Cayley-Dickson constants

non real constants More...

Variables
constexpr tags::callable_abs	kyosu::abs = {}
	Computes the absolute value of the parameter.
constexpr tags::callable_acos	kyosu::acos = {}
	Computes the acosine of the argument.
constexpr tags::callable_acosh	kyosu::acosh = {}
	Computes the inverse hyperbolic cosine of the argument.
constexpr tags::callable_acospi	kyosu::acospi = {}
	Computes the arc cosine of the argument in \(\pi\) multiples.
constexpr tags::callable_acot	kyosu::acot = {}
	Computes the arc cotangent of the argument.
constexpr tags::callable_acoth	kyosu::acoth = {}
	Computes the inverse hyperbolic cotangent of the argument.
constexpr tags::callable_acotpi	kyosu::acotpi = {}
	Computes the arc cotangent of the argument in \(\pi\) multiples.
constexpr tags::callable_acsc	kyosu::acsc = {}
	Computes the arccosecant of the argument.
constexpr tags::callable_acsch	kyosu::acsch = {}
	Computes the inverse hyperbolic cosecant of the argument.
constexpr tags::callable_acscpi	kyosu::acscpi = {}
	Computes the arc cosecant of the argume!nt in \(\pi\) multiples.
constexpr tags::callable_arg	kyosu::arg = {}
	argument.
constexpr tags::callable_asec	kyosu::asec = {}
	Computes the arcsecant of the argument.
constexpr tags::callable_asech	kyosu::asech = {}
	Computes the inverse hyperbolic secant of the argument.
constexpr tags::callable_asecpi	kyosu::asecpi = {}
	Computes the arc secant of the argument in \(\pi\) multiples.
constexpr tags::callable_asin	kyosu::asin = {}
	Computes the arcsine of the argument.
constexpr tags::callable_asinh	kyosu::asinh = {}
	Computes the inverse hyperbolic sine of the argument.
constexpr tags::callable_asinpi	kyosu::asinpi = {}
	Computes the arc sine of the argument in \(\pi\) multiples.
constexpr tags::callable_associator	kyosu::associator = {}
	Computes the associator of the three parameters.
constexpr tags::callable_atan	kyosu::atan = {}
	Computes the arctangent of the argument.
constexpr tags::callable_atanh	kyosu::atanh = {}
	Computes the inverse hyperbolic tangent of the argument.
constexpr tags::callable_atanpi	kyosu::atanpi = {}
	Computes the arc tangent of the argument in \(\pi\) multiples.
constexpr tags::callable_average	kyosu::average = {}
	Computes the average of the parameters.
constexpr tags::callable_beta	kyosu::beta = {}
	Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) for real or complex entries.
constexpr tags::callable_ceil	kyosu::ceil = {}
	Computes the ceil value.
constexpr tags::callable_commutator	kyosu::commutator = {}
	Computes the commutator of the two parameters.
constexpr tags::callable_complex	kyosu::complex = {}
	Constructs a kyosu::complex.
constexpr tags::callable_conj	kyosu::conj = {}
	Computes the conjugate value.
constexpr tags::callable_convert	kyosu::convert = {}
	convert to a target typek
constexpr tags::callable_cos	kyosu::cos = {}
	Computes the cosine of the argument.
constexpr tags::callable_cosh	kyosu::cosh = {}
	Computes the hyperbolic cosine of the argument.
constexpr tags::callable_cospi	kyosu::cospi = {}
	Computes the cosine from the argument in \(\pi\) multiples.
constexpr tags::callable_cot	kyosu::cot = {}
	Computes the cotangent of the argument.
constexpr tags::callable_coth	kyosu::coth = {}
	Computes the hyperbolic cotangent of the argument.
constexpr tags::callable_cotpi	kyosu::cotpi = {}
	Computes the cotangent from the argument in \(\pi\) multiples.
constexpr tags::callable_csc	kyosu::csc = {}
	Computes the cosecant of the argument.
constexpr tags::callable_csch	kyosu::csch = {}
	Computes the hyperbolic cosecant of the argument.
constexpr tags::callable_cscpi	kyosu::cscpi = {}
	Computes the cosecant from the argument in \(\pi\) multiples.
constexpr tags::callable_cyl_bessel_h1	kyosu::cyl_bessel_h1 = {}
	Computes the Bessel functions of the third kind \(H^{(1)}\),.
constexpr tags::callable_cyl_bessel_h12	kyosu::cyl_bessel_h12 = {}
	Computes the Bessel functions of the third kind \( H^{(1)} \) and \( H^{(2)} \),.
constexpr tags::callable_cyl_bessel_h1_0	kyosu::cyl_bessel_h1_0 = {}
	Computes the Bessel function of the third kind, \( H^{(1)}_0(x)\),.
constexpr tags::callable_cyl_bessel_h1_1	kyosu::cyl_bessel_h1_1 = {}
	Computes the Bessel function of the third kind, \( H^{(1)}_1(x)\),.
constexpr tags::callable_cyl_bessel_h1n	kyosu::cyl_bessel_h1n = {}
	Computes the Bessel/Hankel functions of the third kind, \( H_n^{(1)}(z) = J_n(z)+iY_n(z)\).
constexpr tags::callable_cyl_bessel_h2	kyosu::cyl_bessel_h2 = {}
	Computes the Bessel functions of the third kind \( H^{(2)}_\nu \),.
constexpr tags::callable_cyl_bessel_h2_0	kyosu::cyl_bessel_h2_0 = {}
	Computes the Bessel function of the third kind, \( H^{(2)}_0(x)\).
constexpr tags::callable_cyl_bessel_h2_1	kyosu::cyl_bessel_h2_1 = {}
	Computes the Bessel function of the third kind, \( H^{(2)}_1(x)\),.
constexpr tags::callable_cyl_bessel_h2n	kyosu::cyl_bessel_h2n = {}
	Computes the Bessel/Hankel functions of the third kind , \( H_n^{(2)} = J_n(z)-iY_n(z)\).
constexpr tags::callable_cyl_bessel_i	kyosu::cyl_bessel_i = {}
	Computes the Modified Bessel functions of the first kind.
constexpr tags::callable_cyl_bessel_i0	kyosu::cyl_bessel_i0 = {}
	Computes the modified Bessel function of the first kind \(I_{0}(x)=J_{0}(ix)\) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_cyl_bessel_i1	kyosu::cyl_bessel_i1 = {}
	Computes the modified Bessel function of the first kind, \( I_1(x)= iJ_1(ix) \) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_cyl_bessel_ik	kyosu::cyl_bessel_ik = {}
	Computes the modified Bessel functions \(I\) and \(K\),.
constexpr tags::callable_cyl_bessel_ikn	kyosu::cyl_bessel_ikn = {}
	Computes the Bessel functions of the second kind \(I\) and \(K \)of integral order,.
constexpr tags::callable_cyl_bessel_in	kyosu::cyl_bessel_in = {}
	Computes the modified Bessel functions of the first kind \(I_{n}(x)=i^{-n}J_{n }(ix)\), extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_cyl_bessel_j	kyosu::cyl_bessel_j = {}
	Computes the Bessel functions of the first kind, \( J_{\nu}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+\nu +1)}} {\left({x \over 2}\right)}^{2p+\nu }\) extended to the complex plane and cayley_dickson values.
constexpr tags::callable_cyl_bessel_j0	kyosu::cyl_bessel_j0 = {}
	Computes the Bessel function of the first kind, \( J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau) \,\mathrm {d} \tau \) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_cyl_bessel_j1	kyosu::cyl_bessel_j1 = {}
	Computes the Bessel function of the first kind, \( J_1\).
constexpr tags::callable_cyl_bessel_jn	kyosu::cyl_bessel_jn = {}
	Computes the Bessel functions of the first kind, \( J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}} {\left({x \over 2}\right)}^{2p+n }\) extended to the complex plane and cayley_dickson values.
constexpr tags::callable_cyl_bessel_k	kyosu::cyl_bessel_k = {}
	Computes the Modified Bessel functions of the second kind.
constexpr tags::callable_cyl_bessel_k0	kyosu::cyl_bessel_k0 = {}
	Computes the modified Bessel function of the second kind, \( K_0(x)=\lim_{\alpha\to 0}{\frac {\pi }{2}}{\frac {I_{-\alpha }(x)-I_{\alpha }(x)}{\sin \alpha \pi }}\). extended to the complex plane and cayley_dickson values.
constexpr tags::callable_cyl_bessel_k1	kyosu::cyl_bessel_k1 = {}
	Computes the Bessel function of the second kind, \( K_1(x)\lim_{\alpha\to 1}{\frac {\pi }{2}}{\frac {I_{-\alpha }(x)-I_{\alpha }(x)}{\sin \alpha \pi }}\) extended to the complex plane and cayley_dickson values.
constexpr tags::callable_cyl_bessel_kn	kyosu::cyl_bessel_kn = {}
	Computes the modified Bessel functions of the second kind, \( K_{n}(x)=\lim_{\alpha\to n}{\frac {\pi }{2}}{\frac {I_{-\alpha }(x)-I_{\alpha }(x)}{\sin \alpha \pi }}\). extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_cyl_bessel_y	kyosu::cyl_bessel_y = {}
	Computes the Bessel functions of the second kind,.
constexpr tags::callable_cyl_bessel_y0	kyosu::cyl_bessel_y0 = {}
	Computes the Bessel function of the second kind, \( Y_0(x)=\lim_{\alpha\to 0}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_cyl_bessel_y1	kyosu::cyl_bessel_y1 = {}
	Computes the Bessel function of the second kind, \( Y_1(x)=\lim_{\alpha\to 1}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_cyl_bessel_yn	kyosu::cyl_bessel_yn = {}
	Computes the modified Bessel functions of the second kind, \( Y_n(x)=\lim_{\alpha\to n}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_dec	kyosu::dec = {}
	decrements the argument by 1.
constexpr tags::callable_deta	kyosu::deta = {}
	Computes the Dirichlet sums \( \displaystyle \sum_{n = 0}^\infty \frac{(-1)^n}{(kn+1)^z}\).
constexpr tags::callable_digamma	kyosu::digamma = {}
	Computes the Digamma function i.e. the logarithmic derivative of the \(\Gamma\) function.
constexpr tags::callable_dist	kyosu::dist = {}
	Computes the distance between the two parameters.
constexpr tags::callable_dot	kyosu::dot = {}
	Computes elementwise the dot product of the coordinates of the corresponding element.
constexpr tags::callable_erf	kyosu::erf = {}
	Computes the error function: \( \displaystyle \mbox{erf}(x)=\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\) or its extension to complex and general cayley-dickson values.
constexpr tags::callable_erfcx	kyosu::erfcx = {}
	Computes the normalized complementary error function \( \displaystyle \mbox{erfcx}(x) = e^{x^2} \mbox{erfc}(x)\).
constexpr tags::callable_erfi	kyosu::erfi = {}
	Callable object computing The imaginary error function \( \displaystyle \mathrm{erfi}(z) = -i\mathrm{erf}(iz)\).
constexpr tags::callable_eta	kyosu::eta = {}
	Computes the Dirichlet sum \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(n+1)^z}\). Sometimes this function is for obvious reasons called the alternative \(\zeta\) function .
constexpr tags::callable_exp	kyosu::exp = {}
	Computes the exponential of the argument.
constexpr tags::callable_exp10	kyosu::exp10 = {}
	Computes the base 10 exponential of the argument.
constexpr tags::callable_exp2	kyosu::exp2 = {}
	Computes the base 2 exponential of the argument.
constexpr tags::callable_exp_i	kyosu::exp_i = {}
	Computes the exponential of i times the argument.
constexpr tags::callable_exp_ipi	kyosu::exp_ipi = {}
	Computes the exponential of \(i\pi\) times the argument.
constexpr tags::callable_expm1	kyosu::expm1 = {}
	Computes the exponential of the argument minus 1.
constexpr tags::callable_expmx2	kyosu::expmx2 = {}
	Computes the exponential of the opposite of the squared argument.
constexpr tags::callable_expx2	kyosu::expx2 = {}
	Computes the exponential of the squared argument.
constexpr tags::callable_faddeeva	kyosu::faddeeva = {}
	Callable object computing \(e^{-z^2}\mathrm{erfc}(-iz)\) the scaled complex error func.
constexpr tags::callable_fam	kyosu::fam = {}
	Computes fused add multiply.
constexpr tags::callable_floor	kyosu::floor = {}
	Computes the floor value.
constexpr tags::callable_fma	kyosu::fma = {}
	Computes fused multiply add.
constexpr tags::callable_fms	kyosu::fms = {}
	Computes fused multiply add.
constexpr tags::callable_fnma	kyosu::fnma = {}
	Computes fused negate multiply add.
constexpr tags::callable_fnms	kyosu::fnms = {}
	Computes fused negate multiply sub.
constexpr tags::callable_frac	kyosu::frac = {}
	Computes the frac value.
constexpr tags::callable_from_angle_axis	kyosu::from_angle_axis = {}
	Callable object computing an an unitary quaternion from an angle value and a 3 dimensionnal axis vector.
constexpr tags::callable_fsm	kyosu::fsm = {}
	Computes fused sub multiply.
constexpr tags::callable_horner	kyosu::horner = {}
	Implement the horner scheme to evaluate polynomials.
constexpr tags::callable_hypot	kyosu::hypot = {}
	Callable object computing the hypot operation.
constexpr tags::callable_i	kyosu::i = {}
	Computes the complex number cinf i.e. complex(nan, inf) in the chosen type.
constexpr tags::callable_if_else	kyosu::if_else = {}
	Select a value between two arguments based on a logical mask.
constexpr tags::callable_ipart	kyosu::imag = {}
	Alias for ipart.
constexpr tags::callable_inc	kyosu::inc = {}
	Increments the argument.
constexpr tags::callable_ipart	kyosu::ipart = {}
	Extracts the imaginary part of a value.
constexpr tags::callable_is_denormal	kyosu::is_denormal = {}
	test if the parameter is denormal.
constexpr tags::callable_is_equal	kyosu::is_equal = {}
	retuen true if and only if the two parameters are equal.
constexpr tags::callable_is_eqz	kyosu::is_eqz = {}
	test the parameter for equality to zero.
constexpr tags::callable_is_finite	kyosu::is_finite = {}
	test if the parameter is finite.
constexpr tags::callable_is_pure	kyosu::is_imag = {}
	alias of is_pure
constexpr tags::callable_is_infinite	kyosu::is_infinite = {}
	test if the parameter is infinite.
constexpr tags::callable_is_nan	kyosu::is_nan = {}
	test if the parameter is nan.
constexpr tags::callable_is_nez	kyosu::is_nez = {}
	test the parameter for non zero equality.
constexpr tags::callable_is_not_denormal	kyosu::is_not_denormal = {}
	test if the parameter is not denormal.
constexpr tags::callable_is_not_equal	kyosu::is_not_equal = {}
	return true if and only if the two parameters are not equal.
constexpr tags::callable_is_not_finite	kyosu::is_not_finite = {}
	test if the parameter is not finite.
constexpr tags::callable_is_not_infinite	kyosu::is_not_infinite = {}
	test if the parameter is not infinite.
constexpr tags::callable_is_not_nan	kyosu::is_not_nan = {}
	test if the parameter is not a Nan.
constexpr tags::callable_is_not_real	kyosu::is_not_real = {}
	test if the parameter is not_real.
constexpr tags::callable_is_pure	kyosu::is_pure = {}
	test if the parameter is pure.
constexpr tags::callable_is_real	kyosu::is_real = {}
	test if the parameter is real.
constexpr tags::callable_is_unitary	kyosu::is_unitary = {}
	test if the parameter is unitary (absolute value one).
constexpr tags::callable_jpart	kyosu::jpart = {}
	Extracts the \(j\) part of a value.
constexpr tags::callable_kpart	kyosu::kpart = {}
	Extracts the \(k\) part of a value.
constexpr tags::callable_lambda	kyosu::lambda = {}
	Callable object computing The Dirichlet \( \displaystyle \lambda(z) = \sum_0^\infty \frac{1}{(2n+1)^z}\).
constexpr tags::callable_lbeta	kyosu::lbeta = {}
	Computes the natural logarithm of the lbeta function.
constexpr tags::callable_ldiv	kyosu::ldiv = {}
	Computes the left division of the two parameters.
constexpr tags::callable_lerp	kyosu::lerp = {}
	Computes the linear interpolation.
constexpr tags::callable_lipart	kyosu::lipart = {}
	Extracts the li (sixth) part of a value.
constexpr tags::callable_ljpart	kyosu::ljpart = {}
	Extracts the lj (seventh) part of a value.
constexpr tags::callable_lkpart	kyosu::lkpart = {}
	Extracts the lk (eighth) part of a value.
constexpr tags::callable_log	kyosu::log = {}
	Computes the natural logarithm of the argument.
constexpr tags::callable_log10	kyosu::log10 = {}
	Computes the base 10 logarithm of the argument.
constexpr tags::callable_log1p	kyosu::log1p = {}
	Computes the natural logarithm of the argument plus 1.
constexpr tags::callable_log2	kyosu::log2 = {}
	Computes the base 2 logarithm of the argument.
constexpr tags::callable_log_abs	kyosu::log_abs = {}
	Computes the natural logarithm of the absolute value of the argument.
constexpr tags::callable_log_abs_gamma	kyosu::log_abs_gamma = {}
	Computes the log of the modulus of the \(\Gamma\) function of the parameter.
constexpr tags::callable_log_gamma	kyosu::log_gamma = {}
	Computes the log of the \(\Gamma\) function.
constexpr tags::callable_lpart	kyosu::lpart = {}
	Extracts the l (fifth) part of a value.
constexpr tags::callable_lpnorm	kyosu::lpnorm = {}
	Callable object computing the lpnorm operation \( \left(\sum_{i = 0}^n |x_i|^p\right)^{\frac1p} \).
constexpr tags::callable_lrising_factorial	kyosu::lrising_factorial = {}
	Computes the lrising_factorial function: \(\log\frac{\Gamma(x+y)}{\Gamma(x)}\).
constexpr tags::callable_manhattan	kyosu::manhattan = {}
	Callable object computing the manhattan operation.
constexpr tags::callable_maxabs	kyosu::maxabs = {}
	Callable object computing the maxabs operation.
constexpr tags::callable_maxmag	kyosu::maxmag = {}
	Callable object computing the maxmag operation.
constexpr tags::callable_minabs	kyosu::minabs = {}
	Callable object computing the minabs operation.
constexpr tags::callable_minmag	kyosu::minmag = {}
	Callable object computing the minmag operation.
constexpr tags::callable_minus	kyosu::minus = {}
	Computes the opposite value.
constexpr tags::callable_muli	kyosu::muli = {}
	Computes the value of the parameter multiplied by i on the left side. For real complex and quaternion the computation is an optimization over the call to * operator.
constexpr tags::callable_mulmi	kyosu::mulmi = {}
	Computes the value of the parameter multiplied by i on the left side. For real complex and quaternion the computation is an optimization over the call to * operator.
constexpr tags::callable_nearest	kyosu::nearest = {}
	Computes the nearest value.
constexpr tags::callable_negmaxabs	kyosu::negmaxabs = {}
	Callable object computing the negmaxabs operation.
constexpr tags::callable_negminabs	kyosu::negminabs = {}
	Callable object computing the negminabs operation.
constexpr tags::callable_oneminus	kyosu::oneminus = {}
	Computes the value one minus the argument.
constexpr tags::callable_pow	kyosu::pow = {}
	Computes the computing the pow operation \(x^y\).
constexpr tags::callable_pow1p	kyosu::pow1p = {}
	Computes the computing the pow1p operation \((x+1)^y\).
constexpr tags::callable_pow_abs	kyosu::pow_abs = {}
	Computes the computing the pow_abs operation \(|x|^y\).
constexpr tags::callable_powm1	kyosu::powm1 = {}
	Computes the computing the powm1 operation \(x^y-1\).
constexpr tags::callable_proj	kyosu::proj = {}
	Callable object computing proj(x), the projection of the cayley_dickson number z onto the (hyper) Riemann sphere.
constexpr tags::callable_pure	kyosu::pure = {}
	Extracts the imaginary part of a value.
constexpr tags::callable_quaternion	kyosu::quaternion = {}
	Constructs a kyosu::quaternion.
constexpr tags::callable_radinpi	kyosu::radinpi = {}
	Computes the parameter divided by \(\pi\).
constexpr tags::callable_real	kyosu::real = {}
	Extracts the real part of a value.
constexpr tags::callable_rec	kyosu::rec = {}
	Computes the inverse of the argument.
constexpr tags::callable_reldist	kyosu::reldist = {}
	Computes the relative distance between the two parameters.
constexpr tags::callable_reverse_horner	kyosu::reverse_horner = {}
	Implement the reverse_horner scheme to evaluate polynomials.
constexpr tags::callable_right_horner	kyosu::right_horner = {}
	Implement the right_horner scheme to evaluate polynomials.
constexpr tags::callable_right_reverse_horner	kyosu::right_reverse_horner = {}
	Implement the right_reverse_horner scheme to evaluate polynomials.
constexpr tags::callable_rising_factorial	kyosu::rising_factorial = {}
	Computes the rising_factorial function: \(\frac{\Gamma(x+y)}{\Gamma(x)}\).
constexpr tags::callable_sec	kyosu::sec = {}
	Computes the secant of the argument.
constexpr tags::callable_sech	kyosu::sech = {}
	Computes the hyperbolic secant of the argument.
constexpr tags::callable_secpi	kyosu::secpi = {}
	Computes the secant of the argument in \(\pi\) multiples.
constexpr tags::callable_sign	kyosu::sign = {}
	Computes tne normalized value z/abs(z) if z is not zero else 0.
constexpr tags::callable_sin	kyosu::sin = {}
	Computes the sine of the argument.
constexpr tags::callable_sinc	kyosu::sinc = {}
	Computes the sine cardinal of the argument.
constexpr tags::callable_sincos	kyosu::sincos = {}
	Computes simultaneously the sine and cosine of the argument.
constexpr tags::callable_sinh	kyosu::sinh = {}
	Computes the hyperbolic sine of the argument.
constexpr tags::callable_sinhc	kyosu::sinhc = {}
	Computes the hyperbolic sine cardinal of the argument.
constexpr tags::callable_sinhcosh	kyosu::sinhcosh = {}
	Computes simultaneously the hyperbolic sine and cosine of the argument.
constexpr tags::callable_sinpi	kyosu::sinpi = {}
	Computes the sine of the argument in \(\pi\) multiples.
constexpr tags::callable_sinpicospi	kyosu::sinpicospi = {}
	Computes simultaneously the sine and cosine of the argument in \(\pi\) multiples.
constexpr tags::callable_slerp	kyosu::slerp = {}
	Computes the spherical interpolation between unitary quaternions.
constexpr tags::callable_sph_bessel_h1_0	kyosu::sph_bessel_h1_0 = {}
	Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(1)}(z) = j_1(z)+iy_1(z)\).
constexpr tags::callable_sph_bessel_h1_1	kyosu::sph_bessel_h1_1 = {}
	Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(1)}(z) = j_1(z)+iy_1(z)\).
constexpr tags::callable_sph_bessel_h1n	kyosu::sph_bessel_h1n = {}
	Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(1)}(z) = j_n(z)+iy_n(z)\).
constexpr tags::callable_sph_bessel_h2_0	kyosu::sph_bessel_h2_0 = {}
	Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(2)}(z) = j_0(z)-iy_0(z)\).
constexpr tags::callable_sph_bessel_h2_1	kyosu::sph_bessel_h2_1 = {}
	Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(2)}(z) = j_1(z)-iy_1(z)\).
constexpr tags::callable_sph_bessel_h2n	kyosu::sph_bessel_h2n = {}
	Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(2)}(z) = j_n(z)-iy_n(z)\).
constexpr tags::callable_sph_bessel_i1_0	kyosu::sph_bessel_i1_0 = {}
	Computes the Bessel function, \( i_0^{(1)}(z) = j_n(iz)\) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sph_bessel_i1_1	kyosu::sph_bessel_i1_1 = {}
	Computes the Bessel function, \( i_1^{(1)}(z) = -i j_1(iz)\) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sph_bessel_i1n	kyosu::sph_bessel_i1n = {}
	Computes the spherical Bessel functions \( i_n^{(1)}(z) = i^{-n}j_n(iz)\).
constexpr tags::callable_sph_bessel_i2_0	kyosu::sph_bessel_i2_0 = {}
	Computes the Bessel function, \( i_0^{(2)}(z) = -i y_n(iz)\) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sph_bessel_i2_1	kyosu::sph_bessel_i2_1 = {}
	Computes the Bessel function, \( i_1^{(2)}(z) = -y_1(iz)\) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sph_bessel_i2n	kyosu::sph_bessel_i2n = {}
	Computes the spherical Bessel functions \( i_n^{(2)}(z) = i^{-n-1}y_n(iz)\).
constexpr tags::callable_sph_bessel_j0	kyosu::sph_bessel_j0 = {}
	Computes the Bessel function of the first kind, \( j_0(x)=\sin z/z \) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sph_bessel_jn	kyosu::sph_bessel_jn = {}
	Computes the spherical Bessel functions of the first kind \(j_{n}(x)\), extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sph_bessel_k0	kyosu::sph_bessel_k0 = {}
	Computes the spherical Bessel function of the first kind, \( k_0(x)= \pi e^{-z}/(2z) \) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sph_bessel_k1	kyosu::sph_bessel_k1 = {}
	Computes the spherical Bessel function of the first kind, \( k_1(x)= (\pi/2) e^{-z}(1/z+1/z^2)\) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sph_bessel_kn	kyosu::sph_bessel_kn = {}
	Computes the spherical Bessel functions \(k_{n}(x)\), extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sph_bessel_y0	kyosu::sph_bessel_y0 = {}
	Computes the spherical Bessel function of the first kind, \( y_0(x)=\cos z/z \) extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sph_bessel_yn	kyosu::sph_bessel_yn = {}
	Computes the spherical Bessel functions of the first kind \(y_{n}(x)\), extended to the complex plane and cayley_dickson algebras.
constexpr tags::callable_sqr	kyosu::sqr = {}
	Computes the square value.
constexpr tags::callable_sqr_abs	kyosu::sqr_abs = {}
	Computes the squared absolute value of the parameter.
constexpr tags::callable_sqrt	kyosu::sqrt = {}
	Computes a square root value.
constexpr tags::callable_tan	kyosu::tan = {}
	Computes the tangent of the argument.
constexpr tags::callable_tanh	kyosu::tanh = {}
	Computes the hyperbolic tangent of the argument.
constexpr tags::callable_tanpi	kyosu::tanpi = {}
	Computes the tangent of the argument in \(\pi\) multiples.
constexpr tags::callable_tgamma	kyosu::tgamma = {}
	Computes \(\Gamma(z)\)r.
constexpr tags::callable_trunc	kyosu::trunc = {}
	Computes the trunc value.
constexpr tags::callable_zeta	kyosu::zeta = {}
	Computes the Riemann \( \displaystyle\zeta(z)=\sum_0^\infty \frac{1}{(n+1)^z}\).
constexpr tags::callable_airy	kyosu::airy = {}
	Computes simultaneously the airy functions \(Ai\) and \(Bi\).