Standard library header <cmath>

 

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Standard library headers

Language support <cfloat> <climits> <compare> (C++20) <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) Concepts <concepts> (C++20) Diagnostics <cassert> <cerrno> <debugging> (C++26) <stacktrace> (C++23) <stdexcept> <system_error> (C++11) Memory management <memory> <memory_resource> (C++17) <scoped_allocator> (C++11) Metaprogramming <type_traits> (C++11) <ratio> (C++11)

General utilities <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) Containers <array> (C++11) <deque> <flat_map> (C++23) <flat_set> (C++23) <forward_list> (C++11) <inplace_vector> (C++26)    <list> <map> <mdspan> (C++23) <queue> <set> <span> (C++20) <stack> <unordered_map> (C++11) <unordered_set> (C++11) <vector> Iterators <iterator> Ranges <generator> (C++23) <ranges> (C++20)

Algorithms <algorithm> <numeric> Strings <cctype> <cstring> <cuchar> (C++11) <cwchar> <cwctype> <string_view> (C++17) <string> Text processing <clocale> <codecvt> (C++11/17/26*) <locale> <regex> (C++11) <text_encoding> (C++26)    Numerics <cfenv> (C++11) <cmath> <complex> <linalg> (C++26) <numbers> (C++20) <random> (C++11) <valarray> Time <chrono> (C++11) <ctime> C compatibility <ccomplex> (C++11/17/20*) <ciso646> (until C++20) <cstdalign> (C++11/17/20*) <cstdbool> (C++11/17/20*) <ctgmath> (C++11/17/20*)

Input/output <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) Concurrency support <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) Execution support <execution> (C++17)

 

This header was originally in the C standard library as <math.h>.

This header is part of the numeric library.

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
HUGE_VALFHUGE_VALHUGE_VALL (C++11)(C++11)	indicates the overflow value for float, double and long double respectively (macro constant)
INFINITY (C++11)	evaluates to positive infinity or the value guaranteed to overflow a float (macro constant)
NAN (C++11)	evaluates to a quiet NaN of type float (macro constant)
math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)(C++11)(C++11)	defines the error handling mechanism used by the common mathematical functions (macro constant)
Classification
FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(C++11)	indicates a floating-point category (macro constant)
Functions
Basic operations
abs(float)fabsfabsffabsl (C++11)(C++11)	absolute value of a floating point value (\(\small{|x|}\)|x|) (function)
fmodfmodffmodl (C++11)(C++11)	remainder of the floating point division operation (function)
remainderremainderfremainderl (C++11)(C++11)(C++11)	signed remainder of the division operation (function)
remquoremquofremquol (C++11)(C++11)(C++11)	signed remainder as well as the three last bits of the division operation (function)
fmafmaffmal (C++11)(C++11)(C++11)	fused multiply-add operation (function)
fmaxfmaxffmaxl (C++11)(C++11)(C++11)	larger of two floating-point values (function)
fminfminffminl (C++11)(C++11)(C++11)	smaller of two floating point values (function)
fdimfdimffdiml (C++11)(C++11)(C++11)	positive difference of two floating point values (\({\small\max{(0, x-y)}}\)max(0, x-y)) (function)
nannanfnanl (C++11)(C++11)(C++11)	not-a-number (NaN) (function)
Linear interpolation
lerp (C++20)	linear interpolation function (function)
Exponential functions
expexpfexpl (C++11)(C++11)	returns e raised to the given power (\({\small e^x}\)ex) (function)
exp2exp2fexp2l (C++11)(C++11)(C++11)	returns 2 raised to the given power (\({\small 2^x}\)2x) (function)
expm1expm1fexpm1l (C++11)(C++11)(C++11)	returns e raised to the given power, minus one (\({\small e^x-1}\)ex-1) (function)
loglogflogl (C++11)(C++11)	computes natural (base e) logarithm (\({\small\ln{x}}\)ln(x)) (function)
log10log10flog10l (C++11)(C++11)	computes common (base 10) logarithm (\({\small\log_{10}{x}}\)log10(x)) (function)
log2log2flog2l (C++11)(C++11)(C++11)	base 2 logarithm of the given number (\({\small\log_{2}{x}}\)log2(x)) (function)
log1plog1pflog1pl (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
powpowfpowl (C++11)(C++11)	raises a number to the given power (\(\small{x^y}\)xy) (function)
sqrtsqrtfsqrtl (C++11)(C++11)	computes square root (\(\small{\sqrt{x}}\)√x) (function)
cbrtcbrtfcbrtl (C++11)(C++11)(C++11)	computes cube root (\(\small{\sqrt[3]{x}}\)3√x) (function)
hypothypotfhypotl (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
sinsinfsinl (C++11)(C++11)	computes sine (\({\small\sin{x}}\)sin(x)) (function)
coscosfcosl (C++11)(C++11)	computes cosine (\({\small\cos{x}}\)cos(x)) (function)
tantanftanl (C++11)(C++11)	computes tangent (\({\small\tan{x}}\)tan(x)) (function)
asinasinfasinl (C++11)(C++11)	computes arc sine (\({\small\arcsin{x}}\)arcsin(x)) (function)
acosacosfacosl (C++11)(C++11)	computes arc cosine (\({\small\arccos{x}}\)arccos(x)) (function)
atanatanfatanl (C++11)(C++11)	computes arc tangent (\({\small\arctan{x}}\)arctan(x)) (function)
atan2atan2fatan2l (C++11)(C++11)	arc tangent, using signs to determine quadrants (function)
Hyperbolic functions
sinhsinhfsinhl (C++11)(C++11)	computes hyperbolic sine (\({\small\sinh{x}}\)sinh(x)) (function)
coshcoshfcoshl (C++11)(C++11)	computes hyperbolic cosine (\({\small\cosh{x}}\)cosh(x)) (function)
tanhtanhftanhl (C++11)(C++11)	computes hyperbolic tangent (\({\small\tanh{x}}\)tanh(x)) (function)
asinhasinhfasinhl (C++11)(C++11)(C++11)	computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x}}\)arsinh(x)) (function)
acoshacoshfacoshl (C++11)(C++11)(C++11)	computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x}}\)arcosh(x)) (function)
atanhatanhfatanhl (C++11)(C++11)(C++11)	computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x}}\)artanh(x)) (function)
Error and gamma functions
erferfferfl (C++11)(C++11)(C++11)	error function (function)
erfcerfcferfcl (C++11)(C++11)(C++11)	complementary error function (function)
tgammatgammaftgammal (C++11)(C++11)(C++11)	gamma function (function)
lgammalgammaflgammal (C++11)(C++11)(C++11)	natural logarithm of the gamma function (function)
Nearest integer floating-point operations
ceilceilfceill (C++11)(C++11)	nearest integer not less than the given value (function)
floorfloorffloorl (C++11)(C++11)	nearest integer not greater than the given value (function)
trunctruncftruncl (C++11)(C++11)(C++11)	nearest integer not greater in magnitude than the given value (function)
roundroundfroundllroundlroundflroundlllroundllroundfllroundl (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)
nearbyintnearbyintfnearbyintl (C++11)(C++11)(C++11)	nearest integer using current rounding mode (function)
rintrintfrintllrintlrintflrintlllrintllrintfllrintl (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
frexpfrexpffrexpl (C++11)(C++11)	decomposes a number into significand and base-2 exponent (function)
ldexpldexpfldexpl (C++11)(C++11)	multiplies a number by 2 raised to an integral power (function)
modfmodffmodfl (C++11)(C++11)	decomposes a number into integer and fractional parts (function)
scalbnscalbnfscalbnlscalblnscalblnfscalblnl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	multiplies a number by FLT_RADIX raised to a power (function)
ilogbilogbfilogbl (C++11)(C++11)(C++11)	extracts exponent of the number (function)
logblogbflogbl (C++11)(C++11)(C++11)	extracts exponent of the number (function)
nextafternextafterfnextafterlnexttowardnexttowardfnexttowardl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	next representable floating-point value towards the given value (function)
copysigncopysignfcopysignl (C++11)(C++11)(C++11)	copies the sign of a floating point value (function)
Classification and comparison
fpclassify (C++11)	categorizes the given floating-point value (function)
isfinite (C++11)	checks if the given number has finite value (function)
isinf (C++11)	checks if the given number is infinite (function)
isnan (C++11)	checks if the given number is NaN (function)
isnormal (C++11)	checks if the given number is normal (function)
signbit (C++11)	checks if the given number is negative (function)
isgreater (C++11)	checks if the first floating-point argument is greater than the second (function)
isgreaterequal (C++11)	checks if the first floating-point argument is greater or equal than the second (function)
isless (C++11)	checks if the first floating-point argument is less than the second (function)
islessequal (C++11)	checks if the first floating-point argument is less or equal than the second (function)
islessgreater (C++11)	checks if the first floating-point argument is less or greater than the second (function)
isunordered (C++11)	checks if two floating-point values are unordered (function)
Mathematical special functions
assoc_laguerreassoc_laguerrefassoc_laguerrel (C++17)(C++17)(C++17)	associated Laguerre polynomials (function)
assoc_legendreassoc_legendrefassoc_legendrel (C++17)(C++17)(C++17)	associated Legendre polynomials (function)
betabetafbetal (C++17)(C++17)(C++17)	beta function (function)
comp_ellint_1comp_ellint_1fcomp_ellint_1l (C++17)(C++17)(C++17)	(complete) elliptic integral of the first kind (function)
comp_ellint_2comp_ellint_2fcomp_ellint_2l (C++17)(C++17)(C++17)	(complete) elliptic integral of the second kind (function)
comp_ellint_3comp_ellint_3fcomp_ellint_3l (C++17)(C++17)(C++17)	(complete) elliptic integral of the third kind (function)
cyl_bessel_icyl_bessel_ifcyl_bessel_il (C++17)(C++17)(C++17)	regular modified cylindrical Bessel functions (function)
cyl_bessel_jcyl_bessel_jfcyl_bessel_jl (C++17)(C++17)(C++17)	cylindrical Bessel functions (of the first kind) (function)
cyl_bessel_kcyl_bessel_kfcyl_bessel_kl (C++17)(C++17)(C++17)	irregular modified cylindrical Bessel functions (function)
cyl_neumanncyl_neumannfcyl_neumannl (C++17)(C++17)(C++17)	cylindrical Neumann functions (function)
ellint_1ellint_1fellint_1l (C++17)(C++17)(C++17)	(incomplete) elliptic integral of the first kind (function)
ellint_2ellint_2fellint_2l (C++17)(C++17)(C++17)	(incomplete) elliptic integral of the second kind (function)
ellint_3ellint_3fellint_3l (C++17)(C++17)(C++17)	(incomplete) elliptic integral of the third kind (function)
expintexpintfexpintl (C++17)(C++17)(C++17)	exponential integral (function)
hermitehermitefhermitel (C++17)(C++17)(C++17)	Hermite polynomials (function)
legendrelegendreflegendrel (C++17)(C++17)(C++17)	Legendre polynomials (function)
laguerrelaguerreflaguerrel (C++17)(C++17)(C++17)	Laguerre polynomials (function)
riemann_zetariemann_zetafriemann_zetal (C++17)(C++17)(C++17)	Riemann zeta function (function)
sph_besselsph_besselfsph_bessell (C++17)(C++17)(C++17)	spherical Bessel functions (of the first kind) (function)
sph_legendresph_legendrefsph_legendrel (C++17)(C++17)(C++17)	spherical associated Legendre functions (function)
sph_neumannsph_neumannfsph_neumannl (C++17)(C++17)(C++17)	spherical Neumann functions (function)

Synopsis

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);                     // 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);
}