1 // Auto-generated file. Do not edit!
2 // Template: src/f32-raddstoreexpminusmax/psimd-p5.c.in
3 // Generator: tools/xngen
4 //
5 // Copyright 2019 Google LLC
6 //
7 // This source code is licensed under the BSD-style license found in the
8 // LICENSE file in the root directory of this source tree.
9
10 #include <assert.h>
11
12 #include <psimd.h>
13
14 #include <xnnpack/common.h>
15 #include <xnnpack/raddstoreexpminusmax.h>
16
17
xnn_f32_raddstoreexpminusmax_ukernel__psimd_p5_x16_acc2(size_t elements,const float * input,float * output,float * sum,float max)18 void xnn_f32_raddstoreexpminusmax_ukernel__psimd_p5_x16_acc2(
19 size_t elements,
20 const float* input,
21 float* output,
22 float* sum,
23 float max)
24 {
25 assert(elements % sizeof(float) == 0);
26
27 const psimd_f32 vmagic_bias = psimd_splat_f32(0x1.8000FEp23f);
28 // The smallest x for which expf(x) is normalized.
29 const psimd_f32 vdenorm_cutoff = psimd_splat_f32(-0x1.5D589Ep6f);
30 const psimd_f32 vlog2e = psimd_splat_f32(0x1.715476p+0f);
31 // Last 7 bits are zeroes
32 const psimd_f32 vminus_ln2_hi = psimd_splat_f32(-0x1.62E400p-1f);
33 const psimd_f32 vminus_ln2_lo = psimd_splat_f32(-0x1.7F7D1Cp-20f);
34
35 const psimd_f32 vc1 = psimd_splat_f32(0x1.FFFFF6p-1f);
36 const psimd_f32 vc2 = psimd_splat_f32(0x1.FFFDC6p-2f);
37 const psimd_f32 vc3 = psimd_splat_f32(0x1.555A80p-3f);
38 const psimd_f32 vc4 = psimd_splat_f32(0x1.573A1Ap-5f);
39 const psimd_f32 vc5 = psimd_splat_f32(0x1.0F9F9Cp-7f);
40
41 const psimd_f32 vi_max = psimd_splat_f32(max);
42
43 psimd_f32 vacc0 = psimd_zero_f32();
44 psimd_f32 vacc1 = psimd_zero_f32();
45 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
46 // Load 16 (4x4) inputs at a time.
47 const psimd_f32 vi0123 = psimd_load_f32(input);
48 const psimd_f32 vi4567 = psimd_load_f32(input + 4);
49 const psimd_f32 vi89AB = psimd_load_f32(input + 8);
50 const psimd_f32 viCDEF = psimd_load_f32(input + 12);
51 input += 16;
52
53 // Subtract maximum input x := i - i_max. This implies x <= 0.
54 const psimd_f32 vx0123 = psimd_sub_f32(vi0123, vi_max);
55 const psimd_f32 vx4567 = psimd_sub_f32(vi4567, vi_max);
56 const psimd_f32 vx89AB = psimd_sub_f32(vi89AB, vi_max);
57 const psimd_f32 vxCDEF = psimd_sub_f32(viCDEF, vi_max);
58
59 // Compute reduced argument elements := round(x / log(2)).
60 psimd_f32 vn0123 = psimd_qfma_f32(vmagic_bias, vx0123, vlog2e);
61 psimd_f32 vn4567 = psimd_qfma_f32(vmagic_bias, vx4567, vlog2e);
62 psimd_f32 vn89AB = psimd_qfma_f32(vmagic_bias, vx89AB, vlog2e);
63 psimd_f32 vnCDEF = psimd_qfma_f32(vmagic_bias, vxCDEF, vlog2e);
64
65 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
66 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
67 const psimd_f32 vs0123 = (psimd_f32) ((psimd_u32) vn0123 << 23);
68 const psimd_f32 vs4567 = (psimd_f32) ((psimd_u32) vn4567 << 23);
69 const psimd_f32 vs89AB = (psimd_f32) ((psimd_u32) vn89AB << 23);
70 const psimd_f32 vsCDEF = (psimd_f32) ((psimd_u32) vnCDEF << 23);
71
72 // Subtract the large number back to get final elements := round(x / log(2)).
73 vn0123 = psimd_sub_f32(vn0123, vmagic_bias);
74 vn4567 = psimd_sub_f32(vn4567, vmagic_bias);
75 vn89AB = psimd_sub_f32(vn89AB, vmagic_bias);
76 vnCDEF = psimd_sub_f32(vnCDEF, vmagic_bias);
77
78 // Compute reduced argument t := x - elements * log(2).
79 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
80 psimd_f32 vt0123 = psimd_qfma_f32(vx0123, vn0123, vminus_ln2_hi);
81 psimd_f32 vt4567 = psimd_qfma_f32(vx4567, vn4567, vminus_ln2_hi);
82 psimd_f32 vt89AB = psimd_qfma_f32(vx89AB, vn89AB, vminus_ln2_hi);
83 psimd_f32 vtCDEF = psimd_qfma_f32(vxCDEF, vnCDEF, vminus_ln2_hi);
84
85 vt0123 = psimd_qfma_f32(vt0123, vn0123, vminus_ln2_lo);
86 vt4567 = psimd_qfma_f32(vt4567, vn4567, vminus_ln2_lo);
87 vt89AB = psimd_qfma_f32(vt89AB, vn89AB, vminus_ln2_lo);
88 vtCDEF = psimd_qfma_f32(vtCDEF, vnCDEF, vminus_ln2_lo);
89
90 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
91 psimd_f32 vp0123 = psimd_qfma_f32(vc4, vc5, vt0123);
92 psimd_f32 vp4567 = psimd_qfma_f32(vc4, vc5, vt4567);
93 psimd_f32 vp89AB = psimd_qfma_f32(vc4, vc5, vt89AB);
94 psimd_f32 vpCDEF = psimd_qfma_f32(vc4, vc5, vtCDEF);
95
96 vp0123 = psimd_qfma_f32(vc3, vp0123, vt0123);
97 vp4567 = psimd_qfma_f32(vc3, vp4567, vt4567);
98 vp89AB = psimd_qfma_f32(vc3, vp89AB, vt89AB);
99 vpCDEF = psimd_qfma_f32(vc3, vpCDEF, vtCDEF);
100
101 vp0123 = psimd_qfma_f32(vc2, vp0123, vt0123);
102 vp4567 = psimd_qfma_f32(vc2, vp4567, vt4567);
103 vp89AB = psimd_qfma_f32(vc2, vp89AB, vt89AB);
104 vpCDEF = psimd_qfma_f32(vc2, vpCDEF, vtCDEF);
105
106 vp0123 = psimd_qfma_f32(vc1, vp0123, vt0123);
107 vp4567 = psimd_qfma_f32(vc1, vp4567, vt4567);
108 vp89AB = psimd_qfma_f32(vc1, vp89AB, vt89AB);
109 vpCDEF = psimd_qfma_f32(vc1, vpCDEF, vtCDEF);
110
111 // Reconstruct the final f value:
112 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
113 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
114 // = s + (t * s) * p
115 vt0123 = psimd_mul_f32(vt0123, vs0123);
116 vt4567 = psimd_mul_f32(vt4567, vs4567);
117 vt89AB = psimd_mul_f32(vt89AB, vs89AB);
118 vtCDEF = psimd_mul_f32(vtCDEF, vsCDEF);
119
120 psimd_f32 vf0123 = psimd_qfma_f32(vs0123, vt0123, vp0123);
121 psimd_f32 vf4567 = psimd_qfma_f32(vs4567, vt4567, vp4567);
122 psimd_f32 vf89AB = psimd_qfma_f32(vs89AB, vt89AB, vp89AB);
123 psimd_f32 vfCDEF = psimd_qfma_f32(vsCDEF, vtCDEF, vpCDEF);
124
125 // For inputs below zero cutoff, replace output with +0.0f.
126 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
127 vf0123 = psimd_andnotmask_f32(vx0123 < vdenorm_cutoff, vf0123);
128 vf4567 = psimd_andnotmask_f32(vx4567 < vdenorm_cutoff, vf4567);
129 vf89AB = psimd_andnotmask_f32(vx89AB < vdenorm_cutoff, vf89AB);
130 vfCDEF = psimd_andnotmask_f32(vxCDEF < vdenorm_cutoff, vfCDEF);
131
132 // Store 16 (4x4) outputs at a time.
133 psimd_store_f32(output, vf0123);
134 psimd_store_f32(output + 4, vf4567);
135 psimd_store_f32(output + 8, vf89AB);
136 psimd_store_f32(output + 12, vfCDEF);
137 output += 16;
138
139 // Accumulate computed exponents.
140 vacc0 = psimd_add_f32(vacc0, vf0123);
141 vacc0 = psimd_add_f32(vacc0, vf4567);
142 vacc0 = psimd_add_f32(vacc0, vf89AB);
143 vacc0 = psimd_add_f32(vacc0, vfCDEF);
144 }
145 // Add up all accumulators to vacc0
146 vacc0 = psimd_add_f32(vacc0, vacc1);
147
148 psimd_f32 vacc = vacc0;
149 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
150 // Load 4 inputs at a time.
151 const psimd_f32 vi = psimd_load_f32(input);
152 input += 4;
153
154 // Subtract maximum input x := i - i_max. This implies x <= 0.
155 const psimd_f32 vx = psimd_sub_f32(vi, vi_max);
156
157 // Compute reduced argument elements := round(x / log(2)).
158 psimd_f32 vn = psimd_qfma_f32(vmagic_bias, vx, vlog2e);
159
160 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
161 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
162 const psimd_f32 vs = (psimd_f32) ((psimd_u32) vn << 23);
163
164 // Subtract the large number back to get final elements := round(x / log(2)).
165 vn = psimd_sub_f32(vn, vmagic_bias);
166
167 // Compute reduced argument t := x - elements * log(2).
168 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
169 psimd_f32 vt = psimd_qfma_f32(vx, vn, vminus_ln2_hi);
170 vt = psimd_qfma_f32(vt, vn, vminus_ln2_lo);
171
172 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
173 psimd_f32 vp = psimd_qfma_f32(vc4, vc5, vt);
174 vp = psimd_qfma_f32(vc3, vp, vt);
175 vp = psimd_qfma_f32(vc2, vp, vt);
176 vp = psimd_qfma_f32(vc1, vp, vt);
177
178 // Reconstruct the final f value:
179 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
180 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
181 // = s + (t * s) * p
182 vt = psimd_mul_f32(vt, vs);
183 psimd_f32 vf = psimd_qfma_f32(vs, vt, vp);
184
185 // For inputs below zero cutoff, replace output with +0.0f.
186 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
187 vf = psimd_andnotmask_f32(vx < vdenorm_cutoff, vf);
188
189 // Store 4 outputs at a time.
190 psimd_store_f32(output, vf);
191 output += 4;
192
193 // Accumulate computed exponents.
194 vacc = psimd_add_f32(vacc, vf);
195 }
196 if (elements != 0) {
197 assert(elements >= 1 * sizeof(float));
198 assert(elements <= 3 * sizeof(float));
199 // Load 4 inputs at a time.
200 const psimd_f32 vi = psimd_load_f32(input);
201
202 // Subtract maximum input x := i - i_max. This implies x <= 0.
203 const psimd_f32 vx = psimd_sub_f32(vi, vi_max);
204
205 // Compute reduced argument elements := round(x / log(2)).
206 psimd_f32 vn = psimd_qfma_f32(vmagic_bias, vx, vlog2e);
207
208 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
209 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
210 const psimd_f32 vs = (psimd_f32) ((psimd_u32) vn << 23);
211
212 // Subtract the large number back to get final elements := round(x / log(2)).
213 vn = psimd_sub_f32(vn, vmagic_bias);
214
215 // Compute reduced argument t := x - elements * log(2).
216 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
217 psimd_f32 vt = psimd_qfma_f32(vx, vn, vminus_ln2_hi);
218 vt = psimd_qfma_f32(vt, vn, vminus_ln2_lo);
219
220 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
221 psimd_f32 vp = psimd_qfma_f32(vc4, vc5, vt);
222 vp = psimd_qfma_f32(vc3, vp, vt);
223 vp = psimd_qfma_f32(vc2, vp, vt);
224 vp = psimd_qfma_f32(vc1, vp, vt);
225
226 // Reconstruct the final f value:
227 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
228 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
229 // = s + (t * s) * p
230 vt = psimd_mul_f32(vt, vs);
231 psimd_f32 vf = psimd_qfma_f32(vs, vt, vp);
232
233 // For inputs below zero cutoff, replace output with +0.0f.
234 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
235 vf = psimd_andnotmask_f32(vx < vdenorm_cutoff, vf);
236
237 if (elements & (2 * sizeof(float))) {
238 // Store 2 outputs at a time.
239 psimd_store2_f32(output, vf);
240 output += 2;
241
242 // Accumulate 2 computed exponents.
243 vacc = psimd_add_f32(vacc, psimd_concat_lo_f32(vf, psimd_zero_f32()));
244
245 vf = psimd_concat_hi_f32(vf, vf);
246 }
247 if (elements & (1 * sizeof(float))) {
248 // Store 1 output at a time.
249 psimd_store1_f32(output, vf);
250
251 // Accumulate 1 computed exponent.
252 const psimd_f32 vzero = psimd_zero_f32();
253 vf = psimd_concat_lo_f32(vf, vzero);
254 vf = psimd_concat_even_f32(vf, vzero);
255 vacc = psimd_add_f32(vacc, vf);
256 }
257 }
258 // Reduce 4 elements in the SIMD register
259 *sum = psimd_reduce_sum_f32(vacc);
260 }
261