| // Auto-generated file. Do not edit! |
| // Template: src/f32-sigmoid/avx2-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 <immintrin.h> |
| |
| #include <xnnpack/common.h> |
| #include <xnnpack/vunary.h> |
| |
| |
| static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0}; |
| |
| void xnn_f32_sigmoid_ukernel__avx2_rr1_p5_nr2fma_x16( |
| size_t n, |
| const float* x, |
| float* y, |
| const void* params) |
| { |
| assert(n % sizeof(float) == 0); |
| |
| const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f); |
| // The smallest x for which sigmoidf(x) is normalized. |
| // This number is also the smallest x for which expf(x) is normalized. |
| const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep+6f); |
| const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f); |
| const __m256 vminus_ln2 = _mm256_set1_ps(-0x1.62E43p-1f); |
| const __m256 vone = _mm256_set1_ps(1.0f); |
| const __m256 vsign_mask = _mm256_set1_ps(-0.0f); |
| |
| const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f); |
| const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f); |
| const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f); |
| const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f); |
| const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f); |
| |
| for (; n >= 16 * sizeof(float); n -= 16 * sizeof(float)) { |
| const __m256 vx0 = _mm256_loadu_ps(x); |
| const __m256 vx1 = _mm256_loadu_ps(x + 8); |
| x += 16; |
| |
| // 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 __m256 vz0 = _mm256_or_ps(vx0, vsign_mask); |
| const __m256 vz1 = _mm256_or_ps(vx1, vsign_mask); |
| |
| // Compute reduced argument n := round(z / log(2)). |
| // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result |
| // to an integer, then subtracing the large number back. 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. |
| __m256 vn0 = _mm256_fmadd_ps(vz0, vlog2e, vmagic_bias); |
| __m256 vn1 = _mm256_fmadd_ps(vz1, vlog2e, vmagic_bias); |
| |
| // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| // -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly. |
| const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23)); |
| const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23)); |
| |
| // Subtract the large number back to get final n := round(z / log(2)). |
| vn0 = _mm256_sub_ps(vn0, vmagic_bias); |
| vn1 = _mm256_sub_ps(vn1, vmagic_bias); |
| |
| // Compute reduced argument t := z - n * log(2). |
| __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2, vz0); |
| __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2, vz1); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4); |
| __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4); |
| |
| vp0 = _mm256_fmadd_ps(vp0, vt0, vc3); |
| vp1 = _mm256_fmadd_ps(vp1, vt1, vc3); |
| |
| vp0 = _mm256_fmadd_ps(vp0, vt0, vc2); |
| vp1 = _mm256_fmadd_ps(vp1, vt1, vc2); |
| |
| vp0 = _mm256_fmadd_ps(vp0, vt0, vc1); |
| vp1 = _mm256_fmadd_ps(vp1, vt1, vc1); |
| |
| // 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 |
| vt0 = _mm256_mul_ps(vt0, vs0); |
| vt1 = _mm256_mul_ps(vt1, vs1); |
| |
| const __m256 ve0 = _mm256_fmadd_ps(vt0, vp0, vs0); |
| const __m256 ve1 = _mm256_fmadd_ps(vt1, vp1, vs1); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(z) |
| const __m256 vd0 = _mm256_add_ps(ve0, vone); |
| const __m256 vd1 = _mm256_add_ps(ve1, vone); |
| |
| // Use Newton-Raphson method to compute reciprocal of denominator. |
| // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0. |
| // Thus the reciprocal of the denominator never overflows. |
| __m256 vr0 = _mm256_rcp_ps(vd0); |
| __m256 vr1 = _mm256_rcp_ps(vd1); |
| |
| vr0 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr0, vd0, vone), vr0, vr0); |
| vr1 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr1, vd1, vone), vr1, vr1); |
| |
| vr0 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr0, vd0, vone), vr0, vr0); |
| vr1 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr1, vd1, vone), vr1, vr1); |
| |
| // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z)) |
| __m256 vf0 = _mm256_mul_ps(ve0, vr0); |
| __m256 vf1 = _mm256_mul_ps(ve1, vr1); |
| |
| // For inputs below denormal cutoff, replace output with +0.0f. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vz0, vdenorm_cutoff, _CMP_LT_OS), vf0); |
| vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vz1, vdenorm_cutoff, _CMP_LT_OS), vf1); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z) |
| vf0 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf0), vf0, vx0); |
| vf1 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf1), vf1, vx1); |
| |
| _mm256_storeu_ps(y, vf0); |
| _mm256_storeu_ps(y + 8, vf1); |
| y += 16; |
| } |
| for (; n >= 8 * sizeof(float); n -= 8 * sizeof(float)) { |
| const __m256 vx = _mm256_loadu_ps(x); |
| x += 8; |
| |
| // 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 __m256 vz = _mm256_or_ps(vx, vsign_mask); |
| |
| // Compute reduced argument n := round(z / log(2)). |
| // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result |
| // to an integer, then subtracing the large number back. 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. |
| __m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias); |
| |
| // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| // -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly. |
| const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23)); |
| |
| // Subtract the large number back to get final n := round(z / log(2)). |
| vn = _mm256_sub_ps(vn, vmagic_bias); |
| |
| // Compute reduced argument t := z - n * log(2). |
| __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4); |
| vp = _mm256_fmadd_ps(vp, vt, vc3); |
| vp = _mm256_fmadd_ps(vp, vt, vc2); |
| vp = _mm256_fmadd_ps(vp, vt, vc1); |
| |
| // 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 = _mm256_mul_ps(vt, vs); |
| const __m256 ve = _mm256_fmadd_ps(vt, vp, vs); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(z) |
| const __m256 vd = _mm256_add_ps(ve, vone); |
| |
| // Use Newton-Raphson method to compute reciprocal of denominator. |
| // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0. |
| // Thus the reciprocal of the denominator never overflows. |
| __m256 vr = _mm256_rcp_ps(vd); |
| vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr); |
| vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr); |
| |
| // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z)) |
| __m256 vf = _mm256_mul_ps(ve, vr); |
| |
| // 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 = _mm256_andnot_ps(_mm256_cmp_ps(vz, vdenorm_cutoff, _CMP_LT_OS), vf); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z) |
| vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx); |
| |
| _mm256_storeu_ps(y, vf); |
| y += 8; |
| } |
| if XNN_UNLIKELY(n != 0) { |
| assert(n >= 1 * sizeof(float)); |
| assert(n <= 7 * sizeof(float)); |
| __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - n)); |
| |
| const __m256 vx = _mm256_maskload_ps(x, vmask); |
| |
| // 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 __m256 vz = _mm256_or_ps(vx, vsign_mask); |
| |
| // Compute reduced argument n := round(z / log(2)). |
| // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result |
| // to an integer, then subtracing the large number back. 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. |
| __m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias); |
| |
| // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| // -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly. |
| const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23)); |
| |
| // Subtract the large number back to get final n := round(z / log(2)). |
| vn = _mm256_sub_ps(vn, vmagic_bias); |
| |
| // Compute reduced argument t := z - n * log(2). |
| __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4); |
| vp = _mm256_fmadd_ps(vp, vt, vc3); |
| vp = _mm256_fmadd_ps(vp, vt, vc2); |
| vp = _mm256_fmadd_ps(vp, vt, vc1); |
| |
| // 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 = _mm256_mul_ps(vt, vs); |
| const __m256 ve = _mm256_fmadd_ps(vt, vp, vs); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(z) |
| const __m256 vd = _mm256_add_ps(ve, vone); |
| |
| // Use Newton-Raphson method to compute reciprocal of denominator. |
| // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0. |
| // Thus the reciprocal of the denominator never overflows. |
| __m256 vr = _mm256_rcp_ps(vd); |
| vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr); |
| vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr); |
| |
| // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z)) |
| __m256 vf = _mm256_mul_ps(ve, vr); |
| |
| // 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 = _mm256_andnot_ps(_mm256_cmp_ps(vz, vdenorm_cutoff, _CMP_LT_OS), vf); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z) |
| vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx); |
| |
| _mm256_maskstore_ps(y, vmask, vf); |
| } |
| } |