1 // Auto-generated file. Do not edit!
2 // Template: src/f32-sigmoid/neon-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 <arm_neon.h>
13
14 #include <xnnpack/common.h>
15 #include <xnnpack/vunary.h>
16
17
xnn_f32_sigmoid_ukernel__neon_rr2_p5_nr2recps_x24(size_t n,const float * x,float * y,const void * params)18 void xnn_f32_sigmoid_ukernel__neon_rr2_p5_nr2recps_x24(
19 size_t n,
20 const float* x,
21 float* y,
22 const void* params)
23 {
24 assert(n % sizeof(float) == 0);
25
26 const float32x4_t vmagic_bias = vmovq_n_f32(0x1.8000FEp23f);
27 // The largest z for which sigmoidf(-z) is normalized.
28 // This number is also the largest z for which expf(-z) is normalized.
29 const float32x4_t vdenorm_cutoff = vmovq_n_f32(0x1.5D589Ep+6f);
30 const float32x4_t vminus_log2e = vmovq_n_f32(-0x1.715476p+0f);
31 // Last 7 bits are zeroes
32 const float32x4_t vln2_hi = vmovq_n_f32(0x1.62E400p-1f);
33 const float32x4_t vln2_lo = vmovq_n_f32(0x1.7F7D1Cp-20f);
34 const float32x4_t vone = vmovq_n_f32(1.0f);
35
36 const float32x4_t vc1 = vmovq_n_f32(-0x1.FFFFF6p-1f);
37 const float32x4_t vc2 = vmovq_n_f32(0x1.FFFDC6p-2f);
38 const float32x4_t vc3 = vmovq_n_f32(-0x1.555A80p-3f);
39 const float32x4_t vc4 = vmovq_n_f32(0x1.573A1Ap-5f);
40 const float32x4_t vc5 = vmovq_n_f32(-0x1.0F9F9Cp-7f);
41
42 for (; n >= 24 * sizeof(float); n -= 24 * sizeof(float)) {
43 const float32x4_t vx0123 = vld1q_f32(x); x += 4;
44 const float32x4_t vx4567 = vld1q_f32(x); x += 4;
45 const float32x4_t vx89AB = vld1q_f32(x); x += 4;
46 const float32x4_t vxCDEF = vld1q_f32(x); x += 4;
47 const float32x4_t vxGHIJ = vld1q_f32(x); x += 4;
48 const float32x4_t vxKLMN = vld1q_f32(x); x += 4;
49
50 // General structure of the algorithm:
51 // / exp(x) / (1 + exp(x)) if x <= 0
52 // f[x] :=
53 // \ 1 - f[-x] if x >= 0
54 //
55 // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x),
56 // then replace result with 1 - f[z] if x >= 0.
57 const float32x4_t vz0123 = vabsq_f32(vx0123);
58 const float32x4_t vz4567 = vabsq_f32(vx4567);
59 const float32x4_t vz89AB = vabsq_f32(vx89AB);
60 const float32x4_t vzCDEF = vabsq_f32(vxCDEF);
61 const float32x4_t vzGHIJ = vabsq_f32(vxGHIJ);
62 const float32x4_t vzKLMN = vabsq_f32(vxKLMN);
63
64 // Compute reduced argument n := round(-z / log(2)).
65 // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the
66 // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
67 // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because
68 // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x)
69 // anyway. We fixup the result for such inputs at the very end of the algorithm.
70 float32x4_t vn0123 = vmlaq_f32(vmagic_bias, vz0123, vminus_log2e);
71 float32x4_t vn4567 = vmlaq_f32(vmagic_bias, vz4567, vminus_log2e);
72 float32x4_t vn89AB = vmlaq_f32(vmagic_bias, vz89AB, vminus_log2e);
73 float32x4_t vnCDEF = vmlaq_f32(vmagic_bias, vzCDEF, vminus_log2e);
74 float32x4_t vnGHIJ = vmlaq_f32(vmagic_bias, vzGHIJ, vminus_log2e);
75 float32x4_t vnKLMN = vmlaq_f32(vmagic_bias, vzKLMN, vminus_log2e);
76
77 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
78 // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly.
79 const float32x4_t vs0123 = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn0123), 23));
80 const float32x4_t vs4567 = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn4567), 23));
81 const float32x4_t vs89AB = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn89AB), 23));
82 const float32x4_t vsCDEF = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vnCDEF), 23));
83 const float32x4_t vsGHIJ = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vnGHIJ), 23));
84 const float32x4_t vsKLMN = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vnKLMN), 23));
85
86 // Subtract the large number back to get final n := round(-z / log(2)).
87 vn0123 = vsubq_f32(vn0123, vmagic_bias);
88 vn4567 = vsubq_f32(vn4567, vmagic_bias);
89 vn89AB = vsubq_f32(vn89AB, vmagic_bias);
90 vnCDEF = vsubq_f32(vnCDEF, vmagic_bias);
91 vnGHIJ = vsubq_f32(vnGHIJ, vmagic_bias);
92 vnKLMN = vsubq_f32(vnKLMN, vmagic_bias);
93
94 // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)).
95 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
96 float32x4_t vt0123 = vmlaq_f32(vz0123, vn0123, vln2_hi);
97 float32x4_t vt4567 = vmlaq_f32(vz4567, vn4567, vln2_hi);
98 float32x4_t vt89AB = vmlaq_f32(vz89AB, vn89AB, vln2_hi);
99 float32x4_t vtCDEF = vmlaq_f32(vzCDEF, vnCDEF, vln2_hi);
100 float32x4_t vtGHIJ = vmlaq_f32(vzGHIJ, vnGHIJ, vln2_hi);
101 float32x4_t vtKLMN = vmlaq_f32(vzKLMN, vnKLMN, vln2_hi);
102
103 vt0123 = vmlaq_f32(vt0123, vn0123, vln2_lo);
104 vt4567 = vmlaq_f32(vt4567, vn4567, vln2_lo);
105 vt89AB = vmlaq_f32(vt89AB, vn89AB, vln2_lo);
106 vtCDEF = vmlaq_f32(vtCDEF, vnCDEF, vln2_lo);
107 vtGHIJ = vmlaq_f32(vtGHIJ, vnGHIJ, vln2_lo);
108 vtKLMN = vmlaq_f32(vtKLMN, vnKLMN, vln2_lo);
109
110 // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2].
111 float32x4_t vp0123 = vmlaq_f32(vc4, vc5, vt0123);
112 float32x4_t vp4567 = vmlaq_f32(vc4, vc5, vt4567);
113 float32x4_t vp89AB = vmlaq_f32(vc4, vc5, vt89AB);
114 float32x4_t vpCDEF = vmlaq_f32(vc4, vc5, vtCDEF);
115 float32x4_t vpGHIJ = vmlaq_f32(vc4, vc5, vtGHIJ);
116 float32x4_t vpKLMN = vmlaq_f32(vc4, vc5, vtKLMN);
117
118 vp0123 = vmlaq_f32(vc3, vp0123, vt0123);
119 vp4567 = vmlaq_f32(vc3, vp4567, vt4567);
120 vp89AB = vmlaq_f32(vc3, vp89AB, vt89AB);
121 vpCDEF = vmlaq_f32(vc3, vpCDEF, vtCDEF);
122 vpGHIJ = vmlaq_f32(vc3, vpGHIJ, vtGHIJ);
123 vpKLMN = vmlaq_f32(vc3, vpKLMN, vtKLMN);
124
125 vp0123 = vmlaq_f32(vc2, vp0123, vt0123);
126 vp4567 = vmlaq_f32(vc2, vp4567, vt4567);
127 vp89AB = vmlaq_f32(vc2, vp89AB, vt89AB);
128 vpCDEF = vmlaq_f32(vc2, vpCDEF, vtCDEF);
129 vpGHIJ = vmlaq_f32(vc2, vpGHIJ, vtGHIJ);
130 vpKLMN = vmlaq_f32(vc2, vpKLMN, vtKLMN);
131
132 vp0123 = vmlaq_f32(vc1, vp0123, vt0123);
133 vp4567 = vmlaq_f32(vc1, vp4567, vt4567);
134 vp89AB = vmlaq_f32(vc1, vp89AB, vt89AB);
135 vpCDEF = vmlaq_f32(vc1, vpCDEF, vtCDEF);
136 vpGHIJ = vmlaq_f32(vc1, vpGHIJ, vtGHIJ);
137 vpKLMN = vmlaq_f32(vc1, vpKLMN, vtKLMN);
138
139 // Reconstruct the exp(-z) value:
140 // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
141 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
142 // = s + (t * s) * p
143 vt0123 = vmulq_f32(vt0123, vs0123);
144 vt4567 = vmulq_f32(vt4567, vs4567);
145 vt89AB = vmulq_f32(vt89AB, vs89AB);
146 vtCDEF = vmulq_f32(vtCDEF, vsCDEF);
147 vtGHIJ = vmulq_f32(vtGHIJ, vsGHIJ);
148 vtKLMN = vmulq_f32(vtKLMN, vsKLMN);
149
150 float32x4_t ve0123 = vmlaq_f32(vs0123, vp0123, vt0123);
151 float32x4_t ve4567 = vmlaq_f32(vs4567, vp4567, vt4567);
152 float32x4_t ve89AB = vmlaq_f32(vs89AB, vp89AB, vt89AB);
153 float32x4_t veCDEF = vmlaq_f32(vsCDEF, vpCDEF, vtCDEF);
154 float32x4_t veGHIJ = vmlaq_f32(vsGHIJ, vpGHIJ, vtGHIJ);
155 float32x4_t veKLMN = vmlaq_f32(vsKLMN, vpKLMN, vtKLMN);
156
157 // Denominator of the sigmoid fraction: 1.0 + exp(-z)
158 float32x4_t vd0123 = vaddq_f32(ve0123, vone);
159 float32x4_t vd4567 = vaddq_f32(ve4567, vone);
160 float32x4_t vd89AB = vaddq_f32(ve89AB, vone);
161 float32x4_t vdCDEF = vaddq_f32(veCDEF, vone);
162 float32x4_t vdGHIJ = vaddq_f32(veGHIJ, vone);
163 float32x4_t vdKLMN = vaddq_f32(veKLMN, vone);
164
165 // Use Newton-Raphson method (2 iterations) to compute reciprocal of denominator.
166 // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
167 // Thus the reciprocal of the denominator never overflows.
168 float32x4_t vr0123 = vrecpeq_f32(vd0123);
169 float32x4_t vr4567 = vrecpeq_f32(vd4567);
170 float32x4_t vr89AB = vrecpeq_f32(vd89AB);
171 float32x4_t vrCDEF = vrecpeq_f32(vdCDEF);
172 float32x4_t vrGHIJ = vrecpeq_f32(vdGHIJ);
173 float32x4_t vrKLMN = vrecpeq_f32(vdKLMN);
174
175 vr0123 = vmulq_f32(vr0123, vrecpsq_f32(vr0123, vd0123));
176 vr4567 = vmulq_f32(vr4567, vrecpsq_f32(vr4567, vd4567));
177 vr89AB = vmulq_f32(vr89AB, vrecpsq_f32(vr89AB, vd89AB));
178 vrCDEF = vmulq_f32(vrCDEF, vrecpsq_f32(vrCDEF, vdCDEF));
179 vrGHIJ = vmulq_f32(vrGHIJ, vrecpsq_f32(vrGHIJ, vdGHIJ));
180 vrKLMN = vmulq_f32(vrKLMN, vrecpsq_f32(vrKLMN, vdKLMN));
181
182 vr0123 = vmulq_f32(vr0123, vrecpsq_f32(vr0123, vd0123));
183 vr4567 = vmulq_f32(vr4567, vrecpsq_f32(vr4567, vd4567));
184 vr89AB = vmulq_f32(vr89AB, vrecpsq_f32(vr89AB, vd89AB));
185 vrCDEF = vmulq_f32(vrCDEF, vrecpsq_f32(vrCDEF, vdCDEF));
186 vrGHIJ = vmulq_f32(vrGHIJ, vrecpsq_f32(vrGHIJ, vdGHIJ));
187 vrKLMN = vmulq_f32(vrKLMN, vrecpsq_f32(vrKLMN, vdKLMN));
188
189 // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z))
190 float32x4_t vf0123 = vmulq_f32(ve0123, vr0123);
191 float32x4_t vf4567 = vmulq_f32(ve4567, vr4567);
192 float32x4_t vf89AB = vmulq_f32(ve89AB, vr89AB);
193 float32x4_t vfCDEF = vmulq_f32(veCDEF, vrCDEF);
194 float32x4_t vfGHIJ = vmulq_f32(veGHIJ, vrGHIJ);
195 float32x4_t vfKLMN = vmulq_f32(veKLMN, vrKLMN);
196
197 // For inputs below denormal cutoff, replace output with +0.0f.
198 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
199 vf0123 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf0123), vcagtq_f32(vx0123, vdenorm_cutoff)));
200 vf4567 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf4567), vcagtq_f32(vx4567, vdenorm_cutoff)));
201 vf89AB = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf89AB), vcagtq_f32(vx89AB, vdenorm_cutoff)));
202 vfCDEF = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfCDEF), vcagtq_f32(vxCDEF, vdenorm_cutoff)));
203 vfGHIJ = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfGHIJ), vcagtq_f32(vxGHIJ, vdenorm_cutoff)));
204 vfKLMN = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfKLMN), vcagtq_f32(vxKLMN, vdenorm_cutoff)));
205
206 // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z)
207 const uint32x4_t vm0123 = vcltq_f32(vx0123, vmovq_n_f32(0.0f));
208 const uint32x4_t vm4567 = vcltq_f32(vx4567, vmovq_n_f32(0.0f));
209 const uint32x4_t vm89AB = vcltq_f32(vx89AB, vmovq_n_f32(0.0f));
210 const uint32x4_t vmCDEF = vcltq_f32(vxCDEF, vmovq_n_f32(0.0f));
211 const uint32x4_t vmGHIJ = vcltq_f32(vxGHIJ, vmovq_n_f32(0.0f));
212 const uint32x4_t vmKLMN = vcltq_f32(vxKLMN, vmovq_n_f32(0.0f));
213
214 vf0123 = vbslq_f32(vm0123, vf0123, vsubq_f32(vone, vf0123));
215 vf4567 = vbslq_f32(vm4567, vf4567, vsubq_f32(vone, vf4567));
216 vf89AB = vbslq_f32(vm89AB, vf89AB, vsubq_f32(vone, vf89AB));
217 vfCDEF = vbslq_f32(vmCDEF, vfCDEF, vsubq_f32(vone, vfCDEF));
218 vfGHIJ = vbslq_f32(vmGHIJ, vfGHIJ, vsubq_f32(vone, vfGHIJ));
219 vfKLMN = vbslq_f32(vmKLMN, vfKLMN, vsubq_f32(vone, vfKLMN));
220
221 vst1q_f32(y, vf0123); y += 4;
222 vst1q_f32(y, vf4567); y += 4;
223 vst1q_f32(y, vf89AB); y += 4;
224 vst1q_f32(y, vfCDEF); y += 4;
225 vst1q_f32(y, vfGHIJ); y += 4;
226 vst1q_f32(y, vfKLMN); y += 4;
227 }
228 for (; n >= 4 * sizeof(float); n -= 4 * sizeof(float)) {
229 const float32x4_t vx = vld1q_f32(x); x += 4;
230
231 // General structure of the algorithm:
232 // / exp(x) / (1 + exp(x)) if x <= 0
233 // f[x] :=
234 // \ 1 - f[-x] if x >= 0
235 //
236 // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x),
237 // then replace result with 1 - f[z] if x <= 0.
238 const float32x4_t vz = vabsq_f32(vx);
239
240 // Compute reduced argument n := round(-z / log(2)).
241 // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the
242 // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
243 // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because
244 // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x)
245 // anyway. We fixup the result for such inputs at the very end of the algorithm.
246 float32x4_t vn = vmlaq_f32(vmagic_bias, vz, vminus_log2e);
247
248 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
249 // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly.
250 const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23));
251
252 // Subtract the large number back to get final n := round(-z / log(2)).
253 vn = vsubq_f32(vn, vmagic_bias);
254
255 // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)).
256 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
257 float32x4_t vt = vmlaq_f32(vz, vn, vln2_hi);
258 vt = vmlaq_f32(vt, vn, vln2_lo);
259
260 // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2].
261 float32x4_t vp = vmlaq_f32(vc4, vc5, vt);
262 vp = vmlaq_f32(vc3, vp, vt);
263 vp = vmlaq_f32(vc2, vp, vt);
264 vp = vmlaq_f32(vc1, vp, vt);
265
266 // Reconstruct the exp(-z) value:
267 // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
268 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
269 // = s + (t * s) * p
270 vt = vmulq_f32(vt, vs);
271 float32x4_t ve = vmlaq_f32(vs, vp, vt);
272
273 // Denominator of the sigmoid fraction: 1.0 + exp(-z)
274 float32x4_t vd = vaddq_f32(ve, vone);
275
276 // Use Newton-Raphson method (2 iterations) to compute reciprocal of denominator.
277 // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
278 // Thus the reciprocal of the denominator never overflows.
279 float32x4_t vr = vrecpeq_f32(vd);
280
281 vr = vmulq_f32(vr, vrecpsq_f32(vr, vd));
282
283 vr = vmulq_f32(vr, vrecpsq_f32(vr, vd));
284
285 // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z))
286 float32x4_t vf = vmulq_f32(ve, vr);
287
288 // For inputs below denormal cutoff, replace output with +0.0f.
289 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
290 vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcagtq_f32(vx, vdenorm_cutoff)));
291
292 // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z)
293 const uint32x4_t vm = vcltq_f32(vx, vmovq_n_f32(0.0f));
294 vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf));
295
296 vst1q_f32(y, vf); y += 4;
297 }
298 if XNN_UNLIKELY(n != 0) {
299 const float32x4_t vx = vld1q_f32(x);
300
301 // General structure of the algorithm:
302 // / exp(x) / (1 + exp(x)) if x <= 0
303 // f[x] :=
304 // \ 1 - f[-x] if x >= 0
305 //
306 // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x),
307 // then replace result with 1 - f[z] if x <= 0.
308 const float32x4_t vz = vabsq_f32(vx);
309
310 // Compute reduced argument n := round(-z / log(2)).
311 // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the
312 // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
313 // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because
314 // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x)
315 // anyway. We fixup the result for such inputs at the very end of the algorithm.
316 float32x4_t vn = vmlaq_f32(vmagic_bias, vz, vminus_log2e);
317
318 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
319 // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly.
320 const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23));
321
322 // Subtract the large number back to get final n := round(-z / log(2)).
323 vn = vsubq_f32(vn, vmagic_bias);
324
325 // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)).
326 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
327 float32x4_t vt = vmlaq_f32(vz, vn, vln2_hi);
328 vt = vmlaq_f32(vt, vn, vln2_lo);
329
330 // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2].
331 float32x4_t vp = vmlaq_f32(vc4, vc5, vt);
332 vp = vmlaq_f32(vc3, vp, vt);
333 vp = vmlaq_f32(vc2, vp, vt);
334 vp = vmlaq_f32(vc1, vp, vt);
335
336 // Reconstruct the exp(-z) value:
337 // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
338 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
339 // = s + (t * s) * p
340 vt = vmulq_f32(vt, vs);
341 float32x4_t ve = vmlaq_f32(vs, vp, vt);
342
343 // Denominator of the sigmoid fraction: 1.0 + exp(-z)
344 float32x4_t vd = vaddq_f32(ve, vone);
345
346 // Use Newton-Raphson method (2 iterations) to compute reciprocal of denominator.
347 // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
348 // Thus the reciprocal of the denominator never overflows.
349 float32x4_t vr = vrecpeq_f32(vd);
350
351 vr = vmulq_f32(vr, vrecpsq_f32(vr, vd));
352
353 vr = vmulq_f32(vr, vrecpsq_f32(vr, vd));
354
355 // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z))
356 float32x4_t vf = vmulq_f32(ve, vr);
357
358 // For inputs below denormal cutoff, replace output with +0.0f.
359 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
360 vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcagtq_f32(vx, vdenorm_cutoff)));
361
362 // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z)
363 const uint32x4_t vm = vcltq_f32(vx, vmovq_n_f32(0.0f));
364 vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf));
365
366 float32x2_t vf_lo = vget_low_f32(vf);
367 if (n & (2 * sizeof(float))) {
368 vst1_f32(y, vf_lo); y += 2;
369 vf_lo = vget_high_f32(vf);
370 }
371 if (n & (1 * sizeof(float))) {
372 vst1_lane_f32(y, vf_lo, 0);
373 }
374 }
375 }
376