text: // Auto-generated file. Do not edit!
  //   Template: src/f32-sigmoid/neon-p5.c.in
  //   Generator: tools/xngen
  //
  // 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 <arm_neon.h>
  
  #include <xnnpack/common.h>
  #include <xnnpack/vunary.h>
  
  
  void xnn_f32_sigmoid_ukernel__neonfma_rr1_p5_nr2recps_x8(
      size_t n,
      const float* x,
      float* y,
      const void* params) XNN_DISABLE_TSAN
  {
    assert(n % sizeof(float) == 0);
  
    const float32x4_t vmagic_bias = vmovq_n_f32(0x1.8000FEp23f);
    // 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 >= 8 * sizeof(float); n -= 8 * sizeof(float)) {
      const float32x4_t vx0123 = vld1q_f32(x); x += 4;
      const float32x4_t vx4567 = vld1q_f32(x); x += 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 vz0123 = vabsq_f32(vx0123);
      const float32x4_t vz4567 = vabsq_f32(vx4567);
  
      // 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 vn0123 = vfmaq_f32(vmagic_bias, vz0123, vminus_log2e);
      float32x4_t vn4567 = vfmaq_f32(vmagic_bias, vz4567, 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 vs0123 = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn0123), 23));
      const float32x4_t vs4567 = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn4567), 23));
  
      // Subtract the large number back to get final n := round(-z / log(2)).
      vn0123 = vsubq_f32(vn0123, vmagic_bias);
      vn4567 = vsubq_f32(vn4567, vmagic_bias);
  
      // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)).
      float32x4_t vt0123 = vfmaq_f32(vz0123, vn0123, vln2);
      float32x4_t vt4567 = vfmaq_f32(vz4567, vn4567, vln2);
  
      // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2].
      float32x4_t vp0123 = vfmaq_f32(vc4, vc5, vt0123);
      float32x4_t vp4567 = vfmaq_f32(vc4, vc5, vt4567);
  
      vp0123 = vfmaq_f32(vc3, vp0123, vt0123);
      vp4567 = vfmaq_f32(vc3, vp4567, vt4567);
  
      vp0123 = vfmaq_f32(vc2, vp0123, vt0123);
      vp4567 = vfmaq_f32(vc2, vp4567, vt4567);
  
      vp0123 = vfmaq_f32(vc1, vp0123, vt0123);
      vp4567 = vfmaq_f32(vc1, vp4567, vt4567);
  
      // 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
      vt0123 = vmulq_f32(vt0123, vs0123);
      vt4567 = vmulq_f32(vt4567, vs4567);
  
      float32x4_t ve0123 = vfmaq_f32(vs0123, vp0123, vt0123);
      float32x4_t ve4567 = vfmaq_f32(vs4567, vp4567, vt4567);
  
      // Denominator of the sigmoid fraction: 1.0 + exp(-z)
      float32x4_t vd0123 = vaddq_f32(ve0123, vone);
      float32x4_t vd4567 = vaddq_f32(ve4567, 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 vr0123 = vrecpeq_f32(vd0123);
      float32x4_t vr4567 = vrecpeq_f32(vd4567);
  
      vr0123 = vmulq_f32(vr0123, vrecpsq_f32(vr0123, vd0123));
      vr4567 = vmulq_f32(vr4567, vrecpsq_f32(vr4567, vd4567));
  
      vr0123 = vmulq_f32(vr0123, vrecpsq_f32(vr0123, vd0123));
      vr4567 = vmulq_f32(vr4567, vrecpsq_f32(vr4567, vd4567));
  
      // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z))
      float32x4_t vf0123 = vmulq_f32(ve0123, vr0123);
      float32x4_t vf4567 = vmulq_f32(ve4567, vr4567);
  
      // For inputs below denormal cutoff, replace output with +0.0f.
      // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
      vf0123 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf0123), vcagtq_f32(vx0123, vdenorm_cutoff)));
      vf4567 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf4567), vcagtq_f32(vx4567, vdenorm_cutoff)));
  
      // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z)
      const uint32x4_t vm0123 = vcltq_f32(vx0123, vmovq_n_f32(0.0f));
      const uint32x4_t vm4567 = vcltq_f32(vx4567, vmovq_n_f32(0.0f));
  
      vf0123 = vbslq_f32(vm0123, vf0123, vsubq_f32(vone, vf0123));
      vf4567 = vbslq_f32(vm4567, vf4567, vsubq_f32(vone, vf4567));
  
      vst1q_f32(y, vf0123); y += 4;
      vst1q_f32(y, vf4567); y += 4;
    }
    for (; n >= 4 * sizeof(float); n -= 4 * sizeof(float)) {
      const float32x4_t vx = vld1q_f32(x); x += 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)).
      float32x4_t vt = vfmaq_f32(vz, vn, vln2);
  
      // 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 = vmulq_f32(vr, vrecpsq_f32(vr, vd));
  
      vr = vmulq_f32(vr, vrecpsq_f32(vr, vd));
  
      // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z))
      float32x4_t vf = vmulq_f32(ve, vr);
  
      // 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), vcagtq_f32(vx, vdenorm_cutoff)));
  
      // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z)
      const uint32x4_t vm = vcltq_f32(vx, vmovq_n_f32(0.0f));
      vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf));
  
      vst1q_f32(y, vf); y += 4;
    }
    if XNN_UNLIKELY(n != 0) {
      const float32x4_t vx = vld1q_f32(x);
  
      // 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)).
      float32x4_t vt = vfmaq_f32(vz, vn, vln2);
  
      // 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 = vmulq_f32(vr, vrecpsq_f32(vr, vd));
  
      vr = vmulq_f32(vr, vrecpsq_f32(vr, vd));
  
      // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z))
      float32x4_t vf = vmulq_f32(ve, vr);
  
      // 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), vcagtq_f32(vx, vdenorm_cutoff)));
  
      // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z)
      const uint32x4_t vm = vcltq_f32(vx, vmovq_n_f32(0.0f));
      vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf));
  
      float32x2_t vf_lo = vget_low_f32(vf);
      if (n & (2 * sizeof(float))) {
        vst1_f32(y, vf_lo); y += 2;
        vf_lo = vget_high_f32(vf);
      }
      if (n & (1 * sizeof(float))) {
        vst1_lane_f32(y, vf_lo, 0);
      }
    }
  }
  