1 // Copyright 2019 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
8 #include <immintrin.h>
9
10 #include <xnnpack/math-stubs.h>
11
12
xnn_math_f32_exp__avx512f_rr2_p5_scalef(size_t n,const float * input,float * output)13 void xnn_math_f32_exp__avx512f_rr2_p5_scalef(
14 size_t n,
15 const float* input,
16 float* output)
17 {
18 assert(n % (16 * sizeof(float)) == 0);
19
20 const __m512 vlog2e = _mm512_set1_ps(0x1.715476p+0f);
21
22 // The smallest x for which expf(x) is non-zero.
23 const __m512 vzero_cutoff = _mm512_set1_ps(-0x1.9FE368p+6f);
24 // The largest x for which expf(x) is finite.
25 const __m512 vinf_cutoff = _mm512_set1_ps(0x1.62E42Ep+6f);
26
27 const __m512 vminus_ln2_hi = _mm512_set1_ps(-0x1.62E43p-1f);
28 const __m512 vminus_ln2_lo = _mm512_set1_ps(0x1.05C61p-29f);
29
30 const __m512 vc0 = _mm512_set1_ps(1.0f);
31 const __m512 vc1 = _mm512_set1_ps(0x1.FFFFF6p-1f);
32 const __m512 vc2 = _mm512_set1_ps(0x1.FFFDC6p-2f);
33 const __m512 vc3 = _mm512_set1_ps(0x1.555A80p-3f);
34 const __m512 vc4 = _mm512_set1_ps(0x1.573A1Ap-5f);
35 const __m512 vc5 = _mm512_set1_ps(0x1.0F9F9Cp-7f);
36
37 for (; n != 0; n -= 16 * sizeof(float)) {
38 const __m512 vx = _mm512_loadu_ps(input);
39
40 // Compute reduced argument n := round(x / log(2)).
41 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
42
43 // Detect underflow and overflow of expf(x) for further special handling.
44 // For large positive or negative inputs the range reduction may produce degenerate reduced arguments:
45 // - Reduced argument t can fall outside of [-log(2)/2, log(2)/2] range, leading to polynomial approximation p
46 // being negative, and exp(n) * p being either -0.0f (in underflow case) or -inf (in overflow case) instead of
47 // +0.0f and +inf respectively.
48 // - Reduced argument n can overflow and become +inf or -inf, and leading to NaN in reduced argument t.
49 const __mmask16 vinvof = _mm512_cmp_ps_mask(vx, vinf_cutoff, _CMP_NGT_UQ);
50 const __mmask16 vinvuf = _mm512_cmp_ps_mask(vx, vzero_cutoff, _CMP_NLT_UQ);
51
52 // Compute reduced argument t := x - n * log(2).
53 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
54 // Use masking to explicitly zero the result for large positive inputs, to avoid propagating NaN in reduced
55 // argument t into further computations. Zeroing the reduced argument t would instead result in polynomial
56 // approximation being 1.0f, which correctly overflows to +inf when scaled by n = +inf.
57 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
58 vt = _mm512_maskz_fmadd_ps(vinvof, vn, vminus_ln2_lo, vt);
59
60 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
61 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
62 vp = _mm512_fmadd_ps(vp, vt, vc3);
63 vp = _mm512_fmadd_ps(vp, vt, vc2);
64 vp = _mm512_fmadd_ps(vp, vt, vc1);
65 vp = _mm512_fmadd_ps(vp, vt, vc0);
66
67 // Reconstruct the final value as f = exp2(n) * p.
68 // Use masking to explicitly zero (set to +0.0f) the result for large negative inputs, because for some of these
69 // inputs the polynomial approximation p is negative and thus exp2(n) * p == -0.0f.
70 const __m512 vf = _mm512_maskz_scalef_ps(vinvuf, vp, vn);
71 _mm512_storeu_ps(output, vf);
72
73 input += 16;
74 output += 16;
75 }
76 }
77