Eigen/src/Core/arch/ZVector/MathFunctions.h - eigen - Git at Google


            
            // This file is part of Eigen, a lightweight C++ template library

            
            // for linear algebra.

            
            //

            
            // Copyright (C) 2007 Julien Pommier

            
            // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>

            
            // Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>

            
            //

            
            // This Source Code Form is subject to the terms of the Mozilla

            
            // Public License v. 2.0. If a copy of the MPL was not distributed

            
            // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.


            /* The sin, cos, exp, and log functions of this file come from

            
             * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/

            
             */


            #ifndef EIGEN_MATH_FUNCTIONS_ZVECTOR_H

            
            #define EIGEN_MATH_FUNCTIONS_ZVECTOR_H


            // IWYU pragma: private

            
            #include "../../InternalHeaderCheck.h"


            namespace Eigen {


            namespace internal {


            EIGEN_DOUBLE_PACKET_FUNCTION(atanh, Packet2d)

            
            EIGEN_DOUBLE_PACKET_FUNCTION(log, Packet2d)

            
            EIGEN_DOUBLE_PACKET_FUNCTION(log2, Packet2d)

            
            EIGEN_DOUBLE_PACKET_FUNCTION(tanh, Packet2d)


            EIGEN_FLOAT_PACKET_FUNCTION(atanh, Packet4f)

            
            EIGEN_FLOAT_PACKET_FUNCTION(log, Packet4f)

            
            EIGEN_FLOAT_PACKET_FUNCTION(log2, Packet4f)


            EIGEN_GENERIC_PACKET_FUNCTION(atan, Packet2d)

            
            EIGEN_GENERIC_PACKET_FUNCTION(atan, Packet4f)

            
            EIGEN_GENERIC_PACKET_FUNCTION(exp2, Packet2d)

            
            EIGEN_GENERIC_PACKET_FUNCTION(exp2, Packet4f)


            #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)

            
            static EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);

            
            static EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);

            
            static EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);

            
            static EIGEN_DECLARE_CONST_Packet4i(23, 23);


            static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);


            /* the smallest non denormalized float number */

            
            static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);

            
            static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000);  // -1.f/0.f

            
            static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff);


            /* natural logarithm computed for 4 simultaneous float

            
              return NaN for x <= 0

            
            */

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, -1.1514610310E-1f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, -1.2420140846E-1f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, +1.4249322787E-1f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, -1.6668057665E-1f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, +2.0000714765E-1f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, -2.4999993993E-1f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, +3.3333331174E-1f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);


            static EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);

            
            static EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);


            static EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);


            static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);

            
            static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);

            
            #endif


            static EIGEN_DECLARE_CONST_Packet2d(1, 1.0);

            
            static EIGEN_DECLARE_CONST_Packet2d(2, 2.0);

            
            static EIGEN_DECLARE_CONST_Packet2d(half, 0.5);


            static EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);

            
            static EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);


            static EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);


            static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);

            
            static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);

            
            static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);


            static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);

            
            static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);

            
            static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);

            
            static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);


            static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);

            
            static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);


            template <>

            
            EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d pexp<Packet2d>(const Packet2d& _x) {

            
              Packet2d x = _x;


              Packet2d tmp, fx;

            
              Packet2l emm0;


              // clamp x

            
              x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);

            
              /* express exp(x) as exp(g + n*log(2)) */

            
              fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);


              fx = vec_floor(fx);


              tmp = pmul(fx, p2d_cephes_exp_C1);

            
              Packet2d z = pmul(fx, p2d_cephes_exp_C2);

            
              x = psub(x, tmp);

            
              x = psub(x, z);


              Packet2d x2 = pmul(x, x);


              Packet2d px = p2d_cephes_exp_p0;

            
              px = pmadd(px, x2, p2d_cephes_exp_p1);

            
              px = pmadd(px, x2, p2d_cephes_exp_p2);

            
              px = pmul(px, x);


              Packet2d qx = p2d_cephes_exp_q0;

            
              qx = pmadd(qx, x2, p2d_cephes_exp_q1);

            
              qx = pmadd(qx, x2, p2d_cephes_exp_q2);

            
              qx = pmadd(qx, x2, p2d_cephes_exp_q3);


              x = pdiv(px, psub(qx, px));

            
              x = pmadd(p2d_2, x, p2d_1);


              // build 2^n

            
              emm0 = vec_ctsl(fx, 0);


              static const Packet2l p2l_1023 = {1023, 1023};

            
              static const Packet2ul p2ul_52 = {52, 52};


              emm0 = emm0 + p2l_1023;

            
              emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);


              // Altivec's max & min operators just drop silent NaNs. Check NaNs in

            
              // inputs and return them unmodified.

            
              Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));

            
              return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x), isnumber_mask);

            
            }


            template <>

            
            EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f pexp<Packet4f>(const Packet4f& _x) {

            
            #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)

            
              Packet4f x = _x;


              Packet4f tmp, fx;

            
              Packet4i emm0;


              // clamp x

            
              x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);


              // express exp(x) as exp(g + n*log(2))

            
              fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);


              fx = pfloor(fx);


              tmp = pmul(fx, p4f_cephes_exp_C1);

            
              Packet4f z = pmul(fx, p4f_cephes_exp_C2);

            
              x = psub(x, tmp);

            
              x = psub(x, z);


              z = pmul(x, x);


              Packet4f y = p4f_cephes_exp_p0;

            
              y = pmadd(y, x, p4f_cephes_exp_p1);

            
              y = pmadd(y, x, p4f_cephes_exp_p2);

            
              y = pmadd(y, x, p4f_cephes_exp_p3);

            
              y = pmadd(y, x, p4f_cephes_exp_p4);

            
              y = pmadd(y, x, p4f_cephes_exp_p5);

            
              y = pmadd(y, z, x);

            
              y = padd(y, p4f_1);


              // build 2^n

            
              emm0 = Packet4i{(int)fx[0], (int)fx[1], (int)fx[2], (int)fx[3]};

            
              emm0 = emm0 + p4i_0x7f;

            
              emm0 = emm0 << reinterpret_cast<Packet4i>(p4i_23);


              return pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x);

            
            #else

            
              Packet4f res;

            
              res.v4f[0] = pexp<Packet2d>(_x.v4f[0]);

            
              res.v4f[1] = pexp<Packet2d>(_x.v4f[1]);

            
              return res;

            
            #endif

            
            }


            template <>

            
            EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d psqrt<Packet2d>(const Packet2d& x) {

            
              return vec_sqrt(x);

            
            }


            template <>

            
            EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f psqrt<Packet4f>(const Packet4f& x) {

            
              Packet4f res;

            
            #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)

            
              res = vec_sqrt(x);

            
            #else

            
              res.v4f[0] = psqrt<Packet2d>(x.v4f[0]);

            
              res.v4f[1] = psqrt<Packet2d>(x.v4f[1]);

            
            #endif

            
              return res;

            
            }


            template <>

            
            EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d prsqrt<Packet2d>(const Packet2d& x) {

            
              return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);

            
            }


            template <>

            
            EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f prsqrt<Packet4f>(const Packet4f& x) {

            
              Packet4f res;

            
            #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)

            
              res = pset1<Packet4f>(1.0) / psqrt<Packet4f>(x);

            
            #else

            
              res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]);

            
              res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]);

            
            #endif

            
              return res;

            
            }


            // Hyperbolic Tangent function.

            
            template <>

            
            EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f ptanh<Packet4f>(const Packet4f& x) {

            
              return ptanh_float(x);

            
            }


            }  // end namespace internal


            }  // end namespace Eigen


            #endif  // EIGEN_MATH_FUNCTIONS_ZVECTOR_H
	// This file is part of Eigen, a lightweight C++ template library
	// for linear algebra.
	//
	// Copyright (C) 2007 Julien Pommier
	// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
	// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
	//
	// This Source Code Form is subject to the terms of the Mozilla
	// Public License v. 2.0. If a copy of the MPL was not distributed
	// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

	/* The sin, cos, exp, and log functions of this file come from
	* Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
	*/

	#ifndef EIGEN_MATH_FUNCTIONS_ZVECTOR_H
	#define EIGEN_MATH_FUNCTIONS_ZVECTOR_H

	// IWYU pragma: private
	#include "../../InternalHeaderCheck.h"

	namespace Eigen {

	namespace internal {

	EIGEN_DOUBLE_PACKET_FUNCTION(atanh, Packet2d)
	EIGEN_DOUBLE_PACKET_FUNCTION(log, Packet2d)
	EIGEN_DOUBLE_PACKET_FUNCTION(log2, Packet2d)
	EIGEN_DOUBLE_PACKET_FUNCTION(tanh, Packet2d)

	EIGEN_FLOAT_PACKET_FUNCTION(atanh, Packet4f)
	EIGEN_FLOAT_PACKET_FUNCTION(log, Packet4f)
	EIGEN_FLOAT_PACKET_FUNCTION(log2, Packet4f)

	EIGEN_GENERIC_PACKET_FUNCTION(atan, Packet2d)
	EIGEN_GENERIC_PACKET_FUNCTION(atan, Packet4f)
	EIGEN_GENERIC_PACKET_FUNCTION(exp2, Packet2d)
	EIGEN_GENERIC_PACKET_FUNCTION(exp2, Packet4f)

	#if !defined(__ARCH__) \|\| (defined(__ARCH__) && __ARCH__ >= 12)
	static EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);
	static EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
	static EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
	static EIGEN_DECLARE_CONST_Packet4i(23, 23);

	static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);

	/* the smallest non denormalized float number */
	static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
	static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f
	static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff);

	/* natural logarithm computed for 4 simultaneous float
	return NaN for x <= 0
	*/
	static EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, -1.1514610310E-1f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, -1.2420140846E-1f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, +1.4249322787E-1f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, -1.6668057665E-1f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, +2.0000714765E-1f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, -2.4999993993E-1f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, +3.3333331174E-1f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);

	static EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
	static EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);

	static EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);

	static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
	static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
	#endif

	static EIGEN_DECLARE_CONST_Packet2d(1, 1.0);
	static EIGEN_DECLARE_CONST_Packet2d(2, 2.0);
	static EIGEN_DECLARE_CONST_Packet2d(half, 0.5);

	static EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
	static EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);

	static EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);

	static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
	static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
	static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);

	static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
	static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
	static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
	static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);

	static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
	static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);

	template <>
	EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d pexp<Packet2d>(const Packet2d& _x) {
	Packet2d x = _x;

	Packet2d tmp, fx;
	Packet2l emm0;

	// clamp x
	x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
	/* express exp(x) as exp(g + nlog(2)) /
	fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);

	fx = vec_floor(fx);

	tmp = pmul(fx, p2d_cephes_exp_C1);
	Packet2d z = pmul(fx, p2d_cephes_exp_C2);
	x = psub(x, tmp);
	x = psub(x, z);

	Packet2d x2 = pmul(x, x);

	Packet2d px = p2d_cephes_exp_p0;
	px = pmadd(px, x2, p2d_cephes_exp_p1);
	px = pmadd(px, x2, p2d_cephes_exp_p2);
	px = pmul(px, x);

	Packet2d qx = p2d_cephes_exp_q0;
	qx = pmadd(qx, x2, p2d_cephes_exp_q1);
	qx = pmadd(qx, x2, p2d_cephes_exp_q2);
	qx = pmadd(qx, x2, p2d_cephes_exp_q3);

	x = pdiv(px, psub(qx, px));
	x = pmadd(p2d_2, x, p2d_1);

	// build 2^n
	emm0 = vec_ctsl(fx, 0);

	static const Packet2l p2l_1023 = {1023, 1023};
	static const Packet2ul p2ul_52 = {52, 52};

	emm0 = emm0 + p2l_1023;
	emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);

	// Altivec's max & min operators just drop silent NaNs. Check NaNs in
	// inputs and return them unmodified.
	Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));
	return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x), isnumber_mask);
	}

	template <>
	EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f pexp<Packet4f>(const Packet4f& _x) {
	#if !defined(__ARCH__) \|\| (defined(__ARCH__) && __ARCH__ >= 12)
	Packet4f x = _x;

	Packet4f tmp, fx;
	Packet4i emm0;

	// clamp x
	x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);

	// express exp(x) as exp(g + n*log(2))
	fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);

	fx = pfloor(fx);

	tmp = pmul(fx, p4f_cephes_exp_C1);
	Packet4f z = pmul(fx, p4f_cephes_exp_C2);
	x = psub(x, tmp);
	x = psub(x, z);

	z = pmul(x, x);

	Packet4f y = p4f_cephes_exp_p0;
	y = pmadd(y, x, p4f_cephes_exp_p1);
	y = pmadd(y, x, p4f_cephes_exp_p2);
	y = pmadd(y, x, p4f_cephes_exp_p3);
	y = pmadd(y, x, p4f_cephes_exp_p4);
	y = pmadd(y, x, p4f_cephes_exp_p5);
	y = pmadd(y, z, x);
	y = padd(y, p4f_1);

	// build 2^n
	emm0 = Packet4i{(int)fx[0], (int)fx[1], (int)fx[2], (int)fx[3]};
	emm0 = emm0 + p4i_0x7f;
	emm0 = emm0 << reinterpret_cast<Packet4i>(p4i_23);

	return pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x);
	#else
	Packet4f res;
	res.v4f[0] = pexp<Packet2d>(_x.v4f[0]);
	res.v4f[1] = pexp<Packet2d>(_x.v4f[1]);
	return res;
	#endif
	}

	template <>
	EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d psqrt<Packet2d>(const Packet2d& x) {
	return vec_sqrt(x);
	}

	template <>
	EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f psqrt<Packet4f>(const Packet4f& x) {
	Packet4f res;
	#if !defined(__ARCH__) \|\| (defined(__ARCH__) && __ARCH__ >= 12)
	res = vec_sqrt(x);
	#else
	res.v4f[0] = psqrt<Packet2d>(x.v4f[0]);
	res.v4f[1] = psqrt<Packet2d>(x.v4f[1]);
	#endif
	return res;
	}

	template <>
	EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d prsqrt<Packet2d>(const Packet2d& x) {
	return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);
	}

	template <>
	EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f prsqrt<Packet4f>(const Packet4f& x) {
	Packet4f res;
	#if !defined(__ARCH__) \|\| (defined(__ARCH__) && __ARCH__ >= 12)
	res = pset1<Packet4f>(1.0) / psqrt<Packet4f>(x);
	#else
	res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]);
	res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]);
	#endif
	return res;
	}

	// Hyperbolic Tangent function.
	template <>
	EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f ptanh<Packet4f>(const Packet4f& x) {
	return ptanh_float(x);
	}

	} // end namespace internal

	} // end namespace Eigen

	#endif // EIGEN_MATH_FUNCTIONS_ZVECTOR_H