1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2016 Pedro Gonnet ([email protected])
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10 #ifndef THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_
11 #define THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_
12
13 namespace Eigen {
14
15 namespace internal {
16
17 // Disable the code for older versions of gcc that don't support many of the required avx512 instrinsics.
18 #if EIGEN_GNUC_AT_LEAST(5, 3) || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC >= 1923
19
20 #define _EIGEN_DECLARE_CONST_Packet16f(NAME, X) \
21 const Packet16f p16f_##NAME = pset1<Packet16f>(X)
22
23 #define _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(NAME, X) \
24 const Packet16f p16f_##NAME = preinterpret<Packet16f,Packet16i>(pset1<Packet16i>(X))
25
26 #define _EIGEN_DECLARE_CONST_Packet8d(NAME, X) \
27 const Packet8d p8d_##NAME = pset1<Packet8d>(X)
28
29 #define _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(NAME, X) \
30 const Packet8d p8d_##NAME = _mm512_castsi512_pd(_mm512_set1_epi64(X))
31
32 #define _EIGEN_DECLARE_CONST_Packet16bf(NAME, X) \
33 const Packet16bf p16bf_##NAME = pset1<Packet16bf>(X)
34
35 #define _EIGEN_DECLARE_CONST_Packet16bf_FROM_INT(NAME, X) \
36 const Packet16bf p16bf_##NAME = preinterpret<Packet16bf,Packet16i>(pset1<Packet16i>(X))
37
38 template <>
39 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
40 plog<Packet16f>(const Packet16f& _x) {
41 return plog_float(_x);
42 }
43
44 template <>
45 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d
46 plog<Packet8d>(const Packet8d& _x) {
47 return plog_double(_x);
48 }
49
F16_PACKET_FUNCTION(Packet16f,Packet16h,plog)50 F16_PACKET_FUNCTION(Packet16f, Packet16h, plog)
51 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog)
52
53 template <>
54 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
55 plog2<Packet16f>(const Packet16f& _x) {
56 return plog2_float(_x);
57 }
58
59 template <>
60 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d
61 plog2<Packet8d>(const Packet8d& _x) {
62 return plog2_double(_x);
63 }
64
F16_PACKET_FUNCTION(Packet16f,Packet16h,plog2)65 F16_PACKET_FUNCTION(Packet16f, Packet16h, plog2)
66 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog2)
67
68 // Exponential function. Works by writing "x = m*log(2) + r" where
69 // "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then
70 // "exp(x) = 2^m*exp(r)" where exp(r) is in the range [-1,1).
71 template <>
72 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
73 pexp<Packet16f>(const Packet16f& _x) {
74 _EIGEN_DECLARE_CONST_Packet16f(1, 1.0f);
75 _EIGEN_DECLARE_CONST_Packet16f(half, 0.5f);
76 _EIGEN_DECLARE_CONST_Packet16f(127, 127.0f);
77
78 _EIGEN_DECLARE_CONST_Packet16f(exp_hi, 88.3762626647950f);
79 _EIGEN_DECLARE_CONST_Packet16f(exp_lo, -88.3762626647949f);
80
81 _EIGEN_DECLARE_CONST_Packet16f(cephes_LOG2EF, 1.44269504088896341f);
82
83 _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p0, 1.9875691500E-4f);
84 _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p1, 1.3981999507E-3f);
85 _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p2, 8.3334519073E-3f);
86 _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p3, 4.1665795894E-2f);
87 _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p4, 1.6666665459E-1f);
88 _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p5, 5.0000001201E-1f);
89
90 // Clamp x.
91 Packet16f x = pmax(pmin(_x, p16f_exp_hi), p16f_exp_lo);
92
93 // Express exp(x) as exp(m*ln(2) + r), start by extracting
94 // m = floor(x/ln(2) + 0.5).
95 Packet16f m = _mm512_floor_ps(pmadd(x, p16f_cephes_LOG2EF, p16f_half));
96
97 // Get r = x - m*ln(2). Note that we can do this without losing more than one
98 // ulp precision due to the FMA instruction.
99 _EIGEN_DECLARE_CONST_Packet16f(nln2, -0.6931471805599453f);
100 Packet16f r = _mm512_fmadd_ps(m, p16f_nln2, x);
101 Packet16f r2 = pmul(r, r);
102 Packet16f r3 = pmul(r2, r);
103
104 // Evaluate the polynomial approximant,improved by instruction-level parallelism.
105 Packet16f y, y1, y2;
106 y = pmadd(p16f_cephes_exp_p0, r, p16f_cephes_exp_p1);
107 y1 = pmadd(p16f_cephes_exp_p3, r, p16f_cephes_exp_p4);
108 y2 = padd(r, p16f_1);
109 y = pmadd(y, r, p16f_cephes_exp_p2);
110 y1 = pmadd(y1, r, p16f_cephes_exp_p5);
111 y = pmadd(y, r3, y1);
112 y = pmadd(y, r2, y2);
113
114 // Build emm0 = 2^m.
115 Packet16i emm0 = _mm512_cvttps_epi32(padd(m, p16f_127));
116 emm0 = _mm512_slli_epi32(emm0, 23);
117
118 // Return 2^m * exp(r).
119 return pmax(pmul(y, _mm512_castsi512_ps(emm0)), _x);
120 }
121
122 template <>
123 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d
124 pexp<Packet8d>(const Packet8d& _x) {
125 return pexp_double(_x);
126 }
127
F16_PACKET_FUNCTION(Packet16f,Packet16h,pexp)128 F16_PACKET_FUNCTION(Packet16f, Packet16h, pexp)
129 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexp)
130
131 template <>
132 EIGEN_STRONG_INLINE Packet16h pfrexp(const Packet16h& a, Packet16h& exponent) {
133 Packet16f fexponent;
134 const Packet16h out = float2half(pfrexp<Packet16f>(half2float(a), fexponent));
135 exponent = float2half(fexponent);
136 return out;
137 }
138
139 template <>
pldexp(const Packet16h & a,const Packet16h & exponent)140 EIGEN_STRONG_INLINE Packet16h pldexp(const Packet16h& a, const Packet16h& exponent) {
141 return float2half(pldexp<Packet16f>(half2float(a), half2float(exponent)));
142 }
143
144 template <>
pfrexp(const Packet16bf & a,Packet16bf & exponent)145 EIGEN_STRONG_INLINE Packet16bf pfrexp(const Packet16bf& a, Packet16bf& exponent) {
146 Packet16f fexponent;
147 const Packet16bf out = F32ToBf16(pfrexp<Packet16f>(Bf16ToF32(a), fexponent));
148 exponent = F32ToBf16(fexponent);
149 return out;
150 }
151
152 template <>
pldexp(const Packet16bf & a,const Packet16bf & exponent)153 EIGEN_STRONG_INLINE Packet16bf pldexp(const Packet16bf& a, const Packet16bf& exponent) {
154 return F32ToBf16(pldexp<Packet16f>(Bf16ToF32(a), Bf16ToF32(exponent)));
155 }
156
157 // Functions for sqrt.
158 // The EIGEN_FAST_MATH version uses the _mm_rsqrt_ps approximation and one step
159 // of Newton's method, at a cost of 1-2 bits of precision as opposed to the
160 // exact solution. The main advantage of this approach is not just speed, but
161 // also the fact that it can be inlined and pipelined with other computations,
162 // further reducing its effective latency.
163 #if EIGEN_FAST_MATH
164 template <>
165 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
166 psqrt<Packet16f>(const Packet16f& _x) {
167 Packet16f neg_half = pmul(_x, pset1<Packet16f>(-.5f));
168 __mmask16 denormal_mask = _mm512_kand(
169 _mm512_cmp_ps_mask(_x, pset1<Packet16f>((std::numeric_limits<float>::min)()),
170 _CMP_LT_OQ),
171 _mm512_cmp_ps_mask(_x, _mm512_setzero_ps(), _CMP_GE_OQ));
172
173 Packet16f x = _mm512_rsqrt14_ps(_x);
174
175 // Do a single step of Newton's iteration.
176 x = pmul(x, pmadd(neg_half, pmul(x, x), pset1<Packet16f>(1.5f)));
177
178 // Flush results for denormals to zero.
179 return _mm512_mask_blend_ps(denormal_mask, pmul(_x,x), _mm512_setzero_ps());
180 }
181
182 template <>
183 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d
184 psqrt<Packet8d>(const Packet8d& _x) {
185 Packet8d neg_half = pmul(_x, pset1<Packet8d>(-.5));
186 __mmask16 denormal_mask = _mm512_kand(
187 _mm512_cmp_pd_mask(_x, pset1<Packet8d>((std::numeric_limits<double>::min)()),
188 _CMP_LT_OQ),
189 _mm512_cmp_pd_mask(_x, _mm512_setzero_pd(), _CMP_GE_OQ));
190
191 Packet8d x = _mm512_rsqrt14_pd(_x);
192
193 // Do a single step of Newton's iteration.
194 x = pmul(x, pmadd(neg_half, pmul(x, x), pset1<Packet8d>(1.5)));
195
196 // Do a second step of Newton's iteration.
197 x = pmul(x, pmadd(neg_half, pmul(x, x), pset1<Packet8d>(1.5)));
198
199 return _mm512_mask_blend_pd(denormal_mask, pmul(_x,x), _mm512_setzero_pd());
200 }
201 #else
202 template <>
203 EIGEN_STRONG_INLINE Packet16f psqrt<Packet16f>(const Packet16f& x) {
204 return _mm512_sqrt_ps(x);
205 }
206
207 template <>
208 EIGEN_STRONG_INLINE Packet8d psqrt<Packet8d>(const Packet8d& x) {
209 return _mm512_sqrt_pd(x);
210 }
211 #endif
212
F16_PACKET_FUNCTION(Packet16f,Packet16h,psqrt)213 F16_PACKET_FUNCTION(Packet16f, Packet16h, psqrt)
214 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psqrt)
215
216 // prsqrt for float.
217 #if defined(EIGEN_VECTORIZE_AVX512ER)
218
219 template <>
220 EIGEN_STRONG_INLINE Packet16f prsqrt<Packet16f>(const Packet16f& x) {
221 return _mm512_rsqrt28_ps(x);
222 }
223 #elif EIGEN_FAST_MATH
224
225 template <>
226 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
227 prsqrt<Packet16f>(const Packet16f& _x) {
228 _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(inf, 0x7f800000);
229 _EIGEN_DECLARE_CONST_Packet16f(one_point_five, 1.5f);
230 _EIGEN_DECLARE_CONST_Packet16f(minus_half, -0.5f);
231
232 Packet16f neg_half = pmul(_x, p16f_minus_half);
233
234 // Identity infinite, negative and denormal arguments.
235 __mmask16 inf_mask = _mm512_cmp_ps_mask(_x, p16f_inf, _CMP_EQ_OQ);
236 __mmask16 not_pos_mask = _mm512_cmp_ps_mask(_x, _mm512_setzero_ps(), _CMP_LE_OQ);
237 __mmask16 not_finite_pos_mask = not_pos_mask | inf_mask;
238
239 // Compute an approximate result using the rsqrt intrinsic, forcing +inf
240 // for denormals for consistency with AVX and SSE implementations.
241 Packet16f y_approx = _mm512_rsqrt14_ps(_x);
242
243 // Do a single step of Newton-Raphson iteration to improve the approximation.
244 // This uses the formula y_{n+1} = y_n * (1.5 - y_n * (0.5 * x) * y_n).
245 // It is essential to evaluate the inner term like this because forming
246 // y_n^2 may over- or underflow.
247 Packet16f y_newton = pmul(y_approx, pmadd(y_approx, pmul(neg_half, y_approx), p16f_one_point_five));
248
249 // Select the result of the Newton-Raphson step for positive finite arguments.
250 // For other arguments, choose the output of the intrinsic. This will
251 // return rsqrt(+inf) = 0, rsqrt(x) = NaN if x < 0, and rsqrt(0) = +inf.
252 return _mm512_mask_blend_ps(not_finite_pos_mask, y_newton, y_approx);
253 }
254 #else
255
256 template <>
257 EIGEN_STRONG_INLINE Packet16f prsqrt<Packet16f>(const Packet16f& x) {
258 _EIGEN_DECLARE_CONST_Packet16f(one, 1.0f);
259 return _mm512_div_ps(p16f_one, _mm512_sqrt_ps(x));
260 }
261 #endif
262
F16_PACKET_FUNCTION(Packet16f,Packet16h,prsqrt)263 F16_PACKET_FUNCTION(Packet16f, Packet16h, prsqrt)
264 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, prsqrt)
265
266 // prsqrt for double.
267 #if EIGEN_FAST_MATH
268 template <>
269 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d
270 prsqrt<Packet8d>(const Packet8d& _x) {
271 _EIGEN_DECLARE_CONST_Packet8d(one_point_five, 1.5);
272 _EIGEN_DECLARE_CONST_Packet8d(minus_half, -0.5);
273 _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(inf, 0x7ff0000000000000LL);
274
275 Packet8d neg_half = pmul(_x, p8d_minus_half);
276
277 // Identity infinite, negative and denormal arguments.
278 __mmask8 inf_mask = _mm512_cmp_pd_mask(_x, p8d_inf, _CMP_EQ_OQ);
279 __mmask8 not_pos_mask = _mm512_cmp_pd_mask(_x, _mm512_setzero_pd(), _CMP_LE_OQ);
280 __mmask8 not_finite_pos_mask = not_pos_mask | inf_mask;
281
282 // Compute an approximate result using the rsqrt intrinsic, forcing +inf
283 // for denormals for consistency with AVX and SSE implementations.
284 #if defined(EIGEN_VECTORIZE_AVX512ER)
285 Packet8d y_approx = _mm512_rsqrt28_pd(_x);
286 #else
287 Packet8d y_approx = _mm512_rsqrt14_pd(_x);
288 #endif
289 // Do one or two steps of Newton-Raphson's to improve the approximation, depending on the
290 // starting accuracy (either 2^-14 or 2^-28, depending on whether AVX512ER is available).
291 // The Newton-Raphson algorithm has quadratic convergence and roughly doubles the number
292 // of correct digits for each step.
293 // This uses the formula y_{n+1} = y_n * (1.5 - y_n * (0.5 * x) * y_n).
294 // It is essential to evaluate the inner term like this because forming
295 // y_n^2 may over- or underflow.
296 Packet8d y_newton = pmul(y_approx, pmadd(neg_half, pmul(y_approx, y_approx), p8d_one_point_five));
297 #if !defined(EIGEN_VECTORIZE_AVX512ER)
298 y_newton = pmul(y_newton, pmadd(y_newton, pmul(neg_half, y_newton), p8d_one_point_five));
299 #endif
300 // Select the result of the Newton-Raphson step for positive finite arguments.
301 // For other arguments, choose the output of the intrinsic. This will
302 // return rsqrt(+inf) = 0, rsqrt(x) = NaN if x < 0, and rsqrt(0) = +inf.
303 return _mm512_mask_blend_pd(not_finite_pos_mask, y_newton, y_approx);
304 }
305 #else
306 template <>
307 EIGEN_STRONG_INLINE Packet8d prsqrt<Packet8d>(const Packet8d& x) {
308 _EIGEN_DECLARE_CONST_Packet8d(one, 1.0f);
309 return _mm512_div_pd(p8d_one, _mm512_sqrt_pd(x));
310 }
311 #endif
312
313 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
314 Packet16f plog1p<Packet16f>(const Packet16f& _x) {
315 return generic_plog1p(_x);
316 }
317
F16_PACKET_FUNCTION(Packet16f,Packet16h,plog1p)318 F16_PACKET_FUNCTION(Packet16f, Packet16h, plog1p)
319 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog1p)
320
321 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
322 Packet16f pexpm1<Packet16f>(const Packet16f& _x) {
323 return generic_expm1(_x);
324 }
325
F16_PACKET_FUNCTION(Packet16f,Packet16h,pexpm1)326 F16_PACKET_FUNCTION(Packet16f, Packet16h, pexpm1)
327 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexpm1)
328
329 #endif
330
331
332 template <>
333 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
334 psin<Packet16f>(const Packet16f& _x) {
335 return psin_float(_x);
336 }
337
338 template <>
339 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
340 pcos<Packet16f>(const Packet16f& _x) {
341 return pcos_float(_x);
342 }
343
344 template <>
345 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
346 ptanh<Packet16f>(const Packet16f& _x) {
347 return internal::generic_fast_tanh_float(_x);
348 }
349
350 F16_PACKET_FUNCTION(Packet16f, Packet16h, psin)
351 F16_PACKET_FUNCTION(Packet16f, Packet16h, pcos)
352 F16_PACKET_FUNCTION(Packet16f, Packet16h, ptanh)
353
354 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psin)
355 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pcos)
356 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, ptanh)
357
358 } // end namespace internal
359
360 } // end namespace Eigen
361
362 #endif // THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_
363