標準庫標頭檔案 <cmath>

 

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標準庫標頭檔案

語言支援 <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) 診斷 <cassert> <cerrno> <debugging> (C++26) <stacktrace> (C++23) <stdexcept> <system_error> (C++11) 記憶體管理 <memory> <memory_resource> (C++17) <scoped_allocator> (C++11) 超程式設計 <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)

演算法 <algorithm> <numeric> 字串 <cctype> <cstring> <cuchar> (C++11) <cwchar> <cwctype> <string_view> (C++17) <string> 文字處理 <clocale> <codecvt> (C++11/17/26*) <locale> <regex> (C++11) <text_encoding> (C++26)    數值 <cfenv> (C++11) <cmath> <complex> <linalg> (C++26) <numbers> (C++20) <random> (C++11) <simd> (C++26) <valarray> 時間 <chrono> (C++11) <ctime> C 相容性 <ccomplex> (C++11/17/20*) <ciso646> (until C++20) <cstdalign> (C++11/17/20*) <cstdbool> (C++11/17/20*) <ctgmath> (C++11/17/20*)

輸入/輸出 <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) 併發支援 <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) 執行支援 <execution> (C++17)

 

此標頭檔案最初是 C 標準庫的一部分，命名為 <math.h>。

此標頭檔案是 numeric 庫的一部分。

型別
float_t (C++11)	至少與 float 同樣寬的最有效的浮點型別 (typedef)
double_t (C++11)	至少與 double 同樣寬的最有效的浮點型別 (typedef)
宏
HUGE_VALFHUGE_VALHUGE_VALL (C++11)(C++11)	分別表示 float、double 和 long double 的溢位值 (宏常量)
INFINITY (C++11)	評估為正無窮大或保證使 float 溢位的值 (宏常量)
NAN (C++11)	評估為 float 型別的靜默 NaN (宏常量)
math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)(C++11)(C++11)	定義常用數學函式使用的錯誤處理機制 (宏常量)
分類
FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(C++11)	指示浮點類別 (宏常量)
函式
基本操作
abs(float)fabsfabsffabsl (C++11)(C++11)	浮點值的絕對值（\(\small{|x|}\)|x|） (函式)
fmodfmodffmodl (C++11)(C++11)	浮點除法運算的餘數 (函式)
remainderremainderfremainderl (C++11)(C++11)(C++11)	除法運算的帶符號餘數 (函式)
remquoremquofremquol (C++11)(C++11)(C++11)	帶符號餘數以及除法運算的最後三位 (函式)
fmafmaffmal (C++11)(C++11)(C++11)	融合乘加運算 (函式)
fmaxfmaxffmaxl (C++11)(C++11)(C++11)	兩個浮點值中較大的那個 (函式)
fminfminffminl (C++11)(C++11)(C++11)	兩個浮點值中較小的那個 (函式)
fdimfdimffdiml (C++11)(C++11)(C++11)	兩個浮點值的正差（\({\small\max{(0, x-y)}}\)max(0, x-y)） (函式)
nannanfnanl (C++11)(C++11)(C++11)	非數字（NaN） (函式)
線性插值
lerp (C++20)	線性插值函式 (函式)
指數函式
expexpfexpl (C++11)(C++11)	返回 e 的給定冪（\({\small e^x}\)ex） (函式)
exp2exp2fexp2l (C++11)(C++11)(C++11)	返回 2 的給定冪（\({\small 2^x}\)2x） (函式)
expm1expm1fexpm1l (C++11)(C++11)(C++11)	返回 e 的給定冪減去 1（\({\small e^x-1}\)ex-1） (函式)
loglogflogl (C++11)(C++11)	計算自然（底數為 e）對數（\({\small\ln{x}}\)ln(x)） (函式)
log10log10flog10l (C++11)(C++11)	計算常用（底數為 10）對數（\({\small\log_{10}{x}}\)log10(x)） (函式)
log2log2flog2l (C++11)(C++11)(C++11)	給定數字的底數為 2 的對數（\({\small\log_{2}{x}}\)log2(x)） (函式)
log1plog1pflog1pl (C++11)(C++11)(C++11)	1 加上給定數字的自然（底數為 e）對數（\({\small\ln{(1+x)}}\)ln(1+x)） (函式)
冪函式
powpowfpowl (C++11)(C++11)	將數字提升到給定冪（\(\small{x^y}\)xy） (函式)
sqrtsqrtfsqrtl (C++11)(C++11)	計算平方根（\(\small{\sqrt{x}}\)√x） (函式)
cbrtcbrtfcbrtl (C++11)(C++11)(C++11)	計算立方根（\(\small{\sqrt[3]{x}}\)3√x） (函式)
hypothypotfhypotl (C++11)(C++11)(C++11)	計算斜邊 \(\scriptsize{\sqrt{x^2+y^2}}\)√x2 +y2 和 \(\scriptsize{\sqrt{x^2+y^2+z^2}}\)√x2 +y2 +z2 (自 C++17 起) (函式)
三角函式
sinsinfsinl (C++11)(C++11)	計算正弦（\({\small\sin{x}}\)sin(x)） (函式)
coscosfcosl (C++11)(C++11)	計算餘弦（\({\small\cos{x}}\)cos(x)） (函式)
tantanftanl (C++11)(C++11)	計算正切（\({\small\tan{x}}\)tan(x)） (函式)
asinasinfasinl (C++11)(C++11)	計算反正弦（\({\small\arcsin{x}}\)arcsin(x)） (函式)
acosacosfacosl (C++11)(C++11)	計算反餘弦（\({\small\arccos{x}}\)arccos(x)） (函式)
atanatanfatanl (C++11)(C++11)	計算反正切（\({\small\arctan{x}}\)arctan(x)） (函式)
atan2atan2fatan2l (C++11)(C++11)	反正切，使用符號確定象限 (函式)
雙曲函式
sinhsinhfsinhl (C++11)(C++11)	計算雙曲正弦（\({\small\sinh{x}}\)sinh(x)） (函式)
coshcoshfcoshl (C++11)(C++11)	計算雙曲餘弦（\({\small\cosh{x}}\)cosh(x)） (函式)
tanhtanhftanhl (C++11)(C++11)	計算雙曲正切（\({\small\tanh{x}}\)tanh(x)） (函式)
asinhasinhfasinhl (C++11)(C++11)(C++11)	計算反雙曲正弦（\({\small\operatorname{arsinh}{x}}\)arsinh(x)） (函式)
acoshacoshfacoshl (C++11)(C++11)(C++11)	計算反雙曲餘弦（\({\small\operatorname{arcosh}{x}}\)arcosh(x)） (函式)
atanhatanhfatanhl (C++11)(C++11)(C++11)	計算反雙曲正切（\({\small\operatorname{artanh}{x}}\)artanh(x)） (函式)
誤差函式和伽馬函式
erferfferfl (C++11)(C++11)(C++11)	誤差函式 (函式)
erfcerfcferfcl (C++11)(C++11)(C++11)	互補誤差函式 (函式)
tgammatgammaftgammal (C++11)(C++11)(C++11)	伽馬函式 (函式)
lgammalgammaflgammal (C++11)(C++11)(C++11)	伽馬函式的自然對數 (函式)
最接近整數的浮點運算
ceilceilfceill (C++11)(C++11)	不小於給定值的最接近整數 (函式)
floorfloorffloorl (C++11)(C++11)	不大於給定值的最接近整數 (函式)
trunctruncftruncl (C++11)(C++11)(C++11)	不大於給定值幅度的最接近整數 (函式)
roundroundfroundllroundlroundflroundlllroundllroundfllroundl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	最接近整數，在半數情況下遠離零舍入 (函式)
nearbyintnearbyintfnearbyintl (C++11)(C++11)(C++11)	使用當前舍入模式的最接近整數 (函式)
rintrintfrintllrintlrintflrintlllrintllrintfllrintl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	使用當前舍入模式的最接近整數， 如果結果不同則丟擲異常 (函式)
浮點操作函式
frexpfrexpffrexpl (C++11)(C++11)	將數字分解為有效數字和以 2 為底的指數 (函式)
ldexpldexpfldexpl (C++11)(C++11)	將數字乘以 2 的整數次冪 (函式)
modfmodffmodfl (C++11)(C++11)	將數字分解為整數部分和小數部分 (函式)
scalbnscalbnfscalbnlscalblnscalblnfscalblnl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	將數字乘以 FLT_RADIX 的冪 (函式)
ilogbilogbfilogbl (C++11)(C++11)(C++11)	提取數字的指數 (函式)
logblogbflogbl (C++11)(C++11)(C++11)	提取數字的指數 (函式)
nextafternextafterfnextafterlnexttowardnexttowardfnexttowardl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	朝給定值方向的下一個可表示浮點值 (函式)
copysigncopysignfcopysignl (C++11)(C++11)(C++11)	複製浮點值的符號 (函式)
分類和比較
fpclassify (C++11)	對給定浮點值進行分類 (函式)
isfinite (C++11)	檢查給定數字是否具有有限值 (函式)
isinf (C++11)	檢查給定數字是否為無窮大 (函式)
isnan (C++11)	檢查給定數字是否為 NaN (函式)
isnormal (C++11)	檢查給定數字是否為正常數 (函式)
signbit (C++11)	檢查給定數字是否為負數 (函式)
isgreater (C++11)	檢查第一個浮點引數是否大於第二個 (函式)
isgreaterequal (C++11)	檢查第一個浮點引數是否大於或等於第二個 (函式)
isless (C++11)	檢查第一個浮點引數是否小於第二個 (函式)
islessequal (C++11)	檢查第一個浮點引數是否小於或等於第二個 (函式)
islessgreater (C++11)	檢查第一個浮點引數是否小於或大於第二個 (函式)
isunordered (C++11)	檢查兩個浮點值是否無序 (函式)
數學特殊函式
assoc_laguerreassoc_laguerrefassoc_laguerrel (C++17)(C++17)(C++17)	伴隨拉蓋爾多項式 (函式)
assoc_legendreassoc_legendrefassoc_legendrel (C++17)(C++17)(C++17)	伴隨勒讓德多項式 (函式)
betabetafbetal (C++17)(C++17)(C++17)	Beta 函式 (函式)
comp_ellint_1comp_ellint_1fcomp_ellint_1l (C++17)(C++17)(C++17)	（完全）第一類橢圓積分 (函式)
comp_ellint_2comp_ellint_2fcomp_ellint_2l (C++17)(C++17)(C++17)	（完全）第二類橢圓積分 (函式)
comp_ellint_3comp_ellint_3fcomp_ellint_3l (C++17)(C++17)(C++17)	（完全）第三類橢圓積分 (函式)
cyl_bessel_icyl_bessel_ifcyl_bessel_il (C++17)(C++17)(C++17)	正則修正柱貝塞爾函式 (函式)
cyl_bessel_jcyl_bessel_jfcyl_bessel_jl (C++17)(C++17)(C++17)	柱貝塞爾函式（第一類） (函式)
cyl_bessel_kcyl_bessel_kfcyl_bessel_kl (C++17)(C++17)(C++17)	非正則修正柱貝塞爾函式 (函式)
cyl_neumanncyl_neumannfcyl_neumannl (C++17)(C++17)(C++17)	柱諾依曼函式 (函式)
ellint_1ellint_1fellint_1l (C++17)(C++17)(C++17)	（不完全）第一類橢圓積分 (函式)
ellint_2ellint_2fellint_2l (C++17)(C++17)(C++17)	（不完全）第二類橢圓積分 (函式)
ellint_3ellint_3fellint_3l (C++17)(C++17)(C++17)	（不完全）第三類橢圓積分 (函式)
expintexpintfexpintl (C++17)(C++17)(C++17)	指數積分 (函式)
hermitehermitefhermitel (C++17)(C++17)(C++17)	埃爾米特多項式 (函式)
legendrelegendreflegendrel (C++17)(C++17)(C++17)	勒讓德多項式 (函式)
laguerrelaguerreflaguerrel (C++17)(C++17)(C++17)	拉蓋爾多項式 (函式)
riemann_zetariemann_zetafriemann_zetal (C++17)(C++17)(C++17)	黎曼zeta函式 (函式)
sph_besselsph_besselfsph_bessell (C++17)(C++17)(C++17)	球貝塞爾函式（第一類） (函式)
sph_legendresph_legendrefsph_legendrel (C++17)(C++17)(C++17)	球伴隨勒讓德函式 (函式)
sph_neumannsph_neumannfsph_neumannl (C++17)(C++17)(C++17)	球諾依曼函式 (函式)

概要

對於每個至少有一個型別為 /* 浮點型別 */ 的引數的函式，將提供針對每個 cv-unqualified 浮點型別的過載，其中函式簽名中所有 /* 浮點型別 */ 的使用都將替換為該浮點型別。

對於每個至少有一個型別為 /* 浮點型別 */ 的引數（`std::abs` 除外）的函式，還提供額外的過載，以確保如果對應於 /* 浮點型別 */ 引數的每個引數都具有算術型別，那麼每個此類引數都將有效地轉換為在所有此類引數的型別中具有最高 浮點轉換等級 和最高 浮點轉換子等級 的浮點型別，其中整數型別引數被視為與 double 具有相同的浮點轉換等級。如果不存在具有最高等級和子等級的此類浮點型別，則過載決議不會從提供的過載中產生可用的候選。

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);
}