1 /* 2 * Double-precision vector log(x) function. 3 * 4 * Copyright (c) 2019, Arm Limited. 5 * SPDX-License-Identifier: MIT 6 */ 7 8 #include "mathlib.h" 9 #include "v_math.h" 10 #include "v_log.h" 11 #if V_SUPPORTED 12 13 /* Worst-case error: 1.17 + 0.5 ulp. */ 14 15 static const f64_t Poly[] = { 16 /* rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */ 17 -0x1.ffffffffffff7p-2, 18 0x1.55555555170d4p-2, 19 -0x1.0000000399c27p-2, 20 0x1.999b2e90e94cap-3, 21 -0x1.554e550bd501ep-3, 22 }; 23 24 #define A0 v_f64 (Poly[0]) 25 #define A1 v_f64 (Poly[1]) 26 #define A2 v_f64 (Poly[2]) 27 #define A3 v_f64 (Poly[3]) 28 #define A4 v_f64 (Poly[4]) 29 #define Ln2 v_f64 (0x1.62e42fefa39efp-1) 30 #define N (1 << V_LOG_TABLE_BITS) 31 #define OFF v_u64 (0x3fe6900900000000) 32 33 struct entry 34 { 35 v_f64_t invc; 36 v_f64_t logc; 37 }; 38 39 static inline struct entry 40 lookup (v_u64_t i) 41 { 42 struct entry e; 43 #ifdef SCALAR 44 e.invc = __v_log_data[i].invc; 45 e.logc = __v_log_data[i].logc; 46 #else 47 e.invc[0] = __v_log_data[i[0]].invc; 48 e.logc[0] = __v_log_data[i[0]].logc; 49 e.invc[1] = __v_log_data[i[1]].invc; 50 e.logc[1] = __v_log_data[i[1]].logc; 51 #endif 52 return e; 53 } 54 55 VPCS_ATTR 56 __attribute__ ((noinline)) static v_f64_t 57 specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp) 58 { 59 return v_call_f64 (log, x, y, cmp); 60 } 61 62 VPCS_ATTR 63 v_f64_t 64 V_NAME(log) (v_f64_t x) 65 { 66 v_f64_t z, r, r2, p, y, kd, hi; 67 v_u64_t ix, iz, tmp, top, i, cmp; 68 v_s64_t k; 69 struct entry e; 70 71 ix = v_as_u64_f64 (x); 72 top = ix >> 48; 73 cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010)); 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 = ix - OFF; 79 i = (tmp >> (52 - V_LOG_TABLE_BITS)) % N; 80 k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift */ 81 iz = ix - (tmp & v_u64 (0xfffULL << 52)); 82 z = v_as_f64_u64 (iz); 83 e = lookup (i); 84 85 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ 86 r = v_fma_f64 (z, e.invc, v_f64 (-1.0)); 87 kd = v_to_f64_s64 (k); 88 89 /* hi = r + log(c) + k*Ln2. */ 90 hi = v_fma_f64 (kd, Ln2, e.logc + r); 91 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 92 r2 = r * r; 93 y = v_fma_f64 (A3, r, A2); 94 p = v_fma_f64 (A1, r, A0); 95 y = v_fma_f64 (A4, r2, y); 96 y = v_fma_f64 (y, r2, p); 97 y = v_fma_f64 (y, r2, hi); 98 99 if (unlikely (v_any_u64 (cmp))) 100 return specialcase (x, y, cmp); 101 return y; 102 } 103 VPCS_ALIAS 104 #endif 105