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// Copyright 2020 Google LLC
//
// This source code is licensed under the BSD-style license found in the
// LICENSE file in the root directory of this source tree.
#include <assert.h>
#include <stddef.h>
#include <immintrin.h>
#include <xnnpack/math-stubs.h>
void xnn_math_f32_sigmoid__avx512f_rr2_lut32_p2_perm2_scalef_div(
size_t n,
const float* input,
float* output)
{
assert(n % (16 * sizeof(float)) == 0);
// Floating-point mask with only the sign bit set
const __m512i vsign_mask = _mm512_set1_epi32(0x80000000);
// Large number such that ulp(magic bias) == exp2(-5)
const __m512 vmagic_bias = _mm512_set1_ps(0x1.800000p18f);
const __m512 vlog2e = _mm512_set1_ps(0x1.715476p0f);
// Table of exp2(k / 32) values, k = 0..31
const __m512 vtable_hi = _mm512_set_ps(
0x1.F50766p+0f, 0x1.EA4AFAp+0f, 0x1.DFC974p+0f, 0x1.D5818Ep+0f,
0x1.CB720Ep+0f, 0x1.C199BEp+0f, 0x1.B7F770p+0f, 0x1.AE89FAp+0f,
0x1.A5503Cp+0f, 0x1.9C4918p+0f, 0x1.93737Cp+0f, 0x1.8ACE54p+0f,
0x1.82589Ap+0f, 0x1.7A1148p+0f, 0x1.71F75Ep+0f, 0x1.6A09E6p+0f);
const __m512 vtable_lo = _mm512_set_ps(
0x1.6247ECp+0f, 0x1.5AB07Ep+0f, 0x1.5342B6p+0f, 0x1.4BFDAEp+0f,
0x1.44E086p+0f, 0x1.3DEA64p+0f, 0x1.371A74p+0f, 0x1.306FE0p+0f,
0x1.29E9E0p+0f, 0x1.2387A6p+0f, 0x1.1D4874p+0f, 0x1.172B84p+0f,
0x1.11301Ep+0f, 0x1.0B5586p+0f, 0x1.059B0Ep+0f, 0x1.000000p+0f);
const __m512 vminus_ln2_hi = _mm512_set1_ps(-0x1.62e43p-1f);
const __m512 vminus_ln2_lo = _mm512_set1_ps(0x1.05c61p-29f);
// Coefficient of polynomial approximation of
// exp(t) ~ 1 + t * (c1 + t * c2) on [-log(2)/64, log(2)/64]
const __m512 vc2 = _mm512_set1_ps(0x1.000000p-1f);
const __m512 vc1 = _mm512_set1_ps(0x1.0000F6p-0f);
const __m512 vone = _mm512_set1_ps(1.0f);
for (; n != 0; n -= 16 * sizeof(float)) {
const __m512 vx = _mm512_loadu_ps(input);
// General structure of the algorithm:
//
// / exp(x) / (1 + exp(x)) if x <= 0
// f[x] :=
// \ 1 - f[-x] if x >= 0
//
// First we compute f[z] := exp(z) / (1 + exp(z)) where z = -abs(x), then replace result with 1 - f[z] if x >= 0.
const __m512 vz = _mm512_castsi512_ps(_mm512_or_epi32(_mm512_castps_si512(vx), vsign_mask));
// Compute reduced argument n := round(z / log(2), 5).
// We do it by adding a large number (magic bias), which cause rounding of the result to 5 fractional bits, then
// subtracing the large number back. The addition is combined with multiplication by log2e into a single FMA
// instruction. The trick with adding large number is valid only within certain bounds (|z / log(2)| <= 2**17,
// i.e. |z| <= 0x1.62E43p+16 = 90852.1875), but that is acceptable, because inputs x outside of
// [-87.336544, 17.328678] (i.e. z outsize [87.336544, 0]) underflow or saturate sigmoidf(x). We fixup the result
// for such inputs at the very end of the algorithm.
__m512 vn = _mm512_fmadd_ps(vz, vlog2e, vmagic_bias);
// Use the low 5 bits of n (as integer) for table lookup.
const __m512 vl = _mm512_permutex2var_ps(vtable_lo, _mm512_castps_si512(vn), vtable_hi);
// Subtract the large number back to get the final n := round(z / log(2), 5) as a floating-point number.
vn = _mm512_sub_ps(vn, vmagic_bias);
// Compute reduced argument t := z - n * log(2).
// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
__m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vz);
vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
// Compute degree-2 polynomial approximation for exp(t) on [-log(2)/64, log(2)/64].
// P(t) = 1 + t * (c1 + t * c2)
// p = l * P(t)
// = l + l * t * (c1 + t * c2)
__m512 vp = _mm512_fmadd_ps(vt, vc2, vc1);
vt = _mm512_mul_ps(vt, vl);
vp = _mm512_fmadd_ps(vt, vp, vl);
// Reconstruct the exp(z) value: e = exp2(floor(n)) * p.
const __m512 ve = _mm512_scalef_ps(vp, vn);
// Denominator of the sigmoid fraction: 1.0 + exp(z)
const __m512 vd = _mm512_add_ps(ve, vone);
// Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z))
__m512 vf = _mm512_div_ps(ve, vd);
// Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
vf = _mm512_mask_sub_ps(vf, _mm512_testn_epi32_mask(_mm512_castps_si512(vx), vsign_mask), vone, vf);
_mm512_storeu_ps(output, vf);
input += 16;
output += 16;
}
}