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1 // 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 
18 extern XNN_INTERNAL const float xnn_table_exp2_k_over_64[64];
19 
xnn_f32_raddstoreexpminusmax_ukernel__neonfma_lut64_p2_x16_acc2(size_t elements,const float * input,float * output,float * sum,float max)20 void xnn_f32_raddstoreexpminusmax_ukernel__neonfma_lut64_p2_x16_acc2(
21     size_t elements,
22     const float* input,
23     float* output,
24     float* sum,
25     float max)
26 {
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   const float32x4_t vminus_ln2_o64_hi = vmovq_n_f32(-0x1.62e43p-7f);
34   const float32x4_t vminus_ln2_o64_lo = vmovq_n_f32(0x1.05c61p-35f);
35 
36   const float32x4_t vc2 = vmovq_n_f32(0x1.FFFF0Ap-2f);
37 
38   const int32x4_t vindex_mask = vmovq_n_s32(INT32_C(0x3F));
39 
40   const float32x4_t vi_max = vdupq_n_f32(max);
41 
42   float32x4_t vacc0 = vmovq_n_f32(0.0f);
43   float32x4_t vacc1 = 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 = vfmaq_f32(vmagic_bias, vx0123, vlog2e_x64);
65     float32x4_t vn4567 = vfmaq_f32(vmagic_bias, vx4567, vlog2e_x64);
66     float32x4_t vn89AB = vfmaq_f32(vmagic_bias, vx89AB, vlog2e_x64);
67     float32x4_t vnCDEF = vfmaq_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 = vfmaq_f32(vx0123, vn0123, vminus_ln2_o64_hi);
135     float32x4_t vt4567 = vfmaq_f32(vx4567, vn4567, vminus_ln2_o64_hi);
136     float32x4_t vt89AB = vfmaq_f32(vx89AB, vn89AB, vminus_ln2_o64_hi);
137     float32x4_t vtCDEF = vfmaq_f32(vxCDEF, vnCDEF, vminus_ln2_o64_hi);
138 
139     vt0123 = vfmaq_f32(vt0123, vn0123, vminus_ln2_o64_lo);
140     vt4567 = vfmaq_f32(vt4567, vn4567, vminus_ln2_o64_lo);
141     vt89AB = vfmaq_f32(vt89AB, vn89AB, vminus_ln2_o64_lo);
142     vtCDEF = vfmaq_f32(vtCDEF, vnCDEF, vminus_ln2_o64_lo);
143 
144     // Compute degree-2 polynomial approxiatmion for exp(t) on [-log(2)/128, log(2)/128].
145     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 = vfmaq_f32(vt0123, vt0123, vp0123);
151     vp4567 = vfmaq_f32(vt4567, vt4567, vp4567);
152     vp89AB = vfmaq_f32(vt89AB, vt89AB, vp89AB);
153     vpCDEF = vfmaq_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 = vfmaq_f32(vs0123, vs0123, vp0123);
161     float32x4_t vf4567 = vfmaq_f32(vs4567, vs4567, vp4567);
162     float32x4_t vf89AB = vfmaq_f32(vs89AB, vs89AB, vp89AB);
163     float32x4_t vfCDEF = vfmaq_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   // Add up all accumulators to vacc0
185   vacc0 = vaddq_f32(vacc0, vacc1);
186 
187   float32x4_t vacc = vacc0;
188   for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
189     // Load 4 inputs at a time.
190     const float32x4_t vi = vld1q_f32(input); input += 4;
191 
192     // Subtract maximum input x := i - i_max. This implies x <= 0.
193     const float32x4_t vx = vsubq_f32(vi, vi_max);
194 
195     // Compute reduced argument n := round(x * 64 / log(2)).
196     // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing
197     // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
198     // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e.
199     // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0]
200     // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the
201     // algorithm.
202     float32x4_t vn = vfmaq_f32(vmagic_bias, vx, vlog2e_x64);
203 
204     // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized,
205     // 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
206     // e := int(n / 64). We create s in two steps:
207     // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the
208     //    fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
209     // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized
210     //    number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0,
211     //    and thus the adjusted exponent is not lower than -126.
212     //
213     // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent).
214     const int32x4_t ve = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn), vmovq_n_s32(INT32_C(0x3F))), 17);
215 
216     // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64).
217     const uint64x2_t vidx = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn), vindex_mask));
218     const uint64_t vidx_lo = vgetq_lane_u64(vidx, 0);
219     const uint64_t vidx_hi = vgetq_lane_u64(vidx, 1);
220     float32x2_t vl_lo = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_lo]);
221     float32x2_t vl_hi = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_hi]);
222     vl_lo = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_lo >> 32)], vl_lo, 1);
223     vl_hi = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_hi >> 32)], vl_hi, 1);
224     const float32x4_t vl = vcombine_f32(vl_lo, vl_hi);
225     // Adjust exponent of the value l fetched from the table to get the final s value.
226     const float32x4_t vs = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl), ve));
227 
228     // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number.
229     vn = vsubq_f32(vn, vmagic_bias);
230 
231     // Compute reduced argument t := x - n * log(2) / 64.
232     // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy.
233     float32x4_t vt = vfmaq_f32(vx, vn, vminus_ln2_o64_hi);
234     vt = vfmaq_f32(vt, vn, vminus_ln2_o64_lo);
235 
236     // Compute degree-2 polynomial approxiatmion for exp(t) on [-log(2)/128, log(2)/128].
237     float32x4_t vp = vmulq_f32(vt, vc2);
238     vp = vfmaq_f32(vt, vt, vp);
239 
240     // Reconstruct the final f value:
241     //   f = s * (1 + t * (1 + t * c2))
242     //     = s * (1 + t + t * (t * c2))
243     //     = s + s * (t + t * (t * c2))
244     //     = s + s * p
245     float32x4_t vf = vfmaq_f32(vs, vs, vp);
246 
247     // For inputs below denormal cutoff, replace output with +0.0f.
248     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
249     vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff)));
250 
251     // Store 4 outputs at a time.
252     vst1q_f32(output, vf); output += 4;
253 
254     // Accumulate computed exponents.
255     vacc = vaddq_f32(vacc, vf);
256   }
257 #if XNN_ARCH_ARM64
258   float vacc_lo = vaddvq_f32(vacc);
259 #else
260   float32x2_t vacc_lo = vadd_f32(vget_high_f32(vacc), vget_low_f32(vacc));
261 #endif
262   if (elements != 0) {
263     assert(elements >= 1 * sizeof(float));
264     assert(elements <= 3 * sizeof(float));
265     // Load 4 inputs at a time.
266     const float32x4_t vi = vld1q_f32(input); input += 4;
267 
268     // Subtract maximum input x := i - i_max. This implies x <= 0.
269     const float32x4_t vx = vsubq_f32(vi, vi_max);
270 
271     // Compute reduced argument n := round(x * 64 / log(2)).
272     // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing
273     // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
274     // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e.
275     // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0]
276     // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the
277     // algorithm.
278     float32x4_t vn = vfmaq_f32(vmagic_bias, vx, vlog2e_x64);
279 
280     // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized,
281     // 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
282     // e := int(n / 64). We create s in two steps:
283     // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the
284     //    fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
285     // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized
286     //    number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0,
287     //    and thus the adjusted exponent is not lower than -126.
288     //
289     // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent).
290     const int32x4_t ve = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn), vmovq_n_s32(INT32_C(0x3F))), 17);
291 
292     // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64).
293     const uint64x2_t vidx = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn), vindex_mask));
294     const uint64_t vidx_lo = vgetq_lane_u64(vidx, 0);
295     const uint64_t vidx_hi = vgetq_lane_u64(vidx, 1);
296     float32x2_t vl_lo = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_lo]);
297     float32x2_t vl_hi = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_hi]);
298     vl_lo = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_lo >> 32)], vl_lo, 1);
299     vl_hi = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_hi >> 32)], vl_hi, 1);
300     const float32x4_t vl = vcombine_f32(vl_lo, vl_hi);
301     // Adjust exponent of the value l fetched from the table to get the final s value.
302     const float32x4_t vs = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl), ve));
303 
304     // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number.
305     vn = vsubq_f32(vn, vmagic_bias);
306 
307     // Compute reduced argument t := x - n * log(2) / 64.
308     // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy.
309     float32x4_t vt = vfmaq_f32(vx, vn, vminus_ln2_o64_hi);
310     vt = vfmaq_f32(vt, vn, vminus_ln2_o64_lo);
311 
312     // Compute degree-2 polynomial approxiatmion for exp(t) on [-log(2)/128, log(2)/128].
313     float32x4_t vp = vmulq_f32(vt, vc2);
314     vp = vfmaq_f32(vt, vt, vp);
315 
316     // Reconstruct the final f value:
317     //   f = s * (1 + t * (1 + t * c2))
318     //     = s * (1 + t + t * (t * c2))
319     //     = s + s * (t + t * (t * c2))
320     //     = s + s * p
321     float32x4_t vf = vfmaq_f32(vs, vs, vp);
322 
323     // For inputs below denormal cutoff, replace output with +0.0f.
324     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
325     vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff)));
326 
327     float32x2_t vf_lo = vget_low_f32(vf);
328     if (elements & (2 * sizeof(float))) {
329       // Store 2 outputs at a time.
330       vst1_f32(output, vf_lo); output += 2;
331 
332       // Accumulate 2 computed exponents.
333       #if XNN_ARCH_ARM64
334         vacc_lo += vaddv_f32(vf_lo);
335       #else
336         vacc_lo = vadd_f32(vacc_lo, vf_lo);
337       #endif
338 
339       vf_lo = vget_high_f32(vf);
340     }
341     if (elements & (1 * sizeof(float))) {
342       // Store 1 output at a time.
343       vst1_lane_f32(output, vf_lo, 0);
344 
345       // Accumulate 1 computed exponent.
346       #if XNN_ARCH_ARM64
347         vacc_lo += vget_lane_f32(vf_lo, 0);
348       #else
349         vacc_lo = vadd_f32(vacc_lo, vreinterpret_f32_u64(vshl_n_u64(vreinterpret_u64_f32(vf_lo), 32)));
350       #endif
351     }
352   }
353   // Reduce 4 elements in the SIMD register
354 #if XNN_ARCH_ARM64
355   *sum = vacc_lo;
356 #else
357   vst1_lane_f32(sum, vpadd_f32(vacc_lo, vacc_lo), 0);
358 #endif
359 }
360