blob: 35851408a438e294aff6cb1e8ecceb409b1092db [file] [log] [blame]
Marat Dukhan8137e4c2020-01-25 12:56:58 -08001// Auto-generated file. Do not edit!
2// Template: src/f32-raddstoreexpminusmax/neon-lut64-p2.c.in
3// Generator: tools/xngen
4//
5// Copyright 2020 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 <arm_neon.h>
13
14#include <xnnpack/common.h>
15#include <xnnpack/raddstoreexpminusmax.h>
16
17
18extern XNN_INTERNAL const float xnn_table_exp2_k_over_64[64];
19
20void xnn_f32_raddstoreexpminusmax_ukernel__neon_lut64_p2_x16(
21 size_t elements,
22 const float* input,
23 float* output,
24 float* sum,
Marat Dukhanb2217dd2020-05-28 17:30:28 -070025 float max) XNN_DISABLE_TSAN
Marat Dukhan8137e4c2020-01-25 12:56:58 -080026{
27 assert(elements % sizeof(float) == 0);
28
29 const float32x4_t vmagic_bias = vmovq_n_f32(0x1.800000p23f);
30 // The smallest x for which expf(x) is normalized.
31 const float32x4_t vdenorm_cutoff = vmovq_n_f32(-0x1.5D589Ep6f);
32 const float32x4_t vlog2e_x64 = vmovq_n_f32(0x1.715476p6f);
33 // Last 13 bits are zeroes
34 const float32x4_t vminus_ln2_o64_hi = vmovq_n_f32(-0x1.630000p-7f);
35 const float32x4_t vminus_ln2_o64_lo = vmovq_n_f32(0x1.BD0106p-19f);
36
37 const float32x4_t vc2 = vmovq_n_f32(0x1.FFFF0Ap-2f);
38
39 const int32x4_t vindex_mask = vmovq_n_s32(INT32_C(0x3F));
40
41 const float32x4_t vi_max = vdupq_n_f32(max);
42
43 float32x4_t vacc0 = vmovq_n_f32(0.0f);
44 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
45 // Load 16 (4x4) inputs at a time.
46 const float32x4_t vi0123 = vld1q_f32(input); input += 4;
47 const float32x4_t vi4567 = vld1q_f32(input); input += 4;
48 const float32x4_t vi89AB = vld1q_f32(input); input += 4;
49 const float32x4_t viCDEF = vld1q_f32(input); input += 4;
50
51 // Subtract maximum input x := i - i_max. This implies x <= 0.
52 const float32x4_t vx0123 = vsubq_f32(vi0123, vi_max);
53 const float32x4_t vx4567 = vsubq_f32(vi4567, vi_max);
54 const float32x4_t vx89AB = vsubq_f32(vi89AB, vi_max);
55 const float32x4_t vxCDEF = vsubq_f32(viCDEF, vi_max);
56
57 // Compute reduced argument n := round(x * 64 / log(2)).
58 // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing
59 // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
60 // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e.
61 // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0]
62 // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the
63 // algorithm.
64 float32x4_t vn0123 = vmlaq_f32(vmagic_bias, vx0123, vlog2e_x64);
65 float32x4_t vn4567 = vmlaq_f32(vmagic_bias, vx4567, vlog2e_x64);
66 float32x4_t vn89AB = vmlaq_f32(vmagic_bias, vx89AB, vlog2e_x64);
67 float32x4_t vnCDEF = vmlaq_f32(vmagic_bias, vxCDEF, vlog2e_x64);
68
69 // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized,
70 // i.e. -87.33642 <= x <= 0.0. As n has 6 fractional bits, we split s == 2**(n / 64) = 2**e * 2**(n / 64 - e), where
71 // e := int(n / 64). We create s in two steps:
72 // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the
73 // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
74 // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized
75 // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0,
76 // and thus the adjusted exponent is not lower than -126.
77 //
78 // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent).
79 const int32x4_t ve0123 = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn0123), vmovq_n_s32(INT32_C(0x3F))), 17);
80 const int32x4_t ve4567 = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn4567), vmovq_n_s32(INT32_C(0x3F))), 17);
81 const int32x4_t ve89AB = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn89AB), vmovq_n_s32(INT32_C(0x3F))), 17);
82 const int32x4_t veCDEF = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vnCDEF), vmovq_n_s32(INT32_C(0x3F))), 17);
83
84 // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64).
85 const uint64x2_t vidx0123 = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn0123), vindex_mask));
86 const uint64_t vidx01 = vgetq_lane_u64(vidx0123, 0);
87 const uint64_t vidx23 = vgetq_lane_u64(vidx0123, 1);
88 const uint64x2_t vidx4567 = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn4567), vindex_mask));
89 const uint64_t vidx45 = vgetq_lane_u64(vidx4567, 0);
90 const uint64_t vidx67 = vgetq_lane_u64(vidx4567, 1);
91 const uint64x2_t vidx89AB = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn89AB), vindex_mask));
92 const uint64_t vidx89 = vgetq_lane_u64(vidx89AB, 0);
93 const uint64_t vidxAB = vgetq_lane_u64(vidx89AB, 1);
94 const uint64x2_t vidxCDEF = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vnCDEF), vindex_mask));
95 const uint64_t vidxCD = vgetq_lane_u64(vidxCDEF, 0);
96 const uint64_t vidxEF = vgetq_lane_u64(vidxCDEF, 1);
97
98 float32x2_t vl01 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx01]);
99 float32x2_t vl23 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx23]);
100 float32x2_t vl45 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx45]);
101 float32x2_t vl67 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx67]);
102 float32x2_t vl89 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx89]);
103 float32x2_t vlAB = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidxAB]);
104 float32x2_t vlCD = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidxCD]);
105 float32x2_t vlEF = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidxEF]);
106
107 vl01 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx01 >> 32)], vl01, 1);
108 vl23 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx23 >> 32)], vl23, 1);
109 const float32x4_t vl0123 = vcombine_f32(vl01, vl23);
110 vl45 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx45 >> 32)], vl45, 1);
111 vl67 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx67 >> 32)], vl67, 1);
112 const float32x4_t vl4567 = vcombine_f32(vl45, vl67);
113 vl89 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx89 >> 32)], vl89, 1);
114 vlAB = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidxAB >> 32)], vlAB, 1);
115 const float32x4_t vl89AB = vcombine_f32(vl89, vlAB);
116 vlCD = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidxCD >> 32)], vlCD, 1);
117 vlEF = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidxEF >> 32)], vlEF, 1);
118 const float32x4_t vlCDEF = vcombine_f32(vlCD, vlEF);
119
120 // Adjust exponent of the value l fetched from the table to get the final s value.
121 const float32x4_t vs0123 = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl0123), ve0123));
122 const float32x4_t vs4567 = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl4567), ve4567));
123 const float32x4_t vs89AB = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl89AB), ve89AB));
124 const float32x4_t vsCDEF = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vlCDEF), veCDEF));
125
126 // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number.
127 vn0123 = vsubq_f32(vn0123, vmagic_bias);
128 vn4567 = vsubq_f32(vn4567, vmagic_bias);
129 vn89AB = vsubq_f32(vn89AB, vmagic_bias);
130 vnCDEF = vsubq_f32(vnCDEF, vmagic_bias);
131
132 // Compute reduced argument t := x - n * log(2) / 64.
133 // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy.
134 float32x4_t vt0123 = vmlaq_f32(vx0123, vn0123, vminus_ln2_o64_hi);
135 float32x4_t vt4567 = vmlaq_f32(vx4567, vn4567, vminus_ln2_o64_hi);
136 float32x4_t vt89AB = vmlaq_f32(vx89AB, vn89AB, vminus_ln2_o64_hi);
137 float32x4_t vtCDEF = vmlaq_f32(vxCDEF, vnCDEF, vminus_ln2_o64_hi);
138
139 vt0123 = vmlaq_f32(vt0123, vn0123, vminus_ln2_o64_lo);
140 vt4567 = vmlaq_f32(vt4567, vn4567, vminus_ln2_o64_lo);
141 vt89AB = vmlaq_f32(vt89AB, vn89AB, vminus_ln2_o64_lo);
142 vtCDEF = vmlaq_f32(vtCDEF, vnCDEF, vminus_ln2_o64_lo);
143
Marat Dukhan102a7392020-11-20 01:18:10 -0800144 // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/128, log(2)/128].
Marat Dukhan8137e4c2020-01-25 12:56:58 -0800145 float32x4_t vp0123 = vmulq_f32(vt0123, vc2);
146 float32x4_t vp4567 = vmulq_f32(vt4567, vc2);
147 float32x4_t vp89AB = vmulq_f32(vt89AB, vc2);
148 float32x4_t vpCDEF = vmulq_f32(vtCDEF, vc2);
149
150 vp0123 = vmlaq_f32(vt0123, vt0123, vp0123);
151 vp4567 = vmlaq_f32(vt4567, vt4567, vp4567);
152 vp89AB = vmlaq_f32(vt89AB, vt89AB, vp89AB);
153 vpCDEF = vmlaq_f32(vtCDEF, vtCDEF, vpCDEF);
154
155 // Reconstruct the final f value:
156 // f = s * (1 + t * (1 + t * c2))
157 // = s * (1 + t + t * (t * c2))
158 // = s + s * (t + t * (t * c2))
159 // = s + s * p
160 float32x4_t vf0123 = vmlaq_f32(vs0123, vs0123, vp0123);
161 float32x4_t vf4567 = vmlaq_f32(vs4567, vs4567, vp4567);
162 float32x4_t vf89AB = vmlaq_f32(vs89AB, vs89AB, vp89AB);
163 float32x4_t vfCDEF = vmlaq_f32(vsCDEF, vsCDEF, vpCDEF);
164
165 // For inputs below denormal cutoff, replace output with +0.0f.
166 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
167 vf0123 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf0123), vcltq_f32(vx0123, vdenorm_cutoff)));
168 vf4567 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf4567), vcltq_f32(vx4567, vdenorm_cutoff)));
169 vf89AB = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf89AB), vcltq_f32(vx89AB, vdenorm_cutoff)));
170 vfCDEF = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfCDEF), vcltq_f32(vxCDEF, vdenorm_cutoff)));
171
172 // Store 16 (4x4) outputs at a time.
173 vst1q_f32(output, vf0123); output += 4;
174 vst1q_f32(output, vf4567); output += 4;
175 vst1q_f32(output, vf89AB); output += 4;
176 vst1q_f32(output, vfCDEF); output += 4;
177
178 // Accumulate computed exponents.
179 vacc0 = vaddq_f32(vacc0, vf0123);
180 vacc0 = vaddq_f32(vacc0, vf4567);
181 vacc0 = vaddq_f32(vacc0, vf89AB);
182 vacc0 = vaddq_f32(vacc0, vfCDEF);
183 }
184
185 float32x4_t vacc = vacc0;
186 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
187 // Load 4 inputs at a time.
188 const float32x4_t vi = vld1q_f32(input); input += 4;
189
190 // Subtract maximum input x := i - i_max. This implies x <= 0.
191 const float32x4_t vx = vsubq_f32(vi, vi_max);
192
193 // Compute reduced argument n := round(x * 64 / log(2)).
194 // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing
195 // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
196 // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e.
197 // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0]
198 // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the
199 // algorithm.
200 float32x4_t vn = vmlaq_f32(vmagic_bias, vx, vlog2e_x64);
201
202 // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized,
203 // i.e. -87.33642 <= x <= 0.0. As n has 6 fractional bits, we split s == 2**(n / 64) = 2**e * 2**(n / 64 - e), where
204 // e := int(n / 64). We create s in two steps:
205 // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the
206 // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
207 // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized
208 // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0,
209 // and thus the adjusted exponent is not lower than -126.
210 //
211 // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent).
212 const int32x4_t ve = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn), vmovq_n_s32(INT32_C(0x3F))), 17);
213
214 // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64).
215 const uint64x2_t vidx = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn), vindex_mask));
216 const uint64_t vidx_lo = vgetq_lane_u64(vidx, 0);
217 const uint64_t vidx_hi = vgetq_lane_u64(vidx, 1);
218 float32x2_t vl_lo = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_lo]);
219 float32x2_t vl_hi = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_hi]);
220 vl_lo = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_lo >> 32)], vl_lo, 1);
221 vl_hi = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_hi >> 32)], vl_hi, 1);
222 const float32x4_t vl = vcombine_f32(vl_lo, vl_hi);
223 // Adjust exponent of the value l fetched from the table to get the final s value.
224 const float32x4_t vs = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl), ve));
225
226 // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number.
227 vn = vsubq_f32(vn, vmagic_bias);
228
229 // Compute reduced argument t := x - n * log(2) / 64.
230 // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy.
231 float32x4_t vt = vmlaq_f32(vx, vn, vminus_ln2_o64_hi);
232 vt = vmlaq_f32(vt, vn, vminus_ln2_o64_lo);
233
Marat Dukhan102a7392020-11-20 01:18:10 -0800234 // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/128, log(2)/128].
Marat Dukhan8137e4c2020-01-25 12:56:58 -0800235 float32x4_t vp = vmulq_f32(vt, vc2);
236 vp = vmlaq_f32(vt, vt, vp);
237
238 // Reconstruct the final f value:
239 // f = s * (1 + t * (1 + t * c2))
240 // = s * (1 + t + t * (t * c2))
241 // = s + s * (t + t * (t * c2))
242 // = s + s * p
243 float32x4_t vf = vmlaq_f32(vs, vs, vp);
244
245 // For inputs below denormal cutoff, replace output with +0.0f.
246 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
247 vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff)));
248
249 // Store 4 outputs at a time.
250 vst1q_f32(output, vf); output += 4;
251
252 // Accumulate computed exponents.
253 vacc = vaddq_f32(vacc, vf);
254 }
255#if XNN_ARCH_ARM64
256 float vacc_lo = vaddvq_f32(vacc);
257#else
258 float32x2_t vacc_lo = vadd_f32(vget_high_f32(vacc), vget_low_f32(vacc));
259#endif
260 if (elements != 0) {
261 assert(elements >= 1 * sizeof(float));
262 assert(elements <= 3 * sizeof(float));
263 // Load 4 inputs at a time.
264 const float32x4_t vi = vld1q_f32(input); input += 4;
265
266 // Subtract maximum input x := i - i_max. This implies x <= 0.
267 const float32x4_t vx = vsubq_f32(vi, vi_max);
268
269 // Compute reduced argument n := round(x * 64 / log(2)).
270 // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing
271 // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
272 // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e.
273 // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0]
274 // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the
275 // algorithm.
276 float32x4_t vn = vmlaq_f32(vmagic_bias, vx, vlog2e_x64);
277
278 // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized,
279 // i.e. -87.33642 <= x <= 0.0. As n has 6 fractional bits, we split s == 2**(n / 64) = 2**e * 2**(n / 64 - e), where
280 // e := int(n / 64). We create s in two steps:
281 // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the
282 // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
283 // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized
284 // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0,
285 // and thus the adjusted exponent is not lower than -126.
286 //
287 // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent).
288 const int32x4_t ve = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn), vmovq_n_s32(INT32_C(0x3F))), 17);
289
290 // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64).
291 const uint64x2_t vidx = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn), vindex_mask));
292 const uint64_t vidx_lo = vgetq_lane_u64(vidx, 0);
293 const uint64_t vidx_hi = vgetq_lane_u64(vidx, 1);
294 float32x2_t vl_lo = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_lo]);
295 float32x2_t vl_hi = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_hi]);
296 vl_lo = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_lo >> 32)], vl_lo, 1);
297 vl_hi = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_hi >> 32)], vl_hi, 1);
298 const float32x4_t vl = vcombine_f32(vl_lo, vl_hi);
299 // Adjust exponent of the value l fetched from the table to get the final s value.
300 const float32x4_t vs = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl), ve));
301
302 // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number.
303 vn = vsubq_f32(vn, vmagic_bias);
304
305 // Compute reduced argument t := x - n * log(2) / 64.
306 // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy.
307 float32x4_t vt = vmlaq_f32(vx, vn, vminus_ln2_o64_hi);
308 vt = vmlaq_f32(vt, vn, vminus_ln2_o64_lo);
309
Marat Dukhan102a7392020-11-20 01:18:10 -0800310 // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/128, log(2)/128].
Marat Dukhan8137e4c2020-01-25 12:56:58 -0800311 float32x4_t vp = vmulq_f32(vt, vc2);
312 vp = vmlaq_f32(vt, vt, vp);
313
314 // Reconstruct the final f value:
315 // f = s * (1 + t * (1 + t * c2))
316 // = s * (1 + t + t * (t * c2))
317 // = s + s * (t + t * (t * c2))
318 // = s + s * p
319 float32x4_t vf = vmlaq_f32(vs, vs, vp);
320
321 // For inputs below denormal cutoff, replace output with +0.0f.
322 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
323 vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff)));
324
325 float32x2_t vf_lo = vget_low_f32(vf);
326 if (elements & (2 * sizeof(float))) {
327 // Store 2 outputs at a time.
328 vst1_f32(output, vf_lo); output += 2;
329
330 // Accumulate 2 computed exponents.
331 #if XNN_ARCH_ARM64
332 vacc_lo += vaddv_f32(vf_lo);
333 #else
334 vacc_lo = vadd_f32(vacc_lo, vf_lo);
335 #endif
336
337 vf_lo = vget_high_f32(vf);
338 }
339 if (elements & (1 * sizeof(float))) {
340 // Store 1 output at a time.
341 vst1_lane_f32(output, vf_lo, 0);
342
343 // Accumulate 1 computed exponent.
344 #if XNN_ARCH_ARM64
345 vacc_lo += vget_lane_f32(vf_lo, 0);
346 #else
347 vacc_lo = vadd_f32(vacc_lo, vreinterpret_f32_u64(vshl_n_u64(vreinterpret_u64_f32(vf_lo), 32)));
348 #endif
349 }
350 }
351 // Reduce 4 elements in the SIMD register
352#if XNN_ARCH_ARM64
353 *sum = vacc_lo;
354#else
355 vst1_lane_f32(sum, vpadd_f32(vacc_lo, vacc_lo), 0);
356#endif
357}