// Auto-generated file. Do not edit! // Template: src/f32-raddextexp/avx512f-p5-scalef.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 #include #include void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x144_acc3( size_t elements, const float* x, float* sum) { assert(elements % sizeof(float) == 0); const __m512 vlog2e = _mm512_set1_ps(0x1.715476p+0f); const __m512 vminus_ln2_hi = _mm512_set1_ps(-0x1.62E43p-1f); const __m512 vminus_ln2_lo = _mm512_set1_ps(0x1.05C61p-29f); const __m512 vc0 = _mm512_set1_ps(1.0f); const __m512 vc1 = _mm512_set1_ps(0x1.FFFFF6p-1f); const __m512 vc2 = _mm512_set1_ps(0x1.FFFDC6p-2f); const __m512 vc3 = _mm512_set1_ps(0x1.555A80p-3f); const __m512 vc4 = _mm512_set1_ps(0x1.573A1Ap-5f); const __m512 vc5 = _mm512_set1_ps(0x1.0F9F9Cp-7f); const __m512 vminus_inf = _mm512_set1_ps(-INFINITY); __m512 vaccv0 = _mm512_setzero_ps(); __m512 vaccv1 = _mm512_setzero_ps(); __m512 vaccv2 = _mm512_setzero_ps(); __m512 vacce0 = vminus_inf; __m512 vacce1 = vminus_inf; __m512 vacce2 = vminus_inf; for (; elements >= 144 * sizeof(float); elements -= 144 * sizeof(float)) { // Load 144 (9x16) inputs at a time. const __m512 vx0 = _mm512_loadu_ps(x); const __m512 vx1 = _mm512_loadu_ps(x + 16); const __m512 vx2 = _mm512_loadu_ps(x + 32); const __m512 vx3 = _mm512_loadu_ps(x + 48); const __m512 vx4 = _mm512_loadu_ps(x + 64); const __m512 vx5 = _mm512_loadu_ps(x + 80); const __m512 vx6 = _mm512_loadu_ps(x + 96); const __m512 vx7 = _mm512_loadu_ps(x + 112); const __m512 vx8 = _mm512_loadu_ps(x + 128); x += 144; // Compute reduced argument elements := round(x / log(2)). const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0); const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0); const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0); const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0); const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0); const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0); const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0); const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, vlog2e), 0); const __m512 vn8 = _mm512_roundscale_ps(_mm512_mul_ps(vx8, vlog2e), 0); // Compute reduced argument t := x - elements * log(2). // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. __m512 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_hi, vx0); __m512 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_hi, vx1); __m512 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_hi, vx2); __m512 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_hi, vx3); __m512 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_hi, vx4); __m512 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_hi, vx5); __m512 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_hi, vx6); __m512 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_hi, vx7); __m512 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_hi, vx8); vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0); vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1); vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2); vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3); vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4); vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5); vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6); vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7); vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_lo, vt8); // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4); __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4); __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4); __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4); __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4); __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4); __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4); __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4); __m512 vp8 = _mm512_fmadd_ps(vc5, vt8, vc4); vp0 = _mm512_fmadd_ps(vp0, vt0, vc3); vp1 = _mm512_fmadd_ps(vp1, vt1, vc3); vp2 = _mm512_fmadd_ps(vp2, vt2, vc3); vp3 = _mm512_fmadd_ps(vp3, vt3, vc3); vp4 = _mm512_fmadd_ps(vp4, vt4, vc3); vp5 = _mm512_fmadd_ps(vp5, vt5, vc3); vp6 = _mm512_fmadd_ps(vp6, vt6, vc3); vp7 = _mm512_fmadd_ps(vp7, vt7, vc3); vp8 = _mm512_fmadd_ps(vp8, vt8, vc3); vp0 = _mm512_fmadd_ps(vp0, vt0, vc2); vp1 = _mm512_fmadd_ps(vp1, vt1, vc2); vp2 = _mm512_fmadd_ps(vp2, vt2, vc2); vp3 = _mm512_fmadd_ps(vp3, vt3, vc2); vp4 = _mm512_fmadd_ps(vp4, vt4, vc2); vp5 = _mm512_fmadd_ps(vp5, vt5, vc2); vp6 = _mm512_fmadd_ps(vp6, vt6, vc2); vp7 = _mm512_fmadd_ps(vp7, vt7, vc2); vp8 = _mm512_fmadd_ps(vp8, vt8, vc2); vp0 = _mm512_fmadd_ps(vp0, vt0, vc1); vp1 = _mm512_fmadd_ps(vp1, vt1, vc1); vp2 = _mm512_fmadd_ps(vp2, vt2, vc1); vp3 = _mm512_fmadd_ps(vp3, vt3, vc1); vp4 = _mm512_fmadd_ps(vp4, vt4, vc1); vp5 = _mm512_fmadd_ps(vp5, vt5, vc1); vp6 = _mm512_fmadd_ps(vp6, vt6, vc1); vp7 = _mm512_fmadd_ps(vp7, vt7, vc1); vp8 = _mm512_fmadd_ps(vp8, vt8, vc1); vp0 = _mm512_fmadd_ps(vp0, vt0, vc0); vp1 = _mm512_fmadd_ps(vp1, vt1, vc0); vp2 = _mm512_fmadd_ps(vp2, vt2, vc0); vp3 = _mm512_fmadd_ps(vp3, vt3, vc0); vp4 = _mm512_fmadd_ps(vp4, vt4, vc0); vp5 = _mm512_fmadd_ps(vp5, vt5, vc0); vp6 = _mm512_fmadd_ps(vp6, vt6, vc0); vp7 = _mm512_fmadd_ps(vp7, vt7, vc0); vp8 = _mm512_fmadd_ps(vp8, vt8, 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 add three "extended" floating-point numbers at a time. __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0); __m512 vmax_e1 = _mm512_max_ps(vacce1, vn1); __m512 vmax_e2 = _mm512_max_ps(vacce2, vn2); vmax_e0 = _mm512_max_ps(vmax_e0, vn3); vmax_e1 = _mm512_max_ps(vmax_e1, vn4); vmax_e2 = _mm512_max_ps(vmax_e2, vn5); vmax_e0 = _mm512_max_ps(vmax_e0, vn6); vmax_e1 = _mm512_max_ps(vmax_e1, vn7); vmax_e2 = _mm512_max_ps(vmax_e2, vn8); const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0); const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_e1); const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_e2); const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0); const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e1); const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e2); const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e0); const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e1); const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e2); const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e0); const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e1); const __m512 vdelta_e8 = _mm512_sub_ps(vn8, vmax_e2); // Update accumulated "mantissa" and "exponent" values vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0); vaccv1 = _mm512_scalef_ps(vaccv1, vdelta_acce1); vaccv2 = _mm512_scalef_ps(vaccv2, vdelta_acce2); vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0)); vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp1, vdelta_e1)); vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp2, vdelta_e2)); vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp3, vdelta_e3)); vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp4, vdelta_e4)); vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp5, vdelta_e5)); vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp6, vdelta_e6)); vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp7, vdelta_e7)); vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp8, vdelta_e8)); vacce0 = vmax_e0; vacce1 = vmax_e1; vacce2 = vmax_e2; } // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums. const __m512 vmax_acce01 = _mm512_max_ps(vacce0, vacce1); const __m512 vmax_acce2 = vacce2; const __m512 vmax_acce012 = _mm512_max_ps(vmax_acce01, vmax_acce2); const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_acce012); const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_acce012); const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_acce012); __m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0); vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv1, vdelta_acce1)); vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv2, vdelta_acce2)); __m512 vacce = vmax_acce012; for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) { // Load 16 inputs at a time. const __m512 vx = _mm512_loadu_ps(x); x += 16; // Compute reduced argument elements := round(x / log(2)). const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0); // Compute reduced argument t := x - elements * log(2). // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx); vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt); // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4); vp = _mm512_fmadd_ps(vp, vt, vc3); vp = _mm512_fmadd_ps(vp, vt, vc2); vp = _mm512_fmadd_ps(vp, vt, vc1); vp = _mm512_fmadd_ps(vp, vt, vc0); // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation. const __m512 vmax_e = _mm512_max_ps(vacce, vn); const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e); const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e); vaccv = _mm512_scalef_ps(vaccv, vdelta_acce); vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e)); vacce = vmax_e; } if XNN_UNLIKELY(elements != 0) { // Prepare mask for valid 32-bit elements (depends on elements). elements >>= 2 /* log2(sizeof(float)) */; const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1))); // Load up to 15 inputs at a time. const __m512 vx = _mm512_maskz_loadu_ps(vmask, x); // Compute reduced argument elements := round(x / log(2)). const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0); // Compute reduced argument t := x - elements * log(2). // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx); vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt); // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4); vp = _mm512_fmadd_ps(vp, vt, vc3); vp = _mm512_fmadd_ps(vp, vt, vc2); vp = _mm512_fmadd_ps(vp, vt, vc1); vp = _mm512_fmadd_ps(vp, vt, vc0); // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation. const __m512 vmax_e = _mm512_mask_max_ps(vacce, vmask, vacce, vn); const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e); const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e); vaccv = _mm512_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce); vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e)); vacce = vmax_e; } // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum. const float vmax_acce = _mm512_reduce_max_ps(vacce); const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce)); sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce)); sum[1] = vmax_acce; _mm256_zeroupper(); }