This header was originally in the C standard library as<math.h>.
This header is part of thenumeric library.
Types | ||
float_t (C++11) | most efficient floating-point type at least as wide asfloat (typedef)[edit] | |
double_t (C++11) | most efficient floating-point type at least as wide asdouble (typedef)[edit] | |
Macros | ||
(C++11)(C++11) | indicates the overflow value forfloat,double andlongdouble respectively (macro constant)[edit] | |
(C++11) | evaluates to positive infinity or the value guaranteed to overflow afloat (macro constant)[edit] | |
(C++11) | evaluates to a quiet NaN of typefloat (macro constant)[edit] | |
(C++11)(C++11)(C++11) | 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 | ||
(C++11)(C++11) | absolute value of a floating point value (\(\small{|x|}\)|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 (\({\small\max{(0, x-y)}}\)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) | returnse raised to the given power (\({\small e^x}\)ex) (function)[edit] | |
(C++11)(C++11)(C++11) | returns2 raised to the given power (\({\small 2^x}\)2x) (function)[edit] | |
(C++11)(C++11)(C++11) | returnse raised to the given power, minus1 (\({\small e^x-1}\)ex-1) (function)[edit] | |
(C++11)(C++11) | computes natural (basee) logarithm (\({\small\ln{x}}\)ln(x)) (function)[edit] | |
(C++11)(C++11) | computes common (base10) logarithm (\({\small\log_{10}{x}}\)log10(x)) (function)[edit] | |
(C++11)(C++11)(C++11) | base2 logarithm of the given number (\({\small\log_{2}{x}}\)log2(x)) (function)[edit] | |
(C++11)(C++11)(C++11) | natural logarithm (to basee) of1 plus the given number (\({\small\ln{(1+x)}}\)ln(1+x)) (function)[edit] | |
Power functions | ||
(C++11)(C++11) | raises a number to the given power (\(\small{x^y}\)xy) (function)[edit] | |
(C++11)(C++11) | computes square root (\(\small{\sqrt{x}}\)√x) (function)[edit] | |
(C++11)(C++11)(C++11) | computes cube root (\(\small{\sqrt[3]{x}}\)3√x) (function)[edit] | |
(C++11)(C++11)(C++11) | computes hypotenuse\(\scriptsize{\sqrt{x^2+y^2}}\)√x2 +y2 and\(\scriptsize{\sqrt{x^2+y^2+z^2}}\)√x2 +y2 +z2 (since C++17) (function)[edit] | |
Trigonometric functions | ||
(C++11)(C++11) | computes sine (\({\small\sin{x}}\)sin(x)) (function)[edit] | |
(C++11)(C++11) | computes cosine (\({\small\cos{x}}\)cos(x)) (function)[edit] | |
(C++11)(C++11) | computes tangent (\({\small\tan{x}}\)tan(x)) (function)[edit] | |
(C++11)(C++11) | computes arc sine (\({\small\arcsin{x}}\)arcsin(x)) (function)[edit] | |
(C++11)(C++11) | computes arc cosine (\({\small\arccos{x}}\)arccos(x)) (function)[edit] | |
(C++11)(C++11) | computes arc tangent (\({\small\arctan{x}}\)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 (\({\small\sinh{x}}\)sinh(x)) (function)[edit] | |
(C++11)(C++11) | computes hyperbolic cosine (\({\small\cosh{x}}\)cosh(x)) (function)[edit] | |
(C++11)(C++11) | computes hyperbolic tangent (\({\small\tanh{x}}\)tanh(x)) (function)[edit] | |
(C++11)(C++11)(C++11) | computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x}}\)arsinh(x)) (function)[edit] | |
(C++11)(C++11)(C++11) | computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x}}\)arcosh(x)) (function)[edit] | |
(C++11)(C++11)(C++11) | computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x}}\)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 by2 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 byFLT_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 | ||
(C++11) | 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] | |
(C++11) | 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] | |
(C++11) | checks if the first floating-point argument is less or equal than the second (function)[edit] | |
(C++11) | checks if the first floating-point argument is less or greater than the second (function)[edit] | |
(C++11) | checks if two floating-point values are unordered (function)[edit] | |
Mathematical special functions | ||
(C++17)(C++17)(C++17) | associated Laguerre polynomials (function)[edit] | |
(C++17)(C++17)(C++17) | associated Legendre polynomials (function)[edit] | |
(C++17)(C++17)(C++17) | beta function (function)[edit] | |
(C++17)(C++17)(C++17) | (complete) elliptic integral of the first kind (function)[edit] | |
(C++17)(C++17)(C++17) | (complete) elliptic integral of the second kind (function)[edit] | |
(C++17)(C++17)(C++17) | (complete) elliptic integral of the third kind (function)[edit] | |
(C++17)(C++17)(C++17) | regular modified cylindrical Bessel functions (function)[edit] | |
(C++17)(C++17)(C++17) | cylindrical Bessel functions (of the first kind) (function)[edit] | |
(C++17)(C++17)(C++17) | irregular modified cylindrical Bessel functions (function)[edit] | |
(C++17)(C++17)(C++17) | 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] | |
(C++17)(C++17)(C++17) | Riemann zeta function (function)[edit] | |
(C++17)(C++17)(C++17) | spherical Bessel functions (of the first kind) (function)[edit] | |
(C++17)(C++17)(C++17) | spherical associated Legendre functions (function)[edit] | |
(C++17)(C++17)(C++17) | spherical Neumann functions (function)[edit] | |
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 thanstd::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 greatestfloating-point conversion rank and greatestfloating-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 asdouble. 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);longdouble acosl(longdouble x); /* floating-point-type */ asin(/* floating-point-type */ x);float asinf(float x);longdouble asinl(longdouble x); /* floating-point-type */ atan(/* floating-point-type */ x);float atanf(float x);longdouble atanl(longdouble x); /* floating-point-type */ atan2(/* floating-point-type */ y,/* floating-point-type */ x);float atan2f(float y,float x);longdouble atan2l(longdouble y,longdouble x); /* floating-point-type */ cos(/* floating-point-type */e x);float cosf(float x);longdouble cosl(longdouble x); /* floating-point-type */ sin(/* floating-point-type */ x);float sinf(float x);longdouble sinl(longdouble x); /* floating-point-type */ tan(/* floating-point-type */ x);float tanf(float x);longdouble tanl(longdouble x); /* floating-point-type */ acosh(/* floating-point-type */ x);float acoshf(float x);longdouble acoshl(longdouble x); /* floating-point-type */ asinh(/* floating-point-type */ x);float asinhf(float x);longdouble asinhl(longdouble x); /* floating-point-type */ atanh(/* floating-point-type */ x);float atanhf(float x);longdouble atanhl(longdouble x); /* floating-point-type */ cosh(/* floating-point-type */ x);float coshf(float x);longdouble coshl(longdouble x); /* floating-point-type */ sinh(/* floating-point-type */ x);float sinhf(float x);longdouble sinhl(longdouble x); /* floating-point-type */ tanh(/* floating-point-type */ x);float tanhf(float x);longdouble tanhl(longdouble x); /* floating-point-type */ exp(/* floating-point-type */ x);float expf(float x);longdouble expl(longdouble x); /* floating-point-type */ exp2(/* floating-point-type */ x);float exp2f(float x);longdouble exp2l(longdouble x); /* floating-point-type */ expm1(/* floating-point-type */ x);float expm1f(float x);longdouble expm1l(longdouble x); constexpr/* floating-point-type */ frexp(/* floating-point-type */ value,int* exp);constexprfloat frexpf(float value,int* exp);constexprlongdouble frexpl(longdouble value,int* exp); constexprint ilogb(/* floating-point-type */ x);constexprint ilogbf(float x);constexprint ilogbl(longdouble x); constexpr/* floating-point-type */ ldexp(/* floating-point-type */ x,int exp);constexprfloat ldexpf(float x,int exp);constexprlongdouble ldexpl(longdouble x,int exp); /* floating-point-type */ log(/* floating-point-type */ x);float logf(float x);longdouble logl(longdouble x); /* floating-point-type */ log10(/* floating-point-type */ x);float log10f(float x);longdouble log10l(longdouble x); /* floating-point-type */ log1p(/* floating-point-type */ x);float log1pf(float x);longdouble log1pl(longdouble x); /* floating-point-type */ log2(/* floating-point-type */ x);float log2f(float x);longdouble log2l(longdouble x); constexpr/* floating-point-type */ logb(/* floating-point-type */ x);constexprfloat logbf(float x);constexprlongdouble logbl(longdouble x); constexpr/* floating-point-type */ modf(/* floating-point-type */ value,/* floating-point-type */* iptr);constexprfloat modff(float value,float* iptr);constexprlongdouble modfl(longdouble value,longdouble* iptr); constexpr/* floating-point-type */ scalbn(/* floating-point-type */ x,int n);constexprfloat scalbnf(float x,int n);constexprlongdouble scalbnl(longdouble x,int n); constexpr/* floating-point-type */ scalbln(/* floating-point-type */ x,longint n);constexprfloat scalblnf(float x,longint n);constexprlongdouble scalblnl(longdouble x,longint n); /* floating-point-type */ cbrt(/* floating-point-type */ x);float cbrtf(float x);longdouble cbrtl(longdouble x); // absolute valuesconstexprint abs(int j);// freestandingconstexprlongint abs(longint j);// freestandingconstexprlonglongint abs(longlongint j);// freestandingconstexpr/* floating-point-type */ abs(/* floating-point-type */ j);// freestanding-deleted constexpr/* floating-point-type */ fabs(/* floating-point-type */ x);constexprfloat fabsf(float x);constexprlongdouble fabsl(longdouble x); /* floating-point-type */ hypot(/* floating-point-type */ x,/* floating-point-type */ y);float hypotf(float x,float y);longdouble hypotl(longdouble x,longdouble y); // three-dimensional hypotenusefloat 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);longdouble powl(longdouble x,longdouble y); /* floating-point-type */ sqrt(/* floating-point-type */ x);float sqrtf(float x);longdouble sqrtl(longdouble x); /* floating-point-type */ erf(/* floating-point-type */ x);float erff(float x);longdouble erfl(longdouble x); /* floating-point-type */ erfc(/* floating-point-type */ x);float erfcf(float x);longdouble erfcl(longdouble x); /* floating-point-type */ lgamma(/* floating-point-type */ x);float lgammaf(float x);longdouble lgammal(longdouble x); /* floating-point-type */ tgamma(/* floating-point-type */ x);float tgammaf(float x);longdouble tgammal(longdouble x); constexpr/* floating-point-type */ ceil(/* floating-point-type */ x);constexprfloat ceilf(float x);constexprlongdouble ceill(longdouble x); constexpr/* floating-point-type */ floor(/* floating-point-type */ x);constexprfloat floorf(float x);constexprlongdouble floorl(longdouble x); /* floating-point-type */ nearbyint(/* floating-point-type */ x);float nearbyintf(float x);longdouble nearbyintl(longdouble x); /* floating-point-type */ rint(/* floating-point-type */ x);float rintf(float x);longdouble rintl(longdouble x); longint lrint(/* floating-point-type */ x);longint lrintf(float x);longint lrintl(longdouble x); longlongint llrint(/* floating-point-type */ x);longlongint llrintf(float x);longlongint llrintl(longdouble x); constexpr/* floating-point-type */ round(/* floating-point-type */ x);constexprfloat roundf(float x);constexprlongdouble roundl(longdouble x); constexprlongint lround(/* floating-point-type */ x);constexprlongint lroundf(float x);constexprlongint lroundl(longdouble x); constexprlonglongint llround(/* floating-point-type */ x);constexprlonglongint llroundf(float x);constexprlonglongint llroundl(longdouble x); constexpr/* floating-point-type */ trunc(/* floating-point-type */ x);constexprfloat truncf(float x);constexprlongdouble truncl(longdouble x); constexpr/* floating-point-type */ fmod(/* floating-point-type */ x,/* floating-point-type */ y);constexprfloat fmodf(float x,float y);constexprlongdouble fmodl(longdouble x,longdouble y); constexpr/* floating-point-type */ remainder(/* floating-point-type */ x,/* floating-point-type */ y);constexprfloat remainderf(float x,float y);constexprlongdouble remainderl(longdouble x,longdouble y); constexpr/* floating-point-type */ remquo(/* floating-point-type */ x,/* floating-point-type */ y,int* quo);constexprfloat remquof(float x,float y,int* quo);constexprlongdouble remquol(longdouble x,longdouble y,int* quo); constexpr/* floating-point-type */ copysign(/* floating-point-type */ x,/* floating-point-type */ y);constexprfloat copysignf(float x,float y);constexprlongdouble copysignl(longdouble x,longdouble y); double nan(constchar* tagp);float nanf(constchar* tagp);longdouble nanl(constchar* tagp); constexpr/* floating-point-type */ nextafter(/* floating-point-type */ x,/* floating-point-type */ y);constexprfloat nextafterf(float x,float y);constexprlongdouble nextafterl(longdouble x,longdouble y); constexpr/* floating-point-type */ nexttoward(/* floating-point-type */ x,longdouble y);constexprfloat nexttowardf(float x,longdouble y);constexprlongdouble nexttowardl(longdouble x,longdouble y); constexpr/* floating-point-type */ fdim(/* floating-point-type */ x,/* floating-point-type */ y);constexprfloat fdimf(float x,float y);constexprlongdouble fdiml(longdouble x,longdouble y); constexpr/* floating-point-type */ fmax(/* floating-point-type */ x,/* floating-point-type */ y);constexprfloat fmaxf(float x,float y);constexprlongdouble fmaxl(longdouble x,longdouble y); constexpr/* floating-point-type */ fmin(/* floating-point-type */ x,/* floating-point-type */ y);constexprfloat fminf(float x,float y);constexprlongdouble fminl(longdouble x,longdouble y); constexpr/* floating-point-type */ fma(/* floating-point-type */ x,/* floating-point-type */ y,/* floating-point-type */ z);constexprfloat fmaf(float x,float y,float z);constexprlongdouble fmal(longdouble x,longdouble y,longdouble z); // linear interpolationconstexpr/* floating-point-type */ lerp(/* floating-point-type */ a,/* floating-point-type */ b,/* floating-point-type */ t)noexcept; // classification / comparison functionsconstexprint fpclassify(/* floating-point-type */ x); constexprbool isfinite(/* floating-point-type */ x); constexprbool isinf(/* floating-point-type */ x); constexprbool isnan(/* floating-point-type */ x); constexprbool isnormal(/* floating-point-type */ x); constexprbool signbit(/* floating-point-type */ x); constexprbool isgreater(/* floating-point-type */ x,/* floating-point-type */ y); constexprbool isgreaterequal(/* floating-point-type */ x,/* floating-point-type */ y); constexprbool isless(/* floating-point-type */ x,/* floating-point-type */ y); constexprbool islessequal(/* floating-point-type */ x,/* floating-point-type */ y); constexprbool islessgreater(/* floating-point-type */ x,/* floating-point-type */ y); constexprbool 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);longdouble assoc_laguerrel(unsigned n,unsigned m,longdouble 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);longdouble assoc_legendrel(unsigned l,unsigned m,longdouble x); // beta function/* floating-point-type */ beta(/* floating-point-type */ x,/* floating-point-type */ y);float betaf(float x,float y);longdouble betal(longdouble x,longdouble y); // complete elliptic integral of the first kind/* floating-point-type */ comp_ellint_1(/* floating-point-type */ k);float comp_ellint_1f(float k);longdouble comp_ellint_1l(longdouble k); // complete elliptic integral of the second kind/* floating-point-type */ comp_ellint_2(/* floating-point-type */ k);float comp_ellint_2f(float k);longdouble comp_ellint_2l(longdouble 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);longdouble comp_ellint_3l(longdouble k,longdouble 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);longdouble cyl_bessel_il(longdouble nu,longdouble 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);longdouble cyl_bessel_jl(longdouble nu,longdouble 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);longdouble cyl_bessel_kl(longdouble nu,longdouble 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);longdouble cyl_neumannl(longdouble nu,longdouble 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);longdouble ellint_1l(longdouble k,longdouble 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);longdouble ellint_2l(longdouble k,longdouble 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);longdouble ellint_3l(longdouble k,longdouble nu,longdouble phi); // exponential integral/* floating-point-type */ expint(/* floating-point-type */ x);float expintf(float x);longdouble expintl(longdouble x); // Hermite polynomials/* floating-point-type */ hermite(unsigned n,/* floating-point-type */ x);float hermitef(unsigned n,float x);longdouble hermitel(unsigned n,longdouble x); // Laguerre polynomials/* floating-point-type */ laguerre(unsigned n,/* floating-point-type */ x);float laguerref(unsigned n,float x);longdouble laguerrel(unsigned n,longdouble x); // Legendre polynomials/* floating-point-type */ legendre(unsigned l,/* floating-point-type */ x);float legendref(unsigned l,float x);longdouble legendrel(unsigned l,longdouble x); // Riemann zeta function/* floating-point-type */ riemann_zeta(/* floating-point-type */ x);float riemann_zetaf(float x);longdouble riemann_zetal(longdouble 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);longdouble sph_bessell(unsigned n,longdouble 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);longdouble sph_legendrel(unsigned l,unsigned m,longdouble 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);longdouble sph_neumannl(unsigned n,longdouble x);}
