Eigen/src/Core/arch/ZVector/MathFunctions.h
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2007 Julien Pommier
5 // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
6 // Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
7 //
8 // This Source Code Form is subject to the terms of the Mozilla
9 // Public License v. 2.0. If a copy of the MPL was not distributed
10 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
11 
12 /* The sin, cos, exp, and log functions of this file come from
13  * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
14  */
15 
16 #ifndef EIGEN_MATH_FUNCTIONS_ALTIVEC_H
17 #define EIGEN_MATH_FUNCTIONS_ALTIVEC_H
18 
19 namespace Eigen {
20 
21 namespace internal {
22 
23 #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
24 static _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
25 static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
26 static _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
27 static _EIGEN_DECLARE_CONST_Packet4i(23, 23);
28 
29 static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
30 
31 /* the smallest non denormalized float number */
32 static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
33 static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f
34 static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff);
35 
36 /* natural logarithm computed for 4 simultaneous float
37  return NaN for x <= 0
38 */
39 static _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
40 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
41 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
42 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
43 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
44 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
45 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
46 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
47 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
48 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
49 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
50 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
51 
52 static _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
53 static _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
54 
55 static _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
56 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
57 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
58 
59 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
60 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
61 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
62 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
63 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
64 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
65 #endif
66 
67 static _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
68 static _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
69 static _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
70 
71 static _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
72 static _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
73 
74 static _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
75 
76 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
77 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
78 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
79 
80 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
81 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
82 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
83 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
84 
85 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
86 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
87 
88 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
89 Packet2d pexp<Packet2d>(const Packet2d& _x)
90 {
91  Packet2d x = _x;
92 
93  Packet2d tmp, fx;
94  Packet2l emm0;
95 
96  // clamp x
97  x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
98  /* express exp(x) as exp(g + n*log(2)) */
99  fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
100 
101  fx = vec_floor(fx);
102 
103  tmp = pmul(fx, p2d_cephes_exp_C1);
104  Packet2d z = pmul(fx, p2d_cephes_exp_C2);
105  x = psub(x, tmp);
106  x = psub(x, z);
107 
108  Packet2d x2 = pmul(x,x);
109 
110  Packet2d px = p2d_cephes_exp_p0;
111  px = pmadd(px, x2, p2d_cephes_exp_p1);
112  px = pmadd(px, x2, p2d_cephes_exp_p2);
113  px = pmul (px, x);
114 
115  Packet2d qx = p2d_cephes_exp_q0;
116  qx = pmadd(qx, x2, p2d_cephes_exp_q1);
117  qx = pmadd(qx, x2, p2d_cephes_exp_q2);
118  qx = pmadd(qx, x2, p2d_cephes_exp_q3);
119 
120  x = pdiv(px,psub(qx,px));
121  x = pmadd(p2d_2,x,p2d_1);
122 
123  // build 2^n
124  emm0 = vec_ctsl(fx, 0);
125 
126  static const Packet2l p2l_1023 = { 1023, 1023 };
127  static const Packet2ul p2ul_52 = { 52, 52 };
128 
129  emm0 = emm0 + p2l_1023;
130  emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);
131 
132  // Altivec's max & min operators just drop silent NaNs. Check NaNs in
133  // inputs and return them unmodified.
134  Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));
135  return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x),
136  isnumber_mask);
137 }
138 
139 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
140 Packet4f pexp<Packet4f>(const Packet4f& _x)
141 {
142 #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
143  Packet4f x = _x;
144 
145  Packet4f tmp, fx;
146  Packet4i emm0;
147 
148  // clamp x
149  x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
150 
151  // express exp(x) as exp(g + n*log(2))
152  fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
153 
154  fx = pfloor(fx);
155 
156  tmp = pmul(fx, p4f_cephes_exp_C1);
157  Packet4f z = pmul(fx, p4f_cephes_exp_C2);
158  x = psub(x, tmp);
159  x = psub(x, z);
160 
161  z = pmul(x,x);
162 
163  Packet4f y = p4f_cephes_exp_p0;
164  y = pmadd(y, x, p4f_cephes_exp_p1);
165  y = pmadd(y, x, p4f_cephes_exp_p2);
166  y = pmadd(y, x, p4f_cephes_exp_p3);
167  y = pmadd(y, x, p4f_cephes_exp_p4);
168  y = pmadd(y, x, p4f_cephes_exp_p5);
169  y = pmadd(y, z, x);
170  y = padd(y, p4f_1);
171 
172  // build 2^n
173  emm0 = (Packet4i){ (int)fx[0], (int)fx[1], (int)fx[2], (int)fx[3] };
174  emm0 = emm0 + p4i_0x7f;
175  emm0 = emm0 << reinterpret_cast<Packet4i>(p4i_23);
176 
177  return pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x);
178 #else
179  Packet4f res;
180  res.v4f[0] = pexp<Packet2d>(_x.v4f[0]);
181  res.v4f[1] = pexp<Packet2d>(_x.v4f[1]);
182  return res;
183 #endif
184 }
185 
186 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
187 Packet2d psqrt<Packet2d>(const Packet2d& x)
188 {
189  return vec_sqrt(x);
190 }
191 
192 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
193 Packet4f psqrt<Packet4f>(const Packet4f& x)
194 {
195  Packet4f res;
196 #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
197  res = vec_sqrt(x);
198 #else
199  res.v4f[0] = psqrt<Packet2d>(x.v4f[0]);
200  res.v4f[1] = psqrt<Packet2d>(x.v4f[1]);
201 #endif
202  return res;
203 }
204 
205 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
206 Packet2d prsqrt<Packet2d>(const Packet2d& x) {
207  return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);
208 }
209 
210 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
211 Packet4f prsqrt<Packet4f>(const Packet4f& x) {
212  Packet4f res;
213 #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
214  res = pset1<Packet4f>(1.0) / psqrt<Packet4f>(x);
215 #else
216  res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]);
217  res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]);
218 #endif
219  return res;
220 }
221 
222 // Hyperbolic Tangent function.
223 template <>
224 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
225 ptanh<Packet4f>(const Packet4f& x) {
226  return internal::generic_fast_tanh_float(x);
227 }
228 
229 } // end namespace internal
230 
231 } // end namespace Eigen
232 
233 #endif // EIGEN_MATH_FUNCTIONS_ALTIVEC_H
Eigen::internal::_EIGEN_DECLARE_CONST_Packet4i
static _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f)
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Definition: Eigen/src/Core/arch/SSE/MathFunctions.h:110
Eigen::internal::_EIGEN_DECLARE_CONST_Packet4f_FROM_INT
static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000)
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Definition: GenericPacketMath.h:215
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autogenerated on Tue Jul 4 2023 02:34:45