| // 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 <stddef.h> |
| |
| #include <psimd.h> |
| |
| #include <xnnpack/common.h> |
| #include <xnnpack/math-stubs.h> |
| |
| |
| void xnn_math_f32_sigmoid__psimd_p5_div( |
| size_t n, |
| const float* input, |
| float* output) |
| { |
| assert(n % (4 * sizeof(float)) == 0); |
| |
| const psimd_f32 vmagic_bias = psimd_splat_f32(0x1.8000FEp23f); |
| // The largest z for which sigmoidf(-z) is normalized. |
| // This number is also the largest z for which expf(-z) is normalized. |
| const psimd_f32 vdenorm_cutoff = psimd_splat_f32(0x1.5D589Ep+6f); |
| const psimd_f32 vminus_log2e = psimd_splat_f32(-0x1.715476p+0f); |
| // Last 7 bits are zeroes |
| const psimd_f32 vln2_hi = psimd_splat_f32(0x1.62E400p-1f); |
| const psimd_f32 vln2_lo = psimd_splat_f32(0x1.7F7D1Cp-20f); |
| const psimd_f32 vone = psimd_splat_f32(1.0f); |
| |
| 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); |
| |
| for (; n != 0; n -= 4 * sizeof(float)) { |
| const psimd_f32 vx = psimd_load_f32(input); |
| input += 4; |
| |
| // 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 psimd_f32 vz = psimd_abs_f32(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. |
| psimd_f32 vn = psimd_qfma_f32(vmagic_bias, vz, vminus_log2e); |
| |
| // 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 psimd_f32 vs = (psimd_f32) ((psimd_u32) vn << 23); |
| |
| // Subtract the large number back to get the final n := round(-z / log(2)) as a floating-point number. |
| vn = psimd_sub_f32(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. |
| psimd_f32 vt = psimd_qfma_f32(vz, vn, vln2_hi); |
| vt = psimd_qfma_f32(vt, vn, vln2_lo); |
| |
| // 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)))) |
| psimd_f32 vp = psimd_qfma_f32(vc4, vt, vc5); |
| vp = psimd_qfma_f32(vc3, vt, vp); |
| vp = psimd_qfma_f32(vc2, vt, vp); |
| vp = psimd_qfma_f32(vc1, vt, vp); |
| |
| // 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 = psimd_mul_f32(vt, vs); |
| const psimd_f32 ve = psimd_qfma_f32(vs, vt, vp); |
| |
| // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z)) |
| psimd_f32 vf = psimd_div_f32(ve, psimd_add_f32(ve, 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. |
| vf = psimd_andnotmask_f32(vz > vdenorm_cutoff, vf); |
| |
| // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z) |
| vf = psimd_signblend_f32(vx, vf, psimd_sub_f32(vone, vf)); |
| |
| psimd_store_f32(output, vf); |
| output += 4; |
| } |
| } |