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Standard library header <cmath>

From cppreference.net
C++
Standard library headers

该头文件最初作为 <math.h> 存在于C标准库中。

此头文件是 数值 库的组成部分。

Contents

Types

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

(C++11) (C++11)
indicates the overflow value for float , double and long double respectively
(macro constant)
(C++11)
evaluates to positive infinity or the value guaranteed to overflow a float
(macro constant)
(C++11)
evaluates to a quiet NaN of type float
(macro constant)
(C++11) (C++11) (C++11)
defines the error handling mechanism used by the common mathematical functions
(macro constant)
Classification
(C++11) (C++11) (C++11) (C++11) (C++11)
indicates a floating-point category
(macro constant)

Functions

Basic operations
(C++11) (C++11)
absolute value of a floating point value ( |x| )
(function)
(C++11) (C++11)
remainder of the floating point division operation
(function)
(C++11) (C++11) (C++11)
signed remainder of the division operation
(function)
(C++11) (C++11) (C++11)
signed remainder as well as the three last bits of the division operation
(function)
(C++11) (C++11) (C++11)
fused multiply-add operation
(function)
(C++11) (C++11) (C++11)
larger of two floating-point values
(function)
(C++11) (C++11) (C++11)
smaller of two floating point values
(function)
(C++11) (C++11) (C++11)
positive difference of two floating point values ( max(0, x-y) )
(function)
(C++11) (C++11) (C++11)
not-a-number (NaN)
(function)
Linear interpolation
(C++20)
linear interpolation function
(function)
Exponential functions
(C++11) (C++11)
returns e raised to the given power ( e x )
(function)
(C++11) (C++11) (C++11)
returns 2 raised to the given power ( 2 x )
(function)
(C++11) (C++11) (C++11)
returns e raised to the given power, minus 1 ( e x -1 )
(function)
(C++11) (C++11)
computes natural (base e ) logarithm ( ln(x) )
(function)
(C++11) (C++11)
computes common (base 10 ) logarithm ( log 10 (x) )
(function)
(C++11) (C++11) (C++11)
base 2 logarithm of the given number ( log 2 (x) )
(function)
(C++11) (C++11) (C++11)
natural logarithm (to base e ) of 1 plus the given number ( ln(1+x) )
(function)
Power functions
(C++11) (C++11)
raises a number to the given power ( x y )
(function)
(C++11) (C++11)
computes square root ( √ x )
(function)
(C++11) (C++11) (C++11)
computes cube root ( 3 √ x )
(function)
(C++11) (C++11) (C++11)
computes hypotenuse √ x 2
+y 2
and √ x 2
+y 2
+z 2
(since C++17)
(function)
Trigonometric functions
(C++11) (C++11)
computes sine ( sin(x) )
(function)
(C++11) (C++11)
computes cosine ( cos(x) )
(function)
(C++11) (C++11)
computes tangent ( tan(x) )
(function)
(C++11) (C++11)
computes arc sine ( arcsin(x) )
(function)
(C++11) (C++11)
computes arc cosine ( arccos(x) )
(function)
(C++11) (C++11)
computes arc tangent ( arctan(x) )
(function)
(C++11) (C++11)
arc tangent, using signs to determine quadrants
(function)
Hyperbolic functions
(C++11) (C++11)
computes hyperbolic sine ( sinh(x) )
(function)
(C++11) (C++11)
computes hyperbolic cosine ( cosh(x) )
(function)
(C++11) (C++11)
computes hyperbolic tangent ( tanh(x) )
(function)
(C++11) (C++11) (C++11)
computes the inverse hyperbolic sine ( arsinh(x) )
(function)
(C++11) (C++11) (C++11)
computes the inverse hyperbolic cosine ( arcosh(x) )
(function)
(C++11) (C++11) (C++11)
computes the inverse hyperbolic tangent ( artanh(x) )
(function)
Error and gamma functions
(C++11) (C++11) (C++11)
error function
(function)
(C++11) (C++11) (C++11)
complementary error function
(function)
(C++11) (C++11) (C++11)
gamma function
(function)
(C++11) (C++11) (C++11)
natural logarithm of the gamma function
(function)
Nearest integer floating-point operations
(C++11) (C++11)
nearest integer not less than the given value
(function)
(C++11) (C++11)
nearest integer not greater than the given value
(function)
(C++11) (C++11) (C++11)
nearest integer not greater in magnitude than the given value
(function)
(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)
(C++11) (C++11) (C++11)
nearest integer using current rounding mode
(function)
(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
(C++11) (C++11)
decomposes a number into significand and base- 2 exponent
(function)
(C++11) (C++11)
multiplies a number by 2 raised to an integral power
(function)
(C++11) (C++11)
decomposes a number into integer and fractional parts
(function)
(C++11) (C++11) (C++11) (C++11) (C++11) (C++11)
multiplies a number by FLT_RADIX raised to a power
(function)
(C++11) (C++11) (C++11)
extracts exponent of the number
(function)
(C++11) (C++11) (C++11)
extracts exponent of the number
(function)
(C++11) (C++11) (C++11) (C++11) (C++11) (C++11)
next representable floating-point value towards the given value
(function)
(C++11) (C++11) (C++11)
copies the sign of a floating point value
(function)
Classification and comparison
(C++11)
categorizes the given floating-point value
(function)
(C++11)
checks if the given number has finite value
(function)
(C++11)
checks if the given number is infinite
(function)
(C++11)
checks if the given number is NaN
(function)
(C++11)
checks if the given number is normal
(function)
(C++11)
checks if the given number is negative
(function)
(C++11)
checks if the first floating-point argument is greater than the second
(function)
(C++11)
checks if the first floating-point argument is greater or equal than the second
(function)
(C++11)
checks if the first floating-point argument is less than the second
(function)
(C++11)
checks if the first floating-point argument is less or equal than the second
(function)
(C++11)
checks if the first floating-point argument is less or greater than the second
(function)
(C++11)
checks if two floating-point values are unordered
(function)
Mathematical special functions
(C++17) (C++17) (C++17)
associated Laguerre polynomials
(function)
(C++17) (C++17) (C++17)
associated Legendre polynomials
(function)
(C++17) (C++17) (C++17)
beta function
(function)
(C++17) (C++17) (C++17)
(complete) elliptic integral of the first kind
(function)
(C++17) (C++17) (C++17)
(complete) elliptic integral of the second kind
(function)
(C++17) (C++17) (C++17)
(complete) elliptic integral of the third kind
(function)
(C++17) (C++17) (C++17)
regular modified cylindrical Bessel functions
(function)
(C++17) (C++17) (C++17)
cylindrical Bessel functions (of the first kind)
(function)
(C++17) (C++17) (C++17)
irregular modified cylindrical Bessel functions
(function)
(C++17) (C++17) (C++17)
cylindrical Neumann functions
(function)
(C++17) (C++17) (C++17)
(incomplete) elliptic integral of the first kind
(function)
(C++17) (C++17) (C++17)
(incomplete) elliptic integral of the second kind
(function)
(C++17) (C++17) (C++17)
(incomplete) elliptic integral of the third kind
(function)
(C++17) (C++17) (C++17)
exponential integral
(function)
(C++17) (C++17) (C++17)
Hermite polynomials
(function)
(C++17) (C++17) (C++17)
Legendre polynomials
(function)
(C++17) (C++17) (C++17)
Laguerre polynomials
(function)
(C++17) (C++17) (C++17)
Riemann zeta function
(function)
(C++17) (C++17) (C++17)
spherical Bessel functions (of the first kind)
(function)
(C++17) (C++17) (C++17)
spherical associated Legendre functions
(function)
(C++17) (C++17) (C++17)
spherical Neumann functions
(function)

概要

对于每个至少包含一个 /* floating-point-type */ 类型参数的函数，都会为每个无cv限定符的浮点类型提供一个重载版本，其中函数签名中所有 /* floating-point-type */ 的使用都将被替换为该浮点类型。

对于每个至少有一个 /* 浮点类型 */ 参数（除 std::abs 外）的函数，均提供了额外的重载以确保：若每个对应 /* 浮点类型 */ 参数的实参均具有算术类型，则每个此类实参都会被隐式转换为具有最高 浮点转换等级 和最高 浮点转换子等级 的浮点类型（该等级从所有此类实参的类型中选取），其中整数类型的实参被视为具有与 double 相同的浮点转换等级。若不存在具有最高等级和子等级的浮点类型，则重载解析无法从提供的重载中得到可用候选。 

namespace std {
  using float_t = /* 参见描述 */;
  using double_t = /* 参见描述 */;
}
#define HUGE_VAL /* 参见描述 */
#define HUGE_VALF /* 参见描述 */
#define HUGE_VALL /* 参见描述 */
#define INFINITY /* 参见描述 */
#define NAN /* 参见描述 */
#define FP_INFINITE /* 参见描述 */
#define FP_NAN /* 参见描述 */
#define FP_NORMAL /* 参见描述 */
#define FP_SUBNORMAL /* 参见描述 */
#define FP_ZERO /* 参见描述 */
#define FP_FAST_FMA /* 参见描述 */
#define FP_FAST_FMAF /* 参见描述 */
#define FP_FAST_FMAL /* 参见描述 */
#define FP_ILOGB0 /* 参见描述 */
#define FP_ILOGBNAN /* 参见描述 */
#define MATH_ERRNO /* 参见描述 */
#define MATH_ERREXCEPT /* 参见描述 */
#define math_errhandling /* 参见描述 */
namespace std {
  /* 浮点类型 */ acos(/* 浮点类型 */ x);
  float acosf(float x);
  long double acosl(long double x);
  /* 浮点类型 */ asin(/* 浮点类型 */ x);
  float asinf(float x);
  long double asinl(long double x);
  /* 浮点类型 */ atan(/* 浮点类型 */ x);
  float atanf(float x);
  long double atanl(long double x);
  /* 浮点类型 */ atan2(/* 浮点类型 */ y,
                                  /* 浮点类型 */ x);
  float atan2f(float y, float x);
  long double atan2l(long double y, long double x);
  /* 浮点类型 */ cos(/* 浮点类型 */e x);
  float cosf(float x);
  long double cosl(long double x);
  /* 浮点类型 */ sin(/* 浮点类型 */ x);
  float sinf(float x);
  long double sinl(long double x);
  /* 浮点类型 */ tan(/* 浮点类型 */ x);
  float tanf(float x);
  long double tanl(long double x);
  /* 浮点类型 */ acosh(/* 浮点类型 */ x);
  float acoshf(float x);
  long double acoshl(long double x);
  /* 浮点类型 */ asinh(/* 浮点类型 */ x);
  float asinhf(float x);
  long double asinhl(long double x);
  /* 浮点类型 */ atanh(/* 浮点类型 */ x);
  float atanhf(float x);
  long double atanhl(long double x);
  /* 浮点类型 */ cosh(/* 浮点类型 */ x);
  float coshf(float x);
  long double coshl(long double x);
  /* 浮点类型 */ sinh(/* 浮点类型 */ x);
  float sinhf(float x);
  long double sinhl(long double x);
  /* 浮点类型 */ tanh(/* 浮点类型 */ x);
  float tanhf(float x);
  long double tanhl(long double x);
  /* 浮点类型 */ exp(/* 浮点类型 */ x);
  float expf(float x);
  long double expl(long double x);
  /* 浮点类型 */ exp2(/* 浮点类型 */ x);
  float exp2f(float x);
  long double exp2l(long double x);
  /* 浮点类型 */ expm1(/* 浮点类型 */ x);
  float expm1f(float x);
  long double expm1l(long double x);
  constexpr /* 浮点类型 */ frexp(/* 浮点类型 */ value, int* exp);
  constexpr float frexpf(float value, int* exp);
  constexpr long double frexpl(long double value, int* exp);
  constexpr int</