1 /* 2 * Double-precision vector log(x) function - inline version 3 * 4 * Copyright (c) 2019-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "v_math.h" 9 #include "math_config.h" 10 11 #ifndef V_LOG_INLINE_POLY_ORDER 12 # error Cannot use inline log helper without specifying poly order (options are 4 or 5) 13 #endif 14 15 #if V_LOG_INLINE_POLY_ORDER == 4 16 # define POLY \ 17 { \ 18 V2 (-0x1.ffffffffcbad3p-2), V2 (0x1.555555578ed68p-2), \ 19 V2 (-0x1.0000d3a1e7055p-2), V2 (0x1.999392d02a63ep-3) \ 20 } 21 #elif V_LOG_INLINE_POLY_ORDER == 5 22 # define POLY \ 23 { \ 24 V2 (-0x1.ffffffffffff7p-2), V2 (0x1.55555555170d4p-2), \ 25 V2 (-0x1.0000000399c27p-2), V2 (0x1.999b2e90e94cap-3), \ 26 V2 (-0x1.554e550bd501ep-3) \ 27 } 28 #else 29 # error Can only choose order 4 or 5 for log poly 30 #endif 31 32 struct v_log_inline_data 33 { 34 float64x2_t poly[V_LOG_INLINE_POLY_ORDER]; 35 float64x2_t ln2; 36 uint64x2_t off, sign_exp_mask; 37 }; 38 39 #define V_LOG_CONSTANTS \ 40 { \ 41 .poly = POLY, .ln2 = V2 (0x1.62e42fefa39efp-1), \ 42 .sign_exp_mask = V2 (0xfff0000000000000), .off = V2 (0x3fe6900900000000) \ 43 } 44 45 #define A(i) d->poly[i] 46 #define N (1 << V_LOG_TABLE_BITS) 47 #define IndexMask (N - 1) 48 49 struct entry 50 { 51 float64x2_t invc; 52 float64x2_t logc; 53 }; 54 55 static inline struct entry 56 log_lookup (uint64x2_t i) 57 { 58 /* Since N is a power of 2, n % N = n & (N - 1). */ 59 struct entry e; 60 uint64_t i0 = (i[0] >> (52 - V_LOG_TABLE_BITS)) & IndexMask; 61 uint64_t i1 = (i[1] >> (52 - V_LOG_TABLE_BITS)) & IndexMask; 62 float64x2_t e0 = vld1q_f64 (&__v_log_data.table[i0].invc); 63 float64x2_t e1 = vld1q_f64 (&__v_log_data.table[i1].invc); 64 e.invc = vuzp1q_f64 (e0, e1); 65 e.logc = vuzp2q_f64 (e0, e1); 66 return e; 67 } 68 69 static inline float64x2_t 70 v_log_inline (float64x2_t x, const struct v_log_inline_data *d) 71 { 72 float64x2_t z, r, r2, p, y, kd, hi; 73 uint64x2_t ix, iz, tmp; 74 int64x2_t k; 75 struct entry e; 76 77 ix = vreinterpretq_u64_f64 (x); 78 79 /* x = 2^k z; where z is in range [Off,2*Off) and exact. 80 The range is split into N subintervals. 81 The ith subinterval contains z and c is near its center. */ 82 tmp = vsubq_u64 (ix, d->off); 83 k = vshrq_n_s64 (vreinterpretq_s64_u64 (tmp), 52); /* arithmetic shift. */ 84 iz = vsubq_u64 (ix, vandq_u64 (tmp, d->sign_exp_mask)); 85 z = vreinterpretq_f64_u64 (iz); 86 e = log_lookup (tmp); 87 88 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ 89 r = vfmaq_f64 (v_f64 (-1.0), z, e.invc); 90 kd = vcvtq_f64_s64 (k); 91 92 /* hi = r + log(c) + k*Ln2. */ 93 hi = vfmaq_f64 (vaddq_f64 (e.logc, r), kd, d->ln2); 94 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 95 r2 = vmulq_f64 (r, r); 96 y = vfmaq_f64 (A (2), A (3), r); 97 p = vfmaq_f64 (A (0), A (1), r); 98 #if V_LOG_POLY_ORDER == 5 99 y = vfmaq_f64 (y, A (4), r2); 100 #endif 101 y = vfmaq_f64 (p, y, r2); 102 103 return vfmaq_f64 (hi, y, r2); 104 } 105