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);
38 _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
39 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
40 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
41 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
42 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
43 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
44 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
45 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
46 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
47 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
48 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
49 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
54 Packet4f invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps());
56 x = pmax(x, p4f_min_norm_pos);
57 emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
60 x = _mm_and_ps(x, p4f_inv_mant_mask);
61 x = _mm_or_ps(x, p4f_half);
63 emm0 = _mm_sub_epi32(emm0, p4i_0x7f);
64 Packet4f e = padd(_mm_cvtepi32_ps(emm0), p4f_1);
72 Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);
73 Packet4f tmp = _mm_and_ps(x, mask);
75 e = psub(e, _mm_and_ps(p4f_1, mask));
78 Packet4f x2 = pmul(x,x);
79 Packet4f x3 = pmul(x2,x);
82 y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
83 y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
84 y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
85 y = pmadd(y , x, p4f_cephes_log_p2);
86 y1 = pmadd(y1, x, p4f_cephes_log_p5);
87 y2 = pmadd(y2, x, p4f_cephes_log_p8);
92 y1 = pmul(e, p4f_cephes_log_q1);
93 tmp = pmul(x2, p4f_half);
96 y2 = pmul(e, p4f_cephes_log_q2);
99 return _mm_or_ps(x, invalid_mask);
102 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
103 Packet4f pexp<Packet4f>(
const Packet4f& _x)
106 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
107 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
108 _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
111 _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
112 _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
114 _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
115 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
116 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
118 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
119 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
120 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
121 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
122 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
123 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
125 Packet4f tmp = _mm_setzero_ps(), fx;
129 x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
132 fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
135 emm0 = _mm_cvttps_epi32(fx);
136 tmp = _mm_cvtepi32_ps(emm0);
138 Packet4f mask = _mm_cmpgt_ps(tmp, fx);
139 mask = _mm_and_ps(mask, p4f_1);
140 fx = psub(tmp, mask);
142 tmp = pmul(fx, p4f_cephes_exp_C1);
143 Packet4f z = pmul(fx, p4f_cephes_exp_C2);
149 Packet4f y = p4f_cephes_exp_p0;
150 y = pmadd(y, x, p4f_cephes_exp_p1);
151 y = pmadd(y, x, p4f_cephes_exp_p2);
152 y = pmadd(y, x, p4f_cephes_exp_p3);
153 y = pmadd(y, x, p4f_cephes_exp_p4);
154 y = pmadd(y, x, p4f_cephes_exp_p5);
159 emm0 = _mm_cvttps_epi32(fx);
160 emm0 = _mm_add_epi32(emm0, p4i_0x7f);
161 emm0 = _mm_slli_epi32(emm0, 23);
162 return pmul(y, _mm_castsi128_ps(emm0));
177 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
178 Packet4f psin<Packet4f>(
const Packet4f& _x)
181 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
182 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
184 _EIGEN_DECLARE_CONST_Packet4i(1, 1);
185 _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
186 _EIGEN_DECLARE_CONST_Packet4i(2, 2);
187 _EIGEN_DECLARE_CONST_Packet4i(4, 4);
189 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
191 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
192 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
193 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
194 _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
195 _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
196 _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
197 _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
198 _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
199 _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
200 _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);
202 Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
212 sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);
215 y = pmul(x, p4f_cephes_FOPI);
218 emm2 = _mm_cvttps_epi32(y);
220 emm2 = _mm_add_epi32(emm2, p4i_1);
221 emm2 = _mm_and_si128(emm2, p4i_not1);
222 y = _mm_cvtepi32_ps(emm2);
224 emm0 = _mm_and_si128(emm2, p4i_4);
225 emm0 = _mm_slli_epi32(emm0, 29);
232 emm2 = _mm_and_si128(emm2, p4i_2);
233 emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
235 Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
236 Packet4f poly_mask = _mm_castsi128_ps(emm2);
237 sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
241 xmm1 = pmul(y, p4f_minus_cephes_DP1);
242 xmm2 = pmul(y, p4f_minus_cephes_DP2);
243 xmm3 = pmul(y, p4f_minus_cephes_DP3);
250 Packet4f z = _mm_mul_ps(x,x);
252 y = pmadd(y, z, p4f_coscof_p1);
253 y = pmadd(y, z, p4f_coscof_p2);
256 Packet4f tmp = pmul(z, p4f_half);
262 Packet4f y2 = p4f_sincof_p0;
263 y2 = pmadd(y2, z, p4f_sincof_p1);
264 y2 = pmadd(y2, z, p4f_sincof_p2);
270 y2 = _mm_and_ps(poly_mask, y2);
271 y = _mm_andnot_ps(poly_mask, y);
274 return _mm_xor_ps(y, sign_bit);
278 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
279 Packet4f pcos<Packet4f>(
const Packet4f& _x)
282 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
283 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
285 _EIGEN_DECLARE_CONST_Packet4i(1, 1);
286 _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
287 _EIGEN_DECLARE_CONST_Packet4i(2, 2);
288 _EIGEN_DECLARE_CONST_Packet4i(4, 4);
290 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
291 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
292 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
293 _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
294 _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
295 _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
296 _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
297 _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
298 _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
299 _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);
301 Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
307 y = pmul(x, p4f_cephes_FOPI);
310 emm2 = _mm_cvttps_epi32(y);
312 emm2 = _mm_add_epi32(emm2, p4i_1);
313 emm2 = _mm_and_si128(emm2, p4i_not1);
314 y = _mm_cvtepi32_ps(emm2);
316 emm2 = _mm_sub_epi32(emm2, p4i_2);
319 emm0 = _mm_andnot_si128(emm2, p4i_4);
320 emm0 = _mm_slli_epi32(emm0, 29);
322 emm2 = _mm_and_si128(emm2, p4i_2);
323 emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
325 Packet4f sign_bit = _mm_castsi128_ps(emm0);
326 Packet4f poly_mask = _mm_castsi128_ps(emm2);
330 xmm1 = pmul(y, p4f_minus_cephes_DP1);
331 xmm2 = pmul(y, p4f_minus_cephes_DP2);
332 xmm3 = pmul(y, p4f_minus_cephes_DP3);
339 Packet4f z = pmul(x,x);
341 y = pmadd(y,z,p4f_coscof_p1);
342 y = pmadd(y,z,p4f_coscof_p2);
345 Packet4f tmp = _mm_mul_ps(z, p4f_half);
350 Packet4f y2 = p4f_sincof_p0;
351 y2 = pmadd(y2, z, p4f_sincof_p1);
352 y2 = pmadd(y2, z, p4f_sincof_p2);
354 y2 = pmadd(y2, x, x);
357 y2 = _mm_and_ps(poly_mask, y2);
358 y = _mm_andnot_ps(poly_mask, y);
362 return _mm_xor_ps(y, sign_bit);
367 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
368 Packet4f psqrt<Packet4f>(
const Packet4f& _x)
370 Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
373 Packet4f non_zero_mask = _mm_cmpgt_ps(_x, pset1<Packet4f>(std::numeric_limits<float>::epsilon()));
374 Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
376 x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
384 #endif // EIGEN_MATH_FUNCTIONS_SSE_H