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_lut16_p3_perm_scalef(size_t n,const float * input,float * output)14 void xnn_math_f32_exp__avx512f_rr2_lut16_p3_perm_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(0x1.800000p19f);
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 vc2 = _mm512_set1_ps(0x1.00021Ep-1f);
27 const __m512 vc3 = _mm512_set1_ps(0x1.55559Ap-3f);
28 const __m512 vtable = _mm512_set_ps(
29 0x1.EA4AFAp+0f, 0x1.D5818Ep+0f, 0x1.C199BEp+0f, 0x1.AE89FAp+0f,
30 0x1.9C4918p+0f, 0x1.8ACE54p+0f, 0x1.7A1148p+0f, 0x1.6A09E6p+0f,
31 0x1.5AB07Ep+0f, 0x1.4BFDAEp+0f, 0x1.3DEA64p+0f, 0x1.306FE0p+0f,
32 0x1.2387A6p+0f, 0x1.172B84p+0f, 0x1.0B5586p+0f, 0x1.000000p+0f);
33
34 for (; n != 0; n -= 16 * sizeof(float)) {
35 const __m512 vx = _mm512_loadu_ps(input);
36
37 // Compute reduced argument n := round(x / log(2), 4).
38 // We do it by adding a large number (magic bias), which cause rounding of result to an 4 fractional bits, then
39 // subtracing the large number back. The first addition is combined with multiplication by log2e into a single
40 // FMA instruction. The trick with adding large number is valid only within certain bounds (|x| <= 2**18), but
41 // thats ok, because inputs outside of [-103.97207, 88.72283] underflow or overflow expf(x) anyway. We fixup
42 // the result for such inputs at the very end of the algorithm.
43 __m512 vn = _mm512_fmadd_ps(vx, vlog2e, vmagic_bias);
44
45 // Use the low 4 bits of n (as integer) for table lookup.
46 const __m512 vl = _mm512_permutexvar_ps(_mm512_castps_si512(vn), vtable);
47
48 // Subtract the large number back to get final n := round(x / log(2), 4).
49 vn = _mm512_sub_ps(vn, vmagic_bias);
50
51 // Compute reduced argument t := x - n * log(2).
52 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
53 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
54 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
55
56 // Compute degree-3 polynomial approximation for exp(t) on [-log(2)/32, log(2)/32].
57 // P = l * (1 + t * (1 + t * (c2 + t * c3)))
58 // = l + l * (t + t * (t * (c2 + t * c3)))
59 __m512 vp = _mm512_fmadd_ps(vt, vc3, vc2);
60 vp = _mm512_mul_ps(vp, vt);
61 vp = _mm512_fmadd_ps(vt, vp, vt);
62 vp = _mm512_fmadd_ps(vl, vp, vl);
63
64 // Reconstruct the final value as f = exp2(floor(n)) * p.
65 const __m512 vf = _mm512_scalef_ps(vp, vn);
66 _mm512_storeu_ps(output, vf);
67
68 input += 16;
69 output += 16;
70 }
71 }
72