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 "pl_sig.h" 10 #include "pl_test.h" 11 #include "poly_sve_f64.h" 12 13 #define Min 0x0010000000000000 14 #define Max 0x7ff0000000000000 15 #define Thres 0x7fe0000000000000 /* Max - Min. */ 16 #define Off 0x3fe6900900000000 17 #define N (1 << V_LOG10_TABLE_BITS) 18 19 static svfloat64_t NOINLINE 20 special_case (svfloat64_t x, svfloat64_t y, svbool_t special) 21 { 22 return sv_call_f64 (log10, x, y, special); 23 } 24 25 /* SVE log10 algorithm. 26 Maximum measured error is 2.46 ulps. 27 SV_NAME_D1 (log10)(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6 28 want 0x1.fffbdf6eaa667p-6. */ 29 svfloat64_t SV_NAME_D1 (log10) (svfloat64_t x, const svbool_t pg) 30 { 31 svuint64_t ix = svreinterpret_u64 (x); 32 svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres); 33 34 /* x = 2^k z; where z is in range [Off,2*Off) and exact. 35 The range is split into N subintervals. 36 The ith subinterval contains z and c is near its center. */ 37 svuint64_t tmp = svsub_x (pg, ix, Off); 38 svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG10_TABLE_BITS); 39 i = svand_x (pg, i, (N - 1) << 1); 40 svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52)); 41 svfloat64_t z = svreinterpret_f64 ( 42 svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52))); 43 44 /* log(x) = k*log(2) + log(c) + log(z/c). */ 45 svfloat64_t invc = svld1_gather_index (pg, &__v_log10_data.table[0].invc, i); 46 svfloat64_t logc 47 = svld1_gather_index (pg, &__v_log10_data.table[0].log10c, i); 48 49 /* We approximate log(z/c) with a polynomial P(x) ~= log(x + 1): 50 r = z/c - 1 (we look up precomputed 1/c) 51 log(z/c) ~= P(r). */ 52 svfloat64_t r = svmad_x (pg, invc, z, -1.0); 53 54 /* hi = log(c) + k*log(2). */ 55 svfloat64_t w = svmla_x (pg, logc, r, __v_log10_data.invln10); 56 svfloat64_t hi = svmla_x (pg, w, k, __v_log10_data.log10_2); 57 58 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 59 svfloat64_t r2 = svmul_x (pg, r, r); 60 svfloat64_t y = sv_pw_horner_4_f64_x (pg, r, r2, __v_log10_data.poly); 61 62 if (unlikely (svptest_any (pg, special))) 63 return special_case (x, svmla_x (svnot_z (pg, special), hi, r2, y), 64 special); 65 return svmla_x (pg, hi, r2, y); 66 } 67 68 PL_SIG (SV, D, 1, log10, 0.01, 11.1) 69 PL_TEST_ULP (SV_NAME_D1 (log10), 1.97) 70 PL_TEST_INTERVAL (SV_NAME_D1 (log10), -0.0, -0x1p126, 100) 71 PL_TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-149, 0x1p-126, 4000) 72 PL_TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-126, 0x1p-23, 50000) 73 PL_TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-23, 1.0, 50000) 74 PL_TEST_INTERVAL (SV_NAME_D1 (log10), 1.0, 100, 50000) 75 PL_TEST_INTERVAL (SV_NAME_D1 (log10), 100, inf, 50000) 76