| // Auto-generated file. Do not edit! |
| // Template: src/f32-sigmoid/sse-p5-div.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 <emmintrin.h> |
| |
| #include <xnnpack/common.h> |
| #include <xnnpack/vunary.h> |
| |
| |
| void xnn_f32_sigmoid_ukernel__sse2_p5_div_x16( |
| size_t n, |
| const float* x, |
| float* y, |
| const void* params) |
| { |
| assert(n % sizeof(float) == 0); |
| |
| const __m128 vmagic_bias = _mm_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 __m128 vdenorm_cutoff = _mm_set1_ps(-0x1.5D589Ep+6f); |
| // The largest x for which sigmoidf(x) is not equal 1.0. |
| const __m128 vone_cutoff = _mm_set1_ps(0x1.154244p+4f); |
| const __m128 vlog2e = _mm_set1_ps(0x1.715476p+0f); |
| // Last 8 bits are zeroes |
| const __m128 vminus_ln2_hi = _mm_set1_ps(-0x1.62E400p-1f); |
| const __m128 vminus_ln2_lo = _mm_set1_ps(-0x1.7F7D1Cp-20f); |
| const __m128 vone = _mm_set1_ps(1.0f); |
| const __m128 vsign_mask = _mm_set1_ps(-0.0f); |
| |
| const __m128 vc1 = _mm_set1_ps(0x1.FFFFF6p-1f); |
| const __m128 vc2 = _mm_set1_ps(0x1.FFFDC6p-2f); |
| const __m128 vc3 = _mm_set1_ps(0x1.555A80p-3f); |
| const __m128 vc4 = _mm_set1_ps(0x1.573A1Ap-5f); |
| const __m128 vc5 = _mm_set1_ps(0x1.0F9F9Cp-7f); |
| |
| for (; n >= 16 * sizeof(float); n -= 16 * sizeof(float)) { |
| const __m128 vx0123 = _mm_loadu_ps(x); |
| const __m128 vx4567 = _mm_loadu_ps(x + 4); |
| const __m128 vx89AB = _mm_loadu_ps(x + 8); |
| const __m128 vxCDEF = _mm_loadu_ps(x + 12); |
| |
| // 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 __m128 vz0123 = _mm_or_ps(vx0123, vsign_mask); |
| const __m128 vz4567 = _mm_or_ps(vx4567, vsign_mask); |
| const __m128 vz89AB = _mm_or_ps(vx89AB, vsign_mask); |
| const __m128 vzCDEF = _mm_or_ps(vxCDEF, 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. |
| __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vz0123, vlog2e), vmagic_bias); |
| __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vz4567, vlog2e), vmagic_bias); |
| __m128 vn89AB = _mm_add_ps(_mm_mul_ps(vz89AB, vlog2e), vmagic_bias); |
| __m128 vnCDEF = _mm_add_ps(_mm_mul_ps(vzCDEF, 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 __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23)); |
| const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23)); |
| const __m128 vs89AB = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn89AB), 23)); |
| const __m128 vsCDEF = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnCDEF), 23)); |
| |
| // Subtract the large number back to get final n := round(z / log(2)). |
| vn0123 = _mm_sub_ps(vn0123, vmagic_bias); |
| vn4567 = _mm_sub_ps(vn4567, vmagic_bias); |
| vn89AB = _mm_sub_ps(vn89AB, vmagic_bias); |
| vnCDEF = _mm_sub_ps(vnCDEF, vmagic_bias); |
| |
| // Compute reduced argument t := z - n * log(2). |
| // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vz0123); |
| __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vz4567); |
| __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vz89AB); |
| __m128 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_hi), vzCDEF); |
| |
| vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123); |
| vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567); |
| vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB); |
| vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_lo), vtCDEF); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4); |
| __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4); |
| __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4); |
| __m128 vpCDEF = _mm_add_ps(_mm_mul_ps(vc5, vtCDEF), vc4); |
| |
| vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3); |
| vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3); |
| vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3); |
| vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc3); |
| |
| vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2); |
| vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2); |
| vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2); |
| vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc2); |
| |
| vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1); |
| vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1); |
| vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1); |
| vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), 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 |
| vt0123 = _mm_mul_ps(vt0123, vs0123); |
| vt4567 = _mm_mul_ps(vt4567, vs4567); |
| vt89AB = _mm_mul_ps(vt89AB, vs89AB); |
| vtCDEF = _mm_mul_ps(vtCDEF, vsCDEF); |
| |
| __m128 ve0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123); |
| __m128 ve4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567); |
| __m128 ve89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB); |
| __m128 veCDEF = _mm_add_ps(_mm_mul_ps(vtCDEF, vpCDEF), vsCDEF); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(z) |
| __m128 vd0123 = _mm_add_ps(ve0123, vone); |
| __m128 vd4567 = _mm_add_ps(ve4567, vone); |
| __m128 vd89AB = _mm_add_ps(ve89AB, vone); |
| __m128 vdCDEF = _mm_add_ps(veCDEF, vone); |
| |
| // Reconstruct sigmoid(-z) = exp(z) / (1.0 + exp(z)) |
| __m128 vf0123 = _mm_div_ps(ve0123, vd0123); |
| __m128 vf4567 = _mm_div_ps(ve4567, vd4567); |
| __m128 vf89AB = _mm_div_ps(ve89AB, vd89AB); |
| __m128 vfCDEF = _mm_div_ps(veCDEF, vdCDEF); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z) |
| __m128 vm0123 = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx0123))); |
| __m128 vm4567 = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx4567))); |
| __m128 vm89AB = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx89AB))); |
| __m128 vmCDEF = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vxCDEF))); |
| |
| vf0123 = _mm_or_ps(_mm_and_ps(vf0123, vm0123), _mm_andnot_ps(vm0123, _mm_sub_ps(vone, vf0123))); |
| vf4567 = _mm_or_ps(_mm_and_ps(vf4567, vm4567), _mm_andnot_ps(vm4567, _mm_sub_ps(vone, vf4567))); |
| vf89AB = _mm_or_ps(_mm_and_ps(vf89AB, vm89AB), _mm_andnot_ps(vm89AB, _mm_sub_ps(vone, vf89AB))); |
| vfCDEF = _mm_or_ps(_mm_and_ps(vfCDEF, vmCDEF), _mm_andnot_ps(vmCDEF, _mm_sub_ps(vone, vfCDEF))); |
| |
| // For inputs above 1.0 cutoff, replace output with 1.0. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| vm0123 = _mm_cmpgt_ps(vx0123, vone_cutoff); |
| vm4567 = _mm_cmpgt_ps(vx4567, vone_cutoff); |
| vm89AB = _mm_cmpgt_ps(vx89AB, vone_cutoff); |
| vmCDEF = _mm_cmpgt_ps(vxCDEF, vone_cutoff); |
| |
| vf0123 = _mm_or_ps(_mm_and_ps(vone, vm0123), _mm_andnot_ps(vm0123, vf0123)); |
| vf4567 = _mm_or_ps(_mm_and_ps(vone, vm4567), _mm_andnot_ps(vm4567, vf4567)); |
| vf89AB = _mm_or_ps(_mm_and_ps(vone, vm89AB), _mm_andnot_ps(vm89AB, vf89AB)); |
| vfCDEF = _mm_or_ps(_mm_and_ps(vone, vmCDEF), _mm_andnot_ps(vmCDEF, vfCDEF)); |
| |
| // 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 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123); |
| vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567); |
| vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB); |
| vfCDEF = _mm_andnot_ps(_mm_cmplt_ps(vxCDEF, vdenorm_cutoff), vfCDEF); |
| |
| _mm_storeu_ps(y, vf0123); |
| _mm_storeu_ps(y + 4, vf4567); |
| _mm_storeu_ps(y + 8, vf89AB); |
| _mm_storeu_ps(y + 12, vfCDEF); |
| |
| x += 16; |
| y += 16; |
| } |
| for (; n >= 4 * sizeof(float); n -= 4 * sizeof(float)) { |
| const __m128 vx0123 = _mm_loadu_ps(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 __m128 vz0123 = _mm_or_ps(vx0123, 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. |
| __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vz0123, 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 __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23)); |
| |
| // Subtract the large number back to get final n := round(z / log(2)). |
| vn0123 = _mm_sub_ps(vn0123, vmagic_bias); |
| |
| // Compute reduced argument t := z - n * log(2). |
| // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vz0123); |
| vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4); |
| vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3); |
| vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2); |
| vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), 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 |
| vt0123 = _mm_mul_ps(vt0123, vs0123); |
| __m128 ve0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(z) |
| __m128 vd0123 = _mm_add_ps(ve0123, vone); |
| |
| // Reconstruct sigmoid(-z) = exp(z) / (1.0 + exp(z)) |
| __m128 vf0123 = _mm_div_ps(ve0123, vd0123); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z) |
| __m128 vm0123 = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx0123))); |
| vf0123 = _mm_or_ps(_mm_and_ps(vf0123, vm0123), _mm_andnot_ps(vm0123, _mm_sub_ps(vone, vf0123))); |
| |
| // For inputs above 1.0 cutoff, replace output with 1.0. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| vm0123 = _mm_cmpgt_ps(vx0123, vone_cutoff); |
| vf0123 = _mm_or_ps(_mm_and_ps(vone, vm0123), _mm_andnot_ps(vm0123, vf0123)); |
| |
| // 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 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123); |
| |
| _mm_storeu_ps(y, vf0123); |
| |
| x += 4; |
| y += 4; |
| } |
| if XNN_UNLIKELY(n != 0) { |
| const __m128 vx0123 = _mm_loadu_ps(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 __m128 vz0123 = _mm_or_ps(vx0123, 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. |
| __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vz0123, 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 __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23)); |
| |
| // Subtract the large number back to get final n := round(z / log(2)). |
| vn0123 = _mm_sub_ps(vn0123, vmagic_bias); |
| |
| // Compute reduced argument t := z - n * log(2). |
| // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vz0123); |
| vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4); |
| vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3); |
| vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2); |
| vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), 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 |
| vt0123 = _mm_mul_ps(vt0123, vs0123); |
| __m128 ve0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(z) |
| __m128 vd0123 = _mm_add_ps(ve0123, vone); |
| |
| // Reconstruct sigmoid(-z) = exp(z) / (1.0 + exp(z)) |
| __m128 vf0123 = _mm_div_ps(ve0123, vd0123); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z) |
| __m128 vm0123 = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx0123))); |
| vf0123 = _mm_or_ps(_mm_and_ps(vf0123, vm0123), _mm_andnot_ps(vm0123, _mm_sub_ps(vone, vf0123))); |
| |
| // For inputs above 1.0 cutoff, replace output with 1.0. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| vm0123 = _mm_cmpgt_ps(vx0123, vone_cutoff); |
| vf0123 = _mm_or_ps(_mm_and_ps(vone, vm0123), _mm_andnot_ps(vm0123, vf0123)); |
| |
| // 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 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123); |
| |
| if (n & (2 * sizeof(float))) { |
| _mm_storel_pi((__m64*) y, vf0123); |
| vf0123 = _mm_movehl_ps(vf0123, vf0123); |
| y += 2; |
| } |
| if (n & (1 * sizeof(float))) { |
| _mm_store_ss(y, vf0123); |
| } |
| } |
| } |