Sigmoid evaluation stubs, micro-kernels, and operator
Only ARM64 architecture is supported
PiperOrigin-RevId: 280671182
diff --git a/src/math/sigmoid-neonfma-p5.c b/src/math/sigmoid-neonfma-p5.c
new file mode 100644
index 0000000..e65b628
--- /dev/null
+++ b/src/math/sigmoid-neonfma-p5.c
@@ -0,0 +1,110 @@
+// Copyright 2019 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 <arm_neon.h>
+
+#include <xnnpack/math-stubs.h>
+
+
+void xnn_math_f32_sigmoid__neonfma_p5(
+ size_t n,
+ const float* input,
+ float* output)
+{
+ assert(n % (4 * sizeof(float)) == 0);
+
+ const float32x4_t vmagic_bias = vmovq_n_f32(0x1.8000FEp23f);
+ // The smallest x for which sigmoidf(x) is normalized.
+ // This number is also the smallest x for which expf(x) is normalized.
+ const float32x4_t vdenorm_cutoff = vmovq_n_f32(-0x1.5D589Ep+6f);
+ // The largest x for which sigmoidf(x) is not equal 1.0.
+ const float32x4_t vone_cutoff = vmovq_n_f32(0x1.154244p+4f);
+ const float32x4_t vminus_log2e = vmovq_n_f32(-0x1.715476p+0f);
+ const float32x4_t vln2_hi = vmovq_n_f32(0x1.62E43p-1f);
+ const float32x4_t vln2_lo = vmovq_n_f32(-0x1.05C61p-29f);
+ 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
+ //
+ // 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 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.
+ 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.
+ // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly.
+ const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23));
+
+ // Subtract the large number back to get final n := round(-z / log(2)).
+ vn = vsubq_f32(vn, vmagic_bias);
+
+ // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)).
+ // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
+ float32x4_t vt = vfmaq_f32(vz, vn, vln2_hi);
+ vt = vfmaq_f32(vt, vn, vln2_lo);
+
+ // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2].
+ float32x4_t vp = vfmaq_f32(vc4, vc5, vt);
+ vp = vfmaq_f32(vc3, vp, vt);
+ vp = vfmaq_f32(vc2, vp, vt);
+ vp = vfmaq_f32(vc1, vp, vt);
+
+ // 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 + (t * s) * p
+ vt = vmulq_f32(vt, vs);
+ float32x4_t ve = vfmaq_f32(vs, vp, vt);
+
+ // Denominator of the sigmoid fraction: 1.0 + exp(z)
+ float32x4_t vd = vaddq_f32(ve, vone);
+
+ // Use Newton-Raphson method (2 iterations) 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.
+ float32x4_t vr = vrecpeq_f32(vd);
+ vr = vfmaq_f32(vr, vr, vfmsq_f32(vone, vr, vd));
+ vr = vfmaq_f32(vr, vr, vfmsq_f32(vone, vr, vd));
+
+ // Reconstruct sigmoid(-z) = exp(z) / (1.0 + exp(z))
+ float32x4_t vf = vmulq_f32(ve, vr);
+
+ // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
+ const uint32x4_t vm = vcltq_s32(vreinterpretq_f32_s32(vx), vmovq_n_s32(0));
+ vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf));
+
+ // For inputs above 1.0 cutoff, replace output with 1.0.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ vf = vbslq_f32(vcgtq_f32(vx, vone_cutoff), vone, vf);
+
+ // For inputs below denormal cutoff, replace output with +0.0f.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff)));
+
+ vst1q_f32(output, vf); output += 4;
+ }
+}