1 // Copyright 2020 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_f32_expm1minus__avx512f_rr1_p6(size_t n,const float * input,float * output)14 void xnn_math_f32_expm1minus__avx512f_rr1_p6(
15 size_t n,
16 const float* input,
17 float* output)
18 {
19 assert(n % (16 * sizeof(float)) == 0);
20
21 // The largest x for which expm1f(x) is saturated at -1.0f.
22 const __m512 vsat_cutoff = _mm512_set1_ps(-0x1.154246p+4f);
23 // Large number such that ulp(magic bias) == 1 and magic bias === 127 mod 2**22.
24 const __m512 vmagic_bias = _mm512_set1_ps(0x1.8000FEp23f);
25 const __m512 vlog2e = _mm512_set1_ps(0x1.715476p+0f);
26 const __m512 vminus_ln2 = _mm512_set1_ps(-0x1.62E43p-1f);
27 // Coefficient of polynomial approximation
28 // exp(t) - 1 ~ t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))
29 // on [-log(2)/2, log(2)/2]
30 const __m512 vc6 = _mm512_set1_ps(0x1.6b7338p-10f);
31 const __m512 vc5 = _mm512_set1_ps(0x1.12278Ep-7f);
32 const __m512 vc4 = _mm512_set1_ps(0x1.555716p-5f);
33 const __m512 vc3 = _mm512_set1_ps(0x1.5554B0p-3f);
34 const __m512 vc2 = _mm512_set1_ps(0x1.FFFFFEp-2f);
35 const __m512 vone = _mm512_set1_ps(1.0f);
36
37 for (; n != 0; n -= 16 * sizeof(float)) {
38 __m512 vx = _mm512_loadu_ps(input);
39
40 // The function saturates at -1 for large negative inputs: expm1f(x) == -1.0f for x <= sat_cutoff ~= -17.328680.
41 // To guarantee this behaviour, we clip input at sat_cutoff, and leverage the fact that for our implementation
42 // expm1f(sat_cutoff) == -1.0f. The order of operands in the [V]MAXPS instruction matters: it ensures that NaN
43 // inputs are passed unchanged.
44 vx = _mm512_max_ps(vsat_cutoff, vx);
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 first addition is combined with multiplication by log2e into a single FMA
49 // instruction. The trick with adding large number is valid only within certain bounds (|x / log(2)| <= 2**22,
50 // i.e. |x| <= 0x1.62E43p+21 = 2907270.0), but that is acceptable, because inputs x are restricted to
51 // [-17.328680, 0].
52 // Note that addition-subtraction of the large number doesn't cause overflow for inputs in this range.
53 __m512 vn = _mm512_fmadd_ps(vx, vlog2e, vmagic_bias);
54
55 // Create a floating-point number s (scale) such that s == 2**n for valid inputs, i.e.
56 // -17.328680 <= x <= 0.0, and -25 <= n <= 0 accordingly.
57 // For NaN inputs, s would have zero mantissa and can have arbitrary sign and exponent, depending on the input
58 // NaN payload. In these cases, n and t are NaNs with the same payload as input while s is non-NaN, and thus
59 // input payload would be propagated in all computations.
60 const __m512 vs = _mm512_castsi512_ps(_mm512_slli_epi32(_mm512_castps_si512(vn), 23));
61
62 // Subtract the large number back to get final n := round(x / log(2)).
63 vn = _mm512_sub_ps(vn, vmagic_bias);
64
65 // Compute reduced argument t := x - n * log(2).
66 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2, vx);
67
68 // Compute degree-6 polynomial approximation for exp(t) - 1 on [-log(2)/2, log(2)/2].
69 // P(t) = t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))
70 // = t + t * (t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6))))) = t + t * p
71 __m512 vp = _mm512_fmadd_ps(vc6, vt, vc5);
72 vp = _mm512_fmadd_ps(vp, vt, vc4);
73 vp = _mm512_fmadd_ps(vp, vt, vc3);
74 vp = _mm512_fmadd_ps(vp, vt, vc2);
75 vp = _mm512_mul_ps(vp, vt);
76
77 // Reconstruct the exp(x) - 1 value:
78 // exp(x) - 1 = s * (1 + t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))) - 1
79 // = (s - 1) + s * (t + t * p)
80 // = ((t * s) + (t * s) * p) + (s - 1)
81 vt = _mm512_mul_ps(vt, vs);
82 const __m512 vsm1 = _mm512_sub_ps(vs, vone);
83 vp = _mm512_fmadd_ps(vp, vt, vt);
84 const __m512 vf = _mm512_add_ps(vp, vsm1);
85
86 _mm512_storeu_ps(output, vf);
87
88 input += 16;
89 output += 16;
90 }
91 }
92