1 /* 2 * Double-precision SVE 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 "sv_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 #include "poly_sve_f64.h" 12 13 #define N (1 << V_LOG2_TABLE_BITS) 14 #define Off 0x3fe6900900000000 15 #define Max (0x7ff0000000000000) 16 #define Min (0x0010000000000000) 17 #define Thresh (0x7fe0000000000000) /* Max - Min. */ 18 19 static svfloat64_t NOINLINE 20 special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp) 21 { 22 return sv_call_f64 (log2, x, y, cmp); 23 } 24 25 /* Double-precision SVE log2 routine. 26 Implements the same algorithm as AdvSIMD log10, with coefficients and table 27 entries scaled in extended precision. 28 The maximum observed error is 2.58 ULP: 29 SV_NAME_D1 (log2)(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5 30 want 0x1.fffb34198d9ddp-5. */ 31 svfloat64_t SV_NAME_D1 (log2) (svfloat64_t x, const svbool_t pg) 32 { 33 svuint64_t ix = svreinterpret_u64 (x); 34 svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thresh); 35 36 /* x = 2^k z; where z is in range [Off,2*Off) and exact. 37 The range is split into N subintervals. 38 The ith subinterval contains z and c is near its center. */ 39 svuint64_t tmp = svsub_x (pg, ix, Off); 40 svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG2_TABLE_BITS); 41 i = svand_x (pg, i, (N - 1) << 1); 42 svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52)); 43 svfloat64_t z = svreinterpret_f64 ( 44 svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52))); 45 46 svfloat64_t invc = svld1_gather_index (pg, &__v_log2_data.table[0].invc, i); 47 svfloat64_t log2c 48 = svld1_gather_index (pg, &__v_log2_data.table[0].log2c, i); 49 50 /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */ 51 52 svfloat64_t r = svmad_x (pg, invc, z, -1.0); 53 svfloat64_t w = svmla_x (pg, log2c, r, __v_log2_data.invln2); 54 55 svfloat64_t r2 = svmul_x (pg, r, r); 56 svfloat64_t y = sv_pw_horner_4_f64_x (pg, r, r2, __v_log2_data.poly); 57 w = svadd_x (pg, k, w); 58 59 if (unlikely (svptest_any (pg, special))) 60 return special_case (x, svmla_x (svnot_z (pg, special), w, r2, y), 61 special); 62 return svmla_x (pg, w, r2, y); 63 } 64 65 PL_SIG (SV, D, 1, log2, 0.01, 11.1) 66 PL_TEST_ULP (SV_NAME_D1 (log2), 2.09) 67 PL_TEST_EXPECT_FENV_ALWAYS (SV_NAME_D1 (log2)) 68 PL_TEST_INTERVAL (SV_NAME_D1 (log2), -0.0, -0x1p126, 1000) 69 PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0.0, 0x1p-126, 4000) 70 PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-126, 0x1p-23, 50000) 71 PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-23, 1.0, 50000) 72 PL_TEST_INTERVAL (SV_NAME_D1 (log2), 1.0, 100, 50000) 73 PL_TEST_INTERVAL (SV_NAME_D1 (log2), 100, inf, 50000) 74