src/f32-sigmoid/avx2-p5.c.in - platform/external/XNNPACK - Git at Google

 // 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.

 $assert BATCH_TILE % 8 == 0
 $assert BATCH_TILE >= 8
 $assert RR_STEPS in [1, 2]
 $assert DIV_ALGO in ["div", "nr1fma", "nr2fma"]
 $ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
 $SIMD_TILE = BATCH_TILE // 8
 #include <assert.h>

 #include <immintrin.h>

 #include <xnnpack/common.h>
 #include <xnnpack/vunary.h>


 static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0};

 void xnn_f32_sigmoid_ukernel__avx2_rr${RR_STEPS}_p5_${DIV_ALGO}_x${BATCH_TILE}(
     size_t n,
     const float* x,
     float* y,
     const void* params)
 {
   assert(n % sizeof(float) == 0);

   const __m256 vmagic_bias = _mm256_set1_ps(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 __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep+6f);
   const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
   $if RR_STEPS == 1:
     const __m256 vminus_ln2 = _mm256_set1_ps(-0x1.62E43p-1f);
   $else:
     const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
     const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);
   const __m256 vone = _mm256_set1_ps(1.0f);
   const __m256 vsign_mask = _mm256_set1_ps(-0.0f);

   const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
   const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
   const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
   const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
   const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);

   $if BATCH_TILE > 8:
     for (; n >= ${BATCH_TILE} * sizeof(float); n -= ${BATCH_TILE} * sizeof(float)) {
       const __m256 vx${ABC[0]} = _mm256_loadu_ps(x);
       $for N in range(1, SIMD_TILE):
         const __m256 vx${ABC[N]} = _mm256_loadu_ps(x + ${N * 8});
       x += ${BATCH_TILE};

       // 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.
       $for N in range(SIMD_TILE):
         const __m256 vz${ABC[N]} = _mm256_or_ps(vx${ABC[N]}, vsign_mask);

       // Compute reduced argument n := round(z / log(2)).
       // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
       // to an integer, then subtracing the large number back. 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.
       $for N in range(SIMD_TILE):
         __m256 vn${ABC[N]} = _mm256_fmadd_ps(vz${ABC[N]}, vlog2e, vmagic_bias);

       // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
       // -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly.
       $for N in range(SIMD_TILE):
         const __m256 vs${ABC[N]} = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn${ABC[N]}), 23));

       // Subtract the large number back to get final n := round(z / log(2)).
       $for N in range(SIMD_TILE):
         vn${ABC[N]} = _mm256_sub_ps(vn${ABC[N]}, vmagic_bias);

       // Compute reduced argument t := z - n * log(2).
       $if RR_STEPS == 1:
         $for N in range(SIMD_TILE):
           __m256 vt${ABC[N]} = _mm256_fmadd_ps(vn${ABC[N]}, vminus_ln2, vz${ABC[N]});
       $else:
         // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
         $for N in range(SIMD_TILE):
           __m256 vt${ABC[N]} = _mm256_fmadd_ps(vn${ABC[N]}, vminus_ln2_hi, vz${ABC[N]});

         $for N in range(SIMD_TILE):
           vt${ABC[N]} = _mm256_fmadd_ps(vn${ABC[N]}, vminus_ln2_lo, vt${ABC[N]});

       // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
       $for N in range(SIMD_TILE):
         __m256 vp${ABC[N]} = _mm256_fmadd_ps(vc5, vt${ABC[N]}, vc4);

       $for N in range(SIMD_TILE):
         vp${ABC[N]} = _mm256_fmadd_ps(vp${ABC[N]}, vt${ABC[N]}, vc3);

       $for N in range(SIMD_TILE):
         vp${ABC[N]} = _mm256_fmadd_ps(vp${ABC[N]}, vt${ABC[N]}, vc2);

       $for N in range(SIMD_TILE):
         vp${ABC[N]} = _mm256_fmadd_ps(vp${ABC[N]}, vt${ABC[N]}, vc1);

       // 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
       $for N in range(SIMD_TILE):
         vt${ABC[N]} = _mm256_mul_ps(vt${ABC[N]}, vs${ABC[N]});

       $for N in range(SIMD_TILE):
         const __m256 ve${ABC[N]} = _mm256_fmadd_ps(vt${ABC[N]}, vp${ABC[N]}, vs${ABC[N]});

       // Denominator of the sigmoid fraction: 1.0 + exp(z)
       $for N in range(SIMD_TILE):
         const __m256 vd${ABC[N]} = _mm256_add_ps(ve${ABC[N]}, vone);

       $if DIV_ALGO == "div":
         // Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z))
         $for N in range(SIMD_TILE):
           __m256 vf${ABC[N]} = _mm256_div_ps(ve${ABC[N]}, vd${ABC[N]});
       $else:
         // Use Newton-Raphson method 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.
         $for N in range(SIMD_TILE):
           __m256 vr${ABC[N]} = _mm256_rcp_ps(vd${ABC[N]});

         $for N in range(SIMD_TILE):
           vr${ABC[N]} = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr${ABC[N]}, vd${ABC[N]}, vone), vr${ABC[N]}, vr${ABC[N]});

         $if DIV_ALGO == "nr2fma":
           $for N in range(SIMD_TILE):
             vr${ABC[N]} = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr${ABC[N]}, vd${ABC[N]}, vone), vr${ABC[N]}, vr${ABC[N]});

         // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
         $for N in range(SIMD_TILE):
           __m256 vf${ABC[N]} = _mm256_mul_ps(ve${ABC[N]}, vr${ABC[N]});

       // For inputs below denormal cutoff, replace output with +0.0f.
       // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
       $for N in range(SIMD_TILE):
         vf${ABC[N]} = _mm256_andnot_ps(_mm256_cmp_ps(vz${ABC[N]}, vdenorm_cutoff, _CMP_LT_OS), vf${ABC[N]});

       // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
       $for N in range(SIMD_TILE):
         vf${ABC[N]} = _mm256_blendv_ps(_mm256_sub_ps(vone, vf${ABC[N]}), vf${ABC[N]}, vx${ABC[N]});

       _mm256_storeu_ps(y, vf${ABC[0]});
       $for N in range(1, SIMD_TILE):
         _mm256_storeu_ps(y + ${N * 8}, vf${ABC[N]});
       y += ${BATCH_TILE};
     }
   for (; n >= 8 * sizeof(float); n -= 8 * sizeof(float)) {
     const __m256 vx = _mm256_loadu_ps(x);
     x += 8;

     // 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 __m256 vz = _mm256_or_ps(vx, vsign_mask);

     // Compute reduced argument n := round(z / log(2)).
     // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
     // to an integer, then subtracing the large number back. 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.
     __m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias);

     // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
     // -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly.
     const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));

     // Subtract the large number back to get final n := round(z / log(2)).
     vn = _mm256_sub_ps(vn, vmagic_bias);

     // Compute reduced argument t := z - n * log(2).
     $if RR_STEPS == 1:
       __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz);
     $else:
       // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
       __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vz);
       vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);

     // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
     __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
     vp = _mm256_fmadd_ps(vp, vt, vc3);
     vp = _mm256_fmadd_ps(vp, vt, vc2);
     vp = _mm256_fmadd_ps(vp, vt, vc1);

     // 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 = _mm256_mul_ps(vt, vs);
     const __m256 ve = _mm256_fmadd_ps(vt, vp, vs);

     // Denominator of the sigmoid fraction: 1.0 + exp(z)
     const __m256 vd = _mm256_add_ps(ve, vone);

     $if DIV_ALGO == "div":
       // Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z))
       __m256 vf = _mm256_div_ps(ve, vd);
     $else:
       // Use Newton-Raphson method 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.
       __m256 vr = _mm256_rcp_ps(vd);
       vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);
       $if DIV_ALGO == "nr2fma":
         vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);

       // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
       __m256 vf = _mm256_mul_ps(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 = _mm256_andnot_ps(_mm256_cmp_ps(vz, vdenorm_cutoff, _CMP_LT_OS), vf);

     // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
     vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx);

     _mm256_storeu_ps(y, vf);
     y += 8;
   }
   if XNN_UNLIKELY(n != 0) {
     assert(n >= 1 * sizeof(float));
     assert(n <= 7 * sizeof(float));
     __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - n));

     const __m256 vx = _mm256_maskload_ps(x, vmask);

     // 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 __m256 vz = _mm256_or_ps(vx, vsign_mask);

     // Compute reduced argument n := round(z / log(2)).
     // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
     // to an integer, then subtracing the large number back. 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.
     __m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias);

     // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
     // -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly.
     const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));

     // Subtract the large number back to get final n := round(z / log(2)).
     vn = _mm256_sub_ps(vn, vmagic_bias);

     // Compute reduced argument t := z - n * log(2).
     $if RR_STEPS == 1:
       __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz);
     $else:
       // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
       __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vz);
       vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);

     // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
     __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
     vp = _mm256_fmadd_ps(vp, vt, vc3);
     vp = _mm256_fmadd_ps(vp, vt, vc2);
     vp = _mm256_fmadd_ps(vp, vt, vc1);

     // 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 = _mm256_mul_ps(vt, vs);
     const __m256 ve = _mm256_fmadd_ps(vt, vp, vs);

     // Denominator of the sigmoid fraction: 1.0 + exp(z)
     const __m256 vd = _mm256_add_ps(ve, vone);

     $if DIV_ALGO == "div":
       // Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z))
       __m256 vf = _mm256_div_ps(ve, vd);
     $else:
       // Use Newton-Raphson method 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.
       __m256 vr = _mm256_rcp_ps(vd);
       vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);
       $if DIV_ALGO == "nr2fma":
         vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);

       // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
       __m256 vf = _mm256_mul_ps(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 = _mm256_andnot_ps(_mm256_cmp_ps(vz, vdenorm_cutoff, _CMP_LT_OS), vf);

     // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
     vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx);

     // _mm256_maskstore_ps(y, vmask, vf) could be used here, but triggers msan failures (probably an msan bug).
     __m128 vf_lo = _mm256_castps256_ps128(vf);
     if (n & (4 * sizeof(float))) {
       _mm_storeu_ps(y, vf_lo);
       vf_lo = _mm256_extractf128_ps(vf, 1);
       y += 4;
     }
     if (n & (2 * sizeof(float))) {
       _mm_storel_pi((__m64*) y, vf_lo);
       vf_lo = _mm_movehl_ps(vf_lo, vf_lo);
       y += 2;
     }
     if (n & (1 * sizeof(float))) {
       _mm_store_ss(y, vf_lo);
     }
   }
 }
	// 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.

	$assert BATCH_TILE % 8 == 0
	$assert BATCH_TILE >= 8
	$assert RR_STEPS in [1, 2]
	$assert DIV_ALGO in ["div", "nr1fma", "nr2fma"]
	$ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
	$SIMD_TILE = BATCH_TILE // 8
	#include <assert.h>

	#include <immintrin.h>

	#include <xnnpack/common.h>
	#include <xnnpack/vunary.h>


	static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0};

	void xnn_f32_sigmoid_ukernel__avx2_rr${RR_STEPS}_p5_${DIV_ALGO}_x${BATCH_TILE}(
	size_t n,
	const float* x,
	float* y,
	const void* params)
	{
	assert(n % sizeof(float) == 0);

	const __m256 vmagic_bias = _mm256_set1_ps(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 __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep+6f);
	const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
	$if RR_STEPS == 1:
	const __m256 vminus_ln2 = _mm256_set1_ps(-0x1.62E43p-1f);
	$else:
	const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
	const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);
	const __m256 vone = _mm256_set1_ps(1.0f);
	const __m256 vsign_mask = _mm256_set1_ps(-0.0f);

	const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
	const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
	const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
	const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
	const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);

	$if BATCH_TILE > 8:
	for (; n >= ${BATCH_TILE} * sizeof(float); n -= ${BATCH_TILE} * sizeof(float)) {
	const __m256 vx${ABC[0]} = _mm256_loadu_ps(x);
	$for N in range(1, SIMD_TILE):
	const __m256 vx${ABC[N]} = _mm256_loadu_ps(x + ${N * 8});
	x += ${BATCH_TILE};

	// 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.
	$for N in range(SIMD_TILE):
	const __m256 vz${ABC[N]} = _mm256_or_ps(vx${ABC[N]}, vsign_mask);

	// Compute reduced argument n := round(z / log(2)).
	// We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
	// to an integer, then subtracing the large number back. 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.
	$for N in range(SIMD_TILE):
	__m256 vn${ABC[N]} = _mm256_fmadd_ps(vz${ABC[N]}, vlog2e, vmagic_bias);

	// Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
	// -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly.
	$for N in range(SIMD_TILE):
	const __m256 vs${ABC[N]} = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn${ABC[N]}), 23));

	// Subtract the large number back to get final n := round(z / log(2)).
	$for N in range(SIMD_TILE):
	vn${ABC[N]} = _mm256_sub_ps(vn${ABC[N]}, vmagic_bias);

	// Compute reduced argument t := z - n * log(2).
	$if RR_STEPS == 1:
	$for N in range(SIMD_TILE):
	__m256 vt${ABC[N]} = _mm256_fmadd_ps(vn${ABC[N]}, vminus_ln2, vz${ABC[N]});
	$else:
	// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
	$for N in range(SIMD_TILE):
	__m256 vt${ABC[N]} = _mm256_fmadd_ps(vn${ABC[N]}, vminus_ln2_hi, vz${ABC[N]});

	$for N in range(SIMD_TILE):
	vt${ABC[N]} = _mm256_fmadd_ps(vn${ABC[N]}, vminus_ln2_lo, vt${ABC[N]});

	// Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
	$for N in range(SIMD_TILE):
	__m256 vp${ABC[N]} = _mm256_fmadd_ps(vc5, vt${ABC[N]}, vc4);

	$for N in range(SIMD_TILE):
	vp${ABC[N]} = _mm256_fmadd_ps(vp${ABC[N]}, vt${ABC[N]}, vc3);

	$for N in range(SIMD_TILE):
	vp${ABC[N]} = _mm256_fmadd_ps(vp${ABC[N]}, vt${ABC[N]}, vc2);

	$for N in range(SIMD_TILE):
	vp${ABC[N]} = _mm256_fmadd_ps(vp${ABC[N]}, vt${ABC[N]}, vc1);

	// 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
	$for N in range(SIMD_TILE):
	vt${ABC[N]} = _mm256_mul_ps(vt${ABC[N]}, vs${ABC[N]});

	$for N in range(SIMD_TILE):
	const __m256 ve${ABC[N]} = _mm256_fmadd_ps(vt${ABC[N]}, vp${ABC[N]}, vs${ABC[N]});

	// Denominator of the sigmoid fraction: 1.0 + exp(z)
	$for N in range(SIMD_TILE):
	const __m256 vd${ABC[N]} = _mm256_add_ps(ve${ABC[N]}, vone);

	$if DIV_ALGO == "div":
	// Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z))
	$for N in range(SIMD_TILE):
	__m256 vf${ABC[N]} = _mm256_div_ps(ve${ABC[N]}, vd${ABC[N]});
	$else:
	// Use Newton-Raphson method 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.
	$for N in range(SIMD_TILE):
	__m256 vr${ABC[N]} = _mm256_rcp_ps(vd${ABC[N]});

	$for N in range(SIMD_TILE):
	vr${ABC[N]} = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr${ABC[N]}, vd${ABC[N]}, vone), vr${ABC[N]}, vr${ABC[N]});

	$if DIV_ALGO == "nr2fma":
	$for N in range(SIMD_TILE):
	vr${ABC[N]} = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr${ABC[N]}, vd${ABC[N]}, vone), vr${ABC[N]}, vr${ABC[N]});

	// Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
	$for N in range(SIMD_TILE):
	__m256 vf${ABC[N]} = _mm256_mul_ps(ve${ABC[N]}, vr${ABC[N]});

	// For inputs below denormal cutoff, replace output with +0.0f.
	// Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
	$for N in range(SIMD_TILE):
	vf${ABC[N]} = _mm256_andnot_ps(_mm256_cmp_ps(vz${ABC[N]}, vdenorm_cutoff, _CMP_LT_OS), vf${ABC[N]});

	// Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
	$for N in range(SIMD_TILE):
	vf${ABC[N]} = _mm256_blendv_ps(_mm256_sub_ps(vone, vf${ABC[N]}), vf${ABC[N]}, vx${ABC[N]});

	_mm256_storeu_ps(y, vf${ABC[0]});
	$for N in range(1, SIMD_TILE):
	_mm256_storeu_ps(y + ${N * 8}, vf${ABC[N]});
	y += ${BATCH_TILE};
	}
	for (; n >= 8 * sizeof(float); n -= 8 * sizeof(float)) {
	const __m256 vx = _mm256_loadu_ps(x);
	x += 8;

	// 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 __m256 vz = _mm256_or_ps(vx, vsign_mask);

	// Compute reduced argument n := round(z / log(2)).
	// We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
	// to an integer, then subtracing the large number back. 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.
	__m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias);

	// Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
	// -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly.
	const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));

	// Subtract the large number back to get final n := round(z / log(2)).
	vn = _mm256_sub_ps(vn, vmagic_bias);

	// Compute reduced argument t := z - n * log(2).
	$if RR_STEPS == 1:
	__m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz);
	$else:
	// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
	__m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vz);
	vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);

	// Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
	__m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
	vp = _mm256_fmadd_ps(vp, vt, vc3);
	vp = _mm256_fmadd_ps(vp, vt, vc2);
	vp = _mm256_fmadd_ps(vp, vt, vc1);

	// 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 = _mm256_mul_ps(vt, vs);
	const __m256 ve = _mm256_fmadd_ps(vt, vp, vs);

	// Denominator of the sigmoid fraction: 1.0 + exp(z)
	const __m256 vd = _mm256_add_ps(ve, vone);

	$if DIV_ALGO == "div":
	// Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z))
	__m256 vf = _mm256_div_ps(ve, vd);
	$else:
	// Use Newton-Raphson method 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.
	__m256 vr = _mm256_rcp_ps(vd);
	vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);
	$if DIV_ALGO == "nr2fma":
	vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);

	// Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
	__m256 vf = _mm256_mul_ps(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 = _mm256_andnot_ps(_mm256_cmp_ps(vz, vdenorm_cutoff, _CMP_LT_OS), vf);

	// Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
	vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx);

	_mm256_storeu_ps(y, vf);
	y += 8;
	}
	if XNN_UNLIKELY(n != 0) {
	assert(n >= 1 * sizeof(float));
	assert(n <= 7 * sizeof(float));
	__m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - n));

	const __m256 vx = _mm256_maskload_ps(x, vmask);

	// 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 __m256 vz = _mm256_or_ps(vx, vsign_mask);

	// Compute reduced argument n := round(z / log(2)).
	// We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
	// to an integer, then subtracing the large number back. 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.
	__m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias);

	// Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
	// -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly.
	const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));

	// Subtract the large number back to get final n := round(z / log(2)).
	vn = _mm256_sub_ps(vn, vmagic_bias);

	// Compute reduced argument t := z - n * log(2).
	$if RR_STEPS == 1:
	__m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz);
	$else:
	// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
	__m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vz);
	vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);

	// Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
	__m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
	vp = _mm256_fmadd_ps(vp, vt, vc3);
	vp = _mm256_fmadd_ps(vp, vt, vc2);
	vp = _mm256_fmadd_ps(vp, vt, vc1);

	// 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 = _mm256_mul_ps(vt, vs);
	const __m256 ve = _mm256_fmadd_ps(vt, vp, vs);

	// Denominator of the sigmoid fraction: 1.0 + exp(z)
	const __m256 vd = _mm256_add_ps(ve, vone);

	$if DIV_ALGO == "div":
	// Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z))
	__m256 vf = _mm256_div_ps(ve, vd);
	$else:
	// Use Newton-Raphson method 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.
	__m256 vr = _mm256_rcp_ps(vd);
	vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);
	$if DIV_ALGO == "nr2fma":
	vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);

	// Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
	__m256 vf = _mm256_mul_ps(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 = _mm256_andnot_ps(_mm256_cmp_ps(vz, vdenorm_cutoff, _CMP_LT_OS), vf);

	// Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
	vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx);

	// _mm256_maskstore_ps(y, vmask, vf) could be used here, but triggers msan failures (probably an msan bug).
	__m128 vf_lo = _mm256_castps256_ps128(vf);
	if (n & (4 * sizeof(float))) {
	_mm_storeu_ps(y, vf_lo);
	vf_lo = _mm256_extractf128_ps(vf, 1);
	y += 4;
	}
	if (n & (2 * sizeof(float))) {
	_mm_storel_pi((__m64*) y, vf_lo);
	vf_lo = _mm_movehl_ps(vf_lo, vf_lo);
	y += 2;
	}
	if (n & (1 * sizeof(float))) {
	_mm_store_ss(y, vf_lo);
	}
	}
	}