src/f32-raddstoreexpminusmax/gen/sse2-p5-x16-acc4.c - platform/external/XNNPACK - Gitiles

 // Auto-generated file. Do not edit!
 //   Template: src/f32-raddstoreexpminusmax/sse2-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 <emmintrin.h>

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


 void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x16_acc4(
     size_t elements,
     const float* input,
     float* output,
     float* sum,
     float max) XNN_DISABLE_TSAN
 {
   assert(elements % sizeof(float) == 0);

   const __m128 vmagic_bias = _mm_set1_ps(0x1.8000FEp23f);
   // The smallest x for which expf(x) is normalized.
   const __m128 vdenorm_cutoff = _mm_set1_ps(-0x1.5D589Ep6f);
   const __m128 vlog2e = _mm_set1_ps(0x1.715476p+0f);
   // Last 7 bits are zeroes
   const __m128 vminus_ln2_hi = _mm_set1_ps(-0x1.62E400p-1f);
   const __m128 vminus_ln2_lo = _mm_set1_ps(-0x1.7F7D1Cp-20f);

   const __m128 vc1 = _mm_set1_ps(0x1.FFFFF6p-1f);
   const __m128 vc2 = _mm_set1_ps(0x1.FFFDC6p-2f);
   const __m128 vc3 = _mm_set1_ps(0x1.555A80p-3f);
   const __m128 vc4 = _mm_set1_ps(0x1.573A1Ap-5f);
   const __m128 vc5 = _mm_set1_ps(0x1.0F9F9Cp-7f);

   const __m128 vi_max = _mm_set1_ps(max);

   __m128 vacc0 = _mm_setzero_ps();
   __m128 vacc1 = _mm_setzero_ps();
   __m128 vacc2 = _mm_setzero_ps();
   __m128 vacc3 = _mm_setzero_ps();
   for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
     // Load 16 (4x4) inputs at a time.
     const __m128 vi0123 = _mm_loadu_ps(input);
     const __m128 vi4567 = _mm_loadu_ps(input + 4);
     const __m128 vi89AB = _mm_loadu_ps(input + 8);
     const __m128 viCDEF = _mm_loadu_ps(input + 12);
     input += 16;

     // Subtract maximum input x := i - i_max. This implies x <= 0.
     const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
     const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
     const __m128 vx89AB = _mm_sub_ps(vi89AB, vi_max);
     const __m128 vxCDEF = _mm_sub_ps(viCDEF, vi_max);

     // Compute reduced argument elements := round(x / log(2)).
     __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
     __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
     __m128 vn89AB = _mm_add_ps(_mm_mul_ps(vx89AB, vlog2e), vmagic_bias);
     __m128 vnCDEF = _mm_add_ps(_mm_mul_ps(vxCDEF, vlog2e), vmagic_bias);

     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
     const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
     const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
     const __m128 vs89AB = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn89AB), 23));
     const __m128 vsCDEF = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnCDEF), 23));

     // Subtract the large number back to get final elements := round(x / log(2)).
     vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
     vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
     vn89AB = _mm_sub_ps(vn89AB, vmagic_bias);
     vnCDEF = _mm_sub_ps(vnCDEF, vmagic_bias);

     // Compute reduced argument t := x - elements * log(2).
     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
     __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
     __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
     __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
     __m128 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_hi), vxCDEF);

     vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
     vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
     vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
     vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_lo), vtCDEF);

     // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
     __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
     __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
     __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
     __m128 vpCDEF = _mm_add_ps(_mm_mul_ps(vc5, vtCDEF), vc4);

     vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
     vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
     vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
     vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc3);

     vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
     vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
     vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
     vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc2);

     vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
     vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
     vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
     vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc1);

     // 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 = _mm_mul_ps(vt0123, vs0123);
     vt4567 = _mm_mul_ps(vt4567, vs4567);
     vt89AB = _mm_mul_ps(vt89AB, vs89AB);
     vtCDEF = _mm_mul_ps(vtCDEF, vsCDEF);

     __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
     __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
     __m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
     __m128 vfCDEF = _mm_add_ps(_mm_mul_ps(vtCDEF, vpCDEF), vsCDEF);

     // For inputs below zero cutoff, replace output with +0.0f.
     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
     vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
     vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
     vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
     vfCDEF = _mm_andnot_ps(_mm_cmplt_ps(vxCDEF, vdenorm_cutoff), vfCDEF);

     // Store 16 (4x4) outputs at a time.
     _mm_storeu_ps(output, vf0123);
     _mm_storeu_ps(output + 4, vf4567);
     _mm_storeu_ps(output + 8, vf89AB);
     _mm_storeu_ps(output + 12, vfCDEF);
     output += 16;

     // Accumulate computed exponents.
     vacc0 = _mm_add_ps(vacc0, vf0123);
     vacc0 = _mm_add_ps(vacc0, vf4567);
     vacc0 = _mm_add_ps(vacc0, vf89AB);
     vacc0 = _mm_add_ps(vacc0, vfCDEF);
   }
   // Add up all accumulators to vacc0
   vacc0 = _mm_add_ps(vacc0, vacc1);
   vacc2 = _mm_add_ps(vacc2, vacc3);
   vacc0 = _mm_add_ps(vacc0, vacc2);

   __m128 vacc = vacc0;
   for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
     // Load 4 inputs at a time.
     const __m128 vi = _mm_loadu_ps(input);
     input += 4;

     // Subtract maximum input x := i - i_max. This implies x <= 0.
     const __m128 vx = _mm_sub_ps(vi, vi_max);

     // Compute reduced argument elements := round(x / log(2)).
     __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);

     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
     const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));

     // Subtract the large number back to get final elements := round(x / log(2)).
     vn = _mm_sub_ps(vn, vmagic_bias);

     // Compute reduced argument t := x - elements * log(2).
     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
     __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
     vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);

     // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
     __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
     vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
     vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
     vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);

     // 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 = _mm_mul_ps(vt, vs);
     __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);

     // For inputs below zero cutoff, replace output with +0.0f.
     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
     vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);

     // Store 4 outputs at a time.
     _mm_storeu_ps(output, vf);
     output += 4;

     // Accumulate computed exponents.
     vacc = _mm_add_ps(vacc, vf);
   }
   if (elements != 0) {
     assert(elements >= 1 * sizeof(float));
     assert(elements <= 3 * sizeof(float));
     // Load 4 inputs at a time.
     const __m128 vi = _mm_loadu_ps(input);

     // Subtract maximum input x := i - i_max. This implies x <= 0.
     const __m128 vx = _mm_sub_ps(vi, vi_max);

     // Compute reduced argument elements := round(x / log(2)).
     __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);

     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
     const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));

     // Subtract the large number back to get final elements := round(x / log(2)).
     vn = _mm_sub_ps(vn, vmagic_bias);

     // Compute reduced argument t := x - elements * log(2).
     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
     __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
     vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);

     // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
     __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
     vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
     vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
     vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);

     // 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 = _mm_mul_ps(vt, vs);
     __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);

     // For inputs below zero cutoff, replace output with +0.0f.
     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
     vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);

     if (elements & (2 * sizeof(float))) {
       // Store 2 outputs at a time.
       _mm_storel_pi((__m64*) output, vf);
       output += 2;

       // Accumulate 2 computed exponents.
       vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));

       vf = _mm_movehl_ps(vf, vf);
     }
     if (elements & (1 * sizeof(float))) {
       // Store 1 output at a time.
       _mm_store_ss(output, vf);

       // Accumulate 1 computed exponent.
       vacc = _mm_add_ss(vacc, vf);
     }
   }
   // Reduce 4 elements in the SIMD register
   vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
   vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
   _mm_store_ss(sum, vacc);
 }
	// Auto-generated file. Do not edit!
	// Template: src/f32-raddstoreexpminusmax/sse2-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 <emmintrin.h>

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


	void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x16_acc4(
	size_t elements,
	const float* input,
	float* output,
	float* sum,
	float max) XNN_DISABLE_TSAN
	{
	assert(elements % sizeof(float) == 0);

	const __m128 vmagic_bias = _mm_set1_ps(0x1.8000FEp23f);
	// The smallest x for which expf(x) is normalized.
	const __m128 vdenorm_cutoff = _mm_set1_ps(-0x1.5D589Ep6f);
	const __m128 vlog2e = _mm_set1_ps(0x1.715476p+0f);
	// Last 7 bits are zeroes
	const __m128 vminus_ln2_hi = _mm_set1_ps(-0x1.62E400p-1f);
	const __m128 vminus_ln2_lo = _mm_set1_ps(-0x1.7F7D1Cp-20f);

	const __m128 vc1 = _mm_set1_ps(0x1.FFFFF6p-1f);
	const __m128 vc2 = _mm_set1_ps(0x1.FFFDC6p-2f);
	const __m128 vc3 = _mm_set1_ps(0x1.555A80p-3f);
	const __m128 vc4 = _mm_set1_ps(0x1.573A1Ap-5f);
	const __m128 vc5 = _mm_set1_ps(0x1.0F9F9Cp-7f);

	const __m128 vi_max = _mm_set1_ps(max);

	__m128 vacc0 = _mm_setzero_ps();
	__m128 vacc1 = _mm_setzero_ps();
	__m128 vacc2 = _mm_setzero_ps();
	__m128 vacc3 = _mm_setzero_ps();
	for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
	// Load 16 (4x4) inputs at a time.
	const __m128 vi0123 = _mm_loadu_ps(input);
	const __m128 vi4567 = _mm_loadu_ps(input + 4);
	const __m128 vi89AB = _mm_loadu_ps(input + 8);
	const __m128 viCDEF = _mm_loadu_ps(input + 12);
	input += 16;

	// Subtract maximum input x := i - i_max. This implies x <= 0.
	const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
	const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
	const __m128 vx89AB = _mm_sub_ps(vi89AB, vi_max);
	const __m128 vxCDEF = _mm_sub_ps(viCDEF, vi_max);

	// Compute reduced argument elements := round(x / log(2)).
	__m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
	__m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
	__m128 vn89AB = _mm_add_ps(_mm_mul_ps(vx89AB, vlog2e), vmagic_bias);
	__m128 vnCDEF = _mm_add_ps(_mm_mul_ps(vxCDEF, vlog2e), vmagic_bias);

	// Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
	// -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
	const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
	const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
	const __m128 vs89AB = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn89AB), 23));
	const __m128 vsCDEF = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnCDEF), 23));

	// Subtract the large number back to get final elements := round(x / log(2)).
	vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
	vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
	vn89AB = _mm_sub_ps(vn89AB, vmagic_bias);
	vnCDEF = _mm_sub_ps(vnCDEF, vmagic_bias);

	// Compute reduced argument t := x - elements * log(2).
	// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
	__m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
	__m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
	__m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
	__m128 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_hi), vxCDEF);

	vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
	vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
	vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
	vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_lo), vtCDEF);

	// Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
	__m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
	__m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
	__m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
	__m128 vpCDEF = _mm_add_ps(_mm_mul_ps(vc5, vtCDEF), vc4);

	vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
	vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
	vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
	vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc3);

	vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
	vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
	vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
	vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc2);

	vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
	vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
	vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
	vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc1);

	// 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 = _mm_mul_ps(vt0123, vs0123);
	vt4567 = _mm_mul_ps(vt4567, vs4567);
	vt89AB = _mm_mul_ps(vt89AB, vs89AB);
	vtCDEF = _mm_mul_ps(vtCDEF, vsCDEF);

	__m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
	__m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
	__m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
	__m128 vfCDEF = _mm_add_ps(_mm_mul_ps(vtCDEF, vpCDEF), vsCDEF);

	// For inputs below zero cutoff, replace output with +0.0f.
	// Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
	vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
	vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
	vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
	vfCDEF = _mm_andnot_ps(_mm_cmplt_ps(vxCDEF, vdenorm_cutoff), vfCDEF);

	// Store 16 (4x4) outputs at a time.
	_mm_storeu_ps(output, vf0123);
	_mm_storeu_ps(output + 4, vf4567);
	_mm_storeu_ps(output + 8, vf89AB);
	_mm_storeu_ps(output + 12, vfCDEF);
	output += 16;

	// Accumulate computed exponents.
	vacc0 = _mm_add_ps(vacc0, vf0123);
	vacc0 = _mm_add_ps(vacc0, vf4567);
	vacc0 = _mm_add_ps(vacc0, vf89AB);
	vacc0 = _mm_add_ps(vacc0, vfCDEF);
	}
	// Add up all accumulators to vacc0
	vacc0 = _mm_add_ps(vacc0, vacc1);
	vacc2 = _mm_add_ps(vacc2, vacc3);
	vacc0 = _mm_add_ps(vacc0, vacc2);

	__m128 vacc = vacc0;
	for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
	// Load 4 inputs at a time.
	const __m128 vi = _mm_loadu_ps(input);
	input += 4;

	// Subtract maximum input x := i - i_max. This implies x <= 0.
	const __m128 vx = _mm_sub_ps(vi, vi_max);

	// Compute reduced argument elements := round(x / log(2)).
	__m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);

	// Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
	// -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
	const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));

	// Subtract the large number back to get final elements := round(x / log(2)).
	vn = _mm_sub_ps(vn, vmagic_bias);

	// Compute reduced argument t := x - elements * log(2).
	// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
	__m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
	vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);

	// Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
	__m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
	vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
	vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
	vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);

	// 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 = _mm_mul_ps(vt, vs);
	__m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);

	// For inputs below zero cutoff, replace output with +0.0f.
	// Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
	vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);

	// Store 4 outputs at a time.
	_mm_storeu_ps(output, vf);
	output += 4;

	// Accumulate computed exponents.
	vacc = _mm_add_ps(vacc, vf);
	}
	if (elements != 0) {
	assert(elements >= 1 * sizeof(float));
	assert(elements <= 3 * sizeof(float));
	// Load 4 inputs at a time.
	const __m128 vi = _mm_loadu_ps(input);

	// Subtract maximum input x := i - i_max. This implies x <= 0.
	const __m128 vx = _mm_sub_ps(vi, vi_max);

	// Compute reduced argument elements := round(x / log(2)).
	__m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);

	// Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
	// -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
	const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));

	// Subtract the large number back to get final elements := round(x / log(2)).
	vn = _mm_sub_ps(vn, vmagic_bias);

	// Compute reduced argument t := x - elements * log(2).
	// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
	__m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
	vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);

	// Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
	__m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
	vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
	vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
	vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);

	// 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 = _mm_mul_ps(vt, vs);
	__m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);

	// For inputs below zero cutoff, replace output with +0.0f.
	// Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
	vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);

	if (elements & (2 * sizeof(float))) {
	// Store 2 outputs at a time.
	_mm_storel_pi((__m64*) output, vf);
	output += 2;

	// Accumulate 2 computed exponents.
	vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));

	vf = _mm_movehl_ps(vf, vf);
	}
	if (elements & (1 * sizeof(float))) {
	// Store 1 output at a time.
	_mm_store_ss(output, vf);

	// Accumulate 1 computed exponent.
	vacc = _mm_add_ss(vacc, vf);
	}
	}
	// Reduce 4 elements in the SIMD register
	vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
	vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
	_mm_store_ss(sum, vacc);
	}