| // 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 <assert.h> |
| #include <math.h> |
| |
| #include <immintrin.h> |
| |
| #include <xnnpack/raddextexp.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_raddextexp_ukernel__avx2_p5_x64_acc2( |
| 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 vaccv1 = _mm256_setzero_ps(); |
| __m256 vacce0 = vminus_inf; |
| __m256 vacce1 = 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); |
| __m256 vmax_e1 = _mm256_max_ps(vacce1, vn1); |
| vmax_e0 = _mm256_max_ps(vmax_e0, vn2); |
| vmax_e1 = _mm256_max_ps(vmax_e1, vn3); |
| vmax_e0 = _mm256_max_ps(vmax_e0, vn4); |
| vmax_e1 = _mm256_max_ps(vmax_e1, vn5); |
| vmax_e0 = _mm256_max_ps(vmax_e0, vn6); |
| vmax_e1 = _mm256_max_ps(vmax_e1, 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_acce1 = _mm256_max_ps(_mm256_sub_ps(vacce1, vmax_e1), 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_e1), 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_e1), 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_e1), 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_e1), 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 vaccs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce1, 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); |
| vaccv1 = _mm256_mul_ps(vaccv1, vaccs1); |
| vaccv0 = _mm256_fmadd_ps(vp0, vs0, vaccv0); |
| vaccv1 = _mm256_fmadd_ps(vp1, vs1, vaccv1); |
| vaccv0 = _mm256_fmadd_ps(vp2, vs2, vaccv0); |
| vaccv1 = _mm256_fmadd_ps(vp3, vs3, vaccv1); |
| vaccv0 = _mm256_fmadd_ps(vp4, vs4, vaccv0); |
| vaccv1 = _mm256_fmadd_ps(vp5, vs5, vaccv1); |
| vaccv0 = _mm256_fmadd_ps(vp6, vs6, vaccv0); |
| vaccv1 = _mm256_fmadd_ps(vp7, vs7, vaccv1); |
| |
| vacce0 = vmax_e0; |
| vacce1 = vmax_e1; |
| } |
| |
| // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums. |
| const __m256 vmax_acce01 = _mm256_max_ps(vacce0, vacce1); |
| |
| const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_acce01), vmin_exponent); |
| const __m256 vdelta_acce1 = _mm256_max_ps(_mm256_sub_ps(vacce1, vmax_acce01), vmin_exponent); |
| |
| const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23)); |
| const __m256 vaccs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce1, vmagic_bias)), 23)); |
| |
| __m256 vaccv = _mm256_mul_ps(vaccv0, vaccs0); |
| vaccv = _mm256_fmadd_ps(vaccv1, vaccs1, vaccv); |
| __m256 vacce = vmax_acce01; |
| |
| 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(); |
| } |