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__neonfma_rr1_p5_nr2recps_x4(size_t n,const float * x,float * y,const void * params)18 void xnn_f32_sigmoid_ukernel__neonfma_rr1_p5_nr2recps_x4(
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 const float32x4_t vln2 = vmovq_n_f32(0x1.62E43p-1f);
32 const float32x4_t vone = vmovq_n_f32(1.0f);
33
34 const float32x4_t vc1 = vmovq_n_f32(-0x1.FFFFF6p-1f);
35 const float32x4_t vc2 = vmovq_n_f32(0x1.FFFDC6p-2f);
36 const float32x4_t vc3 = vmovq_n_f32(-0x1.555A80p-3f);
37 const float32x4_t vc4 = vmovq_n_f32(0x1.573A1Ap-5f);
38 const float32x4_t vc5 = vmovq_n_f32(-0x1.0F9F9Cp-7f);
39
40 for (; n >= 4 * sizeof(float); n -= 4 * sizeof(float)) {
41 const float32x4_t vx = vld1q_f32(x); x += 4;
42
43 // General structure of the algorithm:
44 // / exp(x) / (1 + exp(x)) if x <= 0
45 // f[x] :=
46 // \ 1 - f[-x] if x >= 0
47 //
48 // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x),
49 // then replace result with 1 - f[z] if x <= 0.
50 const float32x4_t vz = vabsq_f32(vx);
51
52 // Compute reduced argument n := round(-z / log(2)).
53 // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the
54 // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
55 // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because
56 // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x)
57 // anyway. We fixup the result for such inputs at the very end of the algorithm.
58 float32x4_t vn = vfmaq_f32(vmagic_bias, vz, vminus_log2e);
59
60 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
61 // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly.
62 const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23));
63
64 // Subtract the large number back to get final n := round(-z / log(2)).
65 vn = vsubq_f32(vn, vmagic_bias);
66
67 // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)).
68 float32x4_t vt = vfmaq_f32(vz, vn, vln2);
69
70 // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2].
71 float32x4_t vp = vfmaq_f32(vc4, vc5, vt);
72 vp = vfmaq_f32(vc3, vp, vt);
73 vp = vfmaq_f32(vc2, vp, vt);
74 vp = vfmaq_f32(vc1, vp, vt);
75
76 // Reconstruct the exp(-z) value:
77 // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
78 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
79 // = s + (t * s) * p
80 vt = vmulq_f32(vt, vs);
81 float32x4_t ve = vfmaq_f32(vs, vp, vt);
82
83 // Denominator of the sigmoid fraction: 1.0 + exp(-z)
84 float32x4_t vd = vaddq_f32(ve, vone);
85
86 // Use Newton-Raphson method (2 iterations) to compute reciprocal of denominator.
87 // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
88 // Thus the reciprocal of the denominator never overflows.
89 float32x4_t vr = vrecpeq_f32(vd);
90
91 vr = vmulq_f32(vr, vrecpsq_f32(vr, vd));
92
93 vr = vmulq_f32(vr, vrecpsq_f32(vr, vd));
94
95 // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z))
96 float32x4_t vf = vmulq_f32(ve, vr);
97
98 // For inputs below denormal cutoff, replace output with +0.0f.
99 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
100 vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcagtq_f32(vx, vdenorm_cutoff)));
101
102 // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z)
103 const uint32x4_t vm = vcltq_f32(vx, vmovq_n_f32(0.0f));
104 vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf));
105
106 vst1q_f32(y, vf); y += 4;
107 }
108 if XNN_UNLIKELY(n != 0) {
109 const float32x4_t vx = vld1q_f32(x);
110
111 // General structure of the algorithm:
112 // / exp(x) / (1 + exp(x)) if x <= 0
113 // f[x] :=
114 // \ 1 - f[-x] if x >= 0
115 //
116 // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x),
117 // then replace result with 1 - f[z] if x <= 0.
118 const float32x4_t vz = vabsq_f32(vx);
119
120 // Compute reduced argument n := round(-z / log(2)).
121 // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the
122 // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
123 // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because
124 // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x)
125 // anyway. We fixup the result for such inputs at the very end of the algorithm.
126 float32x4_t vn = vfmaq_f32(vmagic_bias, vz, vminus_log2e);
127
128 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
129 // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly.
130 const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23));
131
132 // Subtract the large number back to get final n := round(-z / log(2)).
133 vn = vsubq_f32(vn, vmagic_bias);
134
135 // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)).
136 float32x4_t vt = vfmaq_f32(vz, vn, vln2);
137
138 // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2].
139 float32x4_t vp = vfmaq_f32(vc4, vc5, vt);
140 vp = vfmaq_f32(vc3, vp, vt);
141 vp = vfmaq_f32(vc2, vp, vt);
142 vp = vfmaq_f32(vc1, vp, vt);
143
144 // Reconstruct the exp(-z) value:
145 // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
146 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
147 // = s + (t * s) * p
148 vt = vmulq_f32(vt, vs);
149 float32x4_t ve = vfmaq_f32(vs, vp, vt);
150
151 // Denominator of the sigmoid fraction: 1.0 + exp(-z)
152 float32x4_t vd = vaddq_f32(ve, vone);
153
154 // Use Newton-Raphson method (2 iterations) to compute reciprocal of denominator.
155 // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
156 // Thus the reciprocal of the denominator never overflows.
157 float32x4_t vr = vrecpeq_f32(vd);
158
159 vr = vmulq_f32(vr, vrecpsq_f32(vr, vd));
160
161 vr = vmulq_f32(vr, vrecpsq_f32(vr, vd));
162
163 // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z))
164 float32x4_t vf = vmulq_f32(ve, vr);
165
166 // For inputs below denormal cutoff, replace output with +0.0f.
167 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
168 vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcagtq_f32(vx, vdenorm_cutoff)));
169
170 // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z)
171 const uint32x4_t vm = vcltq_f32(vx, vmovq_n_f32(0.0f));
172 vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf));
173
174 float32x2_t vf_lo = vget_low_f32(vf);
175 if (n & (2 * sizeof(float))) {
176 vst1_f32(y, vf_lo); y += 2;
177 vf_lo = vget_high_f32(vf);
178 }
179 if (n & (1 * sizeof(float))) {
180 vst1_lane_f32(y, vf_lo, 0);
181 }
182 }
183 }
184