1 /* 2 * Double-precision SVE log(x) function. 3 * 4 * Copyright (c) 2020-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 12 #if SV_SUPPORTED 13 14 #define A(i) __sv_log_data.poly[i] 15 #define Ln2 (0x1.62e42fefa39efp-1) 16 #define N (1 << SV_LOG_TABLE_BITS) 17 #define OFF (0x3fe6900900000000) 18 19 double 20 optr_aor_log_f64 (double); 21 22 static NOINLINE sv_f64_t 23 __sv_log_specialcase (sv_f64_t x, sv_f64_t y, svbool_t cmp) 24 { 25 return sv_call_f64 (optr_aor_log_f64, x, y, cmp); 26 } 27 28 /* SVE port of Neon log algorithm from math/. 29 Maximum measured error is 2.17 ulp: 30 __sv_log(0x1.a6129884398a3p+0) got 0x1.ffffff1cca043p-2 31 want 0x1.ffffff1cca045p-2. */ 32 sv_f64_t 33 __sv_log_x (sv_f64_t x, const svbool_t pg) 34 { 35 sv_u64_t ix = sv_as_u64_f64 (x); 36 sv_u64_t top = svlsr_n_u64_x (pg, ix, 48); 37 svbool_t cmp = svcmpge_u64 (pg, svsub_n_u64_x (pg, top, 0x0010), 38 sv_u64 (0x7ff0 - 0x0010)); 39 40 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. 41 The range is split into N subintervals. 42 The ith subinterval contains z and c is near its center. */ 43 sv_u64_t tmp = svsub_n_u64_x (pg, ix, OFF); 44 /* Equivalent to (tmp >> (52 - SV_LOG_TABLE_BITS)) % N, since N is a power 45 of 2. */ 46 sv_u64_t i 47 = svand_n_u64_x (pg, svlsr_n_u64_x (pg, tmp, (52 - SV_LOG_TABLE_BITS)), 48 N - 1); 49 sv_s64_t k 50 = svasr_n_s64_x (pg, sv_as_s64_u64 (tmp), 52); /* Arithmetic shift. */ 51 sv_u64_t iz = svsub_u64_x (pg, ix, svand_n_u64_x (pg, tmp, 0xfffULL << 52)); 52 sv_f64_t z = sv_as_f64_u64 (iz); 53 /* Lookup in 2 global lists (length N). */ 54 sv_f64_t invc = sv_lookup_f64_x (pg, __sv_log_data.invc, i); 55 sv_f64_t logc = sv_lookup_f64_x (pg, __sv_log_data.logc, i); 56 57 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ 58 sv_f64_t r = sv_fma_f64_x (pg, z, invc, sv_f64 (-1.0)); 59 sv_f64_t kd = sv_to_f64_s64_x (pg, k); 60 /* hi = r + log(c) + k*Ln2. */ 61 sv_f64_t hi = sv_fma_n_f64_x (pg, Ln2, kd, svadd_f64_x (pg, logc, r)); 62 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 63 sv_f64_t r2 = svmul_f64_x (pg, r, r); 64 sv_f64_t y = sv_fma_n_f64_x (pg, A (3), r, sv_f64 (A (2))); 65 sv_f64_t p = sv_fma_n_f64_x (pg, A (1), r, sv_f64 (A (0))); 66 y = sv_fma_n_f64_x (pg, A (4), r2, y); 67 y = sv_fma_f64_x (pg, y, r2, p); 68 y = sv_fma_f64_x (pg, y, r2, hi); 69 70 if (unlikely (svptest_any (pg, cmp))) 71 return __sv_log_specialcase (x, y, cmp); 72 return y; 73 } 74 75 PL_ALIAS (__sv_log_x, _ZGVsMxv_log) 76 77 PL_SIG (SV, D, 1, log, 0.01, 11.1) 78 PL_TEST_ULP (__sv_log, 1.68) 79 PL_TEST_INTERVAL (__sv_log, -0.0, -0x1p126, 100) 80 PL_TEST_INTERVAL (__sv_log, 0x1p-149, 0x1p-126, 4000) 81 PL_TEST_INTERVAL (__sv_log, 0x1p-126, 0x1p-23, 50000) 82 PL_TEST_INTERVAL (__sv_log, 0x1p-23, 1.0, 50000) 83 PL_TEST_INTERVAL (__sv_log, 1.0, 100, 50000) 84 PL_TEST_INTERVAL (__sv_log, 100, inf, 50000) 85 #endif // SV_SUPPORTED 86