Marat Dukhan | 8137e4c | 2020-01-25 12:56:58 -0800 | [diff] [blame] | 1 | // Auto-generated file. Do not edit! |
| 2 | // Template: src/f32-raddstoreexpminusmax/neon-p5.c.in |
| 3 | // Generator: tools/xngen |
| 4 | // |
| 5 | // Copyright 2020 Google LLC |
| 6 | // |
| 7 | // This source code is licensed under the BSD-style license found in the |
| 8 | // LICENSE file in the root directory of this source tree. |
| 9 | |
| 10 | #include <assert.h> |
| 11 | |
| 12 | #include <arm_neon.h> |
| 13 | |
| 14 | #include <xnnpack/common.h> |
| 15 | #include <xnnpack/raddstoreexpminusmax.h> |
| 16 | |
| 17 | |
| 18 | void xnn_f32_raddstoreexpminusmax_ukernel__neon_p5_x12( |
| 19 | size_t elements, |
| 20 | const float* input, |
| 21 | float* output, |
| 22 | float* sum, |
Marat Dukhan | b2217dd | 2020-05-28 17:30:28 -0700 | [diff] [blame] | 23 | float max) XNN_DISABLE_TSAN |
Marat Dukhan | 8137e4c | 2020-01-25 12:56:58 -0800 | [diff] [blame] | 24 | { |
| 25 | assert(elements % sizeof(float) == 0); |
| 26 | |
| 27 | const float32x4_t vmagic_bias = vmovq_n_f32(0x1.8000FEp23f); |
| 28 | // The smallest x for which expf(x) is normalized. |
| 29 | const float32x4_t vdenorm_cutoff = vmovq_n_f32(-0x1.5D589Ep6f); |
| 30 | const float32x4_t vlog2e = vmovq_n_f32(0x1.715476p+0f); |
| 31 | // Last 7 bits are zeroes |
| 32 | const float32x4_t vminus_ln2_hi = vmovq_n_f32(-0x1.62E400p-1f); |
| 33 | const float32x4_t vminus_ln2_lo = vmovq_n_f32(-0x1.7F7D1Cp-20f); |
| 34 | |
| 35 | const float32x4_t vc1 = vmovq_n_f32(0x1.FFFFF6p-1f); |
| 36 | const float32x4_t vc2 = vmovq_n_f32(0x1.FFFDC6p-2f); |
| 37 | const float32x4_t vc3 = vmovq_n_f32(0x1.555A80p-3f); |
| 38 | const float32x4_t vc4 = vmovq_n_f32(0x1.573A1Ap-5f); |
| 39 | const float32x4_t vc5 = vmovq_n_f32(0x1.0F9F9Cp-7f); |
| 40 | |
| 41 | const float32x4_t vi_max = vdupq_n_f32(max); |
| 42 | |
| 43 | float32x4_t vacc0 = vmovq_n_f32(0.0f); |
| 44 | for (; elements >= 12 * sizeof(float); elements -= 12 * sizeof(float)) { |
| 45 | // Load 12 (3x4) inputs at a time. |
| 46 | const float32x4_t vi0123 = vld1q_f32(input); input += 4; |
| 47 | const float32x4_t vi4567 = vld1q_f32(input); input += 4; |
| 48 | const float32x4_t vi89AB = vld1q_f32(input); input += 4; |
| 49 | |
| 50 | // Subtract maximum input x := i - i_max. This implies x <= 0. |
| 51 | const float32x4_t vx0123 = vsubq_f32(vi0123, vi_max); |
| 52 | const float32x4_t vx4567 = vsubq_f32(vi4567, vi_max); |
| 53 | const float32x4_t vx89AB = vsubq_f32(vi89AB, vi_max); |
| 54 | |
| 55 | // Compute reduced argument n := round(x / log(2)). |
| 56 | // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the |
| 57 | // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. |
slowy07 | ab1127f | 2021-07-27 08:23:22 +0700 | [diff] [blame^] | 58 | // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but that's ok, because |
Marat Dukhan | 8137e4c | 2020-01-25 12:56:58 -0800 | [diff] [blame] | 59 | // inputs outside of [-87.336540, 0.0] underflow expf(x) anyway. We fixup the result for such inputs at the very end |
| 60 | // of the algorithm. |
| 61 | float32x4_t vn0123 = vmlaq_f32(vmagic_bias, vx0123, vlog2e); |
| 62 | float32x4_t vn4567 = vmlaq_f32(vmagic_bias, vx4567, vlog2e); |
| 63 | float32x4_t vn89AB = vmlaq_f32(vmagic_bias, vx89AB, vlog2e); |
| 64 | |
| 65 | // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| 66 | // -87.33642 <= x <= 0.0, and -126 <= n <= 0 accordingly. |
| 67 | const float32x4_t vs0123 = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn0123), 23)); |
| 68 | const float32x4_t vs4567 = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn4567), 23)); |
| 69 | const float32x4_t vs89AB = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn89AB), 23)); |
| 70 | |
| 71 | // Subtract the large number back to get final n := round(x / log(2)). |
| 72 | vn0123 = vsubq_f32(vn0123, vmagic_bias); |
| 73 | vn4567 = vsubq_f32(vn4567, vmagic_bias); |
| 74 | vn89AB = vsubq_f32(vn89AB, vmagic_bias); |
| 75 | |
| 76 | // Compute reduced argument t := z - n * log(2). |
| 77 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 78 | float32x4_t vt0123 = vmlaq_f32(vx0123, vn0123, vminus_ln2_hi); |
| 79 | float32x4_t vt4567 = vmlaq_f32(vx4567, vn4567, vminus_ln2_hi); |
| 80 | float32x4_t vt89AB = vmlaq_f32(vx89AB, vn89AB, vminus_ln2_hi); |
| 81 | |
| 82 | vt0123 = vmlaq_f32(vt0123, vn0123, vminus_ln2_lo); |
| 83 | vt4567 = vmlaq_f32(vt4567, vn4567, vminus_ln2_lo); |
| 84 | vt89AB = vmlaq_f32(vt89AB, vn89AB, vminus_ln2_lo); |
| 85 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame] | 86 | // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. |
Marat Dukhan | 8137e4c | 2020-01-25 12:56:58 -0800 | [diff] [blame] | 87 | float32x4_t vp0123 = vmlaq_f32(vc4, vc5, vt0123); |
| 88 | float32x4_t vp4567 = vmlaq_f32(vc4, vc5, vt4567); |
| 89 | float32x4_t vp89AB = vmlaq_f32(vc4, vc5, vt89AB); |
| 90 | |
| 91 | vp0123 = vmlaq_f32(vc3, vp0123, vt0123); |
| 92 | vp4567 = vmlaq_f32(vc3, vp4567, vt4567); |
| 93 | vp89AB = vmlaq_f32(vc3, vp89AB, vt89AB); |
| 94 | |
| 95 | vp0123 = vmlaq_f32(vc2, vp0123, vt0123); |
| 96 | vp4567 = vmlaq_f32(vc2, vp4567, vt4567); |
| 97 | vp89AB = vmlaq_f32(vc2, vp89AB, vt89AB); |
| 98 | |
| 99 | vp0123 = vmlaq_f32(vc1, vp0123, vt0123); |
| 100 | vp4567 = vmlaq_f32(vc1, vp4567, vt4567); |
| 101 | vp89AB = vmlaq_f32(vc1, vp89AB, vt89AB); |
| 102 | |
| 103 | // Reconstruct the final f value: |
| 104 | // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 105 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 106 | // = s + (t * s) * p |
| 107 | vt0123 = vmulq_f32(vt0123, vs0123); |
| 108 | vt4567 = vmulq_f32(vt4567, vs4567); |
| 109 | vt89AB = vmulq_f32(vt89AB, vs89AB); |
| 110 | |
| 111 | float32x4_t vf0123 = vmlaq_f32(vs0123, vp0123, vt0123); |
| 112 | float32x4_t vf4567 = vmlaq_f32(vs4567, vp4567, vt4567); |
| 113 | float32x4_t vf89AB = vmlaq_f32(vs89AB, vp89AB, vt89AB); |
| 114 | |
| 115 | // For inputs below denormal cutoff, replace output with +0.0f. |
| 116 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 117 | vf0123 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf0123), vcltq_f32(vx0123, vdenorm_cutoff))); |
| 118 | vf4567 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf4567), vcltq_f32(vx4567, vdenorm_cutoff))); |
| 119 | vf89AB = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf89AB), vcltq_f32(vx89AB, vdenorm_cutoff))); |
| 120 | |
| 121 | // Store 12 (3x4) outputs at a time. |
| 122 | vst1q_f32(output, vf0123); output += 4; |
| 123 | vst1q_f32(output, vf4567); output += 4; |
| 124 | vst1q_f32(output, vf89AB); output += 4; |
| 125 | |
| 126 | // Accumulate computed exponents. |
| 127 | vacc0 = vaddq_f32(vacc0, vf0123); |
| 128 | vacc0 = vaddq_f32(vacc0, vf4567); |
| 129 | vacc0 = vaddq_f32(vacc0, vf89AB); |
| 130 | } |
| 131 | |
| 132 | float32x4_t vacc = vacc0; |
| 133 | for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) { |
| 134 | // Load 4 inputs at a time. |
| 135 | const float32x4_t vi = vld1q_f32(input); input += 4; |
| 136 | |
| 137 | // Subtract maximum input x := i - i_max. This implies x <= 0. |
| 138 | const float32x4_t vx = vsubq_f32(vi, vi_max); |
| 139 | |
| 140 | // Compute reduced argument n := round(x / log(2)). |
| 141 | // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the |
| 142 | // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. |
slowy07 | ab1127f | 2021-07-27 08:23:22 +0700 | [diff] [blame^] | 143 | // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but that's ok, because |
Marat Dukhan | 8137e4c | 2020-01-25 12:56:58 -0800 | [diff] [blame] | 144 | // inputs outside of [-87.336540, 0.0] underflow expf(x) anyway. We fixup the result for such inputs at the very end |
| 145 | // of the algorithm. |
| 146 | float32x4_t vn = vmlaq_f32(vmagic_bias, vx, vlog2e); |
| 147 | |
| 148 | // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| 149 | // -87.33642 <= x <= 0.0, and -126 <= n <= 0 accordingly. |
| 150 | const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23)); |
| 151 | |
| 152 | // Subtract the large number back to get final n := round(x / log(2)). |
| 153 | vn = vsubq_f32(vn, vmagic_bias); |
| 154 | |
| 155 | // Compute reduced argument t := z - n * log(2). |
| 156 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 157 | float32x4_t vt = vmlaq_f32(vx, vn, vminus_ln2_hi); |
| 158 | vt = vmlaq_f32(vt, vn, vminus_ln2_lo); |
| 159 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame] | 160 | // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. |
Marat Dukhan | 8137e4c | 2020-01-25 12:56:58 -0800 | [diff] [blame] | 161 | float32x4_t vp = vmlaq_f32(vc4, vc5, vt); |
| 162 | vp = vmlaq_f32(vc3, vp, vt); |
| 163 | vp = vmlaq_f32(vc2, vp, vt); |
| 164 | vp = vmlaq_f32(vc1, vp, vt); |
| 165 | |
| 166 | // Reconstruct the final f value: |
| 167 | // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 168 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 169 | // = s + (t * s) * p |
| 170 | vt = vmulq_f32(vt, vs); |
| 171 | float32x4_t vf = vmlaq_f32(vs, vp, vt); |
| 172 | |
| 173 | // For inputs below denormal cutoff, replace output with +0.0f. |
| 174 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 175 | vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff))); |
| 176 | |
| 177 | // Store 4 outputs at a time. |
| 178 | vst1q_f32(output, vf); output += 4; |
| 179 | |
| 180 | // Accumulate computed exponents. |
| 181 | vacc = vaddq_f32(vacc, vf); |
| 182 | } |
| 183 | #if XNN_ARCH_ARM64 |
| 184 | float vacc_lo = vaddvq_f32(vacc); |
| 185 | #else |
| 186 | float32x2_t vacc_lo = vadd_f32(vget_high_f32(vacc), vget_low_f32(vacc)); |
| 187 | #endif |
| 188 | if (elements != 0) { |
| 189 | assert(elements >= 1 * sizeof(float)); |
| 190 | assert(elements <= 3 * sizeof(float)); |
| 191 | // Load 4 inputs at a time. |
| 192 | const float32x4_t vi = vld1q_f32(input); input += 4; |
| 193 | |
| 194 | // Subtract maximum input x := i - i_max. This implies x <= 0. |
| 195 | const float32x4_t vx = vsubq_f32(vi, vi_max); |
| 196 | |
| 197 | // Compute reduced argument n := round(x / log(2)). |
| 198 | // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the |
| 199 | // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. |
slowy07 | ab1127f | 2021-07-27 08:23:22 +0700 | [diff] [blame^] | 200 | // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but that's ok, because |
Marat Dukhan | 8137e4c | 2020-01-25 12:56:58 -0800 | [diff] [blame] | 201 | // inputs outside of [-87.336540, 0.0] underflow expf(x) anyway. We fixup the result for such inputs at the very end |
| 202 | // of the algorithm. |
| 203 | float32x4_t vn = vmlaq_f32(vmagic_bias, vx, vlog2e); |
| 204 | |
| 205 | // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| 206 | // -87.33642 <= x <= 0.0, and -126 <= n <= 0 accordingly. |
| 207 | const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23)); |
| 208 | |
| 209 | // Subtract the large number back to get final n := round(x / log(2)). |
| 210 | vn = vsubq_f32(vn, vmagic_bias); |
| 211 | |
| 212 | // Compute reduced argument t := z - n * log(2). |
| 213 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 214 | float32x4_t vt = vmlaq_f32(vx, vn, vminus_ln2_hi); |
| 215 | vt = vmlaq_f32(vt, vn, vminus_ln2_lo); |
| 216 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame] | 217 | // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. |
Marat Dukhan | 8137e4c | 2020-01-25 12:56:58 -0800 | [diff] [blame] | 218 | float32x4_t vp = vmlaq_f32(vc4, vc5, vt); |
| 219 | vp = vmlaq_f32(vc3, vp, vt); |
| 220 | vp = vmlaq_f32(vc2, vp, vt); |
| 221 | vp = vmlaq_f32(vc1, vp, vt); |
| 222 | |
| 223 | // Reconstruct the final f value: |
| 224 | // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 225 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 226 | // = s + (t * s) * p |
| 227 | vt = vmulq_f32(vt, vs); |
| 228 | float32x4_t vf = vmlaq_f32(vs, vp, vt); |
| 229 | |
| 230 | // For inputs below denormal cutoff, replace output with +0.0f. |
| 231 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 232 | vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff))); |
| 233 | |
| 234 | float32x2_t vf_lo = vget_low_f32(vf); |
| 235 | if (elements & (2 * sizeof(float))) { |
| 236 | // Store 2 outputs at a time. |
| 237 | vst1_f32(output, vf_lo); output += 2; |
| 238 | |
| 239 | // Accumulate 2 computed exponents. |
| 240 | #if XNN_ARCH_ARM64 |
| 241 | vacc_lo += vaddv_f32(vf_lo); |
| 242 | #else |
| 243 | vacc_lo = vadd_f32(vacc_lo, vf_lo); |
| 244 | #endif |
| 245 | |
| 246 | vf_lo = vget_high_f32(vf); |
| 247 | } |
| 248 | if (elements & (1 * sizeof(float))) { |
| 249 | // Store 1 output at a time. |
| 250 | vst1_lane_f32(output, vf_lo, 0); |
| 251 | |
| 252 | // Accumulate 1 computed exponent. |
| 253 | #if XNN_ARCH_ARM64 |
| 254 | vacc_lo += vget_lane_f32(vf_lo, 0); |
| 255 | #else |
| 256 | vacc_lo = vadd_f32(vacc_lo, vreinterpret_f32_u64(vshl_n_u64(vreinterpret_u64_f32(vf_lo), 32))); |
| 257 | #endif |
| 258 | } |
| 259 | } |
| 260 | // Reduce 4 elements in the SIMD register |
| 261 | #if XNN_ARCH_ARM64 |
| 262 | *sum = vacc_lo; |
| 263 | #else |
| 264 | vst1_lane_f32(sum, vpadd_f32(vacc_lo, vacc_lo), 0); |
| 265 | #endif |
| 266 | } |