| // Auto-generated file. Do not edit! |
| // Template: src/f32-sigmoid/scalar-lut2048-p1-div.c.in |
| // Generator: tools/xngen |
| // |
| // 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. |
| |
| #include <assert.h> |
| #include <math.h> |
| |
| #include <xnnpack/common.h> |
| #include <xnnpack/vunary.h> |
| |
| #include <fp16/bitcasts.h> |
| |
| |
| // Note redefine as uint32[] to avoid redundant bitcasts. |
| extern XNN_INTERNAL const uint32_t xnn_table_exp2_k_over_2048[2048]; |
| |
| void xnn_f32_sigmoid_ukernel__scalar_lut2048_p1_div_x1( |
| size_t n, |
| const float* x, |
| float* y, |
| const void* params) |
| { |
| assert(n % sizeof(float) == 0); |
| |
| const float vmagic_bias = 0x1.800000p23f; |
| // The largest z for which sigmoidf(-z) is normalized. |
| // This number is also the largest z for which expf(-z) is normalized. |
| const float vdenorm_cutoff = 0x1.5D589Ep+6f; |
| const float vminus_log2e_x2048 = -0x1.715476p11f; |
| // Last 18 bits are zeroes |
| const float vln2_o2048_hi = 0x1.600000p-12f; |
| const float vln2_o2048_lo = 0x1.7217F8p-19f; |
| const float vone = 1.0f; |
| |
| const float vc1 = -0x1.FFFFFEp-1f; |
| |
| const uint32_t vindex_mask = UINT32_C(0x7FF); |
| |
| do { |
| const float vx = *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 float vz = fabsf(vx); |
| |
| // Compute reduced argument n := round(-z * 2048 / 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 (|z * 2048 / log(2)| <= 2**22, i.e. |
| // |z| <= 0x1.62E43p+10 = 1419.5654296875), but that is acceptable, because inputs x outside of |
| // [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x). We fixup the result |
| // for such inputs at the very end of the algorithm. |
| float vn = vz * vminus_log2e_x2048 + vmagic_bias; |
| |
| // Create a floating-point number s (scale) such that s := 2**(n / 2048) for such inputs that sigmoidf(-z) is |
| // normalized, i.e. 0 <= z <= 87.33642. As n has 11 fractional bits, we split s == 2**(n / 2048) = |
| // = 2**e * 2**(n / 2048 - e), where e := int(n / 2048). We create s in two steps: |
| // 1. Fetch 2**(n / 2048 - e) = 2**(n % 2048) from 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 0 <= z <= 87.33642 (inputs for which sigmoidf(-z) is normalized) we have -126 <= e <= 0, |
| // and thus the adjusted exponent is not lower than -126. |
| // |
| // Extract e from bits 11:19 of n and shift it into bits 23:31 (position of floating-point exponent). |
| const uint32_t ve = (fp32_to_bits(vn) & ~vindex_mask) << 12; |
| |
| // Use bits 0:11 bits of n, as integer, as an index for table lookup of l := 2**(n % 2048). |
| 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_2048[vidx] + ve); |
| |
| // Subtract the large number back to get the final n := round(-z * 2048 / log(2)) as a floating-point number. |
| vn -= vmagic_bias; |
| |
| // Compute reduced argument t := (z + n * log(2) / 2048). Note that -t = -z - n * log(2) / 2048. |
| // Use Cody-Waite range reduction method (note two constants to represent log(2) / 2048) to improve accuracy. |
| float vt = vn * vln2_o2048_hi + vz; |
| vt = vn * vln2_o2048_lo + vt; |
| |
| // Compute degree-1 polynomial approximation for exp(-t) on [-log(2)/4096, log(2)/4096]: |
| // P1(t) = 1 + t * c1 |
| const float vp = vt * vc1; |
| |
| // Reconstruct the exp(-z) value: |
| // y = s * (1 + t * c1) |
| // = s + s * (t * c1)) |
| // = s + s * p |
| const float vy = vp * vs + vs; |
| |
| // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z)) |
| float vf = vy / (vy + vone); |
| |
| // For inputs above denormal cutoff, replace output with +0.0f. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| if XNN_UNPREDICTABLE(vz > vdenorm_cutoff) { |
| vf = 0.0f; |
| } |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z) |
| if XNN_UNPREDICTABLE(vx > 0.0f) { |
| vf = vone - vf; |
| } |
| |
| *y++ = vf; |
| |
| n -= sizeof(float); |
| } while (n != 0); |
| } |