| // 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 ELEMENTS_TILE % 4 == 0 |
| $assert ELEMENTS_TILE >= 4 |
| $SIMD_TILE = ELEMENTS_TILE // 4 |
| $ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ" |
| #include <assert.h> |
| |
| #include <emmintrin.h> |
| |
| #include <xnnpack/common.h> |
| #include <xnnpack/raddstoreexpminusmax.h> |
| |
| |
| void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x${ELEMENTS_TILE}${"" if ACCUMULATORS == 1 else "_acc%d" % ACCUMULATORS}( |
| size_t elements, |
| const float* input, |
| float* output, |
| float* sum, |
| float max) |
| { |
| assert(elements % sizeof(float) == 0); |
| |
| const __m128 vmagic_bias = _mm_set1_ps(0x1.8000FEp23f); |
| // The smallest x for which expf(x) is normalized. |
| const __m128 vdenorm_cutoff = _mm_set1_ps(-0x1.5D589Ep6f); |
| 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 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); |
| |
| const __m128 vi_max = _mm_set1_ps(max); |
| |
| $for K in range(ACCUMULATORS): |
| __m128 vacc${K} = _mm_setzero_ps(); |
| for (; elements >= ${ELEMENTS_TILE} * sizeof(float); elements -= ${ELEMENTS_TILE} * sizeof(float)) { |
| // Load ${ELEMENTS_TILE} (${SIMD_TILE}x4) inputs at a time. |
| const __m128 vi${ABC[0:4]} = _mm_loadu_ps(input); |
| $for N in range(4, ELEMENTS_TILE, 4): |
| const __m128 vi${ABC[N:N+4]} = _mm_loadu_ps(input + ${N}); |
| input += ${ELEMENTS_TILE}; |
| |
| // Subtract maximum input x := i - i_max. This implies x <= 0. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| const __m128 vx${ABC[N:N+4]} = _mm_sub_ps(vi${ABC[N:N+4]}, vi_max); |
| |
| // Compute reduced argument elements := round(x / log(2)). |
| $for N in range(0, ELEMENTS_TILE, 4): |
| __m128 vn${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vx${ABC[N:N+4]}, vlog2e), vmagic_bias); |
| |
| // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. |
| // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| const __m128 vs${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 elements := round(x / log(2)). |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vn${ABC[N:N+4]} = _mm_sub_ps(vn${ABC[N:N+4]}, vmagic_bias); |
| |
| // Compute reduced argument t := x - elements * log(2). |
| // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| __m128 vt${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vn${ABC[N:N+4]}, vminus_ln2_hi), vx${ABC[N:N+4]}); |
| |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vt${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]. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| __m128 vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vc5, vt${ABC[N:N+4]}), vc4); |
| |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vp${ABC[N:N+4]}, vt${ABC[N:N+4]}), vc3); |
| |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vp${ABC[N:N+4]}, vt${ABC[N:N+4]}), vc2); |
| |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vp${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vp${ABC[N:N+4]}, vt${ABC[N:N+4]}), vc1); |
| |
| // Reconstruct the final f value: |
| // f = 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 |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vt${ABC[N:N+4]} = _mm_mul_ps(vt${ABC[N:N+4]}, vs${ABC[N:N+4]}); |
| |
| $for N in range(0, ELEMENTS_TILE, 4): |
| __m128 vf${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]}); |
| |
| // For inputs below zero cutoff, replace output with +0.0f. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vf${ABC[N:N+4]} = _mm_andnot_ps(_mm_cmplt_ps(vx${ABC[N:N+4]}, vdenorm_cutoff), vf${ABC[N:N+4]}); |
| |
| // Store ${ELEMENTS_TILE} (${SIMD_TILE}x4) outputs at a time. |
| _mm_storeu_ps(output, vf${ABC[0:4]}); |
| $for N in range(4, ELEMENTS_TILE, 4): |
| _mm_storeu_ps(output + ${N}, vf${ABC[N:N+4]}); |
| output += ${ELEMENTS_TILE}; |
| |
| // Accumulate computed exponents. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vacc${N % ACCUMULATORS} = _mm_add_ps(vacc${N % ACCUMULATORS}, vf${ABC[N:N+4]}); |
| } |
| $if ACCUMULATORS > 1: |
| // Add up all accumulators to vacc0 |
| $ACC_SLICE = 1 |
| $while ACC_SLICE < ACCUMULATORS: |
| $for A in range(0, ACCUMULATORS, ACC_SLICE * 2): |
| $if A + ACC_SLICE < ACCUMULATORS: |
| vacc${A} = _mm_add_ps(vacc${A}, vacc${A + ACC_SLICE}); |
| $ACC_SLICE *= 2 |
| |
| __m128 vacc = vacc0; |
| for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) { |
| // Load 4 inputs at a time. |
| const __m128 vi = _mm_loadu_ps(input); |
| input += 4; |
| |
| // Subtract maximum input x := i - i_max. This implies x <= 0. |
| const __m128 vx = _mm_sub_ps(vi, vi_max); |
| |
| // Compute reduced argument elements := round(x / log(2)). |
| __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias); |
| |
| // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. |
| // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. |
| const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23)); |
| |
| // Subtract the large number back to get final elements := round(x / log(2)). |
| vn = _mm_sub_ps(vn, vmagic_bias); |
| |
| // Compute reduced argument t := x - elements * 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), vx); |
| 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 final f value: |
| // f = 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 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs); |
| |
| // For inputs below zero 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(vx, vdenorm_cutoff), vf); |
| |
| // Store 4 outputs at a time. |
| _mm_storeu_ps(output, vf); |
| output += 4; |
| |
| // Accumulate computed exponents. |
| vacc = _mm_add_ps(vacc, vf); |
| } |
| if (elements != 0) { |
| assert(elements >= 1 * sizeof(float)); |
| assert(elements <= 3 * sizeof(float)); |
| // Load 4 inputs at a time. |
| const __m128 vi = _mm_loadu_ps(input); |
| |
| // Subtract maximum input x := i - i_max. This implies x <= 0. |
| const __m128 vx = _mm_sub_ps(vi, vi_max); |
| |
| // Compute reduced argument elements := round(x / log(2)). |
| __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias); |
| |
| // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. |
| // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. |
| const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23)); |
| |
| // Subtract the large number back to get final elements := round(x / log(2)). |
| vn = _mm_sub_ps(vn, vmagic_bias); |
| |
| // Compute reduced argument t := x - elements * 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), vx); |
| 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 final f value: |
| // f = 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 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs); |
| |
| // For inputs below zero 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(vx, vdenorm_cutoff), vf); |
| |
| if (elements & (2 * sizeof(float))) { |
| // Store 2 outputs at a time. |
| _mm_storel_pi((__m64*) output, vf); |
| output += 2; |
| |
| // Accumulate 2 computed exponents. |
| vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps())); |
| |
| vf = _mm_movehl_ps(vf, vf); |
| } |
| if (elements & (1 * sizeof(float))) { |
| // Store 1 output at a time. |
| _mm_store_ss(output, vf); |
| |
| // Accumulate 1 computed exponent. |
| vacc = _mm_add_ss(vacc, vf); |
| } |
| } |
| // Reduce 4 elements in the SIMD register |
| vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc)); |
| vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1))); |
| _mm_store_ss(sum, vacc); |
| } |