1 /* 2 * Double-precision vector log(x) function. 3 * 4 * Copyright (c) 2019-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "mathlib.h" 9 #include "v_math.h" 10 11 static const struct data 12 { 13 uint64x2_t min_norm; 14 uint32x4_t special_bound; 15 float64x2_t poly[5]; 16 float64x2_t ln2; 17 uint64x2_t sign_exp_mask; 18 } data = { 19 /* Worst-case error: 1.17 + 0.5 ulp. 20 Rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */ 21 .poly = { V2 (-0x1.ffffffffffff7p-2), V2 (0x1.55555555170d4p-2), 22 V2 (-0x1.0000000399c27p-2), V2 (0x1.999b2e90e94cap-3), 23 V2 (-0x1.554e550bd501ep-3) }, 24 .ln2 = V2 (0x1.62e42fefa39efp-1), 25 .min_norm = V2 (0x0010000000000000), 26 .special_bound = V4 (0x7fe00000), /* asuint64(inf) - min_norm. */ 27 .sign_exp_mask = V2 (0xfff0000000000000) 28 }; 29 30 #define A(i) d->poly[i] 31 #define N (1 << V_LOG_TABLE_BITS) 32 #define IndexMask (N - 1) 33 #define Off v_u64 (0x3fe6900900000000) 34 35 struct entry 36 { 37 float64x2_t invc; 38 float64x2_t logc; 39 }; 40 41 static inline struct entry 42 lookup (uint64x2_t i) 43 { 44 /* Since N is a power of 2, n % N = n & (N - 1). */ 45 struct entry e; 46 uint64_t i0 = (i[0] >> (52 - V_LOG_TABLE_BITS)) & IndexMask; 47 uint64_t i1 = (i[1] >> (52 - V_LOG_TABLE_BITS)) & IndexMask; 48 float64x2_t e0 = vld1q_f64 (&__v_log_data.table[i0].invc); 49 float64x2_t e1 = vld1q_f64 (&__v_log_data.table[i1].invc); 50 e.invc = vuzp1q_f64 (e0, e1); 51 e.logc = vuzp2q_f64 (e0, e1); 52 return e; 53 } 54 55 static float64x2_t VPCS_ATTR NOINLINE 56 special_case (float64x2_t x, float64x2_t y, float64x2_t hi, float64x2_t r2, 57 uint32x2_t cmp) 58 { 59 return v_call_f64 (log, x, vfmaq_f64 (hi, y, r2), vmovl_u32 (cmp)); 60 } 61 62 float64x2_t VPCS_ATTR V_NAME_D1 (log) (float64x2_t x) 63 { 64 const struct data *d = ptr_barrier (&data); 65 float64x2_t z, r, r2, p, y, kd, hi; 66 uint64x2_t ix, iz, tmp; 67 uint32x2_t cmp; 68 int64x2_t k; 69 struct entry e; 70 71 ix = vreinterpretq_u64_f64 (x); 72 cmp = vcge_u32 (vsubhn_u64 (ix, d->min_norm), 73 vget_low_u32 (d->special_bound)); 74 75 /* x = 2^k z; where z is in range [Off,2*Off) and exact. 76 The range is split into N subintervals. 77 The ith subinterval contains z and c is near its center. */ 78 tmp = vsubq_u64 (ix, Off); 79 k = vshrq_n_s64 (vreinterpretq_s64_u64 (tmp), 52); /* arithmetic shift. */ 80 iz = vsubq_u64 (ix, vandq_u64 (tmp, d->sign_exp_mask)); 81 z = vreinterpretq_f64_u64 (iz); 82 e = lookup (tmp); 83 84 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ 85 r = vfmaq_f64 (v_f64 (-1.0), z, e.invc); 86 kd = vcvtq_f64_s64 (k); 87 88 /* hi = r + log(c) + k*Ln2. */ 89 hi = vfmaq_f64 (vaddq_f64 (e.logc, r), kd, d->ln2); 90 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 91 r2 = vmulq_f64 (r, r); 92 y = vfmaq_f64 (A (2), A (3), r); 93 p = vfmaq_f64 (A (0), A (1), r); 94 y = vfmaq_f64 (y, A (4), r2); 95 y = vfmaq_f64 (p, y, r2); 96 97 if (unlikely (v_any_u32h (cmp))) 98 return special_case (x, y, hi, r2, cmp); 99 return vfmaq_f64 (hi, y, r2); 100 } 101