1 // Copyright 2022 Google LLC
2 //
3 // This source code is licensed under the BSD-style license found in the
4 // LICENSE file in the root directory of this source tree.
5
6 #include <assert.h>
7 #include <stddef.h>
8
9 #include <immintrin.h>
10
11 #include <xnnpack/math-stubs.h>
12
13
xnn_math_f16_sigmoid__avx2_rr1_p2_div(size_t n,const void * input,void * output)14 void xnn_math_f16_sigmoid__avx2_rr1_p2_div(
15 size_t n,
16 const void* input,
17 void* output)
18 {
19 assert(n % (8 * sizeof(uint16_t)) == 0);
20
21 // Floating-point mask with only the sign bit set
22 const __m256 vsign_mask = _mm256_set1_ps(-0.0f);
23 // Large number such that ulp(magic bias) == 1 and magic bias === 127 mod 2**22.
24 const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
25 const __m256 vlog2e = _mm256_set1_ps(0x1.715476p0f);
26 const __m256 vminus_ln2 = _mm256_set1_ps(-0x1.62E43p-1f);
27 // Coefficient of polynomial approximation of
28 // exp(t) ~ 1 + t * (c1 + t * c2) on [-log(2)/2, log(2)/2]
29 const __m256 vc2 = _mm256_set1_ps(0x1.FF3A32p-2f);
30 const __m256 vc1 = _mm256_set1_ps(0x1.039E10p+0f);
31 const __m256 vone = _mm256_set1_ps(1.0f);
32 // The smallest x for which sigmoidh(x) is normalized.
33 // This number is also the smallest x for which exph(x) is normalized.
34 const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.368000p+3f);
35
36 const uint16_t* i = (const uint16_t*) input;
37 uint16_t* o = (uint16_t*) output;
38 for (; n != 0; n -= 8 * sizeof(uint16_t)) {
39 const __m256 vx = _mm256_cvtph_ps(_mm_loadu_si128((const __m128i*) i));
40 i += 8;
41
42 // General structure of the algorithm:
43 //
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), then replace result with 1 - f[z] if x >= 0.
49 const __m256 vz = _mm256_or_ps(vx, vsign_mask);
50
51 // Compute reduced argument n := round(z / log(2)).
52 // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the
53 // result to an integer, then subtracing the large number back. The first addition is combined with multiplication
54 // by log2e into a single FMA instruction. The trick with adding large number is valid only within certain bounds
55 // (|x / log(2)| <= 2**9, i.e. |z| <= 0x1.630p+8 = 355.0), but that is acceptable, because inputs x outside
56 // of [-9.703125, 8.3125] (i.e. z outside [9.703125, 0]) underflow or saturate sigmoidh(x). We fixup the result for
57 // such inputs at the very end of the algorithm.
58 __m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias);
59
60 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
61 // -9.703125 <= z <= 0.0, and -14 <= n <= 0 accordingly.
62 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
63
64 // Subtract the large number back to get the final n := round(z / log(2)) as a floating-point number.
65 vn = _mm256_sub_ps(vn, vmagic_bias);
66
67 // Compute reduced argument t := z - n * log(2).
68 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
69 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz);
70
71 // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
72 // P(t) = 1 + t * (c1 + t * c2) = 1 + t * p
73 const __m256 vp = _mm256_fmadd_ps(vc2, vt, vc1);
74
75 // Reconstruct the exp(z) value:
76 // e = s * (1 + t * (c1 + t * c2))
77 // = s + (t * s) * (c1 + t * c2)
78 // = s + (t * s) * p
79 vt = _mm256_mul_ps(vt, vs);
80 const __m256 ve = _mm256_fmadd_ps(vt, vp, vs);
81
82 // Denominator of the sigmoid fraction: 1.0 + exp(z)
83 const __m256 vd = _mm256_add_ps(ve, vone);
84
85 // Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z))
86 __m256 vf = _mm256_div_ps(ve, vd);
87
88 // For inputs below denormal cutoff, replace output with +0.0f.
89 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
90 vf = _mm256_andnot_ps(_mm256_cmp_ps(vz, vdenorm_cutoff, _CMP_LT_OS), vf);
91
92 // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
93 vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx);
94
95 _mm_storeu_si128((__m128i*) o, _mm256_cvtps_ph(vf, _MM_FROUND_NO_EXC));
96 o += 8;
97 }
98 }
99