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_x8(size_t elements,const float * input,float * output,float * sum,float max)18 void xnn_f32_raddstoreexpminusmax_ukernel__psimd_p5_x8(
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 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
45 // Load 8 (2x4) inputs at a time.
46 const psimd_f32 vi0123 = psimd_load_f32(input);
47 const psimd_f32 vi4567 = psimd_load_f32(input + 4);
48 input += 8;
49
50 // Subtract maximum input x := i - i_max. This implies x <= 0.
51 const psimd_f32 vx0123 = psimd_sub_f32(vi0123, vi_max);
52 const psimd_f32 vx4567 = psimd_sub_f32(vi4567, vi_max);
53
54 // Compute reduced argument elements := round(x / log(2)).
55 psimd_f32 vn0123 = psimd_qfma_f32(vmagic_bias, vx0123, vlog2e);
56 psimd_f32 vn4567 = psimd_qfma_f32(vmagic_bias, vx4567, vlog2e);
57
58 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
59 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
60 const psimd_f32 vs0123 = (psimd_f32) ((psimd_u32) vn0123 << 23);
61 const psimd_f32 vs4567 = (psimd_f32) ((psimd_u32) vn4567 << 23);
62
63 // Subtract the large number back to get final elements := round(x / log(2)).
64 vn0123 = psimd_sub_f32(vn0123, vmagic_bias);
65 vn4567 = psimd_sub_f32(vn4567, vmagic_bias);
66
67 // Compute reduced argument t := x - elements * log(2).
68 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
69 psimd_f32 vt0123 = psimd_qfma_f32(vx0123, vn0123, vminus_ln2_hi);
70 psimd_f32 vt4567 = psimd_qfma_f32(vx4567, vn4567, vminus_ln2_hi);
71
72 vt0123 = psimd_qfma_f32(vt0123, vn0123, vminus_ln2_lo);
73 vt4567 = psimd_qfma_f32(vt4567, vn4567, vminus_ln2_lo);
74
75 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
76 psimd_f32 vp0123 = psimd_qfma_f32(vc4, vc5, vt0123);
77 psimd_f32 vp4567 = psimd_qfma_f32(vc4, vc5, vt4567);
78
79 vp0123 = psimd_qfma_f32(vc3, vp0123, vt0123);
80 vp4567 = psimd_qfma_f32(vc3, vp4567, vt4567);
81
82 vp0123 = psimd_qfma_f32(vc2, vp0123, vt0123);
83 vp4567 = psimd_qfma_f32(vc2, vp4567, vt4567);
84
85 vp0123 = psimd_qfma_f32(vc1, vp0123, vt0123);
86 vp4567 = psimd_qfma_f32(vc1, vp4567, vt4567);
87
88 // Reconstruct the final f value:
89 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
90 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
91 // = s + (t * s) * p
92 vt0123 = psimd_mul_f32(vt0123, vs0123);
93 vt4567 = psimd_mul_f32(vt4567, vs4567);
94
95 psimd_f32 vf0123 = psimd_qfma_f32(vs0123, vt0123, vp0123);
96 psimd_f32 vf4567 = psimd_qfma_f32(vs4567, vt4567, vp4567);
97
98 // For inputs below zero cutoff, replace output with +0.0f.
99 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
100 vf0123 = psimd_andnotmask_f32(vx0123 < vdenorm_cutoff, vf0123);
101 vf4567 = psimd_andnotmask_f32(vx4567 < vdenorm_cutoff, vf4567);
102
103 // Store 8 (2x4) outputs at a time.
104 psimd_store_f32(output, vf0123);
105 psimd_store_f32(output + 4, vf4567);
106 output += 8;
107
108 // Accumulate computed exponents.
109 vacc0 = psimd_add_f32(vacc0, vf0123);
110 vacc0 = psimd_add_f32(vacc0, vf4567);
111 }
112
113 psimd_f32 vacc = vacc0;
114 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
115 // Load 4 inputs at a time.
116 const psimd_f32 vi = psimd_load_f32(input);
117 input += 4;
118
119 // Subtract maximum input x := i - i_max. This implies x <= 0.
120 const psimd_f32 vx = psimd_sub_f32(vi, vi_max);
121
122 // Compute reduced argument elements := round(x / log(2)).
123 psimd_f32 vn = psimd_qfma_f32(vmagic_bias, vx, vlog2e);
124
125 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
126 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
127 const psimd_f32 vs = (psimd_f32) ((psimd_u32) vn << 23);
128
129 // Subtract the large number back to get final elements := round(x / log(2)).
130 vn = psimd_sub_f32(vn, vmagic_bias);
131
132 // Compute reduced argument t := x - elements * log(2).
133 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
134 psimd_f32 vt = psimd_qfma_f32(vx, vn, vminus_ln2_hi);
135 vt = psimd_qfma_f32(vt, vn, vminus_ln2_lo);
136
137 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
138 psimd_f32 vp = psimd_qfma_f32(vc4, vc5, vt);
139 vp = psimd_qfma_f32(vc3, vp, vt);
140 vp = psimd_qfma_f32(vc2, vp, vt);
141 vp = psimd_qfma_f32(vc1, vp, vt);
142
143 // Reconstruct the final f value:
144 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
145 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
146 // = s + (t * s) * p
147 vt = psimd_mul_f32(vt, vs);
148 psimd_f32 vf = psimd_qfma_f32(vs, vt, vp);
149
150 // For inputs below zero cutoff, replace output with +0.0f.
151 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
152 vf = psimd_andnotmask_f32(vx < vdenorm_cutoff, vf);
153
154 // Store 4 outputs at a time.
155 psimd_store_f32(output, vf);
156 output += 4;
157
158 // Accumulate computed exponents.
159 vacc = psimd_add_f32(vacc, vf);
160 }
161 if (elements != 0) {
162 assert(elements >= 1 * sizeof(float));
163 assert(elements <= 3 * sizeof(float));
164 // Load 4 inputs at a time.
165 const psimd_f32 vi = psimd_load_f32(input);
166
167 // Subtract maximum input x := i - i_max. This implies x <= 0.
168 const psimd_f32 vx = psimd_sub_f32(vi, vi_max);
169
170 // Compute reduced argument elements := round(x / log(2)).
171 psimd_f32 vn = psimd_qfma_f32(vmagic_bias, vx, vlog2e);
172
173 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
174 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
175 const psimd_f32 vs = (psimd_f32) ((psimd_u32) vn << 23);
176
177 // Subtract the large number back to get final elements := round(x / log(2)).
178 vn = psimd_sub_f32(vn, vmagic_bias);
179
180 // Compute reduced argument t := x - elements * log(2).
181 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
182 psimd_f32 vt = psimd_qfma_f32(vx, vn, vminus_ln2_hi);
183 vt = psimd_qfma_f32(vt, vn, vminus_ln2_lo);
184
185 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
186 psimd_f32 vp = psimd_qfma_f32(vc4, vc5, vt);
187 vp = psimd_qfma_f32(vc3, vp, vt);
188 vp = psimd_qfma_f32(vc2, vp, vt);
189 vp = psimd_qfma_f32(vc1, vp, vt);
190
191 // Reconstruct the final f value:
192 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
193 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
194 // = s + (t * s) * p
195 vt = psimd_mul_f32(vt, vs);
196 psimd_f32 vf = psimd_qfma_f32(vs, vt, vp);
197
198 // For inputs below zero cutoff, replace output with +0.0f.
199 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
200 vf = psimd_andnotmask_f32(vx < vdenorm_cutoff, vf);
201
202 if (elements & (2 * sizeof(float))) {
203 // Store 2 outputs at a time.
204 psimd_store2_f32(output, vf);
205 output += 2;
206
207 // Accumulate 2 computed exponents.
208 vacc = psimd_add_f32(vacc, psimd_concat_lo_f32(vf, psimd_zero_f32()));
209
210 vf = psimd_concat_hi_f32(vf, vf);
211 }
212 if (elements & (1 * sizeof(float))) {
213 // Store 1 output at a time.
214 psimd_store1_f32(output, vf);
215
216 // Accumulate 1 computed exponent.
217 const psimd_f32 vzero = psimd_zero_f32();
218 vf = psimd_concat_lo_f32(vf, vzero);
219 vf = psimd_concat_even_f32(vf, vzero);
220 vacc = psimd_add_f32(vacc, vf);
221 }
222 }
223 // Reduce 4 elements in the SIMD register
224 *sum = psimd_reduce_sum_f32(vacc);
225 }
226