Refactor Sigmoid evaluation stubs
PiperOrigin-RevId: 334257369
diff --git a/src/math/sigmoid-neonfma-rr1-p5-div.c b/src/math/sigmoid-neonfma-rr1-p5-div.c
index a876213..dc7e232 100644
--- a/src/math/sigmoid-neonfma-rr1-p5-div.c
+++ b/src/math/sigmoid-neonfma-rr1-p5-div.c
@@ -18,24 +18,27 @@
{
assert(n % (4 * sizeof(float)) == 0);
+ // Large number such that ulp(magic bias) == 1 and magic bias === 127 mod 2**22.
const float32x4_t vmagic_bias = vmovq_n_f32(0x1.8000FEp23f);
+ const float32x4_t vminus_log2e = vmovq_n_f32(-0x1.715476p+0f);
+ const float32x4_t vln2 = vmovq_n_f32(0x1.62E43p-1f);
+ // Coefficient of polynomial approximation of
+ // exp(-t) ~ 1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) on [-log(2)/2, log(2)/2]
+ const float32x4_t vc5 = vmovq_n_f32(-0x1.0F9F9Cp-7f);
+ const float32x4_t vc4 = vmovq_n_f32(0x1.573A1Ap-5f);
+ const float32x4_t vc3 = vmovq_n_f32(-0x1.555A80p-3f);
+ const float32x4_t vc2 = vmovq_n_f32(0x1.FFFDC6p-2f);
+ const float32x4_t vc1 = vmovq_n_f32(-0x1.FFFFF6p-1f);
+ const float32x4_t vone = vmovq_n_f32(1.0f);
// The largest z for which sigmoidf(-z) is normalized.
// This number is also the largest z for which expf(-z) is normalized.
const float32x4_t vdenorm_cutoff = vmovq_n_f32(-0x1.5D589Ep+6f);
- const float32x4_t vminus_log2e = vmovq_n_f32(-0x1.715476p+0f);
- const float32x4_t vln2 = vmovq_n_f32(0x1.62E43p-1f);
- const float32x4_t vone = vmovq_n_f32(1.0f);
-
- const float32x4_t vc1 = vmovq_n_f32(-0x1.FFFFF6p-1f);
- const float32x4_t vc2 = vmovq_n_f32(0x1.FFFDC6p-2f);
- const float32x4_t vc3 = vmovq_n_f32(-0x1.555A80p-3f);
- const float32x4_t vc4 = vmovq_n_f32(0x1.573A1Ap-5f);
- const float32x4_t vc5 = vmovq_n_f32(-0x1.0F9F9Cp-7f);
for (; n != 0; n -= 4 * sizeof(float)) {
const float32x4_t vx = vld1q_f32(input); input += 4;
// General structure of the algorithm:
+ //
// / exp(x) / (1 + exp(x)) if x <= 0
// f[x] :=
// \ 1 - f[-x] if x >= 0
@@ -45,11 +48,11 @@
const float32x4_t vz = vabsq_f32(vx);
// Compute reduced argument n := round(-z / log(2)).
- // We do it by adding a large number (magic bias), which cause rounding of result to an integer, 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**22), but thats ok, because
- // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) 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 integer, then subtracing
+ // the large number back. The trick with adding large number is valid only within certain bounds
+ // (|-z / log(2)| <= 2**22, i.e. |z| <= 0x1.62E43p+22 = 5814540.0), but that is acceptable, because inputs x
+ // outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x). We fixup
+ // the result for such inputs at the very end of the algorithm.
float32x4_t vn = vfmaq_f32(vmagic_bias, vz, vminus_log2e);
// Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
@@ -63,7 +66,7 @@
float32x4_t vt = vfmaq_f32(vz, vn, vln2);
// Compute degree-5 polynomial approximation for exp(-t) on [-log(2)/2, log(2)/2]:
- // P5(t) = 1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
+ // P(t) = 1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) = 1 + t * p
float32x4_t vp = vfmaq_f32(vc4, vc5, vt);
vp = vfmaq_f32(vc3, vp, vt);
vp = vfmaq_f32(vc2, vp, vt);
@@ -71,7 +74,7 @@
// Reconstruct the exp(-z) value:
// e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
- // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
+ // = s * (1 + t * p)
// = s + (t * s) * p
vt = vmulq_f32(vt, vs);
float32x4_t ve = vfmaq_f32(vs, vp, vt);