1 /* 2 * Double-precision vector log10(x) 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 A(i) v_f64 (__v_log10_data.poly[i]) 16 #define T(s, i) __v_log10_data.tab[i].s 17 #define Ln2 v_f64 (0x1.62e42fefa39efp-1) 18 #define N (1 << V_LOG10_TABLE_BITS) 19 #define OFF v_u64 (0x3fe6900900000000) 20 21 struct entry 22 { 23 v_f64_t invc; 24 v_f64_t log10c; 25 }; 26 27 static inline struct entry 28 lookup (v_u64_t i) 29 { 30 struct entry e; 31 #ifdef SCALAR 32 e.invc = T (invc, i); 33 e.log10c = T (log10c, i); 34 #else 35 e.invc[0] = T (invc, i[0]); 36 e.log10c[0] = T (log10c, i[0]); 37 e.invc[1] = T (invc, i[1]); 38 e.log10c[1] = T (log10c, i[1]); 39 #endif 40 return e; 41 } 42 43 VPCS_ATTR 44 inline static v_f64_t 45 specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp) 46 { 47 return v_call_f64 (log10, x, y, cmp); 48 } 49 50 /* Our implementation of v_log10 is a slight modification of v_log (1.660ulps). 51 Max ULP error: < 2.5 ulp (nearest rounding.) 52 Maximum measured at 2.46 ulp for x in [0.96, 0.97] 53 __v_log10(0x1.13192407fcb46p+0) got 0x1.fff6be3cae4bbp-6 54 want 0x1.fff6be3cae4b9p-6 55 -0.459999 ulp err 1.96. */ 56 VPCS_ATTR 57 v_f64_t V_NAME (log10) (v_f64_t x) 58 { 59 v_f64_t z, r, r2, p, y, kd, hi; 60 v_u64_t ix, iz, tmp, top, i, cmp; 61 v_s64_t k; 62 struct entry e; 63 64 ix = v_as_u64_f64 (x); 65 top = ix >> 48; 66 cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010)); 67 68 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. 69 The range is split into N subintervals. 70 The ith subinterval contains z and c is near its center. */ 71 tmp = ix - OFF; 72 i = (tmp >> (52 - V_LOG10_TABLE_BITS)) % N; 73 k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift. */ 74 iz = ix - (tmp & v_u64 (0xfffULL << 52)); 75 z = v_as_f64_u64 (iz); 76 e = lookup (i); 77 78 /* log10(x) = log1p(z/c-1)/log(10) + log10(c) + k*log10(2). */ 79 r = v_fma_f64 (z, e.invc, v_f64 (-1.0)); 80 kd = v_to_f64_s64 (k); 81 82 /* hi = r / log(10) + log10(c) + k*log10(2). 83 Constants in `v_log10_data.c` are computed (in extended precision) as 84 e.log10c := e.logc * ivln10. */ 85 v_f64_t w = v_fma_f64 (r, v_f64 (__v_log10_data.invln10), e.log10c); 86 87 /* y = log10(1+r) + n * log10(2). */ 88 hi = v_fma_f64 (kd, v_f64 (__v_log10_data.log10_2), w); 89 90 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 91 r2 = r * r; 92 y = v_fma_f64 (A (3), r, A (2)); 93 p = v_fma_f64 (A (1), r, A (0)); 94 y = v_fma_f64 (A (4), r2, y); 95 y = v_fma_f64 (y, r2, p); 96 y = v_fma_f64 (y, r2, hi); 97 98 if (unlikely (v_any_u64 (cmp))) 99 return specialcase (x, y, cmp); 100 return y; 101 } 102 VPCS_ALIAS 103 104 PL_SIG (V, D, 1, log10, 0.01, 11.1) 105 PL_TEST_ULP (V_NAME (log10), 1.97) 106 PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (log10)) 107 PL_TEST_INTERVAL (V_NAME (log10), 0, 0xffff000000000000, 10000) 108 PL_TEST_INTERVAL (V_NAME (log10), 0x1p-4, 0x1p4, 400000) 109 PL_TEST_INTERVAL (V_NAME (log10), 0, inf, 400000) 110 #endif 111