| // Auto-generated file. Do not edit! |
| // Template: src/f32-sigmoid/neon-p5.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 <assert.h> |
| |
| #include <arm_neon.h> |
| |
| #include <xnnpack/common.h> |
| #include <xnnpack/vunary.h> |
| |
| |
| void xnn_f32_sigmoid_ukernel__neonfma_rr1_p5_div_x24( |
| size_t n, |
| const float* x, |
| float* y, |
| const void* params) |
| { |
| assert(n % sizeof(float) == 0); |
| |
| const float32x4_t vmagic_bias = vmovq_n_f32(0x1.8000FEp23f); |
| // The largest z for which sigmoidf(-z) is normalized. |
| // This number is also the largest z for which expf(-z) is normalized. |
| const float32x4_t vdenorm_cutoff = vmovq_n_f32(0x1.5D589Ep+6f); |
| const float32x4_t vminus_log2e = vmovq_n_f32(-0x1.715476p+0f); |
| const float32x4_t vln2 = vmovq_n_f32(0x1.62E43p-1f); |
| const float32x4_t vone = vmovq_n_f32(1.0f); |
| |
| const float32x4_t vc1 = vmovq_n_f32(-0x1.FFFFF6p-1f); |
| const float32x4_t vc2 = vmovq_n_f32(0x1.FFFDC6p-2f); |
| const float32x4_t vc3 = vmovq_n_f32(-0x1.555A80p-3f); |
| const float32x4_t vc4 = vmovq_n_f32(0x1.573A1Ap-5f); |
| const float32x4_t vc5 = vmovq_n_f32(-0x1.0F9F9Cp-7f); |
| |
| for (; n >= 24 * sizeof(float); n -= 24 * sizeof(float)) { |
| const float32x4_t vx0123 = vld1q_f32(x); x += 4; |
| const float32x4_t vx4567 = vld1q_f32(x); x += 4; |
| const float32x4_t vx89AB = vld1q_f32(x); x += 4; |
| const float32x4_t vxCDEF = vld1q_f32(x); x += 4; |
| const float32x4_t vxGHIJ = vld1q_f32(x); x += 4; |
| const float32x4_t vxKLMN = vld1q_f32(x); x += 4; |
| |
| // General structure of the algorithm: |
| // / exp(x) / (1 + exp(x)) if x <= 0 |
| // f[x] := |
| // \ 1 - f[-x] if x >= 0 |
| // |
| // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x), |
| // then replace result with 1 - f[z] if x >= 0. |
| const float32x4_t vz0123 = vabsq_f32(vx0123); |
| const float32x4_t vz4567 = vabsq_f32(vx4567); |
| const float32x4_t vz89AB = vabsq_f32(vx89AB); |
| const float32x4_t vzCDEF = vabsq_f32(vxCDEF); |
| const float32x4_t vzGHIJ = vabsq_f32(vxGHIJ); |
| const float32x4_t vzKLMN = vabsq_f32(vxKLMN); |
| |
| // Compute reduced argument n := round(-z / log(2)). |
| // We do it by adding a large number (magic bias), which cause rounding of 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| <= 2**22), but thats ok, because |
| // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x) |
| // anyway. We fixup the result for such inputs at the very end of the algorithm. |
| float32x4_t vn0123 = vfmaq_f32(vmagic_bias, vz0123, vminus_log2e); |
| float32x4_t vn4567 = vfmaq_f32(vmagic_bias, vz4567, vminus_log2e); |
| float32x4_t vn89AB = vfmaq_f32(vmagic_bias, vz89AB, vminus_log2e); |
| float32x4_t vnCDEF = vfmaq_f32(vmagic_bias, vzCDEF, vminus_log2e); |
| float32x4_t vnGHIJ = vfmaq_f32(vmagic_bias, vzGHIJ, vminus_log2e); |
| float32x4_t vnKLMN = vfmaq_f32(vmagic_bias, vzKLMN, vminus_log2e); |
| |
| // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly. |
| const float32x4_t vs0123 = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn0123), 23)); |
| const float32x4_t vs4567 = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn4567), 23)); |
| const float32x4_t vs89AB = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn89AB), 23)); |
| const float32x4_t vsCDEF = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vnCDEF), 23)); |
| const float32x4_t vsGHIJ = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vnGHIJ), 23)); |
| const float32x4_t vsKLMN = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vnKLMN), 23)); |
| |
| // Subtract the large number back to get final n := round(-z / log(2)). |
| vn0123 = vsubq_f32(vn0123, vmagic_bias); |
| vn4567 = vsubq_f32(vn4567, vmagic_bias); |
| vn89AB = vsubq_f32(vn89AB, vmagic_bias); |
| vnCDEF = vsubq_f32(vnCDEF, vmagic_bias); |
| vnGHIJ = vsubq_f32(vnGHIJ, vmagic_bias); |
| vnKLMN = vsubq_f32(vnKLMN, vmagic_bias); |
| |
| // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)). |
| float32x4_t vt0123 = vfmaq_f32(vz0123, vn0123, vln2); |
| float32x4_t vt4567 = vfmaq_f32(vz4567, vn4567, vln2); |
| float32x4_t vt89AB = vfmaq_f32(vz89AB, vn89AB, vln2); |
| float32x4_t vtCDEF = vfmaq_f32(vzCDEF, vnCDEF, vln2); |
| float32x4_t vtGHIJ = vfmaq_f32(vzGHIJ, vnGHIJ, vln2); |
| float32x4_t vtKLMN = vfmaq_f32(vzKLMN, vnKLMN, vln2); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2]. |
| float32x4_t vp0123 = vfmaq_f32(vc4, vc5, vt0123); |
| float32x4_t vp4567 = vfmaq_f32(vc4, vc5, vt4567); |
| float32x4_t vp89AB = vfmaq_f32(vc4, vc5, vt89AB); |
| float32x4_t vpCDEF = vfmaq_f32(vc4, vc5, vtCDEF); |
| float32x4_t vpGHIJ = vfmaq_f32(vc4, vc5, vtGHIJ); |
| float32x4_t vpKLMN = vfmaq_f32(vc4, vc5, vtKLMN); |
| |
| vp0123 = vfmaq_f32(vc3, vp0123, vt0123); |
| vp4567 = vfmaq_f32(vc3, vp4567, vt4567); |
| vp89AB = vfmaq_f32(vc3, vp89AB, vt89AB); |
| vpCDEF = vfmaq_f32(vc3, vpCDEF, vtCDEF); |
| vpGHIJ = vfmaq_f32(vc3, vpGHIJ, vtGHIJ); |
| vpKLMN = vfmaq_f32(vc3, vpKLMN, vtKLMN); |
| |
| vp0123 = vfmaq_f32(vc2, vp0123, vt0123); |
| vp4567 = vfmaq_f32(vc2, vp4567, vt4567); |
| vp89AB = vfmaq_f32(vc2, vp89AB, vt89AB); |
| vpCDEF = vfmaq_f32(vc2, vpCDEF, vtCDEF); |
| vpGHIJ = vfmaq_f32(vc2, vpGHIJ, vtGHIJ); |
| vpKLMN = vfmaq_f32(vc2, vpKLMN, vtKLMN); |
| |
| vp0123 = vfmaq_f32(vc1, vp0123, vt0123); |
| vp4567 = vfmaq_f32(vc1, vp4567, vt4567); |
| vp89AB = vfmaq_f32(vc1, vp89AB, vt89AB); |
| vpCDEF = vfmaq_f32(vc1, vpCDEF, vtCDEF); |
| vpGHIJ = vfmaq_f32(vc1, vpGHIJ, vtGHIJ); |
| vpKLMN = vfmaq_f32(vc1, vpKLMN, vtKLMN); |
| |
| // Reconstruct the exp(-z) value: |
| // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| // = s + (t * s) * p |
| vt0123 = vmulq_f32(vt0123, vs0123); |
| vt4567 = vmulq_f32(vt4567, vs4567); |
| vt89AB = vmulq_f32(vt89AB, vs89AB); |
| vtCDEF = vmulq_f32(vtCDEF, vsCDEF); |
| vtGHIJ = vmulq_f32(vtGHIJ, vsGHIJ); |
| vtKLMN = vmulq_f32(vtKLMN, vsKLMN); |
| |
| float32x4_t ve0123 = vfmaq_f32(vs0123, vp0123, vt0123); |
| float32x4_t ve4567 = vfmaq_f32(vs4567, vp4567, vt4567); |
| float32x4_t ve89AB = vfmaq_f32(vs89AB, vp89AB, vt89AB); |
| float32x4_t veCDEF = vfmaq_f32(vsCDEF, vpCDEF, vtCDEF); |
| float32x4_t veGHIJ = vfmaq_f32(vsGHIJ, vpGHIJ, vtGHIJ); |
| float32x4_t veKLMN = vfmaq_f32(vsKLMN, vpKLMN, vtKLMN); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(-z) |
| float32x4_t vd0123 = vaddq_f32(ve0123, vone); |
| float32x4_t vd4567 = vaddq_f32(ve4567, vone); |
| float32x4_t vd89AB = vaddq_f32(ve89AB, vone); |
| float32x4_t vdCDEF = vaddq_f32(veCDEF, vone); |
| float32x4_t vdGHIJ = vaddq_f32(veGHIJ, vone); |
| float32x4_t vdKLMN = vaddq_f32(veKLMN, vone); |
| |
| // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z)) |
| float32x4_t vf0123 = vdivq_f32(ve0123, vd0123); |
| float32x4_t vf4567 = vdivq_f32(ve4567, vd4567); |
| float32x4_t vf89AB = vdivq_f32(ve89AB, vd89AB); |
| float32x4_t vfCDEF = vdivq_f32(veCDEF, vdCDEF); |
| float32x4_t vfGHIJ = vdivq_f32(veGHIJ, vdGHIJ); |
| float32x4_t vfKLMN = vdivq_f32(veKLMN, vdKLMN); |
| |
| // 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), vcagtq_f32(vx0123, vdenorm_cutoff))); |
| vf4567 = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf4567), vcagtq_f32(vx4567, vdenorm_cutoff))); |
| vf89AB = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf89AB), vcagtq_f32(vx89AB, vdenorm_cutoff))); |
| vfCDEF = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfCDEF), vcagtq_f32(vxCDEF, vdenorm_cutoff))); |
| vfGHIJ = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfGHIJ), vcagtq_f32(vxGHIJ, vdenorm_cutoff))); |
| vfKLMN = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vfKLMN), vcagtq_f32(vxKLMN, vdenorm_cutoff))); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z) |
| const uint32x4_t vm0123 = vcltq_f32(vx0123, vmovq_n_f32(0.0f)); |
| const uint32x4_t vm4567 = vcltq_f32(vx4567, vmovq_n_f32(0.0f)); |
| const uint32x4_t vm89AB = vcltq_f32(vx89AB, vmovq_n_f32(0.0f)); |
| const uint32x4_t vmCDEF = vcltq_f32(vxCDEF, vmovq_n_f32(0.0f)); |
| const uint32x4_t vmGHIJ = vcltq_f32(vxGHIJ, vmovq_n_f32(0.0f)); |
| const uint32x4_t vmKLMN = vcltq_f32(vxKLMN, vmovq_n_f32(0.0f)); |
| |
| vf0123 = vbslq_f32(vm0123, vf0123, vsubq_f32(vone, vf0123)); |
| vf4567 = vbslq_f32(vm4567, vf4567, vsubq_f32(vone, vf4567)); |
| vf89AB = vbslq_f32(vm89AB, vf89AB, vsubq_f32(vone, vf89AB)); |
| vfCDEF = vbslq_f32(vmCDEF, vfCDEF, vsubq_f32(vone, vfCDEF)); |
| vfGHIJ = vbslq_f32(vmGHIJ, vfGHIJ, vsubq_f32(vone, vfGHIJ)); |
| vfKLMN = vbslq_f32(vmKLMN, vfKLMN, vsubq_f32(vone, vfKLMN)); |
| |
| vst1q_f32(y, vf0123); y += 4; |
| vst1q_f32(y, vf4567); y += 4; |
| vst1q_f32(y, vf89AB); y += 4; |
| vst1q_f32(y, vfCDEF); y += 4; |
| vst1q_f32(y, vfGHIJ); y += 4; |
| vst1q_f32(y, vfKLMN); y += 4; |
| } |
| for (; n >= 4 * sizeof(float); n -= 4 * sizeof(float)) { |
| const float32x4_t vx = vld1q_f32(x); x += 4; |
| |
| // General structure of the algorithm: |
| // / exp(x) / (1 + exp(x)) if x <= 0 |
| // f[x] := |
| // \ 1 - f[-x] if x >= 0 |
| // |
| // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x), |
| // then replace result with 1 - f[z] if x <= 0. |
| const float32x4_t vz = vabsq_f32(vx); |
| |
| // Compute reduced argument n := round(-z / log(2)). |
| // We do it by adding a large number (magic bias), which cause rounding of 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| <= 2**22), but thats ok, because |
| // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x) |
| // anyway. We fixup the result for such inputs at the very end of the algorithm. |
| float32x4_t vn = vfmaq_f32(vmagic_bias, vz, vminus_log2e); |
| |
| // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly. |
| const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23)); |
| |
| // Subtract the large number back to get final n := round(-z / log(2)). |
| vn = vsubq_f32(vn, vmagic_bias); |
| |
| // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)). |
| float32x4_t vt = vfmaq_f32(vz, vn, vln2); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2]. |
| float32x4_t vp = vfmaq_f32(vc4, vc5, vt); |
| vp = vfmaq_f32(vc3, vp, vt); |
| vp = vfmaq_f32(vc2, vp, vt); |
| vp = vfmaq_f32(vc1, vp, vt); |
| |
| // Reconstruct the exp(-z) value: |
| // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| // = s + (t * s) * p |
| vt = vmulq_f32(vt, vs); |
| float32x4_t ve = vfmaq_f32(vs, vp, vt); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(-z) |
| float32x4_t vd = vaddq_f32(ve, vone); |
| |
| // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z)) |
| float32x4_t vf = vdivq_f32(ve, vd); |
| |
| // 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), vcagtq_f32(vx, vdenorm_cutoff))); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z) |
| const uint32x4_t vm = vcltq_f32(vx, vmovq_n_f32(0.0f)); |
| vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf)); |
| |
| vst1q_f32(y, vf); y += 4; |
| } |
| if XNN_UNLIKELY(n != 0) { |
| const float32x4_t vx = vld1q_f32(x); |
| |
| // General structure of the algorithm: |
| // / exp(x) / (1 + exp(x)) if x <= 0 |
| // f[x] := |
| // \ 1 - f[-x] if x >= 0 |
| // |
| // First we compute f[z] := exp(-z) / (1 + exp(-z)) where z = abs(x), |
| // then replace result with 1 - f[z] if x <= 0. |
| const float32x4_t vz = vabsq_f32(vx); |
| |
| // Compute reduced argument n := round(-z / log(2)). |
| // We do it by adding a large number (magic bias), which cause rounding of 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| <= 2**22), but thats ok, because |
| // inputs x outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x) |
| // anyway. We fixup the result for such inputs at the very end of the algorithm. |
| float32x4_t vn = vfmaq_f32(vmagic_bias, vz, vminus_log2e); |
| |
| // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly. |
| const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23)); |
| |
| // Subtract the large number back to get final n := round(-z / log(2)). |
| vn = vsubq_f32(vn, vmagic_bias); |
| |
| // Compute reduced argument -t := -z - n * log(2) = -(z + n * log(2)). |
| float32x4_t vt = vfmaq_f32(vz, vn, vln2); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(-t) on [-log(2)/2, log(2)/2]. |
| float32x4_t vp = vfmaq_f32(vc4, vc5, vt); |
| vp = vfmaq_f32(vc3, vp, vt); |
| vp = vfmaq_f32(vc2, vp, vt); |
| vp = vfmaq_f32(vc1, vp, vt); |
| |
| // Reconstruct the exp(-z) value: |
| // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| // = s + (t * s) * p |
| vt = vmulq_f32(vt, vs); |
| float32x4_t ve = vfmaq_f32(vs, vp, vt); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(-z) |
| float32x4_t vd = vaddq_f32(ve, vone); |
| |
| // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z)) |
| float32x4_t vf = vdivq_f32(ve, vd); |
| |
| // 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), vcagtq_f32(vx, vdenorm_cutoff))); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z) |
| const uint32x4_t vm = vcltq_f32(vx, vmovq_n_f32(0.0f)); |
| vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf)); |
| |
| float32x2_t vf_lo = vget_low_f32(vf); |
| if (n & (2 * sizeof(float))) { |
| vst1_f32(y, vf_lo); y += 2; |
| vf_lo = vget_high_f32(vf); |
| } |
| if (n & (1 * sizeof(float))) { |
| vst1_lane_f32(y, vf_lo, 0); |
| } |
| } |
| } |