1 /* 2 * Double-precision vector log2 function. 3 * 4 * Copyright (c) 2022-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "v_math.h" 9 #include "include/mathlib.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 #if V_SUPPORTED 14 15 #define InvLn2 v_f64 (0x1.71547652b82fep0) 16 #define N (1 << V_LOG2_TABLE_BITS) 17 #define OFF v_u64 (0x3fe6900900000000) 18 #define P(i) v_f64 (__v_log2_data.poly[i]) 19 20 struct entry 21 { 22 v_f64_t invc; 23 v_f64_t log2c; 24 }; 25 26 static inline struct entry 27 lookup (v_u64_t i) 28 { 29 struct entry e; 30 #ifdef SCALAR 31 e.invc = __v_log2_data.tab[i].invc; 32 e.log2c = __v_log2_data.tab[i].log2c; 33 #else 34 e.invc[0] = __v_log2_data.tab[i[0]].invc; 35 e.log2c[0] = __v_log2_data.tab[i[0]].log2c; 36 e.invc[1] = __v_log2_data.tab[i[1]].invc; 37 e.log2c[1] = __v_log2_data.tab[i[1]].log2c; 38 #endif 39 return e; 40 } 41 42 VPCS_ATTR 43 NOINLINE static v_f64_t 44 specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp) 45 { 46 return v_call_f64 (log2, x, y, cmp); 47 } 48 49 /* Double-precision vector log2 routine. Implements the same algorithm as vector 50 log10, with coefficients and table entries scaled in extended precision. 51 The maximum observed error is 2.58 ULP: 52 __v_log2(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5 53 want 0x1.fffb34198d9ddp-5. */ 54 VPCS_ATTR 55 v_f64_t V_NAME (log2) (v_f64_t x) 56 { 57 v_u64_t ix = v_as_u64_f64 (x); 58 v_u64_t top = ix >> 48; 59 v_u64_t special 60 = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010)); 61 62 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. 63 The range is split into N subintervals. 64 The ith subinterval contains z and c is near its center. */ 65 v_u64_t tmp = ix - OFF; 66 v_u64_t i = (tmp >> (52 - V_LOG2_TABLE_BITS)) % N; 67 v_s64_t k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift. */ 68 v_u64_t iz = ix - (tmp & v_u64 (0xfffULL << 52)); 69 v_f64_t z = v_as_f64_u64 (iz); 70 struct entry e = lookup (i); 71 72 /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */ 73 74 v_f64_t r = v_fma_f64 (z, e.invc, v_f64 (-1.0)); 75 v_f64_t kd = v_to_f64_s64 (k); 76 v_f64_t w = v_fma_f64 (r, InvLn2, e.log2c); 77 78 v_f64_t r2 = r * r; 79 v_f64_t p_23 = v_fma_f64 (P (3), r, P (2)); 80 v_f64_t p_01 = v_fma_f64 (P (1), r, P (0)); 81 v_f64_t y = v_fma_f64 (P (4), r2, p_23); 82 y = v_fma_f64 (r2, y, p_01); 83 y = v_fma_f64 (r2, y, kd + w); 84 85 if (unlikely (v_any_u64 (special))) 86 return specialcase (x, y, special); 87 return y; 88 } 89 VPCS_ALIAS 90 91 PL_SIG (V, D, 1, log2, 0.01, 11.1) 92 PL_TEST_ULP (V_NAME (log2), 2.09) 93 PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (log2)) 94 PL_TEST_INTERVAL (V_NAME (log2), -0.0, -0x1p126, 100) 95 PL_TEST_INTERVAL (V_NAME (log2), 0x1p-149, 0x1p-126, 4000) 96 PL_TEST_INTERVAL (V_NAME (log2), 0x1p-126, 0x1p-23, 50000) 97 PL_TEST_INTERVAL (V_NAME (log2), 0x1p-23, 1.0, 50000) 98 PL_TEST_INTERVAL (V_NAME (log2), 1.0, 100, 50000) 99 PL_TEST_INTERVAL (V_NAME (log2), 100, inf, 50000) 100 #endif 101