Marat Dukhan | 8d3c07e | 2020-01-02 01:20:59 -0800 | [diff] [blame^] | 1 | // Auto-generated file. Do not edit! |
| 2 | // Template: src/f32-sigmoid/neon-p5.c.in |
| 3 | // Generator: tools/xngen |
| 4 | // |
| 5 | // Copyright 2019 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/vunary.h> |
| 16 | |
| 17 | |
| 18 | void xnn_f32_sigmoid_ukernel__neonfma_p5_nr1recps1fma_x20( |
| 19 | size_t n, |
| 20 | const float* x, |
| 21 | float* y, |
| 22 | const void* params) |
| 23 | { |
| 24 | assert(n % sizeof(float) == 0); |
| 25 | |
| 26 | const float32x4_t vmagic_bias = vmovq_n_f32(0x1.8000FEp23f); |
| 27 | // The largest z for which sigmoidf(-z) is normalized. |
| 28 | // This number is also the largest z for which expf(-z) is normalized. |
| 29 | const float32x4_t vdenorm_cutoff = vmovq_n_f32(0x1.5D589Ep+6f); |
| 30 | const float32x4_t vminus_log2e = vmovq_n_f32(-0x1.715476p+0f); |
| 31 | const float32x4_t vln2_hi = vmovq_n_f32(0x1.62E43p-1f); |
| 32 | const float32x4_t vln2_lo = vmovq_n_f32(-0x1.05C61p-29f); |
| 33 | const float32x4_t vone = vmovq_n_f32(1.0f); |
| 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 | for (; n >= 20 * sizeof(float); n -= 20 * sizeof(float)) { |
| 42 | const float32x4_t vx0123 = vld1q_f32(x); x += 4; |
| 43 | const float32x4_t vx4567 = vld1q_f32(x); x += 4; |
| 44 | const float32x4_t vx89AB = vld1q_f32(x); x += 4; |
| 45 | const float32x4_t vxCDEF = vld1q_f32(x); x += 4; |
| 46 | const float32x4_t vxGHIJ = vld1q_f32(x); x += 4; |
| 47 | |
| 48 | // General structure of the algorithm: |
| 49 | // / exp(x) / (1 + exp(x)) if x <= 0 |
| 50 | // f[x] := |
| 51 | // \ 1 - f[-x] if x >= 0 |
| 52 | // |
| 53 | // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x), |
| 54 | // then replace result with 1 - f[z] if x >= 0. |
| 55 | const float32x4_t vz0123 = vabsq_f32(vx0123); |
| 56 | const float32x4_t vz4567 = vabsq_f32(vx4567); |
| 57 | const float32x4_t vz89AB = vabsq_f32(vx89AB); |
| 58 | const float32x4_t vzCDEF = vabsq_f32(vxCDEF); |
| 59 | const float32x4_t vzGHIJ = vabsq_f32(vxGHIJ); |
| 60 | |
| 61 | // Compute reduced argument n := round(-z / log(2)). |
| 62 | // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the |
| 63 | // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. |
| 64 | // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because |
| 65 | // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x) |
| 66 | // anyway. We fixup the result for such inputs at the very end of the algorithm. |
| 67 | float32x4_t vn0123 = vfmaq_f32(vmagic_bias, vz0123, vminus_log2e); |
| 68 | float32x4_t vn4567 = vfmaq_f32(vmagic_bias, vz4567, vminus_log2e); |
| 69 | float32x4_t vn89AB = vfmaq_f32(vmagic_bias, vz89AB, vminus_log2e); |
| 70 | float32x4_t vnCDEF = vfmaq_f32(vmagic_bias, vzCDEF, vminus_log2e); |
| 71 | float32x4_t vnGHIJ = vfmaq_f32(vmagic_bias, vzGHIJ, vminus_log2e); |
| 72 | |
| 73 | // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| 74 | // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly. |
| 75 | const float32x4_t vs0123 = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn0123), 23)); |
| 76 | const float32x4_t vs4567 = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn4567), 23)); |
| 77 | const float32x4_t vs89AB = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn89AB), 23)); |
| 78 | const float32x4_t vsCDEF = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vnCDEF), 23)); |
| 79 | const float32x4_t vsGHIJ = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vnGHIJ), 23)); |
| 80 | |
| 81 | // Subtract the large number back to get final n := round(-z / log(2)). |
| 82 | vn0123 = vsubq_f32(vn0123, vmagic_bias); |
| 83 | vn4567 = vsubq_f32(vn4567, vmagic_bias); |
| 84 | vn89AB = vsubq_f32(vn89AB, vmagic_bias); |
| 85 | vnCDEF = vsubq_f32(vnCDEF, vmagic_bias); |
| 86 | vnGHIJ = vsubq_f32(vnGHIJ, vmagic_bias); |
| 87 | |
| 88 | // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)). |
| 89 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 90 | float32x4_t vt0123 = vfmaq_f32(vz0123, vn0123, vln2_hi); |
| 91 | float32x4_t vt4567 = vfmaq_f32(vz4567, vn4567, vln2_hi); |
| 92 | float32x4_t vt89AB = vfmaq_f32(vz89AB, vn89AB, vln2_hi); |
| 93 | float32x4_t vtCDEF = vfmaq_f32(vzCDEF, vnCDEF, vln2_hi); |
| 94 | float32x4_t vtGHIJ = vfmaq_f32(vzGHIJ, vnGHIJ, vln2_hi); |
| 95 | |
| 96 | vt0123 = vfmaq_f32(vt0123, vn0123, vln2_lo); |
| 97 | vt4567 = vfmaq_f32(vt4567, vn4567, vln2_lo); |
| 98 | vt89AB = vfmaq_f32(vt89AB, vn89AB, vln2_lo); |
| 99 | vtCDEF = vfmaq_f32(vtCDEF, vnCDEF, vln2_lo); |
| 100 | vtGHIJ = vfmaq_f32(vtGHIJ, vnGHIJ, vln2_lo); |
| 101 | |
| 102 | // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2]. |
| 103 | float32x4_t vp0123 = vfmaq_f32(vc4, vc5, vt0123); |
| 104 | float32x4_t vp4567 = vfmaq_f32(vc4, vc5, vt4567); |
| 105 | float32x4_t vp89AB = vfmaq_f32(vc4, vc5, vt89AB); |
| 106 | float32x4_t vpCDEF = vfmaq_f32(vc4, vc5, vtCDEF); |
| 107 | float32x4_t vpGHIJ = vfmaq_f32(vc4, vc5, vtGHIJ); |
| 108 | |
| 109 | vp0123 = vfmaq_f32(vc3, vp0123, vt0123); |
| 110 | vp4567 = vfmaq_f32(vc3, vp4567, vt4567); |
| 111 | vp89AB = vfmaq_f32(vc3, vp89AB, vt89AB); |
| 112 | vpCDEF = vfmaq_f32(vc3, vpCDEF, vtCDEF); |
| 113 | vpGHIJ = vfmaq_f32(vc3, vpGHIJ, vtGHIJ); |
| 114 | |
| 115 | vp0123 = vfmaq_f32(vc2, vp0123, vt0123); |
| 116 | vp4567 = vfmaq_f32(vc2, vp4567, vt4567); |
| 117 | vp89AB = vfmaq_f32(vc2, vp89AB, vt89AB); |
| 118 | vpCDEF = vfmaq_f32(vc2, vpCDEF, vtCDEF); |
| 119 | vpGHIJ = vfmaq_f32(vc2, vpGHIJ, vtGHIJ); |
| 120 | |
| 121 | vp0123 = vfmaq_f32(vc1, vp0123, vt0123); |
| 122 | vp4567 = vfmaq_f32(vc1, vp4567, vt4567); |
| 123 | vp89AB = vfmaq_f32(vc1, vp89AB, vt89AB); |
| 124 | vpCDEF = vfmaq_f32(vc1, vpCDEF, vtCDEF); |
| 125 | vpGHIJ = vfmaq_f32(vc1, vpGHIJ, vtGHIJ); |
| 126 | |
| 127 | // Reconstruct the exp(-z) value: |
| 128 | // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 129 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 130 | // = s + (t * s) * p |
| 131 | vt0123 = vmulq_f32(vt0123, vs0123); |
| 132 | vt4567 = vmulq_f32(vt4567, vs4567); |
| 133 | vt89AB = vmulq_f32(vt89AB, vs89AB); |
| 134 | vtCDEF = vmulq_f32(vtCDEF, vsCDEF); |
| 135 | vtGHIJ = vmulq_f32(vtGHIJ, vsGHIJ); |
| 136 | |
| 137 | float32x4_t ve0123 = vfmaq_f32(vs0123, vp0123, vt0123); |
| 138 | float32x4_t ve4567 = vfmaq_f32(vs4567, vp4567, vt4567); |
| 139 | float32x4_t ve89AB = vfmaq_f32(vs89AB, vp89AB, vt89AB); |
| 140 | float32x4_t veCDEF = vfmaq_f32(vsCDEF, vpCDEF, vtCDEF); |
| 141 | float32x4_t veGHIJ = vfmaq_f32(vsGHIJ, vpGHIJ, vtGHIJ); |
| 142 | |
| 143 | // Denominator of the sigmoid fraction: 1.0 + exp(-z) |
| 144 | float32x4_t vd0123 = vaddq_f32(ve0123, vone); |
| 145 | float32x4_t vd4567 = vaddq_f32(ve4567, vone); |
| 146 | float32x4_t vd89AB = vaddq_f32(ve89AB, vone); |
| 147 | float32x4_t vdCDEF = vaddq_f32(veCDEF, vone); |
| 148 | float32x4_t vdGHIJ = vaddq_f32(veGHIJ, vone); |
| 149 | |
| 150 | // Use Newton-Raphson method (2 iterations) to compute reciprocal of denominator. |
| 151 | // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0. |
| 152 | // Thus the reciprocal of the denominator never overflows. |
| 153 | float32x4_t vr0123 = vrecpeq_f32(vd0123); |
| 154 | float32x4_t vr4567 = vrecpeq_f32(vd4567); |
| 155 | float32x4_t vr89AB = vrecpeq_f32(vd89AB); |
| 156 | float32x4_t vrCDEF = vrecpeq_f32(vdCDEF); |
| 157 | float32x4_t vrGHIJ = vrecpeq_f32(vdGHIJ); |
| 158 | |
| 159 | vr0123 = vmulq_f32(vr0123, vrecpsq_f32(vr0123, vd0123)); |
| 160 | vr4567 = vmulq_f32(vr4567, vrecpsq_f32(vr4567, vd4567)); |
| 161 | vr89AB = vmulq_f32(vr89AB, vrecpsq_f32(vr89AB, vd89AB)); |
| 162 | vrCDEF = vmulq_f32(vrCDEF, vrecpsq_f32(vrCDEF, vdCDEF)); |
| 163 | vrGHIJ = vmulq_f32(vrGHIJ, vrecpsq_f32(vrGHIJ, vdGHIJ)); |
| 164 | |
| 165 | vr0123 = vfmaq_f32(vr0123, vr0123, vfmsq_f32(vone, vr0123, vd0123)); |
| 166 | vr4567 = vfmaq_f32(vr4567, vr4567, vfmsq_f32(vone, vr4567, vd4567)); |
| 167 | vr89AB = vfmaq_f32(vr89AB, vr89AB, vfmsq_f32(vone, vr89AB, vd89AB)); |
| 168 | vrCDEF = vfmaq_f32(vrCDEF, vrCDEF, vfmsq_f32(vone, vrCDEF, vdCDEF)); |
| 169 | vrGHIJ = vfmaq_f32(vrGHIJ, vrGHIJ, vfmsq_f32(vone, vrGHIJ, vdGHIJ)); |
| 170 | |
| 171 | // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z)) |
| 172 | float32x4_t vf0123 = vmulq_f32(ve0123, vr0123); |
| 173 | float32x4_t vf4567 = vmulq_f32(ve4567, vr4567); |
| 174 | float32x4_t vf89AB = vmulq_f32(ve89AB, vr89AB); |
| 175 | float32x4_t vfCDEF = vmulq_f32(veCDEF, vrCDEF); |
| 176 | float32x4_t vfGHIJ = vmulq_f32(veGHIJ, vrGHIJ); |
| 177 | |
| 178 | // For inputs below denormal cutoff, replace output with +0.0f. |
| 179 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 180 | vf0123 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf0123), vcagtq_f32(vx0123, vdenorm_cutoff))); |
| 181 | vf4567 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf4567), vcagtq_f32(vx4567, vdenorm_cutoff))); |
| 182 | vf89AB = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf89AB), vcagtq_f32(vx89AB, vdenorm_cutoff))); |
| 183 | vfCDEF = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfCDEF), vcagtq_f32(vxCDEF, vdenorm_cutoff))); |
| 184 | vfGHIJ = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfGHIJ), vcagtq_f32(vxGHIJ, vdenorm_cutoff))); |
| 185 | |
| 186 | // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z) |
| 187 | const uint32x4_t vm0123 = vcltq_f32(vx0123, vmovq_n_f32(0.0f)); |
| 188 | const uint32x4_t vm4567 = vcltq_f32(vx4567, vmovq_n_f32(0.0f)); |
| 189 | const uint32x4_t vm89AB = vcltq_f32(vx89AB, vmovq_n_f32(0.0f)); |
| 190 | const uint32x4_t vmCDEF = vcltq_f32(vxCDEF, vmovq_n_f32(0.0f)); |
| 191 | const uint32x4_t vmGHIJ = vcltq_f32(vxGHIJ, vmovq_n_f32(0.0f)); |
| 192 | |
| 193 | vf0123 = vbslq_f32(vm0123, vf0123, vsubq_f32(vone, vf0123)); |
| 194 | vf4567 = vbslq_f32(vm4567, vf4567, vsubq_f32(vone, vf4567)); |
| 195 | vf89AB = vbslq_f32(vm89AB, vf89AB, vsubq_f32(vone, vf89AB)); |
| 196 | vfCDEF = vbslq_f32(vmCDEF, vfCDEF, vsubq_f32(vone, vfCDEF)); |
| 197 | vfGHIJ = vbslq_f32(vmGHIJ, vfGHIJ, vsubq_f32(vone, vfGHIJ)); |
| 198 | |
| 199 | vst1q_f32(y, vf0123); y += 4; |
| 200 | vst1q_f32(y, vf4567); y += 4; |
| 201 | vst1q_f32(y, vf89AB); y += 4; |
| 202 | vst1q_f32(y, vfCDEF); y += 4; |
| 203 | vst1q_f32(y, vfGHIJ); y += 4; |
| 204 | } |
| 205 | for (; n >= 4 * sizeof(float); n -= 4 * sizeof(float)) { |
| 206 | const float32x4_t vx = vld1q_f32(x); x += 4; |
| 207 | |
| 208 | // General structure of the algorithm: |
| 209 | // / exp(x) / (1 + exp(x)) if x <= 0 |
| 210 | // f[x] := |
| 211 | // \ 1 - f[-x] if x >= 0 |
| 212 | // |
| 213 | // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x), |
| 214 | // then replace result with 1 - f[z] if x <= 0. |
| 215 | const float32x4_t vz = vabsq_f32(vx); |
| 216 | |
| 217 | // Compute reduced argument n := round(-z / log(2)). |
| 218 | // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the |
| 219 | // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. |
| 220 | // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because |
| 221 | // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x) |
| 222 | // anyway. We fixup the result for such inputs at the very end of the algorithm. |
| 223 | float32x4_t vn = vfmaq_f32(vmagic_bias, vz, vminus_log2e); |
| 224 | |
| 225 | // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| 226 | // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly. |
| 227 | const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23)); |
| 228 | |
| 229 | // Subtract the large number back to get final n := round(-z / log(2)). |
| 230 | vn = vsubq_f32(vn, vmagic_bias); |
| 231 | |
| 232 | // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)). |
| 233 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 234 | float32x4_t vt = vfmaq_f32(vz, vn, vln2_hi); |
| 235 | vt = vfmaq_f32(vt, vn, vln2_lo); |
| 236 | |
| 237 | // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2]. |
| 238 | float32x4_t vp = vfmaq_f32(vc4, vc5, vt); |
| 239 | vp = vfmaq_f32(vc3, vp, vt); |
| 240 | vp = vfmaq_f32(vc2, vp, vt); |
| 241 | vp = vfmaq_f32(vc1, vp, vt); |
| 242 | |
| 243 | // Reconstruct the exp(-z) value: |
| 244 | // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 245 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 246 | // = s + (t * s) * p |
| 247 | vt = vmulq_f32(vt, vs); |
| 248 | float32x4_t ve = vfmaq_f32(vs, vp, vt); |
| 249 | |
| 250 | // Denominator of the sigmoid fraction: 1.0 + exp(-z) |
| 251 | float32x4_t vd = vaddq_f32(ve, vone); |
| 252 | |
| 253 | // Use Newton-Raphson method (2 iterations) to compute reciprocal of denominator. |
| 254 | // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0. |
| 255 | // Thus the reciprocal of the denominator never overflows. |
| 256 | float32x4_t vr = vrecpeq_f32(vd); |
| 257 | |
| 258 | vr = vmulq_f32(vr, vrecpsq_f32(vr, vd)); |
| 259 | |
| 260 | vr = vfmaq_f32(vr, vr, vfmsq_f32(vone, vr, vd)); |
| 261 | |
| 262 | // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z)) |
| 263 | float32x4_t vf = vmulq_f32(ve, vr); |
| 264 | |
| 265 | // For inputs below denormal cutoff, replace output with +0.0f. |
| 266 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 267 | vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcagtq_f32(vx, vdenorm_cutoff))); |
| 268 | |
| 269 | // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z) |
| 270 | const uint32x4_t vm = vcltq_f32(vx, vmovq_n_s32(0.0f)); |
| 271 | vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf)); |
| 272 | |
| 273 | vst1q_f32(y, vf); y += 4; |
| 274 | } |
| 275 | if XNN_UNLIKELY(n != 0) { |
| 276 | const float32x4_t vx = vld1q_f32(x); |
| 277 | |
| 278 | // General structure of the algorithm: |
| 279 | // / exp(x) / (1 + exp(x)) if x <= 0 |
| 280 | // f[x] := |
| 281 | // \ 1 - f[-x] if x >= 0 |
| 282 | // |
| 283 | // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x), |
| 284 | // then replace result with 1 - f[z] if x <= 0. |
| 285 | const float32x4_t vz = vabsq_f32(vx); |
| 286 | |
| 287 | // Compute reduced argument n := round(-z / log(2)). |
| 288 | // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the |
| 289 | // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. |
| 290 | // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because |
| 291 | // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x) |
| 292 | // anyway. We fixup the result for such inputs at the very end of the algorithm. |
| 293 | float32x4_t vn = vfmaq_f32(vmagic_bias, vz, vminus_log2e); |
| 294 | |
| 295 | // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| 296 | // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly. |
| 297 | const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23)); |
| 298 | |
| 299 | // Subtract the large number back to get final n := round(-z / log(2)). |
| 300 | vn = vsubq_f32(vn, vmagic_bias); |
| 301 | |
| 302 | // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)). |
| 303 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 304 | float32x4_t vt = vfmaq_f32(vz, vn, vln2_hi); |
| 305 | vt = vfmaq_f32(vt, vn, vln2_lo); |
| 306 | |
| 307 | // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2]. |
| 308 | float32x4_t vp = vfmaq_f32(vc4, vc5, vt); |
| 309 | vp = vfmaq_f32(vc3, vp, vt); |
| 310 | vp = vfmaq_f32(vc2, vp, vt); |
| 311 | vp = vfmaq_f32(vc1, vp, vt); |
| 312 | |
| 313 | // Reconstruct the exp(-z) value: |
| 314 | // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 315 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 316 | // = s + (t * s) * p |
| 317 | vt = vmulq_f32(vt, vs); |
| 318 | float32x4_t ve = vfmaq_f32(vs, vp, vt); |
| 319 | |
| 320 | // Denominator of the sigmoid fraction: 1.0 + exp(-z) |
| 321 | float32x4_t vd = vaddq_f32(ve, vone); |
| 322 | |
| 323 | // Use Newton-Raphson method (2 iterations) to compute reciprocal of denominator. |
| 324 | // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0. |
| 325 | // Thus the reciprocal of the denominator never overflows. |
| 326 | float32x4_t vr = vrecpeq_f32(vd); |
| 327 | |
| 328 | vr = vmulq_f32(vr, vrecpsq_f32(vr, vd)); |
| 329 | |
| 330 | vr = vfmaq_f32(vr, vr, vfmsq_f32(vone, vr, vd)); |
| 331 | |
| 332 | // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z)) |
| 333 | float32x4_t vf = vmulq_f32(ve, vr); |
| 334 | |
| 335 | // For inputs below denormal cutoff, replace output with +0.0f. |
| 336 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 337 | vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcagtq_f32(vx, vdenorm_cutoff))); |
| 338 | |
| 339 | // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z) |
| 340 | const uint32x4_t vm = vcltq_f32(vx, vmovq_n_f32(0.0f)); |
| 341 | vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf)); |
| 342 | |
| 343 | float32x2_t vf_lo = vget_low_f32(vf); |
| 344 | if (n & (2 * sizeof(float))) { |
| 345 | vst1_f32(y, vf_lo); y += 2; |
| 346 | vf_lo = vget_high_f32(vf); |
| 347 | } |
| 348 | if (n & (1 * sizeof(float))) { |
| 349 | vst1_lane_f32(y, vf_lo, 0); |
| 350 | } |
| 351 | } |
| 352 | } |