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_expm1minus__avx2_rr1_p3(size_t n,const void * input,void * output)14 void xnn_math_f16_expm1minus__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 // The largest x for which expm1f(x) is saturated at -1.0f.
22 const __m256 vsat_cutoff = _mm256_set1_ps(-0x1.0A4000p+3f);
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
28 // exp(t) - 1 ~ t * (1 + t * (c2 + t * c3))
29 // on [-log(2)/2, log(2)/2]
30 const __m256 vc3 = _mm256_set1_ps(0x1.5554DCp-3f);
31 const __m256 vc2 = _mm256_set1_ps(0x1.01EBB2p-1f);
32 const __m256 vc1 = _mm256_set1_ps(0x1.0002F2p0f);
33 const __m256 vone = _mm256_set1_ps(1.0f);
34
35 const uint16_t* i = (const uint16_t*) input;
36 uint16_t* o = (uint16_t*) output;
37 for (; n != 0; n -= 8 * sizeof(uint16_t)) {
38 __m256 vx = _mm256_cvtph_ps(_mm_loadu_si128((const __m128i*) i));
39 i += 8;
40
41 // The function saturates at -1 for large negative inputs: expm1h(x) == -1.0h for x <= sat_cutoff ~= -8.3203125.
42 // To guarantee this behaviour, we clip input at sat_cutoff, and leverage the fact that for our implementation
43 // expm1m(sat_cutoff) == -1.0f. NaN inputs are passed unchanged.
44 vx = _mm256_max_ps(vx, vsat_cutoff);
45
46 // Compute reduced argument n := round(x / log(2)).
47 // We do it by adding a large number (magic bias), which cause rounding of the result to integer, then subtracing
48 // the large number back. The addition is combined with multiplication by log2e into a single FMA instruction. The
49 // trick with adding large number is valid only within certain bounds (|x / log(2)| <= 2**9, i.e.
50 // |x| <= 0x1.630p+8 = 355.0), but that is acceptable, because inputs x are restricted to [-8.3203125, 0].
51 // Note that addition-subtraction of the large number doesn't cause overflow for inputs in this range.
52 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
53
54 // Create a floating-point number s (scale) such that s == 2**n for valid inputs, i.e.
55 // -8.3203125 <= x <= 0.0, and -12 <= n <= 0 accordingly.
56 // For NaN inputs, s would have zero mantissa and can have arbitrary sign and exponent, depending on the input
57 // NaN payload. In these cases, n and t are NaNs with the same payload as input while s is non-NaN, and thus
58 // input payload would be propagated in all computations.
59 __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
60
61 // Subtract the large number back to get final n := round(x / log(2)).
62 vn = _mm256_sub_ps(vn, vmagic_bias);
63
64 // Compute reduced argument t := x - n * log(2).
65 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vx);
66
67 // Compute degree-3 polynomial approximation for exp(t) - 1 on [-log(2)/2, log(2)/2].
68 // P(t) = t * (c1 + t * (c2 + t * c3))
69 // = t * p
70 __m256 vp = _mm256_fmadd_ps(vc3, vt, vc2);
71 vp = _mm256_fmadd_ps(vp, vt, vc1);
72
73 // Reconstruct the exp(x) - 1 value:
74 // exp(x) - 1 = s * (1 + t * p) - 1
75 // = (s - 1) + (s * t) * p
76 // = (t * s) * p + (s - 1)
77 vt = _mm256_mul_ps(vt, vs);
78 vs = _mm256_sub_ps(vs, vone);
79 const __m256 vf = _mm256_fmadd_ps(vp, vt, vs);
80
81 _mm_storeu_si128((__m128i*) o, _mm256_cvtps_ph(vf, _MM_FROUND_NO_EXC));
82 o += 8;
83 }
84 }
85