Namespaces
Variants
Views
Actions

Standard library header <cmath>

From cppreference.com
< cpp‎ | header
 
 
Standard library headers
Language support
Concepts
<concepts> (C++20)
Diagnostics
<system_error> (C++11)

Memory management
<memory_resource> (C++17)  
Metaprogramming
<type_traits> (C++11)
<ratio> (C++11)
General utilities
<utility>
<tuple> (C++11)
<optional> (C++17)
<variant> (C++17)
<any> (C++17)
<debugging> (C++26)
<expected> (C++23)
<bitset>
<charconv> (C++17)
<format> (C++20)
<bit> (C++20)

Strings
<cuchar> (C++11)

Containers
<flat_set> (C++23)
<span> (C++20)
<mdspan> (C++23)

Iterators
<iterator>
Ranges
<ranges> (C++20)
<generator> (C++23)
Algorithms
Numerics
<cfenv> (C++11)
<complex>
<cmath>
<linalg> (C++26)
<numbers> (C++20)

Time
<chrono> (C++11)
Localization
<codecvt> (C++11/17/26*)
<text_encoding> (C++26)
Input/output
<filesystem> (C++17)
<cstdio>
<cinttypes> (C++11)
<strstream> (C++98/26*)
Regular expressions
<regex> (C++11)
Concurrency support
<stop_token> (C++20)
<thread> (C++11)
<atomic> (C++11)
<rcu> (C++26)
<stdatomic.h> (C++23)
<mutex> (C++11)
<shared_mutex> (C++14)

<condition_variable> (C++11)  
<semaphore> (C++20)
<latch> (C++20)

<barrier> (C++20)
<future> (C++11)
<hazard_pointer> (C++26)

C compatibility
<cstdbool> (C++11/17/20*)  
<ccomplex> (C++11/17/20*)
<ctgmath> (C++11/17/20*)

<cstdalign> (C++11/17/20*)

<ciso646> (until C++20)

 

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

This header is part of the numeric library.

Contents

Types

float_t
(C++11)
most efficient floating-point type at least as wide as float
(typedef) [edit]
double_t
(C++11)
most efficient floating-point type at least as wide as double
(typedef) [edit]

Macros

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

Functions

Basic operations
absolute value of a floating point value (|x|)
(function) [edit]
(C++11)(C++11)
remainder of the floating point division operation
(function) [edit]
(C++11)(C++11)(C++11)
signed remainder of the division operation
(function) [edit]
(C++11)(C++11)(C++11)
signed remainder as well as the three last bits of the division operation
(function) [edit]
(C++11)(C++11)(C++11)
fused multiply-add operation
(function) [edit]
(C++11)(C++11)(C++11)
larger of two floating-point values
(function) [edit]
(C++11)(C++11)(C++11)
smaller of two floating point values
(function) [edit]
(C++11)(C++11)(C++11)
positive difference of two floating point values (max(0, x-y))
(function) [edit]
(C++11)(C++11)(C++11)
not-a-number (NaN)
(function) [edit]
Linear interpolation
(C++20)
linear interpolation function
(function) [edit]
Exponential functions
(C++11)(C++11)
returns e raised to the given power (ex)
(function) [edit]
(C++11)(C++11)(C++11)
returns 2 raised to the given power (2x)
(function) [edit]
(C++11)(C++11)(C++11)
returns e raised to the given power, minus one (ex-1)
(function) [edit]
(C++11)(C++11)
computes natural (base e) logarithm (ln(x))
(function) [edit]
(C++11)(C++11)
computes common (base 10) logarithm (log10(x))
(function) [edit]
(C++11)(C++11)(C++11)
base 2 logarithm of the given number (log2(x))
(function) [edit]
(C++11)(C++11)(C++11)
natural logarithm (to base e) of 1 plus the given number (ln(1+x))
(function) [edit]
Power functions
(C++11)(C++11)
raises a number to the given power (xy)
(function) [edit]
(C++11)(C++11)
computes square root (x)
(function) [edit]
(C++11)(C++11)(C++11)
computes cube root (3x)
(function) [edit]
(C++11)(C++11)(C++11)
computes square root of the sum of the squares of two or three(since C++17) given numbers (x2
+y2
), (x2
+y2
+z2
)
(since C++17)

(function) [edit]
Trigonometric functions
(C++11)(C++11)
computes sine (sin(x))
(function) [edit]
(C++11)(C++11)
computes cosine (cos(x))
(function) [edit]
(C++11)(C++11)
computes tangent (tan(x))
(function) [edit]
(C++11)(C++11)
computes arc sine (arcsin(x))
(function) [edit]
(C++11)(C++11)
computes arc cosine (arccos(x))
(function) [edit]
(C++11)(C++11)
computes arc tangent (arctan(x))
(function) [edit]
(C++11)(C++11)
arc tangent, using signs to determine quadrants
(function) [edit]
Hyperbolic functions
(C++11)(C++11)
computes hyperbolic sine (sinh(x))
(function) [edit]
(C++11)(C++11)
computes hyperbolic cosine (cosh(x))
(function) [edit]
(C++11)(C++11)
computes hyperbolic tangent (tanh(x))
(function) [edit]
(C++11)(C++11)(C++11)
computes the inverse hyperbolic sine (arsinh(x))
(function) [edit]
(C++11)(C++11)(C++11)
computes the inverse hyperbolic cosine (arcosh(x))
(function) [edit]
(C++11)(C++11)(C++11)
computes the inverse hyperbolic tangent (artanh(x))
(function) [edit]
Error and gamma functions
(C++11)(C++11)(C++11)
error function
(function) [edit]
(C++11)(C++11)(C++11)
complementary error function
(function) [edit]
(C++11)(C++11)(C++11)
gamma function
(function) [edit]
(C++11)(C++11)(C++11)
natural logarithm of the gamma function
(function) [edit]
Nearest integer floating-point operations
(C++11)(C++11)
nearest integer not less than the given value
(function) [edit]
(C++11)(C++11)
nearest integer not greater than the given value
(function) [edit]
(C++11)(C++11)(C++11)
nearest integer not greater in magnitude than the given value
(function) [edit]
(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) [edit]
(C++11)(C++11)(C++11)
nearest integer using current rounding mode
(function) [edit]
(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) [edit]
Floating-point manipulation functions
(C++11)(C++11)
decomposes a number into significand and base-2 exponent
(function) [edit]
(C++11)(C++11)
multiplies a number by 2 raised to an integral power
(function) [edit]
(C++11)(C++11)
decomposes a number into integer and fractional parts
(function) [edit]
(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)
multiplies a number by FLT_RADIX raised to a power
(function) [edit]
(C++11)(C++11)(C++11)
extracts exponent of the number
(function) [edit]
(C++11)(C++11)(C++11)
extracts exponent of the number
(function) [edit]
(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)
next representable floating-point value towards the given value
(function) [edit]
(C++11)(C++11)(C++11)
copies the sign of a floating point value
(function) [edit]
Classification and comparison
categorizes the given floating-point value
(function) [edit]
(C++11)
checks if the given number has finite value
(function) [edit]
(C++11)
checks if the given number is infinite
(function) [edit]
(C++11)
checks if the given number is NaN
(function) [edit]
(C++11)
checks if the given number is normal
(function) [edit]
(C++11)
checks if the given number is negative
(function) [edit]
(C++11)
checks if the first floating-point argument is greater than the second
(function) [edit]
checks if the first floating-point argument is greater or equal than the second
(function) [edit]
(C++11)
checks if the first floating-point argument is less than the second
(function) [edit]
checks if the first floating-point argument is less or equal than the second
(function) [edit]
checks if the first floating-point argument is less or greater than the second
(function) [edit]
checks if two floating-point values are unordered
(function) [edit]
Mathematical special functions
associated Laguerre polynomials
(function) [edit]
associated Legendre polynomials
(function) [edit]
(C++17)(C++17)(C++17)
beta function
(function) [edit]
(complete) elliptic integral of the first kind
(function) [edit]
(complete) elliptic integral of the second kind
(function) [edit]
(complete) elliptic integral of the third kind
(function) [edit]
regular modified cylindrical Bessel functions
(function) [edit]
cylindrical Bessel functions (of the first kind)
(function) [edit]
irregular modified cylindrical Bessel functions
(function) [edit]
cylindrical Neumann functions
(function) [edit]
(C++17)(C++17)(C++17)
(incomplete) elliptic integral of the first kind
(function) [edit]
(C++17)(C++17)(C++17)
(incomplete) elliptic integral of the second kind
(function) [edit]
(C++17)(C++17)(C++17)
(incomplete) elliptic integral of the third kind
(function) [edit]
(C++17)(C++17)(C++17)
exponential integral
(function) [edit]
(C++17)(C++17)(C++17)
Hermite polynomials
(function) [edit]
(C++17)(C++17)(C++17)
Legendre polynomials
(function) [edit]
(C++17)(C++17)(C++17)
Laguerre polynomials
(function) [edit]
Riemann zeta function
(function) [edit]
spherical Bessel functions (of the first kind)
(function) [edit]
spherical associated Legendre functions
(function) [edit]
spherical Neumann functions
(function) [edit]

[edit] 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);
}