标准库头文件 <cmath>

 

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标准库头文件

语言支持 <cfloat> <climits> <compare> (C++20) <contracts> (C++26) <coroutine> (C++20) <csetjmp> <csignal> <cstdarg> <cstddef> <cstdint> (C++11) <cstdlib> <exception> <initializer_list> (C++11)    <limits> <new> <source_location> (C++20) <stdfloat> (C++23) <typeinfo> <version> (C++20) 概念 <concepts> (C++20) 诊断 <cassert> <cerrno> <debugging> (C++26) <stacktrace> (C++23) <stdexcept> <system_error> (C++11) 内存管理 <memory> <memory_resource> (C++17) <scoped_allocator> (C++11) 元编程 <type_traits> (C++11) <ratio> (C++11)

通用工具 <any> (C++17) <bitset> <bit> (C++20) <charconv> (C++17) <expected> (C++23) <format> (C++20) <functional> <optional> (C++17) <tuple> (C++11) <typeindex> (C++11) <utility> <variant> (C++17) 容器 <array> (C++11) <deque> <flat_map> (C++23) <flat_set> (C++23) <forward_list> (C++11) <hive> (C++26) <inplace_vector> (C++26)    <list> <map> <mdspan> (C++23) <queue> <set> <span> (C++20) <stack> <unordered_map> (C++11) <unordered_set> (C++11) <vector> 迭代器 <iterator> Ranges <generator> (C++23) <ranges> (C++20)

算法 <algorithm> <numeric> 字符串 <cctype> <cstring> <cuchar> (C++11) <cwchar> <cwctype> <string_view> (C++17) <string> 文本处理 <clocale> <codecvt> (C++11/17/26*) <locale> <regex> (C++11) <text_encoding> (C++26)    数值 <cfenv> (C++11) <cmath> <complex> <linalg> (C++26) <numbers> (C++20) <random> (C++11) <simd> (C++26) <valarray> 时间 <chrono> (C++11) <ctime> C 兼容性 <ccomplex> (C++11/17/20*) <ciso646> (until C++20) <cstdalign> (C++11/17/20*) <cstdbool> (C++11/17/20*) <ctgmath> (C++11/17/20*)

输入/输出 <cinttypes> (C++11) <cstdio> <filesystem> (C++17) <fstream> <iomanip> <iosfwd> <iostream> <ios> <istream> <ostream> <print> (C++23) <spanstream> (C++23) <sstream> <streambuf> <strstream> (C++98/26*) <syncstream> (C++20) 并发支持 <atomic> (C++11) <barrier> (C++20) <condition_variable> (C++11) <future> (C++11) <hazard_pointer> (C++26) <latch> (C++20) <mutex> (C++11) <rcu> (C++26) <semaphore> (C++20) <shared_mutex> (C++14) <stdatomic.h> (C++23) <stop_token> (C++20) <thread> (C++11) 执行支持 <execution> (C++17)

 

此头文件最初是 C 标准库的一部分，命名为 <math.h>。

此头文件是 numeric 库的一部分。

类型
float_t (C++11)	至少与 float 同样宽的最有效的浮点类型 (typedef)
double_t (C++11)	至少与 double 同样宽的最有效的浮点类型 (typedef)
宏
HUGE_VALFHUGE_VALHUGE_VALL (C++11)(C++11)	分别表示 float、double 和 long double 的溢出值 (宏常量)
INFINITY (C++11)	评估为正无穷大或保证使 float 溢出的值 (宏常量)
NAN (C++11)	评估为 float 类型的静默 NaN (宏常量)
math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)(C++11)(C++11)	定义常用数学函数使用的错误处理机制 (宏常量)
分类
FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(C++11)	指示浮点类别 (宏常量)
函数
基本操作
abs(float)fabsfabsffabsl (C++11)(C++11)	浮点值的绝对值（\(\small{|x|}\)|x|） (函数)
fmodfmodffmodl (C++11)(C++11)	浮点除法运算的余数 (函数)
remainderremainderfremainderl (C++11)(C++11)(C++11)	除法运算的带符号余数 (函数)
remquoremquofremquol (C++11)(C++11)(C++11)	带符号余数以及除法运算的最后三位 (函数)
fmafmaffmal (C++11)(C++11)(C++11)	融合乘加运算 (函数)
fmaxfmaxffmaxl (C++11)(C++11)(C++11)	两个浮点值中较大的那个 (函数)
fminfminffminl (C++11)(C++11)(C++11)	两个浮点值中较小的那个 (函数)
fdimfdimffdiml (C++11)(C++11)(C++11)	两个浮点值的正差（\({\small\max{(0, x-y)}}\)max(0, x-y)） (函数)
nannanfnanl (C++11)(C++11)(C++11)	非数字（NaN） (函数)
线性插值
lerp (C++20)	线性插值函数 (函数)
指数函数
expexpfexpl (C++11)(C++11)	返回 e 的给定幂（\({\small e^x}\)ex） (函数)
exp2exp2fexp2l (C++11)(C++11)(C++11)	返回 2 的给定幂（\({\small 2^x}\)2x） (函数)
expm1expm1fexpm1l (C++11)(C++11)(C++11)	返回 e 的给定幂减去 1（\({\small e^x-1}\)ex-1） (函数)
loglogflogl (C++11)(C++11)	计算自然（底数为 e）对数（\({\small\ln{x}}\)ln(x)） (函数)
log10log10flog10l (C++11)(C++11)	计算常用（底数为 10）对数（\({\small\log_{10}{x}}\)log10(x)） (函数)
log2log2flog2l (C++11)(C++11)(C++11)	给定数字的底数为 2 的对数（\({\small\log_{2}{x}}\)log2(x)） (函数)
log1plog1pflog1pl (C++11)(C++11)(C++11)	1 加上给定数字的自然（底数为 e）对数（\({\small\ln{(1+x)}}\)ln(1+x)） (函数)
幂函数
powpowfpowl (C++11)(C++11)	将数字提升到给定幂（\(\small{x^y}\)xy） (函数)
sqrtsqrtfsqrtl (C++11)(C++11)	计算平方根（\(\small{\sqrt{x}}\)√x） (函数)
cbrtcbrtfcbrtl (C++11)(C++11)(C++11)	计算立方根（\(\small{\sqrt[3]{x}}\)3√x） (函数)
hypothypotfhypotl (C++11)(C++11)(C++11)	计算斜边 \(\scriptsize{\sqrt{x^2+y^2}}\)√x2 +y2 和 \(\scriptsize{\sqrt{x^2+y^2+z^2}}\)√x2 +y2 +z2 (自 C++17 起) (函数)
三角函数
sinsinfsinl (C++11)(C++11)	计算正弦（\({\small\sin{x}}\)sin(x)） (函数)
coscosfcosl (C++11)(C++11)	计算余弦（\({\small\cos{x}}\)cos(x)） (函数)
tantanftanl (C++11)(C++11)	计算正切（\({\small\tan{x}}\)tan(x)） (函数)
asinasinfasinl (C++11)(C++11)	计算反正弦（\({\small\arcsin{x}}\)arcsin(x)） (函数)
acosacosfacosl (C++11)(C++11)	计算反余弦（\({\small\arccos{x}}\)arccos(x)） (函数)
atanatanfatanl (C++11)(C++11)	计算反正切（\({\small\arctan{x}}\)arctan(x)） (函数)
atan2atan2fatan2l (C++11)(C++11)	反正切，使用符号确定象限 (函数)
双曲函数
sinhsinhfsinhl (C++11)(C++11)	计算双曲正弦（\({\small\sinh{x}}\)sinh(x)） (函数)
coshcoshfcoshl (C++11)(C++11)	计算双曲余弦（\({\small\cosh{x}}\)cosh(x)） (函数)
tanhtanhftanhl (C++11)(C++11)	计算双曲正切（\({\small\tanh{x}}\)tanh(x)） (函数)
asinhasinhfasinhl (C++11)(C++11)(C++11)	计算反双曲正弦（\({\small\operatorname{arsinh}{x}}\)arsinh(x)） (函数)
acoshacoshfacoshl (C++11)(C++11)(C++11)	计算反双曲余弦（\({\small\operatorname{arcosh}{x}}\)arcosh(x)） (函数)
atanhatanhfatanhl (C++11)(C++11)(C++11)	计算反双曲正切（\({\small\operatorname{artanh}{x}}\)artanh(x)） (函数)
误差函数和伽马函数
erferfferfl (C++11)(C++11)(C++11)	误差函数 (函数)
erfcerfcferfcl (C++11)(C++11)(C++11)	互补误差函数 (函数)
tgammatgammaftgammal (C++11)(C++11)(C++11)	伽马函数 (函数)
lgammalgammaflgammal (C++11)(C++11)(C++11)	伽马函数的自然对数 (函数)
最接近整数的浮点运算
ceilceilfceill (C++11)(C++11)	不小于给定值的最接近整数 (函数)
floorfloorffloorl (C++11)(C++11)	不大于给定值的最接近整数 (函数)
trunctruncftruncl (C++11)(C++11)(C++11)	不大于给定值幅度的最接近整数 (函数)
roundroundfroundllroundlroundflroundlllroundllroundfllroundl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	最接近整数，在半数情况下远离零舍入 (函数)
nearbyintnearbyintfnearbyintl (C++11)(C++11)(C++11)	使用当前舍入模式的最接近整数 (函数)
rintrintfrintllrintlrintflrintlllrintllrintfllrintl (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， 如果结果不同则抛出异常 (函数)
浮点操作函数
frexpfrexpffrexpl (C++11)(C++11)	将数字分解为有效数字和以 2 为底的指数 (函数)
ldexpldexpfldexpl (C++11)(C++11)	将数字乘以 2 的整数次幂 (函数)
modfmodffmodfl (C++11)(C++11)	将数字分解为整数部分和小数部分 (函数)
scalbnscalbnfscalbnlscalblnscalblnfscalblnl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	将数字乘以 FLT_RADIX 的幂 (函数)
ilogbilogbfilogbl (C++11)(C++11)(C++11)	提取数字的指数 (函数)
logblogbflogbl (C++11)(C++11)(C++11)	提取数字的指数 (函数)
nextafternextafterfnextafterlnexttowardnexttowardfnexttowardl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	朝给定值方向的下一个可表示浮点值 (函数)
copysigncopysignfcopysignl (C++11)(C++11)(C++11)	复制浮点值的符号 (函数)
分类和比较
fpclassify (C++11)	对给定浮点值进行分类 (函数)
isfinite (C++11)	检查给定数字是否具有有限值 (函数)
isinf (C++11)	检查给定数字是否为无穷大 (函数)
isnan (C++11)	检查给定数字是否为 NaN (函数)
isnormal (C++11)	检查给定数字是否为正常数 (函数)
signbit (C++11)	检查给定数字是否为负数 (函数)
isgreater (C++11)	检查第一个浮点参数是否大于第二个 (函数)
isgreaterequal (C++11)	检查第一个浮点参数是否大于或等于第二个 (函数)
isless (C++11)	检查第一个浮点参数是否小于第二个 (函数)
islessequal (C++11)	检查第一个浮点参数是否小于或等于第二个 (函数)
islessgreater (C++11)	检查第一个浮点参数是否小于或大于第二个 (函数)
isunordered (C++11)	检查两个浮点值是否无序 (函数)
数学特殊函数
assoc_laguerreassoc_laguerrefassoc_laguerrel (C++17)(C++17)(C++17)	伴随拉盖尔多项式 (函数)
assoc_legendreassoc_legendrefassoc_legendrel (C++17)(C++17)(C++17)	伴随勒让德多项式 (函数)
betabetafbetal (C++17)(C++17)(C++17)	Beta 函数 (函数)
comp_ellint_1comp_ellint_1fcomp_ellint_1l (C++17)(C++17)(C++17)	（完全）第一类椭圆积分 (函数)
comp_ellint_2comp_ellint_2fcomp_ellint_2l (C++17)(C++17)(C++17)	（完全）第二类椭圆积分 (函数)
comp_ellint_3comp_ellint_3fcomp_ellint_3l (C++17)(C++17)(C++17)	（完全）第三类椭圆积分 (函数)
cyl_bessel_icyl_bessel_ifcyl_bessel_il (C++17)(C++17)(C++17)	正则修正柱贝塞尔函数 (函数)
cyl_bessel_jcyl_bessel_jfcyl_bessel_jl (C++17)(C++17)(C++17)	柱贝塞尔函数（第一类） (函数)
cyl_bessel_kcyl_bessel_kfcyl_bessel_kl (C++17)(C++17)(C++17)	非正则修正柱贝塞尔函数 (函数)
cyl_neumanncyl_neumannfcyl_neumannl (C++17)(C++17)(C++17)	柱诺依曼函数 (函数)
ellint_1ellint_1fellint_1l (C++17)(C++17)(C++17)	（不完全）第一类椭圆积分 (函数)
ellint_2ellint_2fellint_2l (C++17)(C++17)(C++17)	（不完全）第二类椭圆积分 (函数)
ellint_3ellint_3fellint_3l (C++17)(C++17)(C++17)	（不完全）第三类椭圆积分 (函数)
expintexpintfexpintl (C++17)(C++17)(C++17)	指数积分 (函数)
hermitehermitefhermitel (C++17)(C++17)(C++17)	埃尔米特多项式 (函数)
legendrelegendreflegendrel (C++17)(C++17)(C++17)	勒让德多项式 (函数)
laguerrelaguerreflaguerrel (C++17)(C++17)(C++17)	拉盖尔多项式 (函数)
riemann_zetariemann_zetafriemann_zetal (C++17)(C++17)(C++17)	黎曼zeta函数 (函数)
sph_besselsph_besselfsph_bessell (C++17)(C++17)(C++17)	球贝塞尔函数（第一类） (函数)
sph_legendresph_legendrefsph_legendrel (C++17)(C++17)(C++17)	球伴随勒让德函数 (函数)
sph_neumannsph_neumannfsph_neumannl (C++17)(C++17)(C++17)	球诺依曼函数 (函数)

概要

对于每个至少有一个类型为 /* 浮点类型 */ 的参数的函数，将提供针对每个 cv-unqualified 浮点类型的重载，其中函数签名中所有 /* 浮点类型 */ 的使用都将替换为该浮点类型。

对于每个至少有一个类型为 /* 浮点类型 */ 的参数（`std::abs` 除外）的函数，还提供额外的重载，以确保如果对应于 /* 浮点类型 */ 参数的每个参数都具有算术类型，那么每个此类参数都将有效地转换为在所有此类参数的类型中具有最高 浮点转换等级 和最高 浮点转换子等级 的浮点类型，其中整数类型参数被视为与 double 具有相同的浮点转换等级。如果不存在具有最高等级和子等级的此类浮点类型，则重载决议不会从提供的重载中产生可用的候选。

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);                     // freestanding
  constexpr long int abs(long int j);           // freestanding
  constexpr long long int abs(long long int j); // freestanding
  constexpr /* floating-point-type */
    abs(/* floating-point-type */ j);           // freestanding-deleted
 
  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);
}