1 /* 2 * Double-precision SVE 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 "sv_math.h" 9 #include "math_config.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 #if SV_SUPPORTED 14 15 #define OFF 0x3fe6900900000000 16 #define N (1 << V_LOG10_TABLE_BITS) 17 18 #define A(i) __v_log10_data.poly[i] 19 20 static inline sv_f64_t 21 specialcase (sv_f64_t x, sv_f64_t y, svbool_t special) 22 { 23 return sv_call_f64 (log10, x, y, special); 24 } 25 26 /* SVE log10 algorithm. Maximum measured error is 2.46 ulps. 27 __sv_log10(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6 28 want 0x1.fffbdf6eaa667p-6. */ 29 sv_f64_t 30 __sv_log10_x (sv_f64_t x, const svbool_t pg) 31 { 32 sv_u64_t ix = sv_as_u64_f64 (x); 33 sv_u64_t top = svlsr_n_u64_x (pg, ix, 48); 34 35 svbool_t is_special_case 36 = svcmpge_n_u64 (pg, svsub_n_u64_x (pg, top, 0x0010), 0x07ff0 - 0x0010); 37 38 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. 39 The range is split into N subintervals. 40 The ith subinterval contains z and c is near its center. */ 41 sv_u64_t tmp = svsub_n_u64_x (pg, ix, OFF); 42 sv_u64_t i 43 = sv_mod_n_u64_x (pg, svlsr_n_u64_x (pg, tmp, 52 - V_LOG10_TABLE_BITS), N); 44 sv_f64_t k 45 = sv_to_f64_s64_x (pg, svasr_n_s64_x (pg, sv_as_s64_u64 (tmp), 52)); 46 sv_f64_t z = sv_as_f64_u64 ( 47 svsub_u64_x (pg, ix, svand_n_u64_x (pg, tmp, 0xfffULL << 52))); 48 49 /* log(x) = k*log(2) + log(c) + log(z/c). */ 50 51 sv_u64_t idx = svmul_n_u64_x (pg, i, 2); 52 sv_f64_t invc = sv_lookup_f64_x (pg, &__v_log10_data.tab[0].invc, idx); 53 sv_f64_t logc = sv_lookup_f64_x (pg, &__v_log10_data.tab[0].log10c, idx); 54 55 /* We approximate log(z/c) with a polynomial P(x) ~= log(x + 1): 56 r = z/c - 1 (we look up precomputed 1/c) 57 log(z/c) ~= P(r). */ 58 sv_f64_t r = sv_fma_f64_x (pg, z, invc, sv_f64 (-1.0)); 59 60 /* hi = log(c) + k*log(2). */ 61 sv_f64_t w = sv_fma_n_f64_x (pg, __v_log10_data.invln10, r, logc); 62 sv_f64_t hi = sv_fma_n_f64_x (pg, __v_log10_data.log10_2, k, w); 63 64 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 65 sv_f64_t r2 = svmul_f64_x (pg, r, r); 66 sv_f64_t y = sv_fma_n_f64_x (pg, A (3), r, sv_f64 (A (2))); 67 sv_f64_t p = sv_fma_n_f64_x (pg, A (1), r, sv_f64 (A (0))); 68 y = sv_fma_n_f64_x (pg, A (4), r2, y); 69 y = sv_fma_f64_x (pg, y, r2, p); 70 y = sv_fma_f64_x (pg, y, r2, hi); 71 72 if (unlikely (svptest_any (pg, is_special_case))) 73 { 74 return specialcase (x, y, is_special_case); 75 } 76 return y; 77 } 78 79 PL_ALIAS (__sv_log10_x, _ZGVsMxv_log10) 80 81 PL_SIG (SV, D, 1, log10, 0.01, 11.1) 82 PL_TEST_ULP (__sv_log10, 1.97) 83 PL_TEST_INTERVAL (__sv_log10, -0.0, -0x1p126, 100) 84 PL_TEST_INTERVAL (__sv_log10, 0x1p-149, 0x1p-126, 4000) 85 PL_TEST_INTERVAL (__sv_log10, 0x1p-126, 0x1p-23, 50000) 86 PL_TEST_INTERVAL (__sv_log10, 0x1p-23, 1.0, 50000) 87 PL_TEST_INTERVAL (__sv_log10, 1.0, 100, 50000) 88 PL_TEST_INTERVAL (__sv_log10, 100, inf, 50000) 89 #endif 90