Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 1 | // Copyright 2019 Google LLC |
| 2 | // |
| 3 | // This source code is licensed under the BSD-style license found in the |
| 4 | // LICENSE file in the root directory of this source tree. |
| 5 | |
| 6 | #include <assert.h> |
| 7 | #include <stddef.h> |
| 8 | |
| 9 | #include <arm_neon.h> |
| 10 | |
| 11 | #include <xnnpack/math-stubs.h> |
| 12 | |
| 13 | |
Marat Dukhan | 77221d3 | 2020-01-06 10:04:39 -0800 | [diff] [blame] | 14 | void xnn_math_f32_sigmoid__neonfma_rr2_p5_nr2recps( |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 15 | size_t n, |
| 16 | const float* input, |
| 17 | float* output) |
| 18 | { |
| 19 | assert(n % (4 * sizeof(float)) == 0); |
| 20 | |
Marat Dukhan | c3001e1 | 2020-09-28 16:05:37 -0700 | [diff] [blame^] | 21 | // Large number such that ulp(magic bias) == 1 and magic bias === 127 mod 2**22. |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 22 | const float32x4_t vmagic_bias = vmovq_n_f32(0x1.8000FEp23f); |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 23 | const float32x4_t vminus_log2e = vmovq_n_f32(-0x1.715476p+0f); |
| 24 | const float32x4_t vln2_hi = vmovq_n_f32(0x1.62E43p-1f); |
| 25 | const float32x4_t vln2_lo = vmovq_n_f32(-0x1.05C61p-29f); |
Marat Dukhan | c3001e1 | 2020-09-28 16:05:37 -0700 | [diff] [blame^] | 26 | // Coefficient of polynomial approximation of |
| 27 | // exp(-t) ~ 1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) on [-log(2)/2, log(2)/2] |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 28 | const float32x4_t vc5 = vmovq_n_f32(-0x1.0F9F9Cp-7f); |
Marat Dukhan | c3001e1 | 2020-09-28 16:05:37 -0700 | [diff] [blame^] | 29 | const float32x4_t vc4 = vmovq_n_f32(0x1.573A1Ap-5f); |
| 30 | const float32x4_t vc3 = vmovq_n_f32(-0x1.555A80p-3f); |
| 31 | const float32x4_t vc2 = vmovq_n_f32(0x1.FFFDC6p-2f); |
| 32 | const float32x4_t vc1 = vmovq_n_f32(-0x1.FFFFF6p-1f); |
| 33 | const float32x4_t vone = vmovq_n_f32(1.0f); |
| 34 | // The largest z for which sigmoidf(-z) is normalized. |
| 35 | // This number is also the largest z for which expf(-z) is normalized. |
| 36 | const float32x4_t vdenorm_cutoff = vmovq_n_f32(-0x1.5D589Ep+6f); |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 37 | |
| 38 | for (; n != 0; n -= 4 * sizeof(float)) { |
| 39 | const float32x4_t vx = vld1q_f32(input); input += 4; |
| 40 | |
| 41 | // General structure of the algorithm: |
Marat Dukhan | c3001e1 | 2020-09-28 16:05:37 -0700 | [diff] [blame^] | 42 | // |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 43 | // / exp(x) / (1 + exp(x)) if x <= 0 |
Marat Dukhan | ef4ce31 | 2020-09-10 12:29:08 -0700 | [diff] [blame] | 44 | // f[x] := |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 45 | // \ 1 - f[-x] if x >= 0 |
| 46 | // |
Marat Dukhan | 91f8d86 | 2019-11-27 12:25:42 -0800 | [diff] [blame] | 47 | // First we compute f[-z] := exp(-z) / (1 + exp(-z)) where z = abs(x), |
| 48 | // then replace result with 1 - f[-z] if x >= 0. |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 49 | const float32x4_t vz = vabsq_f32(vx); |
| 50 | |
| 51 | // Compute reduced argument n := round(-z / log(2)). |
Marat Dukhan | c3001e1 | 2020-09-28 16:05:37 -0700 | [diff] [blame^] | 52 | // We do it by adding a large number (magic bias), which cause rounding of the result to integer, then subtracing |
| 53 | // the large number back. The trick with adding large number is valid only within certain bounds |
| 54 | // (|-z / log(2)| <= 2**22, i.e. |z| <= 0x1.62E43p+22 = 5814540.0), but that is acceptable, because inputs x |
| 55 | // outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x). We fixup |
| 56 | // the result for such inputs at the very end of the algorithm. |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 57 | float32x4_t vn = vfmaq_f32(vmagic_bias, vz, vminus_log2e); |
| 58 | |
| 59 | // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| 60 | // -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly. |
| 61 | const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23)); |
| 62 | |
Marat Dukhan | 91f8d86 | 2019-11-27 12:25:42 -0800 | [diff] [blame] | 63 | // Subtract the large number back to get the final n := round(-z / log(2)) as a floating-point number. |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 64 | vn = vsubq_f32(vn, vmagic_bias); |
| 65 | |
Marat Dukhan | 91f8d86 | 2019-11-27 12:25:42 -0800 | [diff] [blame] | 66 | // Compute reduced argument t := z + n * log(2). Note that -t = -z - n * log(2). |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 67 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 68 | float32x4_t vt = vfmaq_f32(vz, vn, vln2_hi); |
| 69 | vt = vfmaq_f32(vt, vn, vln2_lo); |
| 70 | |
Marat Dukhan | 91f8d86 | 2019-11-27 12:25:42 -0800 | [diff] [blame] | 71 | // Compute degree-5 polynomial approximation for exp(-t) on [-log(2)/2, log(2)/2]: |
Marat Dukhan | c3001e1 | 2020-09-28 16:05:37 -0700 | [diff] [blame^] | 72 | // P(t) = 1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) = 1 + t * p |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 73 | float32x4_t vp = vfmaq_f32(vc4, vc5, vt); |
| 74 | vp = vfmaq_f32(vc3, vp, vt); |
| 75 | vp = vfmaq_f32(vc2, vp, vt); |
| 76 | vp = vfmaq_f32(vc1, vp, vt); |
| 77 | |
Marat Dukhan | 91f8d86 | 2019-11-27 12:25:42 -0800 | [diff] [blame] | 78 | // Reconstruct the exp(-z) value: |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 79 | // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
Marat Dukhan | c3001e1 | 2020-09-28 16:05:37 -0700 | [diff] [blame^] | 80 | // = s * (1 + t * p) |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 81 | // = s + (t * s) * p |
| 82 | vt = vmulq_f32(vt, vs); |
| 83 | float32x4_t ve = vfmaq_f32(vs, vp, vt); |
| 84 | |
Marat Dukhan | 91f8d86 | 2019-11-27 12:25:42 -0800 | [diff] [blame] | 85 | // Denominator of the sigmoid fraction: 1.0 + exp(-z) |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 86 | float32x4_t vd = vaddq_f32(ve, vone); |
| 87 | |
| 88 | // Use Newton-Raphson method (2 iterations) to compute reciprocal of denominator. |
Marat Dukhan | 91f8d86 | 2019-11-27 12:25:42 -0800 | [diff] [blame] | 89 | // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0. |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 90 | // Thus the reciprocal of the denominator never overflows. |
| 91 | float32x4_t vr = vrecpeq_f32(vd); |
| 92 | vr = vmulq_f32(vr, vrecpsq_f32(vr, vd)); |
| 93 | vr = vmulq_f32(vr, vrecpsq_f32(vr, vd)); |
| 94 | |
Marat Dukhan | 91f8d86 | 2019-11-27 12:25:42 -0800 | [diff] [blame] | 95 | // Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z)) |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 96 | float32x4_t vf = vmulq_f32(ve, vr); |
| 97 | |
Marat Dukhan | 8d3c07e | 2020-01-02 01:20:59 -0800 | [diff] [blame] | 98 | // For inputs below denormal cutoff, replace output with +0.0f. |
| 99 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 100 | vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcagtq_f32(vx, vdenorm_cutoff))); |
| 101 | |
Marat Dukhan | 91f8d86 | 2019-11-27 12:25:42 -0800 | [diff] [blame] | 102 | // Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z) |
Marat Dukhan | 26cda6d | 2020-01-09 13:54:32 -0800 | [diff] [blame] | 103 | const uint32x4_t vm = vcltq_f32(vx, vmovq_n_f32(0.0f)); |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 104 | vf = vbslq_f32(vm, vf, vsubq_f32(vone, vf)); |
| 105 | |
Marat Dukhan | 22aae13 | 2019-11-22 17:10:29 -0800 | [diff] [blame] | 106 | vst1q_f32(output, vf); output += 4; |
| 107 | } |
| 108 | } |