Refactor AVX512F Sigmoid evaluation stubs
- Remove 2-iteration FMA versions (redundant with VRCP14PS)
- Remove non-SCALEF versions (suboptimal)
- Add LUT-based versions
- Add versions with adjustment after multiplication by reciprocal
PiperOrigin-RevId: 333221796
diff --git a/src/math/sigmoid-avx512f-rr1-lut32-p2-perm2-scalef-nr1fma.c b/src/math/sigmoid-avx512f-rr1-lut32-p2-perm2-scalef-nr1fma.c
new file mode 100644
index 0000000..36a6eb3
--- /dev/null
+++ b/src/math/sigmoid-avx512f-rr1-lut32-p2-perm2-scalef-nr1fma.c
@@ -0,0 +1,101 @@
+// 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_rr1_lut32_p2_perm2_scalef_nr1fma(
+ size_t n,
+ const float* input,
+ float* output)
+{
+ assert(n % (16 * sizeof(float)) == 0);
+
+ const __m512i vsign_mask = _mm512_set1_epi32(0x80000000);
+
+ const __m512 vmagic_bias = _mm512_set1_ps(0x1.800000p18f);
+ const __m512 vlog2e = _mm512_set1_ps(0x1.715476p0f);
+ const __m512 vminus_ln2 = _mm512_set1_ps(-0x1.62e43p-1f);
+
+ 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 vc1 = _mm512_set1_ps(0x1.0000F6p-0f);
+ const __m512 vc2 = _mm512_set1_ps(0x1.000000p-1f);
+ 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 result to 5 fractional bits, then
+ // subtracing the large number back. The first addition is combined with multiplication by log2e into a single FMA
+ // instruction. The trick with adding large number is valid only within certain bounds (|x| <= 2**17), but thats
+ // ok, because inputs outside of [-103.97207, 88.72283] underflow or saturate sigmoidf(x) anyway. 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 final n := round(z / log(2), 5).
+ vn = _mm512_sub_ps(vn, vmagic_bias);
+
+ // Compute reduced argument t := z - n * log(2).
+ __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2, vz);
+
+ // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/64, log(2)/64].
+ // p = l * (1 + t * (c1 + t * c2))
+ // = 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);
+
+ // Use Newton-Raphson method (1 iteration) to compute reciprocal of denominator.
+ // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
+ // Thus the reciprocal of the denominator never overflows.
+ __m512 vr = _mm512_rcp14_ps(vd);
+ vr = _mm512_fmadd_ps(_mm512_fnmadd_ps(vr, vd, vone), vr, vr);
+
+ // Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z))
+ __m512 vf = _mm512_mul_ps(ve, vr);
+
+ // 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;
+ }
+}