text: // Auto-generated file. Do not edit!
  //   Template: src/f32-raddstoreexpminusmax/neon-p5.c.in
  //   Generator: tools/xngen
  //
  // 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 <arm_neon.h>
  
  #include <xnnpack/common.h>
  #include <xnnpack/raddstoreexpminusmax.h>
  
  
  void xnn_f32_raddstoreexpminusmax_ukernel__neon_p5_x12(
      size_t elements,
      const float* input,
      float* output,
      float* sum,
      float max) XNN_DISABLE_TSAN
  {
    assert(elements % sizeof(float) == 0);
  
    const float32x4_t vmagic_bias = vmovq_n_f32(0x1.8000FEp23f);
    // The smallest x for which expf(x) is normalized.
    const float32x4_t vdenorm_cutoff = vmovq_n_f32(-0x1.5D589Ep6f);
    const float32x4_t vlog2e = vmovq_n_f32(0x1.715476p+0f);
    // Last 7 bits are zeroes
    const float32x4_t vminus_ln2_hi = vmovq_n_f32(-0x1.62E400p-1f);
    const float32x4_t vminus_ln2_lo = vmovq_n_f32(-0x1.7F7D1Cp-20f);
  
    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);
  
    const float32x4_t vi_max = vdupq_n_f32(max);
  
    float32x4_t vacc0 = vmovq_n_f32(0.0f);
    for (; elements >= 12 * sizeof(float); elements -= 12 * sizeof(float)) {
      // Load 12 (3x4) inputs at a time.
      const float32x4_t vi0123 = vld1q_f32(input); input += 4;
      const float32x4_t vi4567 = vld1q_f32(input); input += 4;
      const float32x4_t vi89AB = vld1q_f32(input); input += 4;
  
      // Subtract maximum input x := i - i_max. This implies x <= 0.
      const float32x4_t vx0123 = vsubq_f32(vi0123, vi_max);
      const float32x4_t vx4567 = vsubq_f32(vi4567, vi_max);
      const float32x4_t vx89AB = vsubq_f32(vi89AB, vi_max);
  
      // Compute reduced argument n := round(x / 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 outside of [-87.336540, 0.0] underflow expf(x) anyway. We fixup the result for such inputs at the very end
      // of the algorithm.
      float32x4_t vn0123 = vmlaq_f32(vmagic_bias, vx0123, vlog2e);
      float32x4_t vn4567 = vmlaq_f32(vmagic_bias, vx4567, vlog2e);
      float32x4_t vn89AB = vmlaq_f32(vmagic_bias, vx89AB, vlog2e);
  
      // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
      // -87.33642 <= x <= 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));
      const float32x4_t vs89AB = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn89AB), 23));
  
      // Subtract the large number back to get final n := round(x / log(2)).
      vn0123 = vsubq_f32(vn0123, vmagic_bias);
      vn4567 = vsubq_f32(vn4567, vmagic_bias);
      vn89AB = vsubq_f32(vn89AB, vmagic_bias);
  
      // Compute reduced argument t := z - n * log(2).
      // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
      float32x4_t vt0123 = vmlaq_f32(vx0123, vn0123, vminus_ln2_hi);
      float32x4_t vt4567 = vmlaq_f32(vx4567, vn4567, vminus_ln2_hi);
      float32x4_t vt89AB = vmlaq_f32(vx89AB, vn89AB, vminus_ln2_hi);
  
      vt0123 = vmlaq_f32(vt0123, vn0123, vminus_ln2_lo);
      vt4567 = vmlaq_f32(vt4567, vn4567, vminus_ln2_lo);
      vt89AB = vmlaq_f32(vt89AB, vn89AB, vminus_ln2_lo);
  
      // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
      float32x4_t vp0123 = vmlaq_f32(vc4, vc5, vt0123);
      float32x4_t vp4567 = vmlaq_f32(vc4, vc5, vt4567);
      float32x4_t vp89AB = vmlaq_f32(vc4, vc5, vt89AB);
  
      vp0123 = vmlaq_f32(vc3, vp0123, vt0123);
      vp4567 = vmlaq_f32(vc3, vp4567, vt4567);
      vp89AB = vmlaq_f32(vc3, vp89AB, vt89AB);
  
      vp0123 = vmlaq_f32(vc2, vp0123, vt0123);
      vp4567 = vmlaq_f32(vc2, vp4567, vt4567);
      vp89AB = vmlaq_f32(vc2, vp89AB, vt89AB);
  
      vp0123 = vmlaq_f32(vc1, vp0123, vt0123);
      vp4567 = vmlaq_f32(vc1, vp4567, vt4567);
      vp89AB = vmlaq_f32(vc1, vp89AB, vt89AB);
  
      // Reconstruct the final f value:
      //   f = 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);
      vt89AB = vmulq_f32(vt89AB, vs89AB);
  
      float32x4_t vf0123 = vmlaq_f32(vs0123, vp0123, vt0123);
      float32x4_t vf4567 = vmlaq_f32(vs4567, vp4567, vt4567);
      float32x4_t vf89AB = vmlaq_f32(vs89AB, vp89AB, vt89AB);
  
      // 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), vcltq_f32(vx0123, vdenorm_cutoff)));
      vf4567 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf4567), vcltq_f32(vx4567, vdenorm_cutoff)));
      vf89AB = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf89AB), vcltq_f32(vx89AB, vdenorm_cutoff)));
  
      // Store 12 (3x4) outputs at a time.
      vst1q_f32(output, vf0123); output += 4;
      vst1q_f32(output, vf4567); output += 4;
      vst1q_f32(output, vf89AB); output += 4;
  
      // Accumulate computed exponents.
      vacc0 = vaddq_f32(vacc0, vf0123);
      vacc0 = vaddq_f32(vacc0, vf4567);
      vacc0 = vaddq_f32(vacc0, vf89AB);
    }
  
    float32x4_t vacc = vacc0;
    for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
      // Load 4 inputs at a time.
      const float32x4_t vi = vld1q_f32(input); input += 4;
  
      // Subtract maximum input x := i - i_max. This implies x <= 0.
      const float32x4_t vx = vsubq_f32(vi, vi_max);
  
      // Compute reduced argument n := round(x / 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 outside of [-87.336540, 0.0] underflow expf(x) anyway. We fixup the result for such inputs at the very end
      // of the algorithm.
      float32x4_t vn = vmlaq_f32(vmagic_bias, vx, vlog2e);
  
      // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
      // -87.33642 <= x <= 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(x / log(2)).
      vn = vsubq_f32(vn, vmagic_bias);
  
      // Compute reduced argument t := z - n * log(2).
      // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
      float32x4_t vt = vmlaq_f32(vx, vn, vminus_ln2_hi);
      vt = vmlaq_f32(vt, vn, vminus_ln2_lo);
  
      // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
      float32x4_t vp = vmlaq_f32(vc4, vc5, vt);
      vp = vmlaq_f32(vc3, vp, vt);
      vp = vmlaq_f32(vc2, vp, vt);
      vp = vmlaq_f32(vc1, vp, vt);
  
      // Reconstruct the final f value:
      //   f = 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 vf = vmlaq_f32(vs, vp, vt);
  
      // 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)));
  
      // Store 4 outputs at a time.
      vst1q_f32(output, vf); output += 4;
  
      // Accumulate computed exponents.
      vacc = vaddq_f32(vacc, vf);
    }
  #if XNN_ARCH_ARM64
    float vacc_lo = vaddvq_f32(vacc);
  #else
    float32x2_t vacc_lo = vadd_f32(vget_high_f32(vacc), vget_low_f32(vacc));
  #endif
    if (elements != 0) {
      assert(elements >= 1 * sizeof(float));
      assert(elements <= 3 * sizeof(float));
      // Load 4 inputs at a time.
      const float32x4_t vi = vld1q_f32(input); input += 4;
  
      // Subtract maximum input x := i - i_max. This implies x <= 0.
      const float32x4_t vx = vsubq_f32(vi, vi_max);
  
      // Compute reduced argument n := round(x / 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 outside of [-87.336540, 0.0] underflow expf(x) anyway. We fixup the result for such inputs at the very end
      // of the algorithm.
      float32x4_t vn = vmlaq_f32(vmagic_bias, vx, vlog2e);
  
      // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
      // -87.33642 <= x <= 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(x / log(2)).
      vn = vsubq_f32(vn, vmagic_bias);
  
      // Compute reduced argument t := z - n * log(2).
      // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
      float32x4_t vt = vmlaq_f32(vx, vn, vminus_ln2_hi);
      vt = vmlaq_f32(vt, vn, vminus_ln2_lo);
  
      // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
      float32x4_t vp = vmlaq_f32(vc4, vc5, vt);
      vp = vmlaq_f32(vc3, vp, vt);
      vp = vmlaq_f32(vc2, vp, vt);
      vp = vmlaq_f32(vc1, vp, vt);
  
      // Reconstruct the final f value:
      //   f = 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 vf = vmlaq_f32(vs, vp, vt);
  
      // 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)));
  
      float32x2_t vf_lo = vget_low_f32(vf);
      if (elements & (2 * sizeof(float))) {
        // Store 2 outputs at a time.
        vst1_f32(output, vf_lo); output += 2;
  
        // Accumulate 2 computed exponents.
        #if XNN_ARCH_ARM64
          vacc_lo += vaddv_f32(vf_lo);
        #else
          vacc_lo = vadd_f32(vacc_lo, vf_lo);
        #endif
  
        vf_lo = vget_high_f32(vf);
      }
      if (elements & (1 * sizeof(float))) {
        // Store 1 output at a time.
        vst1_lane_f32(output, vf_lo, 0);
  
        // Accumulate 1 computed exponent.
        #if XNN_ARCH_ARM64
          vacc_lo += vget_lane_f32(vf_lo, 0);
        #else
          vacc_lo = vadd_f32(vacc_lo, vreinterpret_f32_u64(vshl_n_u64(vreinterpret_u64_f32(vf_lo), 32)));
        #endif
      }
    }
    // Reduce 4 elements in the SIMD register
  #if XNN_ARCH_ARM64
    *sum = vacc_lo;
  #else
    vst1_lane_f32(sum, vpadd_f32(vacc_lo, vacc_lo), 0);
  #endif
  }
  