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 <math.h>
8
9 #include <immintrin.h>
10
11 #include <xnnpack/math-stubs.h>
12
13
xnn_math_f16_expminus__avx2_rr1_p3(size_t n,const void * input,void * output)14 void xnn_math_f16_expminus__avx2_rr1_p3(
15 size_t n,
16 const void* input,
17 void* output)
18 {
19 assert(n % (8 * sizeof(uint16_t)) == 0);
20
21 // Large number such that ulp(magic bias) == 1 and magic bias === 127 mod 2**22.
22 const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
23 const __m256 vlog2e = _mm256_set1_ps(0x1.715476p0f);
24 const __m256 vminus_ln2 = _mm256_set1_ps(-0x1.62E43p-1f);
25 // Coefficient of polynomial approximation of
26 // exp(t) ~ 1 + t * (c1 + t * (c2 + t * c3)) on [-log(2)/2, log(2)/2]
27 const __m256 vc3 = _mm256_set1_ps(0x1.5249A6p-3f);
28 const __m256 vc2 = _mm256_set1_ps(0x1.021D60p-1f);
29 const __m256 vc1 = _mm256_set1_ps(0x1.000CD6p+0f);
30 // The smallest x for which exph(x) is normalized.
31 const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.368000p+3f);
32
33 const uint16_t* i = (const uint16_t*) input;
34 uint16_t* o = (uint16_t*) output;
35 for (; n != 0; n -= 8 * sizeof(float)) {
36 const __m256 vx = _mm256_cvtph_ps(_mm_loadu_si128((const __m128i*) i));
37 i += 8;
38
39 // Compute reduced argument n := round(x / log(2)).
40 // We do it by adding a large number (magic bias) to the product x * (1/log(2)), which cause rounding of the
41 // result to an integer, then subtracing the large number back. The first addition is combined with multiplication
42 // by log2e into a single FMA instruction. The trick with adding large number is valid only within certain bounds
43 // (|x / log(2)| <= 2**9, i.e. |x| <= 0x1.630p+8 = 355.0), but that is acceptable, because inputs x outside
44 // of [-9.703125, 0] underflow expf(x). We fixup the result for such inputs at the very end of the algorithm.
45 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
46
47 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
48 // -9.703125 <= x <= 0.0, and -14 <= n <= 0 accordingly.
49 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
50
51 // Subtract the large number back to get final n := round(x / log(2)) as a floating-point number.
52 vn = _mm256_sub_ps(vn, vmagic_bias);
53
54 // Compute reduced argument t := x - n * log(2).
55 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vx);
56
57 // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]:
58 // P(t) = 1 + t * (c1 + t * (c2 + t * c3)) = 1 + t * p
59 __m256 vp = _mm256_fmadd_ps(vc3, vt, vc2);
60 vp = _mm256_fmadd_ps(vp, vt, vc1);
61
62 // Reconstruct the exp(x) value:
63 // exp(x) = s * (1 + t * (c1 + t * c2))
64 // = s + (t * s) * (c1 + t * c2)
65 // = s + (t * s) * p
66 vt = _mm256_mul_ps(vt, vs);
67 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
68
69 // For inputs below denormal cutoff, replace output with +0.0f.
70 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
71 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
72 _mm_storeu_si128((__m128i*) o, _mm256_cvtps_ph(vf, _MM_FROUND_NO_EXC));
73 o += 8;
74 }
75 }
76