| // 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. |
| |
| $assert BATCH_TILE % 4 == 0 |
| $assert BATCH_TILE >= 4 |
| $ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ" |
| #include <assert.h> |
| |
| $if BLEND: |
| #include <smmintrin.h> |
| $else: |
| #include <emmintrin.h> |
| |
| #include <xnnpack/common.h> |
| #include <xnnpack/vunary.h> |
| |
| |
| void xnn_f32_sigmoid_ukernel__${"sse41" if BLEND else "sse2"}_p5_div_x${BATCH_TILE}( |
| 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); |
| const __m128 vlog2e = _mm_set1_ps(0x1.715476p+0f); |
| // Last 7 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); |
| |
| $if BATCH_TILE > 4: |
| for (; n >= ${BATCH_TILE} * sizeof(float); n -= ${BATCH_TILE} * sizeof(float)) { |
| const __m128 vx${ABC[0:4]} = _mm_loadu_ps(x); |
| $for N in range(4, BATCH_TILE, 4): |
| const __m128 vx${ABC[N:N+4]} = _mm_loadu_ps(x + ${N}); |
| |
| // 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. |
| $for N in range(0, BATCH_TILE, 4): |
| const __m128 vz${ABC[N:N+4]} = _mm_or_ps(vx${ABC[N:N+4]}, 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. |
| $for N in range(0, BATCH_TILE, 4): |
| __m128 vn${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vz${ABC[N:N+4]}, 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. |
| $for N in range(0, BATCH_TILE, 4): |
| const __m128 vs${ABC[N:N+4]} = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn${ABC[N:N+4]}), 23)); |
| |
| // Subtract the large number back to get final n := round(z / log(2)). |
| $for N in range(0, BATCH_TILE, 4): |
| vn${ABC[N:N+4]} = _mm_sub_ps(vn${ABC[N:N+4]}, 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. |
| $for N in range(0, BATCH_TILE, 4): |
| __m128 vt${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vn${ABC[N:N+4]}, vminus_ln2_hi), vz${ABC[N:N+4]}); |
| |
| $for N in range(0, BATCH_TILE, 4): |
| vt${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vn${ABC[N:N+4]}, vminus_ln2_lo), vt${ABC[N:N+4]}); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| $for N in range(0, BATCH_TILE, 4): |
| __m128 vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vc5, vt${ABC[N:N+4]}), vc4); |
| |
| $for N in range(0, BATCH_TILE, 4): |
| vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vp${ABC[N:N+4]}, vt${ABC[N:N+4]}), vc3); |
| |
| $for N in range(0, BATCH_TILE, 4): |
| vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vp${ABC[N:N+4]}, vt${ABC[N:N+4]}), vc2); |
| |
| $for N in range(0, BATCH_TILE, 4): |
| vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vp${ABC[N:N+4]}, vt${ABC[N:N+4]}), 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 |
| $for N in range(0, BATCH_TILE, 4): |
| vt${ABC[N:N+4]} = _mm_mul_ps(vt${ABC[N:N+4]}, vs${ABC[N:N+4]}); |
| |
| $for N in range(0, BATCH_TILE, 4): |
| __m128 ve${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]}); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(z) |
| $for N in range(0, BATCH_TILE, 4): |
| __m128 vd${ABC[N:N+4]} = _mm_add_ps(ve${ABC[N:N+4]}, vone); |
| |
| // Reconstruct sigmoid(-z) = exp(z) / (1.0 + exp(z)) |
| $for N in range(0, BATCH_TILE, 4): |
| __m128 vf${ABC[N:N+4]} = _mm_div_ps(ve${ABC[N:N+4]}, vd${ABC[N:N+4]}); |
| |
| // For inputs below denormal cutoff, replace output with +0.0f. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| $for N in range(0, BATCH_TILE, 4): |
| vf${ABC[N:N+4]} = _mm_andnot_ps(_mm_cmplt_ps(vz${ABC[N:N+4]}, vdenorm_cutoff), vf${ABC[N:N+4]}); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z) |
| $if BLEND: |
| $for N in range(0, BATCH_TILE, 4): |
| vf${ABC[N:N+4]} = _mm_blendv_ps(_mm_sub_ps(vone, vf${ABC[N:N+4]}), vf${ABC[N:N+4]}, vx${ABC[N:N+4]}); |
| $else: |
| $for N in range(0, BATCH_TILE, 4): |
| __m128 vm${ABC[N:N+4]} = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx${ABC[N:N+4]}))); |
| |
| $for N in range(0, BATCH_TILE, 4): |
| vf${ABC[N:N+4]} = _mm_or_ps(_mm_and_ps(vf${ABC[N:N+4]}, vm${ABC[N:N+4]}), _mm_andnot_ps(vm${ABC[N:N+4]}, _mm_sub_ps(vone, vf${ABC[N:N+4]}))); |
| |
| _mm_storeu_ps(y, vf${ABC[0:4]}); |
| $for N in range(4, BATCH_TILE, 4): |
| _mm_storeu_ps(y + ${N}, vf${ABC[N:N+4]}); |
| |
| x += ${BATCH_TILE}; |
| y += ${BATCH_TILE}; |
| } |
| for (; n >= 4 * sizeof(float); n -= 4 * sizeof(float)) { |
| const __m128 vx = _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 vz = _mm_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. |
| __m128 vn = _mm_add_ps(_mm_mul_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 __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23)); |
| |
| // Subtract the large number back to get final n := round(z / log(2)). |
| vn = _mm_sub_ps(vn, 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 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vz); |
| vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4); |
| vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3); |
| vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2); |
| vp = _mm_add_ps(_mm_mul_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 = _mm_mul_ps(vt, vs); |
| __m128 ve = _mm_add_ps(_mm_mul_ps(vt, vp), vs); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(z) |
| __m128 vd = _mm_add_ps(ve, vone); |
| |
| // Reconstruct sigmoid(-z) = exp(z) / (1.0 + exp(z)) |
| __m128 vf = _mm_div_ps(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 = _mm_andnot_ps(_mm_cmplt_ps(vz, vdenorm_cutoff), vf); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z) |
| $if BLEND: |
| vf = _mm_blendv_ps(_mm_sub_ps(vone, vf), vf, vx); |
| $else: |
| __m128 vm = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx))); |
| vf = _mm_or_ps(_mm_and_ps(vf, vm), _mm_andnot_ps(vm, _mm_sub_ps(vone, vf))); |
| |
| _mm_storeu_ps(y, vf); |
| |
| x += 4; |
| y += 4; |
| } |
| if XNN_UNLIKELY(n != 0) { |
| const __m128 vx = _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 vz = _mm_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. |
| __m128 vn = _mm_add_ps(_mm_mul_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 __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23)); |
| |
| // Subtract the large number back to get final n := round(z / log(2)). |
| vn = _mm_sub_ps(vn, 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 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vz); |
| vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4); |
| vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3); |
| vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2); |
| vp = _mm_add_ps(_mm_mul_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 = _mm_mul_ps(vt, vs); |
| __m128 ve = _mm_add_ps(_mm_mul_ps(vt, vp), vs); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(z) |
| __m128 vd = _mm_add_ps(ve, vone); |
| |
| // Reconstruct sigmoid(-z) = exp(z) / (1.0 + exp(z)) |
| __m128 vf = _mm_div_ps(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 = _mm_andnot_ps(_mm_cmplt_ps(vz, vdenorm_cutoff), vf); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z) |
| $if BLEND: |
| vf = _mm_blendv_ps(_mm_sub_ps(vone, vf), vf, vx); |
| $else: |
| __m128 vm = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx))); |
| vf = _mm_or_ps(_mm_and_ps(vf, vm), _mm_andnot_ps(vm, _mm_sub_ps(vone, vf))); |
| |
| if (n & (2 * sizeof(float))) { |
| _mm_storel_pi((__m64*) y, vf); |
| vf = _mm_movehl_ps(vf, vf); |
| y += 2; |
| } |
| if (n & (1 * sizeof(float))) { |
| _mm_store_ss(y, vf); |
| } |
| } |
| } |