15 #ifndef EIGEN_MATH_FUNCTIONS_SSE_H
16 #define EIGEN_MATH_FUNCTIONS_SSE_H
22 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
23 Packet4f plog<Packet4f>(
const Packet4f& _x)
26 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
27 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
28 _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
30 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
33 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
34 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000);
39 _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
40 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
41 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
42 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
43 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
44 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
45 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
46 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
47 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
48 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
49 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
50 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
55 Packet4f invalid_mask = _mm_cmplt_ps(x, _mm_setzero_ps());
56 Packet4f iszero_mask = _mm_cmpeq_ps(x, _mm_setzero_ps());
58 x = pmax(x, p4f_min_norm_pos);
59 emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
62 x = _mm_and_ps(x, p4f_inv_mant_mask);
63 x = _mm_or_ps(x, p4f_half);
65 emm0 = _mm_sub_epi32(emm0, p4i_0x7f);
66 Packet4f e = padd(_mm_cvtepi32_ps(emm0), p4f_1);
74 Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);
75 Packet4f tmp = _mm_and_ps(x, mask);
77 e = psub(e, _mm_and_ps(p4f_1, mask));
80 Packet4f x2 = pmul(x,x);
81 Packet4f x3 = pmul(x2,x);
84 y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
85 y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
86 y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
87 y = pmadd(y , x, p4f_cephes_log_p2);
88 y1 = pmadd(y1, x, p4f_cephes_log_p5);
89 y2 = pmadd(y2, x, p4f_cephes_log_p8);
94 y1 = pmul(e, p4f_cephes_log_q1);
95 tmp = pmul(x2, p4f_half);
98 y2 = pmul(e, p4f_cephes_log_q2);
102 return _mm_or_ps(_mm_andnot_ps(iszero_mask, _mm_or_ps(x, invalid_mask)),
103 _mm_and_ps(iszero_mask, p4f_minus_inf));
106 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
107 Packet4f pexp<Packet4f>(
const Packet4f& _x)
110 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
111 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
112 _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
115 _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
116 _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
118 _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
119 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
120 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
122 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
123 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
124 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
125 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
126 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
127 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
129 Packet4f tmp = _mm_setzero_ps(), fx;
133 x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
136 fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
139 emm0 = _mm_cvttps_epi32(fx);
140 tmp = _mm_cvtepi32_ps(emm0);
142 Packet4f mask = _mm_cmpgt_ps(tmp, fx);
143 mask = _mm_and_ps(mask, p4f_1);
144 fx = psub(tmp, mask);
146 tmp = pmul(fx, p4f_cephes_exp_C1);
147 Packet4f z = pmul(fx, p4f_cephes_exp_C2);
153 Packet4f y = p4f_cephes_exp_p0;
154 y = pmadd(y, x, p4f_cephes_exp_p1);
155 y = pmadd(y, x, p4f_cephes_exp_p2);
156 y = pmadd(y, x, p4f_cephes_exp_p3);
157 y = pmadd(y, x, p4f_cephes_exp_p4);
158 y = pmadd(y, x, p4f_cephes_exp_p5);
163 emm0 = _mm_cvttps_epi32(fx);
164 emm0 = _mm_add_epi32(emm0, p4i_0x7f);
165 emm0 = _mm_slli_epi32(emm0, 23);
166 return pmul(y, _mm_castsi128_ps(emm0));
181 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
182 Packet4f psin<Packet4f>(
const Packet4f& _x)
185 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
186 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
188 _EIGEN_DECLARE_CONST_Packet4i(1, 1);
189 _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
190 _EIGEN_DECLARE_CONST_Packet4i(2, 2);
191 _EIGEN_DECLARE_CONST_Packet4i(4, 4);
193 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
195 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
196 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
197 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
198 _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
199 _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
200 _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
201 _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
202 _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
203 _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
204 _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);
206 Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
216 sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);
219 y = pmul(x, p4f_cephes_FOPI);
222 emm2 = _mm_cvttps_epi32(y);
224 emm2 = _mm_add_epi32(emm2, p4i_1);
225 emm2 = _mm_and_si128(emm2, p4i_not1);
226 y = _mm_cvtepi32_ps(emm2);
228 emm0 = _mm_and_si128(emm2, p4i_4);
229 emm0 = _mm_slli_epi32(emm0, 29);
236 emm2 = _mm_and_si128(emm2, p4i_2);
237 emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
239 Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
240 Packet4f poly_mask = _mm_castsi128_ps(emm2);
241 sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
245 xmm1 = pmul(y, p4f_minus_cephes_DP1);
246 xmm2 = pmul(y, p4f_minus_cephes_DP2);
247 xmm3 = pmul(y, p4f_minus_cephes_DP3);
254 Packet4f z = _mm_mul_ps(x,x);
256 y = pmadd(y, z, p4f_coscof_p1);
257 y = pmadd(y, z, p4f_coscof_p2);
260 Packet4f tmp = pmul(z, p4f_half);
266 Packet4f y2 = p4f_sincof_p0;
267 y2 = pmadd(y2, z, p4f_sincof_p1);
268 y2 = pmadd(y2, z, p4f_sincof_p2);
274 y2 = _mm_and_ps(poly_mask, y2);
275 y = _mm_andnot_ps(poly_mask, y);
278 return _mm_xor_ps(y, sign_bit);
282 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
283 Packet4f pcos<Packet4f>(
const Packet4f& _x)
286 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
287 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
289 _EIGEN_DECLARE_CONST_Packet4i(1, 1);
290 _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
291 _EIGEN_DECLARE_CONST_Packet4i(2, 2);
292 _EIGEN_DECLARE_CONST_Packet4i(4, 4);
294 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
295 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
296 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
297 _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
298 _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
299 _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
300 _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
301 _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
302 _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
303 _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);
305 Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
311 y = pmul(x, p4f_cephes_FOPI);
314 emm2 = _mm_cvttps_epi32(y);
316 emm2 = _mm_add_epi32(emm2, p4i_1);
317 emm2 = _mm_and_si128(emm2, p4i_not1);
318 y = _mm_cvtepi32_ps(emm2);
320 emm2 = _mm_sub_epi32(emm2, p4i_2);
323 emm0 = _mm_andnot_si128(emm2, p4i_4);
324 emm0 = _mm_slli_epi32(emm0, 29);
326 emm2 = _mm_and_si128(emm2, p4i_2);
327 emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
329 Packet4f sign_bit = _mm_castsi128_ps(emm0);
330 Packet4f poly_mask = _mm_castsi128_ps(emm2);
334 xmm1 = pmul(y, p4f_minus_cephes_DP1);
335 xmm2 = pmul(y, p4f_minus_cephes_DP2);
336 xmm3 = pmul(y, p4f_minus_cephes_DP3);
343 Packet4f z = pmul(x,x);
345 y = pmadd(y,z,p4f_coscof_p1);
346 y = pmadd(y,z,p4f_coscof_p2);
349 Packet4f tmp = _mm_mul_ps(z, p4f_half);
354 Packet4f y2 = p4f_sincof_p0;
355 y2 = pmadd(y2, z, p4f_sincof_p1);
356 y2 = pmadd(y2, z, p4f_sincof_p2);
358 y2 = pmadd(y2, x, x);
361 y2 = _mm_and_ps(poly_mask, y2);
362 y = _mm_andnot_ps(poly_mask, y);
366 return _mm_xor_ps(y, sign_bit);
371 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
372 Packet4f psqrt<Packet4f>(
const Packet4f& _x)
374 Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
377 Packet4f non_zero_mask = _mm_cmpgt_ps(_x, pset1<Packet4f>(std::numeric_limits<float>::epsilon()));
378 Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
380 x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
388 #endif // EIGEN_MATH_FUNCTIONS_SSE_H