter of type /* floating-point-type */ other than std::abs, additional overloads are provided to ensure that, if every argument corresponding to a /* floating-point-type */ parameter has arithmetic type, then every such argument is effectively cast to the floating-point type with the greatest floating-point conversion rank and greatest floating-point conversion subrank among the types of all such arguments, where arguments of integer type are considered to have the same floating-point conversion rank as double. If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the provided overloads.
namespace std {
using float_t = /* see description */;
using double_t = /* see description */;
}
#define HUGE_VAL /* see description */
#define HUGE_VALF /* see description */
#define HUGE_VALL /* see description */
#define INFINITY /* see description */
#define NAN /* see description */
#define FP_INFINITE /* see description */
#define FP_NAN /* see description */
#define FP_NORMAL /* see description */
#define FP_SUBNORMAL /* see description */
#define FP_ZERO /* see description */
#define FP_FAST_FMA /* see description */
#define FP_FAST_FMAF /* see description */
#define FP_FAST_FMAL /* see description */
#define FP_ILOGB0 /* see description */
#define FP_ILOGBNAN /* see description */
#define MATH_ERRNO /* see description */
#define MATH_ERREXCEPT /* see description */
#define math_errhandling /* see description */
namespace std {
/* floating-point-type */ acos(/* floating-point-type */ x);
float acosf(float x);
long double acosl(long double x);
/* floating-point-type */ asin(/* floating-point-type */ x);
float asinf(float x);
long double asinl(long double x);
/* floating-point-type */ atan(/* floating-point-type */ x);
float atanf(float x);
long double atanl(long double x);
/* floating-point-type */ atan2(/* floating-point-type */ y,
/* floating-point-type */ x);
float atan2f(float y, float x);
long double atan2l(long double y, long double x);
/* floating-point-type */ cos(/* floating-point-type */e x);
float cosf(float x);
long double cosl(long double x);
/* floating-point-type */ sin(/* floating-point-type */ x);
float sinf(float x);
long double sinl(long double x);
/* floating-point-type */ tan(/* floating-point-type */ x);
float tanf(float x);
long double tanl(long double x);
/* floating-point-type */ acosh(/* floating-point-type */ x);
float acoshf(float x);
long double acoshl(long double x);
/* floating-point-type */ asinh(/* floating-point-type */ x);
float asinhf(float x);
long double asinhl(long double x);
/* floating-point-type */ atanh(/* floating-point-type */ x);
float atanhf(float x);
long double atanhl(long double x);
/* floating-point-type */ cosh(/* floating-point-type */ x);
float coshf(float x);
long double coshl(long double x);
/* floating-point-type */ sinh(/* floating-point-type */ x);
float sinhf(float x);
long double sinhl(long double x);
/* floating-point-type */ tanh(/* floating-point-type */ x);
float tanhf(float x);
long double tanhl(long double x);
/* floating-point-type */ exp(/* floating-point-type */ x);
float expf(float x);
long double expl(long double x);
/* floating-point-type */ exp2(/* floating-point-type */ x);
float exp2f(float x);
long double exp2l(long double x);
/* floating-point-type */ expm1(/* floating-point-type */ x);
float expm1f(float x);
long double expm1l(long double x);
constexpr /* floating-point-type */ frexp(/* floating-point-type */ value, int* exp);
constexpr float frexpf(float value, int* exp);
constexpr long double frexpl(long double value, int* exp);
constexpr int ilogb(/* floating-point-type */ x);
constexpr int ilogbf(float x);
constexpr int ilogbl(long double x);
constexpr /* floating-point-type */ ldexp(/* floating-point-type */ x, int exp);
constexpr float ldexpf(float x, int exp);
constexpr long double ldexpl(long double x, int exp);
/* floating-point-type */ log(/* floating-point-type */ x);
float logf(float x);
long double logl(long double x);
/* floating-point-type */ log10(/* floating-point-type */ x);
float log10f(float x);
long double log10l(long double x);
/* floating-point-type */ log1p(/* floating-point-type */ x);
float log1pf(float x);
long double log1pl(long double x);
/* floating-point-type */ log2(/* floating-point-type */ x);
float log2f(float x);
long double log2l(long double x);
constexpr /* floating-point-type */ logb(/* floating-point-type */ x);
constexpr float logbf(float x);
constexpr long double logbl(long double x);
constexpr /* floating-point-type */ modf(/* floating-point-type */ value,
/* floating-point-type */* iptr);
constexpr float modff(float value, float* iptr);
constexpr long double modfl(long double value, long double* iptr);
constexpr /* floating-point-type */ scalbn(/* floating-point-type */ x, int n);
constexpr float scalbnf(float x, int n);
constexpr long double scalbnl(long double x, int n);
constexpr /* floating-point-type */ scalbln(/* floating-point-type */ x, long int n);
constexpr float scalblnf(float x, long int n);
constexpr long double scalblnl(long double x, long int n);
/* floating-point-type */ cbrt(/* floating-point-type */ x);
float cbrtf(float x);
long double cbrtl(long double x);
// absolute values
constexpr int abs(int j);
constexpr long int abs(long int j);
constexpr long long int abs(long long int j);
constexpr /* floating-point-type */ abs(/* floating-point-type */ j);
constexpr /* floating-point-type */ fabs(/* floating-point-type */ x);
constexpr float fabsf(float x);
constexpr long double fabsl(long double x);
/* floating-point-type */ hypot(/* floating-point-type */ x,
/* floating-point-type */ y);
float hypotf(float x, float y);
long double hypotl(long double x, long double y);
// three-dimensional hypotenuse
float hypot(/* floating-point-type */ x,
/* floating-point-type */ y,
/* floating-point-type */ z);
/* floating-point-type */ pow(/* floating-point-type */ x,
/* floating-point-type */ y);
float powf(float x, float y);
long double powl(long double x, long double y);
/* floating-point-type */ sqrt(/* floating-point-type */ x);
float sqrtf(float x);
long double sqrtl(long double x);
/* floating-point-type */ erf(/* floating-point-type */ x);
float erff(float x);
long double erfl(long double x);
/* floating-point-type */ erfc(/* floating-point-type */ x);
float erfcf(float x);
long double erfcl(long double x);
/* floating-point-type */ lgamma(/* floating-point-type */ x);
float lgammaf(float x);
long double lgammal(long double x);
/* floating-point-type */ tgamma(/* floating-point-type */ x);
float tgammaf(float x);
long double tgammal(long double x);
constexpr /* floating-point-type */ ceil(/* floating-point-type */ x);
constexpr float ceilf(float x);
constexpr long double ceill(long double x);
constexpr /* floating-point-type */ floor(/* floating-point-type */ x);
constexpr float floorf(float x);
constexpr long double floorl(long double x);
/* floating-point-type */ nearbyint(/* floating-point-type */ x);
float nearbyintf(float x);
long double nearbyintl(long double x);
/* floating-point-type */ rint(/* floating-point-type */ x);
float rintf(float x);
long double rintl(long double x);
long int lrint(/* floating-point-type */ x);
long int lrintf(float x);
long int lrintl(long double x);
long long int llrint(/* floating-point-type */ x);
long long int llrintf(float x);
long long int llrintl(long double x);
constexpr /* floating-point-type */ round(/* floating-point-type */ x);
constexpr float roundf(float x);
constexpr long double roundl(long double x);
constexpr long int lround(/* floating-point-type */ x);
constexpr long int lroundf(float x);
constexpr long int lroundl(long double x);
constexpr long long int llround(/* floating-point-type */ x);
constexpr long long int llroundf(float x);
constexpr long long int llroundl(long double x);
constexpr /* floating-point-type */ trunc(/* floating-point-type */ x);
constexpr float truncf(float x);
constexpr long double truncl(long double x);
constexpr /* floating-point-type */ fmod(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr float fmodf(float x, float y);
constexpr long double fmodl(long double x, long double y);
constexpr /* floating-point-type */ remainder(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr float remainderf(float x, float y);
constexpr long double remainderl(long double x, long double y);
constexpr /* floating-point-type */ remquo(/* floating-point-type */ x,
/* floating-point-type */ y, int* quo);
constexpr float remquof(float x, float y, int* quo);
constexpr long double remquol(long double x, long double y, int* quo);
constexpr /* floating-point-type */ copysign(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr float copysignf(float x, float y);
constexpr long double copysignl(long double x, long double y);
double nan(const char* tagp);
float nanf(const char* tagp);
long double nanl(const char* tagp);
constexpr /* floating-point-type */ nextafter(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr float nextafterf(float x, float y);
constexpr long double nextafterl(long double x, long double y);
constexpr /* floating-point-type */ nexttoward(/* floating-point-type */ x,
long double y);
constexpr float nexttowardf(float x, long double y);
constexpr long double nexttowardl(long double x, long double y);
constexpr /* floating-point-type */ fdim(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr float fdimf(float x, float y);
constexpr long double fdiml(long double x, long double y);
constexpr /* floating-point-type */ fmax(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr float fmaxf(float x, float y);
constexpr long double fmaxl(long double x, long double y);
constexpr /* floating-point-type */ fmin(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr float fminf(float x, float y);
constexpr long double fminl(long double x, long double y);
constexpr /* floating-point-type */ fma(/* floating-point-type */ x,
/* floating-point-type */ y,
/* floating-point-type */ z);
constexpr float fmaf(float x, float y, float z);
constexpr long double fmal(long double x, long double y, long double z);
// linear interpolation
constexpr /* floating-point-type */ lerp(/* floating-point-type */ a,
/* floating-point-type */ b,
/* floating-point-type */ t) noexcept;
// classification / comparison functions
constexpr int fpclassify(/* floating-point-type */ x);
constexpr bool isfinite(/* floating-point-type */ x);
constexpr bool isinf(/* floating-point-type */ x);
constexpr bool isnan(/* floating-point-type */ x);
constexpr bool isnormal(/* floating-point-type */ x);
constexpr bool signbit(/* floating-point-type */ x);
constexpr bool isgreater(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr bool isgreaterequal(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr bool isless(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr bool islessequal(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr bool islessgreater(/* floating-point-type */ x,
/* floating-point-type */ y);
constexpr bool isunordered(/* floating-point-type */ x,
/* floating-point-type */ y);
// mathematical special functions
// associated Laguerre polynomials
/* floating-point-type */ assoc_laguerre(unsigned n, unsigned m,
/* floating-point-type */ x);
float assoc_laguerref(unsigned n, unsigned m, float x);
long double assoc_laguerrel(unsigned n, unsigned m, long double x);
// associated Legendre functions
/* floating-point-type */ assoc_legendre(unsigned l, unsigned m,
/* floating-point-type */ x);
float assoc_legendref(unsigned l, unsigned m, float x);
long double assoc_legendrel(unsigned l, unsigned m, long double x);
// beta function
/* floating-point-type */ beta(/* floating-point-type */ x,
/* floating-point-type */ y);
float betaf(float x, float y);
long double betal(long double x, long double y);
// complete elliptic integral of the first kind
/* floating-point-type */ comp_ellint_1(/* floating-point-type */ k);
float comp_ellint_1f(float k);
long double comp_ellint_1l(long double k);
// complete elliptic integral of the second kind
/* floating-point-type */ comp_ellint_2(/* floating-point-type */ k);
float comp_ellint_2f(float k);
long double comp_ellint_2l(long double k);
// complete elliptic integral of the third kind
/* floating-point-type */ comp_ellint_3(/* floating-point-type */ k,
/* floating-point-type */ nu);
float comp_ellint_3f(float k, float nu);
long double comp_ellint_3l(long double k, long double nu);
// regular modified cylindrical Bessel functions
/* floating-point-type */ cyl_bessel_i(/* floating-point-type */ nu,
/* floating-point-type */ x);
float cyl_bessel_if(float nu, float x);
long double cyl_bessel_il(long double nu, long double x);
// cylindrical Bessel functions of the first kind
/* floating-point-type */ cyl_bessel_j(/* floating-point-type */ nu,
/* floating-point-type */ x);
float cyl_bessel_jf(float nu, float x);
long double cyl_bessel_jl(long double nu, long double x);
// irregular modified cylindrical Bessel functions
/* floating-point-type */ cyl_bessel_k(/* floating-point-type */ nu,
/* floating-point-type */ x);
float cyl_bessel_kf(float nu, float x);
long double cyl_bessel_kl(long double nu, long double x);
// cylindrical Neumann functions;
// cylindrical Bessel functions of the second kind
/* floating-point-type */ cyl_neumann(/* floating-point-type */ nu,
/* floating-point-type */ x);
float cyl_neumannf(float nu, float x);
long double cyl_neumannl(long double nu, long double x);
// incomplete elliptic integral of the first kind
/* floating-point-type */ ellint_1(/* floating-point-type */ k,
/* floating-point-type */ phi);
float ellint_1f(float k, float phi);
long double ellint_1l(long double k, long double phi);
// incomplete elliptic integral of the second kind
/* floating-point-type */ ellint_2(/* floating-point-type */ k,
/* floating-point-type */ phi);
float ellint_2f(float k, float phi);
long double ellint_2l(long double k, long double phi);
// incomplete elliptic integral of the third kind
/* floating-point-type */ ellint_3(/* floating-point-type */ k,
/* floating-point-type */ nu,
/* floating-point-type */ phi);
float ellint_3f(float k, float nu, float phi);
long double ellint_3l(long double k, long double nu, long double phi);
// exponential integral
/* floating-point-type */ expint(/* floating-point-type */ x);
float expintf(float x);
long double expintl(long double x);
// Hermite polynomials
/* floating-point-type */ hermite(unsigned n, /* floating-point-type */ x);
float hermitef(unsigned n, float x);
long double hermitel(unsigned n, long double x);
// Laguerre polynomials
/* floating-point-type */ laguerre(unsigned n, /* floating-point-type */ x);
float laguerref(unsigned n, float x);
long double laguerrel(unsigned n, long double x);
// Legendre polynomials
/* floating-point-type */ legendre(unsigned l, /* floating-point-type */ x);
float legendref(unsigned l, float x);
long double legendrel(unsigned l, long double x);
// Riemann zeta function
/* floating-point-type */ riemann_zeta(/* floating-point-type */ x);
float riemann_zetaf(float x);
long double riemann_zetal(long double x);
// spherical Bessel functions of the first kind
/* floating-point-type */ sph_bessel(unsigned n, /* floating-point-type */ x);
float sph_besself(unsigned n, float x);
long double sph_bessell(unsigned n, long double x);
// spherical associated Legendre functions
/* floating-point-type */ sph_legendre(unsigned l, unsigned m,
/* floating-point-type */ theta);
float sph_legendref(unsigned l, unsigned m, float theta);
long double sph_legendrel(unsigned l, unsigned m, long double theta);
// spherical Neumann functions;
// spherical Bessel functions of the second kind
/* floating-point-type */ sph_neumann(unsigned n, /* floating-point-type */ x);
float sph_neumannf(unsigned n, float x);
long double sph_neumannl(unsigned n, long double x);
}
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