| // Auto-generated file. Do not edit! |
| // Template: src/f32-sigmoid/scalar-p5-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> |
| |
| |
| void xnn_f32_sigmoid_ukernel__scalar_p5_div_x1( |
| size_t n, |
| const float* x, |
| float* y, |
| const void* params) |
| { |
| assert(n % sizeof(float) == 0); |
| |
| const float vmagic_bias = 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 float vdenorm_cutoff = -0x1.5D589Ep+6f; |
| // The largest x for which sigmoidf(x) is not equal 1.0. |
| const float vone_cutoff = 0x1.154244p+4f; |
| const float vminus_log2e = -0x1.715476p+0f; |
| // Last 7 bits are zeroes |
| const float vln2_hi = 0x1.62E400p-1f; |
| const float vln2_lo = 0x1.7F7D1Cp-20f; |
| const float vone = 1.0f; |
| |
| const float vc1 = -0x1.FFFFF6p-1f; |
| const float vc2 = 0x1.FFFDC6p-2f; |
| const float vc3 = -0x1.555A80p-3f; |
| const float vc4 = 0x1.573A1Ap-5f; |
| const float vc5 = -0x1.0F9F9Cp-7f; |
| |
| 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 / log(2)). |
| // We do it by adding a large number (magic bias), which cause rounding of 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| <= 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. |
| float vn = vz * vminus_log2e + vmagic_bias; |
| |
| // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly. |
| const float vs = fp32_from_bits(fp32_to_bits(vn) << 23); |
| |
| // Subtract the large number back to get the final n := round(-z / log(2)) as a floating-point number. |
| vn -= vmagic_bias; |
| |
| // Compute reduced argument t := z + n * log(2). Note that -t = -z - n * log(2). |
| // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| float vt = vn * vln2_hi + vz; |
| vt = vn * vln2_lo + vt; |
| |
| // Compute degree-5 polynomial approximation for exp(-t) on [-log(2)/2, log(2)/2]: |
| // P5(t) = 1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| float vp = vt * vc5 + vc4; |
| vp = vt * vp + vc3; |
| vp = vt * vp + vc2; |
| vp = vt * vp + 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 *= vs; |
| const float ve = vt * vp + vs; |
| |
| // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z)) |
| float vf = ve / (ve + vone); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z) |
| if XNN_UNPREDICTABLE(vx > 0.0f) { |
| vf = vone - vf; |
| } |
| |
| // For inputs above 1.0 cutoff, replace output with 1.0. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| if XNN_UNPREDICTABLE(vx > vone_cutoff) { |
| vf = vone; |
| } |
| |
| // 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; |
| } |
| |
| *y++ = vf; |
| |
| n -= sizeof(float); |
| } while (n != 0); |
| } |