| // 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 |
| $ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ" |
| #include <assert.h> |
| |
| #include <psimd.h> |
| |
| #include <xnnpack/common.h> |
| #include <xnnpack/raddstoreexpminusmax.h> |
| |
| |
| void xnn_f32_raddstoreexpminusmax_ukernel__psimd_p5_x${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 psimd_f32 vmagic_bias = psimd_splat_f32(0x1.8000FEp23f); |
| // The smallest x for which expf(x) is normalized. |
| const psimd_f32 vdenorm_cutoff = psimd_splat_f32(-0x1.5D589Ep6f); |
| const psimd_f32 vlog2e = psimd_splat_f32(0x1.715476p+0f); |
| // Last 7 bits are zeroes |
| const psimd_f32 vminus_ln2_hi = psimd_splat_f32(-0x1.62E400p-1f); |
| const psimd_f32 vminus_ln2_lo = psimd_splat_f32(-0x1.7F7D1Cp-20f); |
| |
| const psimd_f32 vc1 = psimd_splat_f32(0x1.FFFFF6p-1f); |
| const psimd_f32 vc2 = psimd_splat_f32(0x1.FFFDC6p-2f); |
| const psimd_f32 vc3 = psimd_splat_f32(0x1.555A80p-3f); |
| const psimd_f32 vc4 = psimd_splat_f32(0x1.573A1Ap-5f); |
| const psimd_f32 vc5 = psimd_splat_f32(0x1.0F9F9Cp-7f); |
| |
| const psimd_f32 vi_max = psimd_splat_f32(max); |
| |
| $for K in range(ACCUMULATORS): |
| psimd_f32 vacc${K} = psimd_zero_f32(); |
| for (; elements >= ${ELEMENTS_TILE} * sizeof(float); elements -= ${ELEMENTS_TILE} * sizeof(float)) { |
| // Load ${ELEMENTS_TILE} (${SIMD_TILE}x4) inputs at a time. |
| const psimd_f32 vi${ABC[0:4]} = psimd_load_f32(input); |
| $for N in range(4, ELEMENTS_TILE, 4): |
| const psimd_f32 vi${ABC[N:N+4]} = psimd_load_f32(input + ${N}); |
| input += ${ELEMENTS_TILE}; |
| |
| // Subtract maximum input x := i - i_max. This implies x <= 0. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| const psimd_f32 vx${ABC[N:N+4]} = psimd_sub_f32(vi${ABC[N:N+4]}, vi_max); |
| |
| // Compute reduced argument elements := round(x / log(2)). |
| $for N in range(0, ELEMENTS_TILE, 4): |
| psimd_f32 vn${ABC[N:N+4]} = psimd_qfma_f32(vmagic_bias, vx${ABC[N:N+4]}, vlog2e); |
| |
| // 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. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| const psimd_f32 vs${ABC[N:N+4]} = (psimd_f32) ((psimd_u32) 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]} = psimd_sub_f32(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. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| psimd_f32 vt${ABC[N:N+4]} = psimd_qfma_f32(vx${ABC[N:N+4]}, vn${ABC[N:N+4]}, vminus_ln2_hi); |
| |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vt${ABC[N:N+4]} = psimd_qfma_f32(vt${ABC[N:N+4]}, vn${ABC[N:N+4]}, vminus_ln2_lo); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| psimd_f32 vp${ABC[N:N+4]} = psimd_qfma_f32(vc4, vc5, vt${ABC[N:N+4]}); |
| |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vp${ABC[N:N+4]} = psimd_qfma_f32(vc3, vp${ABC[N:N+4]}, vt${ABC[N:N+4]}); |
| |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vp${ABC[N:N+4]} = psimd_qfma_f32(vc2, vp${ABC[N:N+4]}, vt${ABC[N:N+4]}); |
| |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vp${ABC[N:N+4]} = psimd_qfma_f32(vc1, vp${ABC[N:N+4]}, vt${ABC[N:N+4]}); |
| |
| // 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]} = psimd_mul_f32(vt${ABC[N:N+4]}, vs${ABC[N:N+4]}); |
| |
| $for N in range(0, ELEMENTS_TILE, 4): |
| psimd_f32 vf${ABC[N:N+4]} = psimd_qfma_f32(vs${ABC[N:N+4]}, vt${ABC[N:N+4]}, vp${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]} = psimd_andnotmask_f32(vx${ABC[N:N+4]} < vdenorm_cutoff, vf${ABC[N:N+4]}); |
| |
| // Store ${ELEMENTS_TILE} (${SIMD_TILE}x4) outputs at a time. |
| psimd_store_f32(output, vf${ABC[0:4]}); |
| $for N in range(4, ELEMENTS_TILE, 4): |
| psimd_store_f32(output + ${N}, vf${ABC[N:N+4]}); |
| output += ${ELEMENTS_TILE}; |
| |
| // Accumulate computed exponents. |
| $for N in range(0, ELEMENTS_TILE, 4): |
| vacc${N % ACCUMULATORS} = psimd_add_f32(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} = psimd_add_f32(vacc${A}, vacc${A + ACC_SLICE}); |
| $ACC_SLICE *= 2 |
| |
| psimd_f32 vacc = vacc0; |
| for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) { |
| // Load 4 inputs at a time. |
| const psimd_f32 vi = psimd_load_f32(input); |
| input += 4; |
| |
| // Subtract maximum input x := i - i_max. This implies x <= 0. |
| const psimd_f32 vx = psimd_sub_f32(vi, vi_max); |
| |
| // Compute reduced argument elements := round(x / log(2)). |
| psimd_f32 vn = psimd_qfma_f32(vmagic_bias, vx, vlog2e); |
| |
| // 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 psimd_f32 vs = (psimd_f32) ((psimd_u32) vn << 23); |
| |
| // Subtract the large number back to get final elements := round(x / log(2)). |
| vn = psimd_sub_f32(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. |
| psimd_f32 vt = psimd_qfma_f32(vx, vn, vminus_ln2_hi); |
| vt = psimd_qfma_f32(vt, vn, vminus_ln2_lo); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| psimd_f32 vp = psimd_qfma_f32(vc4, vc5, vt); |
| vp = psimd_qfma_f32(vc3, vp, vt); |
| vp = psimd_qfma_f32(vc2, vp, vt); |
| vp = psimd_qfma_f32(vc1, vp, vt); |
| |
| // 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 = psimd_mul_f32(vt, vs); |
| psimd_f32 vf = psimd_qfma_f32(vs, vt, vp); |
| |
| // 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 = psimd_andnotmask_f32(vx < vdenorm_cutoff, vf); |
| |
| // Store 4 outputs at a time. |
| psimd_store_f32(output, vf); |
| output += 4; |
| |
| // Accumulate computed exponents. |
| vacc = psimd_add_f32(vacc, vf); |
| } |
| if (elements != 0) { |
| assert(elements >= 1 * sizeof(float)); |
| assert(elements <= 3 * sizeof(float)); |
| // Load 4 inputs at a time. |
| const psimd_f32 vi = psimd_load_f32(input); |
| |
| // Subtract maximum input x := i - i_max. This implies x <= 0. |
| const psimd_f32 vx = psimd_sub_f32(vi, vi_max); |
| |
| // Compute reduced argument elements := round(x / log(2)). |
| psimd_f32 vn = psimd_qfma_f32(vmagic_bias, vx, vlog2e); |
| |
| // 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 psimd_f32 vs = (psimd_f32) ((psimd_u32) vn << 23); |
| |
| // Subtract the large number back to get final elements := round(x / log(2)). |
| vn = psimd_sub_f32(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. |
| psimd_f32 vt = psimd_qfma_f32(vx, vn, vminus_ln2_hi); |
| vt = psimd_qfma_f32(vt, vn, vminus_ln2_lo); |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| psimd_f32 vp = psimd_qfma_f32(vc4, vc5, vt); |
| vp = psimd_qfma_f32(vc3, vp, vt); |
| vp = psimd_qfma_f32(vc2, vp, vt); |
| vp = psimd_qfma_f32(vc1, vp, vt); |
| |
| // 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 = psimd_mul_f32(vt, vs); |
| psimd_f32 vf = psimd_qfma_f32(vs, vt, vp); |
| |
| // 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 = psimd_andnotmask_f32(vx < vdenorm_cutoff, vf); |
| |
| if (elements & (2 * sizeof(float))) { |
| // Store 2 outputs at a time. |
| psimd_store2_f32(output, vf); |
| output += 2; |
| |
| // Accumulate 2 computed exponents. |
| vacc = psimd_add_f32(vacc, psimd_concat_lo_f32(vf, psimd_zero_f32())); |
| |
| vf = psimd_concat_hi_f32(vf, vf); |
| } |
| if (elements & (1 * sizeof(float))) { |
| // Store 1 output at a time. |
| psimd_store1_f32(output, vf); |
| |
| // Accumulate 1 computed exponent. |
| const psimd_f32 vzero = psimd_zero_f32(); |
| vf = psimd_concat_lo_f32(vf, vzero); |
| vf = psimd_concat_even_f32(vf, vzero); |
| vacc = psimd_add_f32(vacc, vf); |
| } |
| } |
| // Reduce 4 elements in the SIMD register |
| *sum = psimd_reduce_sum_f32(vacc); |
| } |