| // 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 % 8 == 0 |
| $assert BATCH_TILE >= 8 |
| $assert RR_STEPS in [1, 2] |
| $assert DIV_ALGO in ["div", "nr1fma", "nr2fma"] |
| $ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ" |
| $SIMD_TILE = BATCH_TILE // 8 |
| #include <assert.h> |
| |
| #include <immintrin.h> |
| |
| #include <xnnpack/common.h> |
| #include <xnnpack/vunary.h> |
| |
| |
| static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0}; |
| |
| void xnn_f32_sigmoid_ukernel__avx2_rr${RR_STEPS}_p5_${DIV_ALGO}_x${BATCH_TILE}( |
| 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); |
| $if RR_STEPS == 1: |
| const __m256 vminus_ln2 = _mm256_set1_ps(-0x1.62E43p-1f); |
| $else: |
| const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f); |
| const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f); |
| 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); |
| |
| $if BATCH_TILE > 8: |
| for (; n >= ${BATCH_TILE} * sizeof(float); n -= ${BATCH_TILE} * sizeof(float)) { |
| const __m256 vx${ABC[0]} = _mm256_loadu_ps(x); |
| $for N in range(1, SIMD_TILE): |
| const __m256 vx${ABC[N]} = _mm256_loadu_ps(x + ${N * 8}); |
| x += ${BATCH_TILE}; |
| |
| // 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. |
| $for N in range(SIMD_TILE): |
| const __m256 vz${ABC[N]} = _mm256_or_ps(vx${ABC[N]}, 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. |
| $for N in range(SIMD_TILE): |
| __m256 vn${ABC[N]} = _mm256_fmadd_ps(vz${ABC[N]}, 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. |
| $for N in range(SIMD_TILE): |
| const __m256 vs${ABC[N]} = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn${ABC[N]}), 23)); |
| |
| // Subtract the large number back to get final n := round(z / log(2)). |
| $for N in range(SIMD_TILE): |
| vn${ABC[N]} = _mm256_sub_ps(vn${ABC[N]}, vmagic_bias); |
| |
| // Compute reduced argument t := z - n * log(2). |
| $if RR_STEPS == 1: |
| $for N in range(SIMD_TILE): |
| __m256 vt${ABC[N]} = _mm256_fmadd_ps(vn${ABC[N]}, vminus_ln2, vz${ABC[N]}); |
| $else: |
| // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| $for N in range(SIMD_TILE): |
| __m256 vt${ABC[N]} = _mm256_fmadd_ps(vn${ABC[N]}, vminus_ln2_hi, vz${ABC[N]}); |
| |
| $for N in range(SIMD_TILE): |
| vt${ABC[N]} = _mm256_fmadd_ps(vn${ABC[N]}, vminus_ln2_lo, vt${ABC[N]}); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| $for N in range(SIMD_TILE): |
| __m256 vp${ABC[N]} = _mm256_fmadd_ps(vc5, vt${ABC[N]}, vc4); |
| |
| $for N in range(SIMD_TILE): |
| vp${ABC[N]} = _mm256_fmadd_ps(vp${ABC[N]}, vt${ABC[N]}, vc3); |
| |
| $for N in range(SIMD_TILE): |
| vp${ABC[N]} = _mm256_fmadd_ps(vp${ABC[N]}, vt${ABC[N]}, vc2); |
| |
| $for N in range(SIMD_TILE): |
| vp${ABC[N]} = _mm256_fmadd_ps(vp${ABC[N]}, vt${ABC[N]}, 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 |
| $for N in range(SIMD_TILE): |
| vt${ABC[N]} = _mm256_mul_ps(vt${ABC[N]}, vs${ABC[N]}); |
| |
| $for N in range(SIMD_TILE): |
| const __m256 ve${ABC[N]} = _mm256_fmadd_ps(vt${ABC[N]}, vp${ABC[N]}, vs${ABC[N]}); |
| |
| // Denominator of the sigmoid fraction: 1.0 + exp(z) |
| $for N in range(SIMD_TILE): |
| const __m256 vd${ABC[N]} = _mm256_add_ps(ve${ABC[N]}, vone); |
| |
| $if DIV_ALGO == "div": |
| // Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z)) |
| $for N in range(SIMD_TILE): |
| __m256 vf${ABC[N]} = _mm256_div_ps(ve${ABC[N]}, vd${ABC[N]}); |
| $else: |
| // 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. |
| $for N in range(SIMD_TILE): |
| __m256 vr${ABC[N]} = _mm256_rcp_ps(vd${ABC[N]}); |
| |
| $for N in range(SIMD_TILE): |
| vr${ABC[N]} = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr${ABC[N]}, vd${ABC[N]}, vone), vr${ABC[N]}, vr${ABC[N]}); |
| |
| $if DIV_ALGO == "nr2fma": |
| $for N in range(SIMD_TILE): |
| vr${ABC[N]} = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr${ABC[N]}, vd${ABC[N]}, vone), vr${ABC[N]}, vr${ABC[N]}); |
| |
| // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z)) |
| $for N in range(SIMD_TILE): |
| __m256 vf${ABC[N]} = _mm256_mul_ps(ve${ABC[N]}, vr${ABC[N]}); |
| |
| // For inputs below denormal cutoff, replace output with +0.0f. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| $for N in range(SIMD_TILE): |
| vf${ABC[N]} = _mm256_andnot_ps(_mm256_cmp_ps(vz${ABC[N]}, vdenorm_cutoff, _CMP_LT_OS), vf${ABC[N]}); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z) |
| $for N in range(SIMD_TILE): |
| vf${ABC[N]} = _mm256_blendv_ps(_mm256_sub_ps(vone, vf${ABC[N]}), vf${ABC[N]}, vx${ABC[N]}); |
| |
| _mm256_storeu_ps(y, vf${ABC[0]}); |
| $for N in range(1, SIMD_TILE): |
| _mm256_storeu_ps(y + ${N * 8}, vf${ABC[N]}); |
| y += ${BATCH_TILE}; |
| } |
| 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). |
| $if RR_STEPS == 1: |
| __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz); |
| $else: |
| // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vz); |
| vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt); |
| |
| // 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); |
| |
| $if DIV_ALGO == "div": |
| // Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z)) |
| __m256 vf = _mm256_div_ps(ve, vd); |
| $else: |
| // 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); |
| $if DIV_ALGO == "nr2fma": |
| 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). |
| $if RR_STEPS == 1: |
| __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz); |
| $else: |
| // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vz); |
| vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt); |
| |
| // 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); |
| |
| $if DIV_ALGO == "div": |
| // Reconstruct sigmoid(z) = exp(z) / (1.0 + exp(z)) |
| __m256 vf = _mm256_div_ps(ve, vd); |
| $else: |
| // 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); |
| $if DIV_ALGO == "nr2fma": |
| 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) could be used here, but triggers msan failures (probably an msan bug). |
| __m128 vf_lo = _mm256_castps256_ps128(vf); |
| if (n & (4 * sizeof(float))) { |
| _mm_storeu_ps(y, vf_lo); |
| vf_lo = _mm256_extractf128_ps(vf, 1); |
| y += 4; |
| } |
| if (n & (2 * sizeof(float))) { |
| _mm_storel_pi((__m64*) y, vf_lo); |
| vf_lo = _mm_movehl_ps(vf_lo, vf_lo); |
| y += 2; |
| } |
| if (n & (1 * sizeof(float))) { |
| _mm_store_ss(y, vf_lo); |
| } |
| } |
| } |