标准库头文件 <cmath>
来自cppreference.com
此头文件原作为 <math.h>
存在于 C 标准库。
此头文件是数值库的一部分。
类型 | |
float_t (C++11) |
至少和 float 一样宽的最高效浮点类型 (typedef) |
double_t (C++11) |
至少和 double 一样宽的最高效浮点类型 (typedef) |
宏 | |
(C++11)(C++11) |
分别指出 float、double 和 long double 的上溢值 (宏常量) |
(C++11) |
求值为正无穷大或保证使 float 上溢的值 (宏常量) |
(C++11) |
求值为 float 类型的静默 NAN (宏常量) |
(C++11)(C++11)(C++11) |
定义常用数学函数所用的错误处理机制 (宏常量) |
分类 | |
(C++11)(C++11)(C++11)(C++11)(C++11) |
指示浮点类别 (宏常量) |
函数 | |
基本运算 | |
(C++11)(C++11) |
浮点值的绝对值( |x| ) (函数) |
(C++11)(C++11) |
浮点除法运算的余数 (函数) |
(C++11)(C++11)(C++11) |
除法运算的有符号余数 (函数) |
(C++11)(C++11)(C++11) |
除法运算的有符号余数和最后三个二进制位 (函数) |
(C++11)(C++11)(C++11) |
混合的乘加运算 (函数) |
(C++11)(C++11)(C++11) |
两个浮点值的较大者 (函数) |
(C++11)(C++11)(C++11) |
两个浮点值的较小者 (函数) |
(C++11)(C++11)(C++11) |
两个浮点值的正数差( max(0, x-y) ) (函数) |
(C++11)(C++11)(C++11) |
非数(NaN) (函数) |
线性插值 | |
(C++20) |
线性插值函数 (函数) |
指数函数 | |
(C++11)(C++11) |
返回 e 的给定次幂( ex ) (函数) |
(C++11)(C++11)(C++11) |
返回 2 的给定次幂( 2x ) (函数) |
(C++11)(C++11)(C++11) |
返回 e 的给定次幂减一( ex-1 ) (函数) |
(C++11)(C++11) |
计算自然(以 e 为底)对数( ln(x) ) (函数) |
(C++11)(C++11) |
计算常用(以 10 为底)对数( log10(x) ) (函数) |
(C++11)(C++11)(C++11) |
给定数值的以 2 为底的对数( log2(x) ) (函数) |
(C++11)(C++11)(C++11) |
1 加上给定数值的自然(以 e 为底)对数( ln(1+x) ) (函数) |
幂函数 | |
(C++11)(C++11) |
求某数的给定次幂( xy ) (函数) |
(C++11)(C++11) |
计算平方根( √x ) (函数) |
(C++11)(C++11)(C++11) |
计算立方根( 3√x ) (函数) |
(C++11)(C++11)(C++11) |
计算两个给定数的平方和的平方根( √x2 +y2 ) (函数) |
三角函数 | |
(C++11)(C++11) |
计算正弦( sin(x) ) (函数) |
(C++11)(C++11) |
计算余弦( cos(x) ) (函数) |
(C++11)(C++11) |
计算正切( tan(x) ) (函数) |
(C++11)(C++11) |
计算反正弦( arcsin(x) ) (函数) |
(C++11)(C++11) |
计算反余弦( arccos(x) ) (函数) |
(C++11)(C++11) |
计算反正切( arctan(x) ) (函数) |
(C++11)(C++11) |
反正切,用符号确定象限 (函数) |
双曲函数 | |
(C++11)(C++11) |
计算双曲正弦( sinh(x) ) (函数) |
(C++11)(C++11) |
计算双曲余弦( cosh(x) ) (函数) |
(C++11)(C++11) |
计算双曲正切( tanh(x) ) (函数) |
(C++11)(C++11)(C++11) |
计算反双曲正弦( arsinh(x) ) (函数) |
(C++11)(C++11)(C++11) |
计算反双曲余弦( arcosh(x) ) (函数) |
(C++11)(C++11)(C++11) |
计算反双曲正切( artanh(x) ) (函数) |
误差与伽马函数 | |
(C++11)(C++11)(C++11) |
误差函数 (函数) |
(C++11)(C++11)(C++11) |
补误差函数 (函数) |
(C++11)(C++11)(C++11) |
gamma 函数 (函数) |
(C++11)(C++11)(C++11) |
gamma 函数的自然对数 (函数) |
临近整数的浮点运算 | |
(C++11)(C++11) |
不小于给定值的最接近整数值 (函数) |
(C++11)(C++11) |
不大于给定值的最接近整数 (函数) |
(C++11)(C++11)(C++11) |
绝对值不大于给定值的最接近整数 (函数) |
(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11) |
最接近整数,中间情况下向远离零舍入 (函数) |
(C++11)(C++11)(C++11) |
使用当前舍入模式的最接近整数 (函数) |
(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11) |
使用当前舍入模式的最接近整数 若结果有别则有异常 (函数) |
浮点操纵函数 | |
(C++11)(C++11) |
将数分解为有效数字和 2 的幂次 (函数) |
(C++11)(C++11) |
将数乘以 2 的幂次 (函数) |
(C++11)(C++11) |
分解数为整数和小数部分 (函数) |
(C++11)(C++11)(C++11)(C++11)(C++11)(C++11) |
将数乘以 FLT_RADIX 的幂次 (函数) |
(C++11)(C++11)(C++11) |
提取数的指数 (函数) |
(C++11)(C++11)(C++11) |
提取数的指数 (函数) |
(C++11)(C++11) (C++11)(C++11)(C++11)(C++11) |
趋向给定值的下个可表示浮点值 (函数) |
(C++11)(C++11)(C++11) |
复制浮点值的符号 (函数) |
分类与比较 | |
(C++11) |
归类给定的浮点值 (函数) |
(C++11) |
检查给定数是否拥有有限值 (函数) |
(C++11) |
检查给定数是否为无限 (函数) |
(C++11) |
检查给定的数是否 NaN (函数) |
(C++11) |
检查给定数是否正规 (函数) |
(C++11) |
检查给定数是否为负 (函数) |
(C++11) |
检查第一个浮点实参是否大于第二个 (函数) |
(C++11) |
检查第一个浮点实参是否大于或等于第二个 (函数) |
(C++11) |
检查第一个浮点实参是否小于第二个 (函数) |
(C++11) |
检查第一个浮点实参是否小于或等于第二个 (函数) |
(C++11) |
检查第一个浮点实参是否小于或大于第二个 (函数) |
(C++11) |
检查两个浮点值是否无顺序 (函数) |
数学特殊函数 | |
(C++17)(C++17)(C++17) |
连带拉盖尔多项式 (函数) |
(C++17)(C++17)(C++17) |
连带勒让德多项式 (函数) |
(C++17)(C++17)(C++17) |
beta 函数 (函数) |
(C++17)(C++17)(C++17) |
第一类(完全)椭圆积分 (函数) |
(C++17)(C++17)(C++17) |
第二类(完全)椭圆积分 (函数) |
(C++17)(C++17)(C++17) |
第三类(完全)椭圆积分 (函数) |
(C++17)(C++17)(C++17) |
规则变形圆柱贝塞尔函数 (函数) |
(C++17)(C++17)(C++17) |
(第一类)圆柱贝塞尔函数 (函数) |
(C++17)(C++17)(C++17) |
不规则变形圆柱贝塞尔函数 (函数) |
(C++17)(C++17)(C++17) |
圆柱诺依曼函数 (函数) |
(C++17)(C++17)(C++17) |
第一类(不完全)椭圆积分 (函数) |
(C++17)(C++17)(C++17) |
第二类(不完全)椭圆积分 (函数) |
(C++17)(C++17)(C++17) |
第三类(不完全)椭圆积分 (函数) |
(C++17)(C++17)(C++17) |
指数积分 (函数) |
(C++17)(C++17)(C++17) |
埃尔米特多项式 (函数) |
(C++17)(C++17)(C++17) |
勒让德多项式 (函数) |
(C++17)(C++17)(C++17) |
拉盖尔多项式 (函数) |
(C++17)(C++17)(C++17) |
黎曼 zeta 函数 (函数) |
(C++17)(C++17)(C++17) |
(第一类)球面贝塞尔函数 (函数) |
(C++17)(C++17)(C++17) |
球面连带勒让德函数 (函数) |
(C++17)(C++17)(C++17) |
球面诺依曼函数 (函数) |
概要
namespace std { using float_t = /* 见描述 */; using double_t = /* 见描述 */; } #define HUGE_VAL /* 见描述 */ #define HUGE_VALF /* 见描述 */ #define HUGE_VALL /* 见描述 */ #define INFINITY /* 见描述 */ #define NAN /* 见描述 */ #define FP_INFINITE /* 见描述 */ #define FP_NAN /* 见描述 */ #define FP_NORMAL /* 见描述 */ #define FP_SUBNORMAL /* 见描述 */ #define FP_ZERO /* 见描述 */ #define FP_FAST_FMA /* 见描述 */ #define FP_FAST_FMAF /* 见描述 */ #define FP_FAST_FMAL /* 见描述 */ #define FP_ILOGB0 /* 见描述 */ #define FP_ILOGBNAN /* 见描述 */ #define MATH_ERRNO /* 见描述 */ #define MATH_ERREXCEPT /* 见描述 */ #define math_errhandling /* 见描述 */ namespace std { float acos(float x); double acos(double x); long double acos(long double x); float acosf(float x); long double acosl(long double x); float asin(float x); double asin(double x); long double asin(long double x); float asinf(float x); long double asinl(long double x); float atan(float x); double atan(double x); long double atan(long double x); float atanf(float x); long double atanl(long double x); float atan2(float y, float x); double atan2(double y, double x); long double atan2(long double y, long double x); float atan2f(float y, float x); long double atan2l(long double y, long double x); float cos(float x); double cos(double x); long double cos(long double x); float cosf(float x); long double cosl(long double x); float sin(float x); double sin(double x); long double sin(long double x); float sinf(float x); long double sinl(long double x); float tan(float x); double tan(double x); long double tan(long double x); float tanf(float x); long double tanl(long double x); float acosh(float x); double acosh(double x); long double acosh(long double x); float acoshf(float x); long double acoshl(long double x); float asinh(float x); double asinh(double x); long double asinh(long double x); float asinhf(float x); long double asinhl(long double x); float atanh(float x); double atanh(double x); long double atanh(long double x); float atanhf(float x); long double atanhl(long double x); float cosh(float x); double cosh(double x); long double cosh(long double x); float coshf(float x); long double coshl(long double x); float sinh(float x); double sinh(double x); long double sinh(long double x); float sinhf(float x); long double sinhl(long double x); float tanh(float x); double tanh(double x); long double tanh(long double x); float tanhf(float x); long double tanhl(long double x); float exp(float x); double exp(double x); long double exp(long double x); float expf(float x); long double expl(long double x); float exp2(float x); double exp2(double x); long double exp2(long double x); float exp2f(float x); long double exp2l(long double x); float expm1(float x); double expm1(double x); long double expm1(long double x); float expm1f(float x); long double expm1l(long double x); float frexp(float value, int* exp); double frexp(double value, int* exp); long double frexp(long double value, int* exp); float frexpf(float value, int* exp); long double frexpl(long double value, int* exp); int ilogb(float x); int ilogb(double x); int ilogb(long double x); int ilogbf(float x); int ilogbl(long double x); float ldexp(float x, int exp); double ldexp(double x, int exp); long double ldexp(long double x, int exp); float ldexpf(float x, int exp); long double ldexpl(long double x, int exp); float log(float x); double log(double x); long double log(long double x); float logf(float x); long double logl(long double x); float log10(float x); double log10(double x); long double log10(long double x); float log10f(float x); long double log10l(long double x); float log1p(float x); double log1p(double x); long double log1p(long double x); float log1pf(float x); long double log1pl(long double x); float log2(float x); double log2(double x); long double log2(long double x); float log2f(float x); long double log2l(long double x); float logb(float x); double logb(double x); long double logb(long double x); float logbf(float x); long double logbl(long double x); float modf(float value, float* iptr); double modf(double value, double* iptr); long double modf(long double value, long double* iptr); float modff(float value, float* iptr); long double modfl(long double value, long double* iptr); float scalbn(float x, int n); double scalbn(double x, int n); long double scalbn(long double x, int n); float scalbnf(float x, int n); long double scalbnl(long double x, int n); float scalbln(float x, long int n); double scalbln(double x, long int n); long double scalbln(long double x, long int n); float scalblnf(float x, long int n); long double scalblnl(long double x, long int n); float cbrt(float x); double cbrt(double x); long double cbrt(long double x); float cbrtf(float x); long double cbrtl(long double x); // 绝对值 int abs(int j); long int abs(long int j); long long int abs(long long int j); float abs(float j); double abs(double j); long double abs(long double j); float fabs(float x); double fabs(double x); long double fabs(long double x); float fabsf(float x); long double fabsl(long double x); float hypot(float x, float y); double hypot(double x, double y); long double hypot(long double x, long double y); float hypotf(float x, float y); long double hypotl(long double x, long double y); // 三维斜边 float hypot(float x, float y, float z); double hypot(double x, double y, double z); long double hypot(long double x, long double y, long double z); float pow(float x, float y); double pow(double x, double y); long double pow(long double x, long double y); float powf(float x, float y); long double powl(long double x, long double y); float sqrt(float x); double sqrt(double x); long double sqrt(long double x); float sqrtf(float x); long double sqrtl(long double x); float erf(float x); double erf(double x); long double erf(long double x); float erff(float x); long double erfl(long double x); float erfc(float x); double erfc(double x); long double erfc(long double x); float erfcf(float x); long double erfcl(long double x); float lgamma(float x); double lgamma(double x); long double lgamma(long double x); float lgammaf(float x); long double lgammal(long double x); float tgamma(float x); double tgamma(double x); long double tgamma(long double x); float tgammaf(float x); long double tgammal(long double x); float ceil(float x); double ceil(double x); long double ceil(long double x); float ceilf(float x); long double ceill(long double x); float floor(float x); double floor(double x); long double floor(long double x); float floorf(float x); long double floorl(long double x); float nearbyint(float x); double nearbyint(double x); long double nearbyint(long double x); float nearbyintf(float x); long double nearbyintl(long double x); float rint(float x); double rint(double x); long double rint(long double x); float rintf(float x); long double rintl(long double x); long int lrint(float x); long int lrint(double x); long int lrint(long double x); long int lrintf(float x); long int lrintl(long double x); long long int llrint(float x); long long int llrint(double x); long long int llrint(long double x); long long int llrintf(float x); long long int llrintl(long double x); float round(float x); double round(double x); long double round(long double x); float roundf(float x); long double roundl(long double x); long int lround(float x); long int lround(double x); long int lround(long double x); long int lroundf(float x); long int lroundl(long double x); long long int llround(float x); long long int llround(double x); long long int llround(long double x); long long int llroundf(float x); long long int llroundl(long double x); float trunc(float x); double trunc(double x); long double trunc(long double x); float truncf(float x); long double truncl(long double x); float fmod(float x, float y); double fmod(double x, double y); long double fmod(long double x, long double y); float fmodf(float x, float y); long double fmodl(long double x, long double y); float remainder(float x, float y); double remainder(double x, double y); long double remainder(long double x, long double y); float remainderf(float x, float y); long double remainderl(long double x, long double y); float remquo(float x, float y, int* quo); double remquo(double x, double y, int* quo); long double remquo(long double x, long double y, int* quo); float remquof(float x, float y, int* quo); long double remquol(long double x, long double y, int* quo); float copysign(float x, float y); double copysign(double x, double y); long double copysign(long double x, long double y); float copysignf(float x, float y); 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); float nextafter(float x, float y); double nextafter(double x, double y); long double nextafter(long double x, long double y); float nextafterf(float x, float y); long double nextafterl(long double x, long double y); float nexttoward(float x, long double y); double nexttoward(double x, long double y); long double nexttoward(long double x, long double y); float nexttowardf(float x, long double y); long double nexttowardl(long double x, long double y); float fdim(float x, float y); double fdim(double x, double y); long double fdim(long double x, long double y); float fdimf(float x, float y); long double fdiml(long double x, long double y); float fmax(float x, float y); double fmax(double x, double y); long double fmax(long double x, long double y); float fmaxf(float x, float y); long double fmaxl(long double x, long double y); float fmin(float x, float y); double fmin(double x, double y); long double fmin(long double x, long double y); float fminf(float x, float y); long double fminl(long double x, long double y); float fma(float x, float y, float z); double fma(double x, double y, double z); long double fma(long double x, long double y, long double z); float fmaf(float x, float y, float z); long double fmal(long double x, long double y, long double z); // 线性插值 constexpr float lerp(float a, float b, float t) noexcept; constexpr double lerp(double a, double b, double t) noexcept; constexpr long double lerp(long double a, long double b, long double t) noexcept; // 分类/比较函数 int fpclassify(float x); int fpclassify(double x); int fpclassify(long double x); bool isfinite(float x); bool isfinite(double x); bool isfinite(long double x); bool isinf(float x); bool isinf(double x); bool isinf(long double x); bool isnan(float x); bool isnan(double x); bool isnan(long double x); bool isnormal(float x); bool isnormal(double x); bool isnormal(long double x); bool signbit(float x); bool signbit(double x); bool signbit(long double x); bool isgreater(float x, float y); bool isgreater(double x, double y); bool isgreater(long double x, long double y); bool isgreaterequal(float x, float y); bool isgreaterequal(double x, double y); bool isgreaterequal(long double x, long double y); bool isless(float x, float y); bool isless(double x, double y); bool isless(long double x, long double y); bool islessequal(float x, float y); bool islessequal(double x, double y); bool islessequal(long double x, long double y); bool islessgreater(float x, float y); bool islessgreater(double x, double y); bool islessgreater(long double x, long double y); bool isunordered(float x, float y); bool isunordered(double x, double y); bool isunordered(long double x, long double y); // 数学特殊函数 // 连带拉盖尔多项式 double assoc_laguerre(unsigned n, unsigned m, double x); float assoc_laguerref(unsigned n, unsigned m, float x); long double assoc_laguerrel(unsigned n, unsigned m, long double x); // 连带勒让德多项式 double assoc_legendre(unsigned l, unsigned m, double x); float assoc_legendref(unsigned l, unsigned m, float x); long double assoc_legendrel(unsigned l, unsigned m, long double x); // beta 函数 double beta(double x, double y); float betaf(float x, float y); long double betal(long double x, long double y); // 第一类完全椭圆积分 double comp_ellint_1(double k); float comp_ellint_1f(float k); long double comp_ellint_1l(long double k); // 第二类完全椭圆积分 double comp_ellint_2(double k); float comp_ellint_2f(float k); long double comp_ellint_2l(long double k); // 第三类完全椭圆积分 double comp_ellint_3(double k, double nu); float comp_ellint_3f(float k, float nu); long double comp_ellint_3l(long double k, long double nu); // 规则变形圆柱贝塞尔函数 double cyl_bessel_i(double nu, double x); float cyl_bessel_if(float nu, float x); long double cyl_bessel_il(long double nu, long double x); // 第一类圆柱贝塞尔函数 double cyl_bessel_j(double nu, double x); float cyl_bessel_jf(float nu, float x); long double cyl_bessel_jl(long double nu, long double x); // 不规则变形圆柱贝塞尔函数 double cyl_bessel_k(double nu, double x); float cyl_bessel_kf(float nu, float x); long double cyl_bessel_kl(long double nu, long double x); // 圆柱诺伊曼函数; // 第二类圆柱贝塞尔函数 double cyl_neumann(double nu, double x); float cyl_neumannf(float nu, float x); long double cyl_neumannl(long double nu, long double x); // 第一类不完全椭圆积分 double ellint_1(double k, double phi); float ellint_1f(float k, float phi); long double ellint_1l(long double k, long double phi); // 第二类不完全椭圆积分 double ellint_2(double k, double phi); float ellint_2f(float k, float phi); long double ellint_2l(long double k, long double phi); // 第三类不完全椭圆积分 double ellint_3(double k, double nu, double phi); float ellint_3f(float k, float nu, float phi); long double ellint_3l(long double k, long double nu, long double phi); // 指数积分 double expint(double x); float expintf(float x); long double expintl(long double x); // 埃尔米特多项式 double hermite(unsigned n, double x); float hermitef(unsigned n, float x); long double hermitel(unsigned n, long double x); // 拉盖尔多项式 double laguerre(unsigned n, double x); float laguerref(unsigned n, float x); long double laguerrel(unsigned n, long double x); // 勒让德多项式 double legendre(unsigned l, double x); float legendref(unsigned l, float x); long double legendrel(unsigned l, long double x); // 黎曼 zeta 函数 double riemann_zeta(double x); float riemann_zetaf(float x); long double riemann_zetal(long double x); // 第一类球面贝塞尔函数 double sph_bessel(unsigned n, double x); float sph_besself(unsigned n, float x); long double sph_bessell(unsigned n, long double x); // 球面连带勒让德函数 double sph_legendre(unsigned l, unsigned m, double theta); float sph_legendref(unsigned l, unsigned m, float theta); long double sph_legendrel(unsigned l, unsigned m, long double theta); // 球面诺依曼函数; // 第二类球面贝塞尔函数 double sph_neumann(unsigned n, double x); float sph_neumannf(unsigned n, float x); long double sph_neumannl(unsigned n, long double x); }