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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_acc4(
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 float32x4_t vacc1 = vmovq_n_f32(0.0f);
45 float32x4_t vacc2 = vmovq_n_f32(0.0f);
46 float32x4_t vacc3 = vmovq_n_f32(0.0f);
47 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
48 // Load 16 (4x4) inputs at a time.
49 const float32x4_t vi0123 = vld1q_f32(input); input += 4;
50 const float32x4_t vi4567 = vld1q_f32(input); input += 4;
51 const float32x4_t vi89AB = vld1q_f32(input); input += 4;
52 const float32x4_t viCDEF = vld1q_f32(input); input += 4;
53
54 // Subtract maximum input x := i - i_max. This implies x <= 0.
55 const float32x4_t vx0123 = vsubq_f32(vi0123, vi_max);
56 const float32x4_t vx4567 = vsubq_f32(vi4567, vi_max);
57 const float32x4_t vx89AB = vsubq_f32(vi89AB, vi_max);
58 const float32x4_t vxCDEF = vsubq_f32(viCDEF, vi_max);
59
60 // Compute reduced argument n := round(x * 64 / log(2)).
61 // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing
62 // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
63 // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e.
64 // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0]
65 // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the
66 // algorithm.
67 float32x4_t vn0123 = vmlaq_f32(vmagic_bias, vx0123, vlog2e_x64);
68 float32x4_t vn4567 = vmlaq_f32(vmagic_bias, vx4567, vlog2e_x64);
69 float32x4_t vn89AB = vmlaq_f32(vmagic_bias, vx89AB, vlog2e_x64);
70 float32x4_t vnCDEF = vmlaq_f32(vmagic_bias, vxCDEF, vlog2e_x64);
71
72 // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized,
73 // 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
74 // e := int(n / 64). We create s in two steps:
75 // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the
76 // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
77 // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized
78 // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0,
79 // and thus the adjusted exponent is not lower than -126.
80 //
81 // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent).
82 const int32x4_t ve0123 = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn0123), vmovq_n_s32(INT32_C(0x3F))), 17);
83 const int32x4_t ve4567 = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn4567), vmovq_n_s32(INT32_C(0x3F))), 17);
84 const int32x4_t ve89AB = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn89AB), vmovq_n_s32(INT32_C(0x3F))), 17);
85 const int32x4_t veCDEF = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vnCDEF), vmovq_n_s32(INT32_C(0x3F))), 17);
86
87 // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64).
88 const uint64x2_t vidx0123 = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn0123), vindex_mask));
89 const uint64_t vidx01 = vgetq_lane_u64(vidx0123, 0);
90 const uint64_t vidx23 = vgetq_lane_u64(vidx0123, 1);
91 const uint64x2_t vidx4567 = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn4567), vindex_mask));
92 const uint64_t vidx45 = vgetq_lane_u64(vidx4567, 0);
93 const uint64_t vidx67 = vgetq_lane_u64(vidx4567, 1);
94 const uint64x2_t vidx89AB = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn89AB), vindex_mask));
95 const uint64_t vidx89 = vgetq_lane_u64(vidx89AB, 0);
96 const uint64_t vidxAB = vgetq_lane_u64(vidx89AB, 1);
97 const uint64x2_t vidxCDEF = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vnCDEF), vindex_mask));
98 const uint64_t vidxCD = vgetq_lane_u64(vidxCDEF, 0);
99 const uint64_t vidxEF = vgetq_lane_u64(vidxCDEF, 1);
100
101 float32x2_t vl01 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx01]);
102 float32x2_t vl23 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx23]);
103 float32x2_t vl45 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx45]);
104 float32x2_t vl67 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx67]);
105 float32x2_t vl89 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx89]);
106 float32x2_t vlAB = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidxAB]);
107 float32x2_t vlCD = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidxCD]);
108 float32x2_t vlEF = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidxEF]);
109
110 vl01 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx01 >> 32)], vl01, 1);
111 vl23 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx23 >> 32)], vl23, 1);
112 const float32x4_t vl0123 = vcombine_f32(vl01, vl23);
113 vl45 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx45 >> 32)], vl45, 1);
114 vl67 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx67 >> 32)], vl67, 1);
115 const float32x4_t vl4567 = vcombine_f32(vl45, vl67);
116 vl89 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx89 >> 32)], vl89, 1);
117 vlAB = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidxAB >> 32)], vlAB, 1);
118 const float32x4_t vl89AB = vcombine_f32(vl89, vlAB);
119 vlCD = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidxCD >> 32)], vlCD, 1);
120 vlEF = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidxEF >> 32)], vlEF, 1);
121 const float32x4_t vlCDEF = vcombine_f32(vlCD, vlEF);
122
123 // Adjust exponent of the value l fetched from the table to get the final s value.
124 const float32x4_t vs0123 = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl0123), ve0123));
125 const float32x4_t vs4567 = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl4567), ve4567));
126 const float32x4_t vs89AB = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl89AB), ve89AB));
127 const float32x4_t vsCDEF = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vlCDEF), veCDEF));
128
129 // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number.
130 vn0123 = vsubq_f32(vn0123, vmagic_bias);
131 vn4567 = vsubq_f32(vn4567, vmagic_bias);
132 vn89AB = vsubq_f32(vn89AB, vmagic_bias);
133 vnCDEF = vsubq_f32(vnCDEF, vmagic_bias);
134
135 // Compute reduced argument t := x - n * log(2) / 64.
136 // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy.
137 float32x4_t vt0123 = vmlaq_f32(vx0123, vn0123, vminus_ln2_o64_hi);
138 float32x4_t vt4567 = vmlaq_f32(vx4567, vn4567, vminus_ln2_o64_hi);
139 float32x4_t vt89AB = vmlaq_f32(vx89AB, vn89AB, vminus_ln2_o64_hi);
140 float32x4_t vtCDEF = vmlaq_f32(vxCDEF, vnCDEF, vminus_ln2_o64_hi);
141
142 vt0123 = vmlaq_f32(vt0123, vn0123, vminus_ln2_o64_lo);
143 vt4567 = vmlaq_f32(vt4567, vn4567, vminus_ln2_o64_lo);
144 vt89AB = vmlaq_f32(vt89AB, vn89AB, vminus_ln2_o64_lo);
145 vtCDEF = vmlaq_f32(vtCDEF, vnCDEF, vminus_ln2_o64_lo);
146
Marat Dukhan102a7392020-11-20 01:18:10 -0800147 // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/128, log(2)/128].
Marat Dukhan8137e4c2020-01-25 12:56:58 -0800148 float32x4_t vp0123 = vmulq_f32(vt0123, vc2);
149 float32x4_t vp4567 = vmulq_f32(vt4567, vc2);
150 float32x4_t vp89AB = vmulq_f32(vt89AB, vc2);
151 float32x4_t vpCDEF = vmulq_f32(vtCDEF, vc2);
152
153 vp0123 = vmlaq_f32(vt0123, vt0123, vp0123);
154 vp4567 = vmlaq_f32(vt4567, vt4567, vp4567);
155 vp89AB = vmlaq_f32(vt89AB, vt89AB, vp89AB);
156 vpCDEF = vmlaq_f32(vtCDEF, vtCDEF, vpCDEF);
157
158 // Reconstruct the final f value:
159 // f = s * (1 + t * (1 + t * c2))
160 // = s * (1 + t + t * (t * c2))
161 // = s + s * (t + t * (t * c2))
162 // = s + s * p
163 float32x4_t vf0123 = vmlaq_f32(vs0123, vs0123, vp0123);
164 float32x4_t vf4567 = vmlaq_f32(vs4567, vs4567, vp4567);
165 float32x4_t vf89AB = vmlaq_f32(vs89AB, vs89AB, vp89AB);
166 float32x4_t vfCDEF = vmlaq_f32(vsCDEF, vsCDEF, vpCDEF);
167
168 // For inputs below denormal cutoff, replace output with +0.0f.
169 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
170 vf0123 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf0123), vcltq_f32(vx0123, vdenorm_cutoff)));
171 vf4567 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf4567), vcltq_f32(vx4567, vdenorm_cutoff)));
172 vf89AB = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf89AB), vcltq_f32(vx89AB, vdenorm_cutoff)));
173 vfCDEF = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfCDEF), vcltq_f32(vxCDEF, vdenorm_cutoff)));
174
175 // Store 16 (4x4) outputs at a time.
176 vst1q_f32(output, vf0123); output += 4;
177 vst1q_f32(output, vf4567); output += 4;
178 vst1q_f32(output, vf89AB); output += 4;
179 vst1q_f32(output, vfCDEF); output += 4;
180
181 // Accumulate computed exponents.
182 vacc0 = vaddq_f32(vacc0, vf0123);
183 vacc0 = vaddq_f32(vacc0, vf4567);
184 vacc0 = vaddq_f32(vacc0, vf89AB);
185 vacc0 = vaddq_f32(vacc0, vfCDEF);
186 }
187 // Add up all accumulators to vacc0
188 vacc0 = vaddq_f32(vacc0, vacc1);
189 vacc2 = vaddq_f32(vacc2, vacc3);
190 vacc0 = vaddq_f32(vacc0, vacc2);
191
192 float32x4_t vacc = vacc0;
193 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
194 // Load 4 inputs at a time.
195 const float32x4_t vi = vld1q_f32(input); input += 4;
196
197 // Subtract maximum input x := i - i_max. This implies x <= 0.
198 const float32x4_t vx = vsubq_f32(vi, vi_max);
199
200 // Compute reduced argument n := round(x * 64 / log(2)).
201 // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing
202 // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
203 // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e.
204 // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0]
205 // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the
206 // algorithm.
207 float32x4_t vn = vmlaq_f32(vmagic_bias, vx, vlog2e_x64);
208
209 // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized,
210 // 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
211 // e := int(n / 64). We create s in two steps:
212 // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the
213 // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
214 // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized
215 // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0,
216 // and thus the adjusted exponent is not lower than -126.
217 //
218 // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent).
219 const int32x4_t ve = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn), vmovq_n_s32(INT32_C(0x3F))), 17);
220
221 // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64).
222 const uint64x2_t vidx = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn), vindex_mask));
223 const uint64_t vidx_lo = vgetq_lane_u64(vidx, 0);
224 const uint64_t vidx_hi = vgetq_lane_u64(vidx, 1);
225 float32x2_t vl_lo = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_lo]);
226 float32x2_t vl_hi = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_hi]);
227 vl_lo = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_lo >> 32)], vl_lo, 1);
228 vl_hi = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_hi >> 32)], vl_hi, 1);
229 const float32x4_t vl = vcombine_f32(vl_lo, vl_hi);
230 // Adjust exponent of the value l fetched from the table to get the final s value.
231 const float32x4_t vs = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl), ve));
232
233 // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number.
234 vn = vsubq_f32(vn, vmagic_bias);
235
236 // Compute reduced argument t := x - n * log(2) / 64.
237 // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy.
238 float32x4_t vt = vmlaq_f32(vx, vn, vminus_ln2_o64_hi);
239 vt = vmlaq_f32(vt, vn, vminus_ln2_o64_lo);
240
Marat Dukhan102a7392020-11-20 01:18:10 -0800241 // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/128, log(2)/128].
Marat Dukhan8137e4c2020-01-25 12:56:58 -0800242 float32x4_t vp = vmulq_f32(vt, vc2);
243 vp = vmlaq_f32(vt, vt, vp);
244
245 // Reconstruct the final f value:
246 // f = s * (1 + t * (1 + t * c2))
247 // = s * (1 + t + t * (t * c2))
248 // = s + s * (t + t * (t * c2))
249 // = s + s * p
250 float32x4_t vf = vmlaq_f32(vs, vs, vp);
251
252 // For inputs below denormal cutoff, replace output with +0.0f.
253 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
254 vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff)));
255
256 // Store 4 outputs at a time.
257 vst1q_f32(output, vf); output += 4;
258
259 // Accumulate computed exponents.
260 vacc = vaddq_f32(vacc, vf);
261 }
262#if XNN_ARCH_ARM64
263 float vacc_lo = vaddvq_f32(vacc);
264#else
265 float32x2_t vacc_lo = vadd_f32(vget_high_f32(vacc), vget_low_f32(vacc));
266#endif
267 if (elements != 0) {
268 assert(elements >= 1 * sizeof(float));
269 assert(elements <= 3 * sizeof(float));
270 // Load 4 inputs at a time.
271 const float32x4_t vi = vld1q_f32(input); input += 4;
272
273 // Subtract maximum input x := i - i_max. This implies x <= 0.
274 const float32x4_t vx = vsubq_f32(vi, vi_max);
275
276 // Compute reduced argument n := round(x * 64 / log(2)).
277 // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing
278 // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
279 // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e.
280 // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0]
281 // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the
282 // algorithm.
283 float32x4_t vn = vmlaq_f32(vmagic_bias, vx, vlog2e_x64);
284
285 // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized,
286 // 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
287 // e := int(n / 64). We create s in two steps:
288 // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the
289 // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
290 // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized
291 // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0,
292 // and thus the adjusted exponent is not lower than -126.
293 //
294 // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent).
295 const int32x4_t ve = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn), vmovq_n_s32(INT32_C(0x3F))), 17);
296
297 // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64).
298 const uint64x2_t vidx = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn), vindex_mask));
299 const uint64_t vidx_lo = vgetq_lane_u64(vidx, 0);
300 const uint64_t vidx_hi = vgetq_lane_u64(vidx, 1);
301 float32x2_t vl_lo = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_lo]);
302 float32x2_t vl_hi = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_hi]);
303 vl_lo = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_lo >> 32)], vl_lo, 1);
304 vl_hi = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_hi >> 32)], vl_hi, 1);
305 const float32x4_t vl = vcombine_f32(vl_lo, vl_hi);
306 // Adjust exponent of the value l fetched from the table to get the final s value.
307 const float32x4_t vs = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl), ve));
308
309 // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number.
310 vn = vsubq_f32(vn, vmagic_bias);
311
312 // Compute reduced argument t := x - n * log(2) / 64.
313 // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy.
314 float32x4_t vt = vmlaq_f32(vx, vn, vminus_ln2_o64_hi);
315 vt = vmlaq_f32(vt, vn, vminus_ln2_o64_lo);
316
Marat Dukhan102a7392020-11-20 01:18:10 -0800317 // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/128, log(2)/128].
Marat Dukhan8137e4c2020-01-25 12:56:58 -0800318 float32x4_t vp = vmulq_f32(vt, vc2);
319 vp = vmlaq_f32(vt, vt, vp);
320
321 // Reconstruct the final f value:
322 // f = s * (1 + t * (1 + t * c2))
323 // = s * (1 + t + t * (t * c2))
324 // = s + s * (t + t * (t * c2))
325 // = s + s * p
326 float32x4_t vf = vmlaq_f32(vs, vs, vp);
327
328 // For inputs below denormal cutoff, replace output with +0.0f.
329 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
330 vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff)));
331
332 float32x2_t vf_lo = vget_low_f32(vf);
333 if (elements & (2 * sizeof(float))) {
334 // Store 2 outputs at a time.
335 vst1_f32(output, vf_lo); output += 2;
336
337 // Accumulate 2 computed exponents.
338 #if XNN_ARCH_ARM64
339 vacc_lo += vaddv_f32(vf_lo);
340 #else
341 vacc_lo = vadd_f32(vacc_lo, vf_lo);
342 #endif
343
344 vf_lo = vget_high_f32(vf);
345 }
346 if (elements & (1 * sizeof(float))) {
347 // Store 1 output at a time.
348 vst1_lane_f32(output, vf_lo, 0);
349
350 // Accumulate 1 computed exponent.
351 #if XNN_ARCH_ARM64
352 vacc_lo += vget_lane_f32(vf_lo, 0);
353 #else
354 vacc_lo = vadd_f32(vacc_lo, vreinterpret_f32_u64(vshl_n_u64(vreinterpret_u64_f32(vf_lo), 32)));
355 #endif
356 }
357 }
358 // Reduce 4 elements in the SIMD register
359#if XNN_ARCH_ARM64
360 *sum = vacc_lo;
361#else
362 vst1_lane_f32(sum, vpadd_f32(vacc_lo, vacc_lo), 0);
363#endif
364}