Marat Dukhan | b39689d | 2020-01-24 13:32:20 -0800 | [diff] [blame] | 1 | // Copyright 2019 Google LLC |
| 2 | // |
| 3 | // This source code is licensed under the BSD-style license found in the |
| 4 | // LICENSE file in the root directory of this source tree. |
| 5 | |
| 6 | $assert ELEMENTS_TILE % 4 == 0 |
| 7 | $assert ELEMENTS_TILE >= 4 |
| 8 | $SIMD_TILE = ELEMENTS_TILE // 4 |
| 9 | $ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ" |
| 10 | #include <assert.h> |
| 11 | |
| 12 | #include <emmintrin.h> |
| 13 | |
| 14 | #include <xnnpack/common.h> |
| 15 | #include <xnnpack/raddstoreexpminusmax.h> |
| 16 | |
| 17 | |
| 18 | void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x${ELEMENTS_TILE}${"" if ACCUMULATORS == 1 else "_acc%d" % ACCUMULATORS}( |
| 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 | b39689d | 2020-01-24 13:32:20 -0800 | [diff] [blame] | 24 | { |
| 25 | assert(elements % sizeof(float) == 0); |
| 26 | |
| 27 | const __m128 vmagic_bias = _mm_set1_ps(0x1.8000FEp23f); |
| 28 | // The smallest x for which expf(x) is normalized. |
| 29 | const __m128 vdenorm_cutoff = _mm_set1_ps(-0x1.5D589Ep6f); |
| 30 | const __m128 vlog2e = _mm_set1_ps(0x1.715476p+0f); |
| 31 | // Last 7 bits are zeroes |
| 32 | const __m128 vminus_ln2_hi = _mm_set1_ps(-0x1.62E400p-1f); |
| 33 | const __m128 vminus_ln2_lo = _mm_set1_ps(-0x1.7F7D1Cp-20f); |
| 34 | |
| 35 | const __m128 vc1 = _mm_set1_ps(0x1.FFFFF6p-1f); |
| 36 | const __m128 vc2 = _mm_set1_ps(0x1.FFFDC6p-2f); |
| 37 | const __m128 vc3 = _mm_set1_ps(0x1.555A80p-3f); |
| 38 | const __m128 vc4 = _mm_set1_ps(0x1.573A1Ap-5f); |
| 39 | const __m128 vc5 = _mm_set1_ps(0x1.0F9F9Cp-7f); |
| 40 | |
| 41 | const __m128 vi_max = _mm_set1_ps(max); |
| 42 | |
| 43 | $for K in range(ACCUMULATORS): |
| 44 | __m128 vacc${K} = _mm_setzero_ps(); |
| 45 | for (; elements >= ${ELEMENTS_TILE} * sizeof(float); elements -= ${ELEMENTS_TILE} * sizeof(float)) { |
| 46 | // Load ${ELEMENTS_TILE} (${SIMD_TILE}x4) inputs at a time. |
| 47 | const __m128 vi${ABC[0:4]} = _mm_loadu_ps(input); |
| 48 | $for N in range(4, ELEMENTS_TILE, 4): |
| 49 | const __m128 vi${ABC[N:N+4]} = _mm_loadu_ps(input + ${N}); |
| 50 | input += ${ELEMENTS_TILE}; |
| 51 | |
| 52 | // Subtract maximum input x := i - i_max. This implies x <= 0. |
| 53 | $for N in range(0, ELEMENTS_TILE, 4): |
| 54 | const __m128 vx${ABC[N:N+4]} = _mm_sub_ps(vi${ABC[N:N+4]}, vi_max); |
| 55 | |
| 56 | // Compute reduced argument elements := round(x / log(2)). |
| 57 | $for N in range(0, ELEMENTS_TILE, 4): |
| 58 | __m128 vn${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vx${ABC[N:N+4]}, vlog2e), vmagic_bias); |
| 59 | |
| 60 | // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. |
| 61 | // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. |
| 62 | $for N in range(0, ELEMENTS_TILE, 4): |
| 63 | const __m128 vs${ABC[N:N+4]} = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn${ABC[N:N+4]}), 23)); |
| 64 | |
| 65 | // Subtract the large number back to get final elements := round(x / log(2)). |
| 66 | $for N in range(0, ELEMENTS_TILE, 4): |
| 67 | vn${ABC[N:N+4]} = _mm_sub_ps(vn${ABC[N:N+4]}, vmagic_bias); |
| 68 | |
| 69 | // Compute reduced argument t := x - elements * log(2). |
| 70 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 71 | $for N in range(0, ELEMENTS_TILE, 4): |
| 72 | __m128 vt${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vn${ABC[N:N+4]}, vminus_ln2_hi), vx${ABC[N:N+4]}); |
| 73 | |
| 74 | $for N in range(0, ELEMENTS_TILE, 4): |
| 75 | vt${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vn${ABC[N:N+4]}, vminus_ln2_lo), vt${ABC[N:N+4]}); |
| 76 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame] | 77 | // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. |
Marat Dukhan | b39689d | 2020-01-24 13:32:20 -0800 | [diff] [blame] | 78 | $for N in range(0, ELEMENTS_TILE, 4): |
| 79 | __m128 vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vc5, vt${ABC[N:N+4]}), vc4); |
| 80 | |
| 81 | $for N in range(0, ELEMENTS_TILE, 4): |
| 82 | vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vp${ABC[N:N+4]}, vt${ABC[N:N+4]}), vc3); |
| 83 | |
| 84 | $for N in range(0, ELEMENTS_TILE, 4): |
| 85 | vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vp${ABC[N:N+4]}, vt${ABC[N:N+4]}), vc2); |
| 86 | |
| 87 | $for N in range(0, ELEMENTS_TILE, 4): |
| 88 | vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vp${ABC[N:N+4]}, vt${ABC[N:N+4]}), vc1); |
| 89 | |
| 90 | // Reconstruct the final f value: |
| 91 | // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 92 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 93 | // = s + (t * s) * p |
| 94 | $for N in range(0, ELEMENTS_TILE, 4): |
| 95 | vt${ABC[N:N+4]} = _mm_mul_ps(vt${ABC[N:N+4]}, vs${ABC[N:N+4]}); |
| 96 | |
| 97 | $for N in range(0, ELEMENTS_TILE, 4): |
| 98 | __m128 vf${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vt${ABC[N:N+4]}, vp${ABC[N:N+4]}), vs${ABC[N:N+4]}); |
| 99 | |
| 100 | // For inputs below zero cutoff, replace output with +0.0f. |
| 101 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 102 | $for N in range(0, ELEMENTS_TILE, 4): |
| 103 | vf${ABC[N:N+4]} = _mm_andnot_ps(_mm_cmplt_ps(vx${ABC[N:N+4]}, vdenorm_cutoff), vf${ABC[N:N+4]}); |
| 104 | |
| 105 | // Store ${ELEMENTS_TILE} (${SIMD_TILE}x4) outputs at a time. |
| 106 | _mm_storeu_ps(output, vf${ABC[0:4]}); |
| 107 | $for N in range(4, ELEMENTS_TILE, 4): |
| 108 | _mm_storeu_ps(output + ${N}, vf${ABC[N:N+4]}); |
| 109 | output += ${ELEMENTS_TILE}; |
| 110 | |
| 111 | // Accumulate computed exponents. |
| 112 | $for N in range(0, ELEMENTS_TILE, 4): |
| 113 | vacc${N % ACCUMULATORS} = _mm_add_ps(vacc${N % ACCUMULATORS}, vf${ABC[N:N+4]}); |
| 114 | } |
| 115 | $if ACCUMULATORS > 1: |
| 116 | // Add up all accumulators to vacc0 |
| 117 | $ACC_SLICE = 1 |
| 118 | $while ACC_SLICE < ACCUMULATORS: |
| 119 | $for A in range(0, ACCUMULATORS, ACC_SLICE * 2): |
| 120 | $if A + ACC_SLICE < ACCUMULATORS: |
| 121 | vacc${A} = _mm_add_ps(vacc${A}, vacc${A + ACC_SLICE}); |
| 122 | $ACC_SLICE *= 2 |
| 123 | |
| 124 | __m128 vacc = vacc0; |
| 125 | for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) { |
| 126 | // Load 4 inputs at a time. |
| 127 | const __m128 vi = _mm_loadu_ps(input); |
| 128 | input += 4; |
| 129 | |
| 130 | // Subtract maximum input x := i - i_max. This implies x <= 0. |
| 131 | const __m128 vx = _mm_sub_ps(vi, vi_max); |
| 132 | |
| 133 | // Compute reduced argument elements := round(x / log(2)). |
| 134 | __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias); |
| 135 | |
| 136 | // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. |
| 137 | // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. |
| 138 | const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23)); |
| 139 | |
| 140 | // Subtract the large number back to get final elements := round(x / log(2)). |
| 141 | vn = _mm_sub_ps(vn, vmagic_bias); |
| 142 | |
| 143 | // Compute reduced argument t := x - elements * log(2). |
| 144 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 145 | __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx); |
| 146 | vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt); |
| 147 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame] | 148 | // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. |
Marat Dukhan | b39689d | 2020-01-24 13:32:20 -0800 | [diff] [blame] | 149 | __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4); |
| 150 | vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3); |
| 151 | vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2); |
| 152 | vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1); |
| 153 | |
| 154 | // Reconstruct the final f value: |
| 155 | // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 156 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 157 | // = s + (t * s) * p |
| 158 | vt = _mm_mul_ps(vt, vs); |
| 159 | __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs); |
| 160 | |
| 161 | // For inputs below zero cutoff, replace output with +0.0f. |
| 162 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 163 | vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf); |
| 164 | |
| 165 | // Store 4 outputs at a time. |
| 166 | _mm_storeu_ps(output, vf); |
| 167 | output += 4; |
| 168 | |
| 169 | // Accumulate computed exponents. |
| 170 | vacc = _mm_add_ps(vacc, vf); |
| 171 | } |
| 172 | if (elements != 0) { |
| 173 | assert(elements >= 1 * sizeof(float)); |
| 174 | assert(elements <= 3 * sizeof(float)); |
| 175 | // Load 4 inputs at a time. |
Marat Dukhan | b2217dd | 2020-05-28 17:30:28 -0700 | [diff] [blame] | 176 | const __m128 vi = _mm_loadu_ps(input); |
Marat Dukhan | b39689d | 2020-01-24 13:32:20 -0800 | [diff] [blame] | 177 | |
| 178 | // Subtract maximum input x := i - i_max. This implies x <= 0. |
| 179 | const __m128 vx = _mm_sub_ps(vi, vi_max); |
| 180 | |
| 181 | // Compute reduced argument elements := round(x / log(2)). |
| 182 | __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias); |
| 183 | |
| 184 | // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. |
| 185 | // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. |
| 186 | const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23)); |
| 187 | |
| 188 | // Subtract the large number back to get final elements := round(x / log(2)). |
| 189 | vn = _mm_sub_ps(vn, vmagic_bias); |
| 190 | |
| 191 | // Compute reduced argument t := x - elements * log(2). |
| 192 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 193 | __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx); |
| 194 | vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt); |
| 195 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame] | 196 | // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. |
Marat Dukhan | b39689d | 2020-01-24 13:32:20 -0800 | [diff] [blame] | 197 | __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4); |
| 198 | vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3); |
| 199 | vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2); |
| 200 | vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1); |
| 201 | |
| 202 | // Reconstruct the final f value: |
| 203 | // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 204 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 205 | // = s + (t * s) * p |
| 206 | vt = _mm_mul_ps(vt, vs); |
| 207 | __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs); |
| 208 | |
| 209 | // For inputs below zero cutoff, replace output with +0.0f. |
| 210 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 211 | vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf); |
| 212 | |
| 213 | if (elements & (2 * sizeof(float))) { |
| 214 | // Store 2 outputs at a time. |
| 215 | _mm_storel_pi((__m64*) output, vf); |
| 216 | output += 2; |
| 217 | |
| 218 | // Accumulate 2 computed exponents. |
| 219 | vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps())); |
| 220 | |
| 221 | vf = _mm_movehl_ps(vf, vf); |
| 222 | } |
| 223 | if (elements & (1 * sizeof(float))) { |
| 224 | // Store 1 output at a time. |
| 225 | _mm_store_ss(output, vf); |
| 226 | |
| 227 | // Accumulate 1 computed exponent. |
| 228 | vacc = _mm_add_ss(vacc, vf); |
| 229 | } |
| 230 | } |
| 231 | // Reduce 4 elements in the SIMD register |
| 232 | vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc)); |
| 233 | vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1))); |
| 234 | _mm_store_ss(sum, vacc); |
| 235 | } |