| // Auto-generated file. Do not edit! |
| // Template: src/f32-raddstoreexpminusmax/scalar-lut64-p2.c.in |
| // Generator: tools/xngen |
| // |
| // Copyright 2020 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 <xnnpack/common.h> |
| #include <xnnpack/raddstoreexpminusmax.h> |
| |
| #include <fp16/bitcasts.h> |
| |
| |
| // Note redefine as uint32[] to avoid redundant bitcasts. |
| extern XNN_INTERNAL const uint32_t xnn_table_exp2_k_over_64[64]; |
| |
| void xnn_f32_raddstoreexpminusmax_ukernel__scalar_lut64_p2_x4( |
| size_t elements, |
| const float* input, |
| float* output, |
| float* sum, |
| float vi_max) |
| { |
| assert(elements % sizeof(float) == 0); |
| |
| const float vmagic_bias = 0x1.800000p23f; |
| // The smallest x for which expf(x) is normalized. |
| const float vdenorm_cutoff = -0x1.5D589Ep6f; |
| const float vlog2e_x64 = 0x1.715476p6f; |
| // Last 13 bits are zeroes |
| const float vminus_ln2_o64_hi = -0x1.630000p-7f; |
| const float vminus_ln2_o64_lo = 0x1.BD0106p-19f; |
| |
| const float vc2 = 0x1.FFFF0Ap-2f; |
| |
| const uint32_t vindex_mask = UINT32_C(0x3F); |
| |
| float vacc0 = 0.0f; |
| for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) { |
| // Load 4 inputs at a time. |
| const float vi0 = input[0]; |
| const float vi1 = input[1]; |
| const float vi2 = input[2]; |
| const float vi3 = input[3]; |
| input += 4; |
| |
| // Subtract maximum input x := i - i_max. This implies x <= 0. |
| const float vx0 = vi0 - vi_max; |
| const float vx1 = vi1 - vi_max; |
| const float vx2 = vi2 - vi_max; |
| const float vx3 = vi3 - vi_max; |
| |
| // Compute reduced argument n := round(x * 64 / log(2)). |
| // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing |
| // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. |
| // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e. |
| // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0] |
| // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the |
| // algorithm. |
| float vn0 = vx0 * vlog2e_x64 + vmagic_bias; |
| float vn1 = vx1 * vlog2e_x64 + vmagic_bias; |
| float vn2 = vx2 * vlog2e_x64 + vmagic_bias; |
| float vn3 = vx3 * vlog2e_x64 + vmagic_bias; |
| |
| // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized, |
| // i.e. -87.33642 <= x <= 0.0. As n has 6 fractional bits, we split s == 2**(n / 64) = 2**e * 2**(n / 64 - e), where |
| // e := int(n / 64). We create s in two steps: |
| // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the |
| // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0. |
| // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized |
| // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0, |
| // and thus the adjusted exponent is not lower than -126. |
| // |
| // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent). |
| const uint32_t ve0 = (fp32_to_bits(vn0) & UINT32_C(0xFFFFFFC0)) << 17; |
| const uint32_t ve1 = (fp32_to_bits(vn1) & UINT32_C(0xFFFFFFC0)) << 17; |
| const uint32_t ve2 = (fp32_to_bits(vn2) & UINT32_C(0xFFFFFFC0)) << 17; |
| const uint32_t ve3 = (fp32_to_bits(vn3) & UINT32_C(0xFFFFFFC0)) << 17; |
| |
| // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64). |
| const uint32_t vidx0 = fp32_to_bits(vn0) & vindex_mask; |
| const uint32_t vidx1 = fp32_to_bits(vn1) & vindex_mask; |
| const uint32_t vidx2 = fp32_to_bits(vn2) & vindex_mask; |
| const uint32_t vidx3 = fp32_to_bits(vn3) & vindex_mask; |
| // Adjust exponent of the value l fetched from the table to get the final s value. |
| const float vs0 = fp32_from_bits(xnn_table_exp2_k_over_64[vidx0] + ve0); |
| const float vs1 = fp32_from_bits(xnn_table_exp2_k_over_64[vidx1] + ve1); |
| const float vs2 = fp32_from_bits(xnn_table_exp2_k_over_64[vidx2] + ve2); |
| const float vs3 = fp32_from_bits(xnn_table_exp2_k_over_64[vidx3] + ve3); |
| |
| // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number. |
| vn0 -= vmagic_bias; |
| vn1 -= vmagic_bias; |
| vn2 -= vmagic_bias; |
| vn3 -= vmagic_bias; |
| |
| // Compute reduced argument t := x - n * log(2) / 64. |
| // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy. |
| float vt0 = vn0 * vminus_ln2_o64_hi + vx0; |
| float vt1 = vn1 * vminus_ln2_o64_hi + vx1; |
| float vt2 = vn2 * vminus_ln2_o64_hi + vx2; |
| float vt3 = vn3 * vminus_ln2_o64_hi + vx3; |
| |
| vt0 = vn0 * vminus_ln2_o64_lo + vt0; |
| vt1 = vn1 * vminus_ln2_o64_lo + vt1; |
| vt2 = vn2 * vminus_ln2_o64_lo + vt2; |
| vt3 = vn3 * vminus_ln2_o64_lo + vt3; |
| |
| // Compute degree-2 polynomial approxiatmion for exp(t) on [-log(2)/128, log(2)/128]. |
| float vp0 = vt0 * vc2; |
| float vp1 = vt1 * vc2; |
| float vp2 = vt2 * vc2; |
| float vp3 = vt3 * vc2; |
| |
| vp0 = vp0 * vt0 + vt0; |
| vp1 = vp1 * vt1 + vt1; |
| vp2 = vp2 * vt2 + vt2; |
| vp3 = vp3 * vt3 + vt3; |
| |
| // Reconstruct the final f value: |
| // f = s * (1 + t * (1 + t * c2)) |
| // = s * (1 + t + t * (t * c2)) |
| // = s + s * (t + t * (t * c2)) |
| // = s + s * p |
| float vf0 = vp0 * vs0 + vs0; |
| float vf1 = vp1 * vs1 + vs1; |
| float vf2 = vp2 * vs2 + vs2; |
| float vf3 = vp3 * vs3 + vs3; |
| |
| // For inputs below denormal cutoff, replace output with +0.0f. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| if XNN_UNPREDICTABLE(vx0 < vdenorm_cutoff) { |
| vf0 = 0.0f; |
| } |
| if XNN_UNPREDICTABLE(vx1 < vdenorm_cutoff) { |
| vf1 = 0.0f; |
| } |
| if XNN_UNPREDICTABLE(vx2 < vdenorm_cutoff) { |
| vf2 = 0.0f; |
| } |
| if XNN_UNPREDICTABLE(vx3 < vdenorm_cutoff) { |
| vf3 = 0.0f; |
| } |
| |
| // Store 4 outputs at a time. |
| output[0] = vf0; |
| output[1] = vf1; |
| output[2] = vf2; |
| output[3] = vf3; |
| output += 4; |
| |
| // Accumulate computed exponents. |
| vacc0 += vf0; |
| vacc0 += vf1; |
| vacc0 += vf2; |
| vacc0 += vf3; |
| } |
| |
| float vacc = vacc0; |
| for (; elements >= sizeof(float); elements -= sizeof(float)) { |
| // Load 1 input at a time. |
| const float vi = *input++; |
| |
| // Subtract maximum input x := i - i_max. This implies x <= 0. |
| const float vx = vi - vi_max; |
| |
| // Compute reduced argument n := round(x * 64 / log(2)). |
| // We do it by adding a large number (magic bias), which cause rounding of the result to an integer, then subtracing |
| // the large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. |
| // The trick with adding large number is valid only within certain bounds (|x * 64 / log(2)| <= 2**22, i.e. |
| // |x| <= 0x1.62E43p+15 = 45426.09375), but that is acceptable, because inputs outside of [-87.336540, 0.0] |
| // result in denormalized or underflown expf(x). We fixup the result for such inputs at the very end of the |
| // algorithm. |
| float vn = vx * vlog2e_x64 + vmagic_bias; |
| |
| // Create a floating-point number s (scale) such that s := 2**(n / 64) for such inputs that expf(x) is normalized, |
| // i.e. -87.33642 <= x <= 0.0. As n has 6 fractional bits, we split s == 2**(n / 64) = 2**e * 2**(n / 64 - e), where |
| // e := int(n / 64). We create s in two steps: |
| // 1. Fetch 2**(n / 64 - e) = 2**(n % 64) from the table using the 6 low bits of n, as integer. Note that the |
| // fetched values are in the [1.0, 2.0) range, i.e. their floating-point exponent is 0. |
| // 2. Adjust fecthed value by addition of e to its floating-point exponent. The result is always a normalized |
| // number, because for -87.33642 <= x <= 0.0 (inputs for which expf(x) is normalized) we have -126 <= e <= 0, |
| // and thus the adjusted exponent is not lower than -126. |
| // |
| // Extract e from bits 6:14 of n and shift it into bits 23:31 (position of floating-point exponent). |
| const uint32_t ve = (fp32_to_bits(vn) & UINT32_C(0xFFFFFFC0)) << 17; |
| |
| // Use bits 0:6 bits of n, as integer, as an index for table lookup of l := 2**(n % 64). |
| const uint32_t vidx = fp32_to_bits(vn) & vindex_mask; |
| // Adjust exponent of the value l fetched from the table to get the final s value. |
| const float vs = fp32_from_bits(xnn_table_exp2_k_over_64[vidx] + ve); |
| |
| // Subtract the large number back to get final n := round(x * 64 / log(2)) as a floating-point number. |
| vn -= vmagic_bias; |
| |
| // Compute reduced argument t := x - n * log(2) / 64. |
| // Use Cody-Waite range reduction method (note the two constants representing log(2) / 64) to improve accuracy. |
| float vt = vn * vminus_ln2_o64_hi + vx; |
| vt = vn * vminus_ln2_o64_lo + vt; |
| |
| // Compute degree-2 polynomial approxiatmion for exp(t) on [-log(2)/128, log(2)/128]. |
| float vp = vt * vc2; |
| vp = vp * vt + vt; |
| |
| // Reconstruct the final f value: |
| // f = s * (1 + t * (1 + t * c2)) |
| // = s * (1 + t + t * (t * c2)) |
| // = s + s * (t + t * (t * c2)) |
| // = s + s * p |
| float vf = vp * vs + vs; |
| |
| // For inputs below denormal cutoff, replace output with +0.0f. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| if XNN_UNPREDICTABLE(vx < vdenorm_cutoff) { |
| vf = 0.0f; |
| } |
| |
| // Store 1 output at a time. |
| *output++ = vf; |
| |
| // Accumulate computed exponents. |
| vacc += vf; |
| } |
| *sum = vacc; |
| } |