Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -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 <math.h> |
| 8 | #include <stddef.h> |
| 9 | |
| 10 | #include <arm_neon.h> |
| 11 | |
Marat Dukhan | f7814d6 | 2020-07-20 23:19:21 -0700 | [diff] [blame] | 12 | #include <xnnpack/common.h> |
Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -0800 | [diff] [blame] | 13 | #include <xnnpack/math-stubs.h> |
| 14 | |
| 15 | |
Marat Dukhan | 189ae80 | 2019-11-26 11:28:44 -0800 | [diff] [blame] | 16 | // Table of exp2(k / 64) values, k = 0..63 |
Marat Dukhan | f7814d6 | 2020-07-20 23:19:21 -0700 | [diff] [blame] | 17 | extern XNN_INTERNAL const float xnn_table_exp2_k_over_64[64]; |
Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -0800 | [diff] [blame] | 18 | |
Marat Dukhan | b7633f2 | 2020-11-20 16:34:56 -0800 | [diff] [blame] | 19 | void xnn_math_f32_exp__neonfma_rr2_lut64_p2( |
Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -0800 | [diff] [blame] | 20 | size_t n, |
| 21 | const float* input, |
| 22 | float* output) |
| 23 | { |
Marat Dukhan | 346a9e5 | 2019-11-15 09:06:30 -0800 | [diff] [blame] | 24 | assert(n % (4 * sizeof(float)) == 0); |
Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -0800 | [diff] [blame] | 25 | |
| 26 | const float32x4_t vmagic_bias = vmovq_n_f32(0x1.800000p23f); |
| 27 | // The smallest x for which expf(x) is non-zero. |
| 28 | const float32x4_t vzero_cutoff = vmovq_n_f32(-0x1.9FE368p6f); |
| 29 | // The largest x for which expf(x) is finite. |
| 30 | const float32x4_t vinf_cutoff = vmovq_n_f32(0x1.62E42Ep6f); |
| 31 | const float32x4_t vlog2e_x64 = vmovq_n_f32(0x1.715476p6f); |
| 32 | const float32x4_t vminus_ln2_o64_hi = vmovq_n_f32(-0x1.62e43p-7f); |
| 33 | const float32x4_t vminus_ln2_o64_lo = vmovq_n_f32(0x1.05c61p-35f); |
| 34 | const float32x4_t vplus_inf = vmovq_n_f32(INFINITY); |
| 35 | |
Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -0800 | [diff] [blame] | 36 | const float32x4_t vc2 = vmovq_n_f32(0x1.FFFF0Ap-2f); |
| 37 | |
| 38 | const int32x4_t vmin_exponent = vmovq_n_s32(INT32_C(0xC1000000)); |
| 39 | const int32x4_t vmax_exponent = vmovq_n_s32(INT32_C(0x3F800000)); |
| 40 | const int32x4_t vdefault_exponent = vmax_exponent; |
Marat Dukhan | 189ae80 | 2019-11-26 11:28:44 -0800 | [diff] [blame] | 41 | const int32x4_t vindex_mask = vmovq_n_s32(INT32_C(0x3F)); |
Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -0800 | [diff] [blame] | 42 | |
| 43 | for (; n != 0; n -= 4 * sizeof(float)) { |
| 44 | const float32x4_t vx = vld1q_f32(input); input += 4; |
| 45 | |
| 46 | // Compute reduced argument n := round(x * 64 / log(2)). |
| 47 | // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the |
| 48 | // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction. |
| 49 | // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because |
| 50 | // inputs outside of [-103.97207, 88.72283] underflow or overflow expf(x) anyway. We fixup the result for such |
| 51 | // inputs at the very end of the algorithm. |
| 52 | float32x4_t vn = vfmaq_f32(vmagic_bias, vx, vlog2e_x64); |
| 53 | |
| 54 | // Create two floating-point numbers, sn (scale, normal) and so (scale, overflow) such that sn * so == 2**n |
| 55 | // for inputs which don't cause overflow, i.e. -103.97207 <= x <= 88.72283, and -150 <= n <= 128 accordingly. |
| 56 | // We need to use two numbers rather than one because a normalized single-precision exponent must be in [-127, 126] |
| 57 | // range, which is insufficient to cover [-150, 128] range of n. |
| 58 | // - When n is within [-127, 126], sn == 2**n and so == 1.0. |
| 59 | // - When n < -127, sn == 2**(-127) and so == 2**(n + 127). |
| 60 | // - When n > 126, sn == 2**126 and so == 2**(n - 126). |
| 61 | // While we explicitly compute sn, the so is fused into the value l fetched from a table by adjusting its exponential. |
Marat Dukhan | 189ae80 | 2019-11-26 11:28:44 -0800 | [diff] [blame] | 62 | int32x4_t veo = vshlq_n_s32(vbicq_s32(vreinterpretq_s32_f32(vn), vmovq_n_s32(INT32_C(0x3F))), 17); |
Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -0800 | [diff] [blame] | 63 | int32x4_t ven = vmaxq_s32(veo, vmin_exponent); |
| 64 | ven = vminq_s32(ven, vmax_exponent); |
| 65 | veo = vsubq_s32(veo, ven); |
| 66 | const float32x4_t vsn = vreinterpretq_f32_s32(vaddq_s32(ven, vdefault_exponent)); |
| 67 | |
Marat Dukhan | 189ae80 | 2019-11-26 11:28:44 -0800 | [diff] [blame] | 68 | // Use the low 6 bits of n (as integer) for table lookup. |
Marat Dukhan | 272139e | 2020-09-21 01:01:31 -0700 | [diff] [blame] | 69 | const uint64x2_t vidx = vreinterpretq_u64_s32(vshlq_n_s32(vandq_s32(vreinterpretq_s32_f32(vn), vindex_mask), 2)); |
Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -0800 | [diff] [blame] | 70 | const uint64_t vidx01 = vgetq_lane_u64(vidx, 0); |
| 71 | const uint64_t vidx23 = vgetq_lane_u64(vidx, 1); |
Marat Dukhan | 272139e | 2020-09-21 01:01:31 -0700 | [diff] [blame] | 72 | float32x2_t vl01 = vld1_dup_f32((const float*) ((uintptr_t) xnn_table_exp2_k_over_64 + (uint32_t) vidx01)); |
| 73 | float32x2_t vl23 = vld1_dup_f32((const float*) ((uintptr_t) xnn_table_exp2_k_over_64 + (uint32_t) vidx23)); |
Marat Dukhan | b32b018 | 2020-09-21 01:21:04 -0700 | [diff] [blame] | 74 | vl01 = vld1_lane_f32((const float*) ((uintptr_t) xnn_table_exp2_k_over_64 + (uint32_t) (vidx01 >> 32)), vl01, 1); |
| 75 | vl23 = vld1_lane_f32((const float*) ((uintptr_t) xnn_table_exp2_k_over_64 + (uint32_t) (vidx23 >> 32)), vl23, 1); |
Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -0800 | [diff] [blame] | 76 | float32x4_t vl = vcombine_f32(vl01, vl23); |
| 77 | // Fuse so into the value l fetched from a table by adjusting its exponential. |
| 78 | vl = vreinterpretq_f32_s32(vaddq_s32(vreinterpretq_s32_f32(vl), veo)); |
| 79 | |
| 80 | // Subtract the large number back to get final n := round(x * 64 / log(2)). |
| 81 | vn = vsubq_f32(vn, vmagic_bias); |
| 82 | |
| 83 | // Compute reduced argument t := x - n * log(2) / 64. |
| 84 | // Use Cody-Waite range reduction method (note two constants to represent log(2) / 64) to improve accuracy. |
| 85 | float32x4_t vt = vfmaq_f32(vx, vn, vminus_ln2_o64_hi); |
| 86 | vt = vfmaq_f32(vt, vn, vminus_ln2_o64_lo); |
| 87 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame] | 88 | // Compute degree-2 polynomial approximation for exp(t) on [-log(2)/128, log(2)/128]. |
Marat Dukhan | 797a8fe | 2019-11-14 20:21:57 -0800 | [diff] [blame] | 89 | float32x4_t vp = vmulq_f32(vt, vc2); |
| 90 | vp = vfmaq_f32(vt, vt, vp); |
| 91 | |
| 92 | // Reconstruct the final f value: |
| 93 | // f = sn * (so * l) * (1 + t * (1 + t * c2)) |
| 94 | // = sn * (so * l) * (1 + t + t * (t * c2)) |
| 95 | // = sn * ((so * l) + (so * l) * (t + t * (t * c2))) |
| 96 | float32x4_t vf = vfmaq_f32(vl, vl, vp); |
| 97 | vf = vmulq_f32(vf, vsn); |
| 98 | |
| 99 | // For inputs below zero cutoff, replace output with +0.0f. |
| 100 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 101 | vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vzero_cutoff))); |
| 102 | // For inputs above inf cutoff, replace output with +inf. |
| 103 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 104 | vf = vbslq_f32(vcgtq_f32(vx, vinf_cutoff), vplus_inf, vf); |
| 105 | vst1q_f32(output, vf); output += 4; |
| 106 | } |
| 107 | } |