1 // Auto-generated file. Do not edit!
2 // Template: src/f32-vscaleexpminusmax/avx2-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 <immintrin.h>
13
14 #include <xnnpack/common.h>
15 #include <xnnpack/vscaleexpminusmax.h>
16
17
18 static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0};
19
xnn_f32_vscaleexpminusmax_ukernel__avx2_p5_x16(size_t elements,const float * input,float * output,float scale,float max)20 void xnn_f32_vscaleexpminusmax_ukernel__avx2_p5_x16(
21 size_t elements,
22 const float* input,
23 float* output,
24 float scale,
25 float max)
26 {
27 assert(elements % sizeof(float) == 0);
28
29 const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
30 // The smallest x for which expf(x) is normalized.
31 const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep6f);
32 const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
33 const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
34 const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);
35
36 const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
37 const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
38 const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
39 const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
40 const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);
41
42 const __m256 vscale = _mm256_set1_ps(scale);
43 const __m256 vi_max = _mm256_set1_ps(max);
44
45 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
46 // Load 16 (2x8) inputs at a time.
47 const __m256 vi0 = _mm256_loadu_ps(input);
48 const __m256 vi1 = _mm256_loadu_ps(input + 8);
49 input += 16;
50
51 // Subtract maximum input x := i - i_max. This implies x <= 0.
52 const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
53 const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
54
55 // Compute reduced argument elements := round(x / log(2)).
56 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
57 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
58
59 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
60 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
61 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
62 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
63
64 // Subtract the large number back to get final elements := round(x / log(2)).
65 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
66 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
67
68 // Compute reduced argument t := x - elements * log(2).
69 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
70 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
71 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
72
73 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
74 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
75
76 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
77 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
78 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
79
80 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
81 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
82
83 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
84 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
85
86 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
87 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
88
89 // Reconstruct the final f value:
90 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
91 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
92 // = s + (t * s) * p
93 vt0 = _mm256_mul_ps(vt0, vs0);
94 vt1 = _mm256_mul_ps(vt1, vs1);
95
96 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
97 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
98
99 // For inputs below zero cutoff, replace output with +0.0f.
100 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
101 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
102 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
103
104 // Multiply by scale.
105 vf0 = _mm256_mul_ps(vf0, vscale);
106 vf1 = _mm256_mul_ps(vf1, vscale);
107
108 // Store 16 (2x8) outputs at a time.
109 _mm256_storeu_ps(output, vf0);
110 _mm256_storeu_ps(output + 8, vf1);
111 output += 16;
112 }
113 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
114 // Load 8 inputs at a time.
115 const __m256 vi = _mm256_loadu_ps(input);
116 input += 8;
117
118 // Subtract maximum input x := i - i_max. This implies x <= 0.
119 const __m256 vx = _mm256_sub_ps(vi, vi_max);
120
121 // Compute reduced argument elements := round(x / log(2)).
122 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
123
124 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
125 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
126 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
127
128 // Subtract the large number back to get final elements := round(x / log(2)).
129 vn = _mm256_sub_ps(vn, vmagic_bias);
130
131 // Compute reduced argument t := x - elements * log(2).
132 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
133 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
134 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
135
136 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
137 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
138 vp = _mm256_fmadd_ps(vp, vt, vc3);
139 vp = _mm256_fmadd_ps(vp, vt, vc2);
140 vp = _mm256_fmadd_ps(vp, vt, vc1);
141
142 // Reconstruct the final f value:
143 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
144 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
145 // = s + (t * s) * p
146 vt = _mm256_mul_ps(vt, vs);
147 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
148
149 // For inputs below zero cutoff, replace output with +0.0f.
150 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
151 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
152
153 // Multiply by scale.
154 vf = _mm256_mul_ps(vf, vscale);
155
156 // Store 64 (8x8) outputs at a time.
157 _mm256_storeu_ps(output, vf);
158 output += 8;
159 }
160 if (elements != 0) {
161 assert(elements >= 1 * sizeof(float));
162 assert(elements <= 7 * sizeof(float));
163 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
164
165 // Load up to 7 inputs at a time.
166 const __m256 vi = _mm256_maskload_ps(input, vmask);
167
168 // Subtract maximum input x := i - i_max. This implies x <= 0.
169 const __m256 vx = _mm256_sub_ps(vi, vi_max);
170
171 // Compute reduced argument elements := round(x / log(2)).
172 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
173
174 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
175 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
176 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
177
178 // Subtract the large number back to get final elements := round(x / log(2)).
179 vn = _mm256_sub_ps(vn, vmagic_bias);
180
181 // Compute reduced argument t := x - elements * log(2).
182 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
183 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
184 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
185
186 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
187 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
188 vp = _mm256_fmadd_ps(vp, vt, vc3);
189 vp = _mm256_fmadd_ps(vp, vt, vc2);
190 vp = _mm256_fmadd_ps(vp, vt, vc1);
191
192 // Reconstruct the final f value:
193 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
194 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
195 // = s + (t * s) * p
196 vt = _mm256_mul_ps(vt, vs);
197 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
198
199 // For inputs below zero cutoff, replace output with +0.0f.
200 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
201 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
202
203 // Multiply by scale.
204 vf = _mm256_mul_ps(vf, vscale);
205
206 // Store up to 7 outputs at a time.
207 _mm256_maskstore_ps(output, vmask, vf);
208 }
209 }
210