// Auto-generated file. Do not edit! // Template: src/f32-raddextexp/avx2-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 #include #include #include static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0}; void xnn_f32_raddextexp_ukernel__avx2_p5_x64( size_t elements, const float* x, float* sum) { assert(elements % sizeof(float) == 0); const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f); const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f); const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f); // The smallest elements such that 2**elements is considered non-negligible. // For smaller elements, 2**elements is replaced with zero. const __m256 vmin_exponent = _mm256_set1_ps(-127.0f); const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f); const __m256 vminus_inf = _mm256_set1_ps(-INFINITY); const __m256 vc0 = _mm256_set1_ps(1.0f); 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); __m256 vaccv0 = _mm256_setzero_ps(); __m256 vacce0 = vminus_inf; for (; elements >= 64 * sizeof(float); elements -= 64 * sizeof(float)) { // Load 64 (8x8) inputs at a time. const __m256 vx0 = _mm256_loadu_ps(x); const __m256 vx1 = _mm256_loadu_ps(x + 8); const __m256 vx2 = _mm256_loadu_ps(x + 16); const __m256 vx3 = _mm256_loadu_ps(x + 24); const __m256 vx4 = _mm256_loadu_ps(x + 32); const __m256 vx5 = _mm256_loadu_ps(x + 40); const __m256 vx6 = _mm256_loadu_ps(x + 48); const __m256 vx7 = _mm256_loadu_ps(x + 56); x += 64; // Compute reduced argument elements := round(x / log(2)). const __m256 vn0 = _mm256_round_ps(_mm256_mul_ps(vx0, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); const __m256 vn1 = _mm256_round_ps(_mm256_mul_ps(vx1, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); const __m256 vn2 = _mm256_round_ps(_mm256_mul_ps(vx2, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); const __m256 vn3 = _mm256_round_ps(_mm256_mul_ps(vx3, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); const __m256 vn4 = _mm256_round_ps(_mm256_mul_ps(vx4, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); const __m256 vn5 = _mm256_round_ps(_mm256_mul_ps(vx5, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); const __m256 vn6 = _mm256_round_ps(_mm256_mul_ps(vx6, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); const __m256 vn7 = _mm256_round_ps(_mm256_mul_ps(vx7, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); // Compute reduced argument t := x - elements * log(2). // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0); __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1); __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2); __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3); __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4); __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5); __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6); __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7); vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0); vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1); vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2); vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3); vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4); vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5); vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6); vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7); // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4); __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4); __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4); __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4); __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4); __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4); __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4); __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4); vp0 = _mm256_fmadd_ps(vp0, vt0, vc3); vp1 = _mm256_fmadd_ps(vp1, vt1, vc3); vp2 = _mm256_fmadd_ps(vp2, vt2, vc3); vp3 = _mm256_fmadd_ps(vp3, vt3, vc3); vp4 = _mm256_fmadd_ps(vp4, vt4, vc3); vp5 = _mm256_fmadd_ps(vp5, vt5, vc3); vp6 = _mm256_fmadd_ps(vp6, vt6, vc3); vp7 = _mm256_fmadd_ps(vp7, vt7, vc3); vp0 = _mm256_fmadd_ps(vp0, vt0, vc2); vp1 = _mm256_fmadd_ps(vp1, vt1, vc2); vp2 = _mm256_fmadd_ps(vp2, vt2, vc2); vp3 = _mm256_fmadd_ps(vp3, vt3, vc2); vp4 = _mm256_fmadd_ps(vp4, vt4, vc2); vp5 = _mm256_fmadd_ps(vp5, vt5, vc2); vp6 = _mm256_fmadd_ps(vp6, vt6, vc2); vp7 = _mm256_fmadd_ps(vp7, vt7, vc2); vp0 = _mm256_fmadd_ps(vp0, vt0, vc1); vp1 = _mm256_fmadd_ps(vp1, vt1, vc1); vp2 = _mm256_fmadd_ps(vp2, vt2, vc1); vp3 = _mm256_fmadd_ps(vp3, vt3, vc1); vp4 = _mm256_fmadd_ps(vp4, vt4, vc1); vp5 = _mm256_fmadd_ps(vp5, vt5, vc1); vp6 = _mm256_fmadd_ps(vp6, vt6, vc1); vp7 = _mm256_fmadd_ps(vp7, vt7, vc1); vp0 = _mm256_fmadd_ps(vp0, vt0, vc0); vp1 = _mm256_fmadd_ps(vp1, vt1, vc0); vp2 = _mm256_fmadd_ps(vp2, vt2, vc0); vp3 = _mm256_fmadd_ps(vp3, vt3, vc0); vp4 = _mm256_fmadd_ps(vp4, vt4, vc0); vp5 = _mm256_fmadd_ps(vp5, vt5, vc0); vp6 = _mm256_fmadd_ps(vp6, vt6, vc0); vp7 = _mm256_fmadd_ps(vp7, vt7, vc0); // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where // - vnX is "exponent" // - vpX is "mantissa" // // exp2(ae) * av + exp2(be) * bv = // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv) // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv) // // For computational efficiency we may add several "extended" floating-point numbers at a time. __m256 vmax_e0 = _mm256_max_ps(vacce0, vn0); vmax_e0 = _mm256_max_ps(vmax_e0, vn1); vmax_e0 = _mm256_max_ps(vmax_e0, vn2); vmax_e0 = _mm256_max_ps(vmax_e0, vn3); vmax_e0 = _mm256_max_ps(vmax_e0, vn4); vmax_e0 = _mm256_max_ps(vmax_e0, vn5); vmax_e0 = _mm256_max_ps(vmax_e0, vn6); vmax_e0 = _mm256_max_ps(vmax_e0, vn7); // For computational efficiency, replace exp2(delta_e) with 0.0f when delta_e <= -127.0. // This replacement is done in two steps: // 1. Clamp minimum delta_e at -127.0. // 2. Map delta_e to scale factor 0.0 when delta_e == -127.0 const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_e0), vmin_exponent); const __m256 vdelta_e0 = _mm256_max_ps(_mm256_sub_ps(vn0, vmax_e0), vmin_exponent); const __m256 vdelta_e1 = _mm256_max_ps(_mm256_sub_ps(vn1, vmax_e0), vmin_exponent); const __m256 vdelta_e2 = _mm256_max_ps(_mm256_sub_ps(vn2, vmax_e0), vmin_exponent); const __m256 vdelta_e3 = _mm256_max_ps(_mm256_sub_ps(vn3, vmax_e0), vmin_exponent); const __m256 vdelta_e4 = _mm256_max_ps(_mm256_sub_ps(vn4, vmax_e0), vmin_exponent); const __m256 vdelta_e5 = _mm256_max_ps(_mm256_sub_ps(vn5, vmax_e0), vmin_exponent); const __m256 vdelta_e6 = _mm256_max_ps(_mm256_sub_ps(vn6, vmax_e0), vmin_exponent); const __m256 vdelta_e7 = _mm256_max_ps(_mm256_sub_ps(vn7, vmax_e0), vmin_exponent); // Convert delta-exponents into scale factors: // - s = exp2(delta_e) when delta_e > -127.0 // - s = 0.0 when delta_e <= -127.0 // // Note: delta-exponents can not exceed 0.0, thus scale factors can not exceed 1.0. const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23)); const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e0, vmagic_bias)), 23)); const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e1, vmagic_bias)), 23)); const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e2, vmagic_bias)), 23)); const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e3, vmagic_bias)), 23)); const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e4, vmagic_bias)), 23)); const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e5, vmagic_bias)), 23)); const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e6, vmagic_bias)), 23)); const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e7, vmagic_bias)), 23)); // Update accumulated "mantissa" and "exponent" values vaccv0 = _mm256_mul_ps(vaccv0, vaccs0); vaccv0 = _mm256_fmadd_ps(vp0, vs0, vaccv0); vaccv0 = _mm256_fmadd_ps(vp1, vs1, vaccv0); vaccv0 = _mm256_fmadd_ps(vp2, vs2, vaccv0); vaccv0 = _mm256_fmadd_ps(vp3, vs3, vaccv0); vaccv0 = _mm256_fmadd_ps(vp4, vs4, vaccv0); vaccv0 = _mm256_fmadd_ps(vp5, vs5, vaccv0); vaccv0 = _mm256_fmadd_ps(vp6, vs6, vaccv0); vaccv0 = _mm256_fmadd_ps(vp7, vs7, vaccv0); vacce0 = vmax_e0; } // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums. __m256 vaccv = vaccv0; __m256 vacce = vacce0; for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) { // Load 8 inputs at a time. const __m256 vx = _mm256_loadu_ps(x); x += 8; // Compute reduced argument elements := round(x / log(2)). const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); // Compute reduced argument t := x - elements * log(2). // 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, vx); vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt); // Compute degree-5 polynomial approximation 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); vp = _mm256_fmadd_ps(vp, vt, vc0); // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation. const __m256 vmax_e = _mm256_max_ps(vacce, vn); // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later. const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent); const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent); // Convert exponents into scale factors. const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23)); const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23)); // Update accumulated "mantissa" and "exponent" values. vaccv = _mm256_mul_ps(vaccv, vaccs); vaccv = _mm256_fmadd_ps(vp, vs, vaccv); vacce = vmax_e; } if XNN_UNLIKELY(elements != 0) { assert(elements >= 1 * sizeof(float)); assert(elements <= 7 * sizeof(float)); const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements)); // Load up to 7 inputs at a time. const __m256 vx = _mm256_maskload_ps(x, vmask); // Compute reduced argument elements := round(x / log(2)). __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC); // Compute reduced argument t := x - elements * log(2). // 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, vx); vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt); // Correct reduced argument elements for masked out elements. vn = _mm256_blendv_ps(vacce, vn, _mm256_castsi256_ps(vmask)); // Compute degree-5 polynomial approximation 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); vp = _mm256_fmadd_ps(vp, vt, vc0); vp = _mm256_and_ps(vp, _mm256_castsi256_ps(vmask)); // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation. const __m256 vmax_e = _mm256_max_ps(vacce, vn); // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later. const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent); const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent); // Convert exponents into scale factors. const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23)); const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23)); // Update accumulated "mantissa" and "exponent" values. vaccv = _mm256_mul_ps(vaccv, vaccs); vaccv = _mm256_fmadd_ps(vp, vs, vaccv); vacce = vmax_e; } // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum. __m256 vmax_acce = _mm256_max_ps(vacce, _mm256_permute2f128_ps(vacce, vacce, 1)); vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(1, 0, 3, 2))); vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(2, 3, 0, 1))); const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_acce), vmin_exponent); const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23)); vaccv = _mm256_mul_ps(vaccv, vaccs); __m128 vaccv_sum = _mm_add_ps(_mm256_castps256_ps128(vaccv), _mm256_extractf128_ps(vaccv, 1)); vaccv_sum = _mm_add_ps(vaccv_sum, _mm_movehl_ps(vaccv_sum, vaccv_sum)); vaccv_sum = _mm_add_ss(vaccv_sum, _mm_movehdup_ps(vaccv_sum)); _mm_store_ss(&sum[0], vaccv_sum); _mm_store_ss(&sum[1], _mm256_castps256_ps128(vmax_acce)); _mm256_zeroupper(); }