Refactor SSE2/AVX/AVX2/AVX512 Sigmoid evaluation stubs
PiperOrigin-RevId: 334105001
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
index 36a6eb3..a971e2b 100644
--- a/src/math/sigmoid-avx512f-rr1-lut32-p2-perm2-scalef-nr1fma.c
+++ b/src/math/sigmoid-avx512f-rr1-lut32-p2-perm2-scalef-nr1fma.c
@@ -18,12 +18,12 @@
{
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);
- const __m512 vminus_ln2 = _mm512_set1_ps(-0x1.62e43p-1f);
-
+ 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,
@@ -34,29 +34,32 @@
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 vminus_ln2 = _mm512_set1_ps(-0x1.62E43p-1f);
+ // 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.
+ // 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.
+ // 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+17 = 181704.375), 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.
@@ -69,7 +72,8 @@
__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))
+ // 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);