// Auto-generated file. Do not edit! // Template: src/f32-raddstoreexpminusmax/neon-lut64-p2.c.in // Generator: tools/xngen // // Copyright 2020 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 extern XNN_INTERNAL const float xnn_table_exp2_k_over_64[64]; void xnn_f32_raddstoreexpminusmax_ukernel__neon_lut64_p2_x16( size_t elements, const float* input, float* output, float* sum, float max) XNN_DISABLE_TSAN { assert(elements % sizeof(float) == 0); const float32x4_t vmagic_bias = vmovq_n_f32(0x1.800000p23f); // The smallest x for which expf(x) is normalized. const float32x4_t vdenorm_cutoff = vmovq_n_f32(-0x1.5D589Ep6f); const float32x4_t vlog2e_x64 = vmovq_n_f32(0x1.715476p6f); // Last 13 bits are zeroes const float32x4_t vminus_ln2_o64_hi = vmovq_n_f32(-0x1.630000p-7f); const float32x4_t vminus_ln2_o64_lo = vmovq_n_f32(0x1.BD0106p-19f); const float32x4_t vc2 = vmovq_n_f32(0x1.FFFF0Ap-2f); const int32x4_t vindex_mask = vmovq_n_s32(INT32_C(0x3F)); const float32x4_t vi_max = vdupq_n_f32(max); float32x4_t vacc0 = vmovq_n_f32(0.0f); for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) { // Load 16 (4x4) inputs at a time. const float32x4_t vi0123 = vld1q_f32(input); input += 4; const float32x4_t vi4567 = vld1q_f32(input); input += 4; const float32x4_t vi89AB = vld1q_f32(input); input += 4; const float32x4_t viCDEF = vld1q_f32(input); input += 4; // Subtract maximum input x := i - i_max. This implies x <= 0. const float32x4_t vx0123 = vsubq_f32(vi0123, vi_max); const float32x4_t vx4567 = vsubq_f32(vi4567, vi_max); const float32x4_t vx89AB = vsubq_f32(vi89AB, vi_max); const float32x4_t vxCDEF = vsubq_f32(viCDEF, vi_max); // Compute reduced argument n := round(x * 64 / log(2)). // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e. // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0] // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the // algorithm. float32x4_t vn0123 = vmlaq_f32(vmagic_bias, vx0123, vlog2e_x64); float32x4_t vn4567 = vmlaq_f32(vmagic_bias, vx4567, vlog2e_x64); float32x4_t vn89AB = vmlaq_f32(vmagic_bias, vx89AB, vlog2e_x64); float32x4_t vnCDEF = vmlaq_f32(vmagic_bias, vxCDEF, vlog2e_x64); // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized, // i.e. -87.33642 <= x <= 0.0. As n has 6 fractional bits, we split s == 2**(n / 64) = 2**e * 2**(n / 64 - e), where // e := int(n / 64). We create s in two steps: // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0. // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0, // and thus the adjusted exponent is not lower than -126. // // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent). const int32x4_t ve0123 = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn0123), vmovq_n_s32(INT32_C(0x3F))), 17); const int32x4_t ve4567 = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn4567), vmovq_n_s32(INT32_C(0x3F))), 17); const int32x4_t ve89AB = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn89AB), vmovq_n_s32(INT32_C(0x3F))), 17); const int32x4_t veCDEF = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vnCDEF), vmovq_n_s32(INT32_C(0x3F))), 17); // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64). const uint64x2_t vidx0123 = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn0123), vindex_mask)); const uint64_t vidx01 = vgetq_lane_u64(vidx0123, 0); const uint64_t vidx23 = vgetq_lane_u64(vidx0123, 1); const uint64x2_t vidx4567 = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn4567), vindex_mask)); const uint64_t vidx45 = vgetq_lane_u64(vidx4567, 0); const uint64_t vidx67 = vgetq_lane_u64(vidx4567, 1); const uint64x2_t vidx89AB = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn89AB), vindex_mask)); const uint64_t vidx89 = vgetq_lane_u64(vidx89AB, 0); const uint64_t vidxAB = vgetq_lane_u64(vidx89AB, 1); const uint64x2_t vidxCDEF = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vnCDEF), vindex_mask)); const uint64_t vidxCD = vgetq_lane_u64(vidxCDEF, 0); const uint64_t vidxEF = vgetq_lane_u64(vidxCDEF, 1); float32x2_t vl01 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx01]); float32x2_t vl23 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx23]); float32x2_t vl45 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx45]); float32x2_t vl67 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx67]); float32x2_t vl89 = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx89]); float32x2_t vlAB = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidxAB]); float32x2_t vlCD = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidxCD]); float32x2_t vlEF = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidxEF]); vl01 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx01 >> 32)], vl01, 1); vl23 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx23 >> 32)], vl23, 1); const float32x4_t vl0123 = vcombine_f32(vl01, vl23); vl45 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx45 >> 32)], vl45, 1); vl67 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx67 >> 32)], vl67, 1); const float32x4_t vl4567 = vcombine_f32(vl45, vl67); vl89 = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx89 >> 32)], vl89, 1); vlAB = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidxAB >> 32)], vlAB, 1); const float32x4_t vl89AB = vcombine_f32(vl89, vlAB); vlCD = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidxCD >> 32)], vlCD, 1); vlEF = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidxEF >> 32)], vlEF, 1); const float32x4_t vlCDEF = vcombine_f32(vlCD, vlEF); // Adjust exponent of the value l fetched from the table to get the final s value. const float32x4_t vs0123 = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl0123), ve0123)); const float32x4_t vs4567 = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl4567), ve4567)); const float32x4_t vs89AB = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl89AB), ve89AB)); const float32x4_t vsCDEF = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vlCDEF), veCDEF)); // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number. vn0123 = vsubq_f32(vn0123, vmagic_bias); vn4567 = vsubq_f32(vn4567, vmagic_bias); vn89AB = vsubq_f32(vn89AB, vmagic_bias); vnCDEF = vsubq_f32(vnCDEF, vmagic_bias); // Compute reduced argument t := x - n * log(2) / 64. // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy. float32x4_t vt0123 = vmlaq_f32(vx0123, vn0123, vminus_ln2_o64_hi); float32x4_t vt4567 = vmlaq_f32(vx4567, vn4567, vminus_ln2_o64_hi); float32x4_t vt89AB = vmlaq_f32(vx89AB, vn89AB, vminus_ln2_o64_hi); float32x4_t vtCDEF = vmlaq_f32(vxCDEF, vnCDEF, vminus_ln2_o64_hi); vt0123 = vmlaq_f32(vt0123, vn0123, vminus_ln2_o64_lo); vt4567 = vmlaq_f32(vt4567, vn4567, vminus_ln2_o64_lo); vt89AB = vmlaq_f32(vt89AB, vn89AB, vminus_ln2_o64_lo); vtCDEF = vmlaq_f32(vtCDEF, vnCDEF, vminus_ln2_o64_lo); // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/128, log(2)/128]. float32x4_t vp0123 = vmulq_f32(vt0123, vc2); float32x4_t vp4567 = vmulq_f32(vt4567, vc2); float32x4_t vp89AB = vmulq_f32(vt89AB, vc2); float32x4_t vpCDEF = vmulq_f32(vtCDEF, vc2); vp0123 = vmlaq_f32(vt0123, vt0123, vp0123); vp4567 = vmlaq_f32(vt4567, vt4567, vp4567); vp89AB = vmlaq_f32(vt89AB, vt89AB, vp89AB); vpCDEF = vmlaq_f32(vtCDEF, vtCDEF, vpCDEF); // Reconstruct the final f value: // f = s * (1 + t * (1 + t * c2)) // = s * (1 + t + t * (t * c2)) // = s + s * (t + t * (t * c2)) // = s + s * p float32x4_t vf0123 = vmlaq_f32(vs0123, vs0123, vp0123); float32x4_t vf4567 = vmlaq_f32(vs4567, vs4567, vp4567); float32x4_t vf89AB = vmlaq_f32(vs89AB, vs89AB, vp89AB); float32x4_t vfCDEF = vmlaq_f32(vsCDEF, vsCDEF, vpCDEF); // For inputs below denormal cutoff, replace output with +0.0f. // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. vf0123 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf0123), vcltq_f32(vx0123, vdenorm_cutoff))); vf4567 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf4567), vcltq_f32(vx4567, vdenorm_cutoff))); vf89AB = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf89AB), vcltq_f32(vx89AB, vdenorm_cutoff))); vfCDEF = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfCDEF), vcltq_f32(vxCDEF, vdenorm_cutoff))); // Store 16 (4x4) outputs at a time. vst1q_f32(output, vf0123); output += 4; vst1q_f32(output, vf4567); output += 4; vst1q_f32(output, vf89AB); output += 4; vst1q_f32(output, vfCDEF); output += 4; // Accumulate computed exponents. vacc0 = vaddq_f32(vacc0, vf0123); vacc0 = vaddq_f32(vacc0, vf4567); vacc0 = vaddq_f32(vacc0, vf89AB); vacc0 = vaddq_f32(vacc0, vfCDEF); } float32x4_t vacc = vacc0; for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) { // Load 4 inputs at a time. const float32x4_t vi = vld1q_f32(input); input += 4; // Subtract maximum input x := i - i_max. This implies x <= 0. const float32x4_t vx = vsubq_f32(vi, vi_max); // Compute reduced argument n := round(x * 64 / log(2)). // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e. // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0] // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the // algorithm. float32x4_t vn = vmlaq_f32(vmagic_bias, vx, vlog2e_x64); // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized, // i.e. -87.33642 <= x <= 0.0. As n has 6 fractional bits, we split s == 2**(n / 64) = 2**e * 2**(n / 64 - e), where // e := int(n / 64). We create s in two steps: // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0. // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0, // and thus the adjusted exponent is not lower than -126. // // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent). const int32x4_t ve = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn), vmovq_n_s32(INT32_C(0x3F))), 17); // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64). const uint64x2_t vidx = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn), vindex_mask)); const uint64_t vidx_lo = vgetq_lane_u64(vidx, 0); const uint64_t vidx_hi = vgetq_lane_u64(vidx, 1); float32x2_t vl_lo = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_lo]); float32x2_t vl_hi = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_hi]); vl_lo = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_lo >> 32)], vl_lo, 1); vl_hi = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_hi >> 32)], vl_hi, 1); const float32x4_t vl = vcombine_f32(vl_lo, vl_hi); // Adjust exponent of the value l fetched from the table to get the final s value. const float32x4_t vs = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl), ve)); // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number. vn = vsubq_f32(vn, vmagic_bias); // Compute reduced argument t := x - n * log(2) / 64. // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy. float32x4_t vt = vmlaq_f32(vx, vn, vminus_ln2_o64_hi); vt = vmlaq_f32(vt, vn, vminus_ln2_o64_lo); // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/128, log(2)/128]. float32x4_t vp = vmulq_f32(vt, vc2); vp = vmlaq_f32(vt, vt, vp); // Reconstruct the final f value: // f = s * (1 + t * (1 + t * c2)) // = s * (1 + t + t * (t * c2)) // = s + s * (t + t * (t * c2)) // = s + s * p float32x4_t vf = vmlaq_f32(vs, vs, vp); // 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 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff))); // Store 4 outputs at a time. vst1q_f32(output, vf); output += 4; // Accumulate computed exponents. vacc = vaddq_f32(vacc, vf); } #if XNN_ARCH_ARM64 float vacc_lo = vaddvq_f32(vacc); #else float32x2_t vacc_lo = vadd_f32(vget_high_f32(vacc), vget_low_f32(vacc)); #endif if (elements != 0) { assert(elements >= 1 * sizeof(float)); assert(elements <= 3 * sizeof(float)); // Load 4 inputs at a time. const float32x4_t vi = vld1q_f32(input); input += 4; // Subtract maximum input x := i - i_max. This implies x <= 0. const float32x4_t vx = vsubq_f32(vi, vi_max); // Compute reduced argument n := round(x * 64 / log(2)). // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e. // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0] // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the // algorithm. float32x4_t vn = vmlaq_f32(vmagic_bias, vx, vlog2e_x64); // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized, // i.e. -87.33642 <= x <= 0.0. As n has 6 fractional bits, we split s == 2**(n / 64) = 2**e * 2**(n / 64 - e), where // e := int(n / 64). We create s in two steps: // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0. // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0, // and thus the adjusted exponent is not lower than -126. // // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent). const int32x4_t ve = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn), vmovq_n_s32(INT32_C(0x3F))), 17); // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64). const uint64x2_t vidx = vreinterpretq_u64_s32(vandq_s32(vreinterpretq_s32_f32(vn), vindex_mask)); const uint64_t vidx_lo = vgetq_lane_u64(vidx, 0); const uint64_t vidx_hi = vgetq_lane_u64(vidx, 1); float32x2_t vl_lo = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_lo]); float32x2_t vl_hi = vld1_dup_f32(&xnn_table_exp2_k_over_64[(uint32_t) vidx_hi]); vl_lo = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_lo >> 32)], vl_lo, 1); vl_hi = vld1_lane_f32(&xnn_table_exp2_k_over_64[(uint32_t) (vidx_hi >> 32)], vl_hi, 1); const float32x4_t vl = vcombine_f32(vl_lo, vl_hi); // Adjust exponent of the value l fetched from the table to get the final s value. const float32x4_t vs = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl), ve)); // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number. vn = vsubq_f32(vn, vmagic_bias); // Compute reduced argument t := x - n * log(2) / 64. // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy. float32x4_t vt = vmlaq_f32(vx, vn, vminus_ln2_o64_hi); vt = vmlaq_f32(vt, vn, vminus_ln2_o64_lo); // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/128, log(2)/128]. float32x4_t vp = vmulq_f32(vt, vc2); vp = vmlaq_f32(vt, vt, vp); // Reconstruct the final f value: // f = s * (1 + t * (1 + t * c2)) // = s * (1 + t + t * (t * c2)) // = s + s * (t + t * (t * c2)) // = s + s * p float32x4_t vf = vmlaq_f32(vs, vs, vp); // 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 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff))); float32x2_t vf_lo = vget_low_f32(vf); if (elements & (2 * sizeof(float))) { // Store 2 outputs at a time. vst1_f32(output, vf_lo); output += 2; // Accumulate 2 computed exponents. #if XNN_ARCH_ARM64 vacc_lo += vaddv_f32(vf_lo); #else vacc_lo = vadd_f32(vacc_lo, vf_lo); #endif vf_lo = vget_high_f32(vf); } if (elements & (1 * sizeof(float))) { // Store 1 output at a time. vst1_lane_f32(output, vf_lo, 0); // Accumulate 1 computed exponent. #if XNN_ARCH_ARM64 vacc_lo += vget_lane_f32(vf_lo, 0); #else vacc_lo = vadd_f32(vacc_lo, vreinterpret_f32_u64(vshl_n_u64(vreinterpret_u64_f32(vf_lo), 32))); #endif } } // Reduce 4 elements in the SIMD register #if XNN_ARCH_ARM64 *sum = vacc_lo; #else vst1_lane_f32(sum, vpadd_f32(vacc_lo, vacc_lo), 0); #endif }