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 <math.h>
8
9 #include <immintrin.h>
10
11 #include <xnnpack/math-stubs.h>
12
13
xnn_math_f32_exp__avx512f_rr2_lut32_p2_perm2_scalef(size_t n,const float * input,float * output)14 void xnn_math_f32_exp__avx512f_rr2_lut32_p2_perm2_scalef(
15 size_t n,
16 const float* input,
17 float* output)
18 {
19 assert(n % (16 * sizeof(float)) == 0);
20
21 const __m512 vmagic_bias = _mm512_set1_ps(0x1.800000p18f);
22 const __m512 vlog2e = _mm512_set1_ps(0x1.715476p0f);
23 const __m512 vminus_ln2_hi = _mm512_set1_ps(-0x1.62e43p-1f);
24 const __m512 vminus_ln2_lo = _mm512_set1_ps(0x1.05c61p-29f);
25
26 const __m512 vc1 = _mm512_set1_ps(0x1.0000F6p-0f);
27 const __m512 vc2 = _mm512_set1_ps(0x1.000000p-1f);
28 const __m512 vtable_hi = _mm512_set_ps(
29 0x1.F50766p+0f, 0x1.EA4AFAp+0f, 0x1.DFC974p+0f, 0x1.D5818Ep+0f,
30 0x1.CB720Ep+0f, 0x1.C199BEp+0f, 0x1.B7F770p+0f, 0x1.AE89FAp+0f,
31 0x1.A5503Cp+0f, 0x1.9C4918p+0f, 0x1.93737Cp+0f, 0x1.8ACE54p+0f,
32 0x1.82589Ap+0f, 0x1.7A1148p+0f, 0x1.71F75Ep+0f, 0x1.6A09E6p+0f);
33 const __m512 vtable_lo = _mm512_set_ps(
34 0x1.6247ECp+0f, 0x1.5AB07Ep+0f, 0x1.5342B6p+0f, 0x1.4BFDAEp+0f,
35 0x1.44E086p+0f, 0x1.3DEA64p+0f, 0x1.371A74p+0f, 0x1.306FE0p+0f,
36 0x1.29E9E0p+0f, 0x1.2387A6p+0f, 0x1.1D4874p+0f, 0x1.172B84p+0f,
37 0x1.11301Ep+0f, 0x1.0B5586p+0f, 0x1.059B0Ep+0f, 0x1.000000p+0f);
38
39 for (; n != 0; n -= 16 * sizeof(float)) {
40 const __m512 vx = _mm512_loadu_ps(input);
41
42 // Compute reduced argument n := round(x / log(2), 5).
43 // We do it by adding a large number (magic bias), which cause rounding of result to 5 fractional bits, then
44 // subtracing the large number back. The first addition is combined with multiplication by log2e into a single FMA
45 // instruction. The trick with adding large number is valid only within certain bounds (|x| <= 2**17), but that's
46 // ok, because inputs outside of [-103.97207, 88.72283] underflow or overflow expf(x) anyway. We fixup the result
47 // for such inputs at the very end of the algorithm.
48 __m512 vn = _mm512_fmadd_ps(vx, vlog2e, vmagic_bias);
49
50 // Use the low 5 bits of n (as integer) for table lookup.
51 const __m512 vl = _mm512_permutex2var_ps(vtable_lo, _mm512_castps_si512(vn), vtable_hi);
52
53 // Subtract the large number back to get final n := round(x / log(2), 5).
54 vn = _mm512_sub_ps(vn, vmagic_bias);
55
56 // Compute reduced argument t := x - n * log(2).
57 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
58 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
59 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
60
61 // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/64, log(2)/64].
62 // p = l * (1 + t * (c1 + t * c2))
63 // = l + l * t * (c1 + t * c2)
64 __m512 vp = _mm512_fmadd_ps(vt, vc2, vc1);
65 vt = _mm512_mul_ps(vt, vl);
66 vp = _mm512_fmadd_ps(vt, vp, vl);
67
68 // Reconstruct the final value as f = exp2(floor(n)) * p.
69 const __m512 vf = _mm512_scalef_ps(vp, vn);
70 _mm512_storeu_ps(output, vf);
71
72 input += 16;
73 output += 16;
74 }
75 }
76